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and p is a chain-bending modulus. Within the limits of the simplifying assumptions made in the development of this diffusion model (45) the numerical factor 0 was found to be equal with 9.1 x lo4. One can assume that for a given penetrant polymer system E * , m* and p* are known or can be determined from appropriate experimental data reported in the literature. Further one can assume that AE has been estimated theoretically using this diffussion model. Then, by substituting these parameters into Eq. 5-4 one could in principle calculate a diffusion coefficient D. The problem is that both Eqs. (5-3 and 5-4) contain one parameter, namely the mean-square “jump” distance, h, which is generally not known or very difficult to determine experimentally. Thus, in order to calculate a D a “shrewd guess” is needed for h, based on similitudes with other penetrant polymer systems. In other words is not possible to use the formula for D given in the framework of this model to effectivelly predict the magnitude of D from “first principles”, i.e. thermodynamic, molecular and structural data on the penetrant polymer system. Moreover it was discussed in (50) that a correct solution of a key problem in the derivation of the statistical mechanical approach used in the Pace and Datyner model is possible only at 0 K. Adding this fact to the “shroud guessing” of h in order to produce (estimate) a diffusion coefficient largely impairs the usefulness of this model for the type of migration estimations which might be envisaged by a process engineer from the packaging sector, see Chapter 15.
c,
Modelsfor diffirsion in polymers
133
Free-volume models Among the popular methods for interpreting the diffusion of small penetrants in polymers are the so called “free-volume’’ models (6,11,13,51-54). The basic assumption of these models is that the mobility of both polymer segments and penetrant molecules is primarly determined by the available free-volume in the penetrant polymer system. The free-volume of the polymer is regarded as an “empty” volume between the chains of the polymer. Similarly the free-volume of the penetrant can be regarded as the volume not occupied between the molecules of the penetrant. Most free-volume models for diffusion in polymers follow the phenomenological basis set in (55) where the self-diffusion of an ideal liquid of hard spheres (“molecules”) has been analysed. These molecules are confined - for most of the time - in a “cage” formed by their immediate neighbours. A local fluctuation in density may open a “hole” within a cage, large enough to permit a considerable displacement of the sphere contained by it. This displacement gives rise to diffusion only if another sphere jumps into the “hole” before the first sphere returns to its initial position. Diffusion occurs not as a result of an activation process in the ordinary sense but rather as a result of the redistribution of the free-volume within the liquid of hard spheres. The model of diffusion of hard spheres is applicable to interpret self-diffusion in liquids which behave according to the van der Waals physical interaction model (56). This might be the case for simple dense fluids at high temperature, T >> T,, but it is an oversimplified model for the real diffusion of small organic penetrants in polymers. The functional relationships derived in the model of hard-spheres have been reinterpreted over course of the time, leading to a series of more sophisticated free-volume diffusion models. Some of these models are presented briefly below. An attempt to correlate experimental diffusion data with free-volume, for the system of organic vapors with polyvinyl acetate, has been made in (57). The experiments showed that in this system, for T > T,, the diffusion is Fickian and that the measured average diffusion coefficient steeply increases with the concentration, c,, of penetrant in the polymer. To quantify such a finding, an empirical relation has been proposed earlier (58): D+
= D,,,exp
(w c,)
(5-5)
where w is a parameter. To refine this approach it was proposed that the diffusion coefficient might be proportional to the frequency with which segments of polymer chains were able to undergo rotational jumps (57). The relationship between the diffusion coefficient and penetrant concentration, expressed as solvent volume fraction, v,, was derived in terms of a theory for polymer segmental mobility (59). Eventually a relation was obtained which allowed examination of the relationship between the intrinsic diffusion coefficient, D’, and v, (57). To calculate with this formula D’, some thermodynamic and free-volume parameters for the penetrant polymer system must be calculated from data given in the literature and two adjustable parameters must be determined by fitting the theoretical curves to experimental diffusion data (57). Once these data were known the formula for D’ showed an excellent fit over the concentration range which covered a 1000-fold increase of D+ (5357). Despite this positive result one can conlcude that the model has only a semi-predictive and correlative character and it would be quiet unpractical to use it for the type of diffusion coeffi-
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cient estimations currently of interest in the field of substance migration through and from polymeric packaging materials. One of the simplest early free-volume diffusion models was formulated in (51,52,60). The concept of this model was considered an advance, because some of the parameters required to describe the concentration dependence of the diffusion coefficient could be obtained from the physico-chemical properties of the polymer and penetrant. The relation proposed for the calculation of the thermodynamic diffusion coefficient, DT, was (51,60):
where Vf is the average fractional free-volume. The proportionality coefficient Ad is considered to be dependent primarily upon the size and shape of the penetrant, while Bd is a parameter which is independent of temperature and penetrant concentration. To work effectively with Eq. 5-6 the magnitude of its parameters must be determined. For this the free-volume of the penetrant poylmer system must be evaluated from viscosity data. Eventually the two adjustable parameters Ad and Bd must be calculated by fitting appropriate experimental diffusion data. For the diffusion of organic vapors in rubbery polymers, the correlation between theoretical curves and experimental data is often acceptable. In such cases the model can be used in a semi-predictive manner in order to estimate diffusion coefficients DT. beyond the penetrant concentration and/or temperature range where experimental results were collected. As already mentioned, the model includes in its formulae the adjustable coefficients Ad and Bd which cannot be determined from “first principles”. Hence, one cannot ascertain true predictive capabilities from the model and thus it is of little efective help for the practical diffusion coefficient estimations envisaged in this work. The free-volume model of Vrentas and Duda
In the last two decades Vrentas, Duda and their co-workers have published a substantial number of papers (61-67) on the free-volume model of diffusion in polymersolvent systems they developed in the late 70’s (68-72). This model, which is often cited and used in the literature, underwent a number of modifications over the years and appears to apply well to the diffusion of organic solvents in rubbery and glassy polymers. In order to develop a consistent free-volume diffusion model, there are some issues which must be addressed, namely: i) how the currently available free-volume for the diffusion process is defined, ii) how this free-volume is distributed among the polymer segments and the penetrant molecules and iii) how much energy is required for the redistribution of the free-volume. Any valid free-volume diffusion model addresses these issues both from the phenomenologic and quantitative points of view such that the diffusion process is described adequately down to the “microscopic” level. Vrentas and Duda stated that their free-volume model addresses these three issues in a more detailed form than previous diffusion models of the same type. Moreover, it was stated that the model allows the calculation of the absolute value of the diffusion coefficient and the activation energy of diffusion mainly from parameters which have physical significance, i.e. so-called “first principles”. In the framework of this model the derivation of the relation for the calculation of the self-diffusion coefficient of the sol-
vent Dls is not a trivial task. A relation can obtained which gives the dependence of Dls on the nature of the penetrant and its concentration in the polymer-solvent system, the temperature and on the molecular weight of the polymer. For a rubery polymer a condensed form of this relation, valid also for low penetrant concentration levels, can be cited from (63):
D,,
=Do
(
exp {-y
exp -RTE')
("'
w 5-+ v i s ) }
"FIi
(5-7)
For the definition of all parameters involved in the above relation see (62,63). The explicit form of Eq. (5-7) contains fifteen parameters of which thirteen can be determined from thermodynamic and molecular data of the penetrant and polymer. These parameters include: two specific hole-free volumes for the components, free-volume parameters for the penetrant and polymer, the thermal expansion coefficient of the polymer, free-volume overlap factors, glass transition temperatures, the fractional composition of the system, etc. For a non initiated reader, the procedures followed to determine these thirteen parameters are not quite simple, although the authors of the model state that the data needed for this purpose are generally available in the literature. In the scheme for the estimation of these parameters presented in (63) one can see that in order to perform calculations with the model, two parameters must be calculated by fitting the theoretical curves to experimental results obtained in the socalled "zero-penetrant" concentration limit. Thus, it is stated that using a non-linear regression analysis "...all of the parameters of the theory can be determined in general with as few as two diffusivity data points" (63). The results obtained with this complex but straightforward procedure have shown that the model provides excellent correlations for diffusivity data in several polymer-solvent systems Fig. 5-3. Having mentioned the correlative capabilities of this model, one can consider its semi-predictive abilities. It was mentioned that a number of diffusion data taken from a limited range of penetrant concentrations are required to calculate two of the parameters of the model. Once these parameters have been determined, one can make theoretical predictions for diffusion coefficients over a wider range of penetrant concentration or temperature variation. This is a critical test for any theoretical model,
0
0.2
0.4 W S
0.6
O8
Figure 5-3: Test of predictive capabilities of proposed free-volume model using data for the toluene polystyrene system. Only data points represented by solid symbols were used to obtain free-volume parameters (73).
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since an useful model should have at least an established semi-predictive capability. These results are encouraging evidence that the proposed model is a suitable tool for a more accurate description of the diffusion process in rubbery polymers. The model was most often tested by its authors for polymer-solvents systems like: polystyrene, polymethylacrylate, polyethylmethacrylate and polyvinylacetate; and for toluene, benzene, ethylbenzene as solvents. The experimental test conditions reported in (6170), especially for high concentration of solvent in the polymers, often differ considerably from what is generally of interest when these polymers are used in the packaging sector. Therefore, to assess the potential use of this free-volume diffusion model in the field of small substance migration in polymeric food packagings, the model must be tested for penetrant polymer systems which are specific for this field (see Chapter 9). Moreover it is to mention that, because the model contains two parameters which cannot be determined from “first principles” but only by fitting a limited amount of experimental data, one cannot ascribe true predictive capabilities to the model. To conclude this section, it may be interesting to mention what was concluded recently in (17) on the future of the free-volume diffusion models: ...“However, phenomenological transport models based on free-volume concepts are likely to become obsolete during the coming decade, due to the development of computational techniques of simulating polymer microstructures” .... The development of such techniques and their results are discussed in Section 5.2.
5.1.2 Diffusion in glassy polymers As already mentioned at the beginning of this section, the diffusion of small penetrants in glassy polymers is a much more complex process than that in rubbery polymers. This is due, at least in part, to the fact that free rotation of the polymer chains is restricted below T,. Thus, it was assumed that fixed microcavities or “holes” of various sizes result throughout the matrix of the polymer below T,. These “holes” are “frozen” into the polymer as it is quenched from the rubbery state (74). The concept that two mechanisms of sorption may be implicated in the diffusion and behaviour of small penetrants in amorphous glassy polymers was first suggested in (75). Here, and later in (76) it was speculated that below T, the “holes” may act to immobilize a portion of the penetrant molecules by binding them at high energy sites at the periphery of the “holes” or by entrapment in the “holes”. Based on this concept it has been suggested (77) that the sorption of organic vapors in a glassy polymer is due to two concurrent mechanisms: (i) ordinary dissolution in the matrix of the polymer (so called Henry’s law sorption) and (ii) a ‘‘hole’’-filling process obeying Langmuir’s law. This phenomenological model was accompanied, for the sorption of simple gases and organic vapors, by the equation (77): C=k,p+
1
a1 P
+
bp
(5-8)
where a], b and kD are adjustable coefficients and p is t h e pressure of the gaseous penetrant. It has been reasoned that al and b are given approximately by the statistical thermodynamic treatment of Langmuir’s isotherm (78) and kD by the lattice theory of penetrant polymer solutions (79). Later it was postulated that in Eq. (5-8) one
Models for difiiision in polymers
137
may equate a l = c‘Hb and designate b and c ’ ~as “hole affinity” and “hole saturation” constants respectively (80). This quantitative description of the solution of a simple penetrant in a glassy polymer is known today as the Dual Sorption Theory (with total immobilization), (DST). The problem is that the basic assumptions of DST cannot be justified “a priori” (9). The possibility that penetrant molecules adsorbed in “holes” may not be completely immobilized is one of these problems and has been addressed (81,82). If that is the case, both the normally dissolved penetrant molecules (according to Henry’s law) and the partialy immobilized ones could diffuse through the matrix of the polymer and contribute to the diffusional flux. Moreover, in order to better describe real systems, another key postulate from the initial DST should be relaxed, namely that the normally dissolved species and those adsorbed into the “holes” are always in local equlibrium (82). That means the diffusion model should incorporate some kinetics for the immobilzation process. There will be cases where the diffusion and immobilization proceed at comparable rates; and limiting cases, where one of the two processes predominates. The phenomenological sorption theory which resulted from taking account of these assumptions is known as Dual Sorption (with partial immobilization) Theory. Because of the assumed dual sorption mechanism present in glassy polymers, the explicit form of the time dependent diffusion equation in these polymers is much more complex than that for rubbery polymers (82-86). As a result exact analytical solutions for this equation can be found only in limiting cases (84,85,87). In all other cases numerical methods must be used to correlate the experimental results with theoretical estimates. Often the numerical procedures require a set of starting values for the parameters of the model. Usually these values are “shroud guessed” in a range where they are expected to lie for the particular penetrant polymer system. Starting from this set of arbitrary parameters, the numerical procedure adjusts the values until the best fit with the experimental data is obtained. The problem which may arise in such a procedure (88), is that the numerical procedures may lead to excellent fits with the experimental data for quite different starting sets of parameters. Of course the physical interpretation of such a result is difficult. However, the mathematical formulae of DST satisfactorily present the dependence of the solubility and diffusion coefficients for simple gases and organic vapors on the concentration of the penetrant in the glassy polymer (9,11,13,15,17,33,34,89). From the point of view of earlier discussions, namely the true prediction of diffusion coefficients for volatile and nonvolatile organic penetrants in glassy polymers, the diffusion equations derived in the framework of the DST have only a limited usefulness. That means that, because the parameters of the DST models are not directly related to “first principles”, the equations can be used with success to correlate experimental results, but not to truly predict diffusion coefficients. One possible solution to this problem is to develop “microscopic” diffusion models for glassy polymers, similar to those already presented for rubbery polymers. Ref. (90) combines some of the results obtained with the statistical model of penetrant diffusion in rubbery polymers, presented in the first part of Section 5.1.1, with simple statistical mechanical arguments to devise a model for sorption of simple penetrants into glassy polymers. This new statistical model is claimed to be applicable at temperatures both above and below T,. The model encompasses dual sorption modes for the glassy polymer and it has been assumed that “hole”-filling is an important sorption mode above as well as below T,. The sites of the “holes” are assumed to be fixed within the matrix
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of the polymer. Starting from these assumptions and using elementary statistical mechanical arguments, the authors of the model estimated the values of parameters approximately, which were then included in relation to the solubility coefficient (90). For a series of simple gases diffusing in some glassy polymers, solubilty data calculated with the model were compared with experimental sorption data. Semiquantitative to qualitative agreements between theory and experiment were found. Unfortunately, for the scope of the present book, the model was not developed for estimating of diffusion coefficients in glassy polymers. Local density fluctuations occur in penetrant polymer systems both above and below T,. It is then reasonable to expect that a free-volume diffusion model should also provide an adequate description of the diffusion of small penetrants in glassy polymers. To reach this goal the free-volume model for diffusion of small penetrants in rubbery polymers, second part of Section 5.1.1, was modified to include transport below T, (64,65,72,91-93). In principle the diffusion process in a penetrant polymer system can be characterized by determining the mutual diffusion coefficient and its dependence on temperature, penetrant concentration, pressure and polymer molecular weight. When molecular relaxation in the polymer-solvent system is much faster than the diffusive transport, the conformational changes in the polymer structures appear to take place instantaneously. The diffusional transport is comparable in such cases to the transport observed in simple liquids. This type of transport mechanism is considered to characterize quite well polymer solvent systems for T > T,. As the temperature decreases towards T, the probability that a local fluctuation in density will produce a “hole” of sufficient size so that a polymer jumping unit or a penetrant molecule can move in decreases. When T < T, the “hole-free’’ volume which can be rebistributed with no energy change in the penetrant-polymer system becomes very small. Below T, the motions of the polymer are so hindered that, for a given penetrant concentration, significant movements do not occur at the time scale of the diffusion experiment. Moreover at a very low penetrant mass fraction, the structure of the glassy polymer is essentially unaffected by the presence of the penetrant and the diffusion process is Fickian (61,72,92). The diffusion process under such conditions has been denoted as an elastic diffusion process (61,71) which can be analysed using the classical theory of diffusion. In the limit of zero penetrant mass fraction these phenomenological assumptions were included into the relations of a mathematical formalism which led eventually to an expression for the dependence of the mutual diffusivity on temperature (72):
where the parameter 9+ describes the character of the change of the volume contraction which can be attributed to the glass transition. For glassy polymers, T < Tg2,the temperature dependence of D at zero penetrant concentration can be described by an apparent activation energy for diffusion, Ed, (72,93): (5-10)
Modelsfor diffiisron in pol.yniers
139
The temperature dependence of D for the n-pentane-polystyrene system both above and below Tg2 has been calculated using the formulae of this free-volume model (64). The results obtained are shown in Fig. 5-4 along with a few experimental data (94) for the same system at three temperatures below Tg2. Similarly to Fig. 5-4 for other glassy polymer-solvent systems also the predictions of this free-volume theory are in general agreement with experimental data on t h e temperature dependence of D in the vicinity of Tg2.,In particular, the theory predicts a step change in Ed at TR2,and this is consistent with most experimental investigations of polymer-solvent diffusion at temperatures just above and below the glass transition temperature (6,11J5). Vrentas, Duda and their co-workers refined in recent years their free-volume model for diffusion in glassy polymers to address also the problem of Fickian diffusion at finite solvent concentrations (64,65,92). For this the free-volume and thermodynamical parameters involved in Eq. (5-7).which gives the solvent self-diffusion coeffcient D,, in a rubbery polymer, were adapted to describe adequately the phenomenology of diffusion below the glass transition temperature,T,,,, of the polymer-solvent mixture at a particular solvent mass fraction. A series of assumptions on the structure, properties and sample history and the introduction of an additional expansion coefficient were necessary (65) to express the behavior of the free-volume parameters below Tgm.Eventually a set of equations was obtained and it was stated that using them "... calculation of D,, for glassy polymers is no more difficult that computing D,, for rubbery polymer-solvent systems" (65). However it was emphasized that the predictions of the model are sensitive to the sample preparation history. that means reasonably good agreement between theory and experiment will be obtained only for sample preparation histories which are similar to the one used in the model. Anyway one can see that up to nineteen parameters are needed to express, with this free-volume model, the concentration and temperature dependence of D1, in a glassy polymer (65,92). It is stated in these publications that all these parameters except two can de estimated from physico-chemical data generally available in the literature. To determine the remaining parameters a small amount of experimental diffusion data is needed.
-7
A
v)
\
N
E
-
-9
0
n
-D -11 -12
2.0
2.5
I/T . 1 0 3
3.0 ( ~ - 1 )
FigureS-4: Comparison of predictions with experiment for the n-pentane-polystyrene system (64.94).
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The reasonably good agreement between theory and experiment shown by this free-volume model (65) recommends it as an interesting tool to model the diffusion in glassy polymers used in the packaging sector. However, the problem is that the correlative, semi-predictive and predictive capabilities of this model do not address exactly the type of diffusion coefficient prediction which is of interest for the estimation of many migration processes in polymeric packagings. When we state this we are thinking not only on how difficult it would be to specify all the parameters of the model for a complex penetrant like an antioxidant or stabilizer but even more if the model is still valid for this type of polymer penetrant systems. The above sections have presented models that link the process of diffusion of small penetrants in polymers to “microscopic” features of the penetrant polymer system. Strictly speaking the type of diffusion models presented above are not truly “microscopic” because they actually describe average and not truly local - “microscopic” - properties of the penetrant polymer system. Sometimes even excellent correlations of experimental data offered by these models are due to the fact that the experimental methods used to determine the diffusion coefficients are in turn probing the penetrant polymer system over %on-microscopic” distances and comparatively long times. Somewhat closer to the designation of a “microscopic” model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller “cells” of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable “average length” of the elementary diffusion jump must be known. But in the framework of this type of “microscopic” model, it is not possible to determine this parameter from “first principles”. To conclude one can state that in the framework of the “classical” diffusion models more or less complex mathematical formulae have been developed with the aim of interpreting experimental data and even offering an insight on the mechanics of diffusion. The mathematical relations for the diffusion coefficient rely on parameters which must be determined from given physico-chemical and structural data about the penetrant polymer system. But, almost without exception, these models also include a number of adjustable parameters which can be determined only by fitting experimental data to theoretical curves. In some models the physical meaning of these adjustable parameters is quite unsubstantiated. Moreover, among the earlier “classical” diffusion models some “shrewd guessing” of some model parameters is needed. Therefore one can state that the main limitation of all these phenomenological models is that they cannot truly predict diffusion coefficients only from “first principles”.
Models for rliffiision in polymers
141
5.2 Diffusion in polymers - The computational approach It was shown in the above section that as a rule, at the base of the “classical” or “microscopic” diffusion models, there are ad hoc (heuristic) assumptions on a certain molecular behaviour of the polymer penetrant system. The fact that the mathematical formulae developed on such bases often lead to excellent correlations and even semipredictions of diffusion coefficients must be aknowledged. It is true that the “classical” models are not capable to predict diffusion coefficients only from “first principles” but this is often not an obstacle to hinder their use in certain types of investigations. Therefore we are quiet sure that this type of diffusion models will certainly be used in the future too for the interpretation of diffusion experiments. The problem of diffusion modeling in polymers changes to some degree when one envisages to develop a really atomistic model, with trully predictive capabilities and without making any ad hoc assumption on the molecular behaviour and/or motions in the polymer penetrant system. In principle, a possibility to develop such diffusion modelings, is to simulate theoretically the process of penetrant diffusion in a polymer matrix by computer calculations. For this one starts by considering only an appropriate set of “first principles” which describe at a trully atomistic level the polymer and the penetrant. Then, these data about the atoms and molecules of the polymer are used to generate, by some means, a polymeric structure that has the “microscopic” and “macroscopic” properties of the true polymer, i.e. a low energetic state, an appropriate distribution of torsional angles, a physically acceptable distribution of unoccupied volume, density, and so on (95-99). Once this structure is generated a number of penetrant molecules are randomly “inserted” in it (where enough unoccupied volume is available). Then, the sytem is left to pursue its “molecular dynamics”, i.e. the atoms and molecules of the system are allowed to move in the force fields and under the interactions acting inside the system over a certain time interval. During this process there is no interference from the outside and, in particular, no heuristic assumptions are made about the molecular motions. If the process is simulated consistently enough time, by observing for example the average displacement of the penetrant species, one can eventually calculate their diffusion coefficient (98). Though, this scheme sounds very elegant and attractive its practical achievement is a complex and demanding task. Because of that computer simulation, as a method for the estimation of the diffusion coefficients in polymers, has only lately become a practicable approach. The prerequisites which make possible the development of “atomistic” simulations of diffusion in polymers are the development of powerful methods for the simulation of polymer microstructures and dynamics and also great computation capabilities of supercomputers. The first attempts in the direction of simulating theoretically at an atomistic level the diffusion of simple gas molecules in a polymer matrix were made more than two decades ago (100). But, the systematic development of “ab initio” computer simulations of penetrant diffusion in polymeric systems dates only from the late 80’s (101104). At the beginning of the 90’s it was achieved to simulate some qualitative aspects such as the diffusion mechanism, temperature, and pressure dependence of diffusion coefficients (105-109). The polymers chosen for investigation mainly fell into two categories: either they were easily described (model elastomers or polyethylene) or they were known to have, for simple permanent gases like H2, 02,N2, H20 or CH4,
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large diffusion coefficients (polydimethylsiloxane (PDMS) (11CL112) and atactic polypropylene (aPP) (113) ). The advantage of simulating at room temperature. for example the diffusive motion of H2 in aPP (D about lo4 cm2/s), is that the diffusive motion of the hydrogen molecules can already be sampled in relatively short simulations (about 0,5 ns (113) ). Based on these encouraging achievements, in the last five or six years, the interest of the researchers shifted from easy-to-compute polymer penetrant systems to those which have interesting technological potentials in such fields as: gas barriers (114117), gas or liquid separation processes (1 18-121), molded objects (packagings for example) (122) or swelling of polymers by solvents (123-126). Trying to model, theoretically, the transport of small penetrants in polymer matrices, one realizes that the characteristic length and time scales vary greatly and depend on the polymer morphology (98). Most of the polymers used technologically are either amorphous or partially crystalline. From experimental results obtained over the past four decades it is commonly assumed that both diffusion and sorption in crystalline polymers are orders of magnitude smaller than in amorphous ones (11,13,16,17,29,30). These facts determine that different theoretical and computational techniques will be appropriate for modeling the diffusion in different polymer penetrant systems (98). For the diffusion of small penetrants, i.e. simple gases and vapors of water and/or simple organic substances, in purely amorphous polymers the computational techniques of choice will be molecular dynamics, MD, (97-99, 127129) or the transition-state approach, TSA, (115,130-132). In a semicrystalline polymer a similar task can be approached for example by a Monte-Carlo 2-phase model (133). So far, the “atomistic” modeling of diffusion of small penetrants in polymers was predominantly done for amorphous polymers and using the MD or TSA techniques, which will be presented briefly in the next sections.
5.2.1 Molecular dynamics Because time is explicitly present in the formulations of MD, this technique is the most straightforward way of computer simulating the motion of penetrant molecules in amorphous polymer matrices (97-99). The MD method allows one to look at a truly “atomistic” level within the system as it evolves in time. Recently, excellent reviews on the use of MD for simulating penetrant diffusion in polymers have been published (96-99). A summary of the basic concepts and some relevant results obtained so far with MD will be presented bellow. To start a MD simulation of a diffusional process an amorphous polymer structure of the host material must first be theoretically generated. This structure must be low in energy and have the known physical properties of the polymer; chain length and distribution of torsional angles of polymer chains, density, distribution of free volume, etc. The origins of the MD approach to the problem of generating polymer structures lies in works done in the late 70’s to investigate theoretically amorphous bulk polymers (134-138). A MD approach to the problem of modeling the structure of amorphous polymers was introduced in (139) and a few years later developed in (140,141) to allow a detailed description of such systems. An overview of the various MD methods used to generate amorphous polymer structures can be found in (142). The principal methods are: (i) structural generation methods which in an ideal case are used to
Models for diffiision in polymers
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generate a structure which needs no further refinement, (ii) structural refinement methods that ideally are so efficient that the starting structure can be arbitrary and (iii) coarse-graining methods in which the atomistic model of a polymer is mapped into a coarse representation of several atoms or even monomers. To generate a polymer structure theoretically its matrix is presented as an ensemble of microscopic structures which satisfy the requirements of detailed mechanical equilibria (140). For every atom its initial position and velocity have to be specified. Chain bond lengths and bond angles are fixed. Molecular movements are allowed to occur exclusively through rotations around the skeletal bonds of macromolecules. A polymer chain meeting these assumptions is built in vacuum by an iterative process that is started from an initially guessed “parent” structure which is then relaxed to a state of minimum potential energy (140). The density of the structure obtained must eventually equal that of the simulated polymer. The free-volume in the polymer can be estimated from the generated structure. To obtain a statistical average of this free-volume, a number of structures are generated starting from different “parent” chain configurations. Once the host structure was generated the next step in the MD simulation of diffusion is to “place” (insert) the diffusant molecules into the computed structure. The condition for inserting the penetrant molecules into the structure is to find “freevolumes” where the energy is below a certain threshold and that any two of the penetrant molecules are separated by some minimum distance. Then the penetrant and polymer molecules are allowed to interact with each other and move within the limits of the constrains they are subjected to. The straightforward technique is now to follow by computer simulation the displacement of the penetrants into the potential field of the system and eventually to estimate the mean-square displacement (MSD) of the penetrant species. Among the first remarcable results of MD simulations was the finding that diffusion of small molecules in amorphous polymeric structures proceeds by “hopping” (jumping) motions (106). From a phenomenologic point of view this is not a new result if one takes into account that such a mechanism was intuitively assumed in some “microscopic” diffusion models long before the development of computer simulation techniques, see the preceeding section. The new aspect is that the computational approach has led to this picture of the diffusion mechanism starting from true “first principles” of the penetrant polymer system and not on the basis of “shrewd guesses”. To illustrate this type of motion in Figure 5-5 a typical trajectory of a water molecule through an amorphous elastomer (PDMS) is presented (119,120). From Fig. 5-5 one can clearly discern that the voids forming the free volume of the rubbery polymer are clearly separated from each other and that there are two types of motion of the penetrant molecule: - for a relatively long period of time (typically a few 100 ps) the penetrant molecule stays confined in certain small regions of space, the “cavities” of the polymer matrix. The molecule explores the cavity thoroughly without being able to move beyond the confines of the volume it resides in. Thereby the penetrant is reflected by the polymer matrix about every few picoseconds (98,119,120); - the quasi-stationary period is interrupted by quick leaps from one such cavity to another close by. The jump between the two neighboring cavities is preceeded by the formation of a channel between them. Under favourable circumstances (right momentum) the penetrant then slips through this opening, essentially without activation energy or more exactly surpassing a small energy barrier, due to the fact that
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Mercea Jump between cavities
I
Movements in
ca76
Figure5-5: A typical trace of the center of mass of one representative water molecule in a PDMS matrix (120).
the channels are on average narrow (98). The jump duration is short compared to the residence time in the cavities. A “hopping” event in a polymer matrix, as found typically in MD simulations is presented in Fig. 5-6 (106). As announced above these findings are in astonishing agreement with the “heuristic” pictures of the diffusion mechanism discussed in the framework of some “microscopic” diffusion models. But, besides being free of the conceptual drawbacks (the ad hoc assumptions) of the “classical” diffusion models, the MD method of computer simulation of diffusion in polymers makes it possible to get an even closer look at the diffusion mechanism and explain from a true atomistic level well known experimental findings. For example the results reported in (119,120) on the “hopping” mechanism reveal the following additional features. In a rubbery polymer with flexible macromolecular chains (PDMS for example) the cavities forming the free-volume are clearly separated from each other. The detailed evaluation of the movement of a penetrant particle from cavity (1) to the neighboring (2), did not show any immediate back jumps (2) + (1). This is mainly do to the fact that the channel between (1) and (2) closes quiet quickly. In a polymer with stiff chains (glassy polyimide (PI) for example) the individual cavities are closer to each other and a rather large number of immediate back jumps ocurred during the time interval simulated (120). This indicates that once a channel between two adjacent cavities in a stiff chain polymer is formed it will stay open for some 100 ps. This makes the back jump (2) -+ (1) of the penetrant more probable than a jump to any other adjacent hole (3). This process seems to be one cause for the general tendency that the diffusion coefficient of small penetrants in stiff chain glassy polymers is smaller than in flexible chain rubbery polymers. The results of MD simulations will be useful if they are able to reproduce with sufficient accuracy diffusion coefficients measured experimentally. Given the scatter between the results of different experiments reported in the literature, a computational method can be considered accurate enough if, for absolute diffusion coefficients, it reproduces the experimental values within one order of magnitude. Such results are presented in Table 5-1.
145
Models for difliision in po1ymer.s
t=11.1 ps
k10.1 ps
t=6.0 PS
(9
-
-
5A
t=12.1 ps
-
5A
t=l2.9PS
t=12.5ps
5A
t=13.3PS
5A
\
I
\
t=13.7PS
t=14.1 ps
Penetrant molecule
)-------I
t=l6.1 PS Figure 5-6: Molecular dynamics simulation of a "jump" of an 0
2
molecule (106)
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Table 5-1: Diffusion coefficients calculated by molecular dynamic simulation and from experiment,
Polymer Polydimethylsiloxane
He
180.0 (300)
144
100.0 (300)
145
144
20.6 (300)
146
Pol ydimethylsiloxane
CH4
21.0 (300)
Polydimethylsiloxane Polydimethylsiloxane
H2O EtOH
15.3 (300)
112
14.5 (298)
147
2.0 (300)
112
4.5 (298)
147
Polydimethylsiloxane Polydimethylsiloxane
H2O EtOH
20.0 (300)
1 I9
14.5 (298)
147
4.4 (300)
119
4.5 (298)
147
Polyisobutylene
He
30.0 (300)
148
5.96 (300)
151
Polyisobutylene
Hz
9.0 (300)
148
1.52 (300)
151
Polyisobutylcne
0 2
0.169 (300)
149
0.081 (300)
151
Polyisobutylene
CH4
0.63 (350)
150
1.7 (375)
152
Polyethylene
CH4
1.12 (300)
150
0.54 (296)
155
Polyethylene
CH4
1.6 (300)
112
0.54 (296)
155
Polyethylene Polyethylene
H20
7.8 (300)
150
4.4 (296)
155
0.7 ( 3 0 )
112
0.15 (296)
155
atactic Polypropylene
H2
44.0 (300)
154
-4.9'** (296)
155
atactic Polypropylene
0 2
4.0 (300)
154
-0.95'** (296) 155
atacticPolypropylene
CHJ
0.48 (300)
154
-0.24'** (296)
Pol yamidimide
HZ
0.97 (300)
143
1.3 (300)
156
Polyimide
N2
0.28 (300)
143
0.52 (300)
156
0.74 (300)
150
EtOH
Polyimide 0 2 Poly[ 1-(trimethylsily1)-I-Propyne] He
465 (300)
2.69 (300)
155
156
121
316 ( 3 0 K )
157
121
30.0 (303)
147
Poly[1-(trimethylsilyl)-1-Propyne] Oz
23.8 (300)
Poly[1-(trimethy1silyl)-1-Propyne] N2
20.5 (300)
121
36.0 (298)
158
Poly[ 1-(trimethy1silyl)-1-Propyne] CH4
16.7 (300)
Poly[l-(trimethylsilyl)-1-Propyne] CO'
121
22.0 (303)
147
4.0 (300)
121
19.5 (303)
147
Polyethylenetherephthalate Polvstvrene
CH4 CHI
-0.0063"
(333)
-0.056" (3251
117
0.0031 (333)
80
116
0.0338 (323)
159
(* diffusion coefficient extrapolated from higher temperatures) (** diffusion coefficient estimated from data for semicrystalline PP)
The results given in Table 5-1 show that the agreement between the diffusion coefficients predicted from MD simulations and experimental ones ranges from reasonable to excellent. At temperatures around 300 K this is found both for polymers which are above their glass transition temperature, T,, (PDMS, PIB, PE and aPP) and for polymers which are below T, (PET, PS, PTMSP, PI and PAI). As a trend one can notice, and this not only from Tab. 5-1 but also from other works published in the last six or seven years, that the agreement between MD simulations of diffusion and solvation of small penetrants in polymers and experiment steadily improved. These are encouraging developments, showing that modern softwares (some of them available for
example from the Molecular Simulations Inc./San Diego. CA, USA) and powerful computers (for example IBM RS 6000 workstations or Cray C916 supercomputers) are capable today to model and predict diffusional processes for a certain range of polymer penetrant systems. The spread of this range is given by the general conditions tied to the ability of the MD procedure to simulate a polymer penetrant system large enough to sample the configurational statistics of the polymer sufficiently well. For a simple polymer like linear polyethylene with flexible chains one may need a few hundred [-CH2-] repeat units or a few hundred to a few thousand atoms (98). To generate a bulk PDMS structure in which 3 water molecules are “inserted” 220 monomer units [-Si(CH3)2-O-], i.e. 2238 atoms, were for example used in (119). One might expect that many more repeat units are needed if the polymer has stiff chains (98). However, it should be noted that it is the number of flexible bonds in a chain and not just the number of repeat units that is a decisive parameter for the achievable quality of the amorphous polymeric structure generated from a chain (143). Other factors determining the range of application of the MD method arise from the mobility of the penetrant itself. To be sufficiently precise with the computer simulation one needs to observe, say, 10 jump events for every single penetrant (which is probably the bare minimum). At equilibrium and assuming hopping motion the diffusion coefficient can be given by Eq. (5-3), where h is now the mean-square “jump” distance and v-’ the average residence time between jumps. Hence for a D of about 5 x lo-‘ cm2/s (a comparatively high diffusion coefficient for packaging applications) and a “jump distance” of about 0,5 nm (see (117) for example) one finds that in an 1 ns simulation one will encounter about 12 jumps on average. It is interesting to notice that if the MD simulation is done in steps of 1 fs (121) 10‘ time steps must be computed to complete a 1 ns simulation. To simulate with MD slower diffusion processes, i.e. smaller D, one must either extend the duration of the simulation (and hence the computing time and costs) or to “insert” several penetrants at the same time in the generated polymer structure and thereby improve the quality of the sampling (98,117,119,120). However, the later option is valid only if the diffusion coefficient is not very sensitive to the penetrant concentration. With nowadays softwares and computers MD simulations can be extended to about 10 ns which brings the D of about 5 . cm2/swithin reach of the method. Diffusion processes which evolve at a rate of 5 . 10-’cm2/s or faster are typical for: - the diffusion, at very low concentrations, of small penetrants (simple gases or vapors) in low barrier polymers: i.e. polyethylenes (112,1.51), polypropylenes (160), polybutadienes (149-151) and siloxanes (112,119,144) at room temperature or polystyrene (116), polyethylenetherephthalate ( I 17) well above room temperature, - the diffusion, at room temperature, of simple gases and vapors through glassy polymers with large interchain regions: i.e. Poly[ 1-(trimethylsily1)-1-propyne](1 17) and cis-poly(tert-butylacetylene) (161). However in the packaging sector the large majority of the diffusion processes in polymers imply penetrants with a relative molecular weight ranging between 100 and 1200 daltons and have often quite complex structures. From experiments one knows that these diffusion processes are characterized by D ranging from lo-’ to 10-’2cm2/s or even lower levels (see Appendix I). In (98) it was stated that, to study with MD techniques polymer penetrant systems in which the D are that small, is certainly out of reach for several generations of supercomputers to come.
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The posibility of extending MD to slower diffusion processes has been discussed (98). But applying such algorithms has a tradeoff on the overall quality of the computational approach. To perform calculations at time scales beyond those accessible to MD is possible nowadays only by using the transition state approach (TSA) proposed in (97,115,132). This method will be presented briefly below.
5.2.2 The transition-state approach As already mentioned in Section 5.1.1 one of the early theoretical models of gas diffusion in solid polymers (3,37,162) was based on the Transition-State Theory (TST) (40). More than fifty years ago it was assumed ad hoc that gas molecules move through a dense polymer in a series of activated “jumps” between “holes” which exist in the polymer matrix. Fortunately, results of “ab initio” MD simulations, Section 5.2.1, demonstrate that the computed trajectories of small penetrants in atomistic structures of dense polymers are consistent with the “heuristic” picture of this early “classical’’ model. In its framework it was estimated, from solubility data, that at room temperature the vibrational frequency v,, of the gas molecule trapped by the surrounding chains is of about 10l2 ssl (163). This finding is also in reasonable agreement with the bouncing frequency of a small gas molecule inside a “cavity” of the polymer matrix, as found in MD simulations. These results indicate that the “jumps” of a penetrant in a dense polymer could be treated as an elementary process, thus justifying the use of TST for developing a computer simulation technique to evaluate the rate of the penetrant’s jumps and out of this the diffusion coefficients. The development of a Transition-State Approach (TSA), based on a simplified description of thermal motions in the host matrix and stochastic methods in treating the penetrant dynamics, promises to allow much longer simulation intervals than MD can practically achieve nowadays (about 10 ns). This feature is important because: (i) the occurence, in some polymer penetrant systems, of anomalous diffusion (115,130) leads to the necessity of carrying out very long MD simulation runs for penetrants to enter the Einstein diffusive regime (97,98) and (ii) unpracticably long MD simulations would be needed to simulate and predict slower diffusion processes, Section 5.2.1 and Appendix I. In the development of the TSA besides the “jumping” mechanism already mentioned another fundamental mechanistic feature assumed is that the penetrant dynamics is coupled to the elastic motion of the polymer chains, but, to a first approximation, is independent from the structural relaxations of the matrix (973 15,130,132). The thermal motion causes the polymer matrix to move in its configurational space. At short times the vibrational modes of motion dominate: vibration of chemical bonds or bond-anlges, small-amplitude rotations of side groups or wiggling of torsion angles. As time goes by, the system tends to perform structural relaxation for example through torsional transitions in the main chain or in side groups. Using MD to simulate an appropriate penetrant trajectory one can specify an upper bond for times at which the system at hand can be treated as essentially executing elastic motions (97). Elastic motion implies that the atoms of the matrix fluctuate about their equilibrium positions. Allow now a small dissolved molecule to reside in the system and suppose that one can neglect the correlation between the structural relaxation of the matrix and the dynamics of the penetrant. In this case one can write a penetrant distribution
Models for diffiision in polymers
149
function p(r) which is obtained by integrating over all possible values of the deviations of the host atoms the result of the potential energy of interaction between the dissolved molecule and the host atoms and a normalized probability density, W((A)), describing the elastic fluctuations (132). The function p(r) is related to the Helmholtz energy, A(r), of the dissolved molecule at location r according to a general equation given in (164). The TST can be used then for describing the spatial movement of a dissolved molecule as a series of activated jumps between adjacent local minima of A(r) (132). The rate constants Ri.j for the penetrant’s transition from site i to site j can be written as (40): (5-11)
where Q,,, and Q, denote partition functions of penetrant on the crest surface between sites i and j and in site i , respectively. In Eq. 5-1 1 k* is a transmission factor taken to be about 0.5 (132). It was shown that in the quasi-classical case one can link Q,,, and Q, to the function p(r) (164). Hence, specification of the elastic fluctuations of the atoms of the host matrix through the probability density W((A))yields p(r) which, in turn, yield the transition rates R,,, (130). If the network of local minima of A(r) with the associated R,.,’s are known, one can use stochastic methods to evaluate the correlation function describing the penetrant dynamics (130,132). The procedures of simulating the dynamics of guest molecules on the network of sites and of evaluating W( (A)) were described in (1 30) and (132), respectively. An important parameter in these procedures is the mean-square deviation, (Am2), of host atom o! from its average position. The values of (A$) are expected to depend on the time scale of averaging: for very short times (Aa’) increases with time approaching then, by definition of elastic motion, an asymptotic value. Using atomistic short-scale trajectories calculated with MD and specifying an averaging time one can calculate for (Am2) a “smearing” factor (A2) and use it in the TSA simulations (97,132). Another possible way to evaluate (A2) is to match the short-time region of the meansquare displacement, (r2), of the penetrant versus time curves obtained from TSA with those from MD calulations (97). To follow to actually carry out a TSA simulation a three-dimensional grid, with grid interval of about 0.2 A ( 5 . lo6 equispaced points in (132)) is built and the Helmholtz energies at all grid points are computed. Before this can be done in practice, a value for (A2)must be found. Then, local minima and the crest surfaces must be found, using the procedures given in (130,132,165). To study the dynamics of the penetrant molecules on the network of sites a Monte-Carlo procedure is employed, which is presented is some detail in (97). Eventually the stochastic trajectory of a dissolved molecule is obtained and subsequently by averaging a large number of such trajectories, about lo3 in (132), the diffusion coefficient D of the penetrant in the polymer can be calculated from the plot of (r2) versus the time t (using for the linear portions (Einstein diffusion) of the curves a simple equation similar to Eq. 5-3). In Figure 5-7 the (r2)’s of He and Ar in glassy polycarbonate, PC, at 300 K , as calculated with TSA, are shown. The results plotted in this figure represent averages over 500 independent simulation paths. The simulations presented in Fig. 5-7 show a region of “anomalous diffusion” of the penetrant He for (r2)’ssmaller than =lo3A2(simulation interval of ~ 0 . ns) 5 . This is similar those reported in (98,166) on the MD simulation of H e diffusion in rubbery polyisobutylene, where the transition to normal diffusion was captured at around (r2)=10A2 and a sim-
150
Mercen
-14
-12
-10
-8
lg t (s)
-6
’
Figures-7: Computed dynamics of He and Ar in polycarbonate at 300 K (132).
ulation interval of 4 . 1 ns. It is believed that this anomalous behavior is caused by a separation of time scales consistent with the jumping pattern (98). The very fast motions of the penetrant molecules inside the cavities (timescales of several 100 ps) is determined by the shape of these cavities. Therefore these motions don’t have a random-walk-like behavior and consequently it is not appropriate to use the Einstein equation, i.e. D = (r2)/6t (which similar to Eq. 5-3), to calculate D. In fact the Einstein equation holds true if the slope of the log (r2)versus log t plot is equal to one. A direct consequence of this fact is that, in order to predict diffusion coefficients, a MD or TSA computation must simulate a time interval long enough to get fulfiled the above requirement. For some polymer penetrant systems this means already the need to carry out simulations over time intervals that are out of reach of the MD method ( t > 10 ns) (120,130,132). In these cases the method of choice will be the TSA. In Table 5-2 a comparison between diffusivities obtained with the TSA method and experimental D is presented. From this table one can see that, in all cases computed D agree with experimental data to within an order of magnitude. Moreover most of these D are considerably smaller than the 5 . lo-’ cm2/s lower threshold assumed to be in reach of nowadays MD simulations Section 5.2.1. This is an encouraging sign that computer simulations of diffusional processes are already able to predict, with a reasonable accuracy and for small and simple penetrants, diffusion coefficients around cm2/s. From the point of view the packaging sector it would be interesting to learn if and when further theoretical developments of the TSA method will be able to simulate (predict) such slow diffusional processes for organic penetrants with a much more complex structure, see Chapter 3 and Appendix I. Two “atomistic” approaches have been presented briefly above: molecular dynamics and the transition-state approach. They are still not ideal tools for the prediction of diffusion constants because: (i) in order to obtain a reliable chain packing with a MD simulation one still needs the experimental density of the polymer and (ii) though TSA does not require classical dynamics it involves a number of simplifying assumptions, i.e. duration of jump mechanism, elastic polymer matrix, size of smearing factor, that impair to a certain degree the “ab initio” character of the method. However MD and TSA are valuable achievements, they are complementary in several
151
Models f o r diffiisinn in polyniers
Table 5-2: Diffusion coefficients calculated with the transition-state approach and from experiment. Polymer
Diffusant
D"dC (cm'is) lo7 Cnl ( K )
Ref.
Dex7 (cm2/s)10 @I ( K )
35.0 (300)
132
64.6 (308)
Ref
Pol ycarbonate
He
Pol ycarbonate
0 2
0.10 (300)
132
0.56 (308)
167
Polycarhonate
N2
0.(19 (300)
112
0.18 (308)
167
Pol yamidimide
H2
120
9.4 (300)
I20
Polyamidimide
0 2
0.40 (300)
120
0.30 (300)
120
NZ
0.20 (300)
120
0.10 (300)
120
15.3 (300)
120
7.40 (300)
120
Polyamidimide Polyimide
0 2
15.9 (300)
Polyimide
N7
2.6 (300)
120
Polyvinylchloride
He
17.0 (318)
97
2.80 (300) 40.0 (318)
167
I20
147.168,169
Polyvinylchloride
Ne
2.0 (318)
97
4.0 (318)
147,168,169
Polyvinylchloride
Ar
0.04 (318)
97
0.05 (318)
147.168.169
Pol yvinylchloride
Kr
0.003 (318)
97
0.01 (318)
147,168,169
ways and can be used to predict the diffusion coefficients of small penetrants (so far simple gases and simple organic vapors) in both rubbery and glassy amorphous polymers. These computational methods can be used to understand the behavior of small penetrants in the matrix of a polymer starting from an "atomistic level" and without ad hoc assumptions on the movements of the polymer chains. In this respect M D is the less coarse-grained of the two methods. The main drawback of M D is the computational cost that nowadays prohibits simulations beyond 10 ns, which are still being far from routine. The TSA is well suited to extend the time-scale of simulations, bringing new phenomena within reach. In this respect it is important to use M D and TSA in conjunction. The limitations of the TSA. as developed so far, are evident when one intends to simulate' penetrant polymer systems where there is strong interaction between the penetrant and the host atoms, or where larger penetrant molecules require a deformation of the polymer structure for their passage. In such systems, as well as in systems where the penetrant induces a swelling of the polymer matrix, MD seems to be the method of choice to properly simulate the diffusion mechanism (125,126,170).
5.3 Conclusions A process or manufacturing engineer is often confronted with the difficult and expensive task of measuring experimentally the migration (diffusion) of rather complex organic molecules in rubbery o r glassy semicrystalline polymer matrices. For such systems the knowledge/prediction of diffusion coefficients would he crucial for the theoretical estimation of substance transfer for example from a polymeric packaging into the wrapped good (foodstuff, medicine, etc.). Therefore a theoretical method/model for performing the true prediction of diffusion coefficients for small organic penetrants in rubbery and glassy polymers would be of great help to reduce
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the costs and worktime nowadays spent in the field of polymer packaging research and law enforcement. The problem is that ideally such a theoretical method/model should be as simple as possible, rely on parameters, which for the penetrant polymer systems specific in the packaging sector, are well known and easily available and, at last but not at least, the use of the method to predict diffusion processes should not consume more time and resources than the direct migration/diffusion experiments. If a given diffusion model cannot meet the one or the other of these requirements, from a purely pragmatic point of view, a process engineer or law enforcer may not see incentives to use the theoretical approach instead of a well established experimental one. Unfortunately, it seems that none of the diffusion models presented in the above sections meets completely these practical goals. It is beyond any question that the type of “classical” diffusion models presented in Section 5.1 were, at the time of their conceivement, important steps for the qualitative understanding of the phenomenology of penetrant diffusion in polymers. Moreover some of these models are very successful in rationalizing average experimental diffusion coefficients with macroscopic parameters as temperature and penetrant concentration. Trying to use these models for predicting diffusion coefficients for penetrant polymer systems which are specific in the packaging sector one is confronted with several problems. First, with no exception, in all “classical” diffusion models one or more adjustable parameters enter in the formula of D. To calculate the magnitude of thislthese parameter/s a number of diffusion experiments must be performed with the very penetrant polymer system which one intends to simulate theoretically. In practice such experiments most often require quite sophisticated equipment to obtain the experimental data, and often non-trivial theoretical schemes to evaluate them. The attempt to save experimental work by using the adjustable parameters determined for a certain penetrant polymer system in order to estimate/predict Ds in a related system is generally not recomendable. Hence, in a first step, in order to use one or other of the “classical” diffusion models, one is forced to replace migration experiments with diffusion ones. Then, as already mentioned, once all adjustable parameters in the formula of D are known semi-predictions and predictions of D can be made most often only if the physico-chemical parameters of the system (temperature, concentration, pressure, degree of swelling, etc.) do not vary beyond a relatively limited range. Finally, in some of the most widely used “classical” models - the free-volume models of Fujita, Vrentas and Duda and their alternatives (171-175) - more than a dozen structural and physical parameters are needed to calculate the free-volume in the penetrant polymer system and subsequently the D. This might prove to be a relatively simple task for simple gases and some organic vapors, but not for the non-volatile organic substances (rest-monomers, additives, stabilizers, fillers, plasticizers) which are typical for polymers used in the packaging sector. As suggested indirectly in (17) sometimes in the future it will maybe possible to calculate all the free-volume parameters of a “classical” model by using MD computer simulations of the penetrant polymer system. On the other hand, based on the rapid progress which was recorded in the last decade in the “atomistic” simulation of diffusion processes in polymers one may be confident that these computational methods will be one day able to cope with the prob-
Models for diffiision in polyniers
153
lem of a true prediction of D for the type o f migration estimations envisaged with polymeric packagings. In our oppinion this will be not an easy target to reach. As is well known todays MD simulations are better suited to describe at a true atomistic level the host matrix and the dynamics of the penetrants. However, most of the MD performed so far are dealing with purely amorphous polymers and with very simple penetrants. In the packaging practice however most of the polymers are partly crystalline and the penetrants are often complex organic molecules. In (98) it was mentioned that a straightforward atomistic MD simulation of a semicrystalline material is not yet achievable, since crystallite dimensions may range from several 10 nm to several microns and crystallites often aggregate to form larger domains of macroscopic dimensions (3536). In contrast, typical MD simulations use, for completely amorphous structures, cells with a length of a few nm. Therefore to simulate a semicrystalline cell several orders of magnitude larger seems to be completely out of question for nowadays computers. The possibility to adopt a less atomistic viewpoint and use a Monte-Carlo 2-phase simulation technique for semicrystalline polymers was analysed in (98). One should also not forget that the typical organic molecule migratingldiffusing from a polymeric packaging has usually a geometry differing strongly from that of the penetrants investigated so far with M D simulations. Moreover, at an atomic level, the interaction of most such organic molecules with the host matrix is much stronger and difficult to quantify that the interaction of simple permanent gases with the same matrix. If further developments of the MD and/or Monte-Carlo 2-phase techniques will be able to simulate at an atomistic level the dynamics of a semicrystalline polymer and of a complex organic penetrant the question remains: how long will be the time interval simulated? According to those mentioned above in Section 5.2.1 simulations of a few 100 ns to a few ps are needed to predict D in the range of 10-"' to 10-"cm2/s, which is often found in technical applications of polymers. From todays perspective the computer time (and costs) needed for a MD simulation of such duration are out of reach in the near future. With the TSA developed in (115,130,132,165) it was possible to almost reach simulation intervals of 1 milisecond. This makes in principle possible to predict D as small as a few cm2/s. Therefore the TSA seems to be a good choice to predict D for the type of diffusion processes encountered in packaging applications. But for this, the actual TSA algorithms must be developed to take also into account strong interactions between the penetrant and the host atoms, and the deformation of the polymer structure at the passage of complex penetrant molecules. We are confident that sometimes in the future suitable computational approaches and powerful hardwares will be available to predict D of additives, stabilizers, monomers, dyes and/or plasticizers in polymeric materials used in packaging applications. To evaluate, if such an endeavour may help to reduce the considerable volume and costs of experimental migration testings peformed nowadays, it is necessary to consider also the following aspects. How much software development and computing time will be needed to predict the D for a penetrant polymer system not yet investigated? In (120) it was stated that even the rather fast TSA simulation technique will presumably not lead to a fast predictability of transport paramaters for large numbers of hypotetical polymers in the near future. This was mainly atributed to the fact, that the construction of well equili-
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brated polymer packing models is still demanding large amounts of computer time (not to mention the much longer time needed to effectively develop the appropriate algorithms). Then an important aspect is how precise the predicted D will be? So far an agreement within one order of magnitude between an experiment and an atomistic simulation is considered to be a good achievement. For completely amorphous polymer structures and simple penetrants even better agreements have been reported in Tables 5-1 and 5-2. From the point of view of estimating the migration from polymeric materials used in the technical sector a prediction of D within the order of magnitude of the experimental one would be a result of certain practical use, see Chapter 15. The question is: to what sophistication must be developed the computer simulation approach to meet this requirement also for the type of penetrant polymer systems which are usual in the named sector? In the end it is legitimate to mention that for a considerable number of process engineers and law enforcement personnel the material costs of using an atomistic computational approach to predict a D and subsequently use it in a migration estimations will also play an important role. Pragmatically speaking one can expect that somebody interested to reduce its expenses for migration testings from polymeric packagings, will not have to much interest to replace these tests with much more expensive and less precise theoretical simulations! Therefore, from the point of view of the practical value of migration estimations in the technological sector, it will be maybe worthwhile to compare the trade-off between the cost and precision of estimating a D with the “upper bond” concept presented in Chapter 15 with the cost and precision of predicting the same D with an atomistic computer simulation (when this will be achievable). References I . Mitchell, J.K., Philadelphia J.Med.Sci., 13 (1831) 36.
2. Graham, T., Phil.Mag., 32 (1866) 401.
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4. Tuwiner. S.B.. “Diffusion and Membrane Technology” ACS Monographies. Reinhold. New York,1962. 5. Rogers, C.E., “Solubility and Diffusivity” in “Physics and Chemistry of the Organic Solid State”, Fox. D., Labes. M.M.. Weissberger. A.. (Eds.),Intescience, New York, 1965, p. 509. 6. Crank, J., Park, G.S., “Diffusion in Polymers”. Academic Press, London, 1968. 7. Stannett, V.T., Hopfenberg, H.B., Petropoulos, J.H., “MTV 1nt.Rev.Sci.. Macromol. Sci.. 8 (1972) 329. 8. Hwang, S.-T.. Kammermeyer, K., “Membranes in Separations”, Wiley Interscience. New York. 1975. 9. Vieth, W.R., Howell, J.H.. Hsieh, J.H.. J. Membrane Sci., l(1976) 177. 10. Meares, P., “Membrane Separation Processes”, Elsevier Scientific, New York, 1976. 11. Stannett,V.T.. Koros, W.J., Paul, D.R., Lonsdale, H.K., Baker, R.W., Adv.Polyrn.Sci., 32 (1979) 71. 12. Mason, E.A.. Lonsdale, H.K., J. Membrane Sci.. 51 (1990) 1. 13. Frisch. H.L., Stern, S.A., “Diffusion of Small Molecules in Polymers”. CRC Crit.Rev. Solid State and Materials Sci. 11 (1983) 123. 14. Rogers, C.E., Machin. D., CRC Crit.Rev. Macrornol. Sci. (1972) 245. 15. Vieth. W.R.. “Diffusion in and through Polymers”. Hanser, Munchen, 1991. 16. Koros. W.J., (Ed.), “Barrier Polymers and Structures”, ACS SyrnpSer. 423, Arn.Chern. Soc., Washington, 1990. 17. Stern. S.A., J. Mcmbrane Sci., 94 (1994) 1.
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Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
6 Prediction of diffusion coefficients in gases, liquids, amorphous solids and plastic materials using an uniform model Otto Piringer
6.1 Introduction Diffusion is a mass transport process resulting from random molecular motions. Such molecular motions occur in gases and condensed phases and can be described in principle as using the commonly held theoretical picture of “random walk”. This means the particles (molecules, atoms) move in a series of small random steps and gradually migrate from their original positions. Each particle can jump through a distance h in a time 7. But the direction o f each step may be different, and the net distance traveled must take the changing directions into account. The coefficient of diffusion D is related to h and z in the Einstein-Smoluchowski equation: 2
D = h
2r
If A/T = C, and h are interpreted as the mean speed of the particle and the mean free path, then Eq. (6-1) has the same structure as the following equation obtained from the kinetic theory of gases:
where k is the Boltzmann constant, >l identical particles. Among the particles there exists an attractive interaction that is responsible for the formation of condensed phases. The particles on the other hand possess a certain degree of freedom of motion in any direction within the system, as required by the liquid state. Because no preferred distribution of particles can be assumed, the system seems on average to be totally homogeneous and isotropic. This leads to an essential simplification of the problem. The background process in all interactions is an energy exchange between the n particles of the system, which is related to a change in position of the particles by oscillation and/or translation.
162
Piritiger
6.2.1 Model assumptions The following assumptions apply to systems of n identical particles (molecules, atoms) that leave their chemical identities essentially unchanged. Above a certain number of particles in the system, the sum of all interactions on a single particle by the other particles of the system becomes independent of the number of particles. This allows identification of a macroscopic system by its specific properties. 1. The interactions between the n particles are based on an exchange of discrete values E, = d~,, of energies E relative to an unit amount E ~ , .The consequence of this exchange is a relative density of interaction energy qGn= ( l + ~ $ n ) "in form of a n-fold product with the limit value q, = exp(e,) for n+w. The exponential expression is assumed because (i) the exponential function represents a mathematical order of magnitude which is higher than that of any other power of E,, this means exp(E,)IEra +ffi for a > 1 and E, +ffi;
($it reaches a constant value, independent of the number of particles in a macroscopic system with n>>l. The relative density q, is again considered a starting point for additional dynamic processes occurring in the system. Self-diffusion of the particles is an example of such a process. Based on the same mathematical assumption (i), the magnitude of the diffusion coefficient D = D,,exp(q,) is derived as an exponential function of q, with an unit amount D,,. This assumption is further supported by many empirically established equations describing dynamic properties of macroscopic systems. 2. A common characteristic of all particles is their extension in space, which means they possess a finite volume surrounded by a surface with area A . This area is equivalent to A for a surface of revolution which equals the product of the length of a meridian y and the length of the path of the center of gravity of y when y is rotated through the angle 211 (the theorem of GuldinIPappus):
The common function of all particles, independent of their specific structure is the ratio AIY = 2 7 ~The amount of energy transferred from one particle during an interaction step (see assumption 1 ) can now be written as E, = E: + a = 211 + a, where a is a specific parameter of the system and E: = 211 is defined as the relative reference exchange energy. 3. Mathematically, the interaction process is assumed to be an exchange of energy between n particles and can be treated as a permutation. Both the n particles and their n starting positions are labeled with the natural numbers 1, 2, ..., n. The whole process of energy exchange can now be understood as a result of n! consecutively occurring individual interaction steps. Each individual step represents a transport of one energy quantum from one partide to another and is interpreted mathematically as one change of places between the two particles. The total number of such place exchanges equals n!. The relative number, pI1,of exchanges related to n! in which n o particle remains in its starting position is then: Pn
=
I
1
-3!
+ .... + (-1) n 2l
;
lini pn = pc = 1 e
n--x
(6-7)
Prediction o,f diffiision coefficients in gases, liquids, amorphous Jolids .__
163
The limit value p e = l/e for n>>l is designated as the maximal probability of a place exchange in a macroscopic system. With these assumptions a common characteristic of all macroscopic particle systems can be expressed as qr = exp(e,) = exp(2n + a) (assumptions 1 and 2). However, taking into consideration a diminution of E, which is proportional to the maximum probability p e of place exchange (assumption 3), the value qr = exp(e,p,) = exp[(a + 2x)/e] = ea/ee2n/r= C 1 ’ e becomes ~ the specific relative density of interaction energy for a system where w = grde and C1le= e(d‘’. A special case occurs whenever the II particles are molecules from a homologous series of chemical compounds, e.g. n-alkanes. In such a case the specific parameter C can be enlarged into C = C0(l+2x/i)’, where i represents the number of carbon atoms in an unbranched alkane chain and C1Ir= C0”c’(1+2x/i)de = Kwi.>l). Assumption 3 is not valid in this case, because the i carbon atoms in the n-alkane molecule are connected by covalent bonds and have mostly lost their individual identities in comparison with the whole molecule that makes up one of the n particles in the macroscopic system. Nevertheless the i sub-structures in form of methylene groups -CH2-, including the two methyl groups -CH3 at the ends of a n-alkane molecule, do manifest their relative individualities in the form of a multiplicative effect on the interaction intensity between the molecules of the macroscopic system. Summarizing the above results, the relative density qr,r of interaction energy between the particles of a macroscopic system of n-alkane with i carbon atoms in the molecular chain is:
If a specific property f(i) of the macroscopic system can be correlated with qCiin form of a direct proportionality, than a simple dimensionless relationship between the values of this property for two members i and k of the homologous series results from Eq. (6-8):
The number w = eZde derived from the three assumptions of the model is the common limit value of the two power sequences:
These power sequences, designated as interaction functions, represent the mathematical backbone of the model described in this chapter.
164
Piringer
6.3 Prerequisites for diffusion coefficients 6.3.1 Critical temperatures of n-alkanes The critical temperature may be considered to be a measure of the intensity of interaction between the n particles of a system, as produced by van der Waals forces. Although the critical temperature for n>>l is practically independent of the number of particles, there exists a possibility for estimating the influence of the number of i structural subunits composing a particle based on the value of the critical temperature of a macroscopic system. Critical temperatures are especially suitable for the comparison of numerical values within a homologous sequence because at these temperatures the systems are in corresponding states. If Tc,iand Tc,kare designated the critical temperatures of two different n-alkanes containing i and k carbon atoms, we may tentatively let the dimensionless ratio Tc,i/Tc,kbe equal to the ratio of the two corresponding interaction functions w ~ and , ~ Wk,e in Eq. (6-9): (6-11)
Experimental values for the critical temperatures of n-alkanes are known up to eicosane (i=20) (Reid et al., 1987). For longer molecular chains the experimental determination of the critical temperature is not possible with sufficient accuracy due to the onset of thermal decomposition. By means of Eq. (6-11) it is possible to calculate, starting from each experimental value corresponding to i carbon atoms, a limit value T , , , (for k +co) (Table 6-1). Due to the fact that the terminal methyl groups in the initial members of the n-alkane represent an important deviation from a system containing only methylene groups, it is more convenient to use alkanes having chains as long as possible for the determination of Tc,m.As seen in Table 6-1 these deviations become unimportant after i=9. This is because the individual Tc,mvalues are irregularly distributed for the 12 longest
800 -Y
.-
2
600 --
I
04 1
3
5
7
9
11
13
15
17
19
i
Figure 6-1: Critical temperatures of n-alkanes as a function of the number i of carbon atoms. Calculated values using Eq. (6-11) (-), measured values ( + ) and limit value, T, (- - -).
Prediction of diffusion coe,fficients in gases, liquids, amorphous solids ...
165
Table 6-1: Critical temperatures of n-alkanes. Number i of carbon atoms
TJK
T,,,/K
T,-T,,,
9
594.6
1039.1
-2.0
10
617.7
1036.8
4.6
11
638.8
1035.5
+0.7
12
658.2
1034.9
+1.3
13
676.0
1034.8
+1.4
14
693.0
1036.0
+0.2
15
707
1034.7
s1.5
16
722
1036.7
-0.5
17
733
1034.4
+1.8
18
748
1039.2
-3.0
19
756
1035.4
+0.8
20
767
1036.8
4.6
chains (i=9-20). The mean limit value obtained from Table 6-1 is Tc,x = T, = 1036.2 K. Figure 6-1 shows the estimated curve for TC,*from Eq. (6-11) using Tc,k = T, = 1036.2 K as well as the experimental values of T,,, for 15 i520. The remarkable coincidence between the ratios of the critical temperatures, T,,,/T, within the homologous series and the ratios of the corresponding values of the interaction function w,.,Iw supports the interpretation that this function is a measure of the energy density of interaction. Due to the translation and rotation of particles in the liquid state of a macroscopic system, the value of the interaction function may be assumed to be independent of the configuration of the particles within the system. Therefore, there is no need for data related to orientation. This is also valid for the i chainlike subunits of an alkane molecule. Due to the possibility of a free rotation of any of the i subunits around the bond axis with the neighboring subunits, a relative motion of segments of several subunits is also possible.
6.3.2 Critical compression factor The first term w l = (1+27t)'/' of the power series w, defined in Eq. (6-10) plays a special role within the interaction model in that it represents a perfect gas phase. If V,, p,, T , and R represent the molar volume of a compound, the critical pressure and critical temperature of the system and the gas constant, then the product prVn is reduced to l i w of the product RT, due to the interaction between the particles in the system. Taking into account an empty (free) volume fraction in the critical state, the critical molar volume is written as V , = wlVo. Consequently, a dimensionless critical compression factor, Z,, is defined using the following equation: (6-12)
166
Piringer
From a data collection with 349 experimental values for the critical compression factor (Reid et al., 1987) obtained with organic and inorganic compounds and elements, a mean value of Z , = 0.2655 is obtained with a standard deviation of o = 0.0346.
6.3.3 The entropy of evaporation Systems with comparable amounts of disorder are especially important for developing a common basis for relationships between diffusion coefficients. Such a comparable amount of disorder is generated when any liquid evaporates and becomes a gas. According to Trouton's Rule the entropy of evaporation has values around 85 JK-'rnol-l for many liquids at their boiling point Th at a standard pressure of 1bar. This rule was modified by Hildebrand (1915; Hildebrand et al., 1970).According to Hildebrand, the value of the molar entropy of evaporation, ASv, for many substances is nearly the same at temperatures where their molar vapor volumes are equal to the standard value of 24.8 dm3 mol-' at 25 "C.The validity of this rule extends over boiling points ranging over three orders of magnitude and for classes of substances as different as monoatomic noble gases, high boiling metals and compounds with polyatomic molecules with complex structures. The deviation from the mean value of 84.9 JK-'mol-' does not exceed 1.5 JK-'mol-' with few exceptions when using the Hildebrand correction. As a conclusion from the Hildebrand/Trouton Rule, the definition of a standard vapor phase in a standard state with a well known amount of disorder can be made. This definition can be used as a starting point for modeling diffusion coefficients of gases and liquids. The change in entropy AS for a reversible isothermal expansion of an ideal gas from its initial volume Vl to a volume Vzis AS = R In(Vz/VI) and therefore V2W1= exp(AS/R). By setting V2/VIequal to the ratio between the molar volume V; = 24.8 dm3 mol-' of an ideal gas under standard conditions ( T = 298.15 K , p = 1 bar) and assigning a volume V i to one mole of a liquid at Th. then VE/V: = exp(AS,/R) = exp(AHv/RTh).Where A H v stands for the molar enthalpy of evaporation at the Hildebrand temperature, Th,and AS, is the molar entropy of evaporation. By using ASv = 84.9 JK-'mol-' the value V ; = 0.91 cm'mol-' is obtained. An interpretation of the Hildebrand/Trouton Rule is that this "free" volume, VL,allows for the freedom of movement of molecules (particles) necessary for the liquid state at the temperature Th.The explanation of the constant entropy of evaporation is that it takes into account only the translational entropy of the vapor and the liquid. It has to be pointed out that VE does not represent the real molar volume of a liquid, but designates only a fraction of the corresponding molar volume of an ideal gas V& derived from the entropy of evaporation. The real molar volume VLof the liquid contains in addition the molar volume occupied by the molecules Vo. As a result the following relations are valid: V L= V i + V ,and V , = V&+ V,. However, while V;*< V , and V Lis practically independent of the pressure, V , > 1 carbon atoms in the molecular chain. Let us first consider the theoretical case with one single macromolecule of infinite length that forms a polymethylene chain in the shape of a disordered coil. Due to the possibility of free rotation of any of the methylene subunits around the bond axis relative to the neighboring subunits, a relative motion of segments of more subunits is also possible. In the following a reference equation for the diffusion coefficient of a n-alkane with a number i of carbon atoms in a hypothetical infinite chain will be derived in manner analogous to that for gases. If in the first approximation we neglect the existence of activation energy, EA, for the diffusion process and the volume and mass of the diffusing solute, a ratio of diffusion coefficients D2/D1= exp(q,) = exp(w) = exp(wR/R) = exp(AS,/R) in two states of the system is the starting point. This conforms to the first assumption of the model where the amount 0 2 is related to a value D I for an initial state. This ratio is a measure of the disordered motion of the methylene groups, with a corresponding increase of the molar entropy ASw = wR, resulting from the interaction between these groups in the polymer matrix with the relative density of interaction energy, qr =w. One mole of polymethylene is defined as one mole of methylene groups, -CH2-. The disordered motion of the methylene groups providing the value D2 related to D I is assumed to be analogous to the reversible expansion in a gas with the same change in entropy ASw In comparison with the behavior of a gas, the expansion of this system is neglected and the ratio V2/Vl z 1.For the reference equation D1 = D, = 1m2s-I. In a second step, a molar activation energy, EA, of the motion of the methylene groups in the polymethylene chain is introduced. This activation energy EA = wRT, = 10.089 . 8.31451 . 1036.2 = 86.923 kJ mol-I is defined as a magnitude proportional to
Prediction of diffusion coefficients in gases, liquids, amorphous solids ...
173
w (analogous to wI for gases) and to the limit value of the critical temperature T, = T,,, = 1036.2 K in the homologous series of n-alkanes. In this way D2 = D,, exp(wE,/RT). The next step takes into account the diffusing solute as described for the gaseous state. Due to the practically immobilized matrix composed of macromolecules, the solute is considered to be a tracer for which only its critical molar volume, Vc,i,must be considered. In the special situation of a n-alkane with repeating -CH2- groups in the molecular chain, a constant value of the ratio VJM,.; can be expected for the homologous series excepting the first few members. The first few members deviate from this substructure because of the presence of the two -CH3- endgroups. For the n-alkanes with i = 5-17 a mean value V J M , ; = 4.2385 x lo4 m'mol-' is obtained (Reid et al., 1987). With this value ~ O O O ( V , , ; / W = ~lOOO(4.2385 )~~~ x l0-h M , ; / w , ) ~ /= ~ 0.1351 Mf,i3results. Finally, analogous to the gas phase an equation for the diffusion coefficient, D,,,of a n-alkane with i carbon atoms in an amorphous polymethylene is obtained (Brandsch et al., 1998): Dp,i
= D,
[
exp w - 1000($)
213 -
F] D, exp (w =
-
213 0.1351M,,i
-
(6-20)
Equation (6-20) can be used as a reference equation for all polymers. It represents a theoretical construction resulting from an asymptotic correlation and the assumption of an infinite chain composed of methylene groups representing the amorphous polymer matrix. Diffusion coefficients of n-alkanes in polyethylene While w = Ap stands for the theoretical structure of polymethylene, other characteristic Ap-values can be obtained for other polymers or solids depending on their specific structure. Nevertheless, the remaining two terms in the exponent of Eq. (6-20) can be held unchanged for polyolefins and alkanes. For other diffusing compounds the corresponding critical molar volumes would be more appropriate than the molecular weights. Taking A P to be a characteristic parameter of the polymer which must be determined experimentally, the following more general equation for the diffusion coefficient Dp,ican be used (Brandsch et al., 1998): Ap
-
0.1351M,.i 213
-
(6-21)
The factor 0.1351 in the exponent of Eq. (6-21) can be used as an acceptable approximation for most hydrocarbons and other solutes with low polarity. Comparison of calculated and experimental data The diffusion coefficients of n-paraffins with 12 to 22 carbon atoms in high density (HDPE) and low density polyethylene (LDPE) have been measured by a permeation method (Koszinowski, 1986). Methanol (MeOH) and ethanol (EtOH) were used as contacting liquid phases which minimized interaction between these polar solvents and the nonpolar polymers. No interaction was observed over the investigated temperature range of 6 to 40 "C for both solvents.
4,
0
-
-10.0 --
... p
.
- -Ap=8,8 -
Ap=lo.o89
-10,4 T
Figure 6-2: Logarithm of diffusion coefficients of n-alkanes in polyolefins at 23°C as a function of the relative molecular mass.
Figure 6-2 contains the measured values of the diffusion coefficients from HDPE and LDPE at 23 "C and the calculated curves obtained with Eqs. (6-20) and (6-21) for the corresponding range of masses. The measured diffusion coefficients are in good agreement with the calculated values obtained with Eq. (6-21) using A P =8.8 for HDPE and AP = 10.6 for LDPE, respectively. The most important finding is the close agreement of experimental values with the M:,y-dependence in the exponent of Eq. (6-21) and the reference Eq. (6-20) with the theoretical value Ap = w = 10.089. Figure 6-3 shows the temperature dependence of the diffusion coefficients obtained with i = 12 to i = 22 in LDPE. Comparison of experimental data with the corresponding curves obtained with Eq. (6-21) and AP = 10.6 for i = 12 and i = 22 shows again a reasonable agreement. This result is used as a proof for the activation energy ( E A ) order of magnitude used in reference Eq. (6-20). The value of 86.923 kJ mo1-l is of the same order of magnitude as that for bimolecular reactions in solution.
I
-.
-8 --
6
3.1
u)
v
0
-9
--
-
--- ---
A
x
0
c12
C14 C16 C18 c20 c22 cak C12 calc C22
a
O cn
2 -10 --
-1 1
4
3,15
3.35
l/r (10001K)
335
Figure 6-3: Logarithm of diffusion coefficients of n-alkanes in LDPE as a function of temperature.
Prediction o f rfiffiisioncoefficienls in gases, liquids, amorphous solids ...
175
A general equation for plastics In the general case of a solute B in a plastic matrix P the parameter AP is a function of temperature and produces a more or less significant deviation from the activation energy, E A = 86.923 kJ mol-' in reference Eq. (6-20). Consequently we can write: A p = Ap'--Zp/T,with the athermal, dimensionless number Ap' and the parameter z p with the dimension of a temperature, respectively. Both values, Ap' and - z can ~ be obtained from two diffusion measurements at different temperatures, using a reference solute B in matrix P (see Chapter 15). The specific contribution of B in the DcB-value can be taken into account by two supplementary dimensionless parameters. While ps,B stands for a structural difference of B in comparison to a hypothetical n-alkane with the same relative molecular mass Mr.B, the number p ~ =p p:f + &/T represents an interaction increment between B and P, due to the different polarities of the solute and plastic. This interaction is generally a function of temperature. The two parameters, vs~B and p s p can be considered as relative mass increments (positive or negative) which vanish in the reference system of n-alkanes in polymethylene. If the diffusion coefficient, DKB, is obtained by measuring the mass transfer of B from P into a liquid phase L in contact with the plastic material, more or less strong interactions can occur between the two phases. If the polarities of the plastic material and the liquid phase are similar, swelling of the plastic occurs and the direct consequence of this interaction is an increase of the DRB-values.This process is also a function of temperature and, taking it into account, two supplementary increments, AL for interaction between P and L and p B L for the interaction between B and L are introduced, respectively. Collecting all these parameters, the following general equation can be written: D P ~ B = DU
with
2/3- 10454 (6-22) ( + AL - 0.1351 ( M ~ . B+ L.B + pBp + pBL) 7)
~ X PAP
Ap = Ap'-TpIT ; AL= AL'--zL/T ;
p ~= p p:p
+ pgp/T ;
+ piL/T.
~(B= L P ~ L
Due to the temperature dependence of the parameters A A A L , P E P and P E L , an apparent activation energy, E A , results which deviates more or less from the reference value of 86.923 kJ mol-'. An open question remains over the influence of solutes with high molecular masses on the DpB-values. Measurements were performed using bilayers of polyethylene and polypropylene, consisting of a thin (0.1 pm) film of deuterated polymer atop a thicker (1-2 pm) film of the corresponding hydrogenated polymer (Gel1 et al., 1997). The bilayers were then annealed for appropriate times and temperatures, permitting diffusion to develop a concentration depth profile of the deuterium nuclei. The deuterium depth profile was determined by the forward recoil spectrometry (FRES) technique. The entangled polymer coils show a remarkable diffusion rate, which is orders of magnitude higher than predicted with Eq. (6-21). For diffusion in amorphous polymers at temperatures above their glass point, Tg, one can assume a behavior with some analogy to a liquid. On the other hand the Stokes-Einstein Eq. (6-4) for liquids was derived under the assumption that the diffusing particle is much larger in size than the matrix particles. If we let the matrix be a
176
Piringer
macroscopic system of identical particles composed of -CHZ- groups and the diffusing solute is the whole entangled macromolecule, then the system fulfills the assumption of Eq. (6-4). The decrease of DeB with increasing M,.Bin this equation is much slower than in Eq. (6-21). In order to cover the whole range of molecular weights for solutes in a polymer matrix we can start with Eq. (6-21) and introduce a supplementary positive term, aM,B: Ap - 0.1351MfjB3
+ aMr,B - 10454/T)
(6-23)
A comparison of predicted and measured values of diffusion coefficients for solutes with a large range of molecular weights in polyolefins is shown in Chapter 15 and allows an empirical selection of the U-value.
Diffusion ofparafins in paraffin
Reference Eq. (6-20) for an infinite chain of covalently bonded methylene groups can be considered to be an asymptotic limit for the homologous series of n-alkanes. By substitution of w into the exponent of Eq. (6-20) by the corresponding term, w ~ , ~ , which represents a matrix composed of a paraffin with i carbon atoms, an equation for the diffusion coefficient Ds,ki for trace amounts of a paraffin with k carbon atoms results:
= D,
exp(wi,e - 0.1351M;,f
-
~
%).
i
~
(6-24)
from using the limit value T, = 1036.2 K and the molecular weight, k f r , k , of solute k or its critical molar volume, v , , k . For self-diffusion i = k and for solutes with structures significantly different compared to paraffins, the critical molar volume instead of the molecular weight is preferred. Diffusion coefficients in liquids
With the exception of the super cooled region below the melting point, the liquid state of a substance occurs between its melting point and its critical state. Correspondingly, an equation of diffusion coefficients for liquids is based on Eqs. (6-19) and (6-24) representing these limits. Starting with the homologous series of n-alkanes as a reference structure series and the entropy of evaporation discussed in section 6.3.3, the development of an equation for the liquid state is possible with the following steps: With Eq. (6-17) a value of the self-diffusion coefficient, D T l for the first member of the reference series is calculated using the critical temperature TC,,= ( W ~ , ~ / W ) T , (Eq. 6-11) and the relation: (6-25)
Prediction of diffusion coefficients in gases, liquids, amorphoits solids ...
177
This relation is used for the reference series in Eq. (6-20), with the value 0.1351 Mf,? = 0.1351 . 162'3for the first member of the series. At the reference temperature T, and the standard pressure of 1 bar, the value D P l = 1.42735 x m2s-' is obtained with Eq. (6-17) for the gas phase. This value is a reference number and not the experimental value found for methane. Taking into account that the same disorder occurs for liquids in equilibrium with their vapor phases having the same molar gas volume, a reference diffusion coefficient, D!,l = D z l / e w = 5.9278 x lo-"' m2s-l is obtained from the reference diffusion coefficient in the gas phase. In the next step, Eq. (6-24) with i = k is used to calculate a temperature, TIo,for which the self-diffusion coefficient, D,,, is equal to the reference value DO,.,: (6-26)
Df,, is a first approximation and is obtained only if T? = T,. Consequently, a correction must be introduced which accounts for the deviation of TP from T, This corrected value, denoted D f , , = (T,/T?)Df.,defines the lower limit of self-diffusion coefficients for a paraffin i at T?. The upper limit of the self-diffusion coefficient in the liquid phase is obtained with Eq. (6-19) at the critical temperature, TC,;= ( W ~ , ~ / Wusing ) T , the critical pressure, p,;=(RT,I VC,;). ( w J w ) from Eq. (6-12) in combination with the Eq. (6-25) for the n-alkane series: & 4 . 2 3 8R 5 . 1 0 - 6 ~ ~ w, r,i.D
D C J. - T~
= 6.3939.
10-9exp(-$
-
exp(-?
0.1351M:%i3)
-
0.1351M:,f) (6.27)
It can be assumed that the self-diffusion coefficient DL,; at a temperature T between T? and Tc,;follows the exponential function D = ae-"'. Collecting all results from the above steps and writing Dt,l = a exp(-h/Tp) and D , ; = a exp(-blT,,J, the following equation is obtained for the diffusion coefficient DL,;:
~
~= a , exp( i -
+)
(6-28)
with
Taking into account that, for the reference homologous series of n-alkanes the relative molecular masses of the member i in the series is M,,= 2 + 14 i, the self-diffusion coefficient D L , can ~ be calculated with Eqs. (6-27) and (6-28). This can be done using only two values based on experimental results, the limit value of the critical temperature, T,, and the mean value for the ratio, Vc,,/Mc,. Table 6-4 shows a comparison between experimental (Landolt-Bornstein, 1969) self-diffusion coefficients and calculated values obtained with Eq. (6-28). A mutual diffusion coefficient, DL,,k,can be defined in the same manner as for gases with Tc.rk = X I TC,If X k Tc.k and Vc.rk (vc,~ + vc,k)/2 and P c , i k = x i ' p c , ~-k x k Pc.k. '
'
178
Piringer
Table 6-4 Self-diffusion coefficientsof n-alkanes. Alkane with i carbon atoms
T/K
D ~ , ~ / ( Icm2 o - ~s-') calc.
Heptane
298
3.23
3.10
Octane
298
2.28
2.75
333
3.8
3.6
298
1.67
1.70
333
2.8
3.0
Nonane
t1~,~/(10-'cm2 s?) exu.
298
1.28
1.31
333
2.2
2.5
Dodecane
333
1.4
1.5
Octadecane
323
0.52
0.46
Dotriakontane
373
0.42
0.30
Decane
In Table 6-5 the mutual diffusion coefficients of a binary mixture of n-heptane and n-hexadecane at 25 "C are calculated for different molar fractions of the solutes and compared with experimental values (Landolt-Bornstein, 1969). Table 6-5: Mutual diffusion coefficients of a binary mixture of n-heptane and n-hexadecane at 25 "C and different molar fractions x. XI6
0.0056
0.1064
0.2024
0.3934
0.5821
0.7920
0.9761
x7
0.9944
0.8936
0.7976
0.6066
0.4179
0.2080
0.0231)
DL.ij talc./( 10-'cm2s-')
1.72
1.59
1.45
1.18
0.95
0.74
0.58
DL-,, exp./(I0-'cm2s-')
1.78
1.59
1.45
1.24
1.07
0.895
0.76
Tc,7= 534.58 K, Tc,,6= 721.68 K, pC,,= 27.4 bar, pC.l6= 14.1 bar, Vc,7= 4.2378E-4 m3 mol-'. Vc,lb= 9.577E-4 m3 mol-'
The tracer or intradiffusion coefficient, DtTkiof an n-alkane k in a solution of n-alkanes i and k at temperature T can be calculated with Eq. (6-28) in two steps: first, the ratio D,?k,/Dzi, for mutual diffusion at T and T,, is calculated. In the next step the tracer dif usion coefficient D$, at the reference temperature T,, is calculated using M , . k instead of M,; in Eq. (6-26) and in the exponent of Eq. (6-27). The corresponding values for TZj and Dc,kiare then used for bki and ak; in Eq. (6-28), respectively. Finally we obtain: (6-29) In order to generalize Eq. (6-28) for any organic solutes, the self-diffusion coefficient DL.Aof a compound A can be calculated in the following manner: (6-30)
with
Prediction ofdiffiaion coqfficierits in gases, liquids, aniorphoirs soli~ls__.
and 1
I n D t , l + 1O3
1
179
(%)
2'3).
The product w . T c , A in the above relation results from Tc.,= T,(wj,,/w) if the critical temperature, T L . , A ,of liquid A, which is not a member of the homologous series, is used instead TC.;.In this case wj,, in Eq. (6-24) is substituted by (TC.,A/TC)w. If no value for the critical molar volume Vc.,Ais available the use of the relative molecular mass, MKA, is an acceptable approximation. In this case Eq. (6-25) has to be used for substitution of Vc,Aby MGAin Eq. (6-30). The mutual diffusion coefficient, D/,,,,R, in a mixture of A and B is defined in the same manner as for n-alkanes, with T c , A = ~ X A . Tc.A + x B . T C ,and ~ V,:, = (Vc.~ + vc,B)/2 and P c , A B = X A ' p c . A + X B 'Pc.B. As shown above for the homologous series for n-alkanes the tracer-diffusion coefficient, Df7BA,of a compound B in the solvent A at temperature Tis obtained within two steps: first the ratio of mutual diffusion coefficients D:,,,/DT". L , A B i ~calculated using Eq. (6-30).Then D;TBAis calculated at the reference temperature T,, using Vc.Binstead of Vc..Ain Eq. (6-30). Finally the value of D;,7jjAresultsas: (6-31) For B = A, the tracer diffusion coefficient equals the self-diffusion coefficient, D:TBA= Dl,A. In Table 6-6 the self-diffusion coefficient of water and some diffusion coefficients of organic solutes in water at infinite dilution calculated with Eq. (6-31) are compared with experimental values (Reid et al., 1987). The experimental value for sucrose is from Cussler (1997). If no value for Vc,B is available, again M Kcan ~ be used as a reasonable approximation, using the substitution 103(Vc,~Iw~)2'3 = 0.1351 . M:,$ (relation 6-25) in Eq. (6-30). With water as the liquid phase A, an upper limit for the mass M G Bof a diffusing solute B at infinite dilution is reached at M G B= 212, because above this value bHA in Eq. (6-30) changes its sign. As mentioned before, for solutes with significantly higher sizes than the sizes of the matrix particles, the Stokes-Einstein equation (6-4) can be used. In this equation the solute radius a is used which can be correlated with V,,,li3 and MKBIi3. Taking this into account in the case of aqueous solutions, the diffusion coefficient D / . , B A for solutes with Mr,B> 212 can be estimated with the following equation:
(z) I /3
'L.l3A
= DL.212A
, with
> 212
(6-32)
D[,2,,A is calculated with Eq. (6-31) using Mr., = 212. In Table 6-7 diffusion coefficients of high molecular solutes in water calculated with Eq. (6-32) are compared with experimental values (Tanford, 1961). With the homologous series of n-alkanes, such an upper limit, Mr.,nn.rk, for the relative molecular mass of a trace paraffin k in a solution of paraffin i is obtained for each member of the series. Consequently, an analogous equation to 6-32 can be written for the series:
180
Piringer
Table 6-6: Diffusion coefficients in water at infinite dilution.
TIK
Solute
DITBA calc. cm2 s-'
Water
D&
exp.
lo-' cm2 SC'
% error
298
2.24
2.13
+ 5.4
273
1.41
0.97
+45
- 28
373
6.24
8.65
275
1.27
0.85
+49
333
3.20
3.55
-
Carbon dioxide
298
1.95
2.00
- 2.7
Propylene
298
1.50
1.44
+
Methanol
288
1,52
1.26
+20
Ethanol
288
1.32
1.00
+32
Acetic acid
293
1.42
1.19
+20
Ethyl acetate
293
1.10
1.oo
+10
Aniline
293
1.13
0.92
+23
Diethylamine
293
1.07
0.97
+10
Pyridine
288
I .09
0.58
+88
Ethylbenzene
293
0.94
0.81
+I7
Methylcyclopentane
275
0.79
0.48
+64
293
1.04
0.85
+22 - 10
Methane
Vinyl chloride Sucrose
9.7 4.2
333
1.72
1.92
298
1.55
1.34
+16
348
3.02
3.67
-18
298
0.5247
0.5228
+ 0.4
Table 6-7: Diffusion coefficients of macromolecules in water at 20°C. Solute B exp. Sucrose
342
5.03
4.59
Ribonuclease
13700
1.47
1.19
Lysozyme
14100
1.46
1.04
Serum albumin
65000
0.88
0.59
Haemoglobin
68000
0.86
0.69
Urease
480000
0.45
0.346
Collagen
345000
0.50
0.069
Myosin
493000
0.45
0.116
Prediction of diffiision coefficients in gases, liquids, nmorphous solids ... DL.ni T --D TL.imxki (Mr.'llaxk)
'I3, with Mr." > Mr,maxk
181 (6-33)
DI,~~,~~~
where is calculated with Eq. (6-29) using M r , k = for which bk reaches a minimum positive value. With increasing values of the relative molecular masses of the solvent, M,;, the corresponding maximum value Mr,,,taxk is approximately M , = (~~,,/0.1351)"~, a value which results from Eq. (6-24) for w ; , ~= 0.1351M,.k2'3. For i +M, w ; , ~+ w and M K m n x k = 645. Above this molecular weight a significant slower decrease of the DeB-values in plastic materials occurs and this is taken into account in Eq. (6-23). References Brandsch J, Mercea P, Piringer 0. 1998: in Risch S (ed). New developments in the chemistry of packaging materials, ACS Symposium Series, Washington. to be published. Cussler E L, 1997: Diffusion. Mass transfer in fluid systems, 2 nd. ed., Cambridge University Press. Cell C B. Graessley W W, Fetters L J, 1997: J. Polymer Science: Part B: Polymer Physics 35 1933. Hildebrand J H. 191.5:J. Am. Chem. SOC.37.970. Hildebrand J H, Prausnitz J M, Scott R L, 1970: Regular and related solutions, van Nostrand Reinhold Company, New York. Kestin J, Knierim K, Mason E A, Najafi B. R o S T. Waldnian M. 1984: J. Phys. Chem. Ref. Data 13 229. Koszinowski J, 1986: J. Applied Polymer Science 31. 1805. Landolt-Bornstein, 1969: Zahlenwerte und Funktionen. 11. Band, 5. Teil. Bandteil a Transportphanomene. Springer-Verlag,Berlin, New York. Reid R C, Prausnitz J M, Poling B E. 1987: The properties of gases and liquids, 4 th ed.. Mc.Graw-Hill Book Company, New York. Tanford C, 1961: Physical chemistry of macromolecules, Wiley. New York.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
7 Transport equations and their solutions Otto Piringer
7.1 The transport equations Interactions between packaging and product are always connected with transport processes occurring within the packaging system. A transport process is understood to be a general movement of mass, energy or other quantity from one location to another. An example of mass transport in packed liquid products is the convection that occurs during the heating or shaking of the package. Macroscopic regions of the liquid move with different speeds relative to one another and cause mixing to occur. With heating, a simultaneous transport of heat takes place along with mass transport. The convection of mass and energy takes place in liquid products during distribution of the packaging from the manufacturer to its final storage destination and during heating and cooling of the package. Mixing by convection in viscous and solid packed products has very little or no practical significance. A special case is the mixing of particulate products by shaking, which gives results similar to convection. The most important transport processes in solid, viscous and liquid filled products during the storage period are diffusion and thermal conductance. Mass transport by diffusion and energy transport by conductance have a common molecular basis. They are both affected by the unordered movement of molecules in the medium in which transport takes place. It is the vibration of atoms and groups of atoms, transmitted to neighboring atoms which is responsible for conductance in solids. Unordered collisions between the mobile molecules of a liquid or gas are also a source of mass transport by diffusion (Chapters 5 and 6). A further example of energy transport through packaging into the filled product is electromagnetic radiation. This radiation in the form of light can start chemical reactions or, in the case of microwaves be transformed into heat and then further distributed through the packaging system by conduction or convection. In addition to mass and energy, other quantities can also experience transfer. Flowing layers with different flow rates in a convection stream can influence one another. The slower flowing layer acts as a brake on the faster layer, while at the same time the faster layer acts to accelerate the slower one. The cause of this behavior is the inner friction of the liquid appearing as a viscosity difference, which is a consequence of the attractive forces between the molecules. Viscosity can be explained as the transport of momentum. The viscosity of different media can be very different and thus plays an important role in transport processes.
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7.1.1 The terminology of flow For the mathematical description and understanding of transport processes, it is advantageous for their descriptions to have several common characteristics, regardless of the nature of the transport quantity, to allow them to be treated in a similar manner. Without knowledge of their fundamental causes at the molecular level, which corresponds to their historical development, transport processes can be described with help from quantities that can be quantitatively measured on a macroscopic level. One such quantity is that of flux. The flux J is understood to be the amount of a quantity transported per unit time through a unit surface area. Flux is a vector for which a direction must be specified in addition to the quantity or contribution J. This is accomplished with the help of the unit vector e giving:
J = Je = Jx
+ J, + Jz = Jxi + J y j + Jzk
(7-1)
J,, J,, J, are the vector components in the x, y and z axis directions of the coordinate system, J,, J,, J, are their contributions and i, j and k are the corresponding unit vectors. Given a mass quantity rn that is transported during time t through an area A, then let J represent the contribution of the mass flux. For energy transport, then J is the contribution of the energy flux with the dimensions J/m2s(where J = Joule). In a very general sense, the flux of a quantity G is proportional at a given location to the gradient of the scalar field produced by the flux, a(x, y, z ) . Mathematically, one obtains the contributions of the three components with the gradient of a, grad a, from the partial derivative of a at the coordinates x, y, z which for the flux G results in:
-b
(& @i
a)
J,(mass,convection)
= p
b)
Jz(momentum in x - direction) = -q
c)
J,(mass,diffusion)
d)
J,(energy,conduction)
J(G)=-bgrada
=
+ “j (b + “k az
(7-2) The location independent proportionality factor is designated b. The minus sign in Eq. (7-2) shows that the flux goes in the direction of decreasing a-values. This means the quantity G “flows” down the gradient. The usefulness of the flow terms as common characteristics for transport processes allows them to illustrate such seemingly diverse processes as convection, momentum transport (viscosity), diffusion and heat conductance. To simplify the written expression, the flux components of the four processes are expressed in Eq. (7-3) in the direction of one axis of the coordinate system whereby, instead of the partial derivative for the function, a variable and useful form of the derivative expression is used:
=
i
-D a dx i =
&x dz
k
(7-3)
-n dx i
In Eq. (7-3a) p and dxldt are the contributions of the density and the velocity of the liquid in the x-direction. The material specific constants q, D and n are for the viscosity, diffusion and thermal conductivity coefficients. The derivatives in the z and x
Trrirrsport equations and their solutions
185
directions, dv,/dz, dc/dx and dT/dx are for the velocity components (in the x-direction), the concentration and temperature. A comparison of the four equations in Eq. (7-3) shows the similarities between the expressions. With respect to their individual historical development, the four expressions above are quite separate. While the above representation of momentum can be traced back to Newton, the expression for heat conductance was first derived by the mathematician and physicist Joseph Fourier at the beginning of the last century. The physiologist Adolf Fick, who was concerned with measuring the transport of oxygen in blood, recognized the analogy of diffusion to heat conductance and published in 1855 the diffusion equation now known as Fick's first law (Eq. 7-3c). The relationships between the different processes at the molecular level was first recognized by Einstein and other physicists and led to quantitative relationships between material specific constants, in particular between D and q , which are important for calculating their respective contributions (see Chapters 5 and 6).
7.1.2 The differential equations of diffusion During a diffusion process, e.g. the migration of an additive from a plastic into the atmosphere, a change in the concentration of the diffusing substance takes place at every location throughout the plastic. The mass flux caused by diffusion is represented by a vector quantity whereas the concentration c and its derivative of time t is a scalar quantity and is connected by the flux with help of the divergence operator. The following example serves to emphasize this relationship. In a body with any given shape, e.g. a piece of soap, there is an aroma compound which is initially uniformly distributed throughout the entire body. During storage without any packaging a decrease in concentration takes place due to diffusion into the atmosphere particularly in the outer layers of the soap. The resulting scalar concentration field with the levels c1 > c2 > c3 (Fig. 7-1) forms a gradient field that describes the external direction of the aroma compound flux.
Figure 7-1. Diffusion and the divergence operator.
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Piringer
Figure 7-2. Diffusion through a volume element.
Now consider only a suitably small section of the soap in the form of a cube with side lengths of Ax, Ay, and Az (Fig. 7-2). The aroma compound will diffuse in as well as out of the cube because of its perpendicular side surface areas. Due to the greater decrease in the aroma near the soap’s external surface, the flux out of the side of the cube closer to the surface is greater than the flux into the side of the cube that lies deeper in the soap. The difference between the aroma diffusing in and out will be positive which means one can consider the cube as an aroma source. As a consequence of the flux out of the cube, the concentration in the cube decreases with time. The concentration is also a function of time, c = c(x, y, z, t) and its decrease with time, i.e. the partial derivative -&/at in the cubic volume AV = Ax Ay Az, represents the net flux out of the cube and designated div J the divergence of the flux. Mathematically the divergence is obtained as the sum of the differences between flux components in and out of the cube in the coordinate axis direction with respect to the cube’s volume. Placing the coordinate axis parallel to the corners of the cube as a helpful construction (Fig. 7-2), then one can label the incoming flux component contributions through the side walls Ay Az at the location x with Jx(x) and the outgoing component through the opposite side wall at x + Ax on the x-axis with Jx(x + Ax). When this is done in the same manner for the other components, then one gets:
+
IJZ(Z+AZ)- J ~ ( z )Ax ] Ay Ax Ay Az
(7-4a)
By letting the length of the cube’s sides Ax, Ay and Az become infinitely small, then the differences on the right side of Eq. (7-4a) become the partial derivatives of the flux component contributions at the location P(x, y, z) and one obtains: (7-4b)
Trnrisport equations and their solutions
187
Then the contribution of the diffusion flux in the direction of the three coordinate axis are according to Eqs. (7-2) and (7-3c):
J, = - D &/Ox, J, = - D i)c/dy and J,
=
-
D &/dz
(7-5)
With help from the divergence and gradient, one obtains the same result in the form of the expression: div J = D div grad c
=
(7-6)
The mathematical operator V, called Nabla or del, appearing in Eq. (7-6) has the structure:
When del is applied to concentration c, Vc = grad c, and to the vector of the diffusion flux J = -D grad c, it gives VJ = - div J = D div grad c = DV'c. The application of the del operator twice leads to a scalar, to a vector and once again to a scalar, then i - i = j - j = k - k = 1 and i . j = i - k =j - k = 0 and subsequently:
Eqs. (7-5) and (7-6) are known as Fick's second law for the case where the diffusion has a constant diffusion coefficient. The immediate result of the above discussion is that the diffusion equation can be transformed into the differential equation for heat conduction by substitution of c by T and D by IC. This analogy has the consequence that practically all mathematical solutions of the heat conductance equation are applicable to the diffusion equation. The analogy between diffusion and conductance should be kept in mind in the following discussion although the topic here will be mainly the treatment of the diffusion equation, which represents the most important process of mass transport.
7.1.3 The general transport equations If diffusion and convection currents are similar in magnitude then the total transport is the sum of all the individual contributions. While convection currents caused by mild shaking of low viscosity liquids lead to a much faster mixing than by diffusion processes, the influence of convection decreases with increasing viscosity (e.g. mayonnaise). A decrease in concentration in addition to physical transport effects can also be the consequence of a chemical reaction taking place. The concentration decrease per unit time caused by chemical reaction is defined as the rate of reaction r and is a function of the concentrations present at the reaction site:
The proportionality factor k is the reaction rate constant. The exponent n, usually 1 or 2, specifies the order of the reaction.
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Piringer
The simultaneous occurrence of reaction and transport processes can be represented by adding the contributions together and, for the total concentration decrease over time at a given point P(x,y,z) in the media considered by the general transport equation one obtains:
II
- _
at total
= div
J (Diffusion)
+ div J (Convection) +
r (reaction)
A typical example of transport and reaction occurring during storage of a package is the spoilage of fat-containing food by oxidation with oxygen transported from the atmosphere through the packaging. Equation (7-10) is a mass balance. At every location a decrease in concentration of substance i takes place by transport and chemical reaction. Thus the total decrease -&/at is equal to the amount of substance leaving the location, which includes the changes due to diffusion and convection plus the loss due to chemical reaction. By this the description of the location where the processes take place is properly described as the source of substance i.
7.2 Solutions of the diffusion equation For interactions between packaging and product the above descriptions of both material transport processes by diffusion and convection as well as the simultaneous chemical reactions come into consideration. The general transport equation (7-10) is the starting point for solutions of all specific cases occurring in practice. Material loss through poorly sealed regions in the package can be considered as convection currents and/or treated as diffusion in the gas phase. A solution of the general equation delivers the concentration contribution at every point in time and at every location throughout the volume considered, thus c = c(x, y, z, t). The general form of the transport equation as a second order partial differential equation has no solution. Analytical solutions are given however for numerous special cases. For solutions involving complicated cases, simplifying approximations are used or numerical solutions are carried out. Since the general equation (7-10) represents a starting point not only for interesting interactions but also for the complete chemical reaction technology, there are numerous solutions described in the literature which can be applied to interaction problems. The usefulness of analogous considerations was already mentioned in the comparison of diffusion and heat conductance. Since Eq. (7-10) is composed of the sum of its members, it is logical to consider next the contribution of each individual component. The fastest step in a group of simultaneous overlapping processes is the most important. If the overall process is the result of a series of processes taking place one after another, for example as a consequence of transport processes through one or more boundary surfaces, then the slowest step of the process determines the rate of the overall process. Mass transport by diffusion is without doubt the most important process throughout the storage of packed products. The discussion of the solution begins then with the diffusion equation Eqs. (7-5) or (7-6). In order to start with the most general case in which the diffusion coefficient D is not constant, one can also write:
Trailsport equations and their solutions
189 (7-11)
While numerical methods come into question for solutions involving variable D, D can be assumed to be constant or practically constant for most cases of practical interest. In addition, simplified solutions for diffusion along the x-axis can be used instead of the general solution, except for some particular cases which will be pointed out later. This greatly simplifies presentation of the problem and the resulting equation for diffusion is:
(7-12)
7.2.1 Steady state The simplest case t o solve is when the concentration stays constant over time in the polymer. If diffusion occurs only along the direction of the x-axis then: (7-13)
D $=O
This particular case exists for example in the diffusion of a substance through a film with thickness d (Fig. 7-3) if the concentrations at the two surfaces C I at x = 0 and c2 at x = d remain constant (stationary case):
0
X
d
Figure 7-3. Diffusion (permeation) through a film at steady state.
A first integration of Eq. (7-13) then gives:
* dx
= constant
(7-14)
A constant concentration gradient exists in the film perpendicular to the film’s surface and consequently there is a constant diffusion flux in the x-axis direction according to Eq. (7-3c) at every location between x = 0 and x = d. Integrating Eq. (7-14) again leads to:
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Piringer
c-c1 ~2 - ~1
-s
(7-15)
d
and the amount of the flux through the film is:
.D & = D dX
d
(7-16)
7.2.2 Nonsteady state A number of solutions exist by integration of the diffusion equation (7-12) that are dependent on the so-called initial and boundary conditions of special applications. It is not the goal of this section to describe the complete mathematical solution of these applications or to make a list of the most well-known solutions. It is much more useful for the user to gain insight into how the solutions are arrived at, their simplifications and the errors stemming from them. The complicated solutions are usually in the form of infinite series from which only the first or first few members are used. In order to understand the literature on the subject it is necessary to know how the most important solutions are arrived at, so that the different assumptions affecting the derivation of the solutions can be critically evaluated. Most solutions of the diffusion equation (7-12) are taken from analogous solutions of the heat conductance equation that has been known for many years: (7-17) which can be directly applied to diffusion problems. The standard reference work on the mathematics of diffusion is by Crank (1975), from which most of the solutions contained in this chapter have been taken. The solutions themselves have their origins in the older and more comprehensive reference work on heat conductance in solids by Carslaw and Jaeger (1959). The selection of diffusion equation solutions included here are: diffusion from films or sheets (hollow bodies) into liquids and solids as well as diffusion in the reverse direction, diffusion controlled evaporation from a surface, influence of barrier layers and diffusion through laminates, influence of swelling and heterogeneity of packaging materials, coupling of diffusion and chemical reactions in filled products as well as permeation through packaging.
7.2.3 Diffusion in a single phase homogeneous system The diffusion problem is simplest to solve analytically if the diffusing substance is concentrated at the beginning of the process in an infinitely thin sheet (plane) and then diffuses perpendicular to the plane of this sheet into an infinite liquid media found on both sides of the sheet. The flowing away from or diverging from the source is, once more, a graphic example for the expression of the diffusion equation in the form represented in Eq. (7-6): -dc/at = div J. A model corresponding to this situation can be represented by a long cylindrical shape made from a polymeric material, e.g. polyethylene, with a cross section of 1 cm2. In the middle of the material there is a very thin layer of material colored with a pigment which acts as a diffusion source (Fig. 7-4a). The color molecules then diffuse outwards towards both ends of the bar
I o,8i "'€1 A Transport equations and their solutions
a
6.
1
1
0
- X t -
191
Ib
0.6
-+X
0.4
i,
Dt=0.3
0.2 0
-3
-2
--
__.I
-1
-x
0
-._
1
2
3
x
Figure 7-4: a ) Two sided diffusion from an infinitely thin layer (source). b) Distribution of concentrations for different values of the product Dt.
along the x-axis of the coordinate system without reaching the ends of the bar during the time interval considered. At t h e beginning of diffusion, time t = 0 and the total amount of color having mass m is located at position x = 0. Because of the theoretically infinitely thin layer 6x of the color source, the initial concentration there is infinite and the concentrations at all other positions of the bar are zero. The solution of the diffusion equation (7-12) is immediately given as: c=
A
exp
(-a&)
(7-18)
1 1 -
where A is the integration constant whose formation can be easily checked from the partial derivatives ocli3 and i)2cldx2 from Eq. (7-12). The expression in Eq. (7-18) is symmetric with respect to x = 0 because of x2 and goes to zero if x becomes positively or negatively infinite and t > 0. With help from the substitution:
_ _ = q2;
dx
=
2 (D t)ll2 dq
(7-19)
and because the total amount m is obtained, which means: +x
m = ,[ c dx
(7-20)
--x
one can write: +x
m = 2 A D1/2
--x
exp (- q2) dq = 2 A (n D)'/'
(7-21)
The values for A resulting from Eq. (7-21) are used in Eq. (7-18) and then one obtains the solution: (7-22) for the spreading of the color by diffusion. The increased spreading with time can be seen in Fig. 7-4b.
192
Piringer
In the above case, half of the substance diffuses in the positive direction and the other half in the negative direction of the x-axis. If an absolute barrier is now assumed to exist at position x = 0 so that diffusion can occur only in the direction x > 0 then the half of m diffusing in the x < 0 is reflected by the barrier and overlaps the other half diffusing in the x > 0 direction (Fig. 7-5a). Because the symmetry of the curve (7-22) with respect to the source at the position x = 0, one obtains a solution for diffusion in a half open media that is double the value of Eq. (7-22): c=-
(7-23)
The requirement of a barrier layer at x = 0 is expressed mathematically by the boundary condition of 8c/& = 0 at x = 0. The first complication for the application of the diffusion equation Eq. (7-12) comes when the complete left half of the plastic bar, x < 0, is uniformly and completely colored with coloring agent which can diffuse in the direction of x > 0 (Fig. 7-5b). The concentration of the color is expressed by the finite concentration of co. In order to find a solution to the problem the colored region x < 0 is thought of as being divided into an infinite number of layers perpendicular to the x-axis. In doing this, the problem can be related to an infinite number of diffusion sources and the mathematical solution can be arrived at by overlapping many solutions of the form of Eq. (7-18). Considering the thickness 6s of such a source (Fig. 7-5b), then one gets the amount of substance contained in the cross section of the bar, co 6s, because it has the unit surface area. One obtains the expression for the concentration c, of the color originating from this source at a distance s at time t according to Eq. (7-22): 2
(K
(7-25)
D t)‘
The integration of c, over all layers 6s gives with Eq. (7-25) the concentration c(x, t) at any position x > 0 at time t:
(7-26)
il a
-X-
0
+X
b
-X-
s
O
-+x
Figure 7-5: a) Single layer diffusion from a source with a bamer on one side. b) Diffusion from an infinite thick layer represented as coming from infinitely many sources.
Trmsport equations and their solutions
193
With c,(x, t), the concentration coming from the source is designated for position x at time t at a distance s from the initial point. In order to make the right side of Eq. (7-26) easier to use, the following relationship can be considered:
1 - erf(z) = erfc
=
(7-28)
(2)
where the error function erf (z) is given by: erf(z) = $Texp(-q2) 0
dq,erf(-z)
=
-erf(z);erf(O) = O;erf(m) = 1
(7-29)
for which complete tables are available (Table 7-1). The complement of erf (z) is designated erfc (z) and is also given in Table 7-1. The solution Eq.(7-26) can now be expressed in a convenient and easily useable form: c (x, t)
= 2:1 c0
erfc
(7-30)
Table 7-1: Table of different error function forms. z
erf z
erfc z
F(Z)
0.00
0.000000
1.000000
0.00000
1.10
0.880205
0.119795
0.59827
0.05
0.056372
0.943628
0.05401
1.20
0.910314
0.089686
0.62146
0.10
0.1 12463
0.887537
0.10354
1.30
0.934008
0.065992
0.64236
0.15
0.167996
0.832004
0.14908
1.40
0.952285
0.047715
0.661 26
0.20
0.222703
0.777297
0.19098
I .so
0.Y66105
0.033895
0.67841
0.25
0.276326
0.723674
0.22965
1.60
0.976348
0.023652
0.69405
0.30
0.328627
0.671373
0.26540
1.70
0.983790
0.016210
0.70834
0.35
0.379382
0.620618
0.29850
1.80
0.989091
0.010909
0.72144
0.40
0.428392
0.571608
0.32921
1.90
0.992790
0.007210
0.73349
0.45
0.475482
0.524518
0.35775
2.00
0.995322
0.004678
0.74460
0.50
0.520500
0.479500
0.3843 I
2.10
0.997021
0.002979
0.75488
0.55
0.563323
0.436677
0.40907
2.20
0.998137
0.001865
0.76441
0.60
0.603856
0.3961 44
0.43220
2.30
0.998857
0.001 143
0.77326
0.65
0.642029
0.357971
0.45382
2.40
0.999311
0.000689
0.78150
0.70
0.677801
0.3221 99
0.47407
2.50
0.999593
0.000407
0.78919
0.75
0.71 1156
0.288844
0.49306
2.60
0.999764
0.000236
0.79640
0.80
0.742101
0.257899
0.51090
2.70
0.999866
0.000134
0.80310
0.85
0.770668
0.229332
0.52767
2.80
0.999925
0.000075
0.80950
0.90
0.796908
0.203092
0.54347
2.90
0.999941
0.000041
0.81540
0.95
0.820891
0.179109
0.55836
3.00
0.999978
0.000022
0.81540
1.00
0.842701
0.157299
0.57242
194
0 1
Piringer
0” 0.5
Figure 7-6: Concentration distribution curve for diffusion from an infinitely thick initial layer.
X __ 2 m
The shape of the concentration curve is shown in Fig. 7-6. At position x = 0, c = 0.5 cg for all values o f t > 0. The amount of substance diffused into the uncolored portion of the bar up to time t (shaded region after x > 0) is equal to the amount of substance diffusing out of the colored portion (shaded region x < 0). Example 7-1. A 10 cm high cylindrical shaped wheel of cheese contains a homogeneously dispersed ingredient with a concentration c,, = 100 mg/kg. A second similar wheel of the same type of cheese without this ingredient is laid on top of the first wheel. Assuming there is intimate contact between the two wheels o f checsc. what is the concentration of this ingredient in the second block of cheese at a depth of 1 mm after 25 hours of contact? D = 3E-7 cm2/s. This problem corresponds to the example in Figure 7-Sb. A 10 cm thick wheel of cheese can be considered to be infinitely thick with respect to the diffusion coefficient provided the contact time is not too long. Eq. (7-30) can be used to solve the problem. For x = 0.1 cm, t = 2Sh 3600s/h = 90000s and D = 3E-7 cm’h on calculates:
Looking up the value for erfc z in Table 7-1. erfc(0.3) = 0.671373, and using this value in Eq. (7-30) the concentration of the ingredient at this time and distance can be calculated to be: c(x, t) = . c0 erfc(z) = 0.5 . 100 0.671373 = 34 mg/kg
f
Example 7-2. What would the distance from the surface of the second wheel for the 34 mg/kg concentration from Example 1 be after a) three months? b) after one year? Assume that the storage conditions remain constant and the properties of the cheese wheels also remain constant during these times. Because the z values from Eqn. (7-30) will always lead to the same concentration (i.e. 34 mg/ kg), one can simply solve z for the distance: After 3 months: (3mo .30d/mo .24h/d 3600s/h = 7776000 s: X X z =- 0.3 x = 0.93 cm 2 ( D ti”’
= 2 (3 09E-7 7776(XXh)’” -
After 1 year: z =
X
2 [D.l)’/’
~
~
-0.3
2 - ( 3 096-7.31 IllJO~Xls)”2 -
x = 1.9 cm
Trrrrisport equations and their solutions
195
Dimensionless parameters and the proportionulity of mass transfer to the square root of time
In order to compare results of studies that are expressed in different quantities, dimensionless representations are always preferred. Examples of dimensionless quantities are the relative concentration c/cOalready mentioned above and the parameter appearing in the error function z = x / 2 (D t)1’2 in Fig. 7-6. Systems described with help from the same model but differing from one another with respect to material constants, e.g. D values, can have the same z and c/co values at different times. As a result, whole series of curves can be represented by a single, easy to read curve. Since the same z values always lead to the same c/co values, the distance xc which is the distance the diffusion front having concentration c has traveled from the surface with a constant initial concentration cg to time t, the definition of z is given as: xc : 2 (D t)lI2 z
(7-31)
Like in the solution given for the diffusion out of a bar colored on one side bar in Eq. (5-30),it can be seen that the same c/co values always result for the same z values. This means that the diffusion front of a given concentration c is proportional to the square root of Dt. The error function used in solving the above diffusion problem occurs as a consequence of the summation of an infinite number of infinitely thin colored layers, which themselves bring about an exponential distribution of the concentration. Because of the error function’s significance for numerous practical cases, this solution will be treated in somewhat more detail. In the same manner, one obtains a solution to the diffusion equation starting with a colored layer having a finite thickness 2d and an initial concentration cg in both directions of the unbounded x-axis (Fig. 7-7): (7-32)
In the next example a short section of length 1 is cut from the plastic bar (Fig. 7-8). The bar is uniformly colored from one end up to a layer thickness of d with a pigment having concentration co. The zero position of the x-axis is assigned to the colored end of the bar. With the mathematical boundary conditions x = 1, ac/ax = 0, one finds that the diffusion of a color molecule in the uncolored section cannot go further than the theoretical barrier existing at x = 1 and is reflected back. For illustration purposes the representation of the concentration profiles of this process are shown by straight lines with different slopes in Fig. 7-8. The reflected path of the curve from a source 6, now overlaps the original curve and the concentration at a given location x of the bar is the
-X
-
0
-+x
Figure7-7: Two sided diffusion from a finitely thick layer.
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Piringer
Figure 7-8: Single sided diffusion from a finite thick layer into a finite layer of the same material.
sum of the two contributions. A further reflection takes place at the other end of the bar at x = 0 and then again at x = 1 and so forth, whereby every reflected curve section overlaps the previous section. Because the original curve is already represented as the sum of two error functions, the complete system is represented by a series of error functions:
’
i co n = O [erf (d 2+ (D2 n l - x t)l/*
)
+
erf
(
d-2nl+x 2 (D t)’/*
)]
(7-33)
Even though the above method of solution of the diffusion equation (Eq. 7-12) becomes impractical for complicated cases, it illustrates the appearance of the error function in problems where diffusion from an infinite number of sources occurs and the solution is obtained in the form of an infinite series as a result of the overlapping of diffusion streams. The overlapping diffusion streams are due to an infinite number of repeated reflections at the ends of the diffusion path which are spaced finite distances apart. As seen in Fig. 7-8 the decrease in concentration is shown by sloping lines so that after each reflection the corresponding amount relative to the total concentration c becomes smaller. Due to the exponential character of the solution, the decrease is much more rapid than in the simplified representation shown in the figure and the series converge very rapidly, so that after a few terms the total concentration at a given location and time stays practically constant. There are other different methods for solving the diffusion equation in Eq. (7-12) which are described in mathematics books. Older methods, in particular separation of variables x and t are worth mentioning. They also produce infinite series in their solutions in the form of the Fourier trigonometric series. A further, very elegant analytical method uses the Laplace transforms (Kreyszig 1993). In addition to analytical solutions the possibility exists to obtain numerous exact solutions using numerical methods with help from computers. The advantage of numerical methods lies primarily with their application for complicated cases, e.g. for non-constant diffusion coefficients, for which there are no analytical solutions.
Transport equations und their solutions
197
Example 7-3. A 100 pm thick plastic film contains an initial concentration of 100 mg/kg of some additive. This film is brought in direct contact with another 100 pm thick plastic film of the same material initially containing no additive. Assuming ideal contact between the two films (i.e. no boundary conditions exist to hinder the transfer across the interface). The exterior sides of the f i l m are no1 permeable (they are in contact with a glass or metal surface). The diffusion coefficient of the additive is 3E-7 cm2/s for both films. What is the concentration on the outside of the second film after one minute contact time? This example corresponds to Fig. 7-8 in the text. The solution can be obtained using Eqn. (7-33). Putting d = 0.01 cm, 1 = 0.02 cm and x = 0.02 cm one gets a constant sum of c = 14.8 mg/kg after two steps n = 0 and n = 1: c =1 ' C() ' 2
5{
erf(ci
;, { (" n=O
erf
cg
n=O
forn=O: forn=O: forn=1: forn=1: forn=-1: forn=-l: c=
1 '
(+ ( ( ( (+ (
f 2 . n . I - x) 2 . (D . t)'/*
2 . (D . t)'I2
d -2.n . I
+
+
(" ("
erf
erf
)=( + )=( + )=( )=( ) =( + )=( +
2.n ' 1 -x
d
x
2 . (D . t)1/2
+
- 2 . n .I x) 2 . (D . t)'/'
- 2 , n . 1 +x) 2 . (D . t)'/'
= -1.1785
0.01 f2 . O -0.02 + 0.02
= 3.5355
2 (3E - 7 . 60)1'2
2 (3E - 7 . 60)'12
0.01
2 (D . t)'/' d-2.n.l-t~
2 . (3E - 7 . 60)'12 0.01 2 ' 1 0.02 + 0.02
2 . (D . t)'/'
}+ }
0.01 f 2 ' 0 0.02 - 0.02
d+2 .n . I -x
2 . 1 .0.02 - 0.02
-
'
2 . (3E - 7 . 60)'12
2.n 1-x
0.01 - 2 1 .0.02 - 0.02
2 . (D . t)"2 d - 2 . n .1 x 2 . (D . t)'/'
2 . (3E - 7 .60)'/' 0.01 2 . 1 '0.02 + 0.02 2 . (3E - 7.60)'/'
d
= 3.5355
=
-1.1785 =
-5.8926
= 8.2496
+ erf(3.5355) + erf(3.5355) + erf(-1.1785)}+ {erf(-1.1785) + erf(3.5355) + erf(-5.8926) + erf(8.2496)) =
100' {erf(-1.1785)
1 100 2 = 50{-0,9012 -.
+
2 . n , 1 - x) 2 . (D . t)1/2
+ 1 + 1 + -0,9012) + 50{ -0.Y012 + 1 - 1 + l } = 9.88 + 4.94 = 14.8 mg/kg
After terms higher than n = 1 the error function terms start canceling themselves out.
Comparison of different solutions for the same special cases
Various methods can give different expressions for the solution of the same application. Even though these lead to the same result, the solutions of problems in the form of infinite series can converge at varying rates. Consequently some solutions are favored over others, depending on the parameters under consideration. Finally, the considerations of the homogenous plastic bar model will be used as an example to show the differences between different solutions.
198
Piringer
-I -X
0
+I
-+x
Figure 7-9: Two-sided diffusion into a finitely thick layer.
A plastic bar of “infinite” length (e.g. 1 m or longer) is uniformly colored with an initial color concentration of co (Fig. 7-9) except for a thin layer in the middle with thickness d = 2 1 (approximately 1 cm). As a simplified approximation it is assumed that the concentration of the color at the location x = f 1 remains constant at co. The boundary conditions are expressed mathematically as: c=co,
x=fl,
g=0,
x=0,
t
> o
t > 0
(7.34)
The condition of &/ax = 0 at the location x = 0 expresses the requirement that no diffusion can take place through the axis of symmetry at x = 0. This leads to the same result as single sided diffusion in a layer having half the thickness. For the solution of the diffusion equation, Eq. (7-12), two different series expressions can be obtained:
The first series converges very rapidly for not too large values of D t / 12, in other words for relatively short diffusion times. For D t / l2 = 1 the concentration ratio c/co at location x = 0: c/co = 0.9590 - 0.0678 + 0.0008 = 0.8920 and for D t / l2 = 0.25: c/co = 0.3146 - 0.0001 = 0.3145. The trigonometric series in Eq. (7-35) converges rapidly for large t values. For D t / l2 = 1 it is: c/co = 1 - 0.01080 = 0.8920 and for D t / I* = 0.25: c/co = 1 - 0.6872 + 0.0017 = 0.3145.
7.2.4 Diffusion in multi-phase systems In this section the important cases for food packaging are treated. These cases differ from the previous examples in that mass transfer takes place across an interface between two different media with different characteristics, e.g. with different diffusion coefficients. If the value of a quantity is desired, for example the concentration of the substance transported across the interface in one of the two media, then a mass balance must be considered that takes into account the ratio of the contact surface area and the volume of the corresponding medium.
Trnrisport equations and their soiuiions
199
Diffusion in polymer / liquid systems For the sake of conformity, in the following every quantity related to the packaging is designated with the index P; and the quantities related to the food are labeled with the index L. Fig. 7-10a shows a model that describes the mass transfer of a component dissolved in the filled product L, e.g. an aroma compound, into the packaging material P. The model is based on the following assumptions: 1. A component i in the liquid phase with an initial concentration C L . ~is sorbed onto the contact surface area A between the liquid and packaging and subsequently diffuses into the matrix of the packaging. In so doing there is a decrease in concentration in the region of the contact surface which leads to further transport of i from the matrix of the liquid to the contact surface. 2. The mass transfer, controlled mainly by diffusion taking place in the packaging during storage, is several orders of magnitude lower than diffusion in the liquid phase. The difference is even greater when mixing (convection) occurs by shaking, e.g. during transport. It can be assumed that the concentration of component i in L, CL,~, is dependent on time t but not on the distance x from the contact surface. 3. A constant distribution of i between L and P takes place that is independent of concentration of i and time. For relatively small concentrations of i (< 1 YO) this approximate assumption is fulfilled and one defines the partition coefficient K as a constant ratio of the concentration i in the packaging material at time t on the contact surface cp., (dp) to the concentration of i in the liquid independent of location at the same time, c ~ , ~ :
(7-36) Where K is the ratio at t = o(j of the equilibrium concentrations of i in P, cp,, to that in L, this concentration ratio is also sometimes referred to as the relative solubility constant, S,, of i in P (relative to cL.,). 4. The second important quantity influencing the mass transport is the diffusion coefficient DP of i in P. For relatively low concentration ranges assumed for i in L, Dp is assumed to be constant. The diffusion controlled mass transport rate of i in P leads to a decrease in concentration of i with increasing distance from the contact surface (Fig. 7-10a). Particularly in the initial stages of diffusion, the total amount of substance i transferred into the package can be concentrated in a region near to the contact surface next to L while the location dependent concentration of i in P in the matrix of the packaging is equal to zero. 5. The mass transport is assumed to occur in the x direction perpendicular to the contact surface. Even though the geometry of the packaging/product system influences the amount of mass transport occurring, it is of minor significance for most practical cases. 6. All above assumptions are valid for mass transfer in the reverse direction as well. This means the migration of component i from the package into the product is also described (Fig. 7-lob). By considering the corresponding initial conditions the mathematical solution of the problem results in the same form. 7. The contact between packaging and product shown in Fig. 7-10a and b is singlesided. This means the external surface of the packaging at location x = 0 is assumed to
200
Piringer
a
L
P
I
I
C
d
I
x =d,
X=O
P
L
L
L
x =dp+dL
c
d,-
P
L
Figure 7-10. Mass transfer between a packaging material and a liquid product; a) diffusion out of the liquid into the package, b) diffusion out of the package into the liquid, c) cross section of a representative container, d) two-sided contact of a package material with a liquid.
Trmsport equutions and their solutions
201
be impermeable to i. The model also establishes an absolute barrier layer at the location x = dp + dL which simplifies the representation of the problem. A representation closer to conditions in practice is shown in Fig. 7-1Oc for a plastic container with a wall thickness of dp. The single difference to Fig. 7-10a is that the sum of the two contact surfaces A‘ in Fig. 7-1Oc is replaced by A = 2 A’ in Fig. 7-10a and b. In the literature one frequently finds a two sided contact with the packaging using the same model shown by the representation in Fig. 7-10d. Because the axis of symmetry at x = 0 serves as a barrier layer in the mathematical boundary conditions, the expression for the solution is not changed when instead of the half layer thickness dJ2 = 1 for two sided-contact of P, the actual layer thickness dp with single-sided contact is used. This is because in the symmetrical model in Fig. 7-10d the total layer thickness of the liquid dL is taken into consideration. The symmetrical model in Fig. 7-10d also illustrates the common two-sided contact migration measurement practice in which a film or sheet is immersed in a liquid. One obtains the corresponding volumes of the packaging, Vp = dp A, and liquid, VL = dL A, using the layer thicknesses dR dL and the contact surface area A. With the corresponding densities of the liquid, pL, and packaging, pp, the mass of liquid, mL = pLVLand mass of packaging, mp = pp Vp can be calculated. In many practical cases the assumption pL = pp E 1 can be made for simplification without significant error. With dimensionless quantities a and T (7-37) one obtains for the mass transfer by diffusion of i from a well mixed liquid (assumption 2) into a package or the migration in the opposite direction the general expression from Crank:
(7-38) Eq. (7-38) is a solution of the diffusion equation (7-12) for the models shown in Fig. 7-10. Where m, is the mass of i diffusing up to time t from L through the boundary surface A into the package or opposite direction and m, is the amount which has migrated at equilibrium. The parameters qn in the series are the positive roots of the trigonometric identity tan q,, = - a 4., Several values of this parameter for various a and n are given in Table 7-2. The values of q, lie between n n ( for a = 0) and (n - 1/2) n (for a = m). For a 1 or a > 100 this approximation must not be used (Chang, 1988). The solutions in Eqs. (7-38), (7-39) and (7-42) are valid for material transfer of a component i from food into the package (Fig. 7-10a) as well as for the migration from packaging into the food (Fig. 7-lob) under the assumptions of the described model. However, because at the beginning of diffusion in the first case the total amount mo of i is in L and in the second case it is in P, the values of m, and mOcrelative to mo must be different for the two cases.
1. Mass transfer from L into R The mass balance for i is given as: VL
CL,m
+
VP
CP>,
= VL CL,0 = mL.0
(7-43)
where cL.0 is the initial concentration of i in L. For the amount m, = mp,nc,the amount of substance i in P after reaching equilibrium is obtained from Eq. (7-43) with the definition K = C ~ , ~ / C from L , ~ Eq. (7-36) when Eq. (7-37) is taken into consideration: (7-44)
Trctnsport equations and their solutions
203
The ratio of mP,= and mL,o labeled Up,, shows the fraction of the total amount of i in the package at equilibrium: (7-45) For a = 1then up t o half of i would diffuse into the package at equilibrium. 2. Migration from P into L.
The total amount mp,o of i is contained in P at time t = 0 and the mass balance is expressed as: VL
CL.X
+
VP CP,,
= VP CP,0 = mp.0
(7-46)
The amount of substance transferred into the food at equilibrium m, = mL,m= V L . C ~ ,is obtained by combining Eqs. (7-36), and (7-37): (7-47) and related to mp.o the fraction of the total amount is given by:
The fraction of i diffused from L into P up to time t, from mL.(] = VL cL.0 and the fraction migrated from P into L up to time t, from mCo= Vp cP,()are: (7-49)
(7-50)
Example 7-4. Ten 4 cm diameter circular 200 pm thick plastic film pieces are mounted on a stainless steel wire and placed in a glass vial containing 100 ml solvent. What percentage of the additives initially contained in the plastic migrate into the liquid over the 24 hour period ( D p = 2.1OE-10 cm2/s)? Note that the plastic additives are readily soluble in the solvent, the solvent has low viscosity and the solvent does not swell the plastic. This case corresponds to Fig. 7-10b with variation 7-10d. Because the additives are readily soluble in the solvent K z 1 can be assumed in Eq. (7-36). The volume of the plastic is: Vp = 10. n:. r2 . h = 10 K 2 cm2 0.02 cm = 2.51 cm3 llsing Eq. (7-37) one gets:
Given the two sided contact of the liquid with the plastic 0.5 d p = 0.5.0.02 cm = 0.01 cm and thus with Eq. (7-37) one gets for T: Dp.1
2 IE-lOcmZ/s (2460.60 s)
(0.01 cm)*
= 0.181
204
Piringer
With a = 39.8 one uses the values for a equal to infinity (00) in Table 7-2 for the roots of tan qn = -CI. q,?.Carrying out calculations with Eq. (7-38) for the fraction of additive migrating at time f to what would migrate at f = co:
1 -
2.3Y.X(l+39.8) I +39.8+3Y.X2I 570S2 exp(-1.570S2
2-39.8(1+39.X)
.0.181) - 1+.3Y.X+39,824,7,242exp(-4.71242 .0.181) =
1 - 0.65544 - 0.001657 = 0.473 Note that for the summation the second term is quite small. Because the mass balance for migration out of plastic into a liquid (Eq. 7-47) shows mL.x, = mp.0: mL.r = mp.0,
a
39.8
= mp.O1+39,
.. I
2 mP.0
Therefore, the percentage of additive that has migrated from the polymer in 24 hours is according to Eq. (7-50) is 46.1 YO:
Example 7-5. What percentage of the additives migrate out of the plastic into the liquid in Example 4 when the partition coefficient K = 133? Starting with Eq. (7-38) one first calculates mt/m,: a = -1 .vL = -1. _100 = 0.300 K
133 2.51
Vp
1 - 0.13368 - 0.00128 = 0.865 Note that the values for q,, are estimated by linear interpolation of Table 7-2 values. Now calculating the fraction migrated from the polymer into the liquid: mL1 a 03 U L ,= ~ 2 - = 0.865 . __ = 0.20 mL.x
]+a
1+03
The percentage remaining in the polymer is 20 YO.Compared with Example 4, this result illustrates the effect of the larger partition coefficient where the migrant is more favorably retained in the polymer as opposed to the liquid. Example 7-6. Solve Example 4 using Eq. (7-39) and compare the two results. Starting with a = 39.8 and T = 0.181 from Example 4 calculate the value for z: T'12
z = - =a
0.181'/z
~- - 0.01069 39.8
Entering this value for z in Eq. (7-39) one can solve for m,/m,: ml -=
my
(1 + a )[l - exp(z2)erfc(z)]= (1 + 39.8) [l - exp(0.010692)erfc(0.01069)]=
(1+ 39.8) [l - e~p(0.01069~) . (0.98795)] = 0.487 Then calculating the fraction migrated using the mass balance equation: mLl a 3Y x U L ,= ~ _ _ . - = 0.487 . __ = 0.475 mLx
l+a
1+3Y.X
Transport equations and their solutions
205
rhus 47.5 % of the additive in the polymer migrates in 24 hours which is very close and within :xperimental error to the result in Example 4 of 46.1 %. Vote the values of erfc(0.01069) are estimated from the Table 7-1 values by linear interpolation.
Example 7-7. Edible oil is stored in a plastic bottle with an external diameter of 10 cm and with a wall thickness of 2 mm. What percent of the antioxidant contained in the plastic bottle nigrates after a) 100 days and b) after 2 years into the oil when the antioxidant has a diffusion :oefficient of D p = 1E-11 cm2/s? I ) This example corresponds to the case shown in Fig. 7-1Oc. Calculating a, Tand z:
, = - I. LV= - AI -d - 1 4 . 8 - 24 K
K dp
Vp
r = -d=i c=-=
1 0.2
IE-llcm2/s (100.24-6l)bOs)
Dp t
= 0.00216
(0.2 cm)2
0.00216'~'
TI/?
24
~
= 0.00194
For small times one can use Eq. (7-39) and performing linear interpolation on the z values between 1 and 0.05 in Table 7-1: mt -=
n,
(1 + a)[l- exp(z2)erfc(z)]= ( I
+ 24)[1 - exp(0.001942)erfc(0.00194)]=
( 1 + 24) [l - e ~ p (0 . 0 0 1 9 4 .~(0.997813)] ) = 0.0546 m~~
UL I = ~.
mLx
a
-=
I+a
24
0.0546 . = 0.0524 1124
Thus 100' mL/mx= 5.24 YO migrates b) Using Eq. (7-39): = Dp' = IE~11cm2/s-(2.3h5.24h0.60s) TI,'*
z = - = a-
= 0.01577
(0.2 cm)2
d;
0.01.5771/2
24
= 0.005232
Using the same Eq. (7-39) and performing a linear interpolation on the erfc values for z between 0.05 and 1.0 in Table 7-1: mt
-= n1
(1
( 1 + a ) [l - exp(z2)erfc(z)]= (1 + 24) [ I
-
e~p(0.00523~)erfc(O.00523)] =
+ 24) [l - e ~ p( 0 . 0 0 5 2 3 ~(0.994104)] ) = 0.1467
UL.t
mLI
a
= -..-= Ita niL
24
0.1467. -= 0.141 1+24
Thus 100. mt/m,= 14.1 %
Example 7-8. Plastic film 100 pm thick are placed between 3 mm thick slices of cheese. How many mg of plastic additive are found per kg cheese after being in contact for one day given the initial concentration of additive is cRo = I g/kg and the diffusion coefficient in the plastic is D p = 2E-10 cm2/s? The diffusion coefficient in the cheese is D L= 1E-7 cm2/s and the partition coefficient between the plastic and cheese is K = 1. The densities are pL = pp = lgkm'. This problem corresponds to the example shown in Fig. 7-1Oc. First it is necessary to calculate (Y and 7?
206
Piringer 2E-IOcm2/s.(24.60.60 s)
Dp.t
T = - d;-
(0.01
-
= 0.1728
Using Eq. (7-38) one calculates m,/m,:
1 - 0.53931 - 0.0020026 Given that: K = l = S
CL.r
’ ; , c L.m
0.45869
= CP.,
One can use the mass balance Eq. (7-46) to calculate C L . ~ . : Using the mass balance Eq. (7-46) to calculate the concentration of additive in the cheese: VL . C L . + ~ VP . CP., = VP . cp.n = mP.0 0.3 cm3 . C L +~ 0.02 cm3 C L , ~ = , 0.02 cm3 . lmg/cm3 cL.%= 0.0625 mg/cm3 = 62.5mg/kg.
By definition: CL.1 mL.1 _ =__
mL.r
CL.%
Then solve for CL.~: CL.1
-=
62.5
0.45869, :. c ~=.28.7 ~ mg/kg
In order to take into account the influence of the rate of diffusion in the cheese, Eq.(7-56) is used to calculate p: D p = -I . ( L)= -1 .
K
DP
The effect of smaller.
1
(-)1E-7 2E-10
‘1’
= 22.4
p on Eq. (7-57) versus Eq. (7-54) without p is about ( p / c I + p )
=
0.957 (4.3 %)
With equations (7-38) and (7-50), taking the mass balance into account, the migrated amount mL.,through the contact surface A during time t can be calculated as follows [if the dimension of cp,gis w/w (mg/g), then cp.0 . pp means w/v (mg/cm3)]: (7-51) The following equation (7-52) represents the simplified form of Eq. (7-51) for a >> 1:
-
(7-52)
qn = (2n-l)n/2.
Equation (7-53) is an alternative migration equation for small t-values using the error function:
Trcmsport equations and [heir sollitions
207 (7-53)
mL.tlmL..x. L 0.5
The following equation (7-54) is a simplified migration equation for K 5 1 and relatively small t-values, for which an infinite thickness of P is assumed: = 2 ~ ~ , ~Dpt)1/2= p p ( 1.128cp7opp(Dpt)'/*rcp30pp(Dpt)' I 2
J=
(7-54)
The maximum amount of migration derived from the mass balance is:
(7-55) Two typical examples of food packages with the corresponding values of the needed parameters are shown below, together with the results obtained with Eqs. (7-51) to (7-54): A = 600 cm2, d p = 0.02 em, pp = 1 g/cm', t = 864000 s (10 d), cp,o= 1000 mg/kg, DP = 1.OE-10 cm%, K = 1. Calculated with equation
vL= 1000 cm'.
a = 83 mL.,/A (mg/dmz)
VL= 300 cm3, a = 25
m~.t/A (mddm')
(7-51)
1.042
1.030
(7-52)
1.047
1.047
(7-53)
1.049
1.049
(7-54)
1.049
1.049
The maximum amounts mL,,/A 1.92 mg/dm2, respectively.
calculated with equation (7-55) are 1.98 and
Example 7-9. Solve example 8 using the approximation equation solution in Eq. (7-54) and compare the two results. Given that: VL= AdL-= 2 cm2 0.3 cm = 0.6 cm' one can then calculate cL., using Eq. (7-54):
-
C L t =--m L ' "L PL
A cp,oK(Dpt)i'2= 1000-2 ( 2 . lo-'()' 2 4 60.60) 112-- 13.9 mg/kg.
06
This is a difference of 6.4 % between the two results which is well within most experimental migration measurement errors.
In order to use the migration equations, especially the generally accepted equation (7-51), values for the partition coefficient K of the migrant between P and L and the diffusion coefficient D P of the migrant in P are needed. For migrants with a high solubility in the foodstuff or simulant, the value K = 1 can be used and a worst case estimation is obtained in this way. For migrants with a low solubility in the foodstuff or simulant water K = 1000 can be used to obtain a worst case estimation (see also Chapters 4 , 9 and 15).
208
Piringer 1 --
I
Figure 7-11: The behavior of mass transfer from a packaging material into food for different a values.
Currently, there exists only a limited number of reliable diffusion coefficients, due to the enormous requirements needed for the experimental determination. However, even for diffusion coefficients useful estimation procedures exist (see Chapters 6 and 15). The diffusion coefficient at a given temperature T depends on the nature of the polymer, the mass and structure of the solute and on the activation energy E, in the diffusion process. The material transport from a liquid assumed to be well mixed, into packaging and the migration from packaging into a liquid both vary proportionally to the square root of time and the square root of the diffusion coefficient. While in the beginning phase (approximation equation is only valid for small z values, meaning short times) the mass transfer of i into the package is proportional to K, the migration of i from the package is independent of K. The partition coefficient plays a deciding role in the sorption (solution) of i in the packaging layer in contact with the liquid. This leads to the total amount of sorbed material being concentrated in a thin layer of packaging material in contact with the liquid and the transport process in the initial stage is independent of the material thickness. In contrast the migration process into the liquid takes place independent of K. Due to good mixing in the initial stages of migration, the total amount of material i is transported away from the contact layer of liquid into the volume of the liquid, so that the concentration in the liquid contact layer goes to zero. The rate of diffusion of i out of the package is the rate determining step and is independent of the layer thickness dp. With longer migration times the partition coefficient also plays a deciding role through the a value because for a > l), mL..u/mp,m+ a and subsequently only a very small fraction of mp,omigrates into L (Eq. 7-50) (Fig.7-11).
Influence of difision in food The diffusion coefficient in the filled product must be taken into account in liquids that are not well mixed and in viscous and solid foods. This is done through the definition of a further dimensionless parameter p:
Transport rqiintions m r l their solutions
209 (7-56)
which, in addition to the parameters K and DP,contains the diffusion coefficient of i in the food. This dimensionless parameter can be combined with the approximation formula in equation (7-54) in the following way: (7-57) From this expression two limiting cases can be derived: 1. Where DL >> Dp and K 5 1,then p/(l+ p) + 1 and Eq. (7-57) goes to Eq. (7-54). This means that for high diffusion rates in the food, the rate of migration is determined by diffusion into packaging. The same result is obtained for DL DP and K 1, then p/(1+ p) + p which in this case gives the following expression instead of Eq. (7-57):
=
(7-58) Here the migration rate of i in the food is determined by the value of the diffusion coefficient in the food as well as by the partition coefficient. The concentration c L , ~of migrants that are poorly dissolved in the food (K > 1) increases more slowly than when they are more easily dissolved. The exact expression for the differential equation (7-12) that takes into consideration the diffusion in food and finite values for Vp and VL is extremely complicated. The extensive calculation required for the exact expression does not justify its use when one compares the accuracy achievable in practice with the errors or deviations resulting from the use of the approximate formula (Reid et al. 1980).
7.2.5 Diffusion through a liquid boundary layer With large K values, that is low solubility of component i in a liquid food, the material transport through A can also be determined from the contribution of diffusion in L under conditions of thorough mixing. Van der Waals attractive forces between the package surface and the molecules of L in intimate contact with P lead to the formation of a thin but immobile layer in which the diffusion coefficient of i in L, DL, controls mass transport (the Nernst diffusion layer). If diffusion through the stagnant boundary layer determines the rate of transport through A for the system, then one can assume a constant, location-independent concentration cp in P. The partition equilibrium is assumed to be reached on the boundary area between P and L at x = 0 and consequently K = cp/cL(0).If one lets the thickness of the diffusion layer in L next to the surface of P be lL and if L assumes a constant concentration of cL, then one can assume a constant material transport flux through the boundary layer for short time intervals that follows Fick's first law and the contribution of the flux to time t is expressed according to Eq. (7-16):
210
Piringer
(7-59) Because up to time t: (7-60)
and CL =!EL “L
one obtains from Eq. (7-59), considering the ratio mp,o/mnc = (1 + a ) / a according to Eq. (7-48) and the definition of a (Eq. 7-37) and because Vp = A . dp: mt (1
+ 41
(7-61)
and after several rearrangements one finally obtains: d(mt/mx) dt
-
D mp.O K d i k m,
(1
- Z.!L
mx)
(7-62)
with the solution: %= mX
1
-
exp
(-0t)
(7-63)
where: (7-64) For short times if mate solution: %c%(T.
mm
(T
.t C A , ~condensation will take place and if CA,G < C A . ~then evaporation will take place.
212
Piringer
The general solution for this problem in the form of the dimensionless ratio mt/mnc according to Crank is:
(7-67) d
k
with L = L. DP
Values of the positive roots of the equation p tan p = L are given in Table 7-3. m, is the amount of material taken up by the packaging or evaporated from the surface up to time t and msc is the corresponding amount at equilibrium. In Fig. 7-13 the ratio of m,/m, is given as a function of the dimensionless quantity (Dp t/d;)li2 for various L values. In the absence of evaporation, the curves show a linear increase at the beginning of diffusion (Fig. 7-11) while the obvious curving shown in Fig. 7-13 for small k values is caused by the slower evaporation process. Table 7-3: Roots of ptanP=L. ~
L
PI
P2
P3
Ps
06
0.00
0.0000
3.1416
6.2832
9.4248
12.5664
15.7080
0.01
0.0998
3.1448
6.2848
9.4258
12.5672
15.7086
0.10
0.31 11
3.1731
6.2991
9.4354
12.5743
15.7143
0.20
0.4328
3.2039
6.3148
9.4459
12.5823
15.7207
0.50
0.6533
3.2923
6.3616
9.4775
12.6060
15.7397
1.00
0.8603
3.4256
6.4373
9.5293
12.6453
15.7713
2.00
1.0769
3.6436
6.5783
9.6296
12.7223
15.8336 16.0107
P4
5.00
1.3138
4.0336
6.9096
9.8928
12.9352
10.00
1.4289
4.3058
7.2281
10.2003
13.2142
16.2594
100.00
1.5552
4.6658
7.7764
10.8871
13.9981
17.1093
1S708
4.71 24
7.8540
10.9956
14.1372
17.2788
cc
0
2
4
dP
u
6
Figure 7-13: Sorption or desorption curves in the valid range of Eq. (7-66) for different L-values
Transport equations and their solutions
213
7.2.7 Permeation through homogeneous materials Steady state permeation which follows Fick’s first law has been previously described in Eq. (7-16). Assuming the concentration of i in P has a constant value cp.1 at the surface (x = 0) and has a constant value C P , ~at the other surface (x = dp) and at the beginning of permeation the concentration in the inside of P has the value cp.0 (t = O), then a nonsteady state of diffusion will take place leading to a change in the concentration cP.[ within P. For simplification one can set cRo= 0 and cr2 = 0. The resulting amount of mass diffusing through the package up to time t is then given as: mt = A dp cp,l
(7
-
5 C [g exp(-Dp XI
-
n = l
n2 n2 t/d$)
This equation becomes asymptotic to the straight line:
(7-69) as t
---f
00.
The intersection of this straight line with the t-axis at location 0 is: (7-70)
This is Barrer’s equation for determining of the diffusion coefficient using permeation measurements (Fig. 9-1). The steady state permeation flux is given by the slope of the straight line (7-69): (7-71) This expression is identical to Eq. (7-16) for
= 0.
7.2.8 Permeation through a functional barrier Let us consider a plain sheet of a laminate made of a solute containing core layer (P) and a virgin layer (B) of the same polymer type (Piringer et al. 1998). The thickness of P and B are a and b, respectively, and d = a+b. The virgin layer is in contact with a liquid layer (L). The thickness of the virgin layer (B) is such that it acts as a barrier against the diffusing solute out of the core layer (Fig.7-14). When the liquid L comes in contact with the laminate, the following two extreme situations can occur: ( i ) The solute is homogeneously distributed in the core layer with the concentration C’~,(,(W/V) or cP.(,(w/w)with the density pp of the polymer. The concentration of the solute in B, cg.0, is 0. (ii)The solute is already homogeneously distributed in the whole laminate with cp,,, the equilibrium concentration, that means cp,, = cp = CB = cp.oa/(a+b)= cp,Oa/d. The starting point for modeling permeation (migration) to the liquid is the second case (ii). This is because it represents the well-studied diffusion of a solute from a polymer of limited volume, Vp, into a stirred solution of limited volume, VL. A suitable equation for all of these cases is Eq. (7-51), where cp,o= cp,,.
214
Piringer
Let us consider the laminate system for situation (ii) with a >> 1 and a very short contact time t = ti. This means the initial solute concentration in the vicinity of x=d at t=O is cp=cp, and cL., 2 0 (Fig. 7-14a). This illustration is the case of a system with diffusion between two semi-infinite media (Crank, 1975) for which Eq. (7-51) reduces to Eq. (7-54). A more realistic situation for diffusion in a laminate is illustrated in Fig. 7-14b, which shows the solute concentration profile in the barrier layer after a short contact time t=tl. In this illustration the concentration profile of the solute just reaches the polymer/liquid interface and cL.t 2 0. If we now consider a similar case with a semi-infinite polymer system with the initial solute concentration (cp,,) at the distance x 5 x, = a+b/2 and cp=O at x>xo and t=O (Fig.7-14c), then the possible concentration profiles for the three different times, t d l , t=tl and t>tl can be illustrated in Fig. 7-14d. If we assume a mass transfer through the interface A at X = X I at t=tl in Fig. 7-14d, then mp,,/A = 0.5cp.,pp(d-xl), which corresponds to mp.,/A = cP.epp(xo-a) = cp.,ppb/2 in Fig. 7-14c. If we combine this result with Eq. (7-54) for t=tl, then we obtain the time (7-72)
a)
) c,=
0
A
0
C X - -
a
d
a
d
1-0
:\0
-A
Figure 7-14: Illustration of the mass transfer through a layered package.
I - t,
Trurisporr equations and their solutions
215
If we allow diffusion to continue until t=t2>tl, then under the same assumptions of a semi-infinite system, the mass transfer during At = t2-tl is (7-73)
As mentioned above, the real concentration of the solute in the laminate at the first moment of IaminateAiquid contact lies between the two extremes (i) and (ii). Let us now consider the special case shown in Fig. 7-14b, where the front of the solute just reaches the barrier/liquid layer interface B/L. By comparing Figure 7-14b with Figure 7-14d, we see similar situations are illustrated. Therefore, using Eq. (7-72) and the notations d-xl = b and t l = 0 , a time 0 = (n/16)(b2/Dp) is defined, which is a little greater than the well-known “time lag” = b2/6Dp. If such a system comes into contact with a liquid-phase L, then the mass transfer after the time At=t2-O=t that results from Eq. (7-73) is:
y -fi +,ppjDP( -
dim -
&)
(7-74)
The specific case in Figure 7-14b and Figure 7-15a can be considered as a general reference case for all other practical cases between the extremes (i) and (ii). Depending on the degree of solute diffusion into the barrier layer before it comes in contact with the liquid-phase L, a fictive time, O’, which is shorter (Fig. 7-1%) or longer (Fig. 7-15c) than 0 described in Figure 7-1Sa, can be determined. By relating
a)
:
t A
0
a
d
0
a
d
C X - -
--X--,
t-0
Distance
Figure 7-15: Illustration of the relative mass transfer for different amounts of contamination of the barrier layer.
216
Piringer
this 0' to 0, a relative time can be defined which is a measure of the efficiency of the barrier layer B. The value of 0' can be deduced from the relation in Eq. (7-75), were
or
(7-75)
DP is the diffusion coefficient of the solute at some temperature (T*) for time t*, for example, the extrusion temperature of the laminate, where the diffusion of the solute into the barrier layer is most significant. Dp is the diffusion coefficient of the solute in the polymer at the temperature during the contact with liquid L. By using the relative time 0, instead of 8 and the general valid Eq. (7-51) instead of Eq. (7-54), a final equation for the migration of the solute from the core layer P through the barrier layer B after the contact time t can be written similar to the form of Eq. (7-51):
x
2a( 1+a)
n= 1
(7-76)
with
(7-77) and cP.e = CP.O
& = CP,O ad
(7-78)
In the extreme case (ii) of complete diffusion of the solute into the barrier layer B, O,=O, Eq. (7-76) reduces to Eq. (7-51). In the following example an application of the above treatment in an actual case is shown (Piringer et al. 1998). Films of coextruded polyethyleneterephthalate (PET) (pp = 1.4 g/cm3) with a symmetric three-layer structure were produced in which the core layer P (320 pm thick) contained chlorobenzene as a contaminant with the initial concentration, cp,o = 104 pg/g. The PET films which were 400 pm thick, had two barrier layers B (40 pm) of virgin PET. The films were obtained by coextrusion at about 270°C during about 1 second. After cooling the films were stored a few days at room temperature and then the amount of migration was measured into isooctane at 50 "C. The migration of the contaminant into B during the storage period was neglected due to the very low diffusion rate at room temperature. In Table 7-4 the measured migration amounts, mF.,/A, are shown together with the calculated values using Eq. (7-76). The last column contains the calculated migration amounts from a film (d = a+b = 160+40 = 200 pm) in which the contaminant was uniform distributed at the equilibrium concentration, cp,, = 83 yg/g. The symmetric structure allows calculation with only one half of the total film thickness. The measured diffusion coefficient of chlorobenzene in PET at 50 "C is Dp = 2.13E-13 cm2/s and the assumed value at 270 "C (Chapter 15) is DG = 7.1E-7 cm2/s.
Tmnsport equations and their soltrtroi~s
217
Tahle 7-4: Migration (pgidm') of chlorohenzene into isooctane at 50°C. Time (days)
Measured
Calculated
10
< 0.5
0.3
5.6
39
0.8
1.2
11.o
69
2.0
2.2
14.8
2.9
17.0
110
3.0
3.4
18.7
130
4.0
4.0
20.2
91
Calculated for b=O
From the above results one can see that a functional barrier limits the amount of migration of a component from the package to food-simulating liquids. But when using a coextrusion process to create a functional barrier, the assumed virgin layer becomes contaminated from components of the core layer (recycled polymer layer) during manufacturing. These effects must be considered if reliable predictions of migration are to be obtained (Chapter 10). A solution obtained with numerical mathematics is also shown in chapter 8.
7.2.9 Permeation through a laminate Diffusion through a barrier layer is a special case of diffusion through a laminate film composed of several layers with different thicknesses and diffusion coefficients. The mathematical treatment of the non-steady state case is complicated. The steady state permeation case allows the overall transport to be simply treated. Let n films with thicknesses dP1, dP2,..., dp, with corresponding diffusion coefficients Dp1, Dp2, ..., Dp, be bound together in a laminate. Because in steady state, the flux J of the diffusing substance i is the same through every individual component of the laminate, one obtains an expression for the concentration gradient:
+
R2
+
... Rn) J
(7-79)
with the resistance R 1= d,l / Dpl etc. The total resistance related to the diffusion is then the sum of the individual resistances and the total flux is practically determined by the layer with the smallest diffusion coefficient.
7.2.10 Concentration dependence of the diffusion coefficient At dilute concentrations DP is usually constant. When swelling is caused by either fat, water, essential oils or other organic components found in the product then DP can become concentration-dependent in the region of a boundary layer in P. In such cases the diffusion equation (7-12) is no longer valid and the general form of the diffusion equation (7-11) must be used.
218
Piringer
I
lo-'
El
10-4
10-5
1r4
10-3
IO-~
lo-' t Ihl
loo
10'
1 02
Figure 7-16: Migration from a system with swelling under various conditions (Chang 1988). Dp.0 = 1 6 5 1 0 cm2/s,Dp = 10E-10 cm'ls: t,, = 0; vo: E-S cmls in A. E-6 cmis in B, E-7 cmk in C and E-8 cmis in D.
In this case D = D(c) is a function of the concentration c of the substance causing the swelling. The literature holds numerous recommended solutions for treating such cases, none of which are universally applicable. A general way for solving problems of this type is to use numerical integration in combination with a representative model suitable for the specific case. In the initial stages when the food or another product is brought in contact with the package (t = 0), the migration of the substance i from P into L takes place with a constant DP because the swelling processes require a certain amount of time before they affect the migration process of i. After this initial contact phase the swelling front, XQ,moves into P with a certain speed vQ (Fig. 7-16). In the region x > XQ the diffusion of i takes place with DP and in the region x < XQ with D ~ >QDp. The swelling front XQ moves into P with the speed vQ: XQ
= VQ (t
-
to)
(7-80)
whereby to > 0 signifies the initial contact phase before swelling takes place. The result of such a process can be qualitatively seen in Fig. 7-14 (Chang et al. 1988).
7.2.11 Diffusion and chemical reaction When a first order irreversible chemical reaction (e.g. oxygen absorption and oxidation) takes place simultaneously with diffusion in food for example, then one obtains the following expression from the general mass transfer equation (7-10): (7-81)
Trrrnsport equations and their sokitions
219
where k is the reaction rate constant. If the reaction takes place in a relatively thin layer near the surface or boundary layer of L to P then one can consider L as a half open medium (infinitely thick). This leads to a considerable simplification of the mathematical treatment. Furthermore, letting cL.0 be a constant surface concentration one obtains the absorbed amount m, up to time t: mt = A CL.O (DL/k)'l2[(k t
+ i)erf (k t)1/2 +
(k t/Jc)'l2 e-
'1
(7-82)
For large k . t values the erf (k .t)1'2 goes to one and: mt = A
C L . ~(DL/k)'/*(t
+ A)
(7-83)
that means m, increases linearly with t. For very small values of k . t one obtains:
(7-84) When k + 0 only diffusion without reaction takes place: mt
E A C L , ~(DL t)II2
(7-85)
Because the diffusion process and the reaction occur in the same medium L the ratio of A N L does not come into consideration. References Carslaw H. S.. Jaeger J. C. 1959, Conduclion c!f'Henr in Solids, Clarendon Press, Oxford. Chang S.-S., Guttman C. M., Sanchez I. C.. Smith L. E.. 1988 in: Hotchkiss J. (ed), Food and Packaging Interactions, ACS Symposium Series No. 365. Washington. Crank J. 1975. Mathematics of Diffusion, Znd ed.. Clarendon Press. Oxford University Press, Oxford. Kreyszig E. 1993, Advanced Engineering Mafhernnrics,7'h ed., John Wiley & Sons, Inc. New York. Piringer O., Franz R.. Huber M., Begley T. H., McNeal T. P,1998, .I Agric.& . Food Cheni. 46,15321538. Reid R. C., Sidman K. R., Schwope A. D.. Till D. E., 1980. Ind. Eng. Chem. Prod. Res. Dev. 19,580-587.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
8 Numerical solutions of the diffusion equation Titus A . Beu
8.1 Why numerical solutions? Despite the large number of analytical solutions available for the diffusion equation, their usefulness is restricted to simple geometries and constant diffusion coefficients. The boundary conditions, which can be analytically handled, are equally simple. However, there are many cases of practical interest where the simplifying assumptions introduced when deriving analytical solutions are unacceptable. For example, the diffusion process in polymer systems is sometimes characterized by markedly concentration-dependent diffusion coefficients, which make any analytical result inapplicable. Moreover, the analytical solutions being generally expressed in the form of infinite series, their numerical evaluation is no trivial task. That is, the simplicity of the adopted models is not necessarily reflected by an equivalent simplicity of evaluation. To obtain solutions to the diffusion equation, which more realistically models practical situations (where, for example, the diffusion coefficient or the boundary conditions are non-linear), one must resort to numerical methods. Basically, these imply restricting the solution of the diffusion problem to a set of gridpoints, conveniently distributed within the integration domain, and approximating the involved derivatives by discrete schemes. Such an approach leads to a system of linear equations, having as unknowns the solution values at the gridpoints. The linear system can be solved in principle by any classical method, even though, for the sake of computational efficiency. more specialized methods are recommended. The numerical discretization methods affect the essence of the physical model much less than analytical approximations do, allowing for much more complex diffusion problems to be treated.
8.2 Finite-difference solution by the explicit method We consider for now the one-dimensional diffusion equation, with constant diffusion coefficient D:
Such an equation is useful for describing the time evolution of the concentration profile of some diffusant across a plane sheet of given thickness L and infinite transverse extension. In order to model a particular experimental arrangement, this equation must be solved in conjunction with certain initial and boundary conditions. We will consider that Eq. (8-1) is subject to the initial condition: c(x, to) = c"(x),
x E [O, L]
(8-2)
222
Beu
which means that the concentration profile at the initial moment to is given over the entire sheet thickness. However, the solution of the initial value (or Cauchy) probZem defined by Eqs. (8-1) and (8-2) cannot be uniquely determined unless supplementary boundary conditions for t > to are specified. For simplicity, we will assume that the concentration values at the outer surfaces of the sheet are constant for any t 2 to: c(0, t ) = c;,
c(L, t) = CL 0
(8-3)
Such boundary conditions, specifying the values of the solution, are known as Dirichlet houndury conditions. The so-called Neumann boundary conditions, which define the derivative of the solution on the boundaries, form another important category, considered among others later in this chapter. The method we use to approximate the solution to the problem (8-1) to (8-3) is based on finite difference schemes for the derivatives involved by the diffusion equation (and, in general, by the boundary conditions, too). The straightforward approach is to choose equally spaced points along the x- and t-axes, covering the space-time integration domain by a regular rectangular grid (Fig. 8-1). Denoting by h and At the corresponding mesh constants (with the stipulation that L/h is an integer), the gridpoints are defined by the discrete coordinates: xi = (i - l ) h ,
tn=nAt,
i
= 1 , 2 , . . . , M:
(8-4)
n = 0 , 1 , 2,...
Here M represents the number of spatial gridpoints and the spatial mesh constant is given by:
(8-5)
h = L/(M - 1).
We use the notation c: = c(xi, t,). The time derivative of c at point (xi, tn) can be obtained from its Taylor series in t for constant x = xi:
Taking the linear approximation and expressing the first order time derivative, one obtains:
+ O(At).
(8-7)
O(At) signifies that in the above approximation the leading term that was neglected is of the order At (we have divided (8-6) by At to get (8-7)). This is the socalled Euler forward-difference scheme. While it is only first-order accurate in At, it has the advantage that it allows for the quantities at timestep n 1 being calculated only from those known at timestep n. The discrete approximation for the second order spatial derivative ( $ c / & ~ ) ~ , ,at x = xi results in a similar manner, namely by expressing the concentrations at the neighboring gridpoints xi-1 and X ~ + Ifrom the Taylor series in x at constant t = t,:
+
223
Nirtnericol solutions of’the diffiision equation
explicit
CrankNicholson
x,= 0
implicit
x,=L
Figure 8-1: Space-time grid for the one-dimensional diffusion equation. evidencing the explicit forward-difference. implicit backward-difference and Crank-Nicholson discretization schemes.
On adding we find
(2)
i, =
c+ : I -2c: +c;- I hz
+ O(h2)
(8-9)
This second order approximation is a centered-difference scheme, since it expresses the spatial derivative at point i by means of data from symmetrically distributed points. All the implied information is known at timestep n. By substituting relations (8-7) and (8-9) in Eq. (8-1), one obtains the following finite-difference approximation to the diffusion equation at point (xl,tn): ,n+l -cn I
At
’ = D
c;+l -2c;+c;-l h2
(8-10)
Having in view only the way the time derivative was approximated, this is the forwrrrd-difference representation of the diffusion equation and it is of order O(h2 At). Slight rearrangement yields a formula, which expresses the time-propagated solution cy+’ for any interior spatial gridpoint in terms of the other quantities known at timestep n: c!l+l = Ac?,-I (1 -2A)c) +Aclntl. (8-11) i = 2 , 3,..., M - 1 ,
+
+
where: Dt
A = p
(8-12)
224
Beu
The concentration values on the boundaries, c;+' and cL++',generally result from the boundary conditions and, within the simple adopted model, are seen to be constant: (8-13) Since the solution of Equation (8-11) propagated at timestep tn+l is expressed solely in terms of data from timestep t,, not requiring any previous information, the forward-difference scheme is said to be explicit, and its essence can be extracted from Fig. 8-1, too. The explicit nature of the recursive process described by Eqs. (8-11) to (8-13) becomes even more apparent if using matrix notation for the involved linear system: n = 0 , 1 , 2 ,....
cn+l = B . c n ,
(8-14)
The components of the column-vector c" are the values of the solution from all spatial gridpoints at timestep t,: (8-15) and the propagation matrix B has tri-diagonal structure, i.e., except for the main diagonal and the neighboring upper and lower co-diagonals, all elements are equal to 0 1 0 h 1-2h
0-
h
B=
h
1-2h 0
0
I
h 1-
(8-16)
When solving the one-dimensional diffusion equation (8-15) by the explicit forward-difference formulation described above, one is faced under certain conditions with severe numerical instability problems. This means that, instead of yielding a relatively smooth spatial profile, the algorithm develops oscillations, which grow exponentially in time, "unweaving" the solution and making it unusable. This critical behavior occurs when the used timestep exceeds a certain upper limit for a given spatial mesh constant and is caused by the increasing dominance of round-off errors. In order to emphasize the critical relationship between the timestep and the spatial step, we consider the one-dimensional diffusion equation with constant diffusion coefficient D = 1: ac -
at
-
8% Q
T
x E [0,1], t > 0,
(8-17)
subject to the simple boundary conditions: c(0, t) = c(1, t)
= 0,
and initial condition:
t
>0
(8-18)
Niinierical soliltions of the diffiision eqiicrtiori
0.16
__
225
numerical solution
0.14 0.12 0.10 c,
0.08 0.06
0.04 0.02 0.00 0.0
0.2
0.6
0.4
0.8
1.o
Y
Figure 8-2: Exact and numerical solutions obtained by the explicit method for the Cauchy problem (8-17) to (8-19). by using the spatial step h = 0.05 and the timestep At = 0.00125.
c(x,0) = sin(nx), x E [0,1].
(8-19)
It can be easily verified that the analytical solution to this problem is: c(x, t) = e-x2t sin(7cx)
(8-20)
We investigate the behavior of the numerical solution to problem (8-17) to (8-19) at the moments t = 2.0, t = 2.5 and t = 3.0 for two different timesteps, by using the constant spatial step h = 0.05. Figure 8-2 shows the spatial concentration profiles obtained by using the timestep At = 0.00125, corresponding to h = 0.5 ( h is defined in Eq. (8-12)). As one may notice, apart from the inaccuracies caused by the finite spatial step size, the profiles resulted from the numerical solution (depicted with dotted lines) fairly reproduce the analytical results (continuous lines). Figure 8-3 shows the spatial concentration profiles obtained with the slightly increased timestep At = 0.0013, corresponding to h = 0.52. Even though the solution at t = 2.0 can hardly be distinguished from the one obtained with At = 0.00125, it is apparent that at t = 2.5 instabilities begin to develop and they dominate the solution entirely at t = 3.0. Hence, a seemingly insignificant change in the timestep leads to a dramatic qualitative change of the solution. This indicates that the value h = 1/2 is critical, and that it separates two domains of numerical parameters characterized by different behavior of the solution: for h < 1/2 the propagation of the solution is stable, while for h > 1/2 it turns out to be unstable.
226
Beu
0.16
-- numerical solution
0.14
0.12 0.10 0
0.08 0.06
0.04 0.02 0.00 0.0
0.2
0.6
0.4
0.8
1.O
Y
A
Figure 8-3: Exact and numerical solutions obtained by the explicit method for the Cauchy problem (8-17) to (8-19) , by using the spatial step h = 0.05 and the timestep At = 0.0013.
8.2.1 von Neumann stability analysis An intuitive way of investigating the stability properties of a finite-difference scheme is the von Neumann stability unulysis, which we briefly outline as follows. The von Neumann analysis is b c a l , being based on the assumption that the coefficients of the difference equation are so slowly varying in space and time as to be considered constant. Under such assumptions, the eigenmodes (the independent solutions) of the difference equation may be written in the general form: u: = t"exp[tk(i
-
l)h]
(8-21)
1 stands for the imaginary unit (not to be confused with the spatial index i), k is the spatial wave number, which can take any real value, and 6 = C(k) is the so-called amplification factor, which is a complex function of k. Apart from the spatial details, the essential feature of the eigenmodes is their time dependence through the timestep index n, as integer powers of the amplification factor. The time propagation of the solution is considered to be stable if the amplification factor satisfies the condition:
since no exponentially growing modes of the difference equation can exist under such circumstances.
Nllnzericnl solutioiis of the difficsiori eqtrntion
227
In order to express the amplification factor for the forward-difference representation of the one-dimensional diffusion equation, one has to replace the general form (8-21) of the eigenmodes into the difference equation (8-11):
5 = hexp(-tkh) + (1 - 2h) + hexp(tkh). By combining the exponentials and employing the trigonometric identity 1 - cosx = 2sin2(x/2),one obtains for the amplification factor:
5 = 1 - 4hsin2(kh/2)
(8-23)
Use of the von Neumann stability criterion (8-18) leads to the condition:
O 100 the curve becomes practically insensitive to the material thickness (Baner et al. 1996) Assessment by application of complex mathematical models
As described in Chapters 7, 11 and 15 of this book predictive mathematical models for migration estimation based on diffusion theory and considering partitioning effects have been developed in the past few years. Although such models are currently still under scientific discussion (Reynier et al. 1999) and refinement or further development they have been proven in whole classes of polymer types such as the polyolefins to work very satisfactorily in terms of providing worse case migration scenarios. This is a prerequisite to finding general acceptance for being used in the field of food packaging compliance testing. The use of these diffusion models to progress the evaluation process of a food packaging plastic will be discussed shortly. In those cases where assessment by mass balance considerations under equilibrium conditions, including partitioning effects, does not provide a clear picture of the plastics conformity status, then the different diffusivities of polymer types and the influence of the migrant molecule size or its molecular weight on its mobility within a plastic can be taken into account to achieve more distinguished views on QM/SML ratios. Based on diffusion theory (Chapters 7 and 15) QM/SML ratios can be described as a function of the migrant molecular weight, for different polymer types as given in Fig. 10-2. For illustration reasons, this figure (Baner et al. 1996) provides two scenarios (i) diffusion controlled migration from different plastics under standard test conditions of 10 days/4O0C under the assumption of infinite thickness and (ii) as for given thicknesses (of any plastic) under the assumption of total mass transfer (KP.F=l). It can be recognised (again) that complete migration transfer calculations are dependent on the material thickness. It should also be noted that complete migration transfer lines are independent of migration test time and temperature conditions. Figure 10-2 shows that for some combinations of polymer type and thickness and substance molecular weight, there are cases where mass balance calculations yield higher QMlSML ratios than diffusion-controlled migration calculations. This is only a virtual contradiction and can be explained by the infinite thickness assumption of the diffusion model. This situation is particularly given in the case of high diffusion coefficients, i.e. high diffusivity of the plastic and/or migrants with low molecular weights. Figure 10-2 can be used to provide an acceptable estimated initial concentration of a substance in a polymer where a related SML value cannot be further exceeded. For example: a migrant with molecular weight 750 has a corresponding QM/SML value of approximately 1000 for the HDPE/PP curve. Now, multiplying this QM/SML value by the legally prescribed SML value will give its maximum acceptable QM in the polymer.
Migration of plastic constituents
l.e+7
i 4
295
Rigid PVC
I I .
l.e+6
/
I /
/
l.e+O t0
1
250
500
-
750
i Non-polyolefins JLDPE
1000 1250 1500
Molecular weight of migrant
Figure 10-2: QMlSML ratio versus molecular weight under standard test conditions (10 days/40 "C) for different polymer types under the assumption of infinite thickness as well as for given thicknesses under the assumption of total mass transfer.
Another attempt t o demonstrate the usefulness of employing diffusion models is made with Fig. 10-3. A dimensionless migration curve can be found for a given food packaging, to allow a quick look-up of possible migration values, for instance for plausability considerations related to measured migration test results or for the design of new plastics additives. This figure is based on the diffusion model presented in Chapter 15 and applies the migration Eq. (7-51) for an individually given food packaging application. It models the migration under standard test conditions of 10 days/40 "C as a function of cRo and the migrant's molecular weights from a HDPE container of thickness dp = 0.06 cm, assuming a surface/volume ratio of 6 dm2/kg and a partition coefficient KP,F= 1 (high solubility in the foodstuff). Analogous figures can be derived for any other food packaging application. With respect to the curve given in this figure, it should be noted that the packaging system under the applied test conditions can be considered nearly infinite or semi-infinite for migrants down to molecular weights of approximately 150. At lower molecular weights where the curve turns down from the steep line, the thickness of the material controls the shape of the migration curve. This particular situation can be considered an intermediate phase between infiniteness and mass balance as discussed above and presented in Fig. 10-2. As an example of how to make use o f Fig. 10-3, a migrant of molecular weight 47.5 may be selected; and the curve then provides a value of 0.5. If this migrant is, for instance, present in the polymer at C P , ~=~200 ppm then migration into the foodstuff can be calculated at 1.0 mg/kg from the equation given on the y-axis.
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Franz
-
3,s
B
3
E
Y
0
e
=
9
2,5 2
Y
29
1,5
0
10 1 1
5
I
.v
$
V
0,5 0 0
100 200 300 400 500 600 700 800 900 1000
molecular weight of migrant
Figure 10-3: Estimation of migration (standard test conditions of 10 days/4O0C) as a function of CP,,) and in dependency of molecular weight of migrant from a HDPE container of thickness dp = 0.06 cm at a surfacelvolume ratio of 6 dm2/kg assuming a partition coefficient KP.F= 1.
Migration assessment by analysis of mass transfer from plastics Until today, the control of transfer from plastics packaging materials into foods has mainly been based on the measurement of the substance(s) in the food or simulant after certain specified, and in most cases standardized, contact conditions. Here, in principal, it can be distinguished between: (i) conventional direct migration measurements where a sample is placed in contact with a food or simulant in a manner representing the contact conditions of actual conditions in use; and (ii) alternative semi-direct migration test approaches where a sample is kept in contact with an appropriate simulant in such a manner that a strong interaction between simulant and plastic takes place (“more severe test conditions”) and - although shorter contact times are then applicable - at least equal or exaggerated extents of migration are obtained. Direct migration measurement The principle of direct migration measurement is, as the term reveals, to measure either directly in foodstuffs or more commonly mimic as closely as possible a given food packaging application, using agreed and authorised food simulants (Chapters 11 and 12). Results obtained with food simulants represent either directly the real rnigration values or can be correlated by the use of so-called reduction factors. The advantage of direct measurement is that the results can be directly and definitely compared with legally prescribed migration limits, thus allowing immediately a statement of conformity or disapproval of the test sample. The disadvantage of direct measurement has been recognised more and more during recent years: analysis of migrants in com-
Migration of plastic constititents
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plex food simulants such as oils and fats is often very time-consuming and costly and at the same time relatively poor in terms of analytical sensivity and precision. This occurs not only in the case of specific migrants such as antioxidants or other non-volatile polymer constituents, but also in the case of overall migration determinations. It is extremely so in contact with oils as fatty food simulants and especially so in the case of high temperature testing and polar plastics. It should be noted that the legally allowed analytical tolerance in oils is stated at 20 mg/kg in relation to 60 mg/kg as the overall migration limit itself. This is really remarkable, taking into account that low diffusivity plastics such as PET release, as a rule, maximum overall migrations which are lower than the analytical tolerance itself. Overall migration testing, carried out according to the methods in the EN (European Standard) or ENV (European Prestandard) 1186 series of CEN (European Committee for Standardization) standards and described in numerous papers and books (Ashby et al. 1997; Katan 1996b; de Kruijf and Rijk 1988; CEN 1998a; Tice 1997), will not be taken up in detail here. Only the major problems related to overall migration testing in contact with oils will be mentioned here; these are: - inherent imprecision of the method due to substracting high values obtained by weighing the sample in order to determine a much smaller overall migration value; - moisture conditioning of polar plastics; - oil uptake by the sample and incompleteness of back extraction; - analytical determination of the absorbed amount of oil due to many possible GC/ FID interferences (according to the amendments of 90/128/EEC some 40 or 50 interfering compounds are in the positive list); - performance and handling at high temperature testing. Numerous examples of measured overall migration values have been collected and the interested reader can find a published data compilation summarized for different polymer types (Van Battum 1996). The whole area of specific migration determinations can be subdivided in two phases: (i) the pre-analytical migration exposure phase, which is more or less identical to that necessary for overall migration determination; and (ii) the pure analytical phase, where the specific migrant must be determined in the respective food or simulant as precisely and reproducibly as possible. This pure analytical migration test phase comprises many considerations to be made and includes so many technical possibilities that it deserves to be described in an own comprehensive section (see Section 10.2). Semi-direct, alternative migration tests The principle of these tests is to apply more severe test conditions by using volatile solvents with strong interactions towards the plastic, to enhance the migration rate from the plastic. Thus, the extraction test is based on an accelerated mass transport mechanism where the diffusion coefficients of migrants are increased by several orders of magnitude compared to the original migration test. As a rule, extraction tests are designed such that they make use of the following principle: I
Polar polymer
+ polar migrant + polar solvent
= worse case = non-polar polymer + non-polar migrant
+ non-polar solvent
I
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Franz
Following this principle, semi-direct and generally quick extraction tests can be established with the aim of determining the migration potential for assessment of the worse case migration. These tests, which do not need to be as exhaustive as for instance necessary for a cp.0 determination, can be considered to be semi-direct because they produce an extraction value which can be directly compared to a legal restriction. But at the same time this value is an exaggerated one and does not always correspond to the real (lower) migration value. For example, a rapid extraction test for overall migration assessment into fatty food simulants, proposed as part 15 of the EN/ENV 1186 series of CEN standards, is presented as follows (CEN 1998b; Berghammer et al. 1994). The method is based on the determination of the extraction of migratable substances from plastics which are intended to come into contact with foodstuffs. It uses total immersion in non-polar isooctane and/or polar ethanol solvents depending on the polarity of the packaging material. According to results obtained by this method and taking physico-chemical considerations into account, the obtained extraction efficiency was generally found to be equivalent to or higher than overall migration results obtained under these test conditions: 10 days at 40"C, 2 h at 70"C, 1 h at 100°C, 30 min at 121 "C and 30 min at 130 "C, as specified in Council Directive 82/711/EEC and its subsequent amendments. To ensure as complete as possible an extraction of the potential migrants requires a strong interaction, e.g. swelling, of the sample by the extraction solvent. For this purpose, iso-octane is used as an extraction solvent for plastics materials and articles containing non-polar food contact layers, such as polyolefins. For test samples with polar food contact plastics such as polyamide and polyethyleneterephthalate, 95 % (v/v) aqueous ethanol is used. For polystyrenes, plasticised PVC and other polymers where the identification or polarity of the polymer is not clear, two parallel extraction tests are conducted using both of the proposed extraction solvents and taking into account the higher value obtained as the relevant result. In the case of unsymmetric structures such as plastics laminates and co-extruded plastics, the nature of the food contact layer determines the selection of the extraction solvent(s). Table 10-1 gives an overview of the allocation of extraction solvents and test conditions to polymer types. Table 10-1: Use of extraction solvents and test conditions in relation to polymer types. Polymer type of the food contact layer
Extraction solvent
Extraction conditions
Polyolefines
iso-octane
24 hours at 40°C
Polyamides
9.5 % ethanol
24 hours at 40 "C
Polystyrene
iso-octane and 95 YO ethanol
24 hours at 40°C
Polyethylene terephthalate
95 YOethanol
24 hours at SO "C
Polyvinyl chloride (plasticised)
iso-octane and 95 Y' O ethanol
24 hours at 40 "C
Polyvinyl chloride (rigid)
95 %, ethanol
24 hours at 50 "C
In case of doubt or unknown
iso-octane and 95 TOethanol
24 hours at SO "C
The test principle is such that the extraction of migratable substances from a sample of the plastics is determined as the mass of non-volatile residue after evaporation of the solvent following immersion. Test specimens of at least 1 dm2 (single side considered) are immersed in the extraction solvent at the specified test conditions and then
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299
removed. The extraction solvent is evaporated to dryness, the mass of the non-volatile residue is determined and the result is expressed as milligrams per square decimetre of surface area of the test specimen. The measured value is compared to the overall migration limit given by Directive 90/128/EEC (and amendments) and taking the analytical tolerance of this method (1 mg/dm') into account. The rapid extraction test was primarily developed for flexible packagings less than 300 ym in thickness. However, if this extraction test is applied to materials with higher thickness than 300 pm and the result does not exceed the allowed overall migation limit, then the material can be considered t o be in compliance with E C regulations. If the test result exceeds the allowed overall migration limit, regardless of the film thickness of the test material, then the extraction test may be repeated. However. in single-sided mode (using a test cell) or the conventional fat test or another alternative test may be used. In any case the rapid extraction test was designed to demonstrate compliance in the case of extraction values lower than the overall migration limit. The test cannot disapprove a material whose extraction value exceeds the limit. Conditions differing from those described above are of course possible as are much quicker tests. But in all cases, a reliable relationship between the short test and the full migration test must be established. In addition, it is also of practical and economic interest to design these tests so that they can be applied as broadly as possible, i.e. in most laboratories without too high an investment. Another quick extraction test has been proposed, especially tailored for rigid PVC material. Treating the samples with methanol for 2 hours under reflux conditions provided values which were considerably higher than those achieved under conventional olive oil conditions but still remained far below the overall migration limit, thus demonstrating fully legal conformity of the test materials (Tice and Cooper 1997). It should be noted here that quick cxtraction tests in general produce higher migration values and are therefore unfavourable when it comes to correlating such a value with the reputation of a test sample. However, when the testing costs can be decreased in this way by 50% to 70% and conformity can still be shown, although with somewhat higher results, then it seems to be only a question of getting accustomed t o extraction values. Substitute fat tests as defined by table 4 of E U Directive 97i48iEC are a further example of semi-direct migration tests. These tests are applicable in cases where technical or analytical difficulties are connected with the regular fatty food simulants. They apply iso-octane and 95 Oh ethanol under conventional test conditions such that an accelerated test based on (swelling) interactions between substitute test solvent and the polymer is conducted. For instance, an analytically impossible 10 daysi40 "C olive oil test on polyolefins can be replaced by a 2 days/2O0C extraction with isooctane. In this case a suitable time point has been chosen on the kinetic curve of an extraction process where an empirically satisfying agreement has been found between isooctane extractions and fat migration tests into olive oil. Another example is where a substitute test is carried out at lower temperatures compared to the required regular test temperatures. For instance, a high temperature fat test under test conditions of 2 hours/l5O0C can be replaced by a 3 hours/60"C iso-octane extraction. In this case again, a semi-direct test strategy is applied, empirically based on corresponding comparative test results. However, it is important to note that nearly all of these comparative long termlhigh temperature migration versus short terniflow temperature extraction measurements have focused more or less on just the overall migration and do not include sufficiently specific migrations. As a consequence, further research work is
300
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necessary to correlate substitute test conditions for specific migration purposes where the chemical and thermal stability of migrants as well as the possible formation of break-down products and solubility questions related to individual migrants must all be taken into account.
10.2 Analysis of specific migrants 10.2.1 The positive list system within the European Union Legislation As described more in detail in Chapter 12, the European regulations on plastics for food contact are characterised by a consolidated positive list system which contains authorized monomers as well as additives for manufacturing or incorporation into any plastic type. This so-called “Plastics Directive” 90/128/EEC and its 5 amendments contain, as an essential element, numerous specific restrictions for listed substances either in terms of specific migration limits (SML values) and/or maximum quantities in the finished food contact material (QM values). Currently, out of approximately 200 listed monomers, nearly 80 are listed with a restriction, in most cases a SML value. Even more SML and/or QM values are expected for the additives’ list with restrictions, which was recently finalized at Commission level as a further (Sh)amendment of the “Plastics Directive” (EU Commission 1999). This situation immediately poses the question of enforcability of this law, since appropriate analytical methods have not been published or referenced in synchrony with the appearance of the positive list system. Although there is a general need for the availability of workable and validated analytical methods for food law compliance testing, the European Union legislative system requires special attention with respect to the analysis of specific migrants.
10.2.2 General requirements to analytical methods for compliance testing When selecting a method of analysis, some pre-considerations are obligatory. The volatility of the analyte must be taken into account as well as the nature of the matrix to be analyzed and, especially, the expected concentration range of the substance being measured. While analysis in aqueous food simulants and some plastics is relatively simple to perform, it is exceptionally difficult in many foods due to their complex chemical composition. As a result of these pre-considerations, a decision is taken about the choice of the most appropriate sample preparation procedure and a suitable chromatographic system. The envisaged analysis can also have various purposes or objectives. The aim may be to achieve a quantitative analysis (e.g. concentration determination) of one or several substances. The concentration range to be measured can be in the range of several mg/kg (ppm) or a few ng/kg (ppt). Analysis for the presence of groups of substances with defined structural characteristics (e.g. epoxides) or the identification of unknown substances may also be desirable. Already from these introductory notes, the very different structures of various analytical laboratories are becoming apparent. Analytical laboratories for small and medium-sized food packaging manufacturers and food producers, in general pay particular attention to the routine control of several substances and as a rule make use of a limited selection of methods. In contrast to this type of laboratory, governmental sur-
Migration of plastic constitiients
301
veillance laboratories, research institutes and central analytical facilities in industry are equipped with the latest state-of-the-art technology and are much more flexible in making use of any kind of analytical methods. Many analysts in these industry, private and public research, governmental and enforcement laboratories are involved in compliance testing of plastics for food contact. The methods applied may vary from sophisticated gaschromatography/mass-spectrometry (GUMS) techniques to classical methods like colorimetric determination. In many cases laboratories apply their own house analytical methods, often without any method validation. However, the use of different methods of determination will most likely lead to discrepancies in the results. In addition, for methods which have never been validated in inter-laboratory studies, no generally accepted analytical tolerances have been established. Consequently, enforcement of legal restrictions given by SML or QM values is poorly or even not possible at all, if validated and generally accepted methods are not available. However, in order to enable proper compliance testing, such methods of analysis commonly accessible and with well-defined analytical tolerances are indispensable. The requirements which must be addressed to analytical methods depend on their purpose. Routine methods for industrial quality control, for instance, need to be quick, cheap, robust and completely reproducible. It is not urgently required to determine a true value but to determine the homogeneity in manufacturing a certain industrial product. Therefore, the measurement of the corresponding parameter must be very precise, even though it may be wrong. On the other hand, very sophisticated, highly technical and expensive methods may be needed when it comes, for instance, to the determining the migration of a polymer constituent of analytically exotic character for the purpose of delivering a technical dossier for a petition to the authorities. In this case, the analytical method need not be cost-efficient in the first place but must provide a true value with high accuracy, or the best approach to it in order to allow decision-making about the need for toxicological testing. A complete intra-laboratory validation is another important requirement in this case. Due to the complexity of this specialised method it may never again find application in another laboratory, such as governmental surveillance methods. In between these two cases, however, the whole class of frequently used methods for food law compliance testing can be placed. Ideally, the major requirement here is: standardized methods should be published as norms and fully validated in inter-laboratory collaborative trials. However, being realistic and pragmatic, one has to recognize that realization of this demand will be more the exception than the rule. Furthermore, the methods should not be at the cutting edge of analytical hardware technology but make use of the state-of-the-art technology available in most analytical laboratories. Only under this premise, as much as possible will laboratories be able to apply the method, thus guaranteeing the most effective quality control and consumer protection. Generally, these methods should allow one to quantify the monomer or plastics additive at the required restriction limit in all relevant food simulants and/or in the polymer, respectively. That means an optimization in sensivity must be achieved, targeted to the necessary range of the method’s limit of detection (LOD), at or well below a given restriction criterion. It should be noted here that optimized methods of known performance and broad applicability with respect to food simulants as matrices may find their limit of workability when applied to real foodstuffs, due to interference problems. However, as a general rule, one can say that at least headspace sampling GC methods for volatiles are applicable and workable in every case.
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10.2.3 Establishing (juristically) valid performance of methods The need f o r validated analytical methods It is generally recognized and accepted that analytical methods must be suitable for the intended use. Furthermore, EU Directives 85/591/EEC, 89/397/EEC and 93/99/ EEC state that analytical procedures for compliance testing with food laws are to be carried out on the basis of validated methods. Method validation is known as the process used to confirm that a procedure is fit for a particular analytical purpose. This process, an essential part of analytical quality assurance, can be described as the set of tests used to establish and document performance characteristics of a method. The performance characteristics of a method are experimentally derived values for the fundamental parameters of importance in assessing the suitability of the method (Horwitz 1988, 1995; Thompson and Wood 1993, 1995; Eurachem 1996; FA0 1998: US EPA 1995; US FDA 1993a). These parameters include:
Applica:bility:
Includes the matrix, analyte and species being measured, concentration ranges and the purpose for which it is suited, limitations of the method. Selectivity: The ability to discriminate between the target analyte and other substances in the test sample. Calibration: The calibration curve is a graphic representation of the detection system’s response as a function of the quantity of analyte. Accuracy: The closeness of agreement between a test result and the accepted reference or true value. Precision: The closeness of agreement between independent test results obtained under stipulated conditions. Range: The interval of concentration within which the analytical procedure demonstrates a suitable level of precision and accuracy. Limit of quantification: The lowest amount or concentration of analyte in a sample which can be quantitatively determined with an acceptable level of precision and accuracy. The smallest amount or concentration of analyte in a sample Limit of detection: that can be reliably distinguished, with stated significance, from the background or blank level. Sensivity: A measure of the magnitude of the response caused by a certain amount of analyte. Ruggedness: The resistance to change of an analytical method when minor deviations are made in the experimental conditions of the procedure. Practica bility: The ease of operation, in terms of sample throughput and costs, to achieve the required performance criteria and thereby meet the specified purpose. Internationally accepted protocols have been established for the “full” validation of a method of analysis by collaborative trial (Horwitz 1988, 1995; I S 0 1994). These protocols require a minimum number of laboratories and test materials to be included in the collaborative trial to fully validate the analytical method. However, before
Migration ofplustic constituents
303
entering the ring trial, the method must undergo pre-validation within a single laboratory, normally the the one which develops or modifies the method. Inclusion of a second laboratory to confirm the performance obtained is another practise used for method pre-validation. Statistical tools for validation and evaluation of analytical methods Even when all conditions required for correctly carrying out an analysis are fulfilled, different values within a certain scatter range will be obtained within a laboratory for repeated measurements of identical samples. As a rule, the differences or scattering will be still larger if different laboratories are involved in the comparison exercise using identical samples. It is therefore necessary to apply statistical tools in order to verify the maintenance of limit values and eventually to evaluate the accuracy of disputed estimates. For this reason standards for measurement precision and accuracy are defined at national level (e.g. ASTM in U.S.A.,DIN in Germany) and at international level by I S 0 (International Organization for Standardization). Clearly, in view of the harmonization of the legal regulations in Europe, standardized methods of analysis and validation principles and certified reference materials are becoming more important. Moreover, due to the globalization of markets, these have worldwide relevance. A relevant juristical statement about the precision of a method can only be made after defining the performance characteristics obtained from a round robin or interlaboratory trial study, as for instance described in I S 0 5725 (IS0 1994). This study is used to determine the statistical key data about the precision of a method. The international standard I S 0 5725 has been adopted by many countries. I S 0 uses two terms, “trueness” and “precision”, to describe the accuracy of a measured value. “Trueness” refers to the closeness of agreement between the average value of a large number of test results and the true or accepted reference value. “Precision” refers to the closeness of agreement of test results, or in other words the variability between repeated tests. The standard deviation of the measured value obtained by repeated determinations under the same conditions is used as a measure of the precision of the measurement procedure. The repeatability limit “r” (an intra-laboratory parameter) and the reproducibility limit “R” (an inter-laboratory parameter) are calculated as measures of precision. Again, “precision” and “trueness” together describe the accuracy of an analytical method. Particularly important definitions and terms for the evaluation of analyses from I S 0 5725 will be briefly discussed in the following section. If the test result as an average of several individual measurements is obtained with the same method from an identical test sample, in the same laboratory, by the same analyst, with the same instrumentation, over a short period of time, then the study takes place under “repeatability” conditions. On the other hand, “reproducibility” conditions occur when the measurements take place following the same procedure and using identical samples but in different laboratories using different analysts with different instrumentation. The parameters describing the scattering of a test result under repeatability and reproducibility conditions are the corresponding standard deviations. The repeatability limit, “r”, is the within-laboratory precision and describes the maximum expected value of the difference between two individual test results obtained under repeatabil-
304
Franz
ity conditions at a defined significance which is in most cases a probability level of 95 %. Similarly, the reproducibility limit, “R”, describes the analogous between-laboratory precision. An important assumption for the use of r and R in practice is that they have been determined in an inter-laboratory test in which the participating laboratories represent those potential candidate appliers of the particular analytical procedure. For the determination of r and R, the method of analysis must be described very clearly and in detail to eliminate as many differences between laboratories as possible. Particular precautions are necessary with regard to the homogeneity and stability of the sample to be studied in the inter-laboratory test. Clearly the sample must withstand transport conditions and arrive unaltered at the participating laboratories. The statistical model for estimating the precision of the analytical method assumes that every individual measurement result y is the sum of three components: y=m
+B+
(10-5)
e
Here m represents the average of all values for the material studied (the characteristic level), B is the scattering between the laboratories and e the random deviation in results occurring in every measurement. The characteristic level m must not necessarily agree completely with the true value. There may be a difference (m - my) from the true value due to a systematic error in the measurement procedure (bias). For contributions B and e, it is assumed that they approximately follow the normal distribution. Then the variance of B, var(B), is the variance between laboratories (02). This include the scattering between different analysts and different instruments. The variance of e, var(e), is referred to as the internal variance of a laboratory (o’,). The average of all the internal variances of the participating laboratories in an inter-laboratory test is expressed as the repeatability variance 0:.While r depends only on the repeatability variance, R is determined by the sum of the repeatability variances and the variance between all laboratories. The standard deviations of repeatability and reproducibility ~ it follows that: are given by or and OR = (0: + o : ) ~ ’and r = f 2 1 / 2 ~ , and R
=f
2’120,
(10-6)
The factor 2”* is based on the fact that r and R are related to the difference between two measurement results. For distributions which are approximately normal and in the case of not too small a number of measurements, the factor f does not vary much from 2 and one can use the approximate value of 2.8 for f .21‘2. Because in practice the true repeatability and reproducibility standard deviations are not known, they are replaced with estimated values s, and sR from the inter-laboratory study and one obtains then: r = 2.8 s, and R = 2.8 SR
(10-7)
The precision of a standard measurement method is expressed using the values of r and R. More specifically, the range of measured values (from ... to ...) or a typical result should be given together with the corresponding estimated value of the standard deviation s, and sR as well as r and R for the corresponding range. The precision of the analytical method can be verbally described as:
Migration of plastic c.on.~titiient.s
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The difference between two individual measurement results, which an analyst obtained on the identical sample material with the same instrument within the shortest time span possible, will on average not exceed the repeatability limit r more than once in 20 cases, provided the measurement procedure has been correctly carried out. The difference between two individual measurement results, reported by two laboratories for identical sample material, will on average not exceed the reproducibility limit R more than one time in 20 cases provided the measurement procedure has been correctly carried out. For probability levels other than 95 %, the values for r and R must be multiplied by the factors in Table 10-2. Table 10-2 Factors to adapt r and R to various probability levels. Probability level P %
Factor
90
0.82
9s
1.00
98
1.16
99
1.25
99.5
1.40
Various critical difference parameters can be derived from r and R as illustrated by the following examples: In one laboratory two measurements are carried out.
In one laboratory two groups of measurements are carried out under repeatability conditions whereby the first group of nl measurements gives an average value of y1 and the second group of n2 measurements gives an average value of y2. With r being the repeatability limit (for two individual measurement results), the critical difference CTD~~(Y~ is -then: Y~)
(10-8) In the case of nl = n2 = 1 then by definition one obtains r as the critical difference.
Two laboratories conduct more than one measurement each. One laboratory carries out nl measurements with an average of y1 while a second laboratory obtains an average of y2 for n2 measurements. The critical difference between the two is then: r2 (I -
(1 0-9)
By definition, for the special case where nl = n2 = 1 the formula simplifies to R and for nl = n2 = 2 one obtains:
(10-10)
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Franz
The mean value from one laboratory is compared with a given value. One laboratory has carried n measurements under repeatability conditions and obtained an average value y which is compared with a given value mo (e.g. a specific migration limit). Then one obtains the critical difference as:
& [R2 - r2 (e)] 112
Cr%(Ifl
- mol) =
(10-11)
The mean value of several laboratories is compared with a given value. A number of p laboratories have carried out ni measurements and obtained the average values yi (i = 1,2, ..., p). The overall mean value over yi, 7,is compared with a given value mo. One obtains the following expression for the critical difference:
[
'cyi
R2 - r2 (1 - ' C L)]1'2, = y= (10-12) (W' P i "i P i If, when making a comparison between two averages or between an individual value and a given value, the measured difference between two values exceeds the corresponding critical difference, then this deviation should be considered suspect. There could be a specific reason why the critical difference is exceeded and this should be rationalized. In particular, if the given or reference value is a true or correct value, then the suspected difference can point to a bias in the measured result. In the case that the given value is a specific migration limit then the critical difference evaluation system allows the decision whether a legal restriction criterion has been exceeded or not. CrD95(Jy - mu[) =
10.2.4 A practical guide for developing and pre-validation of analytical methods Validation of analytical methods -both in-house and standard methods - has been the focus of many scientific, industrial and regulatory activities and working groups (US EPA 1995; US FDA 1987,1993a; Wegschneider 1996). As a consequence, numerous parameters for method validation have been defined and recommended. However, there is no official or generally accepted guiding document such as an I S 0 standard available which de- and prescribes a sequence of individual working steps for the development and validation of analytical methods. In the following, a practical guide for a step-by-step procedure is presented to establish a validated method of analysis both for determination of a specific migrant in a food simulant and the residual concentration in a plastic. This procedure was first developed and then applied in a European project (Franz and Rijk 1997) and found to be very practical. It should be considered as a recommendation based on the great practical experience of the analysts involved. The development procedure consists of the following 8 steps: 1. Scope of the method
Basically, two types of method must be taken into account: Analysis of a specific migrant in a food simulant (SML-methods) - Analysis of a specific migrant in a polymer (QM-methods).
-
Migration of plnstic corzstitirents
307
Generally, the method to be developed should allow quantitative analysis of the analyte at the required restriction limit in all the official food simulants, including substitutes or alternatives and/or in the polymer, respectively. That means that for very low SML values which are assumed to be in the range of the detection limit, the aim should be to obtain a detection limit equal to o r even lower than the restriction criterion. For other, higher SML and QM values, the aim should be to obtain a detection limit at least ten times below the legal or self-defined restriction criterion. It should also kept in mind that the method description should provide the relevant intra-laboratory precision data (at the required SML/QM value) according to I S 0 5725 -(IS0 1094). The most suitable analytical methodology should be selected based on the required performance characteristics. A sound literature search is always of great help with respect to known methods for the respective analyte and matrices. In most cases the search results will not directly provide the method wanted but will allow the most likely successful analytical approach to be set up. In this context, pre-considerations should address the most appropriate sample work-up procedure as well as the suitable analytical separation and detection system. The question of direct analysis of the analyte o r a derivate formed after chemical reaction should be clarified. And finally, some thoughts should already be given to the question of chemical stability of the analyte in the given matrices under the applied conditions.
2. Setting up the chromatographic and detection system First of all, it should be noted by the reader that it is not within the scope of this chapter to give more background and details on analytical chemistry. The corresponding scientific knowledge and technical information have been described elsewhere (for instance Schomburg 1984; Lee et al. 1984; Chapman 1986 and many other lecture books). Having rationalized the most suitable analytical principle as a result from step 1, it is necessary t o demonstrate the adequate specifity and sensivity of the analytical system. This aim can be achieved by carrying out an initial feasibility study where the following points need in-depth consideration: - availability and purity of reference standards; - purity requirements for chemicals, reagents and solvents; - safety considerations; - selection of sampling and chromatographic instruments; - choice of separation column; - suitable detection system; - optimization of instrument parameters; - appropriate internal standard; - solvent to be used for preparation of stock and standard solutions. The feasibility exercise should include preparation of a concentrated (stock) solution as well as diluted standard solutions of various concentrations and establishing a first calibration curve. From the data obtained, preliminary conclusions should be drawn with respect to the approximate precision, its working range and limit of detection. Finally, the results should provide sufficient evidence with respect to the workability of the intended analytical approach. If the method appears inappropriate, it must be optimized by methodological improvements, instrument changes or applica-
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tion of a completely different analytical technique. If no satisfactory improvements can be achieved, a possible way out of the problem may be through compromising the acceptance limits.
3. Preparation and measurement of calibration samples When the initial study has been sucessfully completed, the performance characteristics should be investigated. As a first step on this way, calibration samples should be prepared in order to prove the calibration with respect to fulfilling general acceptance limits for linearity and repeatability performance. Starting from two independent stock solutions, two sets of analyte calibration solutions should be prepared. The solutions should preferably consist of the same medium (i.e. either food simulant for SML methods or swelling/extraction solvent for QM methods) to be used for the final determination of the specific migration or the residual amount in the plastic. Since the method’s performance characteristics are to be established in relation to the intended use, it is not necessary to check the method’s linearity over the full range of the equipment. Therefore, at least five concentration levels are required spanning the given restriction criterion value from 0.1 x value to 2.0 x value, provided this is within the LOD. Solutions without any analyte (blanks) should be analyzed as well. In the case of standard addition procedures, five levels should also be analyzed spanning the QM restriction value by standard additions ranging from 0.5 x value to 5.0 x value. All calibration and blank samples should be measured in triplicate (three injections of one sample) and the calibration graph should be constructed by plotting the detection signal obtained for the analyte (preferably peak area rather than peak height) relative to that of the internal standard versus analyte concentration. With respect to the correlation coefficient obtained (usually “R”)from the - in most cases - linear regression line, a minimum value of R = 0.9996 should be defined as a general acceptance limit. Deviation from this minimum requirement to linearity should only occur in exceptional cases. On the basis of 95 % probability level, the corresponding confidence bounds should be calculated and the within-laboratory LOD determined according to Fig. 10-4. The statistical methodology may be taken from the literature, for instance (DIN 1994). The two independently prepared sets of calibration samples should coincide with the upper and lower confidence bounds as another general acceptance limit with respect to repeatability performance. Full statistical evaluation of the calibration graph provides useful data about the method’s performance characteristics over the applied calibration range such as the standard error of the procedure, sx, or the standard error of estimate, sy 4. Within laboratory (repeatability conditions) precision according to I S 0 5725
The precision of an analytical method is the degree to which individual determinations of a series of standards agree. Since in general only one laboratory is involved in the development of the method the precision, as determined by one laboratory by one operator over a relatively short time, is defined as repeatability “r” ( I S 0 1994; compare also Section 10.2.3). For determining “r”, the following procedure is recommended: SML methods: for conventional or alternative food simulants at least 6 samples should be prepared, having the same concentration at the restriction criterion (SML value). All the samples should be measured by at least double injections and the
309
Migration ofplastic constituents
Y
......-.................. standard error of the analytical procedure s, standard error of estimate s, calibration regression curve
4 LOD
concentration
A
Figure 10-4: Calibration curve and relevant precision parameters.
detector signals obtained should be evaluated using the calibration graph established as described under 3 above. QM methods: for the analysis of polymer matrices, 12 samples should be prepared for headspace sampling technique or 6 samples for liquid injection, respectively. In each case the series of samples should be prepared in the polymer/swelling solvent system with all samples using the same concentration at the restriction criterion (QM value). Headspace samples are measured only once and liquid injection samples in duplicate. If possible, analyte-free polymer should be used here. Again the spiked concentrations should be verified by standard addition calibration procedure carried out as described above under 3. When conducting an additional series of measurements using only the swelling solvent as the matrix without polymer and comparing results to those obtained above, the influence of the polymer matrix on the detection of analyte can be investigated. From the results obtained the repeatability standard deviation “S,” as well as the repeatability limit “r” can be calculated on a 95 % probability level according to Eq. (10-13). r = 2.8 S,
(10-13)
In addition, the results can also be used to calculate the mean recovery % as (the ratio of measured concentrationhominal concentration) * 100 and its standard devia-
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tion in the case of direct analyte determinations without any sample work-up. In cases where a sample work-up procedure such as extraction or chemical derivation has been applied, the mean recovery can be determined by comparing the detector response for the analyte signal after sample work-up with the response obtained from the appropriate standard dissolved in pure solvent.
5. Development of an appropriate confirmation procedure Whenever a measured value exceeds a certain threshold (an internally defined limit or a legal restriction criterion) then a confirmation procedure is recommended or even necessary. The purpose of confirmation analysis is to prove or disapprove the measurement result obtained by the usual analytical method. Generally, the difference from the confirmation procedure compared to the usual test method should be due to only either the use of a completely different separation column (with completely different retention behaviour) in the same detection system or the use of an alternative detection method with sufficient sensivity. For the latter case and especially for GC methods, the prefered procedure should be to apply analyte selective mass spectroscopy (MS) detection. In some cases, derivatisation of the analyte followed by MS detection can also be the method of choice. In the case of HPLC methods, different polarity of another column in connection with full exploitation of modern UV diode array detection systems may be useful to selectively allow confirmation of the analyte. It is extremely important to make sure that the confirmation procedure works at the restriction criterion level or other self-defined concentration limit!
6 . Stability check on stock and standard solutions Stability tests are understood to be time-dependent measurements of a stock and a standard solution at different temperature conditions, for instance at ambient temperature (approx. 22 "C), normal refrigerator conditions (2-8 "C) and at deep freezing temperatures (approx. -20 "C). Stability tests should always be carried out with the exclusion of light. Under these storage conditions, stock and standard solutions should be monitored for constancy of initial analyte concentration. This can be achieved by comparison against freshly pepared solutions. Storage time should be extended to at least three months or until a decrease of 50 % or more has been observed. Sampling frequency depends on the decrease rate of the solutions. It is wise to commence stability checks early enough when starting method development work. The aim here is to find out the optimum storage conditions and maximum practical storage time. Internal standards, if applied, should also be investigated.
7. Workability of the test method under practical conditions After successful completion of all the development steps described above, the analyst still cannot be sure that the developed method will work under realistic conditions. The workability of the method therefore has to be proved. There are two major reasons why this workability test has to be carried out: First of all, it should be demonstrated that the method is not affected by interferences migrating from the polymer matrix. Secondly, it needs to be clarified whether the analyte is stable under the contact conditions applied during the migration exposure, to avoid false-negative migration results. Therefore, a suitable plastic material containing a high residual level of the analyte under investigation should be available for the following experiments:
Migration of plastic constitiients
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SML methods: The selected polymer sample should be brought in contact with the food simulants under the relevant time/temperature conditions. In general, a migration test applying the total immersion principle using olive oil and 15 % ethanol at test conditions of 10 days at 40°C is sufficient. The determination should be performed in triplicate with double injections for analysis of the food simulants. In cases where the analyte level in the migration solutions is found to be below the detection limit, the migration solutions should be fortified with the migrant at the restriction criterion level or some other concentration of concern and measured again. In parallel, to check for migrant stability in the migration solutions, the relevant food simulants should be fortified at the level of concern to ensure that it is sufficiently higher than the LOD. If the test level concerned is in the range of the LOD, then the threefold concentration should be applied. The food simulants spiked in this way should be stored under appropriate timeitemperature conditions and recovery of the analyte determined by cross checking against freshly prepared solutions. QM methods: Triplicate determination of the concentration of the analyte in the selected polymer sample should be performed by the standard addition procedure using the polymer/swelling solvent system. The comparison to a calibration curve of the analyte in the pure swelling solvent only allows significant polymer matrix effects to be recognized. Again the stability of the analyte in the swelling solvent should be studied by fortification at the QM concentration or other relevant level and determination of recovery under the applied swelling and polymer extraction conditions. 8. Method description and reporting
Once the method has been established and validated, it should be described in full detail such that it can be carried out by any other analyst. Besides the numerous experimental details relating to the chemicals, solvents and solutions used and the chromatographic parameters, important observations such as for instance the findings about the stability of standard solutions should be laid down appropriately in the method description as notes or remarks. But potential health risks to the analytical operator should also be addressed, for instance in a warning note at the beginning of the method description. The following structure of a method description, which was agreed upon as a CEN standard format, is a recommended example.
Foreword: 1. Introduction:
2. Scope: -3. Principle:
4. Reagents:
Optional paragraph explaining about the background or history of the method. This chapter gives a rationale why it was necessary to establish this method. In this section the range of applications for the method should be indicated. This paragraph summarizes the applied analytical principle, including sample preparation techniques. It is necessary to describe in full detail the origin and purity of chemicals and solvents, the preparation of stock and standard solutions or other solutions, such as the mobile phase in the case of HPLC analysis. In conjunction with a given set of analytical parameters, the chromatogram obtained or at least an indication of retention times obtained for the analyte and the internal standard should be presented.
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5. Apparatus:
This chapter should describe the complete set of instrumental and other analytical parameters as well as special laboratory equipment and analytical accessories such as size and type of sample vials, pipettes and syringes etc., standard laboratory glassware and equipment excepted. 6. Samples: In this section, the preparation of test samples, blanks and calibration samples has to described, together with an indication of the minimum number of samples needed. If necessary, precautions should be mentioned, for instance to avoid cross-contamination of samples in the case of volatiles or to minimise chemical degradation in the case of unstable analytes etc. Here it is necessary to provide details as to how the analytical 7. Procedure: measurement of test, blank and calibration samples is executed and how the obtained data are evaluated. The measured concentration of the analyte obtained in this way may need further transformation into a different dimension and this should also be addressed in this section. 8. Confirmation: When a certain critical concentration value has been measured and found excessive, then it may be recommendable or even necessary to confirm the result or the identity of the quantified analyte by means of another analytical technique, for instance by specific detection using mass spectrometry. This confirmation procedure should be clearly presented in this paragraph. 9. Precision data: This chapter should give an insight into the validation procedure applied and report the most important performance characteristics: - the achieved limit of detection (LOD) or LOD range, - the achieved repeatability criteria, i.e. the r-values in the different food simulants or in the polymer matrix and the concentration range where they have been determined, - if available the determined reproducibility, i.e. the R-value and the critical difference, i.e. the CrD95-value, as obtained in the most usual situation, i.e. one laboratory carries out n measurements (Eq. 10-11). 10. Test report: The test report should contain all necessary documentation such as - date of analysis and reporting, - clear identification of the test laboratory and the responsible analyst, - analyte and method of test, including references, - sample details like origin and specification, type of food/simulant/material/article, reception date and storage conditions, - results expressed in mg analyte per kg food simulant or plastic material, - details of confirmation procedure, if any, and - reasons for modifications introduced into the test method, if any.
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10.2.5 Availability of (pre)validated methods in Europe About the economical impossibility of meeting the requirements of I S 0 5725 and the need f o r pragmatic solutions
Ideally, and strictly speaking also legally prescribed, the positive list system in Directive 90/128/EEC and its follow-ups would formally only be enforcable on the basis of fully validated analytical methods for specific migration determinations (compare discussion in Section 10.2.3). However, since full collaborative trials according to I S 0 5725 are very time-consuming and expensive and because of the large number of SML values to be validated, it is immediately quite obvious that achieving this ideal situation is an economical impossibility. In addition, the time frame to fulfill such a task would exceed the dimensions of any real life requirement. Furthermore, many of the positively listed plastics constituents obviously have such a low commercial relevance that the question of absurdity would also be raised in these cases. As a consequence, there is clearly a need for pragmatic solutions to this problem. Since provision of “fully validated” methods turns out to be impossible, certain minimum requirements to method validation should be agreed upon at an European level to produce so-called “generally agreed or accepted” methods. Possible ways out of the situation are in-house validation procedures carried out by one laboratory, which however has to fulfill generally agreed requirements for single laboratory validation and as a basic formal prerequisite needs an accreditation to EN45000 (Eurachem 1993). This strategy may be assisted by the definition of minimum requirements for test method precision based on the so-called Horwitz trumpet (Horwitz 1988,1995) which links repeatability to concentration. As an economic alternative to I S 0 5725 and obeying full validation ring trials, small collaborative trials with two or three laboratories can also be considered. Currently, a task group (TG7) within CEN TC194/SCl is investigating the feasibility of such alternative approaches. Among the criteria to be considered, the aspects of practicability and cost-efficiency have also been selected. About the availability of generally accepted or standard methods in Europe In the European Member States there are many laboratories such as research organisations, industry, private, governmental and enforcement laboratories, involved in the measurement of specific migration of monomers and additives from polymeric packaging materials into foods and food simulants. Most of these laboratories apply analytical methods developed by themselves and in most cases without appropriate validation. Dependent on the analytical equipment and level of education within the laboratory, the methods applied may vary from sophisticated and highly selective techniques such as GUMS to classical and often unspecific methods such as colorimetric tests. In other words: laboratories are currently far from applying generally accepted and validated test methods for the determination of specific migrations. As a consequence, the results obtained from different laboratories for a given migration test are likely to vary in such a way that comparable, accurate and precise migration results are hardly obtainable for supporting a successful argument in court. However, also from an economical standpoint viewing a free European market, the requirement of available and generally accepted test methods was and remains essential.
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Vinylchloride EU Directives:
As a consequence of ELI Directive 781142/EEC, which introduced a limitation of vinyl chloride monomer both as residual amount in final articles (QM: lmg/kg) intended to come into contact with foodstuffs and in migration to food (SML not detectable; LOD: 0.01 mg/kg), the corresponding necessary analytical methods were developed between several European expert laboratories and laid down as agreed methods in EU Directives 80/766/EEC and 81/432/EEC, respectively. This piece of the EU harmonization process was too time- and work-consuming to continue in this way. The vinyl chloride Directives therefore remain a unique feature in E U food packaging legislation since this was found to be impractical for generalization.
CEN TCI 94/SCl: Validation and standardization of analytical methods is a recognized basic task of the European Committee for Standardization (CEN). Within the CEN organisation, a working group, CEN TC 1941SC11WG2, has produced fully validated methods for 15 plastics monomers which have been published as European pre-norms (ENV) within the ENV 13130 series (CEN 1999). Whereas Part 1 of this multipart standard gives general guidance t o the specific migration test methodology prior to analysis of the specific migrant, the remaining seven Parts are pure analytical methods for the determination of monomers in food simulants or plastics. Table 10-3 gives an overview of the ENV13130 series. Table 10-3: Overview of CEN ENV13130 standard. No.
Title
Restriction
Part 1 Guide to the test methods for specific migration of substances from plastics into food and food simulants and the determination of substances in plastics and the selection of conditions of exposure to food simulants Part 2 Determination of terephthalic acid in food simulants
SML: 7.5 mg/kg
Part 3 Determination of acrylonitrile in food and food simulants
S M L not detectable. LOD: 0.02 mg/kg
Part 4 Determination of 1,3-butadiene in plastics
QM: 1 mg/kg
Part 5 Determination of vinylidene chloride in food simulants
SML: not detectable, LOD: 0.05 mg/kg
Part 6 Determination of vinylidene chloride in plastics
QM: 5 mg/kg
Part 7 Determination of monoethylene glycol and diethylene glycol in food simulants
SML (T): 30 mg/kg
Part 8 Determination of isocyanates in plastics: - 2,6-toluene diisocyanate - diphenylmethane-4,4'-diisocyanate - 2.4-toluene diisocyanate - hexamethylene diisocyanate - cyclohexyl isocyanate - 1 $naphthalene diisocyanate - diphenylmethane-2,4'-diisocyanate - 2,4-toluene diisocyanate dimer - phenyl isocyanate
QM (T): 1 mgikg (expressed as NCO)
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BCR (S,M & T )project “Monomers”: During the period 1993-1996 a European project was conducted within the Standards, Measurements and Testing programme of DG XII. The scope of this project was to fill the tremendous gap in analytical methods by development and pre-validation of methods of analysis for 36 monomers selected from the “Plastics Directive” positive lists. The project was carried out by a European consortium of 13 laboratories from 9 different Member States, under the co-ordination of the “Fraunhofer-Institute of Process Engeneering and Packaging” (FhIVV) Freising, Germany, and the main partner “TNO-Nutrition and Food Research” Zeist, The Netherlands. From the 36 target monomers (see Table 10-4) the project has elaborated 33 pre-validated methods of analysis for the determination of the specific migration of a selection of monomers listed with a restriction in Directives 90/128/EEC and 92/39/EEC (Franz and Rijk 1997). Since it was the original intention of the project to establish the developed analytical methods as ENVlEN standards within the European Committee for Standardization (CEN), the project structure included the involvement of CEN, in particular the Technical Sub-committee CEN TCl94/SC1 “General chemical methods of test for materials intended to come into contact with food’. Within this CEN sub-committee a working group, WG2, “Methods of test for monomers” is active in which more than 25 European expert analysts in the field of specific migration are collaborating in order to develop and standardize specific migration test methods. As most of the project participants were involved in the work of CEN TC194/SCl/WG2, it was decided in agreement with the “Standards, Measurements & Testing” Programme and DG 111 (Industry) of the European Commission to consult and disseminate the project results to the CEN working group in order to allow the establishment of Europe-wide accepted and agreed test methods. The mechanisms of consultation and dissemination were the following: Before the practical project work started, the project participants were required to deliver for each of their assigned monomers a rationale about the intended analytical procedure. These rationales were then circulated to the CEN group for discussion and expert comment. Only after there was agreement in the CEN group did the practical work start. In t h e course of the project, the CEN group was continuously informed about progress. As soon as a method of analysis was experimentally completed within the project, a draft written in CEN format was circulated to the WG2 members for discussion at the next biannual meeting. In these meetings the methods were either directly approved by the working group as technically suitable for publication as pre-norms, or if necessary after inclusion of the given comments and proposals for amendments. Finally, however, it turned out that CEN WG2 was overloaded with standardization tasks within the funding of the EU mandate for this work. Therefore, the developed and WG2 agreed pre-validated methods of analysis could not be processed forward to EN/ENV standards. Taking the multi-national project structure and the above involvement of CEN TCl94/SCl/WG2 into account, the co-ordinators and all other project participants considered the methods presented (see Table 10-4) to be accepted as Europe-wide agreed analytical methods for specific migration determination of the respective monomers. The project consortium proposed the methods to the European Commission for recommendation as “generally agreed” or as “useful” methods of analysis for the Member States.
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Table 10-4: Overview of BCR project “Monomers” methods of analysis. PM/-Ref. No.
Monomer
10120
Acetic acid, vinylester
10630
Acrylamide
0.01
12788
11-Aminoundecanoic acid 1.3-Benzenedimethaneamine 2,2-Bis(4-hydroxyphenyl)propane
0.01
13000 13480
Restriction [mgkg]
QM
13510
2,2-Bis(4-hydroxyphenyl)propane,bis(2,3-epoxypropyl)ether
136M)
3,3-Bis(3-methyl-4-hydroxy-phenyl)2-indolinone
13630
1.3-Butadiene
SML 12
0.05 3 and
0.02
(BADGE)
1.8 0.02
14200
Caprolactam
15
14230
Caprolactam, sodium salt
15
14380
Carbonyl chloride
15880
1.2-Dihydroxybenzene
6
15910
1,3-Dihydroxybenzene
2.4
15940
1,4-Dihydroxybenzene
0.6
15970
Dihydroxybenzophenone
6
16000
4,4-Dihydroxybenzophenyl
16150
Dimethylaminoethanol
16750
Epichlorohydrin
16960
Ethylenediamine
17005
Ethyleneimine
17020
Ethylene oxide
17260
Formaldehyde
18460
Hexamethylenediamine
6 18
12 0.01
15 2.4
18670
Hexamethylenetetramine
15
19540
Maleic acid
30
19960
Maleic anhydride
30
21490
Methacrylonitrile
0.02
22150
4-Methyl-1-pentene
0.02
22660
1-Octene
23050
1,3-Phenylenediamine
24010
Propylene oxide
25150
Tetrahydrofuran
25360
Trialkyl (C5-Cl5) acetic acid. 2.3-epoxypropylester
25420
2,4,6-Triamino-1.3,5-triazine
25600
1,l.l -Trimethylolpropane
15
0.6 6 30 6
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Methods of analysis in petitions to the European Commission: As another source of analytical methods for monomers and additives, the numerous technical dossiers submitted to the Scientific Committee of Food (SCF) through many European companies should be mentioned. According to the Commission’s request to the petitioners, these methods should have been written in a CEN standard format and meet current analytical requirements. Normally, however, these methods were established in assessing front line human exposure under the envisaged contact application, and were not always suitable for general control purposes. Nevertheless, there seems to be a large potential for technically suitable methods to be further evaluated and processed to a generally agreed level of validation on the Europe-wide scale.
10.2.6 Practical examples During method development and validation, a number of practical difficulties may occur and need control. An already well-known major phenomenon which can cause problems to the analyst is for instance insufficient or even zero recovery of analytes from the migration test solution. Possible reasons for that may be: (i) the chemical instability of analytes under migration test conditions due to oxidation, chemical binding to food simulant, (acid catalyzed) hydrolysis or ethanolysis; or (ii) volatilization during migration exposure and sample preparation (Rijk 1993). To illustrate and put into practise what has been said so far, several examples of methods of analysis are presented in the following, together with some specific difficulties and problems related to SM determination methods.
Acrylnnitrile ( S M L = not detectable at 0.02 nig/kg) The ENV13130-3 standard method (CEN 1999) to determine the specific migration of acrylonitrile in food simulants and foodstuffs originates from the German official BgVV (former BGA) collection of analytical methods according to $35 LMBG. It was already fully validated in Germany within a IS0 5725 collaborative trial before it was translated into English and editorially rearranged to fit into the CEN standard format. Acrylonitrile, CH2=CH-CN (CAS No. 107-13-1; PM/Ref. No. 12100) is a monomer commonly used as a co-monomer with styrene and butadiene to make ABS or SAN plastics for food contact articles such as kitchen utensils, rigid containers, measuring jugs, refrigerator linings, trays and fittings, coatings for nylon and polycarbonate films etc. It should be mentioned that acrylonitrile is a hazardous substance and volatile at room temperature. It requires corresponding precautions with respect to health risk for the analyst and cross-contamination during sample preparation. The method is not only applicable to the EU-official aqueous and fatty food simulant but also to foodstuffs such as beverages and soft margarine. Indeed the collaborative trial included fruit juice, wine and sunflower oil. The level of migrated acrylonitrile is determined by headspace gas chromatography, preferably with automated sample injection and using a nitrogen specific detector, for instance an alkali flame ionization detector (AFID). This gives the method the necessary sensivity to meet the
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restriction criterion requirement “not detectable at 0.02 mg/kg”. Quantification is achieved using propionitrile as an internal standard with calibration against a blank sample matrix fortified with defined amounts of acrylonitrile. Numerous suitable GC columns are described in the method, for instance: - 2 m x 3 mm internal diameter stainless steel column packed with 15 YOpolyethylene glycol 1500 on 60 mesh to 100 mesh diatomite support; or - 12 m x 0.20 mm internal diameter, fused silica capillary column with 0.33 pm film thickness of free fatty acid phase (modified polyethylene glycol). In the case of a measured concentration exceeding the restriction criterion, confirmation of acrylonitrile levels is carried out either by combined gas chroamtography/ mass spectrometry (GUMS) or by re-analysis on a second GC column of different polarity. It should be noted that the GUMS confirmation is considered more appropriate. The procedure makes use of the selected ion detection mode and quantifies acrylonitrile by monitoring the ions m/z = 53 for acrylonitrile and m/z = 55 for propionitrile. It is stated in the method that the level measured in this way shall be the true value which may be lower and in compliance again with legislation despite the initially determined value. Concerning the limit of detection (LOD), the collaborative trial revealed that the participating laboratories could achieve LODs in the range between 0.005 mglkg and 0.02 mglkg. So, in order to allow 95 YOof laboratories to achieve the same LOD, the upper limit, i.e. 0.02 mg/kg, was agreed as relevant for any laboratory. Based on the r (0.005 mg/litre) and R (0.011 mg/litre) values determined in the collaborative trial, a critical difference threshold CrDg5of 0.006 mg/litre can be derived for a duplicate determination in the same laboratory. Consequently, the restriction criterion “not detectable” must be considered to be exceeded when a laboratory measures a concentration higher than 0.026 mg/litre on the basis of a duplicate determination.
1,J-Butadiene ( S M L = not detectable at 0.02 mg/kg, Q M
= Img/kg)
Butadiene, CH2=CH-CH=CH2 (CAS No. 106-99-0; PM/Ref. No. 13630) is commonly copolymerized with styrene and acrylonitrile to make ABS or BS food contact plastics (for applications see acrylonitrile). Butadiene is a suspected carcinogen with extreme volatility (bp 4 . 5 “C) and low water solubility. This makes it very difficult to handle migration and calibration samples where the matrix is of highly aqueous character such as the aqueous food simulants. The Plastics Directive foresees 2 restrictions for this monomer. The reasons for that will be recognized after the following discussion. The method developed in the BCR project (Franz and Rijk 1997) to determine butadiene in all of the official food simulants and probably also in real foodstuffs was pre-validated by a collaborative trial with three laboratories. It was found appropriate in principle for the quantitative determination of butadiene at a range of 0.01 to 0.1 mg/kg in food simulants. Indeed the limit of detection was found to be in the range 4 to 9 pg/kg, thus being even in the worst case significantly lower than originally presumed when establishing the Plastics Directive limit of 0.02 mg/kg. The working principle is as follows: The level of butadiene in a food or food simulant is determined by headspace gas chromatography (HSGC) with automated sample injection and by flame ionisation detection (FID). Quantification is achieved using an internal standard (n-pentane) with calibration against relevant food simulant samples fortified with known amounts of butadiene. Confirmation of butadiene levels is car-
Migrotion of plastic constituents
319
ried out by combined gas chromatography/mass spectrometry (GUMS). In contrast to the acrylonitrile standard, it was agreed in the BCR project that the confirmation is qualitative in the sense that it should demonstrate the correct identity of the measured peak and the absence of interferences. If the G U M S analysis clearly indicates the absence of interferences, then the migration result as obtained by the HSGC/FID method is taken as the true value. In the case of interferences occurring, the peak area ratios of the specified ions obtained from the G U M S method are used to calculate the relevant butadiene level in the food simulant. During the method development and validation work in the project, severe problems had been observed with respect to volatilization of butadiene. Therefore, it is important and crucial to take the following into account when planning and designing a migration test: From migration experiments carried out at 10 days for 40°C it was recognized that irreproducibly considerable loss (up to 90 %) can result from volatilization of 1,3-butadiene when using aqueous food simulants. Just opening and closing vials containing calibration solutions caused significant headspace losses of the volatile analyte. which is due to very unfavourable partitioning from the aqueous phase to the head space. On the other hand olive oil samples were found to provide satisfactory recoveries, due to the much better solubility of butadiene in this non-polar matrix. As a consequence. migration exposure of plastic materials to an aqueous food simulant in a test cell o r glass container combined with sampling steps to prepare food simulant aliquots for analysis will most likely lead to irreproducible results due to uncontrollable loss of analyte. Of course, one can argue that this occurs also in real life with a food package. However, when thinking about reproducibility of analytical standard methods, such an argument must be excluded in the first instance but taken into account again when it comes to the interpretation or down-correction of a reproducibly measured analytical result obtained under conditions without uncontrolled analyte loss. This topic has been discussed many times so far but no concrete solution has been agreed. A very pragmatic solution to this problem could be to divide a specific migration result obtained under controlled conditions by a factor of two to take care of real life losses of analyte into the environment of a food package. Obviously, this kind of problem had been foreseen when the idea of two restriction types for butadiene was born. Indeed, compliance testing with respect to the QM limit of butadiene in plastic according the ENV13130-4 standard method which also originates from the German official BgVV (former BGA) analytical methods according to $35 LMBG, is in all cases highly recommendable since this method is much easier and straight-forward and therefore, much less error-prone.
BADGE ( S M L = not detectable at 0.02 mg/kg, Q M = lmg/kg) 2,2-Bis(4-hydroxyphenyl)propane-bis(2,3-cp~~xypropyl) ether o r bisphenol A diglycidyl ether (BADGE), C21H2404, (CAS No. 1675-543, PM/Ref. No. 13510) is commonly used as a bifunctional monomer or cross-linker in epoxy-based coatings very widely used in food contact applications such as lacquer coatings on food cans, plastic storage vessels e.g. wine vats, or in adhesives for laminates, printing inks and others. For the molecular structure of B A D G E and known reaction products in food simulants see Fig. 10-5 (Philo et al. 1997). The analyst who plans to carry out migration testing for B A D G E is often confronted with the question how to obtain a suitable B A D G E sample, since it is not
320
Franz
(4)
Figure 10-5: Molecular structures of BADGE and hydrolysisiethanolysis products: (1) Bisphenol A diglycidyl ether (BADGE);(2) Bisphenol A (2,3-dihydroxypropyl ether) diglycidyl ether (did-epuxide); (3) Bisphenol A di-(2,3-dihydroxypropyl ether) ( d i d - d i d ) ; (4) Bisphenol A (3-ethoxy-2-hydroxypropyl ether) diglycidyl ether (ether-epoxide); ( 5 ) Bisphenol A (3-ethoxy-2-hydroxypropylether) (2.3-dihydroxypropyl ether) (ether-did).
commercially available on the market of fine chemicals. For this purpose, the analyst may contact national or international reference collection systems as for instance the “Plastics Reference Collection” of the British MAFF Central Food Science Laboratory in Norwich (Bush et al. 1994) which has been established largely within a BCR project funded by the European Commission. On request, this collection provides a 1 g reference standard or solution free of charge to the applicant. Many studies have been published describing the isolation and determination of BADGE monomer from polymer articles, oils or foodstuffs. A number of these papers also give attention to the formation of hydrolysis or other reaction products of BADGE (Roubtsova et al. 1997, Simal Gandara et al. 1993, Paseiro Losada et al. 1993). The BCR project has also provided Europe-wide agreed pre-validated methods both for QM and SML control purposes (Franz and Rijk 1997). The SML method: the scope of this method comprises the determination of BADGE monomer in all four of the official food simulants with a LOD of 0.005 mg/ kg. The method should also be applicable to other, alternative food simulants. The principle is to determine BADGE in aqueous simulant test samples directly by high performance liquid chromatography (HPLC) with fluorescence detection. Determination of BADGE in fat simulant is also conducted by HPLC, after isolating of BADGE from the oil by extraction using acetonitrile. The identity of BADGE may be confirmed either from its fluorescence emission spectrum (1st option) or from the ratio of the areas of its peaks in chromatograms obtained with fluorescence and ultraviolet detection (2nd option), in both cases by comparison with authentic samples. A third option is to use an analytical column with a different selectivity. Although the method was found to be applicable in all food simulants, the observed rapid hydrolysis of BADGE must be taken into account. As expected, BADGE is sen-
Migration of plastic
constituents
321
sitive to hydrolysis in contact with aqueous foodstuffs (Paseiro Losada 1993), so special attention was given in this BCR project study to the stability of BADGE under usual migration test conditions such as 10 days at 40 "C. The formation of mono- and di-hydrolysis products is shown in Fig. 10-5. These investigations were carried out using food simulants spiked in the restriction value range (0.02 to 0.04 mg/kg) and it was found that BADGE was completely hydrolyzed in all the three aqueous food simulants after 10 days at 40°C. On the other hand quantitative recovery was obtained in the case of olive oil under the same test conditions. A kinetic study revealed the following approximate half-lives in aqueous food simulants under the conditions mentioned above: Table 10-5:Hydrolysis of BADGE in aqueous food sirnulants at 40 "C. Food simulant
Half-life time
Distilled water
1.1 days
3 % (wlv) Acetic acid
0.15 days
15 % (vlv) Ethanol
I .4 days
Therefore, the scope of the method seems to be limited only to very short and mild contact conditions in the case of aqueous food simulants, but the method is fully applicable to olive oil and other oils or fats as well as to non-proton-active alternative simulants such as iso-octane. It is important to note that the above study was carried out under the premise of a given SML restriction of 0.02 mglkg. From this, a highly challenging situation existed with respect to the target detection limit. In the meantime the Scientific Committee on Food (SCF) for the Commission has updated its opinion on BADGE (Internet: http://europa.eu.int/en/comm/spc/spc.html). According to this opinion, the restriction included in the Shamendment of the "Plastics Directive" now reads: " S M L = lmg/kg in foodstuffs or in food simulants or Q M ( T ) Irng/6dm2 in FP Both limits shall include the mono-hydrolysisproduct of BADGE, if any. However in aqueous food sirnidants, the S M L should also include the di-hydrolysis product unless the material or article is labelled for use in contact with those foods and/or beverages for which it has been demonstrated that BADGE and its mono-hydrolysisproduct cannot exceed I mg/kg. Since it is also reported in the above SML method that the HPLC method after some modification also allows the detection of two BADGE hydrolysis products, the method may nevertheless be very useful to fulfill the latest regulatory requirements. The QM method: This describes the determination of BADGE monomer in polymers expressing the measured levels as (mg BADGE)/(kg of polymer) or as (mg BADGE)/(dm* food contact area) depending on the type of test material. BADGE is extracted from the polymer with refluxing chloroform and determined by high performance liquid chromatography (HPLC) with fluorescence detection after transfer from chloroform into 90 % (v/v) methanol to obtain a solution compatible with the HPLC mobile phase (acetonitrile/water = 65:35 (v/v)). Quantification is achieved relative to external standards. Confirmation of the identity of BADGE is achieved in the same way as described for the SML method. This is appropriate for the quantitative determination of BADGE at a minimum level of 0.15 mg/kg in the polymer.
322
Frcmz
The method development work was done under the premise of a BADGE QM restriction of 1 mg/kg. However, BADGE is mainly used in coatings on non-plastic supports. Therefore, the amount of coating on a final article (e.g. coated can) can generally not be determined with sufficient accuracy. Consequently, this leads to severe problems with respect to determining the QM restriction in mg/kg coating. Therefore, the idea of determining a surface area related BADGE “concentration”, in mg BADGE per dm2 food contact area was born and followed in this project work. Indeed, as mentioned above, the SCF has now proposed a surface area related QM value of 0.16 mg BADGE per dm2. The method already takes account of this situation and is capable of meeting the most recent BADGE QM restriction. In spite of the fact that two very suitable test methods were available for BADGE determination in food simulants, the need for a sensitive and convenient control method for real foodstuffs was not yet satisfied. This need originated from the socalled BADGE problem observed first in Switzerland (Biedermann et al. 1996) and then in many European countries. Control laboratories found BADGE very frequently exceeding the legal restriction values in samples drawn from the market. It is well known in the area of analysis of complex matrices such as foodstuffs that one of the major problems and in many cases an insurmountable difficulty arises from possible analytical interferences from the oily or fatty foodstuff matrix. In principal, a possible way-out of this problem is application of (i) a separation system which allows elution of the interesting analyte fraction separate from that of the oil matrix or (ii) very specific detection in the presence of oil matrix interference which allows compensation of poor chromatographic separation of the analyte fraction. The latter can be achieved in many cases by modern LC-MS-MS analysis using the atmospheric pressure chemical ionisation (ACPI) technique and operated in single reaction monitoring mode (SRM). Based on this technique, a rapid, convenient and very sensitive method for BADGE determination has been described for foodstuffs such as canned fish products and goulash soup and with general applicability to many other food types (Roubtsova et al. 1997). In t h e following, the HPLC fractionation of the analyte from a fatty matrix and selective MS-MS quantification is described in more detail. In order for the oil matrix fraction to by-pass the mass spectrometer (a Finnigan TSQ-7000), a 6-way-valve was installed after the C18 reversed phase HPLC column. The elution conditions were: Isocratic elution with 100 % methanol (MeOH) from 0-3 minutes. then 100 % tetrahydrofuran (THF) from 3-8 minutes and again 100 % methanol from 8-20 minutes. In this way the column was capable of separating the oil matrix fraction from the analyte fraction. The fraction containing BADGE was eluted from the column within the first 3 minutes during the MeOH elution, followed by the oil fraction being washed during the THF elution. While the column was THF-washed. the 6-way-valve was switched to pass the eluent flow to the waste reservoir in order to avoid the oil matrix entering the mass spectrometer.The mass spectrometer parameters were optimized for the most sensitive detection of BADGE possible. Under these conditions BADGE was detected in the MS mode as a molecular ion-water cluster m/z = 358.1 [M + H20]+ (see Fig. 10-6). In the coupled MS-MS mode a corresponding fragment ion with m/z = 191.0 (Fig. 10-6) was found to be the most intensive. For quantification in the applied SRM mode. only one parent ion ( d z = 358.1 [M + H201’) was selected for fragmentation and only one fragment ion (daughter ion m/z = 191.0) was detected. While in the MS mode both the analyte molecule ion and other matrix molecules with the
I mlz= 358.1
m/z = 191
K+ 05 1.17
1.K + O 3 0.41
I
Figure 10-6: Mass spectrum of BADGE [M + HzO] at n ~ / z= 358.1 (upper) and its fragment ion n?/z = 191 (lower) selected as daughter ion for SRM detection.
324
Franz
,
P.04
a.903
m/z = 358.1
9+04 3.961
I,
mlz = 191
Figure 10-7: Selective analysis of BADGE in a food sample: detection of the parent ion t d z = 358.1 in the MS mode (upper) and daughter ion d z = 191 in the MS-MS mode (lower).
Migration of plastic constituents
325
same m/z = 358.1 value are detected, the SRM mode detects only the specific BADGE fragment. In this way it was possible to detect BADGE very selectively in the HPLC analyte fraction. The advantage of detection in the SRM mode is illustrated by Fig. 10-7. The same sample of fortified “herring in vegetable sauce” was detected in MS mode, where the m/z =358.1 was monitored (Fig. 10-7: upper mass chromatogram), and in the SRM mode where the fragment m/z = 191.0 was monitored (Fig. 107: lower mass chromatogram). This demonstrates impressively how a selective detection procedure allows suppression of the matrix influence for unambigous detection and quantification of the analyte. In contrast, conventional HPLC/UV or HPLC/fluorescence detection systems will be disturbed in such a case by many interfering peaks originating from the food matrix. It may even be difficult or impossible to recognize the analyte peak, especially when there is no blank food sample (free of BADGE) available for comparison. The described HPLC-MS-MS method was also found to be capable of detecting selectively the BADGE hydrolysis and ethanolysis products in foodstuffs. This is highly advantageous over the BCR project SML method since it is much more suitable for meeting the analytical requirements derived from the updated SCF opinion on BADGE.
Carhonyl chloride ( Q M
= 1 rng/kg)
Carbonyl chloride, CI-C(=O)-C1, (CAS No. 75-44-5; PM Ref. No. 14380), also known as phosgene, is an important starting compound in the production of intermediates and end products in many branches of large-scale industrial chemistry due to its high chemical reactivity. Carbonyl chloride is mainly used for the production of diisocyanates as starting materials for polyurethane chemistry. A large part of carbonyl production is also used for the manufacture of polycarbonate plastics (polycarbonates), produced by the reaction of 2,2-bis(4-hydroxyphenyl)propane (bisphenol A) with carbonyl chloride. Typical food packaging applications are multi-trip containers for drinking water and milk products, coatings for cookware, tableware, containers for automatic dispensers and baby feeding bottles (Bush et al. 1994, Gmeiner et al. 1998). For the analyst it is important to note that carbonyl chloride is an extremely acute toxic substance (irritant capable of producing delayed pulmonary edema) and is gaseous at room temperature (b.p. 7.5 “C/1013 mbar).Therefore, all processes in which carbonyl chloride may be liberated must be carried out in a fume cupboard. Skin and eye contact with carbonyl chloride solutions and especially the inhalation of carbonyl chloride vapour must be avoided. It is recommended not to work with pure carbonyl chloride but with commercially available solutions, for instance 20 % carbonyl chloride in toluene (density at 20 “ C 0.935 kg/l) corresponding to a concentration of 1.93 Mol per litre or 191 g/l. Stock solutions and standard solutions should be prepared and stored in closed containers. The analytical method developed in the BCR project (Franz and Rijk, 1997) to determine residual carbonyl chloride monomer in polymers was pre-validated by two laboratories and found appropriate for the quantitative determination of carbonyl chloride with a LOD = 0.3 mglkg below and in the range of the restriction criterion of 1 mg/kg polymer, with observed repeatability values of r = 0.23 and 0.32 mg carbonyl chloride/kg polymer, respectively. The method is applicable to polycarbonate as well as to other polymers and copolymers where these are soluble in methylene chloride.
326
Franz
Working principle of the method: The level of carbonyl chloride in the polymer is determined by dissolution of the polymer in methylene chloride and concurrent derivation with 2-aminophenol to form 2-benzoxazolinone (Box) under hydrochloric acid elimination (see Fig. 10-8).
2-arnincphend
carbonyl chloride
2-benzoxazolinone (Box)
Figure 10-8: Chemical derivation of carbonyl chloride with 2-aminophenol
Whereas carbonyl chloride itself is very moisture sensitive and requires the corresponding precautions such as efficiently dried glassware and solvents, the Box derivative is very stable and can be analysed by high performance liquid chromatography (HPLC) with ultra violet (UV) detection at 270 nm. Quantification is achieved by the standard addition procedure spiking carbonyl chloride into the test polymer solution. However, since Box is a commercially available chemical, it is advisable to work also with Box standards, especially when the method is used for the first time and when problems are experienced in the HPLC determination or the derivation procedure. The standards of the carbonyl chloride derivative are particularly useful to establish the analytical system and to check linearity of detector response as well as for the recovery check. For illustration purposes, in the following the determination of carbonyl chloride in test sample is described in detail. From the measurements of the calibration samples prepared according to the standard addition procedure a calibration graph is obtained as depicted in Fig. 10-9.
rng carbonyl chloride added per kg polymer
Figure 10-9: Calibration graph obtained from the standard addition procedure
Migration of plastic constituents
327
Graphically, the determination can be achieved as follows: The carbonyl chloride concentration of the test sample can be read from the calibration graph by back extrapolation to the x-axis where the magnitude of the intercept Z is equal to the carbonyl chloride concentration. The sample concentration can also be calculated from the regression parameters, specifically from the regression line of the calibration graph including the sample value, which is given by the following equation: y=ax+b
(10-14)
The residual carbonyl chloride concentration in the test Sample Ccarhonyl chloride. po~ymer is then obtained from the regression parameters a and b where y = 0 according to: Ccarhonyl chloride. polymer =
b/a
(10-15)
From both procedures the carbonyl chloride concentration in the test material is obtained directly in mg of carbonyl chloride in 1 kg polymer. In the BCR project it was agreed that the method applying calculation from the regression parameters should be preferred. In case of measured concentrations exceeding the QM limit, confirmation of the identity of carbonyl chloride is carried out by diode array detection. This is achieved by recording the spectral profiles of the samples, blanks and calibration samples over the wavelength range of 200-320 nm at the front, apex and tail of the peak identified as the carbonyl chloride derivative. Box can be identified as having an absorbance peak maximum at 272 nm and a minimum at 245 nm with an absorbance ratio of 40 (at 260 nm) : 100 (at 272 nm) : 70 (at 280 nm). I f the peak is pure, the overlaid spectral profiles of the front, apex and tail of the peak should be identical. Therefore, if the three profiles are normalized, they should superimpose on top of each other. A pecularity observed during method development,and which illustrates what the analyst must be aware of when working with a derivation procedure was the following: After some remarkable and confusing experiences indicating that the HPLC peak of Box in the completely worked-up sample was still increasing with time and inhibiting reproducible results, it was found that the derivation agent 2-aminophenol is capable of reacting not only with carbonyl chloride but also at a much slower rate with oligomers or the polymer residues dissolved in the sample solution. The final evidence for this was derived from the following control experiment: A polycarbonate sample was dissolved and re-precipitated to ensure a polymer matrix completely free of carbonyl chloride monomer. This purified polymer sample was then treated by the derivation procedure with 2-aminophenol but without removal of the excess derivation reagent with hydrochloric acid after the standard derivatisation reaction. The sample was then analysed for Box as a function of time and in comparison against both, a polymer blank (without derivation reagent) and a reagent blank (without polymer). The results obtained after 2 hours and 13hours storage time of the HPLC sample vial at room are depicted in Fig. 10-10. They demonstrate clearly an effect which can only be explained by the chemical reaction of 2-aminophenol with residual polycarbonate oligomers or polymer present in the sample solution. In conclusion and as a consequence, the method requires from the analyst a timely and very disciplined sample preparation, including the need €or acidic removal of the stochiometrically excess aminophenol.
328
Franz 3.27-
3.27-
(a)
3.17-
3.17-
2sri 5.w
,
,
,
700
8.00
n.w
I
2.67-
I
5.00
m 7 4
, 5w
1
I
7.w
9.00
,
,
7.w 9w AarcnUon Urn h mdfwces
I
I
ll.W
, n.w
Figure 10-10: HPLC chromatograms of phosgene-free polycarbonate samples derived with 2-aminophenol as a function of time: (a) sample after 2 hours, (b) sample after 13 hours, (c) polymer blank, (d) reagent blank.
Epichlorohydrin ( Q M = lmg/kg) Epichlorohydrin (l-chloro-2,3-epoxypropane), C3H50C1, (CAS-No 106-89-8; PM/ Ref.No 16750) is a toxicologically important starting substance, reacting for instance with bisphenol A to form bisphenol A diglycidyl ether (BADGE, see above) used for the production of epoxy lacquers. It is also used for epoxy resins with p-hydroxybenzoic acid and resins with dimethylamine. Food contact applications are coating cans for fruit, vegetables and beverages as well as coating storage vats and silos for wine, beer, fats and dry foods. Another application is its use for adhesives. The “Plastics Directive” foresees a QM value as a restriction criterion for ECH. As a consequence a pre-validated QM method was developed in the BCR project entitled “Determination of the residual content of epichlorohydrin (ECH) in coatings”. Similar to the BADGE discussion to justify determination of an area-related QM value, in this method it is stated that epichlorohydrin is mainly used in coatings on a non-plastic support. Therefore the amount of coating on a final article (e.g. coated cans) cannot be determined within an acceptable accuracy and, in consequence, the amount of residual epichlorohydrin should be measured and related to the area and given in mg/ dm2. The method was found to be appropriate for the quantitative determination of ECH at 1pg per dm2 of coating. In general this allows for the detection of ECH at the level of 1 mglkg polymer.
Migrution of plastic constitirents
329
The working principle of the method is to extract the sample material with dioxane for 6 hours at room temperature. It is important to note that the dioxane quality used must be of the highest purity (>99.5 YO)with a water content ~ 0 . 0 YO 1 (dried over a molecular sieve). From a practical standpoint, the extraction of ECH can be carried out in the case of cans by filling with 50 ml dioxane and closing the can with an epoxide-free coated plate and, in the case of other coated packaging material, by cutting 2 dm2 coated material into pieces and immersing them in the extraction solvent. Typical surfacelvolume ratio is 2.5 dm2 packaging material area per 50 ml extraction solvent. After extraction, the extract is distilled by means of a micro-distillation depicted in Fig. 10-11. In the distilled fraction thus obtained, the concentration of epichlorohydrin is determined by derivation of the epoxide with an aromatic sulphonic acid, i.e. 9,lOdimethoxyanthracene-2-sulphonic acid (DAS), followed by reversed phase HPLC with fluorescence detection (HPLC column: stainless steel 250 mm x 4.6 mm, filled with C8 coated silica, particle size 5 pm, load of 10 % carbon and end capped; acetonitrile-water gradient elution; fluorescence detector set to hexcltation 262 nm and hemission 490 nm). The DAS solution prepared in acetonitrile is only stable for one day at room temperature and must be prepared freshly before use and protected against light. Depending on the quality and type of the HPLC column, it is possible to separate the two isomers formed in the derivation reaction of epichlorohydrin with DAS. In this case, for calibration and quantification purposes the sum of both peak areas has to applied. Quantification is achieved by means of external standard calibration using dioxane solutions fortified with known amounts of epichlorohydrin. Confirmation of ECH identity is carried out by straight phase HPLC with fluorescence detection. A conclusion drawn from the BCR project work was the following: Expression of the measured ECH concentration in mg/kg in final product is difficult or even impossible because data on thickness and weight of the coating in food contact materials are often missing. Since the determination of the area weight of the coating layer is troublesome, it was proposed to the E U Commission to set a maximum content limit of 20 pg ECH per 6 dm2 food contact area which translates to 20 ppb (pg/kg) food in the case of total mass transfer.
Cold waterlice
bath
Hot plate and magnetic stirrer
Figure 10.11: Schematic picture of the micro-distillation of epichlorohydrin from the dioxane extract of the polymer in vial A into cooled vial B: (1) Vial A; (2) Vial €3; (3) PTFE lined septum; (4) Sleeve of PTFE tube for isolation; (5) Stainless steel tubing. ends are injection needle type sharpened. Int. diameter 1 mm,lenght approx. 20 cm; (6) Injection needle for venting; (7) 3 ml mark.
330
Franz
However, due to the rapid decomposition of ECH in aqueous foods the migration measurements for such products are very problematic and not reproducible (Piringer 1993,1980). Bronsted had already studied the kinetics of the ring opening of epoxides over 60 years ago. Because of the large ring tension, epoxides are very reactive and indeed react in water with nucleophilic substances at any pH-value. The hydrolysis mechanism occurs according to the so-called S$ mechanism. In alkaline and neutral media the chemical reaction can be described by the following equation (Fig. 10-12).
yLk
0-
+
OH-
OH
\/c-c I
slow
\,c-cI
slow
OH
1 0 \
0-
OH
\I /c-c
HzO
1 0
0
I\
fast
H,O+
*
,\c-cI
+
\
fast
OH'
OH
/ I\
OH
Figure 10-12: Alkalineheutral hydrolysis of epichlorohydrin.
In acidic media the nucleophilic attack on the epoxy ring proceeds by a proton attachment. The intermediate species formed very quickly in step a) is present in very low equilibrium concentrations and favors the rate determining nucleophilic ring opening b) whereby the acid functions as a catalyst for the whole process (Fig. 10-13) H
0
O+
H
yzk
b)
OH
OH
+
HzO
slow
\/c-c I
0
/c-c
I\
'I
fast
H,O+
OH
Figure 10-13: Acidic hydrolysis of epichlorohydrin.
The hydrolysis product of ECH in neutral and acidic aqueous media is 3-chloro-1,2propanediol and at high pH values the reaction proceeds up to the formation of glycerine (Fig. 10-14). 0
/ \
C-C-C-CI
-I
OH OH
H', HzO
I
C-C-C-CI
-I OH-
OH C-C-C
0
/ \
OH OH
-I OH-
I
C-C-C-OH
Figure 10-14: Hydrolysis products formed from epichlorohydrin.
The hydrolysis reaction follows a first order mechanism with respect to ECH: (10-16)
Migration ofplastic constiriients
331
where kECHrepresents an overall rate constant which contains the contributions of all nucleophilic reaction partners present in the system as well as that of water. Numerous publications in earlier years dealing with the kinetics of this reaction were limited by the analytical determination in ECH concentration ranges of 0.01-0.2 mol/l. The control of these residual monomcrs. however, requires methods and knowledge of the reaction process in the trace amount concentration region of approximately 1 . mol/l for pH values from 2 to 12. Combined GUMS using headspace and SIM techniques allows the quantitative determination of ECH at a limit of detection of 0.5. moll1 (40 ppb ECH in aqueous solution). Values obtained for halflife times t 1 / 2 of the hydrolysis using this method are given in Table 10-6. Table 10-6: Halflife times tl,z [hours] for ECH in different aqueous systems and foodstuffs in dcpendency of temperature.
20 "C
tli2 PI 40 "C
60 "C
148
23
4.4
62
10
2.0 1.6
Matrix 10 % Ethanol in water ( p H = 7)
NaOH in water (pH
=
12)
3 % Acetic acid in water (pH = 2.5)
79
10
Sunflower oil
45.000 (5.1 years)
-
Sunflower oil + 1 ' 6 water
15.000 ( I .7 years)
-
106
13
Green beans Pectin 5 6 ' (pH = 7)
41
8.2
Processed tomatoes
44
5.6 6.4
Beef + vegetable
41
Mackerals + tomatoes
38
6.2
Sardines in oil
33
4.7
Egg yellow
34
6.0
Egg white
1')
2.6
The hydrolysis of ECH is so rapid at 40 "C, even in neutral aqueous media (water, 10 YOethanol) as well as acidic (3 YOacetic acid, 0.01 N HCl) and alkaline (0.01 N NaOH) media, that specific determination of this residual monomer migration from epoxy lacquers into these media causes inconsistent and erroneous results. Due the fact that the overall rate of hydrolysis contains the sum of all contributions from nucleophiles present in aqueous systems, one can find a rapid decomposition of ECH even in foods with neutral pH, due to their complex composition.
Ethylenediamine (SML = 12 mg/kg) and hexamethylenediamine (SML = 2.4 mg/kg) The two homologous aliphatic diamines are commonly used as bifunctional monomers for polycondensation reactions. Hexamethylenediamine or 1,6-diaminohexane, ChHlhN2(CAS No. 124-09-4, PM Ref.No. 1840), which is most well-known as a polyamide (Nylon 66) monomer, is also copolymerized with sebacic acid to form Nylon 6/ 10, or with isophthalic acid. Besides that, it is applied as a curing agent for expoxy
332
Franz
I
350.00-
i
300.00
I
250.00 200.00-
150.0U 1OO.OD
50.00 A--LI-
I
I
I
1
I
7 I
1
160.0F
120.0cF
80.00-
40.00-
0.00
10.00
20.00 30.00 40.00 Retention time In minutes
50.00
60.00
70.00
Figure 10-15: SFCiFID analysis of olive oil before (upper) and after reaction (lower) with a EDA/ HMDA mixture.
Migration of plastic constiti4ents
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resins. Practical packaging applications are vacuum and modified atmosphere packs, boil-in-packs for packaging meat, fish, coffee and snack foods. In the field of rigid containers, monolayer or multilayer bottles for refilling with soft drinks and water are on the market. Ethylenediamine or 1,2-diaminoethane, CzHgN2 (CAS No. 107-15-3, PM Ref. No. 16960) is also used to make some nylons and thermosetting resins. It finds application as a reactive hardener in epoxy resins and in stabilizing rubber latexes. Examples of practical applications are adhesives, moisture barrier coatings for paper, cellophane or others, and corrosion inhibitor for aluminium alloys. In the BCR project, a group method was developed for both diamines HMDA and EDA in the same way (Franz and Rijk 1997, Demertzis et al. 1995). During the project work a remarkable observation was made: Stability tests in olive oil as a food simulant carried out under test conditions 10 daysi20 “C and 10 days140 “C indicated that both diamines could no longer be recovered, whereas in aqueous food simulants nearly 100 Yo recovery was obtained under the same test conditions. To investigate the mechanism of diamine disappearance a model experiment was carried out. A 1:l mixture by mass of olive oil and diamines was stored for 10 days at 40°C. Then the mixture was analyzed by supercritical fluid chromatography (SFC) using FID detection and compared with the original olive oil SFC pattern. The result is depicted in Fig. 10-15. It can be recognized that the original olive oil triglyceride peaks are nearly completely transformed into a series of different SFC peaks with lower molecular weights. The only reasonable explanation is that the triglycerides react with the diamines to form transamidation products. This was confirmed by LC-MS analysis which demonstrated that the products formed contain the moiety of the diamines. An important conclusion from these findings was that even though this analytical method works in principle with olive oil as a food simulant, the migration test using olive oil or another fat simulant can provide false-negative results. Therefore. the method should only be applied in the case of short exposure periods with olive oil. If the method is carried out with olive oil. a recovery check with spiked olive oil applying the same timehemperature migration test conditions is necessary. In the case that such a recovery check indicates “loss” of HMDA andlor EDA, then alternatively 95 YOethanol or iso-octane should be used as substitute fatty food simulants. As a consequence of these findings, the scope of the analytical method was extended from the determination of the diamine monomers in the aqueous food simulants and in olive oil to the substitute food simulants 95 YO(vh) ethanol and iso-octane. The working principle of the method is as follows: The level of HMDA and EDA in a food simulant is determined by derivation of the free diamine using ethyl chloroformate as derivation agent (see Fig. 10-16) followed by analysis of the resulting diurethane by gas chromatography using automated sample injection and flame ionisation detection (FID). Quantification is achieved using propylenediamine (PDA) as an internal standard with calibration against relevant food simulants samples fortified with known amounts of HMDAIEDA. Confirmation of HMDNEDA levels is carried out by combined gas chromatography/ mass spectrometry (GUMS) of the diurethane. 0
CI H,N-(CH,),-NH,
-CII-OEt
0
II
EtO-C-HN-(CH,),-NH-C-OEt
0
II
EDA (n = 0 ) HMDA (n = 4) Figure 10-16: Chemical derivation of diamines EDA and HMDA with ethyl chloroformate.
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As a result of the pre-validation work, which included a within-laboratory precision experiment carried out in two different laboratories at concentrations of 2.1 mg HMDA and 12.1 mg EDA per kg food simulant, the performance characteristics in Table 10-7 were obtained at the 95 OO/ probability level. Table 10-7: Repeatability values r [mglkg] obtained from two laboratories for HMDA and EDA at concentrations close to the SML values. Food simulant’)
HMDA
EDA
Water
0.30/0.67
0.37/1.5
3 % Acetic acid
0.17/0.62
0.56l0.8
15 % Ethanol
0.13/0.37
0.49/0.7
Olive oil
0.1710.64
0.6810.7
’)
For the substitute food simulants 95 % ethanol and iso-octane a precision experiment has not been carried out. However, from experience with establishment of calibration curves, r-values can be expected to be in the same range as with the other food simulants.
The within-laboratory limit of detection for HMDA was found to be in the range 0.1 to 0.5 mg HMDA/kg (substitute) food simulant depending on the type of food simulant. In case of EDA, the LOD was not determined exactly but was found to be lower than 1 mg EDA/kg (substitute) food simulant regardless of the type of food simulant.
10.2.7 The concept of functionality of validation procedures and precision data for compliance testing As mentioned earlier (Section 10.2.5), there exists a clear need for pragmatic and cost effective solutions to specific migration testing. One possible way to reduce the analytical workload without compromising the requirement of consumer protection with regard to food packaging safety is to follow the policy of functionalizing the extend of validation work and the degree of precision data required. This concept for which the term “ j k c t i o n a l validation & precision” (FVP) is introduced, means that the degree of validation steps to be applied and the amount of necessary precision data to be provided is a function of the analytical demands and the relevance of the migrant or analyte concerned. With respect to FVP, as a general rule, the following maxim is applicable: the more challenging a legal restriction, i.e. the lower the SML or QM value is, the more necessary and justified is the time and work expenditure for validation and production of precision data. and vice versa. The consequence is: in the first place, the analyst has to carry out some basic considerations regarding a healthy ratio between expected benefits and invested time/work load prior to designing and carrying out the analytical validation work. In the following the concept and practical consequences of FVP are explained in more depth. However, first of all, one needs to examine some considerations deviating from the classical analytical understanding. First of all and as a matter of principle, the reader should accept the following premise as a modified understanding of an analytical method: An analytical method may be understood predominantly as a tool for
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compliance testing or, more specifically and since this is the normal case, as a comparative method to prove that a SML or QM value is not or cannot be exceeded. The analytical method may not be understood primarily in the classical sense, i.e. as a tool to determine precisely the exact concentration of an analyte. In principle, the compliance testing analyst has to deal with 3 main categories of legal restrictions: Category I: Authorized compounds on positive lists with very low restrictions. for instance at or very close to the analytical detection limit. In this highly challenging situation the analytical method has to fulfil its classical task, which is to determine the target concentration as accurately as possible and the full extent of validation work is necessary. It is obvious that this does not deserve further explanation, as compromise with respect to the required precision data is not acceptable. Category ZZI: At the other end of the positive list spectrum, are analytes with SML values in the 15 mg/kg to 30 mglkg range such as the PET monomers mono- and diethyleneglycol (MEG and DEG). Such compounds can even be controlled by the overall migration (OM) test itself. So if, for instance, an OM value in the typical range of 6 to 12 mglkg has been obtained for a PET sample, then this could already be considered to be the whole validation process and full set of precision data which is required. In this case, compliance proof has already been achieved with the OM test result. It is important to note that from a purely food regulatory point of view, the accurate MEGlDEG concentration obtained in the migration test is of no interest as long as it can be localized far below the restriction criterion. It should also be noted that this approach is based on experience and supported by modern diffusion models (compare Chapter 15) by which the maximum MEGlDEG migration can be estimated in the 1 pprn range in a food simulant. Taking this into account, development of analytical CEN standard methods for MEG/DEG (ENV 13130 - part 7) (CEN 1999) appear to be a wrongly placed investment. Category ZZ: In between the 2 cases mentioned above, the spectrum of SML values contains numerous “small and medium sized” restrictions. Consequently, category I1 may be subdivided into several subcategories with different requirements for validation and precision. Depending on the target concentration values, more or less validation work may be necessary. This is characteristic of “FVP” and needs to be defined case by case. However, one approach for dealing with this question in a very pragmatic and costefficient way is the method of direct comparative analysis using only one calibration point as a benchmark, at or below the legal restriction concentration. Provided that appropriate safety margins are guaranteed, compliance testing could be achieved in this way very time and cost effectively without posing any risk to consumer health. Logically, the corresponding validation work would be dramatically reduced. The following gives an example to provide a better principal understanding of this approach in practical terms: The relevant migrant or analyte shall have a SML value of 5 ppm (mglkg) and be analyzed by GClFID in food simulants. From the chemical structure and the physico-chemical properties of the migrant the analyst would not foresee any great analytical difficulties and would expect normal linear FID response behaviour. In this case, compliance testing and validation could be achieved simply by fortifying the blank food simulant to a certain concentration. This can be, for instance, 3 ppm (60 70of the SML) or even at 5 ppm (100 70SML), for obtaining just one calibration sample. Then this calibration sample would be analyzed (for instance GC/
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FID) under the same analytical circumstances and in the same test run (same sample preparation etc.) as the migration solution (of the same food simulant) and the blank solution. One must be made certain that all other analytical parameters are kept constant in the different sample solutions and the only variable is the analyte concentration. In the case that an analyte peak in the migration solution is significantly smaller than that of the calibration point, this would demonstrate compliance Of course, depending on the closeness of the calibration sample concentration to the SML, an appropriate one-sided analytical tolerance between the sample and calibrant peaks needs to be defined. What happens in the case that the analyte concentration is in the critical range where it is not smaller than the legal restriction and indeed likely to exceed it? In such a case (which is the exception rather than the rule) a confirmation analysis has to be carried out. This is also the usual practice with standard methods such as the acrylonitrile CEN method where the result of the confirmatory GUMS procedure is taken as the true or relevant value, although this GUMS method has never been approved in a ring trial according to IS0 5725. The confirmatory analysis may be such that the one point calibration is replaced by a full set of calibration points, but using the same analytical principle (GC/FID). If compliance is not clearly shown after that, then confirmatory analysis in the conventional sense, i.e. applying GUMS or another method has to be carried out. In the context of this discussion, it is important to note that the FVP concept can also take account of the plastic type (diffusivity of the polymer) in analogy to the “QM/SML” concept (see Section 10.1.2). In this way, very quick and cost efficient validation strategies based on extraction methods of more severe test character can then be considered. But in depth explanations of such strategies would exceed the frame of this chapter.
10.3 Safety assessment of modern food packaging applications The E U Directive 94/62/EEC on packaging and packaging waste (European Commission 1994) sets out requirements and targets for the reuse and recycling of waste packaging to reduce waste and to save resources. One of the options to meet these requirements is the reuse of food packaging in the sense of refilling used and returned bottles. Well-known examples for many years have been glass milk bottles and in more recent times also plastic containers such as the returnable PET bottle used for soft drinks. Reuse of food packaging in a wider sense can also mean chemical or physical reprocessing, which has been applied for a long time for glass waste and for used cellulosic fibres from paper and board. In the area of food packaging plastics, this topic is of growing concern and its feasibility is under investigation. Indeed and as a matter of fact, considerable progress has been made in this field and different pilot attempts have already entered the European market. Of course, the use of recycled plastic materials in packaging applications has to comply with the regulations and must not be at the expense of public health, nor should it alterate the filling’s quality. But from manufacture to recycling of a package the plastic material is exposed to various influences which may change its composition e.g. uptake of compounds, commingling with other resins and degradation. Particularly plastics are vulnerable to an uptake of contaminants because of their permeable nature. Refilling plastic bottles and recycling plastics for packaging applications for sensitive products such as food-
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stuffs is therefore limited to excellent performance plastics and requires thorough and careful suitability and compliance testing. In the following examples, such modern food packaging applications are presented together with the inherent problems and difficulties in their food safety assessment.
10.3.1 Recycling used packaging plastics into new food packaging Due to modern environmental packaging requirements the question of recyclability of used packaging plastics into new food packaging applications is of increasing interest. This question is currently still enforced since usual market applications for recycled plastics in the non-food area seem to approach saturation. Indeed, recycled plastics have already been used in food-contact plastics for several years around the world. However, these cases must be considered to have more pilot character than real market value and, in most cases, the mass fraction of recycled plastics in these applications was relatively low, due to blending with virgin plastics or sandwiching with functional barrier layers of relatively high thickness extruded also from virgin polymer. Although considerable progress has been made from a scientific point of view in understanding and physico-mathematical modeling of diffusion processes for adventitious hazardous compounds from a recycled plastic in direct contact with food or from a core layer across a functional barrier (Scheirs 1998, Begley and Hollifield 1995, Franz et al. 1994,1996, Laoubi and Vergnaud 1995, 1996, Laoubi et al. 1995, Piringer et al. 1998), the translation of this knowledge about migration into action, i.e. into industrial solutions remains still in a waiting position. One of the reasons has more “European” character, substantiated by the fact that the European legal requirements in this respect are not yet precisely defined. However, in the US a very concrete concept, the so-called “threshold-of-regulation” principle has been established and adopted by FDA. Another reason is clearly the non-availability of simple and economic test methods which in addition would need to be at least generally accepted procedures and, at best, standard test procedures. Due to the lack of regulations within the currently harmonized Europe, the Member States treat this modern challenge individually according to national laws or recommendations. In Germany for instance, it is in principle not forbidden to use recycled materials for direct-contact foodstuff packagings. A statement ( B g W 1995) in a document from the “Kunststoffkommission des Bundesinstituts fur gesundheitlichen Verbraucherschutz und Veterinarmedizin” stressed that the reuse of recycled plastics in foodstuff packaging is legally not excluded. However, the document demands that recycled plastics have to meet the same legal regulations as required for virgin plastics, particularly the requirements of $3 30-32 of the “Lebensmittel- und Bedarfsgegenstandegesetzes (LMBG)” and those of the “Bedarfsgegenstandeverordnung” (which is the nationally implemented European Directive). The BgVV document further demands explicitly that there must not be any risk of health danger to the consumer from any goods made with recycled materials. Moreover, no measurable sensory damage or impairment to the product should result from use of the recycled packaging material. Finally, the document states that it is the responsibility of the company using the recycled packaging to prove that it is suitable from a legal standpoint. It should also be noted that the BgVV document clearly provides no hindrance to the introduction of a suitable test method.
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In the USA, there are also no specific decrees or directives for packaging made from recycled materials. However, the Food and Drug Administration (FDA) has published some basic information about the conditions of use of recycled plastics in food packaging applications (US FDA 1992). This information is based on current legislation in the USA and has the backing of American industry (US NFPA 1995). The safety and quality assurance principles involved here concern three fundamental elements: - Control of the source of raw materials (recycling control), - The effectiveness of the purification steps in the recycling process, - Conditions for the application of the recycled packaging materials. As a judgement criterion, the FDA uses the so-called “Threshold-of-Regulation” concept (US FDA 1993b) which orientates itself on the maxim “De minimis non curat lex”. This concept is backed up by extensive scientific evaluation of toxicological data (Rulis 1986) and also tolerates the transfer of unknown substances into foodstuffs as long as a threshold concentration is not surpassed. This threshold, relating to average dietary intake, is set at 0.5 ppb (0.0005 ppm) and is primarily independent of packaging type and packaging material. By applying so-called “Consumption Factors” (CF) which take account of the percentage of plastics types used in food packaging, the concentrations actually allowed are increased (depending on polymer type). For example, in the case of PET (CF=O.OS), the concentration permitted, for instance in a soft drink, is increased by a factor of 20 to 0.01 ppm (10 ppb).
10.3.2 Recycled plastics covered by functional barriers First of all it should be mentioned that the so-called functional barrier concept corresponds to nothing more than the well-known important classical function of a food packaging material, which is to protect the food against external influences. The requirements are that the food contact layer has to act as a barrier against contamination from the packaging’s environment in general and more specifically from the recycled core layer or outer compartments of the multilayer packaging structure. The published studies on functional barriers to migration have focused predominantly on the question of reusability of recycled plastics for food packaging. This unfortunately, generated such a very rigid link between the terms “recycled plastics” and “functional barrier” that it is often forgotten that the functional barrier concept has general relevance and is applicable to any multilayer structure. It is well known that there is only a very limited number of packaging materials which provide absolute protection properties against penetration by chemical compounds. Therefore, the mass transfer from outside through a packaging (permeation) or from a packaging into the food (migration) can generally not be limited to zero. As a consequence, in most cases an unavoidable mass transfer occurs to a certain extent. This must be understood as a functional quantity which, however, must also comply with food regulations, for instance Article 2 of Framework Directive 89/109/EEC. Therefore, functiona1 barrier efficiency needs to be defined beyond the toxicological meaning (requirement: US-FDA threshold-of-regulation concept) to cover also purely organoleptic food quality considerations. Concerning the efficiency definition of a functional barrier, different understandings seem to exist. On the one hand and in most of the published cases in the litera-
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ture, functional barrier efficiency is related to the mass migrating into a foodstuff, thus allowing a comparison of resulting measured concentrations in the foodstuff with given legislative limits. On the other hand, there is also a time-related understanding which links the F B efficiency to the lag time for the start of migration. The latter definition seems to be questionable since the lag time itself is a priori not linked with a migration-related concentration in a foodstuff or simulant. Exceeding a lag time docs not automatically also mean exceeding a threshold concentration. But a threshold concentration can already be exceeded before the lag time (understood in the classical sense) has been reached. Physically, this can be explained by the non-idealistic behaviour of the migration front and can be recognized from the initial part of a typical permeation curve before the steady state has been achieved (Chapter 7). In the published literature only a few attempts have been made to tackle the functional barrier problem by experimental and theoretical approaches. Most of the papers present a mathematical model solution based on the assumption that the contaminated recycling layer was burried by a contuminunt-free virgin functional barrier layer just after its manufacture. However. other studies (Franz et al. 1997, Piringer et al. 1998) have recently demonstrated that, since multi-layer plastic structures are mostly manufactured under coextrusion conditions where extreme temperatures far above the melting point of the plastic arc applied, a significant inter-diffusion is in reality occurring between the in situ formed polymer layers. Taking into account coextrusion temperatures up to 280 “C it can be estimated, depending on the polymer type and thickness, that middle layer contaminants are penetrating the functional barrier layer partially or completely within a time range of seconds down to fractions of one second. As a consequence, more or less significant impurification of a “virgin” functional barrier layer is likely to occur during manufacture, which compromises and reduces the originally designed functional barrier efficiency. It can even result in the possibility of complete penetration, with the consequence of already having direct food contact with contaminants originating from the middle layer at the start of migration, i.e. after the time point when the foodstuff is filled into the packaging. From the above discussion, one can summarize that functional barrier efficiency does not correspond to an absolute barrier requirement but is related to a “functional” quantity in terms of mass transfer which is dependent of the technological and application-related parameters of the respective food-packaging system. These parameters are: - manufacture conditions of the package - thickness of the functional barrier layer - type of functional barrier plastic - molecular weight and chemical structure of penetrants (contaminants) - concentration and mobility of contaminants in the matrix behind the functional barrier - time period between manufacture of packaging and filling - type of foodstuff, i.e. fat content, polarity etc. - filling conditions and storage (time, temperature) of the packed foodstuffs
How cun the efficiency of functional barriers he verified or tested? Currently, there are two different test principles which have been described and applied in practice:
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A. Migration testing of deliberately contaminated packaging structures using incorporated model contaminants or surrogates. B. Migration testing of real-life recycling packaging structures by monitoring inherently present recycling-related substances. Procedure A has been proposed by the US-FDA and incorporates model contaminants or so-called surrogates into the packaging material. This approach is probably the best choice for individual functional barrier efficiency testing of a given test structure. Despite its individual test character, this procedures also allows the collection of fundamental knowledge on functional barrier packaging design. In fact, recent studies have applied this test approach to validate a physico-mathematical model which is able to describe migration across functional barriers even when they are already partially impurified due to the extrusion process-related in-situ contamination (Franz et al. 1997, Piringer et al. 1998). This migration model subdivides migration out of a contaminated core layer into two separate steps theoretically, one of them being migration from the core-layer into the functional barrier and the other being migration into the foodstuff itself. The other and much more essential key element of the model is to give a solution to the problem of the remaining functional barrier efficiency after the manufacture process. An important conclusion from this study is that the crucial impurification step of the functional barrier occurs during co-extrusion. Compared to this effect, room or slightly increased temperature storage of the packaging material before the time point of filling can be considered negligible. Finally, it was discussed that on the basis of the presented model, migration prediction seemed to be feasible also for functional barrier packaging structures, thus also here offering (and not only with monolayer plastics) a possibility of applying QM/SML relationships for food regulatory purposes in future (see Section 10.1.2). A remarkable drawback of procedure A, however, is that working with surrogates for incorporation in packaging materials is a very laborous process and only possible with special precautionary measures. Therefore this test approach, which has to be applied case by case, again implicates an economically disadvantageous situation. In addition, enforcement laboratories cannot make use of this method. Procedure B has been developed and proposed by Fraunhofer I W (Franz et al. 1994) without incorporating model contaminants. It is a “black-box’’ approach which monitors inherently present recycling-related substances and is applicable to a readyto-use food contact article. In this way, the procedure meets not only the R&D and quality assurance requirements of the manufacturer but also offers a test possibility for enforcement labs. Essentially, procedure B consists of two experimental key steps: (i) Extraction of the packaging material for determination of the migration potential and characterization or identification of recycling specific substances which can serve as indicator compounds to be monitored in the migration test (ii). (ii) Migration testing both under prescribed and more severe conditions. The extent of test work depends on several factors, such as the test packaging structure, the migration potential found under (i) and the practical application itself, i.e. type of foodstuff, filling and storage conditions. In the most advantageous case, only step (i) is required. Important information can be obtained during key step (ii) from additional migration testing under more severe conditions (for instance higher temperature and/or stronger extracting solvent). This introduces a kinetic factor into the test and allows one to consider a possible lag phase effect of the functional barrier layer. From the findings measured under the exaggerated test conditions, migration
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test results likely to be obtained under normal or application-related conditions can be extrapolated down to concentrations far below analytical detection limits. To explain: if one obtains data from two migration tests where one is carried out at 20 "C and the other at 40 "C (under otherwise the same conditions), in each case using the analytical detection limit (which in both cases is the same) as a migration test result, then the real migration value at 20°C must be much lower than the concentration corresponding to the analytical detection limit achieved. The following describes a typical case study representative for test principle B (Franz et al. 1994): Test material was a coextruded three-layer polypropylene (PP) cup of symmetrical structure with recycled post-consumer PP in the middle layer (mass fraction 50 Yo)and virgin food grade PP in the adjacent layers. The recycled PP, which contained about 95 YO PP and 5 YO PS, was completely under return control in the recollection system and had been used in its prior application for packaging yoghurt. The intended application for the recycled material was again packaging milk products such as yoghurt with storage for short times under refrigerated conditions. The point of interest was the functional barrier efficiency of the virgin PP food contact layer under the intended storage conditions. In addition, it was the aim of this R&D research work to establish a simple and cost efficient quality test procedure for future production. This was one of the reasons why procedure A using incorporated model contaminants was not applied. Therefore, the working strategy was to compare the recycled plastic with new, food grade plastic material of the same type. This comparison experimentally included three investigation levels: (1) Compositional analysis of the raw materials (virgin and recycled PP granules), (2) compositional analysis of the food contact articles (virgin and recycled cups), ( 3 ) migration testing on both types of cup (virgin and recycled) under prescribed (10 days/20"C with 3 YOacetic acid) and more severe test conditions (10 days/ 40°C with 3 YOacetic acid, 35 YOethanol or 80 YOethanol). First of all, from levels (1) and (2) the intention was to characterize and if possible to identify and quantify recycling-related (R) polymer components (migrants). Then, R-components with relatively high concentrations should serve as indicator substances to be monitored in migration measurements on level (3). The realization of this principle is demonstrated in Fig. 10-17. In the upper and middle gas chromatograms it compares the components extracted from a virgin and a R-PP cup. This comparison allows immediately assignment of R-substances. In the lower gas chromatogram of Fig. 10-17 one can recognize which of the R-substances really migrate in measurable amounts under the most severe test conditions applied in this investigation. Migrating R-substances are only such with short retention times, i.e. low molecular weight and volatile components. The major component among them was identified as limonene, an aroma or flavour compound which can be found in many foodstuffs and also in the non-food area. The results obtained in this study can be summarized as follows: None of the R-substances could be analytically detected in the food simulant (at a detection limit of 13 ppb) under prescribed migration test conditions. However, from the results obtained under more severe test conditions, it could be concluded finally that the R-substance with the highest migration, limonene, could not migrate into a milk product with a concentration higher than 1 ppb. This concentration is more or less equal to the US-FDA threshold-of-regulation concentration (TRC). With regard to the other R-substances it could be estimated that they migrate far below the TRC. Concerning further quality assurance tests, it turned out that it
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A
A B.0
5.0 4.0
3.0
0.00
10.00
eo.oo
R 7 . 0
R. 30.00
40.00
0
5.Q A.0
3.0 0.00
10.00
20:oo
40100
I1 4-
t
3.8
A
(Limonene) R
3.2
3 .O O D D
8
10.00
I 20.00
8
30.00
8
40.00
Retention time [min]
Figure 10-17: Gas chromatograms of extracts of a virgin (upper) and a recycling PP cup (middle) as well as a migration solution (80 % ethanol, 10 days/4O0C) obtained from a recycling cup (lower picture). Abbreviations: 0 = Oligorner; A = antioxidant: R = recycling-related substance; b = interfering peak from the solvent.
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would suffice to carry out only compositional analysis of the raw materials comparing any future recycled PP granules with the reprocessed PP material of this study as a reference material. The two princicpal test approaches A and B should not be considered suitable only for multilayer plastic structures. Other packaging structures can be tested by the same principles: for instance polymeric coatings on paper and paperboard where the question of functional barrier efficiency is also very important. However, due to the fact that paper as a core layer material is completely different to a polymer and that in most cases very thin films of polyolefins are used as food contact layers, correspondingly specific considerations have to be taken into account. One of the interesting issues in this context is related to the diffusion of inorganic compounds across these very thin polyolefin films. The permeation of organic compounds across such films has been extensively investigated, with the result that plain polyolefin films do not provide efficient barrier properties against organic compounds such as toluene, limonene etc. However, there is very little published about the permeation behaviour of inorganic compounds. Recently, a study was presented about the diffusion behaviour of CuC12, dissolved in various ethanol-water mixtures, across LDPE films at different temperatures (Hampe and Piringer 1998). It was found that the diffusion was very dependent on ethanol concentration. Only at very high ethanol concentrations (8s-100 YO)and relatively high temperatures (60 "C) could measurable permeation results be obtained. The values for the diffusion coefficient measured at 60 "C in 85 YO to 100 YOethanol ranged from 3.4 x cm% to 1.2 x lo-" cm2/s. From the values measured at 60 "C and 40 "C, diffusion coefficients at 20 "C can be estimated for high percentage ethanol in water (80 YOto 100 YO)to range between 1 x cm2/s to 3 x lo-'' cm2/s. For highly aqueous systems (0 YOto 20 YO)such an estimation is nearly impossible. However, the diffusion coefficients are likely to be much smaller than 3 x cm2k (possibly orders of magnitude lower). An attempt to estimate lag times from this for inorganic compounds like CuCI2 across thin LDPE films under practical conditions, i.e room temperature and highly aqueous systems, would lead to predicting a range between over 2 years up to 50 years or even more depending on the film thickness (10 to 50 pm). This demonstrates impressively the barrier properties of polyolefin films against inorganic structures in general. As already mentioned above, the question of reusability of plastics represents only one specific modification of functional barrier packaging design. Mass fractions of recycled plastics burried in this way range currently between 25 YOand 50 YOof the whole package structure. However, it is obvious that the economic benefit correlates with increasing the recycled mass fraction. In the almost ideal case, a homogeneous recycled plastic layer would be covered by extremely thin films with high barrier properties. Such developments have been on the market already for a long time, produced however with another intention: for instance barrier coated polymer films such as metallized, biaxially oriented polypropylene films or acrylic- or PVDC-coated films. Such thin layers were found to improve barrier properties against organic compounds by a factor of 1000 compared to the plain BOPP film (Franz 1995). From these results it can be assumed that such barrier principles are likely also to provide functional barrier efficiency against recycling-originating contaminants. The ideal case and most efficient recycled plastics packaging design, however, is the plain recycled mono-layer with direct food contact. This situation is described in the next section.
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10.3.3 Recycling of post-consumer PET for direct food contact As discussed in 10.3.1, there is an observable industrial hesitation to introduce environmentally friendly packaging solutions to the market based on recycled materials such as the closed-loop bottle recycling. Reasons for that have also been mentioned. Another reason for this hesitation can be found in the current lack of simple and economic test methods which in addition would need to be at least generally accepted procedures and, at best, standard methods. Currently available are the guidelines developed by the FDA and the US Food and Plastics Industry some years ago. These guidelines, however, were established on the basis of a very conservative approach in order to avoid any risks for the consumer. From today's point of view and with our knowledge increasing all the time, these guidelines prove too conservative and require unnecessarily enormous efforts in the performance of the underlying tests. These test schemes, also known as challenge tests, are challenging a recycling process by the artificial introduction of model contaminants, so-called surrogates. They check the cleansing efficiency or surrogate removal potential of this process including, if necessary, migration testing of food contact articles deriving from recycled plastics. In Europe, the results obtained from a European Project, AIR2-CT93-1014 (Castle 1997, Jetten et al. 1999), dealing with the question of recyclability and re-usability of food contact plastics for new food packaging applications, have been taken into consideration by a Packaging Material Expert Group on Plastic Recycling Guidelines. As a result, this expert group has recently published its conclusions on this topic as a guideline document more appropriate to the current state of the art in this matter (ILSI Europe 1998).
A challenge test case study and evaluution scheme The following describes a research work investigating the feasibility of recycling post-consumer PET into new direct food packaging (Franz et al. 1998). One of the interesting points in this study was the purification potential of modern industrial recycling processes, which are able to produce high quality recycled PET granules. Another point of interest was the question how far the actual knowledge about diffusion and migration estimation can be applied to evaluate the suitability of the recycled PET materials at the level of the granulate itself, in order to decide whether or not there is a need to carry out additional migration tests with the food contact articles manufactured from the recycled raw material. Probably the best way to investigate these items is to apply challenge tests to the recyling processes of concern. Therefore another aim of this work was to draw up a modified challenge test for post-consumer poly(ethy1ene terephthalate) PET material in order to make the test more economic and user-friendly, for instance by shortening the FDA-recommended 14 days/40 "C sorption or soaking conditions for the surrogates. A further point of interest was to design the contamination scheme in such a way that only the minimum amounts of solvent and chemical contaminants were necessary, thus avoiding production of unnecessary amounts of hazardous waste. With such optimized framework parameters, the main intention was then to evaluate the cleansing efficiency of a new commercial recycling process for postconsumer PET material collected from used soft drink bottles with the simplified challenge test. The results were expected to give a better understanding of the contaminant removal potential of the particular recycling process.
Migration of plustic. constiricents
345
The recycling process The process consisted essentially of three key steps: washing and heat-drying the incoming PET flakes obtained from grinding used soft drink bottles, (ii) remelting the PET flakes from (i) for extrusion to form new PET granules and (iii) additional solid-phase condensation, using a high vacuum high and temperatures nearly up to the melting point of PET.
The challenge test For challenging the recycling process, virgin PET flakes obtained from ground bottles were contaminated with model contaminants or so-called surrogates of different chemical structures and physical properties. The surrogates were chosen such that they represented the four FDA general categories of chemical compounds: volatile and non-polar, volatile and polar, non-volatile and non-polar and, finally, non-volatile and polar. Additionally, a wide range of functional groups was used in order to reflect the different chemical and physical properties of real-life contaminants (see Table 10-8). Table 10-8: List of the surrogates used for thc contamination cocktail, with chemical structures and properties. ~
~~
~~~
~
Substance
Structure
Functional group
Properties
l.l,l-Trichloroethane
CHyCCI3
Halogenated hydrocarbon
Volatile. polar, aggressive to PET
0
Hydrocarbon
Volatile, non-polar
Halogenated hydrocarbon
Volatile, medium-polar, very aggressive to PET
Hydrocarbon
Non-volatile. non-polar
Toluene
Chlorobenzene
Phenylcyclohexane
1-0ctadecanol
Methyl stearate
a,
I "
6
CH~CHZ)I.IOH CH3(CH2),,COOCH3
Non-volatile, polar
Alcohol
Non-volatile, polar
Ester
Non-volatile. polar
The contamination and the challenge test were carried out several times, starting at three different initial concentration levels of surrogates in PET flakes in order to check the purification efficiency over a wide concentration range. The expectation was that this test scheme would allow an extrapolation of the results to higher or lower initial concentration levels not actually measured in our challenge test. The contaminated PET flakes were then processed through the industrial purification process, entering the process at step (ii) and omitting the washing and heat drying procedure. This protocol was justified by the fact that the cleansing efficiency of a normal wash-
346
Franz
ing step is well known and well documented in the literature and because the washing conditions of the investigated process were no different to conventional washing procedures. Therefore, step (i) was omitted with the contaminated PET flakes going directly into the remelting/extrusion process. It should be noted in this context that even when the flakes are not homogeneously contaminated after contact with the surrogates, such a procedure leads automatically to a homogeneous distribution of the surrogates in the extruded granules. PET samples were taken at the beginning and at sampling points during this process and analysed to determine the concentration of surrogates in the PET material both before introduction into the process and at any relevant stage during the process. Table 10-9 summarizes the results obtained by presenting the relative concentrations of surrogates as a percentage of the initial concentration after step (ii), i.e. remelting to granulate and after step (iii), i.e. in the post-condensed final product. Table 10-9: Percentage recovery of the initial concentration in ppm of the surrogates in the PET material after remelting in the granulate (step (ii)) and in the final product (step (iii)). ~
Initial concentration Toluene
Chlorobenzene
Benzophenone
Octadecanol
Methyl stearate
granules after step (ii)
17
,K I OH
printed PAtlonomerlaminate
Diacetone alcohol
I
t
1
-
lonomer layer
0
t Ham as H2 S - souw
I
0
SH
Figure 1.7-5: Formation mechanism of the off-odor-compound.
The cases described in these examples confirm the variety of interaction possibilities between components of the packaging and filled product. In addition these components must be considered in extremely low trace amounts for the quality assurance of the product.
13.4 Parameters determining odor and taste Article 2 of the framework directive 89/109/EEC forbids the alteration of the sensory properties of food by the transfer of substances from food contact materials. However, this does not represent absolute sensory neutrality. This principal is not defined just for the packaging but is rather a function of the properties of the packaging, the food and their compatibility. The avoidance of complaints and damages is the reason for desiring knowledge of threshold limits of sensory-active substances in packaging materials. With this knowledge, instrumental quality control analysis of packaging materials can be carried out as a preventive measure. Whether or not a certain substance in a given application leads to a perceptible quality change and with it a violation of food regulations depends on numerous parameters. Therefore, no generally valid limit value can be assigned to a substance in comparison to toxicologically relevant substances. The influence of a sensory active component from the packaging on the product is largely determined by the following parameters (Granzer et al. 1986):
420 -
Piringer
Concentration of component in packaging material.
- Solubility of component in packaging material
(partition gas phase/packaging material). Solubility of component in food (partition gas phase / food). Sensory threshold level of component. Type and intensity of food aroma. Diffusion rate of component in packaging material. - Diffusion rate of component in food. - Time and temperature of storage. - Ratio of amount of packaging material to amount of food. Knowledge of these parameters makes it possible for a case by case determination of the limits for avoiding a reduction in quality. The lowest concentration of a substance in air sufficient to give a perceptible odor is defined a the absolute threshold level and is designated OT, in the following (see Table 13-3). A criterion for the selection of a solvent for use in packaging manufacture, e.g. for printing inks, is a possible high OT, value between 10 and 100 mg/m3. The threshold levels of solvents contained in parenthesis in Table 13-3 serve to give a slightly better differentiation between different solvents. The published threshold levels from various authors can in general vary over three orders of magnitude for a given compound. This widely scattered range is partly due to the imprecise definition of the perceptible sensory concentration as either a stimulation- or recognition-threshold and partly due to the different study set-up for the determination of OT, values and the sensitivity of the test participants. In addition, formerly the olfactometer was used almost exclusively for the determination of absolute threshold levels. With this equipment it is not possible to separate the substance being studied from traces of odor active contaminants and therefore to eliminate the possibility that the presence of such contaminants may lead to completely wrong OT, values. The possibility of separating contaminants from the main odor active substance using GC eliminates the largest source of error in these measurements. However, several requirements must be fulfilled to obtain reproducible investigations. The values listed in Table 13-3 are averages of several measurements and published values. The partition coefficient is important in the sensory influence of an aroma compound on food (Chapters 4 and 9). The partition coefficients includes those of the substance between the gas (atmosphere) and packaging material, KGIP = cG/cR and between the gas and food, KG/F = CG/CF, as well as the resulting partition coefficient between the packaging material and food, K ~ / = F KG/F/KG/~ = CP/CF= S,. Here the corresponding concentrations in the packaging material, food and gas are cR cF and CG In Table 13-5 the K G values ~ and diffusion coefficients, DF, are given for several solvents in a selection of liquid, fatty and solid foods at 23°C. It is notable that the limits for the parameters lay four orders of magnitude apart in comparison to the narrow range of the relative molecular masses M, and boiling points TB of the pure solvents. The K values of a strongly polar solvent, e.g. ethylene glycol, can vary over three orders of magnitude depending on the polarity of the food (related to the food’s water content), while a medium polar solvent has a much smaller range. The KG/Fvalues in aqueous systems for the solvents listed in Table 13-5 can be used as approximate values for other solvents with similar structures. The aromatic hydrocarbon, toluene, is in this respect an exception where its partition coefficient in the aidwater system has a value of KGIF= 0.5.
-
421
Sensory problems caiised by food and packaging interactions
Table 13-5: Partition (KCIF)and diffusion (DF)coefficients of several solvents in a selection of liquid, fatty and solid foods at 23 "C. M, = relative molecular mass. T s = boiling point. Solvent
Food
Mr
TB
Ethylacetate
Coconutfat
88
77
"C
Sof tcheese
Buttercookies Water Methylethyl ketone
Coconutfat
72
80
Softcheese Buttercookies
Ethanol
Ethylglycol
K ~ , lo3 ~ .
DF. 10' cm*/s
1.5
1.3*
4.0
0.3
15.0
3.0
5.3
-
1.3
1.5*
1.9
0.5
12.0
3.0
Jam
7.7
-
Water
1.7
-
Coconutfat
46
78
7.7
0.9*
Softcheese
0.59
1.2
Buttercookies
9.1
3.1
Jam
0.91
-
Water
0.29
-
0.23
-
Softcheese
0.02
0.5
Buttercookies
2.2
-
Jam
0.53
-
Water
0.006
-
Coconutfat
90
135
* at 0°C Compared to the KG/F values, the DF values can hardly be differentiated. The measured values in the order of magnitude of l.104 cm2/s lay between that for liquids and those for plastics (< lo-'). These values are in agreement with the firmness of the fatty food studied. The small variation of the diffusion coefficient allows the values in Table 13-5 to be used for other solvents as well. The DF values investigated allow a simple estimation of the rate of penetration of the solvent into the fatty food with the help of the formula (Chapter 7):
(13-1) where dF.tis the average penetration distance of the solvent into the food up to time t. A diffusion coefficient DF = 1.2 . lo4 cm2/s for ethanol in soft cheese corresponds to a penetration of approximately 0.5 cm/day or 8.7 cm/year at 23 "C. Attention should be given when determining odor or taste threshold levels for a substance in a food or other testing medium, that during the "taste test" the compound studied can be detected in the gas headspace in contact with the food where the partition coefficient KG/Fplays an important role.
422
Piringer
One defines the relative threshold level of a substance over a food to be the lowest concentration of the substance in food leading to a perceptible odor in the gas headspace over the food at equilibrium. The relative threshold level is designated by OT, and has the relationship: (13-2) The density of the food is designated pF. The relative threshold values of solvents in several foods are contained in Table 136. The values were determined by placing a dilution series of solvent in weighed amounts of food in sealable glass containers and equilibrating overnight at 23 "C. Each test series was composed of a minimum of eight dilution levels (Ruter, 1992). A scattering of the threshold levels over an order of magnitude is due to the different sensory sensitivity of individual test persons. This relatively narrow region allows the formation of mediated values for the establishment of simple characteristic numbers. However, for sensory evaluation, the lowest value of the most sensitive tester must be given consideration since complaints often originate because of complaints from such sensitive consumers. The sensory evaluation differentiates between the stimulation threshold (a just detectable level where a perceptible but not yet definable deviation of the sample from the standard is observed) and the recognition threshold, a level where the odor is identifiable or creates odor problems (a no longer tolerable quality deterioration caused by a definite off odor andlor taste). The difference between a perceptible and identifiable level is usually only one to two steps of a geometric dilution series. Therefore, only undifferentiated odor and taste thresholds are given in Table 13-6, because of the very different sensitivities of individual testers. The perceptible (stimulation) levels of a less sensitive tester can overlap with the identifiable (recognition) level of another more sensitive tester. Table 13-6: Relative odor and taste thresholds of several solvents in different food. OTJmglkg]. Potatochips Solvent
Odor
Cyclohexane 50-100
Taste
Jelly-Bears
Coffee Odor
Taste
100-1000 SO(k1MW) 200-500
Toluene
20-500
Acetone
20-1000 1W2000 100-2000 1000-5000
20-100
100-500
Methylethylketone
50-200
Taste
20-50
500-1000
Odor
Taste
100-500
1GOG2000
20-25
20-25
100-SOO IOW-2000
20-100
50-100
500-loo0
50-100
100-500
50-500 100-500
200-300
50-100
10-50
20-50
500-2000
20-100
50-100
10
5C.500
500-looO
20-50
50-100
Ethylacetate
10-50
10-100 100-1000
Isopropylacetate
1GS0
50-200
Ethanol
10-20
Odor
100&3000 100-2000
Chocolate
50-100
200-1000 200-2000 500-2000 5000-20000
Isopropanol IW1000 1000-3000 500-1000
500
1-Ethoxy-2- 100-1000 500-2000 500-1000 200400 propanol
2000 1W500 500
1000-2000 500-2000 1000-2000 2000
500-1000 1GOG2000
1000-2000 500-loo0
5Oo-lOOO
Sensory p r o b l e m caitsed by food and packaging interactions
423
Ethyl acetate, one of the most common presently used solvents for printing food contact materials, could cause many sensory problems with its very low odor threshold of 10 mg/kg. Assuming a complete transfer of ethyl acetate from the packaging into the product, it is calculated that the threshold level in Table 13-6 is reached with a package surface area to product mass of > 1 m2/kg based on a content in the material of 10 mg ethylacetate per m2. This could only be the case for small packages or for foods with a low fill weight (e.g. potato chips). With the present state-of-the-art technology the residual amounts of ethylacetate are usually under 10 mg/m2 and can be monitored analytically without difficulty. The relative threshold levels of acrylates and methylacrylates in test foods are contained in Table 13-7. The threshold levels pass through a minimum at the ethyl esters. The values of the acrylates lay approximately an order of magnitude lower than the methylacrylates. The influence of the partition coefficient KG,F can be easily seen when comparing the threshold levels of 2-ethyl-hexylacrylate and acrylic acid. Even though the relative threshold level of acrylic acid is only three times higher than that of the ester, the relative threshold level of the acrylic acid in water is 100 times higher than the ester. This is the consequence of the good aqueous solubility of the polar acrylic acid and the small K G / F values. In sunflower oil the K C / F value of the unpolar ester is much smaller than that of the large acrylic acid value, although the relative threshold levels of the two compounds are practically identical. The relatively small values of acrylic acid in the presence of ethanol as well as acetic acid can be caused by a partial ester formation and a small amount of dissociation along with a high partial pressure over the solution. Table 13-7: Relative odor thresholds of acrylates and methacrylates in test foods, OT, [mg/kg]. Compound Methy lacrylate Ethylacrylate
Water 0.005-0.01 0.0001-0.002
Sunflower-oil
0.005-0.2
0.00141.0s
0.001-0.01
0.01-0.1
0.000541.000~
0.0054.2
0.24
0.014.2
0.01-0.1
0.5-10
0.5-10
0.05-2
0.05-1
0.054.5
0.2-10
0.05-1
0.054.5
0.002-0.02
0.1-1
2-Ethyl-hexylacrylate
0.0054.2
Methylmethacrylate
3 v-% Acetic acid
0.005-0.1
n-Butylacrylate
Acrylic acid
10 v-% Ethanol
0.0054.2
0.05- I
0.02-0.2
0.01-0.1
n-Butylmethacrylate
0.01-0.1
0.14
0.05-0.5
0.05-0.5
2-Ethyhexylmcthacrylate
0.02-0.5
0.5-10
0.05-0.5
0.054.5
Et hylmethacrylate
Methacrvlic acid
0.002-0.05
2-1 00
2- 100
13.5 Derivation of threshold concentrations of sensory-active compounds A finished packaging material for a specific food, e.g. a roll of printed laminate film, often possesses a certain individual odor. Even though from a food regulatory view only the transfer of odor substances to the food is important and not the individ-
424
Piringer
ual odor of the food contact material, the package filler will often evaluate the incoming package material for odors. This case becomes important when a more sensoryneutral product is offered by another manufacturer or when samples from previous deliveries are found to have less odor. Here the interesting question becomes the total amount of sensory-active substance that can be transferred to the packed food. It is simplest analytically to determine the mass of the odor compound per unit mass of packaging material, cp, in mg/kg (ppm) or the mass based on the unit surface area of packaging cb in mg/m2. It should be mentioned here that in the case of packaging material (e.g. laminate films) with a impermeable aroma barrier in the packaging material, transfer is important only in the permeable layer between the food and barrier layer. On the other hand in the case of a semipermeable packaging material a fraction of the odor compound contained in it is lost into the atmosphere during storage. In the derivation of an allowable upper limit for the concentration of a certain odor in a packaging material, it is assumed in the first approximation that a complete transfer of the odor compound into the food occurs. The maximum value of the odor concentration in the food by complete transfer from the package (which can practically never be reached for the above mentioned reasons) is: (13-3) where mF and mp are the mass of the food and packaging material and A is the inner surface area of the packaging material. Setting c b A / m ~equal to the relative threshold level OT, from equation 13-2 then one obtains the maximum allowable amount of an odor substance in a packaging material c;.,,~: (13-4) The threshold level of a substance can be decreased by the presence of less sensorically active substances. In a mixture of ethanol, ethylacetate, ethyleneglycol monoethylether and toluene, the odor threshold level of ethyl acetate was reduced to half and in the case of cookies a factor of 5 decrease was observed. A reason for this finding may be the adsorption process taking place in the solid food. Compared to the solution processes in the complete food, the influence of other components on the ethyl acetate partition coefficient during a simple adsorption on the surface is likely to be larger. The repulsion of ethyl acetate from the surface increases its partial pressure over the food. In the previous discussion of the limit value concentration, the influence of solubility of the odor compound in the packaging material on the limit value has been ignored. When one takes into consideration the KP/F value than in equilibrium one gets instead of Eq. (13-4): (13-5) This expression is a realistic approximation even though it is assumed here that no diffusion of the aroma substances into the atmosphere takes place. The relative solubility KPF of the aroma substance in the packaging material can play an important role in critical cases (high A/mF values) where the ratio mP/mFassumes a maximum
425
Sensory proh1erii.s cniisecl bjl food cind packaging interactions
value for a certain packaging material. If polyolefin packaging material is used for aqueous foods then Kp/F > 1 particularly in the case of weakly polar odor compounds, e.g. toluene. The threshold level concentration of the odor compound can also be greatly increased by its high solubility in the packaging. The threshold level according to Eq. (13-5) are not established regulatory levels. However, when these levels are exceeded, their negative influence on the food and subsequent conflict with Article 2 of the Directive 89/109/EEC cannot be ruled out. In the above discussion it is assumed that during storage a partition equilibrium is established between the packaging and food. However, this is not always the case. Given the time tllz, which is the time required for half of solvent contained in the packaging material to be transferred to the food, then one gets: (13-6) where dp is the thickness of the packaging layer and DP is the diffusion coefficient of the odor compound in the packaging material. It is assumed that single sided migration from the material layer takes place. The tliz values for different DP values are found in Table 13-8. It can be seen from this that with packaging materials with DP < lo-'' cm2/s,for example the polyolefins, the residual solvent can be transferred to the product in a relatively short time. Table 13-8:
dp
1PmI
t1,2
values for different Dp values.
10-8
10-9
Dp [ c m b ] lo-"' lo-.l
I
10-'2
10-13
tu2
10
[hl 0.005
[hl 0.05
SO
0.14
1.4
14
100
0.54
5.4
54
200
2.2
222
22
[hl 0.54
[days1 0.23
5.7
Pays1
2.2
Pays1
23
57
570
23
223
2250
91
910
9100
As already shown above, diffusion in a solid food, e.g. a soft cheese, occurs very slowly and as a consequence the equilibrium state is not reached during the storage time. For time t < t1,2 one calculates the penetration depth dEt of the odor compound in t h e food with Eq. (13-1). The diffusion coefficient of the odor compound in food is given by DF. The average concentration cEt of the odor compound in the outer layer of the food having a thickness of dEt can be estimated by the equation (Chapter 7): (1 3-7) Upon further storage, the concentration in the outer layer decreases until it reaches the equilibrium concentration. The duration of this decrease depends on the DF value and this can decrease rapidly with decreasing temperature. Because of this it is possible to get a concentration of odor compounds in a thin external layer of frozen foods.
426
Piringer
Upon rapid thawing of the food the high concentration of odor compounds in the outer food surface layer it is possible to experience a perceptible sensory effect that may exceed the threshold concentration of c;,,,~. Given a 50 pm thick film with a density of pp = 1 g/cm3, a residual solvent concentration of 100 mg/dm2, DP = 1.10-* cm%, a package area to food mass ratio of 6 dm2/ kg and DF = 1.104 cm2/s,one calculates the initial concentration in the food at tl12to be cE1= 160 mg/kg in the food layer thickness of 313 pm in contact with the packaging material, assuming transfer occurs only into the food from the packaging. This concentration falls to 10 mg/kg after 1.3 days and after 13 days when cool, if one assumes that the diffusion slows down by a factor of 10 at the cooler storage temperature. A final comment is needed on the sensory influence of residual solvents where sensory-active substances present in printing inks can lead to off-odors, for example components in mineral oil used for offset printing. The isolation, identification and quantitative analysis of such traces is very difficult due to the complex composition of the printing inks in which most of the relevant sensory compounds are covered up by unimportant compounds. As a rule no satisfactory correlations have been shown to exist between the total amount of volatile substances or the amount of substances with functional groups and the actual sensory active components. The best way in this application is the testing of the finished package for its global odor and then the transfer of this odor to test foods (e.g. grated milk chocolate). It is furthermore recommended that the paperboard packaging of chocolates and confections in particular be printed with as thin a coating as possible and not completely printed. These types of odors, having low volatility, are strongly retained particularly by relatively thick packaging layers. References Ewender J., Lindner-Steinert A., Riiter M., Piringer 0. 1995, in: Ackermann P., Jagerstad M., Ohlsson T. (Eds), Foods and Packaging Materials - Chemical Interactions. The Royal Society of Chemistry. Thomas Graham House, Cambridge. Franz R., Kluge S., Lindner A., Piringer 0. 1990. Packaging Technology and Science 3,89-95. Granzer R., Koszinowski J.. Robinson-Mand L.. Piringer 0. 1986, Verpack.-Rundsch. 37, tech.-wissensch. Beilage, 53-58. Koszinowski J.. Miiller H.. Piringer 0. 1980, Coating 13,310-314. Koszinowski J., Piringer 0. 1983, Drsch. Lebensm.-Rundsch. 79,179-183. Koszinowski J., Piringer 0. 1986, J. Plasfic Film & Sheeting 2,4C!-SO. Piringer O., Skories H. 1984, in: Schreier P.(Ed.), Analysis of volatiles Walter de Gruyter et Co.. Berlin. Piringer 0..1993, Verpackungen fur Lebensmitte. Eignung, Wechselwirkungen, Sicherheit. VCH-Verlagsgesellschaft mbH, Weinheim, New York. Riiter M. 1992, Verpack.-Rimcfsch.43, techn.-wissensch.Beilage. Saxby M., J. 1993, Food Paints and Off-Flavours,BIackie Academic & Professional, Glasgow. Whitfield F. B.. Ly Nguyen T. H., Last J. H . 1991. J. Sci. Food Agric. 54,595.
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
14 Case study: styrene monomer migration into dairy products in single serve portion packs Albert L. Baner
14.1 Introduction The potential problem of styrene taint in foods is well known and documented in the literature (Saxby 1996). Styrene (see Chapter 2) is the monomer that is polymerized to make polystyrene (PS) (also known as general purpose or GPPS grade). It is also commonly used with butadiene rubber (5-20% w/w) as a block copolymer to form high impact polystyrene (HIPS). In addition there are less common copolymer grades such as acrylonitrile-butadiene-styrene (ABS) having a mixture of 25 %, 1525 YO and 50-65 YO of each monomer respectively or a copolymer with acrylonitrile (styrene-acrylonitrile, SAN).
14.1.1 Content of residual styrene monomer in polystyrene containing food contact materials The level of unpolymerised residual styrene monomer in commercial grades of polystyrene material has been reduced over the years from 1000 mg/kg (0.1 YO w/w) to a target level of 500 mg/kg (0.05 % w/w) by more complete devolatilization after the polymerization step (Brighton 1982). The legal limits for styrene monomer in materials can be much higher (e.g. Australia 2500 mg/kg, AS 2070.3-1992). Hernpel and Riidt (1988) carried out a survey of residual volatiles found in polystyrene and polystyrene copolymers whose results are summarized in Table 14-la. The results of a recent survey by the Inspection Health Protection/Food Inspection Department, Utrecht, Netherlands (van Lierop, Wildervanck 1996), shown in Table 14-lb, found an average residual styrene monomer content of 224 mg/kg in 31 different polystyrene containing food contact articles and packaging. The two highest contents found were 888 and 1459 mgikg and in 14 articles less than 150 mglkg was found. A comparison of the results of the two studies from 1988 and 1996 supports the stated industry objective of reducing styrene monomer contents and shows an overall downward trend. Low monomer content PS materials are commercially available with specified styrene monomer levels of 150 ppm (mg/kg) that have actual contents of 100 ppm (ex. BASF 0 suffix materials 168 NO, 143 10). These materials can be used for injection molding or extrusion and are priced above normal styrene monomer content materials (those where styrene < 500 mg/kg). High impact polystyrene copolymer materials (HIPS) use normal monomer level polystyrene since there has been n o commercial market for such materials.
428
Baner
Table 14-la: Survey of volatile substances in polystyrene materials (Hempel and Riidt, 1988). Type of Polymer
Number of Samples
PS
PS block and mixed copolymer (HIPS, ABS. SAN)
44
Styrene monomer level (mg/kg) range and average 55-2272, Ave. 401
Potential off-flavor substance: frequency measured, range and levels in material (mgW Toluene 33.6-213, Ave. 45 Ethylbenzene, 41.8-473. Ave 50 Cumene, 34, 10-257, Ave. 27 n-Propylbenzene, 28.8-178, Ave. 29
12
320-1281. Ave. 550
Toluene, 12,26-128, Ave. 70 Ethylbenzene. 12.61-202, Ave. 84. Cumene, 12,18-210, Ave. 34 n-Propylbenzene, 11,31-3541, Ave. 56 a-Methylstyrene, 2, Ave. 527 4-Methylstyrene, 4,58-250, Ave. 80 Acrylonitrile, 4,25-116, Ave. 60.
Table 14-lb: Market survey of styrene content (mglkg) in 31 polystyrene material samples in Netherlands (van Lierop and Wildervanck, 1996). Analysis Number
Sample Description
Styrene content (mg/kg)
1418 1421 1549 1561 1582 1564 1565 1761 1762 1763 1763 1763 1791 1792 1793 1797 2037 2340 2494 2582 2863 2886 2887 2288 2898 2890 2892 2893 2894 2895 2869
Tray
198 106 137 238 n.a. 157 229 141 148 18 71 22 340 202 209 67 110 346 888 246 145Y 179 326 175 170 114 109 133 224 164 113
CUP CUP Plate Foam cup Separation sheets for meat CUP CUP CUP CUP Brown Cup Black Cup Tray for hamburger Pizza tray 1 kg tray Hamburger tray Salad tray Small meal tray Dessert plate Yogurt container Meat plate Pudding container Pudding container Curd cheese package Pudding container Spreadable cheese package Spreadable cheese package Pudding container Whipping cream package Yogurt container Curd cheese package
Case study: styrene monomer migration into dairy products ...
429
Polystyrene is quite stable during forming processes and does not readily decompose to produce styrene monomer. At normal thermoforming process conditions for example ( z 120 “C) styrene monomer levels do not increase. PS first starts to decompose at very low levels only after several hours at temperatures greater than 240°C. In general however, injection molding is a more severe process and the monomer content may increase slightly during processing which reflects food industry experience. In addition to styrene migration from the primary package, polystyrene containing toys, surprises and other items packed inside a package together with product can also be a source of styrene monomer off-flavor. The polystyrene used may or may not be food grade and the overwrap for the item is usually not a barrier to the transmission of styrene into the food.
14.1.2 Taste threshold levels for styrene monomer in foods The toxicity and safety of styrene has been extensively studied and is of no health consequence at the levels commonly found in foods. The current European legislation sets no specific migration limits (SML) for styrene in food which means its content is then controlled by the overall migration limit of 60 mg/kg in the food (Chapter 12). The overall migration limit is never reached because the styrene creates a strong astringent “chemical plastic” off-taste at levels in the food much lower than 60 mg/kg. As such styrene monomer migration into foods is more of an organoleptic/quality problem than a health and safety issue. In fact recent surveys of styrene levels in foods by the Ministry of Agriculture Foods and Fisheries (MAFF) in England have led to the conclusion that there is no toxicological concern considering the levels (< 1 to 134 pgikg) found in foods (MAFF, 1994). The residual styrene monomer remaining in the finished material can cause taints by transferring to the packed product in amounts that exceed the taste threshold concentration level in that particular food. Each food matrix has a characteristic styrene concentration (threshold concentration) above which the styrene taint becomes evident (Chapter 13). A series of sensory taste threshold concentrations taken from the literature for different foods are shown in Table 14-2. Ethylbenzene is commonly used as a solvent diluent during the polystyrene polymerization process. It can be found in the finished material and can be a source of taints as well. As seen in Table 14-2 the sensory taste threshold concentrations for ethylbenzene are 2 to 3 times higher than those for styrene. Other volatile compounds found in polystyrene containing packages but of less sensory significance can be 2-methyl-2-propen-I -01, P-methylstyrene, trimethyl- and tetramethylbenzenes. In general, the higher the fat content of the product the higher the taste threshold concentration (Chapters 4, 9, 13). vom Bruck and Hammerschmidt (1977) developed an equation that relates the fat content of the food product to the taste threshold concentration: threshold (mg/L styrene) z 0.0025 . (80. %fat in food
+ % water in food)
Conversely, water and products with high water contents (juices, skim milk etc.) have lower taste thresholds usually on the order of 50 ppb.
430
Baner
Based on taste threshold's published in the literature as well as food industry experience, an average acceptable taste threshold level of styrene monomer in a variety of food products ranges around 0.3 ppm. Table 14-2: Taste thresholds for styrene and ethylbemene in foods. Food
Taste threshold ( m d k d
Reference
Odor threshold in air Water Water Tea Java-Broken Tea Mixture Apple Juice
0.050 0.037 0.022 0.20 0.2 0.050 styrene > 0.10 ethylbenzene 0.025 1:1 styrenekthylbenzene 0.2
Fazzalari 1978 Rosent et al. 1963 Linssen et al. 1991 Jenne 1980 vorn Bruck, Hammerschmidt, 1977 Durst and Laperle 1990
0.50 0.20' 0.30 - 0.50 0.036' 0.099' 0.171' 0.005 0.5
Jenne 1980 Jensen 1972 vom Bruck, Hammerschmidt, 1977 Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 1993 Miltz et al. 1980 vom Bruck, Hammerschrnidt, 1977
0.3 1.2 1.2 2-6 33 5.0 0.001 styrene 0.003 ethylbemene 0.001 1:l styrene/ethylbenzene 0.20' 0.65' 1.18' 1.40' 1.56' 2.08' 2.3 1.82 2.22 0.5 - 2.02 0.5 - 2.02
vom Bruck, Hammerschmidt, 1977 Jenne 1980 vom Bruck, Hammerschmidt, 1977 vom Bruck, Hammerschrnidt, 1977 vom Bruck, Hammerschrnidt, 1977 CSIRO 1969 Linssen et al. 1995
Orange fruit juice drink (0 % fat) Yogurt Yogurt 3 YOFat Yogurt (1.5 % fat) Yogurt (0.1 YOfat) Yogurt (0.15 % fat) Yogurt (0.3 YOfat) Sour cream Vanilla-almond pudding (2.0 %! fat) Skim milk (0 % fat) Whole milk Whole milk ( = 3.8 YOfat) Condensed milk (10 % fat) Cream (33 % fat) Butter 5 YOOil-in-water emulsions 3 YOOil-in-water emulsions 10 % Oil-in-water emulsions 15 YO Oil-in-water emulsions 20 YO Oil-in-water emulsions 25 % Oil-in-water emulsions 30% Oil-in-water emulsions 30 % Oil-in-water emulsions Cocoa powder (10 YO fat) Cocoa powder (20 YOfat)
Milk chocolate flakes Plain chocolate flakes
vom Bruck, Hammerschmidt, 1977
Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 1993 Linssen et al. 19Y3 Linssen et al. 1993 Linssen et al. 1Y90 Linssen et al. 1991 Linssen et al. 1991 Linssen et al. 1991 Linssen et al. 1991
1 SO % taste recognition threshold concentration values (TRTC) 2 Recognizable difference from control sample not a true threshold concentration mglL, mg/kg = ppm to convert from liter to kg assume density of liquids % 1.0 g/ml
Case study: styretir tnononier rnigrution into dairy products ...
431
14.1.3 Analytical methods for measuring styrene Although there are methods for analyzing styrene in materials in the literature (Hempel and Rudt, 1988a, Sugita et al. 1996) and as standard methods (ISO, 1974) there are no official or standard methods available for determining styrene in foods. There are however numerous published methods for measuring styrene in foods (Rossli and Marek, 1977, Hempel and Rudt, 1988b, Durst and Laperle 1990, Linssen et al. 1991, Nerin et al. 1996). For measurements in materials ISO-2561 first dissolves the PS material in chloroform, then the dissolved polymer is precipitated using methanol and water. The level of styrene monomer is quantified by injection of the chloroform solution into a gas chromatograph (GC). The method of Rossli and Marek (1977) uses GC determination of styrene after isolation by co-distillation with water and continuous extraction of the distillate with hexane.
14.2 Case study: styrene taint in coffee creamers and condensed milk packed in portion packs An example of a product that has had styrene taint problems over the years has been dairy products such as coffee creamer and condensed milk packed in thermoformed PS single serve portion pack containers holding 5-10 g of product. The high package mass and surface area ratio to product and high fat content of the product make this packageiproduct system a challenging system to optimize. MAFF carried out a trade survey in 1994 (MAFF, 1994) of 22 coffee creamer portion packs and found styrene monomer levels in the product ranging from 23 to 223 pgikg (ppb) with an average of 134 pglkg. These levels have decreased significantly since an earlier market survey in 1992 of 7 coffee creamers that had styrene monomer concentration ranges from 265-665 pgIkg with an average of 430 pg/kg (MAFF, 1994). There was no indication in this survey if the products were refrigerated or shelf stable. Although the problem has become less severe due to the trend towards reducing residual monomer content in materials there is still potential for taint problems to occur in products. Total styrene content in current materials varies within a range of 250 to 350 ppm (even for laminate materials), Of the commonly polystyrene containing portion pack materials mono-material PS has the greatest migration followed by PSiPE and the material with the lowest migration is from PSIEVOHIPE. Surprisingly, even product packed in PSIEVOHIPE barrier material can contain styrene at a sensory significant level at the end of shelf life despite the EVOH barrier layer between the PS layer and product. The explanation for the styrene in the product comes from the fact that the styrene from the PS layer transfers to the inner PE layer while the material is shipped and stored in role form before forming. This is entirely possible in a few days given the relatively high diffusion coefficients of PS and PE. Measurements of refrigerated products (shelf life unknown) have shown practically no taint. Lower temperatures and shorter shelf life can reduce the amount of styrene transferred to the product.
14.2.1 Threshold concentration of styrene in coffee creamers and condensed milk From experience it has been established that the sensory threshold for coffee creamer and condensed milk products is on the order of 0.1 mglkg (ppm) of styrene in the product. This observation is only partly supported by threshold values from the literature in Table 14-2 where values range from 0.2 ppm for 3 YO yogurt, 1.2 ppm for 3.8 YO fat milk and 2-5 pprn for condensed milk. This points out two problems with threshold concentration values caused by the way they are determined (e.g. experimental methods) and the definition of the threshold value being the value at which the substance is correctly identified by SO Y of the panelists (versus other possible ways of measuring/defining the taste threshold). The intended use of the product also plays a role in the importance of the threshold concentration value. Coffee creamers and condensed milk are not intended to be consumed alone but added to coffee and tea drinks. Taking a threshold forstyrene in tea of 0.2 ppm from Table 14-2, a simple mass balance calculation shows that in a 150 ml cup (vending machine cup size) the 7.5 g cream in a portion pack could contain up to 4 ppm styrene monomer before the styrene becomes noticeable in the tea drink. One could assume that coffee would have a higher threshold concentration level due to a more robust flavor versus tea. However, one should also consider unforeseen uses of the product or package such as the current fad in Europe of collecting creamer lidding material printed with different pictures and designs. The common practice is for people to lick the cream from the lid before placing it in their pockets!
14.3 Estimation of styrene migration from PS The simplified approach to the estimation of migration described in Chapters 7 and 15 can be used to estimate the migration of styrene from polystyrene into the packed food. By estimating the migration of styrene a priori one can make a better initial material selection (e.g. level of residual monomer in material) for a given product application. Afterwards, filling and storage studies can be carried out on the final package system to confirm the material choice.
14.3.1 Mass balance estimation of worst case styrene migration The simplest estimation of migration is to use the mass balance calculation shown in Eq. (14-1) below. This equation assumes that all of the styrene found in the polymer will migrate into the food instantly. This is of course not realistic but the estimation gives an upper limit to the possible migration that could occur at the end of the product's shelf life.
(14-1) where: cF,& the concentration of styrene in the food after a long time (mg kg-'), cp.0 is the initial concentration of styrene in the material (mg kg-'),
Case study: styrene nionorner migration into dairy products ...
433
IF is the thickness of the material (cm), pp is the density (g cm-3) of the PS,
6is the package surface area A (cm2) to food mass ratio (mF = VF. pF in g
wsere VF is the volume of the food or simulant (cm"). mF = PF . VF and mp = pp . Vp are the masses of the foodstuff and polymer. The ratio can be the actual package surface area to food mass ratio or a conmF ventional ratio like 0.6 cm2 g-' (6 dm2 kg-') (used in the European Union) or 0.645 cm2 g-' (1 in2/10 g) (used by the US. FDA). The density of polystyrene is approximately 1.08g ~ r n - ~ . The initial concentration of styrene in the polymer (P), cp.0 (rng kg-'), is known either from the manufacturer of the material or has been determined by analysis of the material. In the absence of initial styrene monomer concentration data one could assume as a worst case a level of 1000 mg/kg which is the highest level usually seen in commercial PS materials. Usually the level found in the material is 500 mg/kg or less which is the industry standard for food grade polystyrene. For simplification one can assume the density of the polymer and food are approximately equal to one, PF "- pp "- 1.0,without large error. Example 14-1:Calculate the amount of styrene monomer that could migrate from a PS coffee creamer portion pack (7.5 g) with a residual styrene monomer content of 1000 ppm (mg/kg) into a coffee creamer containing 10 % fat. 1 ) take pp = 1.08 for average PS density ( g cm-3) from Table 14-1 2) measure wall thickness of portion pack (bottom is thickest part giving worst case) = 0.48 mm 3) calculate surface area of package in contact with food area cylinder = h . JT. r2 = 1.5 . IT (1.55)2= 11.3 cm2 4) enter values into the mass balance equation (14-1): A 11 3 C F . ~= -. pp . I p cp.0 = I s . 1.08.0.048 . 1000 = 78 mg/kg (ppm) mF
Interpretation of result: Assuming complete migration of styrene at this styrene monomer level in the PS, the taste of styrene monomer will be readily detected in the product based on a threshold of 0.1-0.3 ppm. Discussion: In this case the package area to food ratio is extremely high since this is a single serving portion pack (the EU standard package area to food ratio is 0.6 cm2/g compared to ratio here of 1.5). Realistically, one could also assume that since migration occurs in both directions that half of the initial monomer in the material would be lost into the environment (assuming no package overwrap). Even with the current European polystyrene manufacturer specification of < 500 mgikg styrene in the finished material (actual range from 300-400 mgl kg), the styrene concentration would still be 23-31 mgikg in the creamer.
14.3.2 Effect of partitioning on mass balance If there are significant partitioning effects occurring between the PS and product, then the amount of styrene migrating may reach a thermodynamic upper limit (Chapter 4). The partition coefficient is the ratio of the concentration of the migrant in the polymer cp,, to the concentration of migrant in the food C F , ~at equilibrium (long times):
434
Baner
It is possible that styrene will never reach the mass balance migration limit specified by Eq. (14-1) in certain foods because of partitioning effects. The systems most likely to have partitioning effects, i.e. when K >> 1, are those for styrene between aqueous foodstuffs and PS. Migration is usually highest into fats and oils since styrene is readily soluble in both the fats and polymers so that K 5 1. A guide for estimating the general behavior of partition coefficients is “like dissolves like”. Thus styrene, a relatively nonpolar hydrocarbon, will tend to remain in a nonpolar polystyrene polymer if the package contains a polar aqueous food (Chapter 9). Incorporating the effect of the partition coefficient into a mass balance Eq. (14-1) gets (Chapter 7):
(14-3) Note that as K becomes very small (the styrene partitions very readily in the food phase as opposed to the polymer phase, e.g. fatty foods) then Eq. (14-3) simplifies to Eq. (14-1) which assumes complete migration into the food. For this reason migration into foods with high fat contents is generally best estimated using Eq. (14-1). Example 14-2:Taking the same package in Example 14-1 (7.5 g PS portion pack) assume that skim milk is packed in this package instead of coffee creamer product with 10 % fat. In this case, since skim milk contains very little fat, the partition coefficient may limit the transfer of styrene monomer to the product. Assume the same residual styrene monomer content of 1000 ppm (mg/kg) in the PS. 1) Use the same package dimensions and polymer density given in Example 14-1. 2) Assume the partition coefficient for styrene monomer between PS and skim milk to be approximately equal to that for toluene/PS/water (K = 800) (Gavara et al. 1996). 3) Using Eq. (14-3):
The effect of the partition coefficient on the transfer of styrene into an aqueous product is dramatic, the estimated potential migration is reduced by 60 times compared to Example 14-1. However, the taste threshold for styrene in low fat products is lower (around 0.40 mg/kg). In order to be sure no styrene taint will be detected in the product, one would have to reduce the initial concentration of styrene in PS. Rearranging Eq. (14-3) one can estimate the maximum allowable styrene monomer concentration in the material that would ensure the concentration in the product would not exceed 0.4 mg/kg:
This level is within the range of the commercially available PS styrene contents and it should be possible to pack skim milk in a high quality polystyrene that would virtually exclude the likelihood of styrene tainting of the product.
Case sriirly: styrcwe tvotzonler migration into dairy products ...
435
14.3.3 Time dependent styrene migration One can assume that styrene migration out of PS into food is slowed down or braked by the diffusion of styrene in the plastic material (P). Eq. (14-4) the simplified expression for the estimating the concentration, cF,, (mg kg-'),of the styrene in the food (F) at time t can be used:
(14-4) where: c;., is the estimated styrene concentration (as opposed to the true concentration, which would be experimentally measured) (mg kg-' ), Db is the estimated diffusion coefficient of styrene in the plastic material (cm2 s-l) using Eq. (14 - 9 , t is the expected shelf life (s). The statement c;,~ 2 cF., in Eq. (14-4) indicates the tendency of the estimation to overpredict the actual migration due to the estimation of Dp and some simplifications made in deriving Eq. (14-4) (see Chapters 7 and 15). The value calculated for c;,, can be used for comparison with regulatory migration limits (e.g. specific migration limits, SML, given in EU legislation) to evaluate the material's suitability for the intended application with respect to food packaging regulations. Note that the initial concentration o f styrene in PS , c ~ . ~in, Eq. (14-4) must be experimentally determined or given in the material's specifications. The other inputs are readily available except for the diffusion coefficient which can be estimated as explained below or taken from the literature.
14.3.4 Estimation of styrene diffusion coefficient in PS Where no experimental diffusion coefficient data in the polymer is available an estimation for the upper limit diffusion coefficient D; can be made using the empirical correlation given in Eq. (15-1) (Chapter 15):
DpT>T,, where T, is the melting temperature of the polymer. As shown in Chapter 7, the diffusion coefficient appears in all migration rate formulas in the form of its square root. That means for example that, if Dp* is a four-fold over-estimation of DR this will produce only a two-fold over-estimation of the migration rate. Consequently the ratio (D;/Dp)’12 is equivalent with the ratio (mG,t/mF,t)of estimated to measured migration amounts. Most data in Appendix I are for LDPE at room temperature. Figure 15-1 shows the distribution of the ratio (D;/Dp)1’2 for LDPE at room temperature, obtained by using Eq. (15-3) for calculation of DG and Appendix I for extracting the corresponding
449
0
-
0,5 0,8
>0,8 -1,O
-
>1,0 2,O >2,0 - 5,O *5,0
- 10,O >lO,O - 20, >20,0 - 50,
Ratio intervals
Figure 15-1: Distribution of the ratio (Di/Dp)”’ for LDPE at room temperature.
450
Brandsch
experimental Dp-values. The distributions show a sharp maximum for Dp ratios between 1.0 and 5.0. Underestimations below 0.8 are obtained in less than 5 % of cases, whereas the underestimations in the range of 0.8 to 1.0 are at the limits of the precision of the experimental DP In Fig. 15-2 the dependence of the diffusion coefficient, log(Dp*),from M,2'3 calculated with Eq. (15-1) and Ap=ll (curve 2) and with Eq. (15-3) and Ap'=11.5 (curve 1), respectively, is shown in comparison with the experimentally obtained Dp-values extracted from Appendix I for LDPE at room temperature. One can see from this figure that in Eq. (153) with increasing molecular masses, the decrease of the diffusion coefficients is slower than for low molecular masses (Chapter 6). This finding is in agreement with experimental data collected for the diffusion of heavier compounds in polyolefins. With Eq. (15-2) (Limm and Hollifield, 1996) a similar curve as (1) in Fig. 15-2results. Figure 15-2 contains also the curve representing the theoretical reference equation (6-20), which shows a linear decrease of log DP with increasing M:/3. Recently Reynier et al. (1999) measured diffusion coefficients by the film to film method for a series of compounds in polyolefins at 40°C. An advantage of this method lies in the absence of possible interaction (swelling) processes produced from a liquid phase in contact with the polymeric sample. Moreover, using the same procedure and the same sample for a series of migrants, some sources for scatter of results could be avoided. Such scatter of experimental data often results when one compares results obtained in different laboratories with different samples and different experimental methods. The results obtained by Reynier et al. (1999) for HDPE and PP are compared in Fig. 15-3with
-7
-
-8 -9
-
-*'
n
B -10 0
-
-11
-'
-
-12 - ' -13
.-
I
0
20
40
60
MF3
80
t
I
100
120
Figure 15-2: Dependence of the diffusion coefficient from M ": in LDPE at room temperature. Calculated values: (1) with Eq. (15-3). (2) with Eq. (15-1) and (3) with Eq. (6-20); experimental points from Appendix 1-1.
+
451
Possibilities and litnitations of migration modeling
D:-values calculated using Eq. (15-3) and the parameters given in Table 15-2. From this figure one can see that D;-values calculated with Eq. (15-3) show a good agreement with the experimental Dp-values.That means, the D;-values deduced from the data collection in Appendix I are true upper limits but are at the same time quite close to the real values. From a legal view point as presented at the beginning of this Chapter, this is a very important feature of the proposed formula for D;. a) - 7 3 -
-8-A
f
A
*
A
- 8 3 --
(.logDpG' log DP calc ;
A
*.
p"
-m 0
-9
A
--
** A
A A
A
-95
.
c A
4
A
--
* *
A
A
A
A
-10 --
A
-10,5
250
200
b) -8,s
.
T
A
-9
--
A
A
350
300
Mr
A
*
A
**
r
s
* f
0" m
-0
I 450
400
- 9 3 --
A A A
A
A
** A
A
-10 --
A
A
A
452
Brandsch
15.1.2 Estimation of migration values From the above results one can conclude that migration values calculated with the general diffusion equations developed in Chapter 7 can be assumed to come quite near to actual migration values, if the condition Kp,F = 1 is realistic. In cases when large differences exist between calculated m&- and measured mF,,-values when using assumptions for the migration equation (Chapter 7), this means that one or more of those assumptions are violated. Such discrepancies are a natural consequence of applying equations based on a limited set of assumptions to more complex practical situations. On the other hand, discovering the sources of these deviations can lead to a deeper understanding of the processes occurring during migration. In the following DG-values calculated with the refined Eq. (15-3) and partition coefficients Kp,F assumed to equal 1 are used for estimating worst case migration rates for additives from polyolefins with Eq. (7-51). These estimated values are compared with experimentally obtained migration values carried out under well defined conditions for several additives from HDPE and different PP-types (Table 15-3a) into olive oil (O'Brian et al., 1999 and 2000). The results are summarized in Table 15-3b. Table 15-3a: Measured additive concentrations in HDPE and PP. Ranges of concentrations are shown in parenthesis. ~
No.
Chemical name
M,
cP,"[mg/kg]
Polymer
2-Hydroxy -4-n-oct yloxy-benzophenone
326
1540 ( 1400- 1720)
HDPE
Adipic acid, bis(2-ethylhexy1)ester
370
4820 (3970-5640)
HDPE
Octadecyl-3-(3,5-di-t-butyl-4-hydroxyphenyl)propionate 531
840 (77s930)
HDPE
2-(2-Hydroxy-3-t-butyl-5methyl phenyl)-5-chlorobenzotriazole
316
1500 (1400-1670)
HDPE
2-H ydroxy-4-n-octyloxy-benzophenone
326
1470 (136CL1570)
PP
Adipic acid, bis(2-ethylhexy1)ester
370
5260 (SOlG.5730)
PP
Octadecyl-3-(3,S-di-t-butyl-4-hydroxyphenyl)propionate531
890
PP
2-(2-Hydroxy-3-t-butyl-5-methyl pheny1)-5-chlorobenzo-
316
1480 (1420-1560)
PP
2.5-Bis(5-tert-butyl-2-benzoxazolyl)thiophene
43 1
500 146k540)
PP
triazole
(72G980)
The average cP,()values from Table 15-3a were used for calculation in order to compare the estimated migration values in Table 15-3b with the average experimental values. As shown in Table 15-3b, overestimation resulted for all average values and the smallest differences between calculated and measured values appeared at higher temperatures. One reason for the higher overestimation at lower temperatures lies with high probability in the partition coefficients for additives which are in general noticeable increasing with decreasing temperature (Chapter 4). From the quality assurance
453
Possibilities and limitations of migration modeling
Table 15-3b: Measured and calculated migration values [mglkg] of some additives from HDPE and PP into olive oil. ~~~
~
Migration conditions Additive no.
Polymer
1
HDPE
2h/70°C
6h / 7 0 T
exp.
calc.
7.5
19
(5.6-9.8) 2
HDPE
3
HDPE
19
48
HDPE
5.0
20
2
PP
PP PP
42
98
(30-58) 7.2
3.4
8.4
(2.8-4.3)
8.4
34
11
40
(7.9-17)
2h/70"C
10d/40°C
exp.
calc.
exp.
calc.
83
6.8
8.6
9.5
185
240
(5-1 I ) 14
25
(6-17) 23
51
121 13 31 7.7 (5.9-11)
(1244)
(9-28) 20
1.9
2.1
(1.2-3.1) 88
(25-44) 5
39
calc.
(12-18) 4
19
41
(94- 166)
PP
84
4.2
calc.
exp. (33-55)
3
32
exp. (14-24)
(5.5-12)
2 h / 121"C PP
33
(3.1-5.4)
(3.5-7.2)
1
16
(24-41) 4.1
(1.8-4.4) 4
calc.
(8.7-1 7)
(15-25) 3.0
10 d / 40°C
exp.
4.3
9.1
(3-8) 17
0.9 (0.6-1.7)
2.4
4.2
(1.3-4.2) 5.2
19
(3-10) 1.8
1 .o
3.6
(0.5-2)
point of view overprediction is not a concern, however from a technological standpoint more accurate estimation of partition may be of great interest in order to allow predictions closer to actual experimental data. Conclusions can be drawn by making comparisons of estimated migration values with data from experimental data banks containing migration values obtained from petitions for additives in food contact materials (Chapter 11). In Table 15-4 some of the data extracted from migration studies collected in the BgVV (formerly BGA), over the last two decades, are compared with estimated values under the same conditions. In this section data for polyolefins are discussed and the estimation results are based on D;-values calculated with the refined diffusion coefficient estimation Eq. (15-3). The discussion of non-polyolefins is found in the following section. In all cases presented in Table 15-4 the thickness of the plastic samples and the experimental conditions provided a migration process far from reaching the equilibrium state. Here only data obtained with fatty food simulants denoted as D (Chapter 12), that means olive or corn oil or a synthetic fat and in some cases ethanol/water-mixtures are discussed.
454
Brandsch
Table 15-4.Migration data extracted from the data bank of BgVV for several plastic materials. Polymer LDPE LDPE HDPE
dr (cm) M, 0.4 0.2 0.06
43 1 ZOO0 5.53
HDPE
0.2
35 1
HDPE PP PP PP
0.2 0.2 0.2 0.2
39") I178 4.1 1 604
PP
0.2
553
2500 1000 IOW ZOO0
PP
0.2
1465
3000
D
PP PS
0.2 0.1
3900 587
6000 2000
Eth. 95 % D
IPS
0.2
395
5oou
IPS
0.2
425
2000
IPS
0.2
439
2000
D
IPS
0.2
549
5000
Eth. 95 %
PVC PVC
0.1 0.1
330 604
loo00 8600
D D
PVC
0.1
513
5700
D
cP,"(mgikg) 1000 2800 1000 2000 1000 1000 1000 750 6000 10000 100
Food simulant D Eth. 95 % D
D Eth. 95 Yo D D D
0.1
448
t 1Od 1Od 1Od
100
Ih 1Od 2h 2h 3.5h 1Od 1Od 10d 10d Ih
40 70 70 60 40 40 40 40 100
D
40
1Od
100
Ih 1Od 2h 3.5h 1 Od 10d 10d 2h I Od Ih 1Od 2h 0.5t 2h Id 4d 1Od IOd 1Od 2h 1Od 2h 1Od 2h 10d Ih 2h 1Od Ih 2h 10d Ih 1Od lh I Od
40 100
9400 PET
T "C 40 49 40
2500
D
5000
D
60 40 10 40 70 40 100 40 70 66 49 49 49 49 40 40 70 40 70 40 70 40 100
40 100
PET
0.2
587
2500
D
5000
D
1500
Efh. SO Yo D
40
100
POM
0.2
PA 6.6
0.2
PA 12
0.2
553 587
587
5000
D
5000
Eth. SO Yo D Eth. SO Yo
40 100 40 40 100 40 100 49 49 40 49 49
IOd
Ih 1Od Ih 1Od 1Od 1Od 1Od 1Od
mF,, (mg/dm') calc. mF.,(mg/dmz) exp. 6.93 0.34 1.52 3.1 2.1 3.7 1.8 1.4
0.0027 0.93 1.2 I .5 0.59 0.84 1.4 2.0 0.13 0.27 0.0013 0.0084 0.0014 0.055 0.15
0.022 0.13 0.018 0.05 -
0.21 0.047 0.030 0.042 0.030 0.069 0.052 0.01 1 0.045
n.n@
0.021 0.090 0.13 0.015
0.10 0.030 0.21 -
0.076 0.072 0.038 0.060 0.060 -
0.15 0.24 -
2.79 0.89 0.015 0.038 0.13 0.23 0.25 0.16 0.0064 0.18 0.19 0.32 0.17 0.62
0.027 0.48 0.1 0.I 5 0.0084 0.0031 0.0013 0.0072 0.050 0.060 0.40 0.009 0.047 0.183 0.2 13 0.068 0.0 10 0.23 0.008 0.018 0.0016 0.016 0.0031
0.033 0.001 0.019 0.021 0.0014 0.041
0.052 0.0056 0.11 0.012 0.26 0.26 n 023 0m7 0.0015
0.021 0.016 10.3 0.016 0.077 12.6
Possibilities cind limitations of migration modeling
455
From Table 15-4 one can see that, whereas a two-fold overestimation resulted for the migrant with M, = 431 from LDPE into olive oil, an underestimation resulted for an additive with a mean molecular weight M, = 2000 from LDPE into 95 % ethanol. In this later case the additive was a mixture of oligomers with a mass distribution around 2000 dalton. The analysis of oligomeric species was specific for the structure but could not distinguish between their different masses. This is important because at 2000 dalton an estimated migration amount of m*F,t= 0.34 mg dm-2 results and at 1500 dalton m*F,t= 1 mg dm-' is obtained. That means for high molecular weight additives made up of oligomer distributions containing different masses, the mass distribution must be known in order to allow accurate estimation. The species with lower masses diffuse more easily and therefore play a more important role in the mixture than do the higher masses when measuring migration. From Table 15-4 we can see that the calculated migration amounts from HDPE are more or less overestimated in comparison with the measured values, depending on how the migrant partitions itself between the plastic and food simulant. The migration calculated for the additive with M, = 553 is greatly overestimated because this additive has a low solubility in food simulant D. Using a partition coefficient K ~ , J= 10000 instead of 1, which is used for the worst cases, the calculated migration amounts are mF,t = 0.016 and 0.032 mg dm-' for the initial additive concentrations in the plastic sample of ~ ~ ~ ~ ~ and = 1 02000 0 0 mg kg-I. These values are very close to the measured amounts at 40 "C. At 100 "C similar results are obtained with an estimation using a partition coefficient, Kp,F = 1000, mF,t= 0.129 mg dm-2 compared with 0.127 mg dm-' measured after 1 h. The decrease of the KeF-value with increasing temperature means a higher solubility in the simulant at higher temperature. The underestimation in the case of the additive with the main component molecular weight 3900 has the same explanation as that given for the 2000 M, additive in LDPE. It is a mixture of several species with a mass distribution in which the lowest mass provides the highest relative contribution to the overall amount of migration. As in the case of polyethylene, the calculated migration amounts for additives from PP are over estimations. This overestimation is especially high for the additive with M, = 553 at 40 "C, due to a larger partition coefficient as it was shown for HDPE. Due to the higher solubility of the additive at 100°C the degree of overestimation is decreased.
15.2 Migration modeling for non-polyolefins In contrast to the polyolefins, much less well defined migration data are available for non-polyolefins. Therefore if one intends to develop for non-polyolefins a similar approach to estimate Dp*-values as given above for polyolefins the lack of data is a real handicap for predictions requiring a degree of precision. An additional difficulty is the much higher glass temperature, T,, for most non-polyolefins in comparison to the polyolefins. For the most important food packaging non-polyolefins the T,-values are between 50 and 100 "C, that means the temperatures fall between the conditions of food contact at room temperature and hot-fill, pasteurization and sterilization temperatures. In the transition region from the glassy to the rubbery state of the plastic
456
Brandsch
generally a significant change in the activation energy of diffusion occurs. Referring to terms defined for Eqs. (15-1) and (15-3), this change must be taken into account by selecting adequate Ap-values for each state of the plastic phase. Despite these limitations and problems encountered with non-polyolefin materials in Table 15-5 a set of provisional Ap-values can be presented. These Ap-values apply only in the simplified Eq. (15-1). Table 15-5: Ap-values for some non-polyolefins. Polymer
Temperature range ("C)
AP
PS, IPS
< 70
4
HIPS
< 70
-3
PS, IPS, HIPS
2 70
0
PET
5 70
-6
> 70
-3
< 50
4
PBT PVC
2 50
0
< 70
-3 -4
2 70 POM
0
PA 66
< 70
-3
2 70
-2
PA 12
< 70
0
> 70
2
With the set of Ap-values given in Table 15-5 most of the calculated migration amounts from Table 15-4 are overestimations compared with the measured values. The considerable influence of the food simulant can be observed in many cases for non-polyolefins. For example, the migration of an additive with M, = 549 from IPS into 50 % ethanol in water in Table 15-4 shows a decrease of the migration amount measured at 49 "Cafter an initial contact temperature of 66 "C.This phenomenon cannot be explained by changes in diffusion. The decrease in migration must be a consequence of a strong increase of the partition coefficient, KKF,with decreasing temperature that shifts the equilibrium concentration of the migrant to the plastic phase. Other frequent phenomena are strong interactions between the plastic sample and the simulant. For example, the additive with M, = 587 shows a 20-fold enhanced migration from PBT into 50 % ethanollwater at 40 "C compared to olive oil. The interaction effect is dramatic with PA, as can be seen from the migration of the same additive into 50 % ethanol (mEt = 12.6 mg dm-') compared to olive oil (mEt = 0.077 mg dm-') after 10 days at 49 "C. A very important fact is the difference observed between the migration amount measured with IPS samples by full immersion compared with one-sided migration cells (Lickly 1997, Figge 1988). Due to the two-phase structure of the plastic matrix, the normally homogeneous polystyrene-phase near the interface in a real food contact material is destroyed in the material edges after cutting. The consequence is an enhanced migration through the rubbery phase in these regions.
Possibilities mid lirnitutions of migrotion inodeliizg
457
Last but not least, an aging effect of the polymeric samples can produce significant overestimations in modeling, especially in the case of low molecular migrants (Lickly et al., 1997). During long storage periods of packaging materials in the open atmosphere, considerable loss of the migrant occurs near the interface and consequently the migrant is no longer homogeneously distributed in the plastic, as assumed in theory. As a conclusion, careful examination of all migration measurements is necessary for a correct evaluation of estimation results, because many processes are possible which are in direct conflict with the assumptions of the mathematics behind the simplified migration equations (Chapter 7). Overlooking these conflicts between assumptions and experimental behavior produces many pitfalls (Piergiovanni et al. 1999).
15.3 Optimization of modeling From the point of view of compliance applications the use of Eq. (15-3) and the parameters from Table 15-2 for migration estimation may in principle lead to two types of results. The first case occurs when it is found that for a given polyolefin the worst case scenario by using KP,F = 1 and Df. from Eq. (15-3) and Table 15-2 leads to calculated QM values which are within the limits of the technologically required concentrations. The second case is when it is found that the above migration estimation approach leads to QM's which are impractical (too low) from a technological point of view. From a legislative standpoint in such a case for a compliance application with the real polymer it will be necessary to perform experimental migration tests. However, it must be emphasized that often this later case is caused because the worst case scenario developed above overestimates too strongly the migration amount in the actual polymer-migrant system. Thus it is legitimate to ask: what can be done when a more precise migration prediction is desired for a specific additive from an unknown or newly developed plastic formulation ? With the theoretical and experimental background accumulated until now and the discussions in this book, it is in fact not too difficult to provide the needed information quickly with a minimum of experimental effort, get still provide enough precision for modeling all necessary practical applications. The following example outlines an approach applied to polyethylene samples obtained from different manufacturers containing the additives shown in Table 15-6. The aim of this exercise was to demonstrate how precise such investigations can actually be using only generally available laboratory equipment. The initial concentrations, cpv0,shown in Table 15-6 were measured after dissolving the polymer sample in toluene under reflux, precipitating of the polymer with ethanol, filtration, solvent evaporation and dissolving the residue in 95 % ethanol. All additives were analyzed by high performance liquid chromatography (HPLC) on a Spectra Physics chromatograph (Thermo Quest). A Nucleosil 100-5C 18 H D column with a 125 mm length and an inner diameter of 4 mm was eluted using 100 '10 acetonitril as mobile phase at a flow rate of 1 ml min-' at 30°C. 20 pl of the ethanol solution was injected and the UV detector monitored at 195 nm. Under these conditions retention times of 8.2, 12.5, 20.9 and 23.2 min were obtained for Irganox 1330, Irgafos 168 ox, Irganox 1076 and Irgafos 168, respectively (Fig.15-4) (Brandsch et al. 1999).
458
Brandsch
Table 15-6 Polyethylene samples with different densities, pP (g/cm3), and additives with relative molecular masses, M,, and initial concentrations,cp.0 (mg/kg). Polymer LLDPE
PP
1
0.905
Additive Irganox 1076 Irgafos 168
Mr 531 646
2
LDPE
0.918
Irganox 1076 Irgafos 168
531 646
220
3
HDPE
0.946
Irganox 1010 Irgafos 168
1177 646
220 1070
4
LDPE
0.918
Irganox 1330
775
585
No.
__
m
CP.U
130 540 760
W1000-lSSnm
15
Vdb'O,
S
lrgafos 168 ox. 1
0
4,. ,
,
..
,
,
,
.,
,
.________l_.l_,
, , , ,,,, , , _ , ,
, ,
,, ,
-
,.,, ,
,
.,,
,,,, ,_
,
,
, ,
,
,
, ,,
,,
,, , ,,
,
,
,
___
Figure 15-4 HPLC-Chromatogram obtained with a migration solution containing Irgafos 168, oxidized Irgafos 168, Irganox 1076 and Irganox 1330.
Possibilities arid limitations of migration modeling
459
For each migration experiment two pieces measuring 9.8 x 4.9 cm2 were cut from the 0.2 cm thick polymer samples and placed in a double sided glass migration cell (Greiner & Gassner GmbH, Glastechnik Munchen) with an inner diameter of 6 cm. The pieces were covered with 130 ml of 9.5 % ethanol. The surface area of the total immersed pieces in contact with the liquid was 192.08 cm2. The contribution of the edge surface area was about 12 cm2, representing 6 % of the total surface area. This additional 6 % surface area was neglected in the evaluation of the results. This leads to an overestimation, which is acceptable from a regulatory standpoint. For polyethylene the amount of migration per surface area, mF,,/A, from the edges and the contact surface area are of the same magnitude. However, this must not be true in all cases, as will be mentioned later. The migration experiments were conducted at 40°C for 10 d and at 80°C for 6 h. The analysis of the additives from the migration solutions were performed with HPLC as described above. The determination of the migrated amounts was performed using corresponding calibration curves for each additive. In Table 15-7 the migrated amounts per surface area, mF,,/A, are shown in the second column for Irgafos 168 from HDPE with pp = 0.946 g cm-j at 40 “C(Brandsch et al. 1999). The amounts represent the sum of phosphite and phosphate (Irgafos 168ox). Tahle 15-7: Comparison of experimentally measured and calculated migration values, mF,,/A (pg dm ’) for Irgafos from HDPE into 95 % ethanol at 40°C.
~
~
~~
~
~
~
~
~
1
33
707
21
27
0.82
33
1.00
2
43
999
23
40
0.Y3
45
1 .05
4
59
1411
24
57
0.97
61
1.03
10
89
2222
25
91
1.02
88
0.99
All calculated mF,,/A-values were obtained using Eq. (1.5-3) in conjunction with Eq. (7-51). A recently developed software was used for all calculations (Mercea et al. 1997). The calculation was started taking AP from Table 15-2 for 40 “C, which gave an “upper bond” Df; = 1.15E-10 cm2 s-l. Using this D; and taking Kp,F = 1 - the worst case scenario - one can calculate the migrated amount and its ratio against the experimental one. The results obtained are shown in columns 3 and 4 of Table 15-7 from where one can see a 20-fold overestimation of the migrated amount. In other words this means that for this type of HDPE the “conductance” corresponding to an AP = 9.46 was too high. Therefore in a second calculation an adjusted AP = 3.1 was taken and the results obtained are given in columns 5 and 6 of Table 1.5-7. In this case the estimated values are much closer to the experimental ones. But in this and the previous case too, a systematic increase with time is found in the mF,l,ca~c/mF,l.exp ratios. This may be caused by the fact that the real partitioning coefficient is higher than the worst case one. Therefore, adjusting again with Kp,F = 380 and AP = 3.8 the results obtained in columns 7 and 8 show a very good agreement between experiment and modeling.
460
Brandsch
The following conclusions can be immediately drawn from the above results: the actual state of the art in analytical equipment allows very precise determination of the specific migration of some widely applied additives, such as Irgafos 168 in volatile food simulants. The special advantage of this additive is that the phosphate (Irgafos 168 ox) is the only oxidation product. This can be determined in the same analytical run along with the initial phosphite. The migration rates of the two species are practically the same and a full recovery and mass balance is possible. The initial concentration, c ~ ,is~also , the sum of the two species and so one important assumption for Eq. (7-51) (Chapter 7) is fulfilled. Another conclusion is the very sensitive reaction of the calculated amounts to different partition coefficients, Kp,F. Although only less than 20% of the additive is migrated after 10 days from the polymer into the ethanol, a partition influence can be easily detected. The relatively high Kp,F-valuesfor many plastic/liquid-systems,especially at lower temperatures are the reason for high overestimations using the worst case value of KEF = 1. In Table 15-8 experimental (exp) and calculated (calc) migration values for Irganox 1076 and Irganox 1330 from LDPE with pp = 0.918 g cmP3at 40 “C are given. Table 15-8: Migration amounts, mF,,/A (kg dm”) obtained with Irganox 1076 and Irganox 1330 from LDPE into 9.5 % ethanol at 40 “C. t (days) 1
mF,,/Aexp Ire. 1076
mF.,/Acalc AP = 8.6
mErcalci
mF,,/Aexp Ire. 1330
mF,,/Acalc AP = 9.0
mF.1 calc/
142
145
1.02
188
187
0.99
mFr
exu
mF, exu
2
210
204
0.97
259
265
1.02
4
290
288
0.99
366
374
1.02
10
459
454
0.99
593
59 1
1.00
In these two runs, KP.F= 1 was used in Eq. (7-51) and as can be seen, no systematic deviation between the calculated and experimental values occurs with increasing of time. In both cases using AP = 11.5 from Table 15-2 one obtains an overestimation because the estimated DG is larger than the real DF The best fit with experimental values is obtained if one lowers AP to about 9 and then calculates an adjusted Dp < Df. and mF,,/A with Eq. (15-3) and Eq. (7-51) respectively. Phenomenologically the lowering of AP from 11.5 to 9 means that the LDPE sample exhibits a smaller “conductance” for the migrant than that corresponding to the worst case scenario quantified by the parameters given in Table 15-2. It is well known that the density, pR of a polymer plays an important role in determining the mobility and hence the DP of a migrant in its matrix. It is well established by experimental evidence that for a given polymer type the increase of pp leads to a decrease of DP (see for example Appendix I). To illustrate this feature in Table 15-9 the experimental and estimated amounts of migration for Irgafos 168 from three polyethylene samples with different densities into 95 % ethanol at 80°C are given. The first two PE’s are LDPE while the third one is a HDPE sample. In all three cases it was assumed that KP,F= 1 and the DG-values were calculated using Eq. (15-3) and the data from Table 15-2. With these data Eq. (7-51 ) can be used to estimate the migrated amount under the worst case scenario. The results obtained show an overestimation of m,,/A which for the HDPE sample is about 8-fold. On the other hand the overestimations show no systematic deviation with increasing of time which is an indication of
461
Possibilities arid limitations of migration niodeling
the fact that the assumption Kp,F = 1 is valid. Therefore in order to bring the estimated migration amounts closer to the experimental ones it is again necessary to adjust (lower) the Ap-values. In Table 15-9 it is shown that taking AP = 9.9, 9.05 and 5.75 respectively yields a good agreement between experiment and estimation. This is also in agreement with the above phenomenological picture, i.e. a higher density in PE determines smaller diffusion coefficients to which then correspond smaller Ap-values than those given for LDPE and HDPE in Table 15-2. Although a significantly higher amount of Irgafos 168 migrated from HDPE after 6 h at 80°C in comparison to the values obtained after 10 days at 40 "C, the ratio between calculated and experimental value are equal to one at 80 "C. Table 15-9: Migration values, mF.,/A(pg dm-2),of lrgafos 168 from three polyethylene samples with different densities into 95 % ethanol at 80°C.
1
536
578
1.08
534
539
1.01
148
148
2
786
815
1.04
756
761
1.01
210
210
1 .OO
3.5
1077
1075
1.00
979
1010
1.03
284
279
0.98
6
1399
1403
1.00
1310
1314
1.00
394
366
0.93
1.00
This reduced "conductance" of the investigated PE's results in a great part from the interaction between the structure of this additive and the plastic. For additives with a more alkane-like structure, significantly higher migration amounts are found from HDPE and correspondingly the lowering of AP will be less severe. From the above examples and discussions one can derive a general scheme to be used for migration estimations from new polymers (polyolefins in our case) for which experimental diffusion or migration data are not yet available. In such cases a quick migration experiment is recommendable at 80 "C with 95 o/' ethanol, using an incorporated additive (which in many cases is a phosphite or phenolic antioxidant similar to the above examples). From several measurements after different contact times (up to a few hours) the experimental mF,t values must be compared with values calculated with Eq. (7-51) using Eq. (15-3), where in a first approximation Dp* is calculated with AP = 11.5 (as for LDPE) and using Kp,F = 1 (worst case scenario). If the calculated mF.,-values show no systematic deviation from the experimental values for increasing contact times, then the assumption KeF = 1 is valid. On the other hand if the estimated values show an overestimation, this indicates that the new polyolefine requires a smaller real AP than that from Table 15-2. After a few repeated calculation runs with lower Ap-values quickly provide the correct Ap-value. Once the adjusted Ap is found so that there is a good agreement between experiment and calculations, this new value can be used in combination with Eq. (15-3) and Eq. (7-51) to estimate the migration at any temperature T 2 80 "C and for any migrant with any molecular weight, M,, and a similar structure to that of the additive incorporated in the above PE samples. This scheme is valid for a wide range of initial migrant concentrations, c ~ ,in~the , new polyolefine. Most likely this range will cover the technically practicable amounts of additives in the new plastic.
462
Brandsch
15.4 Migration modeling with new polymer-migrant systems From a practical point of view it is useful to develop a scheme as reliable and as simple as possible to model theoretically the migration in new polymer migrant systems for which experimental data are not yet available. In the following such a step by step scheme will be presented. As a first step it is useful to test the interaction between the plastic and food simulants that differ as much as possible from the plastic in their polarities. A quick overview about the absorption behavior of the plastic is obtained by immersion of samples into olive or corn oil at the highest desired used temperature for 1-2 hours and then determining the amount of oil absorbed gravimetrically. In Table 15-10 some results obtained in this way with several plastics are shown. The most important result from this table is the high absorption of olive oil into HDPE and PP at 121" after 2 h. Due to the strong interaction with this fat simulant the actual conditions required in the regulations (Chapters 12 and 11) for migration testing at sterilization conditions using pure fat phases seem to be inadequate. The migration of additives when such strong interaction occurs leads to exaggerated overestimation conditions compared with foodstuffs in practice. In practice the absorption process is greatly reduced by water present in the system. It must not be forgotten, that packaging materials for food are only admissible if interaction processes are negligible in order to fulfill the requirement of inertness (Chapters 11 and 12). Once an adequate simulant is selected which shows no or only little interaction with the plastic, the next step is to perform a migration experiment using a well known additive as a reference compound. This selected additive must be well soluble in the chosen food simulant in order t o give a guarantee of a partition coefficient as low as possible (Chapter 4). In most cases one can select for this purpose an additive used in the plastic sample under investigation and run the migration experiment as shown in the previous section. Once these two experimental steps are done their results can be used to obtain the necessary specific parameters in Eq. (15-3),which then can be used in conjunction with Eq. (7-51) to perform migration estimations for a new or unknown plastic material. There are many possibilities for selecting the most adequate conditions for such determinations. But by such a combination of a few experimental measurements with the existing theoretical background, the actual limitations in modeling could relatively easily be overcome and much loss of time and expensive effort can be avoided. Finally a few remarks are necessary with respect to the analytical procedures required for migration studies. Whereas chromatographic separations in the gas and liquid phases are currently state of the art, additional selective methods will be of considerable importance for future studies. Among these, direct mass spectrometry using for example an electro-spray- ionization (ESI) or API ion source can quickly provide data for several species migrating into a simulant in one run. The whole mass range occurring in practice can be covered in a single measurement. For example, Figs. 15-5 to 15-7 show three applications which demonstrate the necessity of using specific analysis for complex additives such as mixtures of oligomers. Older results obtained using global methods, like radiolabeling, could not distinguish between species with different masses. As a result these methods give results which conflict in many cases with predictions made using the mean molecular weight, as was shown above. The ESI-MS is especially well suited for complex nitrogen-containing and phenolic structures. Fortunately, combinations of HPLC with ESI-MS or API-MS also provide a very powerful tool.
Possibilities imcl linzitations o f migration modelitzg Table 15-10: Oil absorption into several plastic materials. __
Polymer
Simulant
LDPE
Miglyol812
Test conditions [hI"C] 240140 240150 240160
Olive oil
HDPE
Miglyol812
Olive oil
PP
Miglyol812
Olive oil
IPS
Miglyol812
i-Octane Ethanol
ABS
Miglyol812 Ethanol
PBT
Miglyol812
2/70 1 1100 21100 41100 I/lo0 21100 411 00 11120 21I20 4/120 11120 21120 41120 11120 21120 41 120 11120 21120 41120 48/40 96140 168140 240140 240160 2170 240140 2170 240140 2/70 240140 2/70 0.51100 lil00 21100 0.51150 11150 21150
Absorbtion
["/.I
1.2 1.4 1.6 1.0 17.2 27.9 30.4 3.5 5.3 8.3 9.2 10.1 11.7 1.9 2.8 4.3 9.7 12.0 14.2 1.3 2.0 2.5 9.2 11.7 15.0 16.5 54.5 49.8 1.1 1.5 0 0 7.1 8.9 0 0 0 0 0 0
463
464
Brandsch 481.6
100.1
h
80
i
482.5
n
2ol
II 1I m/Z
i
Figure 15-5: Mass spectrum of Tinuvin 770 obtained with the ESI-MS method.
1: 4.5 1214.:
a) 1009590-
90-
3 5 5
9
=P
0.5
80-
7570-
3 5
65-
6055-
2
50-
8
45-
.-
40-
7570-
65-
6055504540-
fY 3530-
353025-
25-
20-
15105- 1182
x
0
8
85-
8580-
0
10095-
b'
-.
-*
20-
837.5
880.9
Figure 15-6: Mass spectrum of a) the double charged and b) the threefold charged HAS molecule with M, = 2426 obtained with the ESI-MS method.
Possibilities and limitations of migration modeling
465
A very effective class of photoantioxidants and long-term heat stabilizers are hindered amine stabilizers (HAS) (Chapter 3). Mononuclear and high-molecular-weight polynuclear compounds of this structure type are used as commercialized stabilizers. In Fig. 15-5 a mass spectrum of the binuclear HAS (Chapter 3, structure 31), bis(2,2,6,6-tetramethyl-4-piperidyl) sebacate (TINUVIN 770), with M, = 480.6, is shown. It was obtained after 10 days migration at 40 "C from HDPE into 95 % ethanol. After adding 10 pl glacial acetic acid to 1 ml of migration solution and dibutylamine (not shown in Fig. 15-5) as an internal standard the migration solution was directly introduced into the ESI-MS with a flow rate of 10 pl min-'. The signal obtained is an average of 25 mass scans. The peak with the masslcharge ratio, mlz = 481.6, represents the (M,+l)+-ion obtained by addition of one proton. The relative abundance of the signal represents a concentration of 0.48 pg ml-' migration solution, corresponding to 0.4 pg dm-* of HDPE. This method is very sensitive, specific and quick. In Fig. 15-6a the positive signal at m/z = 1214 of a double charged ion (M,+2)2+ corresponds to a HAS-molecule with M, = 2426 and in Fig. 15-6b the signal at m/z = 810 is that of a threefold charged HAS-molecule with the same structure. The signals were obtained in the same manner as for the previous case. The additional advantage of the ESI-MS in this example is the possibility to measure mixtures of additives with a large range of molecular masses, including impurities and degradation products with much lower molecular weights as the additive (Chapter 3) in a single run. The above mentioned possibility for direct analysis of a mixture of migrants is shown in Fig. 15-7. In this case a mixture of oligomers was analyzed, representing polyethoxylated alcohols. A difference of 44 dalton between two consecutive ionpeaks represents a structure unit CH2-CHZO-. 7. 705 3
4
661 2
881.1
35352 302 20 z
6 -.
mlr
..
900
...-
Figure 15-7 Mass spectrum of a mixture of polyethoxylated alcohols obtained with the ESI-MS method.
466
Brandsch
Only with such modern analytical tools is it possible to give correct answers to the many problems occurring in interactions between plastics and food. Some of the results obtained with ill-suited analytical methods for high molecular additive mixtures can be re-evaluated in this manner. In addition, answers can be given about the mechanism of degradation and the nature of decomposition products (Chapter 3). Last but not least a much faster determination of low migrants concentrations is possible in many cases. This is an important assumption for quality assurance with low thresholds of concentrations for regulation.
15.5 Modeling of migration from multilayer structures In many examples discussed in this book an actual practical situation is reduced to some kind of an “idealized” plastic migrant system in which the plastic material is a single layer structure with a finite thickness and a homogeneously distributed concentration of the migrant. That means the initial and boundary conditions for analytical solutions of the diffusion equation are fulfilling the assumptions described in Chapter 7. There it is already mentioned that for structures and initial and boundary conditions which deviate from such a relatively simple picture of the migration process the analytical solution for the diffusion equation is very difficult if not impossible. In such cases only the numerical mathematics leads to the desired results (Chapter 8). To exemplify such a problem the migration of an impurity from a core layer into and through a functional barrier made from an identical raw material was analyzed. In the majority of cases in food packaging with multilayer structure different materials are combined 100000
I d
2 10000--
I000
flP I00
10
3d -
--
4d
---
---
8d
--
4d
-
I,
5;
8d p2
1
, p3
jF
I
Figure 15-8: Migrant concentration profiles in a three layered laminate as a function of time and spatial coordinate.
Possibilities atid limitations of migrnrion modeling
467
33T
o ! 0
I 1
2
3
4
5
6
7
8
d Figure 15-9: Concentration of a substance migrated from a laminate into a food simulant as a function o f time.
in a laminate, e.g. polymers, polymeric glues and varnish. Migration modeling in such cases is possible only by numerically solving the diffusion equations. The following example shows modeling results obtained recently with a three layered laminate (Tosa et al. 1999). The system consisted of a thin layer PI with a thickness dl = 1 pm, which adheres with the left side to an impermeable layer (e.g. aluminum) and with the right side to a thicker layer P2 (d2 = 2.7 pm). This second layer adheres to the food contact layer P3 (d3 = 30 pm). While PI and P3 are made of quite similar polymeric raw materials and do not contain initially any potential migrant, the layer Pz is made of a plastified polymeric material which contains a potential migrant with a initial concentration, c2.0 = 12.5 %. The solubility of the migrant in PI and P3 is about the same but it is lower than in P2. That means the partition coefficients, K1,2 = 0.01 and K2,3 = 100 are assumed for the migrant between PI-P2 and P2-P3, respectively. The diffusion coefficient of the migrant at room temperature is D1 = D3 = 1E-12 cm2 s-l and D2 = 1E-10 crn2s-I. In this example it is assumed that the migration starts when the contact between packaging and food is established. An initial storage time of the laminate can also be considered (Tosa et al. 1999). It was further assumed that the migrant has the same solubility in the food simulant F as in P3, that means, K ~ , = F 1. The volume VF/A = 10 cm3 cmP2.This value is exaggerated in comparison with actual VF/A ratios, but it allows a better illustration of the process in Fig. 15-8. The results obtained (Fig. 15-8) show clearly the important role of the partitioning during the migration through the multilayer structure. The effect of the diffusion
468
Brandsch
process through P3 is illustrated after one day. As the migration proceeds, one can see that the concentration of the migrant in P2 decreases rapidly as it migrates through P3 into F. In Fig. 15-9 one can see that after 8 days the system reaches equilibrium, which is shown by the horizontal concentration profiles in PI, P2 and P3 in Fig. 15-8 and the asymptotic value, cF,~= 3.37 ppm in Fig. 15-9. Thus at equilibrium about 336 ppm of the migrant remain “trapped” in Pz, despite the much lower concentration of the migrant in the food simulant. This is due to the effect of the partition between P2 and P3, a result which has an important practical value. There are many cases where it is technologically necessary to include into one of the layers a considerable amount of a migrateable compound (a binding agent from ink or a varnish component). To hold this migrant as long as possible in the laminate it is important to place between the layer containing the migrant and the food another layer (functional barrier) in which the migrant has a considerably smaller solubility that in the parent layer and a diffusion coefficient as small as possible. The above example is a relative simple case of modeling migration in a laminate. But it illustrates the power of numerical mathematics (Chapter 8). The possibilities in modeling with easily available hard- and software opens a large field of complex applications. However, it must be emphasized that such principally simple modeling problems may offer many difficult to solve details and pitfalls. Consequently specialized software offered for migration modeling may be a great help for all people interested in plastic-food interactions. MIGRATEST Lite (1997, 1999), COATINGTEST (1999) and MIGRATEST (2000) are examples of such tools. References Baner A. L., Brandsch J., Franz R., Piringer 0.1996, Food Additive;, and Contaminants 13 587401. Brandsch J., Piringer O., Riiter M. 1999 (unpublishedresults). EU Commission 1999, Practical Guide, Internet. http:l/cpf.jrc.it/webpack. Figge K, 1988, Food Additives and Contaminants 5 397420. Flynn J. H. 1982. Polymer 23 1325-1344. Lickly T.D., Rainey M. L., Burgert L. C., Breder C. V., Borodinski L. 1997, Food Additives and Contaminants 14 65-74. Limm W., Hollifield H. C. 1996. Food Addirives and Contaminanrs 13 949-967. Mercea P, Piringer 0..Petrescu L., 1997, MIGRATESTLite, FABES, Munich. O’Brien A,, Goodson A., Cooper I. 1999, Food Additives and Contaminants 16 367-380 and 2000 (in print) Piergiovanni L., Fava P., Schiraldi A. 1999, Food Additives and Contaminants16 353-359. Piringer 0.1993, Verpackungenfur Lebensmittel, VCH-Verlag, Weinheim. Piringer 0. 1994, Food Additives and Contaminants 11 221-230. Reynier A., Dole P.. Feigenbaum A. 1999, Food Additives and Contaminants 16 137-152. Tosa V.,Mercea P., Piringer 0.1999. (unpublished results).
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
Appendices Appendix I Table 1: Diffusion data for low molecular weight organic substances in Polyethylenes (PE). Low Density Polyethylene (LDPE) and Linear Low Density Polyethylene (LLDPE) 470 Table 2: Diffusion data for low molecular weight organic substances in Polyethylenes (PE). Medium and High Density Polyethylenes (MDPE & HDPE) 498 Table 3: Diffusion data for low molecular weight organic substances in various types of Polypropylenes (PP) 51 1
Appendix I1 Table 1: UNIFAC group volume (Rk) and surface area
(ak)parameters
531
Table 2: UNIFAC group interaction parameters for prediction of vapour-liquid equilibria at temperatures between 250 and 425 K 539
Appendix I11 Table 1: Trivalent phosphorus antioxidants
565
Table 2: Major commercial hindered amine stabilizers 566 Table 3: Major commercial hindered phenolic antioxidants
567
Methane Methane Methane Methane Methane Methane
Name
where:
Diffusing Species
(dalton) 16.0 16.0 16.0 16.0 16.0 16.0
Molec. weight Mr (gkm') 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25) 0.916 (25) 0.915 (25)
PP
-
D D D D D D
(%)
("C) 15 : 45 5 ;55 25 25 15 ; 50 5:50
Experiment Type of Temp. diffusion range of coefficient experim.
29.0 43.0 29.0 43.0 54.0 44.0
-
Polymer Density Cristal@ ("C) linity
diffusion coefficient not measured but extrapolated to 23 "C diffusion coefficient at the temperature given in column 6 (other than 23 "C) diffusion coefficient at the temperature. "C, given in the upperscript.
(*
:''
concentration independent average diffusion coefficient diffusion coefficient at "zero" diffusant concentration diffusion coefficient determined from inverse gas chromatography diffusion coefficient in a polymeric sample in contact with a solventkimulant diffusion coefficient in a swollen polymeric sample diffusion coefficient at the gashapor pressure given in the subscript self-diffusion coefficient of the substance in the PE matrix diffusion coefficient extrapolated on the basis of structure relationships
D D, Dg,=, D, Dsw DIatm DSf Dth
Table 1: Diffusion data for low molecular weight organic substances in Polyethylenes (PE's) Low Density Polyethylene (LDPE) and Linear Low Density Polyethylene (LLDPE) [Densities up to 0.930 g/cm5 (at room temperature)].
Peter Mercea
Appendix I
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Drxp (cm2/s) x lo-' (kJ/mol) 46.4 1.421 43.94 1 17.0 1.282 45.62 1 54.0'** 1 19.3'"" 1 1.93 0.556 46.86 2 15.8 1.546 47.30 3
4
0
4
P
Methane Methane Methane Methane Ethylene Ethylene Ethylene Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Methanol Methanol Methanol Methanol Allene Allene Allene Allene
Name
Diffusing Species
16.0 16.0 16.0 16.0 28.1 28.1 28.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 32.0 32.0 32.0 32.0 40.1 40.1 40.1 40.1
(dalton)
Molec. weight M, 0.915 (25) 0.918 0.921 (23) 0.920 (23) 0.918 0.918 0.923 (25) 0.894 (25) 0.914 (2.5) 0.894 (25) 0.914 (25) 0.920 (23) 0.918 0.910 (25) 0.918 (2.5) 0.919 (25) 0.921 (25) 0.924 (25) 0.916 (25) 0.918 (23) 0.917 (23) 0.920 (25) 0.919 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25)
(g/cm3)
29.0 43.0 29.0 43.0
-
50.0
-
-
-
48.0 -
45.0 45.0 48.0 29.0 43.0 29.0 43.0 -
44.0 45.0 52.1 -
(%)
Polymer Density Cristal@ ("C) linity PP -
-
D D, D Dsw D D D D D
D
Dc 0 D~a,m D Dc + 11 D D D D D D D D D D D D
D
-
23 : 73 5 ; 5s 5 : 55 2s 25 33 : 48 -26 : 25 0 : 50 25 ; 50 0;50 25 ; 50 20 ; 60 25 23 23 15 ;35 30 10:50 10 : 50 25 25
5;35
5;35 125.2 35.50 5 ; 35
7J C L
("C)
Experiment Type of Temp. diffusion range of coefficient experim. 18.0'** 29.8 2500.0'** 17.9'* 13.4 18.1 12.5 21 .0 5 87 24.0"6.8"" 9.3'* 7.9 4.98 4.8'* 4.95 3.48(* 5.38 5.4'** 4.8 1.94 1.6 3.30'*' 27.4 9.16 31 .O(** 10.5"*
-
45.20 49.80 -
-
-
44.36
-
-
1.414 1.750
-
0.031
-
-
34.46 56.52 53.29 55.66 64.07 60.36 51.89 -
-
-
-
-0.948 2.874 2.101 2.505 4.001 3.194 1.888
-
28.52 61.11 67.62 39.18 49.38 53.57 -1.712 3.913 5.191 0.01023 2.036 2.222
43.93
1.226 -
-
1 1 1
1
6 8 9 9 9 9 10 11 12 13 14 15
1 1 1
6 4 4 7 1
5
3 4
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed D,," (Crn*/S);; 10-8 (kJ/mol)
Propylene Propylene Propylene Propylene Propylene Propane Propane Propane Propane Propane Propane Propane Propane Propane Propane Ethanol Propionitrile Isobutylene Isobutylene Acetone Butane Butane Butane n-Butane n-Butane Neopentane n-Pentane
Name
Diffusing Species
(dalton) 42.1 42.1 42.1 42.1 42.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 44.1 46.1 55.1 56.1 56.1 58.1 58.1 58.1 58.1 58.1 58.1 72.1 72.1
Mr
Molec. weight
0.924 (25) 0.922 (25) 0.924 (25) 0.915 (23) 0.921 (23) 0.918 (25) 0.918 (25)
-
0.922 (25) 0.922 (25)
-
(g/cm3) 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25) 0.920 (25) 0.920 (25) 0.894 (25) 0.914 (25) 0.894 (25) 0.914 (25) 0.915 (25) 0.915 (25) 0.918 0.920 0.920
-
-
60.0 60.0 50.0 51.0 46.0 50.0
-
-
0
0
D D D D Dsf D,r D D
-
D D D, n
Dc
D D D D D D Dc D D
-
D
-
D D D D D
-
("c) 10 ; 50 10 ; 50 25 25 0 : 22 0 : 2s 10 ; 50 10;50 25 25 25 25 ; 55 5 ;35 25 30 ;48 49.1 25 -8 ; 30 -8 : 30 25 30 ; 60 25 25 23 23 25 ; 50 25 : 50
Experiment Type of Temp. diffusion range of coefficient experim.
29.0 43.0 29.0 43.0 44.0 44.0 45.0 -
29.0 43.0 29.0 43.0 -
(Yo)
Polymer Density Cristal@ ("C) linity PP -
10.7'* 6.65 10.4 2.76 12.04'' 3.22'*' 2.6'** 2.1'* 5.2 2.0(" 1.98'* 0.027'** 0.5'** 4.0 2.6 0.7'*" 4.2" 1.95"* 1.4'** 10.0 6.0 0.16(' 0.805"
5.8(**
(cm2/s) x lo-' 17.5 5.0 20.0(**
uexp
6.503 4.836
I
-0.4437
4.102 3.607 -
86.73 13.27
-
-
39.25
-
65.16 63.41
-
45.20 -
-
63.19 57.86
3.491 2.929 0.2135 -
-
38.0 23.3 52.31 55.66 -
4.260 -7.176 2.248 2.264 -
-
-
-
(kJ/mol) 48.13 52.31
1.737 1.933
4 6 6 17 18 19 19 18 10 20 20 21 21 9 9
3
1 1 16 16 1 1 1 1 3
. 1
1
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ .r(23 "C) lg DO Ed
r
B 2'
7
b
%
N
!?j
n-Pentane n-Pentane n-Pentane n-Butylaldehyde n-Butylaldehyde Butanal Butanal Butylalcohol B utylalcohol Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene
n-Pentane
Name
Diffusing Species
72.1 72.1 72.1 72.1 72.1 72.1 72.1 74.1 74.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1 78.1
(dalton) 72.1
Molec. weight M,
(23) (23) (23) (25) (25) (25) (25) (25) (25) (25) (25) (25)
0.918 (25) 0.920 (25) 0.920 (25) 0.915 (23) 0.918 (25) 0.918 (25) 0.918 (25) 0.916 (25) 0.917 (25) 0.917 (23)
0.916 (25) 0.916 (25) -
-
0.919 0.921 0.928 0.922 0.924 0.919 0.919 0.922 0.922 0.922 0.922 0.922
(g/cm7) 0.915 (23)
PP
-
-
-
50.0 51.0 60.0 60.0 60.0 70.0 54.0 54.0 70.0 54.0 45.0 45.0 42.0 45.0
-
46.0 48.0 50.0 55.0 50.0 51.0 -
(%)
-
Polymer Density Cristal(3 ("C) Iinity
23 23 23 25 25 25 25 25 25 0 0 0 25 ; 50 25 25 ; 45 23 25 30 ; 40 30 : 40 23 25 ; 45 25 ; 45 25 25 : 35 25 25
LJ
71
(T)
Experiment Temp. Type of diffusion range of coefficient experim.
I'
%'
x
9.2 6.0 4.0 27 1 18'** 1.05". 0.28" 4.12'' 1.08' 0 90'' 0.19' ' 0.33'" 1.05" ' 0.99' 1.29*1.08" 3.0 1.98' 1.41'' 13 5'x 0.38 1.05' 8 26'" 0.4'** 0.14'* 0.82'** I 72'''
(cm /s)
+P
-
-
-3.309
-
4.603 -0.130
-
0.4730 0.9698
-
3.841 -
3.369
-
-
-
-
-
(kJimol)
21 20 20 22 22 20 20 19 19 19 17 24 24 25 26 27 27 28 29 29 30 31 32 33
21
21 21
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) lg Do Ed
4 W
P
4
4
F'
2
b
h
Diffusing Species
Benzene Benzene Benzene Benzene Benzene Benzene Dimethylsulfoxide (DMSO) 1-Hexene 2-Hexene Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Methylenechloride Methylenechloride Met hylenechloride Methylenechloride Pentanal Pentanal n-Hexane n-Hexane
Name
(dalton) 78.1 78.1 78.1 78.1 78.1 78.1 78.1 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.2 84.9 84.9 84.9 84.9 86.1 86.1 86.2 86.2
Molec. weight M,
0.919 (20) 0.912 (25) 0.917 (25) 0.924 (25) 0.924 (25) 0.919 (25) 0.919 (25) 0.918 (25)
0.918 (25) 0.915 (23) 0.915 (23) 0.922 0.922 0.921 (25) 0.920 (25) -
-
-
(glcm') 0.918 (25) 0.919 (25) 0.921 (25) 0.922 (25) 0.928 (25) 0.919 0.915 (25) 0.919 (20)
PP
70.0 -
-
-
-
50.0 45.0 36.5 47.0 50.2 52.0
-
36.5 70.0 70.0 54.0 42.0 42.0 -
(%)
-
Polymer Density Cristal@ ("C) linity -
(OC) 25 25 25 I5 ; 35 25 30 30 :45 25 : 50 25 : SO 25 ; 50 25 23 23 25 ; 30 25 :30 15 ; 35 15 ; 35 25 30 : 45 25 25 25 25 25 25 25 ; 50 25 ; 45
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Dexp (kUmol) (cm2/s) x lo-' 2. 15'" 1.68(** 1.48"' 0.99 2.187 57.75 0.69'"* 0.83'"' 0.29" 1.768 58.35 59.8'* 26.38 -1.568 0.71'* 54.40 1.452 2.388 0.40'* 61.10 0.61'*' 0.20 0.80 0.18'77.00 4.848 3.5'* 40.99 -0.2207 1.04 48.20 0.5264 47.9 15.90 -3.514 4.15(** 24.1'" 32.78 -0.834 9.2'** 8.2'** 7.0'** 7.1''" 0.7"* 1.76'** 0.53'" 3.249 65.29 0.84'. 61.10 2.706 32 38 38 38 39 22 22 23 29
37
33 14
36
33 33 33 33 33 15 34 35 23 23 26 28 28 36
Ref.
c
L
2 7 $
P
n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane 3-Methylpentane 3-Methylpentane Neohexane Tetrafluormethane Ethylacetate Ethylacetate Ethylacetate Ethylacetate
Name
Diffusing Species PP
(g/cm3) 0.918 (25) 0.918 (2.5) 0.918 (25) 0.918 (25) 0.915 (23) 0.919 (23) 0.921 (23) 0.928 (23) 0.928 (23) 0.922 (25) 0.924 (25) 0.918 (25) 0.915 (25) 0.918 (25) 0.928 (25) 0.920 (25) 0.919 (20) 0.919 (20) 0.919 (20) 0.918 (25) 0.922 (25) 0.924 (25) 0.906 (30) -
(dalton) 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 88.0 88.1 88.1 88.1 88.1 54.0 46.0 48.0 50.0 55.0 55.0 50.0 51.0 45.0 43.2 44.7 51.7 50.0 45.0 36.5 41.5 70.0 36.5 70.0 45.0 50.0 51.0 35.8 45.0
-
-
-
(%)
-
Polymer Density Cristal@ ("C) linity
Molec. weight M, -
(T) 25 : 35 25 ; 35 25 ; 50 25 : 45 23 23 23 23 23 25 25 25 25 25 25 15 ; 35 25 30 ;SO 30 $0 25 :50 30 :50 25 ; 50 20 ; 50 25 25 30 25
Experiment Type of Temp. diffusion range of coefficient experim.
1.05'*0.90'"' 0.3"" 1.32'** 1.40'** 0.797'** 62.8 13.2(** 37.6'* 37.6(* 0.41" 34.5'* 0.28'" 0.79 5.3'" 4.7'"3.0'** 3.2'"*
(cm2/s) x lo-' 27.2" 0.14'' 1.04'' 1.05(* 9.0 6.1 4.1 3.4 3.1
Dexp
-
-
-
27.15 23.53 61.94 33.17 64.86 63.15 -
-
-1.633 -1.833 2.547 -0.608 2.900 3.043 -
23.44
-
-
-
-
-
-2.065
-
-
-
-
-
-
-
-
-
-
-
-
(kJ/mol) 48.46 21.71 60.56 65.40 1.985 -5.034 2.703 3.563
-
29 31 40 26 21 21 21 21 21 20 20 30 41 41 41 14 37 35 35 23 35 23 42 20 20 43 37
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
VI
P 4
4
r;'
3 9
x
a h
p-Dioxane 1-Pentan01 2-Pentanol Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Phenole Methylbromide Methylbromide Methylbromide Methylbromide Methylcyclohexane Methylcyclohexane n-Heptane n-Heptane n-Heptane n-Heptane n-Heptane
Name
Diffusing Species
(dalton) 88.1 88.2 88.2 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 94.1 95.0 95.0 95.0 95.0 98.2 98.2 100.2 100.2 100.2 100.2 100.2
Molec. weight M,
0.918 (23) 0.919 (20) 0.922 (25) 0.922 (25) 0.918 0.918 0.919
0.920 (25) 0.918 (23) 0.918 (23) 0.919 (25) 0.922 (25) -
0.919 (25) 0.919 (25) 0.918 (25) 0.918 (25) 0.920 0.918 (30) 0.919 (30) 0.918 (30) 0.918 (30) 0.910 (70) 0.891 (70) -
-
(g/cm')
PP
-
-
-
-
40.6 36.5 -
-
-
58.0 60.0
-
45.0 35.0 50.0 40.6
-
54.0 54.0 45.0 47.3 48.0 -
-
-
(%) 70.0
-
Polymer Density Cristal@ ("C) linity
("c) 25 ; 50 25 25 25 25 ; 45 30 : 50 30 30 30 30 70 70 25 15 : 35 30 23 0 : 30 0 -3.0 15 ; 60 30 30 ;50 25 ; 30 25 ; 30 25 ;35 25 ; 50 30
Experiment Type of Temp. diffusion range of coefficient experim.
0.12(* 0.90(* 1.10'**
8.8'*
34.2'** 52.2"* 31.0'** 73.5 2.13'** 0.45 6.05 1.1 2.9('* 8.48 0.58(** 36.9(* 0.44'*
17.0'**
24.05 61.38 59.69 21.47 70.99 -
-2.189 2.480 3.478 -5.122 4.484 -
42.45 -
-
52.58 -
12.55 -
-
-
0.419 -
-
-3.91 9 2.061 -
-
-
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed *Dev (cm /s) x lo-' (kJlmol) 0.41(* 4.912 75.33 0.64'"' 0.97'** 1.81'1.43'' 7.508 87.00 1.37" 1.604 53.64 4.1(" 3.6"* 4.3"* 23 22 22 26 26 27 44 44 45 45 46 46 47 14 48 12 19 19 49 49 48 35 36 36 31 40 15
Ref.
3
*c ;L
x.o"
m
$ !
n-Heptane n-Heptane n-Hexylaldehyde n-Hexylaldehyde cis-3-Hexen-1-01 Hexanal Hexanal Ethylpropionate Hexylalcohol Hexylalcohol I-Hexanol 1-Hexanol 2-Hexanol Hexylalcohol Hexylalcohol o-Xylene m-Xylene p-Xylene o-Xylene p-Xylene N-Methylaniline p-Cresole An iso1e n-Octane n-Octane n-Octane n-Octane
Name
Diffusing Species
(dalton) 100.2 100.2 100.2 100.2 100.2 100.2 100.2 102.1 102.2 102.2 102.2 102.2 102.2 102.2 102.2 106.2 106.2 106.2 106.2 106.2 107.1 108.1 108.1 114.2 114.2 114.2 114.2
Molec. weight M, (%)
46.0
-
42.0 50.0 51.0
-
-
-
-
-
-
-
-
-
-
-
so.0 51.0
0.922 (25) 0.924 (25) 0.919 (25) 0.919 (25) 0.919 (25) 0.922 (25) 0.924 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.924 (25) 0.918 (23) 0.918 (25) 0.922 (25) 0.924 (25) 0.918 0.915 (23)
-
40.6 36.5 50.0 51.0 -
-
(gicm') (23) (20) (25) (25) (23) (25) (25)
0.918 0.919 0.922 0.925 0.918 0.919 0.919
Polymer Density Cristallinity @ ("C) PP -
30 30 : 50 25 25 23 25 25 30 25 25 25 25 25 25 25 25 25 25 25 : 50 25 ;50 50 23 25 25 25 25 : 50 23
("c)
Experiment Temp. Type of range of diffusion coefficient experim. 0.79"" 30.9(* 0.8'*' 0.6(** 1.40 0.03(** 0.31** 1.22'** 0.7'** 0.5' '* 1.44'** 3.21'*' 0.405'** 0.6'"' 0.5'" 0.94(** 1.46(*" 1.57(** 12.2'* 38.1(** 4.2(** 0.23 1.8(** 0.68(** 0.60('* 0.71(* 5.5
48 35 20 20 50 22 22 51 20 20 22 22 22 20 20 26 26 26 52 52 53 12 54 20 20 40 21
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Dexp (cm'is) x IO-* (kJimol)
P 4 4
4
r;'
4
%
b 'D
Diffusing Species
n-Octane n-Octane n-Octane n-Octane n-Octane iso-Octane iso-Octane 2,2.4-Trimethylpentane Ethylbutyrate Ethylbutyrate Ethylbutyrate Ethylbutyrate Heptanol Heptanol Heptanol Heptanol 1-Heptanol 2-Heptanol 2,3-Benzopyrole (Indole) Chlorophorm Chlorophorm Chlorophorm Phenylmethylketone (Acetophenone) Mesitylene Mesitylene n-Propylbenzene n-Propylbenzene
Name
114.2 114.2 114.2 114.2 114.2 114.2 114.2 114.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 116.2 117.1 119.4 119.4 119.4 120.1 120.2 120.2 120.2 120.2 0.918 0.918 0.918 0.918 0.919 0.919 0.918 0.918 0.922 0.928 0.918 0.920 0.920 0.920 0.920
(23) (23) (23) (23) (25) (25) (23) (25) (25) (25) (23) (25) (25) (25) (25) 45.0 45.0 45.0 45.0
-
-
-
50.0
-
-
-
-
-
-
-
50.0 51.0
-
48.0 50.0 55.0 55.0 36.5 40.6 36.5
-
(23) (23) (23) (23) (20) (23) (20) (25) (25) (25)
-
0.919 0.921 0.928 0.919 0.919 0.918 0.919 0.918 0.922 0.924
(glcm?)
(dalton) (Oh)
Polymer Density Cristal@ ("C) linity PP -
Molec. weight Mr -
23 23 23 23 25 ;50 30 30 : 50 25 : 50 25 25 23 20 ; 40 23 23 23 23 25 25 23 25 25 ;50 25 ; 50 23 30 : 50 30 : 50 30 : 50 30 ; 50
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig D,, Ed Dexp (cm2/s) x (kJ/mol) 4.0 2.5 1.85 1.7 29.59 26.7'* -1.351 0.52("* 8.29'* 0.634 43.72 0.23'' 6.113 83.59 2.2'" 1.75"" 1.79 1.86 -6.291 8.16 0.53 60.9 63.2 0.55 0.049'** 0.139'*' 0.55 1.78'" 17.7'* 4.162 14.68 15.4'" -3.540 18.54 1.10 0.74'* 0.6019 49.47 3.26'" -1.584 33.45 1.16(* 1.083 51.10 20.91 6.2'" -3.517 12 22 22 50 26 58 58 50 27 27 27 27
57
57 57
56
21 21 21 21 35 48 35 40 20 20 55
Ref.
h
h
; 2
b
5 co
Diffusing Species
N,N-Dimethylaniline N,N-Dimethylaniline N.N-Dimethylaniline N,N-Dimethylaniline N,N-Dimethylaniline N.N-Dimethylaniline (DMA) N,N-Dimethylaniline (DMA) N.N-Dimethylaniline (DMA) NNDimethylaniline (DMA) N.N-Dimethylaniline (DMA) N.N-Ethylaniline Cresylmethylether 2-Phenylethylalcohol 3-Octen-2-one (Methylheptenone) n-Octylaldehyde n-Octylaldehyde n-Octanal (Aldehyde C,) n-Octanal (Aldehyde C,) Octanal Octanal Octanal Ethylvalerate Octylalcohol Oct ylalcohol Amylaceticester (Isoamylacetate) Trichloroethylene Trichloroethylene
Name
~
(dalton) 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 121.2 122.2 122.2 126.2 128.2 128.2 128.2 128.2 128.2 128.2 128.2 130.2 130.2 130.2 130.2 131.4 131.4
Molec. weight M,
0.919 (25) 0.919 (25) 0.922 (25) 0.924 (25) 0.918 (23) 0.922 (25) 0.928 (25)
(gicm') 0.916 (25) 0.917 (25) 0.917 (25) 0.918 (25) 0.924 (50) 0.918 (25) 0.918 (25) 0.920 (25) 0.920 (2.5) 0.920 (25) 0.924 (SO) 0.918 (23) 0.918 (23) 0.918 (23) 0.922 (25) 0.924 (25) 0.918 (23) 50.0 51.0 -
42.0 42.0 50.0 50.0 50.0 -
(%) 29.031.0 35.0 42.0 -
Polymer Density Cristal@ ("C) linity PP -
D
25 : 45 25 ; 45 15 :34 15 :35 15 :35 50 23 23 23 25 25 23 23 25 25 20 ; 40 30 25 25 23 25 ; 70 25 ; 70
so
25 25 25 25
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Drxp (cm'is) x (kJimo1) OX'** 0.87'** 0.82(** 0.72(** 6.29'** 69.99 0.38'' 3.934 65.70 0.51(* 3.301 0.741 63.19 3.021 43.58 -0.0702 1.73 15.70 44.2 -3.583 4.54'** 1.20 0.43 0.73 0.43'** 0.40' * * 0.23 0.00196 0.009" * 0.041'*' -4.312 22.39 0.54 LO(** 0.47'** 0.40(** 0.17 25.7'* -3.370 18.25 25.3" -3.951 14.99 20 20 50 55 22 22 56 51 20 20 50 58 58
so
50
so
59 53 60 60 61 14 14 53
59
59 59
Ref.
Diffusing Species
Tetralin 1,l.l - Trichloroethane 1,1,1- Trichloroethane p-Isopropyltoluene (p-Cymene) 2-(2-Ethoxyethoxy) ethanol n-Butylbenzene N-Propylaniline 2,4,6Trimethylphenol 4-Isopropenyl-1 -methyl-1-cyclohexene (Limonene) 4-lsopropenyl-I-methyl-1 -cyclohexene (Limonene) 4-Isopropenyl-1-methyl-I-cyclohexene (Limonene) 4-Isopropenyl-1 -methyl-I-cyclohexene (Limonene) 4-Isopropenyl-1 -methyl-1-cyclohexene (Limonene) 7-Methyl-3-methylene-1.6-octadiene (Myrcene) 7-Methyl-3-methylene-l.6-octadiene(Myrcene) 2-Methyl-benzoic acid (Phenylacetate) 3-Phenyl-1-propano1 2,6,6-Trimethylbicyclo(3,l,l)hept-2-ene (alpha - Pinene) 2,6,6-Trimethylbicyclo(3,l,l)hept-2-ene(alpha - Pinene) 6,6-Dimethyl-2-methylenebicyclo (3,lJ)heptane-ropinene (Beta - Pinene)
Name
23 20 : 40 23 20 ;40 23 23 23 20 :40
-
0.918(23)
-
0.918 (23)
136.2 136.2 136.2 136.2 136.2 136.2 136.2 136.2 136.2
0.918 (23) 0.918 (23) 0.918(23)
-
25 ;45
0.930 (25)
23
25 ;45
23 23
50
25 ;50 23 23 30 ;60
136.2
115 ; 140 25 ; 50
(T)
0.923 (25)
-
136.2
(%)
Experiment Q p e of Temp. diffusion range of coefficient experim.
0.922 (25) 0.928 (25) 0.918 (23) 0.918 (23) 0.920 (25) 0.924 (50) 0.918 (23) 0.918 (23)
(gkm') -
Polymer Density Cristal@ ("C) linity PP -
132.2 133.4 133.4 134.2 134.2 134.2 135.2 136.2 136.2
(dalton)
Molec. weight Mr Dexp
lo4
0.14
2.18
0.70 1.04 0.25 0.28 0.14
1.10
0.00571
0.04(*
0.042("
9.6('15 6.0'' 4.75(* 0.54 0.38 0.64(* 6.51'"' 0.23 0.43
(cm2/s) x
-
-4.169
-
-
-
-4.320
-
4.546
-
-5.243
-
19.79
20.76 -
19.25
-
23.54
39.31
-
-2.436
-
-
-
-
49.33
0.514
-
42.34 27.83 26.04
-1.318 -2.309 -2.728
(kJ/mol)
50
56
50
50
50
50 56
56
55
63
63
50
27 53 12
50 50
58 58
62
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed
+
F'
9
%
1
0
&
Diffusing Species
3,7,7-Trimethyl-bicyclo[4.1 .0]hept-2-ene (Carene) 2,4-Dimethyl-3-cyclohexene-l -carboxyaldehyde cis-Decalin trans-Decalin n-Nonanal (Aldehyde C,) n-Decane n-Decane n-Decane n-Decane cis-3-Hexen-I-yl-acetate 7-Methylchinoline Ethylhexanoate Ethy lhexanoate Ethylhexanoate Nonanol 1.2-Benzopyrone (Cumarin) I -Methoxy-4-(1-propeny1)benzene (Anethol) cis,truns 3,7-Dimethyl-2,6-octadiene-l -nitrile (Citralva) N,N- Di-ethylaniline (DEA) 3,4-Methylene-dioxybenzaldehyde(Heliotropine) Benzylacetate 2,3.5.6 Tetramethylphenol Dimethylbenzylcarbinol
Name
150.2 150.2 150.2
149.2 150.1
138.3 138.3 142.2 142.2 142.2 142.2 142.2 142.2 143.2 144.2 144.2 144.2 144.3 146.2 148.2 149.2
-
0.918 (23)
0.918 (23)
0.918 (23)
50.0
0.920 (25)
(23) (23) (23) (23)
0.918 (23)
0.918 0.918 0.918 0.918
0.918 (23) 0.918 (25) 0.922 (25) 0.924 (2.5) 0.918 (23) 0.918 (23) 0.922 (25) 0.924 (25) -
-
23 23 23
20 ; 39 23
122 ; 132 122 ; 140 23 25 ; 50 25 25 30 ; 80 23 23 25 25 30 23 23 23 23
23
0.918 (23)
138.2
Experiment Type of Temp. diffusion range of coefficient experim.
("C) 23
-
Polymer Cristallinity
(dalton) 136.2
M,
Molec. weight
-
24.12 -
-
4.213
-
-
-
-
0.70 0.16 0.075
2.635
0.21
-
-
-
-
-
-
-
-
-
-
-
-
06.83
8.644 -
-
37.34 38.21 -
-
-
(kJ/mol)
-2.088 -1.919
-
-
0.087
0.81(** 0.40 0.54 0.50 0.17
0.18 0.36'* 0.42'* 0.37" * 0.34' 0.93 0.43 0.90'" 0.27'**
10.1('20)
,39(120)
0.11
1.O
50
50
62 62 50 40 20 20 32 50 50 20 20 51 12 50
50
64
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 " C ) Ig DO Ed (cm-is) >DCXP x IO-' -
Diffusing Species
154.2
154.2 2-cis-3,7-Dimethyl-2,6-octadiene-l-ole (Nerol) 154.2 2-trans-3.7-dimethyl-2.6-octadiene-8-ole (Geraniol) 154.2 2-Isopropyl-5-methylhexanone(Menthon) cis-2[2-Methyl-l-propenyl]-4-methyltetrahydro-154.2 pyran (Roseoxyde L)
1001)
1001)
3.7-Dimethyl-l.6-octadiene-3-ylacetate (Lina-
0.918 (23) 0.918 (23) 0.918 (23)
154.2 154.2 154.2 154.2
0.919 0.922 (25) 0.928 (25) 0.929 (25) 0.918 (23)
&xp
0.21 0.31
23 23
0.27
0.00139
0.10 0.10 0.19
(cm2/s) x 0.11 0.36 0.00320 0.222 0.15 0.08(" 0.66'** 0.29" 0.69'*" 8.0'' 7.63'* 7.53'4" 0.048
0.918 (23) 0.918 (23)
20 : 40
23
23 23 23
(T) 23 23 23 20 : 40 23 25 25 25 : 50 30 25 ; 70 25 ; 70 40 : 60 23
0.21 0.15
-
-
-
-
-
-5.39 1
-
-
-
-
-
-3.009 -3.496 -2.104
-
6.092
-
-0.899 -
-
-
-
-
(kJ/mol)
50 50
50 50
56
55
50 50 50
50 50 55 56 50 30 26 23 15 58 58 65 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed
23 23
("10)
-
Experiment Type of Temp. diffusion range of coefficient experim.
0.918 (23) 0.918 (23)
-
-
0.918 (23) 0.918 (25) 0.918 (25) -
-
(gicm') 0918 (23) 0.918 (23)
PP
Polymer Density Cristal@ ("C) linity
(dalton) 150.2 152.2 152.2 152.2 152.2 153.8 153.8 153.8 153.8 153.8 153.8 153.8 154.2
Molec. weight Mr
3.7-Dimethyl-1,6-octadiene-3-ylacetate (Lina-
1001)
Ethylbenzoate cis,trans 3,7-Dimethyl-2,6-octadienal(Citral) &,trans 3,7-Dimethyl-2,6-octadienal(Citral) cis,trans 3,7-Dimethyl-2,6-octadienal(Citral) 1.7.7-Trimethyl-2.2.1 heptane-2-one (Campher) Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride Carbontetrachloride 1.7,7-Trimethylbicyclo2.2,1 heptane-2-one (Borneol) 3,7-Dimethyl-6-octene-1-al (Citronellal) 1.8-Epoxy-p-Mentone (Eukalyptol) 3,7-Dimethyl-1.6-octadiene-3-ylacetate (Lina-
Name
I
s
5
h
N
&
156.3 156.3 156.3 156.3 156.3 156.3 156.3 156.3 157.0 157.0 158.2 158.2 158.3 158.3 158.3 158.3 160.2 164.2 164.2
156.3
0.922 0.924 0.918 0.918 0.918 0.918 0.918
-
0.918 0.918 0.918 0.918 0.922 0.928 0.918
-
-
20 20 50 50 22 22 66 66 57 57 50 50 58 58 50 51 20 20 50 50 50 50 50 0.24'"' 0.21'"" 0.26 0.14 0.016'** 0.153'*' 1.66'** 1.90'** 0.9 6.6 0.15 0.12 10.7'" 10.4(* 0.47 0.69(** 0.29"* 0.22'** 0.092 0.13 0.44 0.079 0.26 25 25 23 23 25 25 40 40 23 23 23 23 25 ; 70 25 :70 23 30 25 25 23 23 23 23 23 0.922 0.924 0.918 0.918 0.919 0.919
156.3 156.3 156.3
(25) (25) (23) (23) (23) (23) (23)
(23) (23) (23) (23) (25) (25) (23)
(25) (25) (23) (23) (25) (25)
56
0.086
20 ; 40
50
-
(kJ/mol)
154.2
0.22
23
-
0.918 (23)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient @ (23 "C) Ig Du Ed
154.2
Experiment Temp. Type of range of diffusion coefficient experim.
1-Methyl-4-isopropyl-l-cyclohexene-1-01 (Terpineol) 1-Methyl-4-isopropyl-1-cyclohene-1-01 (alpha Terpineol) n-Decylaldehyde n-Decylaldehyde 3,7-Dimethyl-6-octene-l-ol (Citronellol) n-Decanal (Aldehyd Clo) Decanal Decanal Undecane Undecane Undecane Undecane 2,6-Dimethyl-7-0ctene-2-01 (Dihydrornyrcenol) 2-Isopropyl-5-methylcyclohexanole(Menthol) Bromobenzene Bromobenzene 2-Methoxynaphthalene (Yara Yara) Ethylheptanoate Decylalcohol Decylalcohol 3,7-Dimethyl-l-octanol 3,7-Dimethyl-octane-3-o1 Diethylmalonate Dimethylphenylethylcarbinole Methoxy-4(2-propenyl)phenol (Eugenol)
PP
Polymer Density Cristallinity @ ("C)
Molec. weight
Diffusing Species
Name
Diffusing Species
2-Methoxy-4-prophenylphenol (Isoeugenol) 1-Phenylethylacetate 2-Phenylethylacetate Tetrachlorethylene Tetrachlorethylene Perchlorethylene n-Undecene-2-al (Aldehyd C,,) cis-Undecene-8-al (Aldehyd C, 1 inter) Diphenylmethane 1,1,2,2 - Tetrachlorethane 1,1,2.2 - Tetrachlorethane Diphenyloxide Ethyloctanoate Ethy loctanoate n-Undecylaldehyde (Aldehyde C, ,) n-Dodecane n-Dodecane n-Dodecane Dodecane (Alcane CL2) Dodecane (Alcane C12) n-Dodecane n-Dodecane n-Dodecane n-Dodecane 2,4-Di-t-butylphenol 2.6-Di-t-butylphenol Ethyl-Naphtylether (Bromelia)
Name
164.2 164.2 164.2 165.8 165.8 165.8 168.3 168.3 168.3 169.9 169.9 170.2 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.5 170.5 172.2 (23) (23) (23) (25) (25) (23) (25) (25) (23) (25) (25) (23) (23) (23)
(23) (23) (23) (25) (25)
0.918 (23) 0.918 (23) 0.918 (23)
-
-
-
-
0.918 0.918 0.918 0.922 0.928 0.918 0.922 0.924 0.918 0.922 0.924 0.918 0.918 0.918
-
0.918 0.918 0.918 0.922 0.928
PP
(g/cm3)
(dalton) (%)
-
Polymer Density Cristal@ ("C) linity
Molec. weight M,
23 23 23 25 ; 70 25 : 70 25 23 23 23 25 ; 70 25 : 70 23 25 25 23 25 25 23 6 : 40 6 ; 40 40 40 40 40 23 23 23
(T)
Experiment Type of Temp. diffusion range of coefficient experim. uexp
0.155 0.29 0.57 15.S(* 14.2(* 6.2'** 0.096 0.090 0.48 2.88'' 2.59'" 0.37 0.32'** 0.28(** 0.10 0.33'** 0.29(** 0.27 0.26 13.6 1.86'** 1.23'"* 0.99'** 0.78( * 0.012 0.098 0.39
(cm2/s)x 10" -
(kJ/mol) 50 50 50 58 58 37 50 50 SO 58 58 50 20 20 50 20 20 67 67 67 66 66 66 66 12 12 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @n (23 "C) Ig D,, Ed
4
k
%
2
h
b
P
Diffusing Species
nellal) Methyleugenol Butyrated hydroxyanisole (BHA) Butyrated hydroxyanisole (BHA) Butyrated hydroxyanisole (BHA) 2-Methoxy-4-propenylanisol (Methylisoeugenol) Diphenylmethanone (Benzophenone) n-Dodecylaldehyde (Aldehyde C12) 2-Methyl-undecanal (Aldehyde C I 2MNA) n-Undecalacton (Aldehyde C14) n-Dodecylaldehyde n-Dodecylaldehyde Citronellylformiate Tridecane Tridecane Tridecane Tridecane 2,6-Di-t-butyl-4-methylphenol Dodecanol 3-Methoxy-4-hydroxy-benzaldehyde(Verdyla. cetate) 2-Methyl-3-(4-isopropyl)phenylpropanal (Cyclamen aldehyde) Dimethylbenzylcarbinylacetate (DMBCA) 4-[2,6,6-Trimethyl-2-cyclohexene-l-yl]-3butene-2-one (Ionone) 0.918 (23) 0.918 (23) 0.918 (23)
190.3 192.3 192.3
-
(23) (23) (23) (23) (25) (25) (23)
0.918 (23) 0.918 (23) 0.918 (23)
0.918 0.918 0.918 0.918 0.922 0.924 0.918
182.2 184.3 184.3 184.3 184.3 184.3 184.3 184.4 184.4 184.4 184.4 184.6 186.4 190.2
0.918 (23)
23 23
23
23 23 23 23 25 25 23 40 40 40 40 23 23 23
23 31 31 137 ; 169 23
0.918 (23) 0.912 (31) 0.927 (31) -
178.2 180.2 180.2 180.2 178.2
-
Experiment Type of Temp. diffusion range of coefficient experim. ("C) 23
PP
Polymer Density Cristallinity 0 ("C)
(dalton)
Molec. weight M,
3,7-Dimethyl-8-hydroxyoctanal ( H y d r o x y c i K 172.3
Name
1.09 0.12
0.12
0.49 0.019 0.018 0.027 0.19(** 0.16(** 0.23 1.60(** 1.86"' 1.44"" 0.90'** 0.066 0.11 0.21
0.30 0.34(** 0.38'" 6.1(I3O 0.26
-
-
-
41.56
-
-1.828 -
-
-
-
so so
50 68 68 62 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy 0 (23 "C) Ig Do Ed Dexp (cmz/s) x IOU' (kJ/mol) 0.055 so
& VI
D i h i n g Species
194.2
-
0.918 (23)
0.920 (25) 0.918 (23) 0.918 (23) 0.918 (23) 0.918 (23)
-
-
-
50.0 -
-
-
50.0 51.0 44.0
-
-
-
-
-
0.918 (23)
0.918 (23) 0.918 (23) 0.918(23) 0.918 (23) 0.918 (23) 0.922 (25) 0.924 (25) 0.918 0.918 (23) 0.918 (23)
-
-
-
0.918 (23)
0.918 (23) 0.918 (23)
0.918 (23)
(gkm')
(dalton) (%)
Polymer Density Cristal@ ("C) linity PP -
Molec. weight M,
Allyl-3-cyclohexylpropionate 196.3 2.6-Dimethyl-2.6-octadiene-8-yl-acetate (Gera196.3 nylacetate) 1,7,7-Trimethylbicylo-1,2.2-naphtanyl-2-acetate 196.3 (Isobromylacetate) 3,7-Dimethyl-1,6-octadiene-3-yl-acetate 196.3 (Linalylacetate) 1-Methyl-4-isopropyl-l-cyclohexene-4-yl196.3 acetate (Terpinylacetate) Tetradecane (Alcane C14) 198.4 Tetradecane (Alcane CI4) 198.4 Tetradecane (Alcane CI4) 198.4 3,7-Dimethyl-6-octene-l-yl-acetate 198.3 p-tert.-Butylcyclohexylacetate (Oriclene extra) 198.3 Et hyldecanoate 200.3 Ethyldecanoate 200.3 Methylundecanoate 200.3 Am ylcinnamicaldehyde 202.3 3-[4-tert.-Buthylphenyl]-2-methylpropanale 204.3 (Lilial) N.N-Di-n-butyl-aniline (DBA) 205.3 2.4-Di-tert-but ylphenole 206.3 2.6-Di-tert-butylphenole 206.3 3-Methyl-3-phenylglycidate (Aldehyde C l h ) 206.3 5-(2,6,6-Trimethyl-2-cyclohexene-1 -yl)-3-methyl- 206.3 3-butene-2-one (Methyljonone-alpha)
Dimethylphthalate (DMP)
Name
Ds Ds D, D,
Ds
D S
D D D*
D
DS DS Dsw Ds DS
D,
Ds
Ds
Ds DS
D,
0.12
23
24 ; 43 23 23 23 23
0.12(* 0.012 0.098 0.22 0.066
0.25 0.19 10.1 0.29 0.12 0.21'** 0.17"" 1.18 0.14 0.14
0.12
23
23 6 : 40 6 :40 23 23 25 25 20 : 70 23 23
0.23
0.24 0.16
-
-
-
-
-
-
55.01 -
0.8007
-
-
-
-
-
60.39
-
-
2.73
-
-
-
-
73.70 59.84
-
-
-
4.282 3.565
-
-
-
-
-
-
-
50
50
61 12 12 50
50
67 67 67 50 50 20 20 69
50
50
50
50 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed Dexp (cm2/s) x lo-' (kJ/mol) 0.19 50
23
23 23 23
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
P 00
Lc
3&
3
b
6\
Diffusing Species
2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol(BHT) 2.6-Di-tert-butyl-4-methylphenol (Ionol) 2,6-Di-tert-butyl-4-methylphenol (Ionol) 2,6-Di-tert-butyl-4-methylphenol (Ionol) 2,6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol(BHT) 2,6-Di-tert-butyl-4-methylphenol (BHT)
220.4 220.4 220.4 220.4 220.4 220.4 220.4 220.4 220.4
-
0.918 (25) 0.920 (25) 0.917
-
0.918 (25) 0.918 (25)
-
-
0.918 (23)
-
0.918 (23) 0.918 (25) 0.918 (23)
-
0.920 (25) 0.920 (25)
-
-
30 : 60
1o:so 5 ; 60
50 66 66 66 66 70 71 71 72 12 69 50 62 12 72 73 74 74 75 76 77 78
-
0.832 3.842 9.260
1.7'60 0.081 3.45(7" 0.09'** 0.10 0.048 0.012'*
4.150 5.902 6.639
-
-
-
74.47 86.23 93.83
54.82 73.28 109.8
-
-
-
39.22
-2.321 -
66.83 -
-
71.67 77.30
-
-
50 50
-
3.760
-
-
-
2.995 4.210
-
-
0.15'""
0.066
0.022 0.037" 0.42'" 0.05'"' 0.082 0.93 0.16 3.9'i3n
1.50'**
-
1.15'** 1.23'"'
-
-
0.32
-
0.77'**
23 40 40 40 40 5 ;loo 35 ; 75 44 25 23 20 ; 70 23 137 : 169 23 25 65 ; 95 23 ; 74 75 ; 90 25
0.918 (23) -
0.21 0.012
(T) 23 23
-
0.918 (23) 0.918 (23)
(Yo)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) lg Do Ed D,," (cm2/sj; 10-* (kJ/mol) 0.086 50
23
(g/cm3)
(dalton)
-
Experiment Temp. Type of range of diffusion coefficient experim.
0.918 (23)
PP
Polymer Density Cristallinity @ ("C)
Molec. weight Mr
4-(2,6,6-Trimethyl-2-cyclohexene-l-yl)-3-meth-206.3 yl-3-butene-2-one (Methyljonone-gamma) Iso-amylsalicilate 208.3 4-[4-Methyl-4-hydroxyamyl]-3-cyclohexene-ca- 210.3 rboxaldehyde (Lyral) Benzylbenzoate 212.3 212.4 Pentadecane 212.4 Pentadecane 212.4 Pentadecane 212.4 Pentadecane 214.2 2,4-Dihydroxybenzophenone 2.4-Dihydroxybenzophenone 214.2 2,4-Dihydroxybenzophenone 214.2 214.2 2,4-Dihydroxybenzophenone (DHB) Tetradecanol 214.4 Methyllaureate 214.4 2-Hexyl-3-phenylpropenal (Jasmonal) 216.3 220.3 2,5-Tert-butyl-4-hydroxy-toluene (BHT)
Name
Diffusing Species
sorb 90) 2-Hydroxy-4-methoxybenzophenone Methyltridecanoate Phenylethylphenylacetate Hexadecanol Methylmiristate Nonane-l,3-dioldiacetate (Jasmelia) Triphenylmethane Triphenylmethane Brornoforrn Brornoform Hexadecanone Hexadecanone n-Octadecane (Alcane Ci8) n-Octadecane (Alcane CIS) n-Octadecane (Alcane CIS) n-Octadecane (Alcane CIS) n-Octadecane Octadecane Octadecane n-Octadecane
2,6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol(BHT) Hexadecane (Alcane Clh) Hexadecane (Alcane C l h ) Tetradecanamide 2-Hydroxy-4-methoxybenzophenone(Chima-
Name
228.2 228.4 240.3 242.3 242.4 244.3 244.3 244.3 252.7 252.7 254.4 254.4 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5
(dalton) 220.4 220.4 226.4 226.4 227.4 228.2
Molec. weight M,
(23)
(25)
(25) (23) (23)
0.917
-
0.922 (25) 0.928 (25) 0.918 (25) 0.918 (25) 0.918 (23) 0.918 (23) 0.918 (23) 0.917 0.914 -
-
-
0.918 0.918 0.918 0.918 0.918
-
-
-
(g/cm') 0.917 0.917 0.918 (23) 0.918 (23)
PP
(%)
-
Polymer Density Cristal@ ("C) linity
-
70 ;90 20 ; 70 23 23 20 ;70 23 40 40 25 ; 70 25 ;70 30 ; 45 48 ; 70 23 6 ; 40 6 ; 40 30 ; 60 40 ; 90 40 40 30 ; 60
30 ; 60 60 6 : 40 6 ; 40 118 25
(T)
Experiment Type of Temp. diffusion range of coefficient experirn.
4.27(" 0.78 0.30 0.064 0.63 0.082 0.385 0.152(** 3.3(* 3.1(* 0.28" 3.86(4" 0.12 0.095 5.50 0.035(* 1.19(* 0.60'"' 0.40(** 0.078(*
(cm2/s) x lo4 3.03(* 0.83(** 0.10 7.5 280(** 0.70(**
UtXp
-
78.01 62.77 -
4.773 3.952 -
-
81.82 65.49 70.74 53.3 83.80
-
5.416 4.295 3.034 1.491
5.678
-
-
-
-2.428 -2.401 9.550 2.770
-
73.15
28.62 28.91 102.6 61.0
4.710 -
0.2787 4.350 -
50.22 70.60 -
-
-
-
(kJ/mol) 55.44
2.265
81 69 50 12 69 50 66 66 58 58 69 69 67 67 67 79 82 66 66 78
78 79 67 67 80 75
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) IgDo Ed
*
2 2
1
%
%
Diffusing Species
nzctadecane n-Octadecane 2-H ydroxy-4-ethanediolbenzophenone 1,3,4,6,7.8-hexahydro-4.6,6,7.8,8-haxamethylcyclopenta-2-benzopyrane (Galaxolid) 7-Acetyl-1,1,3,4,4,6-Hexamethyl-tetrahydronaphthaline (Tonalid) N,N'-Diphenyl-p-phenylene-diamine (DPPD) Cedrylacetate Trichlormethylphenylcarbinylacetate (Roseacetol) 2.6-Dinitro-l -methyl-3-methoxy-4-tert.-butylbenzene (Moschus Ambrette) Tetramethylpentadecane Tetramethylpentadecane Dicumilperoxyde Dicumilperoxyde 2-Hydroxy-4-n-butoxybenzophenone Octadecanol Methylpalmitate Stearylalcohol Stearylalcohol Di-butyl-phthalate (DBP) Trans-9-octanacide Trans-9-octanacide Eicosane (Alcane C20) Eicosane (Alcane C2")
Name
(%)
(g/cm3)
0.918 (23) -
268.3 268.3 268.3 270.2 270.2 270.3 270.5 270.5 270.5 270.5 270.5 282.5 282.5 282.6 282.6
0.918 (25) 0.918 (25) 0.918 (23) 0.918 (23)
-
-
0.918 (23) 0.918 (25)
-
0.929 (25) 0.929 (25)
-
-
0.918 (23) 0.918 (23)
260.3 264.4 267.5
40 40 40 : 70 70 70 : 90 23 30 : 70 40 40 20 :40 20 ; 40 43 : 65 23 6 : 40
23
22 23 23
23
0.918 (23)
258.4
(T) 30 : 60
0.918 (23)
-
Experiment Type of Temp. range of diffusion coefficient experim.
30 ; 60 5 ;lo0 23
0.917 0.917 -
-
PP
Polymer Density Cristal@ ("C) linity
254.5 254.5 258.3 258.4
(dalton)
Molec. weight Mr
0.56'"' 0.37(** 1.02'~" 32.0'** 2.04"O 0.048 0.44 0.304'** 0.109(** 0.0001 8 0.034 2.4(4s 0.047 0.063
-
-
72.36
4.410
-
87.88
-
81.45 128.1 55.95
-
6.306
2.635 13.14 1.58
-
-
-
68.63
2.763 -
-
124.4 -
-
12.450
-
-
-
-
-
-
-
0.074
-
0.087"" 0.041 0.082
-
-
71.89 57.67 71.56
-
-
5.083 0.389 2.949
0.038
2.49(* 0.0163(' 0.021 0.044
66 66 85 86 81 12 69 66 66 87 69 69 67 67
50
84 50 50
50
78 83 70 50
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed Dexp (cm2/s) x lo-' (kJ/mol)
Diffusing Species
44.0 44.0 44.0 48.0
0.918(25) 0.918 (25) 0.918 (25) 0.918
-
-
5
;loo
0.32'** 0.051
48.0
0.918
94
-
-
D D
-
-
0.49(** 0.38(** 0.023"
44.0 44.0 -
0.918 (25) 0.918 (25) 0.918 (23)
D,
40 40 30 ; 60
-
-
0.057
0.035
3.70 102'" 28.0(** 0.082'4" 6.49(" 0.31" 0.028'*
D D D
D D D D DS -
-
Uexp
(cm2/s) x lo-*
0.12 1.58'40 0.035 2.45 0.135'** 0.096'" 0.11 2.73(40 0.02
23
23
6 ; 40 90; 140 85 40 ; 70 70 ; 90 30 ; 80 30 ; 60
(T)
@ (23°C)
2.754
6.167
-
-
12.091 6.260 -
-
13.940 6.550 7.227 5.203
-
-
7.530 2.800 6.580 5.803
-
4.699 -1.958
-
Pre-expon. coefficient Ig Do
68.28
-
89.60
-
-
-
119.4 85.0
-
-
129.5 86.0 94.54 72.61
-
-
96.38 65.58 85.50 87.00
-
68.72 28.01
(kJ/mol)
Activation energy Ed
Diffusion Parameters Diffusion coefficient
20 ; 38 40 ; 60 6 : 40 6 ; 40 40 40 20 ;40 40 ;70 23 Dsw
D D
DS
D,
-
-
44.0 44.0
-
-
D D D D D
D
Dsw
-
Temp. range of experim.
Experiment Type of diffusion coefficient
0.918 (25) 0.918 (25) 0.918 (23) 0.918(23) -
0.918(23)
0.918 (23)
-
-
-
(%)
-
(g/cm3)
(dalton)
-
0.918 (23) -
PP
Cristallinity
Polymer Density @ ("C)
Molec. weight M,
Eicosane (Alcane C2") 282.6 Octadecanamide 283.4 Octadecanamide 283.4 Stearic acid 284.3 Stearic acid 284.3 Methyl Heptadecanoate 284.5 Methylester 3-(3,5-di-tert.-butyl-4-hydroxy292.2 phenyl) propionic acid 2,6-Dinitro-3.5-dimethyl-l-acetyl-4-tert.-butyl-294.3 benzene (Moschus Ketone) 2,4.6-Trinitro-1,3-dimethyl-5-tert.-butylbenzene 297.3 (Moschus Xylol) Metylstearate 298.5 Metylstearate 298.5 Docosane (Alcane CZ2) 310.6 Docosane (Alcane Czz) 310.6 Docosane 310.6 Docosane 310.6 Methylnonadecanoate 312.5 Methylnonadecanoate 312.5 2-(2-hydroxy-3-t-butyl-5-methylphenyl)-5-chlo- 315.8 ro-benztriazol (Tinuvin 326) Heptadecylbenzene 316.4 Heptadecylbenzene 316.4 Propylester 3-(3,5-di-tert.-butyI-4-hydroxyphe- 320.2 nyl) propionic acid -325 Homogenized paraffin 326.4 2-Hydroxy-4-octoxybenzophenone
Name
89 70
66 66 88
66 66 69 69 12
67
69 69 67
50
50
67 80 80 69 69 69 88
Ref.
4
7-
%2
h
6
0
44.0
43.0 48.0 44.0
0.918 (25)
0.918 (23) 0.916(25) 0.923 (25) 0.918 (25)
326.4 326.4 326.5 326.5 326.6 332.4 338.6 340.4 340.4 340.4
2-Hydroxy-4-octoxybenzophenone (Cyasorb
2-Hydroxy-4-n-octoxybenzophenone Methyl Eicosanate Methyl Eicosanate Behenyl-alcohol 2-Hydroxy-4-ethandiol-thioacetic acid ester Tetracosane (Alcane C21, 2-2-Methylene-bis-(4-methyl-6-t .-butylphenol (Plastanox 2246) 2-2-Methylene-bis-(4-methyl-6-t.-butylphenol) (Plastanox 2246) 2-2-Methylene-bis-(4-methyl-6-t.-butylphenol) (Plastanox 2246) 2-Hydroxy- 4 - ethandiol methylthioacetic acid ester Methyl Docosanate Methyl Docosanate 2(2-hydroxy-3-5-di-tert.-butyl-pheny1)-5-chloro-benzotriazole (Tinuvin 327) 4.4'-thio-bis-(3-rnethyl-6-tert-butylphenol) 4-4-Thio-bis-(6-t.-butyl-metacresol) (Santonox) 4-4-Thio-bis-(6-t.-butyl-metacresol) (Santonox)
uv 531)
48.0 44.0 44.0 0.917 (25) 0.918 (25) 0.918 (25)
358.0 358.5 358.5
44.0
44.0 44.0
-
0.918 (25) 0.918 (25) 0.918 (25)
-
-
-
59.0 44.0 44.0
-
-
0.918 (25) 0.918 (25) -
354.5 354.5 357.5
346.4
44.0
-
0.918 (25)
uv 531)
-
43.0 43.0
0.919 0.919
326.4 326.4 326.4 326.4
2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone (HOB) 2-Hydroxy-4-octoxybenzophenone (Cyasorb
Polymer Density Cristal@ ("C) linity PP -
f%l
Molec. weight Mr (dcm3)
Diffusing Species
fdaltonl
Name
D D D
D D D
D
D
D
D
Dsw
D D D D D
D
D D D D
-
Dexp
0.0038'**
0.224"" 0.02
45 ; 70 10 ; 70 10
0.033 0.96"" 0.016
0.009
0.022
0.042'4"
2.08('" 0.072 1.37'4" 0.022'** 0.0067 1.62 0.125""
0.84'40
0.051("' 2.48"" 0.15'** 0.11
fcm2/s)x
-
2.236 5.84
12.22 5.09 6.770
3.461
8.240
-
65.32 88.09
123.0 78.55 93.83
74 93
92
69 69 74
70
74
101.4 76.54
91
81 69 69 66 70 67 91
74
90 90 72 74
85.83
78.75 80.03 79.89 3.725 6.332 4.430 4.95
56.50 118.5 78.4 -
73.86
84.37
-
88.14 61.23
(kJ/rnol)
0.924 11.77 5.221 -
4.250
5.950
-
19.88 2.002
-
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed
20 ;40 40 ; 80 5;70
5 ; 100
10 ; 70
50 ; 90
50 ; 80
70 :90 20 : 40 40 ; 80 40 5 : 100 5:40
40;70
5 ; 40
25
35 ; 50 60 ; 75
f°C)
Experiment Type of Temp. diffusion range of coefficient experim.
P
.r
3
p
2
Diffusing Species
Hexylester of 3(3,5-di-tert.-butyl-4-hydroxyPhenYl) N-amido bis(2,2,6,6-tetramethyl-4-piperidinyl)p-animo propionamide Hexacosane (Alcane C26) Tri-cresyl-phosphate (TCP) 2-2-Methylene-bis(4-ethyl-6-t.-butyl-phenol) (Plastanox 425) Methyl Tricosanate Methyl Tricosanate 2-Hydroxy-4-n-dodecoxy benzop henone 2-Hydroxy-4 ethandiol t-butylthioacetic acid ester Di-octyl-phthalate (DOP) Octacosane Octacosane Octacosane (Alcane CZ8) 2,2,6,6 -Tetramethyl-4-piperidinol(Dastib 845) 2,2,6,6 -Tetramethyl-4-piperidinol (Dastib 845) 2,2,6,6 -Tetramethyl-4-piperidinol(Dastib 845) 2,2,6,6 -Tetramethyl-4-piperidinol(Dastib 845) 2-2-Methylene-bis-(4-methyl-6-methyl-cyclohexyl-phenole) (Novox WSP) Squalane Squalane Triacontane (Alcane C30) 4-4-Methylene-bis-(2-6 di-tert. butyl-phenole) (Ionox 220)
Name
0.94 0.00004'** 0.0087
5 : 40 40 5:70
20 ; 40 42 : 80 70 ; 90 5 : 100
Dsw D, o D
D D D D
0.918 (23) 0.918 (25)
422.6 422.6 422.7 424.5
-
0.918 (23) 0.921 0.921 0.921 0.917 (25) 0.918 (25)
390.6 394.6 394.6 394.6 411.2 411.2 411.2 411.2 420.5
-
-
-
44.0
-
-
-
23.0 44.0
-
-
-
-
-
-
59.0 -
44.0
44.0
44.0
0.918 (25) 0.918 (2.5) 0.918 (25)
-
-
368.5 368.5 382.5 388.5
-
0.918 (23)
366.7 368.4 368.5
D D Dsw D
Dc (1 D D Dsw D D D, D D
-
+
40 40 5 : 40 5;70
20 ; 40 40 40 5 : 40 50 : 75 23 20 ; 40 25 : 60 5 : 70
1.02'~~
49 ; 80
D
-
0.921
366.6
-
0.146(** 0.073'** 0.34 0.010
0.000047 0.0246(** 0.0141'** 0.59 1.99'" 0.069 0.104 0.018(* 0.0063
0.015 1.47'40 1.6'70 0.0008
(cm2/s) x lo4 0.0066'*
uexp
D
-
(T) 30 : 60
(YO) 48.0
-
(g/cm3) 0.918
PP
9.503 7.96
7.970 1.550 7.902 1.54 7.42
-
18.66 -
14.99 1.930 1.127 4.400
6.744 8.89
-1.60
10.45
-
101.8 101.8
95.68 64.0 99.85
-
91.81 57.20
-
175.6 -
140.6 58.50 58.59 87.85
107.4
-
83.70
38.30
(kJ/mol) 116.9
Ed
66 66 67 74
87 66 66 67 94 94 95 96 74
69 69 81 70
67 87 74
94
88
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) lg Do
Experiment Type of Temp. diffusion range of coefficient experim.
Polymer Density Cristal@ ("C) linity
(dalton) 362.4
Molec. weight M,
%
$
2
b
%
8
Diffusing Species
(Uvitex OB) 3,5-di-tert.-butyl-4-hydroxy-benzoic acid- (2.4di-tert-butyl-phenyl) ester (Tinuvin 120) Methyloctacosanate Methyloctacosanate 2-Hydroxy-4 ethandiol n-octylthioacetic acid ester Dodecylester- 3(3,5-di-tert.-butyl-4-hydroxyphenyl) propionic acid Saturated Hydrocarbon (Ceresin 100) Normal paraffin Dotriacontane (Alcane C3z) n-Dotriacontane n-Dotriacontane n-Dotriacontane bis[2,2,6,6-tetramethyl-4-piperidinyl)-sebacate (Tinuvin 770) bis[2,2,6,6-tetramethyl-4-piperidinyl-l-oxy]sebacate bis[2,2,6,6-tetramethyl-4-piperidinyl1-oxy] sebacate 1,1,3-tris(2-methyl-4-hydroxy-5-butyl phenyl) butane (Topanol) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate (DLTDP)
2.5 di(5-tert-butyl-2-benzoxazolyI)thiophene
Name
0.918 (25) 0.918(25) 0.918
438.6 438.6 445.5 446.3
0.917 0.922 0.918 (23) 0.918 (25) 0.918 (25) 0.916 (25) 0.916 (25)
511.3 511.3
512.6 514.4 514.4 514.4 514.4
-
0.918(23) 0.917 0.917 0.917 0.921
-450 -450 450.7 450.9 450.9 450.9 480.7
-
0.918 (23)
(g/cm3)
44.0 44.0 43.0 43.0
-
24.0
23.0
-
48.0
44.0 44.0 -
-
-
(YO)
Polymer Density Cristal@ ("C) linity PP -
438.6
430.5
(dalton)
Molec. weight M, -
5 ; 40 40 ;70 20 ; 50 50 ; 90
23
40 : 80
40 : 80
120 ; 130 150 : 200 5 ; 40 30 : 60 30 ; 60 60 20 ;40
30 ; 60
20 :40 40 ; 80 5 ;loo
23
22
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
-
2uexP
0.85""
0.002
0.053
o.55'40
0.00054
0.17'4u
0.20(~"
0.20 0.00064'* 0.02'* 0.2'*' 0.054"
56.3('*' 7oo(isri
0.013'"
0.003 0.95'40 0.003
0.0018
0.0204(**
(cm I S ) x
9.940 6.230 15.40 2.740
-
3.683
6.840
-2.873 -2.260 10.28 12.69 16.58 3.587
6.891
14.65 2.21 1.611
-
-
-
-
108.9 86.8 147.8 66.6
-
74.5
93.1
72.83
25.40 23.44 107.5 135.32 148.90
95.06
142.7 61.3 68.92
-
-
(kJ/mol)
74 74 91 91
12
96
96
97 98 67 78 78 79 95
88
69 69 70
12
84
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient energy coefficient @ (23"C) Ig Do Ed
Diffusing Species
Didodecyl-3-3-thiodipropionate(DLTDP) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,S-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3.5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxy phenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3.5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) 1- 1-3-tris(2-rnethyl-4-hydroxy-5-tert. -butylpheny1)butane (Topanol CA) 1-1-3-tris(2-methyl-4-hydroxy-5-tert-butylpheny1)butane (Topanol CA)
Name
(g/cm3) 0.928 (25) 0.918 (25) 0.918 (25) 0.918 (25) 0.916 (25) 0.924 (25) 0.928 (25) 0.916 (25) 0.924 (25) 0.928 (25) 0.918 (23) 0.918 0.918 0.918 0.909 (45)
531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 53 1.4 544.5 544.5
0.12'~~
50 ; 80
Dsw
D
44.0 32.5
Ds
Ds
D
D
D
45 :80
5 ;70
1.35'4Q
0.0078
0.149'4"
0.174(40
50 ; 77 49; 110
0.063'4'
45 ; 80
0 . 0 6 4 '~ ~
0.48'50
50 ; 80
50 ; 80
0.00052'*
30 ; 50
D D
0.001I(*
30 ; 50
D
48.0
48.0
44.5
51.0
48.0
43.0
51.0
48.0
0.38(4"
0.01 1
(crn2/s) x 0.27'50 0.0066"
0.008'*
D
43.0
40 ; 70
5 ; 40
(T)
50 ; 90 30 ; 60
uexp
-
-1.558
6.230
3.690
2.950
4.909
6.75
4.37
1.77
18.54
14.71
10.18
3.46
9.15
-
2.470 8.170
37.81
92.6
75.0
70.17
84.54
98.6
82.1
62.4
169.0
145.5
114.9
71.2
108.2
(kJ/mol) 68.2 104.0
Ed
102
74
101
100
99
91
91
91
91
91
91
74
74
91 88
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do
30 ; 50
D
D
D D
-
Experiment Type of Temp. diffusion range of coefficient experim.
44.0
44.0
51.0 48.0
(%)
Polymer Density Cristal@ ("C) linity PP
(dalton) 514.4 531.4
Molec. weight M,
+
S'
b
%2
P
Diffusing Species Molec. weight M,
(dalton) 1-1-3-tris(2-methvI-4-hvdroxv-5-tert-butvl-uhe544.5 I . ny1)butane (Topanol CA) 2-Hydroxy-4-ethandiol n-dodecylthio acetic 557.5 acid ester 2-Hydroxy-4-ethandiol n- octadecylthio acetic 585.5 acid ester N,N -Dioctadecyl-aniline (DODA) 597.6 597.6 N.N -Dioctadecyl-aniline (DODA) Oligomeric hindered amine -600 Oligorners from PE -600 Saturated Hydrocarbon (Ceresin 80) -600 2.2-Thiodiethyl-bis-[3-(3.5-di-tert-butyl-4-hydr- 643.4 oxy pheny1)-propionat] (Irganox 1035) 2,2-Thiodiethyl-bis-[3-(3.5-di-tert-butyl-4-hydr-643.4 oxy pheny1)-propionat] (Irganox 1035) 2,2-Thiodiethyl-bis-[3-(3,5-di-tert-butyl-4-hydr-643.4 oxy pheny1)-propionat] (Irganox 1035) Docosanyl Docosanate 649.1 Docosanyl Docosanate 649.1 Behenyl Behenate 649.1 Distearyl-thio-dipropionate (DSTDP) 682.5 1.3,5-Trimethyl-2,4,6-tri(3,5-di-tert-butyl-4-hy- 774.6 droxy benzy1)benzene (Ionox 330) 1.3,5-Trimethyl-2,4.6-tri(3,5-di-tert-butyl-4-hy- 774.6 droxy benzy1)benzene (Ionox 330) 810.6 Terephthalate-2-2-methylene-bis(4-methyl-6tert-butyl) phenole (HMP12) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl~4-hy- 1176.0 droxy-cinnamate)
Name
-
42.0 42.0 23.0
-
0.918 (25) 0.918 (2.5) 0.921 0.918 -
44.0 44.0 44.0 -
42.8 43.0 44.0 44.0 44.0 20.0
-
0.918 (25) 0.918 (25) 0.918 (25) -
0.916 (30) 0.916 (25) 0.918 (25) 0.918 (25) 0.918 (25) -
-
44.0
(%)
-
(g/cm3) 0.918 (25)
PP
Polymer Density Cristal@ ("C) linity
0.0018 0.15'" 0.041'* 0.01'-
5 ;loo 5 ;loo
D D D D Dth D, Dc 0 D
40; 70 40 $0
D D D D~am D D
0.00024
5 ; 70 80
D D
0.013(*'
0.0000135~""
0.40'40 0.0079
35.1@' 15.6(""
0.18(40
10
D
90 40 : 80 5 ; 70
80 ; 110
0.00058
5 : 40
D
0.15'4"
-
42.22
-0.6720 26.0' 0.00004'*'
-
-
16.78
-
6.12 6.43
-
6.903 -2.0
4.14
14.00
-
-
160.9
-
87.0 93.7
-
93.7 30.1
77.7
143.0
-
-
-
66.96 11.66
3.002 -7.323
0.02""
70
69.92 1.602
105
74
93
80 104 91 74
80
74
74
60 60 95 103 97 93
70 70.01
1.807
25 : 45 25 ; 45 25 40 100; 120 10
0.0028
10
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig DO Ed Dexp (cm2/s) x (kJ/mol) 93 0.0014'**
D
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusing Species Molec. weight M, PP
-
0.013'"' 0.000268'** O.ooo0436(**
49 45 : 110 10
D D
-
93
101
107
75
D
45.0
-
0.000502'" 25 D
-
106
130.6 0.0046'40
5 ;70
45 $0
D
43.0
105
74
D
44.0
-
105
115.5
80
D
32.4
0.068'"'
-
105
105
105
0.00037
80
D
31.5
0.081(**
-
-
-
(kJ/mol)
205
80
D
28.7
0.016(**
-
-
80
D
25.1
0.0105(**
0.012'**
DtXp (cm2/s) x 10"
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) lg Do Ed
0.028'**
80
D
23.3
(T) 80
D
-
Experiment Type of Temp. diffusion range of coefficient experim.
20.0
(%)
-
Polymer Density Cristal@ ("C) linity
(dalton) (gkm?) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy-1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4-hy- 1176.0 droxy-cinnamate) 1176.0 Pentaerythrityl-tetrabis-(3,5-di-tert-butyl-4hydroxy-cinnama te) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 0.918 (25) propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 0.921 (23) propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) 0.924 Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010)
Name
4
2 2
%
b
& 6\
Diffusing Species
Molec. weight M,
(dalton) Tetrakis(3-(3,5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tetrakis(3-(3.5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethy1)- methane (Irganox 1010) Tertakis[methylene-3-(3',5'-di-tert-butyl-4-hy- 1178.0 droxy-phenyl) propionate]-methane Oligomenc hindered amine -1200 Polyethylene segments -2000 Deuterated polyethylene segments -2280 Deuterated polyethylene segments -2440 Deuterated polyethylene segments -3600 Deuterated polyethylene segments -4600 Deuterated polyethylene segments -8000 Deuterated polyethylene segments -11000 Deuterated polyethylene segments -17000 Deuterated polyethylene segments -20000 Deuterated polyethylene segments -23000 Polvethvlene segments -45000
Name
176 125
-
150
-
176
3.0'**
0.081'** 0.15'**
3.2'** 0.34'** 0.15'*" 0.4"*
1.86'**
-
-
-
-
-
111
80
110
80 80
110
110 110 80 80
95 109
329.1 28.0 -
-
25 120 ; 130 150 150 : 200 176 176 150 176
0.000048'** 0.55"2" 31.0'" 20,0('5"
0.917 (23) -
92
48.44
0.133("
55 :75
0.917 ( 2 5 )
108 -
(T) 30 0.0056'**
-
DS
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ed Ig DIl Dexp (cm2/s) x IO-' (kJ/mol) 0.00021'** 77
25
45.0
(%)
-
Experiment Type of Temp. diffusion range of coefficient experim.
0.917 (23)
(g/cm3) 0.920
PP
Polymer Density Cristal@ ("C) linity
diffusion coefficient not measured but extrapolated to 23 "C diffusion coefficient at the temperature given in column 6 (other than 23 *C) diffusion coefficient at the temperature, "C. given in the upperscript.
Methane Methane Methane Acetylene Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane
Name
Diffusing Species
PP
(glcm') 0.964 (25) 0.931 (25) 0.951 (25) UHO 0.964 (25) 0.950 (25) 0.951 (25) 0.951 (25) 0.963 (25) 0.964 (25) 0.941 (23) 0.954 (23) 0.964 (23)
Molec. weight M, (dalton) 16.0 16.0 16.0 26.0 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 -
D
73.0
(T) 15 : 55 25 : 50 25 24 ; 65 5;55 0;so 25 ; 50 -5 ; 50 25 :50 25 :50 23 23 23
Experiment Type of Temp. diffusion range of coefficient experim.
(%)
-
Polymer Density Cristal@ ("C) linity
(cm /s) x 10" 5.06 2.28" 8.2'** 0.000045" 1.26 1.8 2.06'* 2.72 0.72" 0.93'* 3.4 2.1 1.35
2u,xp
-
ultra highly
-
-
-
-
80.94 52.31 53.57 58.68 48.91 67.68 53.27
-
(kJ/mol) 43.52 48.13 1.941 1.333 1.711 2.668 1.064 3.803 1.372
0.384 0.851
-
1 3 9 112 1 9 9 9 9 9 113 113 113
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ .r(23 "C) Ig Do Ed
Abreviations for the type of polymer where no data about the density and cristallinity are given: IS - isotropic, OR - oriented, CD - cold drawn, CM - compression moulded, QR - quenched & rolled, UHM - ultra high modulus. UHO oriented
(40
(* (**
-
Table 2: Diffusion data for low molecular weight organic substances in Polyethylenes (PE) Medium and High Density Polyethylenes (MDPE & HDPE) [Densities larger than 0.930 g/cm3 (at room temperature)]. where: D concentration independent average diffusion coefficient D, 0 diffusion coefficient at "zero" diffusant concentration D, diffusion coefficient in a polymeric sample in contact with a solvent/simulant Dsw diffusion coefficient in a swollen polymeric sample DI,,, diffusion coefficient at the gadvapor pressure given in the subscript
rr,
F'
3(L
b
$:
\o 00
P
Ethane Ethane Ethane Ethane Ethane Ethane Ethane Ethane Allene Cyclopropane Cyclopropane Propylene Propane Propane n-Butane n-Butane Butane Butane Butane Butane Neopentane Neopentane Neopentane n-Pentane n-Butylalde hyde n-Butylaldehyde Butanal
Name
Diffusing Species
30.1 30.1 30.1 30.1 30.1 30.1 30.1 30.1 40.1 42.1 42.1 42.1 44.1 58.1 58.1 58.1 58.1 58.1 58.1 72.1 72.1 72.1 72. I 72.1 72.1 72.1
44.1
(%)
(glcm") 0.971 (23) 0.972 (23) 0.973 (23) 0.952 (25) 0.955 (25) 0.969 (25) 0.939 (25) 0.948 (25) 0.964 (25) 0.965 (25) 0.965 (25) 0.964 (25) 0.965 (25) 0.940 (25) 0.965 (25) 0.965 (25) 0.951 (25) 0.935 (25) 0.944 (25) 0.958 (25) 0.967 (25) 0.967 (25) 0.9.51 (25) 0.9.51 (25) 0.935 (25) 0.944 (25) 0.939
(dalton)
-
59.0 65.0
-
-
-
-
59.0 65.0 71.4
-
-
-
73.0 73.0 58.0
-
-
73.0
-
-
67.5 71.8 79.2
-
-
-
-
Polymer Density Cristal@ ("C) linity PP
Molec. weight M,
D D D D D D D
DZatIll
D D D D D D D D Dsw D D D D D
D D D
D D
-
23 23 23 25 25 25 43 ; 73 60 : 70 5 : 55 30 : 57 120 : 160 5 : 5s 5 : 50 0 : 40 35: 50 120; 160 25 25 25 23 50 : 80 120 : 140 35 : 50 25 : 50 25 25 25
("C)
Experiment Type of Temp. diffusion range of coefficient experim.
0.27'' 0 64' 0 44'I* 0 36'"
0 24(30
31 1 ' I Z I l
0.36' * 1.o' 0.7' 34.5 0.20'"'
0 SY""
67502"
0.42 8.24
0 92
5.7 2.80 1.55 1.83' 1.63' " 1.16'** 13.6'4" 15.8'"' 2 18 1 40' 930(120
-
-
-
-
-
-
54.91 76.53
87.47 26.91
-
5.900 -1.930 0.845 4.933
-
-
-
57.33 16.86 52.31 56.92 52.66 62.36 18.Y6 -
2.260 -2.790 1.194 1.667 2.208 2.70 -2.65
-
39.74 43.36
-
0.233 3.081
-
-
-
-
-
-
-
-
9 9 20
117 115 115
113 113 113 114 114 114 115 115 1 11s 115 1 1 116 115 115 9 20 20
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed D,," (cm*/s); I 0 Y (kJ/mol)
+
2
2
b b
Tetrahydrofuran Tetrahydrofuran Butylalcohol Butylalcohol Benzene Benzene Benzene Methylenechloride Methylenechloride Methylenechloride Methylenechloride Methylenechloride Methylenechloride Pentanal n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n-Hexane n -H exa ne n-Hexane n-Hexane
Name
(Dichlormethane) (Dichlormethane) (Dichlormethane) (Dichlormethane) (Dichlormethane) (Dichlormethane)
Diffusing Species
(dalton) 72.1 72.1 74.1 74.1 78.1 78.1 78.1 84.9 84.9 84.9 84.9 84.9 84.9 86.1 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2 86.2
Molec. weight Mr
0.939 0.944 0.934 0.937 0.943 0.944 0.948 0.949 0.963 0.964
-
(25) (25) (25) (25) (25) (25) (25) (25) (25) (25)
0.940 (25) 0.940 (25) 0.945 (25) 0.949 (25) 0.949 (25) 0.940 (25) 0.949 (20) IS 0.939 (25) 0.938 (25) 0.954 (25)
(g/cm3) IS OR 0.935 (25) 0.944 (25) -
68.0 75.0 90.0 59.0 65.0 55.8 57.3 62.0 62.5 64.9 66.2 74.9 75.8
-
-
68.0
81.0 71.8 71.8 -
59.0 65.0 90.0 35.0 -
-
-
(%)
Polymer Density Cristallinity @ ("C) PP -
50 50 25 25 23 20 ; 40 22 ; 50 25 25 25 22 25 ; 55 25 25 0 0 23 25 25 25 25 25 25 25 25 25 25
("c)
Experiment Type of Temp. diffusion range of coefficient experim. (cm'/s) x 10'" ll.o't 0.19' 0.48' 0.25' 0.40 0.40 4.5 2.66' 2.7' 7.8' 8.9' ' 0.99' l.l('* 0.28" 0.49'*' 0.23'* 0.30 0.60'** 0.38' 0.301' " * 0.247'*' 0.71(" 0.417'" 0.262'** 0.130(** 0.143(" 0.243(**
ucxp
-
(kJ/mol) 118 118 20 20 25 119 120 121 122 122 120 123 118 22 19 19 25 20 20 41 41 41 41 41 41 41 41
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (_23"C) Ig Do Ed
I
%3
5
b
0
Diffusing Species
n-Hexane n-Hexane n-Hexane Ethylacetate Ethylacetate 1-Pentanol 2-Pentanol Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene cis-1.2-Dichloroethylene [runs-1,2-DichIoroethylene 1,2-Dichloroethane n-Hexylaldehyde
Name
(dalton) 86.2 86.2 86.2 88.1 88.1 88.2 88.2 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 97.0 97.1 99.0 100.2
Molec. weight M, (glcm') 0.965 (25) 0.989 (25) 0.992 (25) 0.939 (25) 0.944 (25) 0.939 (25) 0.939 (2.5) 0.932 0.941 0.954 0.956 CD QR QR QR QR CM CM 0.948 (25) 0.948 (25) 0.940 (2.5) IS OR 0.942 (25) 0.942 (25) 0.940 (25) 0.935 (25)
59.0
-
-
70.0 70.0
-
-
-
-
57.0 63.0 71.6 72.9 -
-
(%) 76.5 92.8 94.8 59.0 65.0
Polymer Density Cristal@ ("C) linity PP -
-
-
-
-
-
-
-
D D, n D, + (I Dc 11 D, o Dc 0 Dc 0 Dsw Dc 0 Dsw Dc o Dsw Dc 0 Dsw Dsw Dsw Dsw Dsw Dsw Dsw D
D
Dc I) Dc 0 Dc u D D
-
-
25 25 25 25 30 30 30 30 30 30 30 30 30 30 30 70 70 22 : 50 50 50 30 30 22 : 50 25
25
25 25
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
-
45.0'** 2.4 0.7'**
18.0'**
0.143(** 0.014(** 0 084'** 0.29'** 0.20'** 0.293'** 0.253'" 2.3'** 1.2'** 1.0'*? 0.61( '* 0 42" * 0 90'"* 5 22"" 0.69'** 3.59'*" 0.34'** 5.53'"" 9.2(** 28.0'** 7 73 13.0'** 0.16'**
(cm2/s) x lo4
4 , p
-
(kJ/mol) 41 41 41 20 20 22 22 44 44 44 44 124 124 124 124 124 124 124 46 46 120 118 118 125 125 120 20
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
-
fJl
e
3
f
b
b
106.2 114.2 114.2 114.2 114.2 116.2 116.2 116.2 116.2 119.4 121.2 122.2
p-Xylene n-Octane n-Octane n-Octane Heptanal Ethylbutyrate Ethylbutyrate 1-Heptanol 2-Heptanol Chloroforrm N,N-Dimethylaniline 2-Phenylethylalcohol
106.2
100.2 100.2 100.2 102.2 102.2 102.2 102.2 104.1 106.2
(dalton) 100.2 100.2
Molec. weight M,
106.2 106.2 106.2
Diffusing Species
cis-3-Hexene-1-01 n-Heptane n-Heptane Hexylalcohol Hexylalcohol 1-Hexanol 2-Hexanol Styrene (Vinylbenzene) p-Xylene p-Xylene o-Xylene p -Xy 1ene p-Xylene
n-Hexylaldehyde Hexanal
Name
0.957 0.939 0.944 0.937 0.939 0.939 0.944 0.939 0.939 0.948 0.945 0.956
(25) (25) (25) (25) (25) (25) (25) (25) (25) (25) (25) (23)
0.956 (23) 0.948 (25) 0.948 (25) 0.939 (25) 0.944 (25) 0.939 (25) 0.939 (25) 0.940 (25) 0.975 0.942 (25) 0.942 (25) 0.955 (25) 0.955 (25)
(g/cm3) 0.944 (25) 0.939 (25)
-
71.9 -
-
59.0 65.0 -
70.0 70.0 59.0 65.0 -
-
(%) 65.0
Polymer Density Cristal@ ("C) linity PP -
Dsw D D D D D D D D Dsw D D5
-
-
DS Dc 0 Dsw D D D D Dsw Dsw Dsw Dsw D, n Dsw
D D
12.7'" 0.34'** 0.215'" 0.26 0.079'** 1.05"" 0.89'** 0.036'** 0.077'" 6.79" 0.168'"' 0.023
25 : 70 25 4 : 45 25 25 25 25 25 25 : 50 25 23
25
0.15 4.8'20.0''A 0.3(** 0.1 85'** 0.112'** 0.144(** 5.24 3.41'** 1 LO'** 5.9'** 0.38'"* 11.1'-
(cmZ/s)x lo-* 0.285'" 0.171'**
Dexp
-
-
-
-
-
22.85 -
-
-
-
-3.136
-
-
-
-
-
-
5.535 -
79.97
-
-1.145 -
32.59
-
-
-
34.08 -
-
-
-1.266
-
-
-
-
-
-
-
-
(kJ/mol)
-
-
52 20 20 20 22 20 20 22 22 58 59 57
56 46 46 20 20 22 22 120 126 125 125 127 127
20 22
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
23 70 70 25 25 25 25 22 ;50 30 30 30 30 30
(T) 25 25
Experiment Type of Temp. diffusion range of coefficient experim.
c
f&
b
b
8
-
Diffusing Species
n-Octylaldehyde n-Octylaldehyde Octanal Naphthalene Octylalcohol Octylalcohol Amylaceticester (Isoamylacetate) Amylacetate (Isoamylacetate) Amylacetate (Isoamylacetate) Trichlorethylene 1.1.1-Trichlorethane 1,1,2-Trichloroethane 4-Isopropenyl-1methyl-I-cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) Decahydronaphthalin (Decalin) n-Decane n-Decane Ethylhexanoate 2-Methylnaphthalene Dimethylbenzylcarbinol Brornobenzene 1,7,7-Trimethyl-2,2,1-heptane-2-one (Carnpher) Carbonte trachloride Carbonte trachloride 3.7-Dimethyl-6-octene-1-al (Citronellal)
Name n IJ,,p
0.021(~" 0.219** 0.14"* 2.02"" 0.36'*= 0.0045 3.49': 0.0022 0.046" 2.63'* 0.0053
80 : 100 25 25 50 25 23 25 : 70 23 25 ;65 25 : 70 23 90.0 59.0 65.0 59.0
(UHM) 0.939 (25) 0.944 (25) 0.939 (25) 0.940 (2.5) 0.9.56 (23) 0.948 (25) 0.956 (23) 0.952 (25) 0.948 (25) 0.956 (23)
138.3 142.2 142.2 144.2 144.2 150.2 150.7 152.2 153.8 153.8 154.2 -
-
70.0
-
-
-
-
0.05
(cm2/s) x 0.20(** 0.175'** 0.031(** 3.33(** 0.20'** 0.135'*' 0.085 0.91(** 0.305'** 12.3'* 1.61'* 1.52 0.057 23
(OC) 25 25 25 50 25 25 23 30 33 25 : 70 25 : 50 22 : 50 23
58 57 30 58 57
-
31.80 85.77 32.75
-
-1 345
-
5.800 -1.801
-
-
-
-
-
-
-
130 20 20 120 20 57
129 88.12 -
-
-
22.16 41.61 50.16
-
-
120 20 20 57 128 128 58 58 120 57
20 20 22
3.740
-
-
-2.999 -0.451 1.033
-
-
-
-
-
-
-
-
-
-
(kJ/mol)
-
-
-
-
Diffision Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed
-
-
Experiment Type of Temp. diffusion range of coefficient experim.
-
-
-
-
-
0.948 0.948 0.940 0.956
(25) (25) (25) (23)
-
-
-
59.0 65.0
-
-
(%) 59.0 65.0
-
(g/cm3) 0.939 (25) 0.944 (25) 0.939 (25) 0.940 (25) 0.939 (25) 0.944 (25) 0.956 (23) -
Polymer Density Cristal@ ("C) linity PP -
136.2
(dalton) 128.2 128.2 128.2 128.2 130.2 130.2 130.2 130.2 130.2 131.4 133.4 133.4 136.2
Molec. weight Mr
Diffusing Species
n-Decylaldehyde n-Decylaldehyde Decanal Undecane 2-Isopropyl-5-methylcyclohexanole(Menthol) Decylalcohol Decylalcohol Methoxy-4(2-propenyl)phenol (Eugenol) Tetrachlorethylene Tetrachlorethylene Tetrachlorethylene Diphenylmethane 1,1,2,2-Tetrachlorethane Diphenyloxide Ethyloctanoate Ethyloctanoate 4-Hydroxyundecanlactonidacide n-Dodecane n-Dodecane Dodecane (Alcane ClZ) Dodecane (Alcane C12) n-Dodecane 2-Tert-butyl-4-methoxyphenol(BHA) n-Dodecylaldehyde (Aldehyde Clz) 3,7-Dimethyl-1,6-octadien-3-ylacetate (Linalyl. acetate) p-Aminoazobenzene (pAAB)
Name
0.956 (23) 0.939 (25) 0.944 (25) 0.956 (23) 0.948 (25) 0.945 (25) 0.945 (25) 0.956 (23) 0.948 (25) 0.956 (23) 0.939 (25) 0.944 (25) 0.956 (23) 0.939 (25) 0.944 (25) 0.956 (23) 0.956 (23) 0.954 (25) 0.939 (25) 0.956 (23) 0.952 (30)
197.3
-
0.939 (25) 0.944 (25) 0.939 (25)
156.3 156.3 156.3 156.3 156.3 158.3 158.3 164.2 165.8 165.8 165.8 168.3 165.8 170.2 170.3 170.3 170.3 170.3 170.3 170.3 170.3 170.3 180.2 184.3 196.3 68.0
-
59.0
-
-
59.0 65.0 -
-
59.0 65.0
-
-
68.0 68.0 -
-
59.0 65.0
-
-
-
-
80
23 25 : 70 23 25 25 23 25 25 23 23 40 10 : 50 25 23
25
25 25 25 40 23 25 25 23 25 ; 70 25
("c)
-
(YO) 59.0 65.0
(glcm')
PP
Experiment Type of Temp. diffusion range of coefficient experim.
Polymer Density Cristal@ ("C) linity
(dalton)
Molec. weight Mr x
5.92'**
0.125'** 0.064 3.8 0.423'** 0.0355 0.073'"" 0.0082'*
0.17'**
0.16'** 0.0048
0.19'**
0.035 0.74" 0.039
8.0'*"
0.013 5.06'" 0.9'**
0.08'**
(cm IS)
10-' 0.135'** 0.103'** 0.018'** 1.03'** 0.0057 0.15(*'
-
*uexp
-
-
-
-
65.28
-
-
-
-
-
-
-
-
45.48
-
-
-
24.03
-
-
-
-
-
(kJImol)
104
20 20 22 66 57 20 20 57 58 131 131 57 58 57 20 20 57 20 20 67 67 66 132 20 57
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed
'r,
22
b b
'c1
g
226.4 226.4 226.4 228.2 240.4 244.2 252.7
201
Hexadecane (Alcane Clh) Hexadecane (Alcane CI6) Hexadecane 2-Hydroxy-4-methoxybenzophenone Heptadecane Triphenylmethane Bromoform
(dalton)
Molec. weight Mr 198.4 198.4 200.3 200.3 200.3 212.4 214.2 214.2 214.2 220.3 220.3 220.3 220.3 220.3 220.3 220.3 220.3 220.3 225.3
Diffusing Species
Tetradecane (Alcane CI4) Tetradecane (Alcane C14) Ethyldecanoate Ethyldecanoate Ethylcaprate Pentadecane 2,4-Dihydroxybenzophenone 2,4-Dihydroxybenzophenone 2,4-Dihydroxybenzophenone 2.6-Di-tert-butyl-4-methylphenol 2.6-Di-tert-butyl-p-cresole 2.6-Di-tert-but yl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenol 2,6-Di-tert-butyl-4-methylphenoI 2-(2'-hydroxy-5'-methyl-phenyl)-2H-benzotna-
Name
~
(23) (23) (25) (25) (30)
-
0.978
-
0.948 (25)
-
70.0 -
-
-
-
-
-
0.956 (23) 0.956 (23)
-
-
0.964
-
-
-
-
-
-
-
68.0 72.0 72.0 64.0 54.0
-
59.0 65.0 68.0
-
-
(%)
0.978
0.953 0.959 0.959 0.948 (25) 0.934
-
0.956 0.956 0.939 0.944 0.952
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
-
23 23 40 80; 110 40 40 25 : 70
23 23 25 25 90 40 60 ; 75 43 ; 75 44 5 : 60 20 : 80 23 30 : 60 30 ; 60 30 : 60 30 ; 60 40 100 40
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
0.029 1.90 0 637' 0.02'x" 0.586' 0 0698' 0 90'
I(
0.049 3.2 0.14'* 0.11'*' 37.3'* 0.778' 0 0783"" 0.041'4" 0 0099' * 0 00027 0 133 0 0138 0 00046' 0.00048' 0.0004" 1.91' 0 01' 12 0' 0 136(
(cm'ls) x I O Y
Dcxp
-
-
-
-0.3476
43.62
-
-
72.82 -
-
-
-
2.477
-
-
-
-
-
-
-
102.60 77.56 106.77 40.71 -
-
6.768 3.372 7.449 4,534
-
-
175.80 54.82
-
102.10 93.32 -1 1.88 0.800
7.406 6.184
-
-
-
-
-
(kJ/mol) -
-
-
-
58
81 66 66
67 66
6
79 79 78 78 134 78 66
77 133 75
104 66 71 71 71
67 20 20
67
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Do Ed
Diffusing Species
Stearyl alcohol Eicosane (Alcane C20) Eicosane (Alcane CzO) Docosane (Alcane (222) Docosane (Alcane C22) Docosane Caprylcaprate Ethylstearate Heptadecylbenzene 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-H ydroxy-4-octoxybenzophenone Behenyl alcohol Tetracosane
2-Hydroxy-4-n-butoxybenzophenone
n-Octadecane (Alcane CIR) n-Octadecane (Alcane Clx) n-Octadecane n-Octadecane n-Octadecane n-Octadecane n-Octadecane Octadecane n-Octadecane n-Butyllaureate Te tramethylpentadecane
Name
(dalton) 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5 256.4 268.6 270.3 270.3 282.6 282.6 310.6 310.6 310.6 313.5 313.4 316.2 326.4 326.4 326.4 326.4 338.6
Molec. weight M,
-
(23) (23) (23) (23)
-
0.953 0.959
-
-
0.952 (30) 0.952 (30)
-
0.956 0.956 0.956 0.956
-
-
-
0.934 0.Y52 (30)
23 23 40 90 90 40 80; 110 55 ;75 55 ; 75 40 40
23
(T) 23 23 24 : 60 24 ; 60 30 ; 60 30 : 60 30 ; 60 40 20 ; 100 90 40 80: 110 40 23
-
(YO)
(g/cm3) 0.956 (23) 0.956 (23) 0.978 0.978 0.978 0.978 0.978
Experiment Type of Temp. diffusion range of coefficient experim.
Polymer Density Cristal@ ("C) linity PP -
0.042"" 0.0066"" 0.0013'4" 0.0169'** 0.0527(**
0.12'**
0.50 0.0033 0.20 0.0417'"" 9.72' * * KO(**
'
-
-
-
-
90.40 166.90 155.00
4.602 16.81 14.98
-
-
-
-
-
-
-
-
-
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 " C ) Ig Do Ed Dexp (crn2/s)x lo-' (kJ/rnol) 0.019 1 I6 0.0035' 9.466 112.86 I .45' 0.337 46.32 0.03 1 -2.838 37.81 7.519 100.15 0.005' 0.0088' 7.029 96.79 0.2 16' 1.4 1.300 51.89 2 I .5' 0.102' 0.029"" 2.919 77.42 0.0819' 0.009
66
66
90
66 104 104 66 81 90
81 66 67 67 67 67
133 104 66
78 78 83 79 79 66
67 67
Ref.
3
4
2
2
2
b
m
Diffusing Species
Di-octyl-phthalate (DOP) Squalane 2,5-Bis-(5-tert-buthyl-benzoxazol-2-yl)-thiophene n-Dotriacontane n-Dotriacontane n-Dotriacontane Laurylstearate Bis-[2,2,6,6-tetramethyl-4-piperidinyl-l-oxy] sebacate Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP) Didodecyl-3-3-thiodipropionate(DLTDP)
Di-(2-ethylhexyl)-phthalate
(Plastanox 2246) 2-2-Methylene-bis-(4-methyl-6-t.-butyl phenol) (Plastanox 2246) 2-2-Methylene-bis-(4-rnethyl-6-t.-butyl phenol) (Plastanox 2246) n-Butylstearate N-Octadecyl-1-diethanolamine (N-ode) Phenylstearate Lauryllaureate Lauryllaureate Lauryllaureate Lauryllaureate 2-Hydroxy-4-n-octadecoxybenzophenone
Name
68.0 54.0 68.0 70.0 71.0 72.1 85.5 70.0 -
0.952 (30) 0.934 (25) 0.952 (30) 0.956 (30) 0.957 (30) 0.964 (30) 0.977 (30)
-
341.4 357.4 361.4 369.6 369.6 369.6 369.6 382.5 390.6 390.6 422.7 430.5 0.978 0.978 0.978 0.952(30) 0.943 0.937 0.952 0.9.54
450.9 450.9 450.9 453.6 511.0 514.4 514.4 514.4
-
-
57.0 68.0 69.0
68.0 46.0
-
-
69.0
0.954 (25)
340.4
-
68.0
0.952 (25)
-
Polymer Density CrislalC3 ("C) linity
340.4
Molec. weight
0.000029'* 0.014'" 0.000064(* 5.77'"' 0.074(60 0.25(b" 0.12'6" 0.12'fJ"
60 : YO 60 : 90 60 : 90
0.0136'"' 0.0016'*" 0.0345"" 0.00933'""
0.08""
7.55' 0.26 7.62'** 1.60'"' 1 1 2'"' 0.9'** l.l(**
0.0062'7"
0.0048'"'
-
-
84.00 83.90 70.0
105.30
7.387 4.580 4.260 2.070
154.40 166.99 144.00 -
-
-
-
-
71.14
14.71 19.629 13.22 -
-
-
-
-
1.431
-
-
-
52.73 0.477
-
51.47 -
111.30
112.38
95.79
(kJimol)
0.500
-
7.800
7.840
6.030
91 91 91
78 78 79 104 96
81 66 87 66 66
135
104 133 104 104 104 135
91
91
91
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ed lg Do
30 : 60 30 : 60 30 ; 60 90 60:100
90 20 ; 78 90 60 : 90 90 85 85 80 ;110 40 70 40 40
50 ; 80
50 :80
Experiment Type of Temp. diffusion range - of coefficient experirn.
Diffusing Species
Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3.5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Stearylstearate 1-1-3-tris(2-methyl-4-hydroxy-5-tert-butylphenyl) butane Laurin Docosanic acid docosanyl ester (Behenyl behenate) Docosanic acid docosanyl ester (Behenyl behenate) Behenyl behenate
Didodecyl-3-3-thiodipropionate (DLTDP) Didodecyl-3-3-thiodipropionate
Name
68.0 54.0 57.0 57.0 68.0 68.0
69.0 69.0 65.0 65.0 65.0 68.0 54.0 68.0 72.1 85.5
(g/cm3)
0.952 0.934 0.937 (25) 0.937 (25) 0.952 (25) 0.952 (25) 0.954 (25) 0.954(25) 0.963 0.963 0.963 0.9.52 (30) 0.934 0.952 (30) 0.964 (30) 0.977 (30) 0.952 (30)
(dalton)
514.4 514.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 531.4 537.6 544.5 639.1 649.1 649.1 649.1
68.0
(%)
Polymer Density Cristal@ ("C) linity PP
Molec. weight M, D
-
Dexp
7.819
0.018(~0 0.0022(~~) 0.00062'40
50 ; 90 50 ; 121
49 ; 110
0.75'Rn 2.75'** 90
-
-12.705
-
30.96
-
75.95
-
2.601
51.06
4.300
3.75'** 0.28""
1.14(** 0.23@'
130.1
114.0
125.1
87.67
171.42
10.330
4.44
18.24
104
135
104 135
133
104
136
101
100
91
91
91
91
147.27 102.82
91
91 133 91 91.44
157.50 51.89 171.6
(kJ/mol)
0.0033'70
85 : 95
90
85 ; 95
90 56 ; 100
77 : 135
9.568
0.000098''
30 ; 50
6.550
0.0083's0
50 ; 90
13.9
5.33
0.00008("
0.035'sn
50 ; 90
18.57
0.5
18.67
-
30 ; 50
0.075" 3.9'70 0.00019'*
(crn2/s) x lo4
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23°C) Ig Do Ed
30 ; 60 78 ; 100 30 ; 50
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
i?:
3
B
-6
5A
%
v1
Diffusing Species
(g/cm')
(dalton)
diene Deuterated polyethylene Three-arms star branched deuterated polybutadiene
-5000 -9300
Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Linear deuterated Polybutadiene (PBD) -2600 Deuterated polyethylene -3000 Three-arms star branched deuterated polybuta-3100
propionyloxymethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010)
Behenyl behenate Behenyl behenate
-
-
-
-
-
-
-
-
65.0
-
-
0.963
65.0
-
70.0 71.O 57.0 68.0 68.0 69.0 68.0 68.0 68.0 68.0
(%)
-
0.963
0.956-(30) 0.957 (30) 0.937 (25) 0.952 (25) 0.952 (25) 0.954 (2.5) 0.952 (30) 0.952 (30) 0.952 (30) 0.952 (30) 0.963
PP
Polymer Density Cristal@ ("C) linity
Molec. weight M,
649.1 649.1 Distearyl-thio-dipropionate (DSTDP) 682.5 Distearyl-thio-dipropionate (DSTDP) 682.5 Distearyl-thio-dipropionate (DSTDP) 682.5 Distearyl-thio-dipropionate (DSTDP) 682.5 Myristin 723.2 Dioctadecyl Octadecanedioate 847.2 Stearin 891.3 Didocosyl Eicosandioate 988.2 Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8
Name
-
176 176
176 176 176
50 ; 130
25
49 ; 135
80 ;125 90 60 : 90 30 :60 60 : YO 60 ; YO 90 90 90 90 49 : 135
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
13.98
0.0000018'40
2.2'** 0.23(**
10.5'** 3.5'** 2.1(**
0.000044~50
0.000502(**
-
143.8
-
-
-
-
-
-
-
-
-
153.0
-
166.0
-
12.394
-
-
7.15 20.94 3.90 4.46
-
11.16
-
-
-
67.38 99.31 183.55 80.10 84.11 -
4.02(90 2.17'** 0.12'"' 0.00035" 0.088''O 0.072"" 0.74'** 1.22'** 0.61(*' 1.02'" 0.000014'""
2.368
139 138
138 139 138
100
75
101
104 104 91 91 91 91 104 104 104 104 137
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Do Ed Dcxp (cm'/s) x lo-' (kJlmol)
\o
5
1
Diffusing Species
Deuterated Polyethylene Linear deuterated polybutadiene (PBD) Deuterated polyethylene Linear deuterated polybutadiene (PBD) Three-arms star branched deuterated polybutadiene
Name
-
-
(dalton) 10200 108oO 18000 -53000 -66300
Molec. weight M,
-
-
-
-
-
(%)
-
-
-
(g/crn') -
Polymer Density Cristallinity @ ("C) PP D D D D D
-
176 176 176 176 176
(T)
Experiment Temp. Type of range of diffusion coefficient experim.
Diffusion Parameters Ref. Pre-expon. Activation Diffusion coefficient coefficient energy @ (23°C) lg Do Ed Dexp (cm2/s) x lo-' (kJlmo1) 0.13'" I39 0.85'** 138 139 0.075(** 0.04(*" 138 0.001(** 138
$
&
B3
-
"D
a
0
diffusion coefficient not measured but extrapolated to 23 "C diffusion coefficient at the temperature given in column 6 (other than 23 "C) diffusion coefficient at the temperature. "C,given in the upperscript.
(* (**
(4"
concentration independent average diffusion coefficient diffusion coefficient at "zero" diffusant concentration diffusion coefficient in a polymeric sample in contact with a solventlsimulant diffusion coefficient in a swollen polymeric sample diffusion coefficient at the gaslvapor pressure given in the subscript
D D, D, Dsw D,,,,
Diffusing Species
Ethylene Methanol Methanol Ethanol Ethanol Ethanol Acetone Dimethylcarbinol(2-Propanol) Benzene Benzene Benzene Cyclohexane Dichloromethane Dichloromethane
Name
(dalton) 28.1 32.0 32.0 46.1 46.1 46.1 58.1 60.1 78.1 78.1 78.1 84.2 84.5 84.5
Molec. weight Mr
-
-
0.902 (23) -(HO) 0.910 (25) 63.0 10.0 (aT) 0.883 47.0 (iT) 0.883 47.0 (iT) 0.883 47.0 (iT) 0.883 47.0 (iT)
-
-
-
64.0 BO BO
(%)
-
-
-
-
(glcm') 0.892
PP
Polymer Density Cristal@ ("C) linity
D
(T) 25 23 23 20 20 10 ; 25 10 ; 25 23 25 15 ; 40 25 25 25 25
Experiment Type of Temp. diffusion range of coefficient experim.
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Drxp (cm'is) x to-' (kJ/mol) 0.45'** 0.0009 0.0004 0.084'** 1.5(** 15.335 140.3 0.038 -8.572 4.99 0.035 0.0012 0.085(*' 0.72 6.557 83.33 19.6'** 10.6(** 0.22'*" 13.0'" -
Abreviations for the type of polypropylene: aT - atactic, iT - isotactic, HO - homopolymer, CO -copolymer, BO - biaxially oriented, UO - uniaxially oriented, SB - stereoblock polymer,
where:
Table 3: Diffusion data for low molecular weight organic substances in various types of Polypropylenes (PP)
140 141 142 142 142 143 143 144 30 145 146 146 146 146
Ref.
Diffusing Species
bis-(2-Chloroethyl)-sulfide Methylcyclohexane Methylcyclohexane Methylcyclohexane Methylmethacrylate
bis-(2-Chloroethyl)-sulfide bis-(2-Chloroethyl)-sulfide
Methylenechloride n-Hexane n-Hexane n-Hexane n-Hexane Tetrafluormethane Tetrafluormethane Tetrafluormethane Tetrafluormethane Tetrafluormethane Tetrafluormethane Toluene Toluene Toluene Toluene Toluene Toluene Toluene Toluene bis-(2-Chloroethyl)-sulfide
Name
(%)
0.889 (25) 0.889 (25) 0.890 0.905 0.897(25)
-
- (BO) 60.3 (iT) 60.3 (iT) 74.0 (iT) - (iT) 65.0(iT) 56.9(iT)
-
0.883 47.0 (iT) 0.910(25) 63.0 43.0 (iT) 43.0 (iT) 0.883 47.0 (iT) 0.895 (25) 47.8 (iT) 0.915 (25) 73.0 (iT) 0.895 (25) 47.6 (iT) 0.914 (25) 72.5 (iT) 0.906 (25) 61.8(iT) 0.915 (25) 72.6 (iT) 74.0 (iT) 0.904 64.0(UO) 0.904 64.0(UO) 0.916 0.916 78.0(OP) 0.883 47.0 (iT) 0.890 - (iT) 0.905 65.0(iT)
(g/cm3)
(dalton)
84.5 86.2 86.2 86.2 84.5 88.0 88.0 88.0 88.0 88.0 88.0 92.1 92.1 92.1 92.1 92.1 92.1 92.1 92.1 96.5 96.5 96.5 96.5 98.2 98.2 98.2 100.1
PP
Cristallinity -
Polymer Density @ ("C)
Molec. weight Mr D,
-
n
25 25 30 ;60 30 ;60 25 40 ;70 40 ;70 40 ; 70 40 ; 70 40 ; 70 40 ; 70 0;50 30 30 30 30 25 40 40 25 ;45 25 : 45 20 : 40 20 ; 30 0;so 40 40 60
(T)
Temp. range of experim.
Experiment Type of diffusion coefficient
0.0204" 0.0091 0.0093 0.0165 30.0('* 10.2(" 0.91'**
0.10''
0.43'3n 0.60('0 0.43(3" 0.67'3n 0.12 0.056(** 42.0"" 0.0028'*' 0.0097'** 10.0(" 78.1"' 33.2'**
0.60'3"
0.24("' 0.06'" 4.68" 400(' 27.0(** 0.51(30
30.24 31.13 94.60 93.07 76.3 -
-3.654 4.196 6.657 6.394 3.683
-
-
-
-
-
-
-
-
-
-
-
53.64 45.84 65.62 65.97 69.38 62.56 67.95 66.55 57.61 -
-
-
-
3.024 3.155 3.598 2.659 3.348 3.297 1.262
-
2.136 2.691
-
-
(kJ/mol) -
Activation energy Ed
Diffusion Parameters Diffusion Pre-expon. coefficient coefficient @ (23"C) Ig Dd Dexp (cm2/s) x lo-* -
152 152 155
150
147 30 148 148 146 149 149 149 149 149 149 150 151 151 151 151 146 152 152 153 153 154 154
Ref.
+
$
9
%
b
N
p
VI
Diffusing Species
Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylme thacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate Methylmethacrylate n-Heptane cis-3-Hexene-1-01 cis-3-Hexene-1-01 cis-3-Hexene-1-01 p-Xylene p-Xylene o-Xylene o-Xylene Chlorobenzene 2,2,4-Trimethylpentane 2.2.4-Trimethylpentane Chloroform Chloroform 2-Phenylethylalcohol 2-Phenylethylalcohol 2-Phenylethylalcohol 2-Phen ylethylalcohol
Name
100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.1 100.2 100.2 100.2 100.2 106.2 106.2 106.2 106.2 112.6 112.6 112.6 119.4 119.4 122.2 122.2 122.2 122.2
(dalton)
Molec. weight M,
-
0.900 0.902 0.900 0.902
(23) (23) (23) (23)
(25) (25) (25) (25) (25) (25) (25) (25) (25) (25)
(%)
-
-
(CO)
- (HO) - (CO) - (HO)
-
62.4 (iT) 65.2 (iT) 66.1 (iT) 68.0 (iT) 74.5 (iT) 75.4 (iT) 76.3 (iT) 77.3 (iT) 56.9 (iT) 68.0 (iT) 74.0 (iT) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.902 (23) - (HO) 0.890 - (iT) 0.905 65.0 (iT) - (iT) 0.890 65.0 (iT) 0.905 0.883 47.0 (iT) 0.890 - (iT) 0.905 65.0 (iT) 0.883 47.0 (iT)
0.902 0.904 0.905 0.907 0.912 0.913 0.914 0.915 0.897 0.907
(g/cm')
PP
Polymer Density Cristal@ ("C) linity -
60 60 60 60 60 60 60 60 20 : 60 20 ; 60 0 : 50 23 23 23 40 40 40 40 25 40 40 25 25 ;SO 23 23 23 23
("c)
Experiment Type of Temp. diffusion range of coefficient experim.
0.32'" 0.24' * ' 0.056 0.0064 0.037 0.017 0.015 0.012 70.0'** 28.0(** 38.0(** KO(** 13.0(** 25.0'** 5.0'** 10.6'** 23.7(* 0.0026 0.0017 0.0016 0.0013
-
-
-
-
-
14.09
-
-
-
-
-
-
-
-
-
-
62.44 66.22 75.2
-
-
-
-
-
0.68'*"
-
(kJ/mol)
-
-
0.77'"* 0.49"* 0.28'** 0.14(** 0.88'"
(cm2/s) x
155 155 155 155 155 155 150 57 57 144 152 152 152 152 146 152 152 146 58 57 57 57 57
155
155 155 155
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Dexp
-
t;
u l
3
b
2
"0
2-Phenylethylalcohol Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Amylaceticester (Isoamylacetate) Trichlorethylene 1J.1-Trichlorethane 4-Isopropenyl-I-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-1 -cyclohexene (Limonene) 4-Isopropenyl-I-methyl-I-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-] -cyclohexene (Limonene) 4-Isopropenyl-I-methyl-] -cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) 4-Isopropenyl-I-methyl-1-cyclohexene (Limonene)
Name
Diffusing Species
-
- (HO)
0.902 (23) 0.902 (23) 0.902 (23)
136.2 136.2 136.2
-
-
136.2 136.2 136.2 136.2
- (UO)
66.0(BO)
24
30
30
30
63.0(UO)
-
136.2
66.0(BO)
30
51.0
-
136.2
30
30
51.0
-
63.O(UO)
23
- (HO)
("c) 23 23 23 23 23 23 25 ;70 25 ;50 23 23
Ds
-
Experiment Type of Temp. diffusion range of coefficient experim.
- (HO)
-
-
(HO) (CO) (HO) (CO) (HO) (HO) -
(YO)
-
-
-
-
-
(g/cm3) 0.902 (23) 0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23) 0.902 (23)
PP
(dalton) 122.2 130.2 130.2 130.2 130.2 130.2 131.4 133.4 136.2
Molec. weight M,
Polymer Density Cristal@ ("C) linity
157
156 0.594(** 0.0003(**
156
156
0.6 1 (** 0.042(*'
156
156
156
141
144
144 57 57 57 57 144 58 58 57
Ref.
0.17(""
4.3'"
0.151('*
0.000375
0.0025
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Dexp (cm2/s) x IO-' (kJ/mol) 0.0089 0.0068 0.0038 0.0045 0.0024 0.003 30.3'' 9.90.0032
+
h
3 B
%
b
VI
,A P
Diffusing Species
4-Isopropenyl-1-methyl-1-cyclohexene (Limonene) Ethyleneglycolmonophenylether (EMPhE) n-Decane bis-(2-Chloroethyl)-ether bis-(2-Chloroethyl)-ether Dimethylbenzylcarbinol Dimethylbenzylcarbinol Dimethylbenzylcarbinol Bromobenzene 1.7,7-Trimethyl-bicyclo12.2.11 heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo[2.2.1] heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo[2.2.1] heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo12.2.11 heptane-2-one (Camphor) 1,7,7-Trimethyl-bicyclo[2.2.1] heptane-2-one (Camphor) Carbontetrachloride Carbontetrachloride Carbontetrachloride 3,7-Dimethyl-6-octene-l-al (Citronellal) 3,7-Dimethyl-6-octene-l-al (Citronellal) 3,7-Dimethyl-6-octene-l-al (Citronellal) 3,7-Dimethyl-6-octene-l-ol (Citronellol) 2-Isopropyl-5-methyl-cyclohexanole (Menthol)
Name
0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23) 0.902 (23) 0.910 (25) 0.883
152.2 152.2 152.2 152.2 153.8 153.8 153.8 154.2 154.2 154.2 156.3 156.3 0.900 0.902 0.902 0.902 0.900
-
-
(23) (23) (23) (23) (23)
0.900 (23) 0.902 (23) 0.900 (23)
-
(g/cm3) -
(UP)
(%)
Polymer Density Cristal@ ("C) linity PP -
138.2 142.3 143.0 143.0 150.2 150.2 150.2 150.7 152.2
136.2
(dalton)
Molec. weight Mr
DS
D
-
25 25 25 ; 70 23 23 23 23 23
23
23
23
23
25 ; 60 70; 110 25 ; 45 25 ; 45 23 23 23 25 ;70 23
24
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
0.02"* 11.0(** 11.3'* 0.0013 0.00071 0.00043 o.ooo5 0.00066
0.00024
0.00039
0.00071
0.00033
0.00046'* 0.53(70 0.171'" 0,029'" 0.00092 0.001 1 0.0012 11.9(* 0.00044
0.016'**
-
-
-2.306
-
-3.934
-
11.715 3.644 4.318 4.994
-
57 57 144
-
-
-
-
-
26.17 -
144
58 57 57 57
30 146
51
-
-
58 57
143 81 153 153 57 57 57
157
17.11 -
-
-
130.6 78.28 25.21 25.76 -
-
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed D'Xp (cm2/s) x (kJ/mol)
s. *
4
%
g
2-Isopropyl-5-methyl-cyclohexanole (Menthol) 2-Isopropyl-5-methyl-cyclohexanole (Menthol) Undecane Methoxy-4(2-propenyl)phenol (Eugenol) Methoxy-4(2-propenyl)phenol (Eugenol) Methoxy-4(2-propenyl)phenol (Eugenol) Methoxy-4(2-propenyl)phenol(Eugenol) Tetrachlorethylene Diphenylmethane Diphenylmethane Diphenylme thane Diphenylmethane Diphenylme thane Diphenylamine (DPA) Diphenylamine (DPA) Diphenylamine (DPA) 1,1,2,2-TetrachIoroethane Diphenyloxide Diphenyloxide Diphenyloxide Diphen yloxide Diphenyloxide n-Dodecane (Alcane C12) n-Dodecane (Alcane C,?) n-Dodecane (Alcane C12) n-Dodecane (Alcane Clz) n-Dodecane
Name
Diffusing Species
156.3 156.3 156.3 164.2 164.2 164.2 164.2 165.8 168.3 168.3 168.3 168.3 168.3 169.2 169.2 169.2 169.9 170.2 170.2 170.2 170.2 170.2 170.3 170.3 170.3 170.3 170.3
(dalton)
M*
Molec. weight
-
-
(aT) -
0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.902 (23) - (HO) 0.900 (23) -(CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902(23) - (HO) -
-
-
0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.900 (23) - (CO) 0.902 (23) - (HO) 0.902 (23) - (HO) - (aT) - (aT)
-
-
(%)
-
(HO) 0.902 (23) - (HO)
(g/cm3) 0.902(23)
PP
Polymer Density Cristallinity @ ("C)
D,
-
40
40 23 23 23 23 25 ;70 23 23 23 23 23 40 ;60 40 :60 40 25 ;70 23 23 23 23 23 23 23 23 23
(T) 23 23
Experiment Temp. Type of diffusion range of coefficient experim. Uexp
0.00026 0.0013 0.212'** 0.0024 0.0015 0.0021 0.00105 16.9'* 0.0029 0.0016 0.0022 0.0015 0.00125 0.073(40 0.51(4" 0.78(** 3.6(* 0.0038 0.002 0.0021 0.0013 0.0018 0.011 0.0059 24.0 34.0 0.0934'*'
(cm2/s) x I O - ~
-
(kJlmo1)
57 144 66 57 57 57 144 58 57 57 57 57 144 158 158 158 58 57 57 57 57 144 67 67 67 67 66
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient @ (23 Ig Dd - "C) Ed
4
52
h b
o\
p
VI
Diffusing Species
y-Undecanlactone Tridecane Methyl decanoate Methyl decanoate 3,7-Dimethyl- 1,6-octadiene-3-ylacetate (Linalylacetate) 3.7-Dimethyl-l,6-octadiene-3-ylacetate (Linalylacetate) 3,7-Dimethyl-1,6-octadiene-3-ylacetate (Linalylacetate) 3,7-Dimethyl-l,6-octadiene-3-ylacetate (Linalylacetate) Phenylbenzoate (PB) Phenylbenzoate (PB) Tetradecane (Alcane C14) Tetradecane (Alcane CI4) Tetradecane (Alcane CI4) Tetradecane (Alcane C14) Phenothiazine 4-Hydroxyundecanelactone acid 4-Hydroxyundecanelactone acid 4-Hydroxyundecanelactone acid Dimethyl-3,3'-thiodipropionate Dimethyl-3,3'-thiodipropionate Dimethyl-3.3'-thiodipropionate 2.6-di-tert-butyl-4-phenylphenol 2,4-Dihydroxybenzophenone
Name
~
- (CO) - (HO) - (CO) 16.0 63.0 (iT)
(aT) - (CO) - (HO) - (CO) - (HO) - (iT) -
-
-
0.898 (25) 56.0 (iT)
-
0.900 (23) 0.902 (23) 0.900 (23) -
-
0.900 0.902 0.900 0.902
(23) (23) (23) (23)
-
198.2 198.2 198.4 198.4 198.4 198.4 199.3 200.4 200.4 200.4 206.3 206.3 206.3 212.3 214.2
-
40 ;60 40 23 23 23 23 70 ; 110 23 23 23 20 ; 40 80 ; 110 140 40 50 ;75
23
(HO)
0.902 (23)
196.3
-
23
(CO)
0.900 (23)
196.3 -
23
(HO)
-
0.902 (23)
196.3
(T) 23 40 50 ; 100 50 ; 100 23
(HO) 64.0(HO) 64.0(HO) 0.900 (23) - (CO)
-
-
(%)
Experiment Temp. Type of diffusion range of coefficient experim.
0.902 (23)
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
184.3 184.3 186.3 186.3 196.3
(dalton)
Molec. weight M,
0.27'4') 0.56(** 0.0082 0.0043 22.0 28.0 1.08(7" 0.0011 0.00062 0.0007 0.141 0.35"' 32.4(*" 0.204(" 0.00078'4'
0.0002
0.0012
0.00078
-
142.3
-
79.93 71.56 -
-
131.2 -
-
-
-
-
-
84.0
-
-
-
12.64
-
5.255 2.447
-
-
-
12.01
-
5.447
-
-
-
Diffusion Parameters Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed Dexp (cm2/s) x (kUmol) 0.0007 0.112(** 0.00117'4' 133.0 11.27 0.00135(4' 128.7 10.614 0.0014
1.58 158 67 67 67 67 160 57 57 57 81 161 162 66 71
144
57
57
144 66 159 159 57
Ref.
2,4-Dihydroxybenzophenone Dibenzylsulphide (DBS) Dibenzylsulphide (DBS) Methyllaureate Methyllaureate 2,5-Di-tert-butyl-4-hydroxy-toluene 2,6-Di-tert-butyl-p-cresol (BHT) 2,6-Di-tert-butyl-p-cresol (BHT) 2.6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol (BHT) 2.6-Di-tert-butyl-4-methylphenol (BHT) 2,6-Di-tert-butyl-4-methylphenol(K4) 2,4-Dihydroxybenzophenone (DHB) 2-(2'-Hydroxy-5'-methylphenyl)-benzotriazole 2-(2'-Hydroxy-5'-methylphenyl)-benzotriazole 2-(2'-hydroxy-5'-methylphenyl)-benzotriazole 2-(2'-Hydroxy-5'-methylphenyl)-benzotriazole Hexadecane (Alcane C16) Hexadecane (Alcane Clh) Hexadecane (Alcane C16) Hexadecane (Alcane Clh) Hexadecane Hexadecane 2-Hydroxy-4-methoxybenzophenone 2-Hydroxy-4-methoxybenzophenone 2-Hydroxy-4-methoxybenzophenone
Name
Diffusing Species
(dalton) 214.2 214.3 214.3 214.4 214.4 220.3 220.3 220.3 220.3 220.3 220.3 220.3 222.2 225.2 225.0 225.3 225.0 226.4 226.4 226.4 226.4 226.4 226.4 228.2 228.2 228.2
M,
Molec. weight
-
-
-
-
-
-
-
-
-
(CO) (HO) (CO)
- (HO) - (iT) (iT) 63.0 (iT) -
-
-
-
48.0 (iT) 48.0 (iT) -
- (iT)
0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23)
0.899 0.899 -
-
-
-
-
-
-
-
-
-
-
-
-
(aT)
64.0(HO) 64.0(HO) - (iT) 54.0
-
56.0 (iT)
(YO)
-
-
(g/cm') 0.898 (25)
Polymer Density Cristal63 ("C) linity PP -
D D
D
DS Dc-n Dsw D D D D D D Ds Dsw D D D D D D Ds D, Dsw Dsw D D
(T) 44 40 : 60 40 50 ;lo0 50 ;loo 60 : 110 70 ; 100 80 : 120 25 30 ;60 30 ;60 140 25 80: 120 40 ; 120 40 ; 120 115 : 160 23 23 23 23 40 70 ; 110 70 ;85 80 ; 110 40 : 90
Experiment Type of Temp. range of diffusion coefficient experim. (cm2/s) x IO-* 0.0055(*" 0.25'4" 0.58'** 0.0007(40 0.00068'4" 0.115'5" 0.116'70 0.446(70 0.005''" 0.00028'' 0.93" 40.1(*' 0.0005'" 1.62'70 0.0083(3" 0.0093(30 4.0"" 0.0074 0.0037 22.0 25.0 0.133'** 0.39(70 2.32'70 0.168'70 0.00237'30
uexp
-
134.3 135.5 94.31 108.8 104.1 11.27 11.45 6.312 7.631 7.503 7.096 3.335
-
3.839 0.0792 2.826 10.473
80.42 50.64 76.17 122.4
-
-
-
-
-
74.67 96.07 94.57 76.35 -
3.583 6.481 6.274 3.299 -
-
-
105.7 64.41
-
-
80.0
-
(kJ/mol)
-
4.748
-
67 66 81 81 161 168
78 78 162 72 165 166 166 167 67 67 67
71 158 158 159 159 160 163 164 72
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy 63 (23 "C) Ig Dd Ed
.c
2
b
2
cc,
+L
VI
Bromoform n-Octadecane (Alcane Cis) n-Octadecane (Alcane CIS) n-Octadecane (Alcane Clx) n-Octadecane (Alcane CI8) Octadecane n-Octadecane n-Ocatdecane n-Ocatdecane 2.6-Di-tert-butyl-4-n-butylphenol 2,6-Di-tert-butyl-4-tert-butylphenol
2,6-Di-tert-butyl-4-i-propylphenol
228.2 228.2 228.4 228.4 228.4 234.3 236.4 239.3 240.4 242.3 242.4 242.4 244.3 247.4 252.7 254.5 254.5 254.5 254.5 254.5 254.5 254.5 254.5 262.4 262.4
2-Hydroxy-4-methoxybenzophenone 2-Hydroxy-4-methoxybenzophenone Ethyllaureate Ethyllaureate Ethyllaureate 2.6 -Di-tert-butyl-phenylphenol 2.6-Di-t-butyl-4-methoxy phenol (Topanol354) 2-(2'-Hydroxy-5'-ethylphenyl)benzotriazole Heptadecane 2-Hydroxy-4-ethyl-benzophenone Methylmiristate Methylmiristate Triphenylmethane
(dalton)
Molec. weight M, 228.2
Diffusing Species
2-Hydroxv-4-methoxybenzophenone (Cyasorb
Name
-
0.900 0.902 0.900 0.902
-
-
(iT) (iT) (iT)
-
-
(CO) - (HO) - (CO) - (HO) -
64.0(HO) -
64.0(HO)
-
-
-
- (iT)
(%)
-
-
(23) (23) (23) (23)
(g/cm3)
PP
Polymer Density Cristal@ ("C) linity
Dsw D D
DS
DS
D
Dsw Dsw
Ds
D D Dsw D Dsw D D D D D D D D D Dsw DS
D
-
25 : 70 23 23 23 23 40 30 ; 60 30 : 60 30 : 60 140 140
140
120 ; 160 60 ; 120 20 20 20 140 120 : 130 80 : 120 40 60 : 120 50 ; 100 50 ; 100 40
30 ; 70
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
S.6"O0 0.283"" 0.015"* 0.0014"" 0.033(** 27.2'** 6.5("" 0.199'70 0.133'" 0.282(5" 0.00038'4'' 0.000404'" 0.0129(** 31.7'** 3.6'" 0.0066 0.0034 23.0 25.0 0.0867'" 0.012(* 0.00086" 3.29'' 14.6'** 3 1.O'**
0.0014'*
-
-
-
-
-
38.78 121.8 56.37
-
-3.084 10.429 2.466
-
-
-
27.72 -
-
-
-2.546
-
73.54 141.3 140.3
-
3.343 12.17 12.02
53.40 82.83
0.099 3.915
-
-
-
-
66.11 77.45
112.4
2.01 3.980
8.970
167 165 170 170 171 162 172 165 66 165 159 159 66 162 58 67 67 67 67 66 83 78 78 162 162
169
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed D,"" (cm2/sj; (kJ/mol)
v1
I
$
Diffusing Species
2-(2'-Hydroxy-5'-t-butylphenyl)-benzotriazole Tetramethylpentadecane 2-Hydroxy-4-n-butoxybenzophenone 2-Hydroxy-4-n-butoxybenzophenone 2-Hydroxy-4-n-butoxybenzophenone Methylpalmitate Methylpalmitate Stearyl alcohol Dibuthylphthalate (DBP) Dibuthylphthalate (DBP) Dibuthylphthalate (DBP) Eicosane (Alcane CzO) Eicosane (Alcane Cz0) Eicosane (Alcane CzO) Eicosane (Alcane C,,,) 2,6-Di-tert-butyl-4-cyc4ohexylphenol 1-Amnio-2-pentyl-antraquinone(Dye I) 1-Amnio-2-pentyl-antraquinone (Dye I) 2-(2'-Hydroxy-5'-cyclohexyl phenyl) benzotriazole 2.6-di-tert-butyl-4-benzyI-phenol Methyloleate Methyloleate Methyloleate Methyloleate
2-(2'-Hydroxy-5'-t-butylphenyl)-benzotriazole
2-(2'-Hydroxy-5'-n-butylphenyl)-benzotriazole
Name
-
-
-
-
64.0(HO) 65.9(HO) 68.0(HO) 70.1 (HO)
-
-
Dsw Dsw D D D
Ds
D D D D D
- (CO) - (HO) - (CO) - (HO) - (iT) - (iT)
0.900 (23) 0.902 (23) 0.900 (23) 0.902 (23) -
-
-
-
-
-
D D D D D D D D D D D D D Ds
296.4 296.5 296.5 296.5 296.5
-
140 70 ; 90 70 ;90 70 ; 90 70 : 90
80 40 70 $5 80 ;110 60 : 120 50; 100 50 ; 100 40 20 20 20 23 23 23 23 140 60 ;70 70 ; 90 80 ; 120
(T) 80 $20 80 ;120
Experiment Type of Temp. diffusion range of coefficient experim.
D
-
64.0(HO) 64.0(HO)
-
24.0(SB) 63.0 (iT) - (iT)
-
-
48.0 (iT)
-
(iT) (iT)
(YO)
-
0.899
-
(g/cm3) -
PP
Polymer Density Cristal@ ("C) linity
(dalton) 267.3 267.3 267.3 268.4 270.3 270.3 270.3 270.4 270.4 270.4 278.3 278.3 278.3 282.6 282.6 282.6 282.6 288.4 293.3 293.3 293.4
Molec. weight M,
4.26(** 0.004(60 0.00375(m 0.0049(60 0.00276'60
0.000194(4" 0.00028'4o 0.021 1(** 0.0051'*' 0.0051("* 0.0051"* 0.0061 0.0031 20.0 17.0 5.8'"" 0.032'50 9.3'70 0.0548(70
0 .0 4 5 0
(cm2/s) x lo-' 0.199(70 0.428'70 1.35'** 0.0278('* 1.21(70 0.104(70
ucxp
-
-
-
11.19 10.494 7.711 10.321
-
27.73 15.28 4.674
-
-
137.6 133.4 114.8 133.1
-
230.2 146.5 91.50
-
-
-
-
-
-
-
62.36 81.61 91.26 142.2 143.3 -
-
-
(kJ/mol) 82.83 82.58
1.580 3.447 5.363 12.02 12.38 -
-
-
3.915 4.209
162 159 159 159 159
165 165 166 66 81 161 165 159 159 66 87 87 87 67 67 67 67 162 173 173 165
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 "C) Ig Dd Ed
+
&
k
20
3 0
Diffusing Species
propy1)-pheny1)-benzotriazole 2-(2'-Hydroxy-3',5'-di-t-butyl-phenyl)-benzotriazole 2-(2'-Hydroxy-3',5'-di-t-butyl-phenyl)-benzotriazole
butyl)-pheny1)-benzotriazole 2-(2'-Hydroxy-3'-t-butyl-S'-(l"-methyI-
(CO) (HO)
0.899 0.899
323.4 323.4
0.899
48.0 (iT)
48.0 (iT)
48.0 (iT)
48.0 (iT)
0.899
318.5 323.4 323.4
-
(iT)
48.0 (iT)
-
- (CO) - (HO) - (iT)
-
-
-
(23) (23) (23) (23)
D
D
D
D D
D D
D
D Ds Ds Dsw Dsw D D
D
- (iT)
0.899
-
-
-
0.900 0.902 0.900 0.902
-
D D D
-
50 ; 80
60 ; 80
80
140 80
40 80
92; 115
140 23 23 23 23 40 80 : 120
90 : 110
5 0 ; 110 50 : 110 65 : 90
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
64.0(HO) 64.0(HO) - (iT)
(YO)
-
316.6 316.6
316.5
310.5 310.6 310.6 310.6 310.6 310.6 315.4
307.4
-
-
-
(g/cm')
(dalton) 298.3 298.3 307.4
PP
Polymer Density Cristal@ ("C) linity
Molec. weight M,
Methylstearate Methylstearate 1-N-Methylamino-2-pent yl-antraquinone (Dye 11) 1-N-Methylamino-2-pentyl-antraquinone (Dye 11) 2,6-di-tert-hutyl-4-(1-pheny1ethyl)phenol Docosane (Alcane C22) Docosane (Alcane C22) Docosane (Alcane C22) Docosane (Alcane Crr) Docosane 2-(2'-Hydroxy-5'-( 1" -phenylethyl) phenyl) benzotriazole 1-(3'-methyl-4'-hydroxy)phenyl-4-phenyl-disazobenzene (Yellow 7) Heptadecylhenzene 2-(2'-Hydroxy-3'-t-butyl -5'-methyl-phenyl)-5benzotriazole 2.6-di-tert-butyl-4-n-octylphenol 2-(2'-Hydroxy-5'-(1",1",3",3"-tetrametyhl-
Name P.
0.0067'"'
0.031(h"
0.613'**
1.95'" 0.319'"*
0.0524'** 0.0537'**
16.0""'
3.89'" 0.0029 0.0026 15.0 13.0 0.0245"" 0.01'~"
60.5""
0.00013'4" 0.000178'4" 7.07"'
(crn2/s) x
ULTp
10.556
9.722
-
128.2
122.5
-
-
-
-
-
133.9
-
-
-
11.96
-
99.24
-
71.14
144.2 147.0 111.3
(kJ/mol)
5.123
4.018
12.180 12.79 9.8
-
166
166
166
162 166
66 166
173
162 67 67 67 67 66 165
173
159 159 173
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient @ (23°C) Ig Dd Ed
Y
h)
cn
%
3 i?: 2
b
Diffusing Species
,
I
L
r
(CAO-5) 2,6-di-tert-butyl-4-dimethylbenzylphenol 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone (HOB) 2-Hydroxy-4-octoxybenzophenone (UV531) 2-Hydroxy-4-n-octoxybenzophenone 2-Hydroxy-4-(2’-ethyIhexyl)benzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 2-Hydroxy-4-octoxybenzophenone 4-Alkoxy-2-hydroxybenzophenone (Cyasorb UV 531) 2-Hydroxy-4-octoxybenzophenone (Cyasorb UV 531) 2-(2’-Hydroxy-5’-(2”-phenyl-2”-propyl) phenyl) benzotriazole Tetracosane (Alcane Cz4) Tetracosane (Alcane CZ4) Tetracosane Di-n-hexyl-3,3’-thiodipropionate Di-n-hexvl-3.3’-thiodi~ro~ionate
2-(2’-Hydroxy-3’,5’-di-t-butyl. .pheny1)-benzo. triazole 2-(2’-Hydroxy-5’-n-octyl phenyl) benzotriazole 2-(2’-Hydroxy-5’-t-octylphenyl) benzotriazole 2.2’-Methylene bis(4-methyl-6-t-butyl phenol)
Name
-
-
(iT)
338.6 338.6 338.6 346.5 346.5
(CO)
- (HO) 24.0 (SB) 63.0 (iT)
-
(iT)
329.5
-
-
326.5
35.4 48.4 58.0
-
- (iT) - (iT)
-
24.0 (SB) 56.0 (iT) 63.0 (iT)
324.5 326.4 326.4 326.4 326.4 326.4 326.4 326.4 326.5 326.5 326.5 326.5
-
(iT)
(%) -
(iT) - (iT) - (iT)
(g/cm’)
Polymer CristalDensity linity @ (“C) PP -
324.4 324.4 324.5
(dalton) 323.4
Molec. weight M,
140 70 ; 85 44 ; 75 80 ; 110 25 125 60 ; 120 60 : 120 30 ; 125 75 ; 90 75 ; 90 60 ; 90
D D D D D D D D D D D D
Dsw Dsw D D D
D
23 23 40 70 ; 85 80 ;110
80 : 120
30 ; 100
80 ; 120 80 : 120 120
D D D
D
(T) 80 ; 120
D
-
Experiment Type of Temp. range of diffusion coefficient experim.
14.0 10.0 0.0561(”* 10.4(7n 0.153(70
0.01(~~’
0.00012‘*
3.58(** I .34”’ 0.0091‘40 0.055‘7” 0.0015(** 20.0‘** 0.00045‘so 0.00079(50 0.00197‘* 0.355‘7” 0.772‘70 0.32‘H’
0.0079(70 0.079‘70 25.0(**
80.35 77.84
5.255 3.041
-
99.24
107.00
120.5 121.2 96.80 119.9 115.0 82.92
67 67 66 81 161
165
169
172 165 165 168 168 168 174
162 81 90 161 72
69.89 93.99 87.05 -
-
165 165 172
106.43 84.53
5.114
6.948
8.135 8.499 6.377 9.81 9.346 4.513
-
-
2.771 5.648 4.000
-
6.107 3.769 -
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 “C) Ig Dd Ed Dexp (cm2/s) x lo-’ (kJ/mol) 0.0146‘7n 7.322 112.64 165
*
k
39
G
k
h)
Diffusing Species
2.4-Dihydroxy-n-dodecoxybenzophenone 2,4-Dihydroxy-dodecoxybenzophenone 2-Hydroxy-4-dodecyloxybenzophenone(Aduvex 2412) 2-Hydroxy-4-n-dodecyloxybenzophenone 2-Hydroxy-4-(2'-ethylhexyl)-5-t-butyl-benzophenone Di-(2-ethylhexyl)-phthalate Phthalic acid bis(2-ethylhexyl ester) (DOP) Octacosane (Alcane Cza) Octacosane (Alcane CZR) Octacosane 2.2.6,6 -tetramethyl-4-piperidinol (Dastib 845) 2.2.6.6 -tetramethyl-4-piperidinol (Dastib 845) Squalane
2,4-Dihydroxy-n-dodecoxybenzophenone
2-(2'-Hydroxy"',5'-di-(l,"l"dimethyl propy1)pheny1)-benzotriazole n-Octadecyldiethanolamine 2-(2'-Hydroxy-3'.5'-di-t-butyl-phenyl)-5-chlorobenzotriazole n-Amido bis(2.3.6.6-tetramethyl-4-piperidinyl)amino Hexacosane (Alcane CZ6) Hexacosane (Alcane CZh) Tritolylester phosphoric acid (TCP) 2-(2'-Hydroxy-5'-n-dodecylphenyl) benzotriazole
Name
-
0.899 0.905 0.900 (23) 0.902 (23)
357.6 357.9 366.6 366.7 366.7 368.4 379.5
0.899 0.905
-
-
(CO) (HO) 48.0 (iT) - (iT)
-
149.7 109.0 -
14.29 8.201 -
-
-
-
-
85.52 -
-
104.38 132.47
2.386
-
0.00377'" 0.00013'4' 10.0 6.9 0.0178(** 0.000074" 0.126'6' 0.0099' '* 40 40 : 70 23 23 40 25 ; 60 60 ; 90 40 D D Dsw Dsw D D D D
-
5.141 9.683
-
0.0332"" 0.0032""
-
-
66 96 94 66
66 87 67 67
165 165
81 161 168 169
-
61.83
-
4717
83.70 89.14 92.56 118.2
165
-
5.079 4.179 5.749 9.578
67 67 87
-
-
133 166 94
-
166
87.64 4.432
100 :120 80; 120
2.14'70 0.04"' 0.0062"' 0.00052"
13.0 7.2 0.00002" 0.0074'7"
0.12(70
-
85.72
-
-
4.156
(kJ/mol)
-
D D
70 3 5 80:llO 40 ;90 30 ; 70
23 23 70 80: 120
80 ; 90
0.29"' 0.347(**
0.621'*'
Drxp
(crn2/s)x lo-'
(iT) (iT)
Dsw Dsw D D
D
78 : 135 80
80
(T)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23 " C ) Ig Dd Ed
D D D D
-
0.900 (23) 0.902 (23)
-
D
Dc n
D
-
Experiment Temp. Type of range of diffusion coefficient experim.
24.0(SB) 63.0 (iT) -
382.5 382.5
-
(iT)
- (CO) - (HO) - (iT)
-
60.0 48.0 (iT)
-
390.4 390.6 394.6 394.6 394.6 411.2 411.2 422.5
(%)
48.0 (iT)
382.5 382.5 382.5 382.5
-
-
0.899
(gkm')
Polymer Density Cristal@ ("C) linity PP -
351.5
(dalton)
Molec. weight M,
Diffusing Species
1,4-di-(2'-Hydroxy-4'-oxy-benzophenone)-nbutane
bis[2,2,6,6-tetramethyl-4-piperidinyl)-sebacate (Tinuvin 770) bis[2,2,6,6-tetramethyl-4-pipetidinyl)-sebacate (Tinuvin 770)
2-Hydroxy -4-n-octadecoxybenzophenone 2-Hydroxy -4-n-octadecoxybenzophenone
2,6-di-tert-butyl-4-n-octadecylphenol
Triacontane (Alcane C30) Triacontane (Alcane C3") 2,5-di(5-tert-butyl-2-benzoxazolyl) thiophene (Uvitex OB) 2,5-di(5-tert-butyl-2-benzoxazolyl) thiophene (Uvitex OB) 2,5-di(5-tert-butyl-2-benzoxazolyl) thiophene (Uvitex OB) 2.5-bis(5-tert-butyl-benzoxazol-2-yl)-thiophene 2-(2'-Hydroxy-3',5'-di-(dimethylbutyl)-phenyl)benzotriazole 2-(2'-Hydroxy-3',5'-di-(dimethylbutyl)-phenyl)benzotriazole Saturated Hydrocarbon (Ceresin 100) Dotriacontane (Alcane C32) Dotriacontane (Alcane &) Dotriacontane Dotriacontane
Name
0.905
480.7 482.5
0.899
-
-
-
-
-
-
-
-
0.902 (23)
-450 450.9 450.9 450.9 450.9 458.8 466.7 466.7 480.7
0.899
447.6
(iT)
- (iT)
-
- (aT) (HO) 24.0(SB) 24.0(SB) 48.0 (iT) -
D
D
D
D5 Ds Dsw D D D
D,-o Dsw
D
48.0 (iT)
0.899 48.0 (iT)
D D
-
-
D
Dsw Dsw D
430.0 447.6
(iT)
-
(CO) (HO)
-
D
-
-
-
-
(%)
60 ; 120
57 : 83
120: 130 23 60 30 : 60 30 : 60 140 70 ; 85 80 ; 110 40 : 80
60 : 120
40 60: 120
120
130
23 23 50 : 125
("C)
Experiment Type of Temp. range of diffusion coefficient experim.
(iT)
-
-
430.5 430.5
0.900(23) 0.902(23) -
(gicm')
Polymer Density Cristallinity @ ("C) PP
422.7 422.7 430.5
(dalton)
Molec. weight M,
0.0104(s"
0.022'5"
70.8"*" 3.9 0.063'** 0.000056'* 0.67'" 0.112'0.65(7" 0.022'~~ 0.00018'*
0.0089'h0
0.0045"* 0.01'6"
6.700
5.802
103.14
95.6
-
76.17 99.18
3.415 5.491
-
-
155.83 78.3
-
-
45.49
113.1
109.1
-
1.524 5.645
-
-0.103
7.698
7.112
-
-
6.0'**
-
94.72
5.172 -
-
-
0.6'**
5.4 0.00712""
(kJlmol) -
165
94
97 67 79 78 78 162 81 161 96
166
166
66
172
175
67 67 168
Diffusion Parameters Ref. Diffusion Pre-expon. Activation energy coefficient coefficient 3 '2 (23°C) Ig Dd Ed
+
h'
33
h
b
3 P
Diffusing Species
phenone)-n-butane Saturated hydrocarbon (Ceresin 80) 1.4-di-(2'-Hydroxy-5'-t-butyl-4'-oxy-benzophenone)-n-octane bis-(2-Hydroxy-3(2'-benzotriazole-5(1',1",3",3"-tetramethyl-buthyl) pheny1)methane 1,4-di-(2'-Hydroxy-S'-(l"-phenyl-ethyl)-4'-oxybemophenone)-n-butane Hexanediol-di-3-(3'-(2''-benzotriazole)-4'hydroxy-5'- t-butyl-pheny1)-propionate
1,4-di-(2'-Hydroxy-5'-t-butyl-4'-oxy-benzo-
3-(3'-(5"-chloro-2'-benzotriazole)-4'-hydroxy5'-t-butyl-phenyl-propionate bis[2,2.6,6-tetramethyl-4-piperidinyl-l -oxy] sebacate Didodecyl-3-3-thiodipropionate(DLTDP) Di-n-dodecyl-3-3-thiodipropionate (DLTDP) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) Octadecyl-3-(3,5-di-tert-butyl-4-hydroxyphenyl) propionate (Irganox 1076) 1.4-di-(2'-Hydroxy-4'-oxy-benzophenone)-noctene 1-1-3-tris(2-methyI-4-hydroxy-5-tert-butylphenyl) butane
Name
60.0 63.0(iT) 60.0
-
514.4 514.4 53 1.4
760.9
690.8
658.9
-600 650.9
594.5
544.5
(iT)
0.899
-
0.899
(iT)
48.0 (iT)
-
48.0 (iT)
(iT)
-
-
(iT)
-
-
60.0
-
60.0
-
-
-
-
0.900
531.4 538.5
0.900
531.4
60.0
48.0 (iT)
0.899
512.0
0.900
48.0 (iT)
0.899
486.0
(gicm')
(%)
Polymer Density Cristal@ ("C) linity PP
(dalton)
Molec. weight M,
-
D
D
D
D
Dc
D
D
D
D,
Ds
D D D,
D
D
o
80
80 ; 120
80
100 ; 120 80 ; 120
80 ; 120
100 ; 150
60;100
4.740
5.067
6.567
I
4.559
3.931 3.756 1.908
6.223
-
9.528
0.0025('" 0.106""
-
0.0771'**
-1.571 32.1"0° 0.0028'~~ 4.960
0.0027""
0.093('O0
0.0195'so
18.8""
0.01'40
50 ; 135
135
0.00341's0 0.066'7" 0.011(~~
0.052'70
166
97 165
165
133
165
136
100
101
133 161
96
-
166
132.18 165
-
35.14 101.88
100.48
100.66
100.64
-
87.23
82.85 84.95 71.0
101.8
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @ (23"C) Ig Dd Ed Dexp (cm'is) x (kJimol) 0.18'"' 166
56 ; 135 80 ; 110 49 ; 121
70 ; 121
80
(T)
Experiment Type of Temp. diffusion range of coefficient experim.
wl
h)
wl
*
3$
+ L
h
Diffusing Species Molec. weight M,
(dalton) 2,4,6~Tris(2,6-di-t-butyl-4-hydroxybenzyl)-l.3,5-774.6 trimethylbenzene (Ionox 330) 774.6 1,3,5-(3,5-di-tert-butyl-4-hydroxy benzyl) mesitylene (Irganox 1330) N,N,N-Tris(2,6-di-t-butyl-4-methyl pheny1)iso- 777.0 cyanurate (Goodrite 31 14) 999.0 N,N,N"-Tris(ethyl[3,5-di-t-butyl-4-hydroxy phenyll-propionate) isocyanurate (Goodrite 3125) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-me thane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Te trakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxyrnethyl]-methane (Irganox 1010) Tetrakis[3-(3-5-di-tert-butyl-4-hydroxy-phenyl) 1177.8 propionyloxymethyl]-methane (Irganox 1010) -2000 Polyethylene segments Atactic polypropylene segments -8000
Name
70; 105
-
48.0 48.0 (aT) (iT)
-
0.900 0.900 -
D
0.000247(40
50 : 135
60.0
0.900
-
-
0.000054(*
49 ; 121
60.0
0.900
-
0.7'**
120
(iT)
-
-
2.011
0.39'"" 5.6'** 0.028""
120 : 150 100
2.890
-
11.15
0.0013(7"
100 : 135
10.397
8.609
5.380
-
-
7.492
-
-
0.000013(4"
49 : 135
1.0'*'
120
(iT)
-
0.0038(70
2.0(**
-
80 ; 120
(T) 120 De*p (cm2/s) x
88.8
-
76.4
144.6
177 .
97
108
108
137
136
121.1 139.4
101
172
172
176
172
100.0
-
-
117.63
-
(kJ/mol)
Diffusion Parameters Ref. Diffusion Pre-expon. Activation coefficient coefficient energy @(23"C) IgDd Ed
-
(iT)
(%) -
-
Experiment Type of Temp. diffusion range of coefficient experim.
-
-
(g/cm3)
Polymer Density Cristal@ ("C) linity PP -
4
2
22
b
m
Appendix I
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
50.
5I .
52. 53. 54. 55.
to Appendix
527
I
Michaels, A. S., Bixler, H. J., J. Polym. Sci., 50 (1961) 413. Kanitz, P J. F., Huang, R. Y. M., J. Appl. Polym. Sci.. 14 (1970) 2739. Bixler, H. J., Michaels, A. S., Salame, S., J. Polym. Sci., A l(1963) 895. Kulkarni, S.S., Stern, A. S., J. Polym. Sci., Polym. Phys. Ed. 21 (1983) 441. Lundberg, J.L., Wilk, M.B., Huyett, M.J., J.Polym.Sci., 57 (1962) 275. MacDonald, R. W., Huang, R. Y. M., J. Appl. Polym. Sci., 26 (1981) 2239. Beret, S., Hager, S. L., J. AppLPolym. Sci., 24 (1979) 1787. Evnochides, S. K.. Henley, E. J., J. PolymSci., A-2.8 (1970) 1987and AIChE Journal, 17 (1971) 880. Brandt, W. W.. J. Polym. Sci., 41 (1959) 403 and 415. Robeson, L. M., Smith, T. M.. J. Appl. Polym. Sci., 11 (1967) 2007 and 12 (1968) 2083. Yasuda. H., Stannett, V.T., Frisch, H.L., Peterlin, A,. Die Makromolekulare Chem., 73 (1964) 188. Koszinowski, J., J. Appl. Polym. Sci., 31 (1986) 27 11. Podkowka, J., Puchalik, A,. J. Appl. Polym. Sci., 27 (1982) 1471. He, Z . , Hammond, G.S., Weiss, R.G.. Macromolecules. 25 (1992) 1568. Izydorczyk. Salwinski, J. Appl. Polym. Sci.. 29 (1984) 3663. Dos Santos, M.L., Leitao, D.M., J. Polym. Sci., A-2 10 (1971) 769 and 10 (1972) 1. Thalmann, W.R., Packaging Tech. Sci., 3 (1990) 67. Cuttler, J. A., Kaplan, E., McLaren, A. D., Mark, H., TAPPI, 34 (1951) 404 and 36 (1953) 423. Rogers, C. E., Stannett, V., Szwarc, M., J. Polym. Sci., 45 (1960) 61. Shimoda, M.. Matsui, T., Osajima, Y., Nippon Shokuhin Koyo Gakkaishi, 34 (1987) 402 and 535. Fleischer. G., Holstein, P., Acta Polymerica, 35 (1984) 738. Johanson, F., Leufvkn, A.. J. Food Sci.. 59 (1994) 1328. McCall. D. W., Schlichter, W. P.,J. Am. Chem. SOC80 (1958) 1861. Fels, M., Huang. R. Y. M., J. Appl. Polym. Sci., 14 (1970) 523 & 537. McCall, D. W., J. Polym. Sci., 26 (1957) 151. Saleem, M., Asfour, A.-F. A., De Kee, D.. Harrison, B., J. Appl. Polym. Sci., 37 (1989) 617. Doong, S. J.. Ho. W. S. W., Ind. Eng.Chem. Res., 31 (1992) 1050. Fleischer, G., Polym. Comm.. 25 (1985) 20. Huang, R. Y. M., Rhim. J.-W., J. Appl. Polym. Sci.. 41 (1990) 535. Kreituss. A., Frisch, H. L., J. Polym.Sci., Polym. Phys.Ed., 19 (1981) 889. Aboul-Nasr, O.T., Huang, R. Y. M., J. Appl. Polym. Sci., 23 (1979) 1819, 1833 and 1851. Gray, D. G., Guillet, J. E.. Macromolecules. 6 (1973) 223. Takeuchi, Y., Okamura, H., J. Chem. Eng. Japan. 9 (1976) 136. Stern, A. S.. Britton, G. W., J. Polym. Sci., Part A-2 10 (1972) 295. Peeters, H.. Vanderstraten, P.. Verhoeye, L., J. Chem. Tech.Biotechnol., 29 (1979) 581. Fels, M., AIChE J., Symposium Series, 120 (1970) 49. Chalkyh. A.Ye., Krivoshei, V.N., Vysokomol. Soed., A24 (1982) 1640. Araimo, L., De Candia. F.,Vittoria, V., Peterlin, A,, J. Polym. Sci., Polym. Phys. Ed., 16(1978) 2087. De Candia, F., Russo, R., F., Vittoria,V., Peterlin. A,, J. Polym. Sci.. Polym. Phys.Ed.. 20 (1982) 269. Asfour, A.-F. A., Saleem, M., De Kee, D., Harrison, B., J. Appl. Polym. Sci., 38 (1989) 1503, Hedenqvist, M., Angelstok, A., Edsberg, L.. Larsson, P.T., Gedde, U.W., Polymer, 37 (1996) 2887. Stern. A. S., Sampat, S. R., Kulkarni, S. S., J. Polym. Sci., Part B Polym. Phys., 24 (1986) 2149. Phillips. J.C., Peterlin, A,, Polym. Eng. Sci., 23 (1983) 734. Ng. H. C.. Leung. W. P., Choy, C. L.. J..Polym.Sci., Polym.Phys. Ed.. 23 (1985) 973. Markevich, M.A., Stogova, V.N., Gorenberg, A.Ya., Vysokomol. Soed.. A33 (1991) 132. Liitzow, N., Tihminlioglu, A,, Danner. R.P.. Duda, J.L., DeHaan, A,, Warnier, G., Zielinski, J.M., Polymer, 40 (1999) 2797. Corbin, G.A.. Cohen, R.E., Baddour, R.F., J. Appl. Polym. Sci.. 30 (1985) 1407. Ghosh. S.K., J. Appl. Polym. Sci., 27 (1982) 331. Sobolev, I., Meyer, J.A., Stannett, V.T., Szwarc. M., Ind. Eng. Chem., 49 (1957) 441. Koszinowski, J., Piringer, O., Verpackungs Rundschau, 41 (1990) 15. Strandburg, G., De Lassus, P. T., Howell. B. A,. in “Barrier Polymers and Packaging”, Ed. Koros. W. J.. ACS Symposium Series, Nr., 423, Washington DC, 1990, pp. 333. Michaels, A.S., Baddour,R.F. ,Bixler,H.J... Choo. C.Y.. Ind. Eng. Chem.,Proc. Des. Dev., l(1962) 14. Serota, D.G., Meyer. M.C., Autian, J., J. Pharm. Sci.. 61 (1972) 416. He, Z., Hammond. G.S., Weiss. R.G.. Macromolecules, 25 (1992) 501. Theodorou, E., Paik, J. S., Packaging. Techn. Sci.. 5 (1992) 21.
528
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530
Appendix I
166. Dudler, V., Muinos, C., in “Polymer Durabi1ity:Degradation. Stabilization and Lifetime Predictions” Eds. Clough, L. R., Billingham, N.C. and Gillen, K. T., ACS Advances in Chemistry Series No. 249, Washington D.C. 1995, pp. 441. 167. Luston, J., Pastusakova, V., Vass, F., J. Appl. Polym. Sci., 47 (1993) 555. 168. Billingham, N. C., Calvert, P. D.. Uzuner, A., Eur. Polyrn. J., 25 (1989) 839. 169. Billingham, N. C., Makromol. Chem. Macromol. Symp., 27 (1989) 187. 170. Barson, C. A., Dong, Y. M., Eur. Polym. J., 26 (1990) 449. 171. Barson, C. A,, Dong, Y. M., Eur. Polyrn. J., 26 (1990) 329. 172. Calvert, P.D., Ryan, T.G., Polymer, 19 (1978) 611. 173. Okajima, S., Sato, N., Tasaka, M., J. Appl. Polym. Sci., 14 (1970) 1563. 174. Hsu, S. C., Lin-Vien, D., French, R.N., Appl. Spectroscopy 46 (1992) 225. 175. Ryan, T.G., Calvert, P.D., Polymer, 23 (1982) 877. 176. Schwarz, T., Steiner, G., Koppelmann, J., J. Appl. Polym. Sci., 37 (1989) 3335. 177. Billingham, N.C., Calvert, P.D., Uzuner, A., Polymer, 31 (1990) 258.
12 13
4
4
“ACCH2”
“ACCH2”
11
3
“ACH”
10
9
8
7
6
3
2
2
2
2
“ACH”
‘.C=c”
“C=C“
“C-C”
“C-C”
5
4
1
“CH2”
2
2 3
1 1
“CH2” “CH2”
“C-C”
1
1
“CH2”
Sub Group Number
Main Group Number
Main Group
Sub Group
1.0396
1.2663
,3652
,5313
,6605
,8886
1.1173
1.1167
1.3454
,2195
,6744 ,4469
,9011
(Rk)
Volume
Group
Table 1: UNIFAC group volume (Rk) and surface area (Qk) parameters.
Appendix I1
27.044 26.036
.66
12.01
13.018
24.020
25.028
26.036
26.036
27.044
12.010
14.026 13.018
15.034
Group Molecular Weight
Sub
,968
.12
.4
,485
,676
,988
367
1.176
0
.54 ,228
,848
Surface Area (Qr)
2-methyl propane 3 C H 3 , l CH Neopentane 4 CH3,l C Hexene-l 1 CH3.3 CH2.1 CH2=CH Hexene-2 2 CH3.2 CH2.1 CH=CH 2-methyl-1-hutene 2 CH3,l CH2.1 CH2=C 2-Methyl-1-hutene 2 CH3.1 CH=C 2.3-dimethylhutene 4 CH3,l C=C Naphthaline 8 ACH. 2 AC Styrene 1 CH2=CH. 5 ACH, 1 AC Toluene 5 ACH. 1 ACCH3 Ethylbenzene 1 CH3.5 ACH, 1 ACCH2
Hexane 2 CH3.4 CH2
Example
Reactivity in Molecular Crystals Copyright @ K d a o r h a Ltd .Tokyo. 1999
Edited by Yuli Ohashi
,8121
14 15
“ACCH”
“OH”
“CH3OH’
4
5
6
7
“ACCH2”
“OH”
“CH30H”
“H20”
“ACOH” 43.044 42.036 29.018 59.044 58.036 45.018 31.034 30.026
1.448 1.18 .948 1.728 1.42 1.188 1.088
.78
1.6724 1.4457 .998 1.9031 1.6764 1.242 1.145 ,9183 ,6908 ,9183
19 20 21 22 23 24 25 26 27 28
“CWCO”
“CH2CO”
THO“
“CH3COO”
“CHZCOO”
“HCOO”
“CH30”
“CH20”
“CH-0”
“FCH2O”
9
9
10
11
11
12
13
13
13
13
“CH2CO”
“CH2CO”
“CHO”
“CCOO”
“CCOO”
“HCOO”
“CH20”
“CH20”
“CH20”
“CH20”
30.026
29.018
.68
3952
18
“‘ACOH”
8
1.1
18.016
1.4
.92
17
“H20”
29.018
32.042
1.432
1.4311
16
,468
17.GO8
1.2
1
Sub Group Molecular Weight 25.028
(Qk)
Surface Area
,348
(Rk)
Group Volume
Sub Group Number
Sub Group
Main Group Number
Main Group
Cumene 2 CH3.5 ACH. I ACCH Propanol-2 2 CH3.1 CH, 1 OH Methanol 1 CH30H Water 1H20 Phenol 5 ACH, 1 ACOH Butanone 1 CH3.1 CH2.1 CH3CO Pentanone-3 2 CH3,l CH2,l CH2CO Propionic aldehyde 1 CH3.1 CH 2, l CHO Butyl acetate 1 CH3,3 CH2.1 CH3COO Methyl propionate 2 CH3.1 CH2COO Ethyl forrnate 1 CH3,l CH2.1 HCOO Dimethyl ether 1 CH3.1 CH3CO Diethyl ether 2 CH3,l CH 2 , l CH2 0 Diisopropyl ether 4 CH3.1 CH, 1 CHO Tetrahydrofuran 3 CH2.1 THF
Example
F’ 2
a.
k-
3m
t d
wl w
32
“CH3NH”
“CH2NH”
15
15
15
16
16
17
“CNH”
“CNH”
(C)3N”
“( C)3N”
“ACNH2”
“pyridine”
“CNH”
,816 2.113 1.833 1.553
,9795 1.1865 ,9597 1.06
2.9993 2.8332 2.667 1.8701
34 35
36 37 38 39 40 41 42 43
“CHNH”
“CH3N”
“CH2N”
”‘ACNH2”
“CSH5N”
“CSH4N”
“C5H3N”
“CH3CN”
TH2CN”
“COOH”
18
18
18
19
19
20
“pyridine”
“pyridine”
“CCN”
“CCN”
“COOH”
“
,936
1.207
33
1.416 1.224
1.6434 1.3013
1.724
,632
.94
.624
1.244
1.4337
,924
1.1417
31
“CHNH2”
14
“CNH2”
1.236
1.3692
30
“CH2NH2”
14
“CNH2”
(ad
Surface Area
1.544
(Rk)
Group Volume
1.5959
29
“CH3NH2”
14
“CNH2”
Sub Group Number
Sub Group
Main Group Number
~
Group
Main
45.018
40.044
41.052
77.082
78.090
79.098
28.034
28.034
29.042
28.034
29.042
30.50
29.042
30.50
31.058
Molecular Weieht
Sub
Group Methylamine 1 CH3NH2 Ethylamine 1 CH3.1 CHNH2 Isopropylamine 2 C H 3 , l CHNH2 Dimethylamine 1 CH3,l CH3NH Diethylamine 2 C H 3 , l C H 2 , l CH2NH Diisopropy lamine 4 CH2,l CH. 1 CHNH Trimethylamine 2 CH3,l CH3N Triethylamine 3 CH3.2 CH2,l CH2N Aniline 5 ACH, 1 ACNH2 Pyridine 1 CSHSN 2-Methylpyridine 1 CH3,l C5H4N 2,3-Dimethylpyridine 2 CH3.1 C5H3N Acetonitrile 1 CH3CN Propionitrile 1 CH3.1 CHZCN Acetic acid 1 CH3.1 COOH
Example
wl w w
“ACCl”
“CHC13”
1.104
58.018 1.4199
58
”ACN02”
27
“ACN02”
59.026
1.248 1.5544
57
“CHN02”
26
“CN02”
60.034 1.56
1.7818
56
“CH2N02”
26
“CN02”
61.042
1.868
2.0086
55
“CH3N02”
26
“CN02”
47.467
,844
1.1562
54
25
“ACCI“
153.838
2.91
3.39
53
“CC14”
24
“CC14’
118.381
2.184
2.6401
52
“CC13”
23
“CC13”
119.389
2.41
2.87
51
23
“CC13”
82.924
1.448
1.8016
50
”CC12”
22
“CC12”
83.932
1.684
2.0606
49
“CHC12”
22
“CC12“
84.940
1.988
2.2564
48
“CH2C12”
22
“CC12”
47.467
.724
1.0106
47
“CCI”
21
“CCI”
48.475
,952
46
1.238
“CHCI”
21
“CCI”
49.483
1.264
1.4654
45
“CH2Cl”
21
“CCI”
46.026
1S32
1.528
(Qk)
44
“HCOOH”
20
“COOH”
(Rk)
Sub Group Molecular Weight
Surface Area
Sub Group Number
Group Volume
Sub Group
Main Group Number
Main Group
Formic acid 1 HCOOH Butane-1-chloro 1 CH3.2 CH2,l CH2CI Propane-2-chloro 2 CH3.1 CHCI 2-Methylpropane-2-chloro 3 CH3,l CCI Methane-dichloro 1 CH2C12 Ethane-1,I -dichloro 1 Ch3.1 CHC12 Propane-2.2 dichloro 2 Ch3.1 CC12 Chloroform 1 CHC13 Ethane-l,l,l-trichloro 1 CH3.1 CC13 Methane-tetrachloro 1 CC14 Benzene-chloro 5 ACH, 1 ACCl Nitromethane 1 CH3N02 Propane- 1-nitro 1 CH3.1 CH2,l CH2N02 Propane-2-nitro 2 Ch3.1 CHNO2 Benzene-nitro 5 ACH. 1 ACN02
Example
P
w
VI
68 69 70 71 72 73
“Me2SO”
“ACRY ’‘
.‘CI(C=C)’.
“ACF”
“DMF-1”
“DMF-2”
36
37
38
39
39
“ACRY”
“CICC”
“ACF”
“DMF”
“DMF’
“C-C”
73.09 71.09
2.736 2.12 2.6322
,6948 3.0856
35.45 31.01
,724
53.06
,524
,791
2.052
78.131
2.472
2.8266 2.3144
24.020
,784
25.028
79.916
126.92
60.052
1.0613
1.088
,832
.9492 1.292
.YY2
1.264
64
“I”
35
34
“C-C”
2.248
2.4088
63
“(CH20H)2”
“Me2SO”
33
“Br”
96.090
2.484
3.168
67
32
“I”
47.100
1.368
1.651
62
“C-C”
31
“DOH”
48.108
1.676
1.877
2.057
Molecular Weight 76.142
(Qk)
1.65
(Rk)
Sub
Group
Surface Area
Group Volume
“furfural”
61
34
30
“furfural”
“CH2SH”
60
66
29
“CH3SH”
“CH3SH”
59
“CH-C”
29
“CH3SH”
“CS2”
Sub Group Number
65
28
“CS2”
~
Sub Group
“Br”
Main Group Number
Main Group
1 DMF
N.N-Diethylformarnide 2 CH3.1 HCON(CH2)2
Carbon disulfide 1c s 2 Methanethiol 1 CH2SH Ethanethiol 1 CH3.1 CH2SH Furfural 1 furfural 1,2-Ethanediol 1 DOH Iodoe thane 1 CH3.1 CH2.1 I Bromoethane 1 CH3,l CH2.1 Br Hexyne-1 1 CH3.3 CH2. I CH=C Hexyne-2 2 CH3,2 CH2.1 CkC Dimethylsulfoxide 1 DMSO Acrylonitrile 1 acrylonitrile Ethene-trichloro 1 C H X , 3 CI-(C=C) Hexafluorobenzene 6 ACF N.N-Dimethylformamide
Example
“NMP
“CCL3F”
“CCL2F”
42
42
42
42
43
43
43
44
45
45
45
“SiH2”
“SiH2”
“SiH2”
“SiH2”
“SiO”
“SiO”
‘SO”
“NMP”
“CCLF”
“CCLF’
“CCLF’
“HCCL2F”
“SiO”
“SiHO”
“SiH20”
2.2287 2.4060
88
3.0356
3.981
1.1044
1.303
87
86
85
84
83
1.4838
1.047
81 82
1.2853
80
“SiH”
“Si”
1.4443
79
1.6035
“SiH2”
78
1.38
77
“COO”
41
“COO”
“SiH3”
1.0105 .615
75 76
“CF2” “CF”
40 40
“CF2” “CF2”
1.406
74
“CF3”
40
“CF2”
(Rk)
Group Volume
Sub Group Number
Sub Group
Main Group Number
Main Group
2.116
1.916
2.644
3.2
,4657
.7639
1.0621
.4099
,7494
1.0063
1.2632
1.2
.92 .46
1.38
(Qk)
Surface Area
102.924
101.916
137.36
99.13
44.085
45.093
46.101
28.086
29.094
30.102
31.110
44.010
50.01 31.01
69.01
Sub Group Molecular Weight
Perfluorometh ylcyclohexane 1 CF3,5 CF5, 1 CF Methyl acrylate 1 CH3.1 CH2=CH, 1 COO Methylsilane 1 CH3.1 SiH3 Diethylsilane 2 CH3.2 C H 2 , l SiH2 Heptamethyltrisiloxane 7 CH3.2 SiO, 1 SiH Heptamethyldisiloxane 6 C H 3 , l SiO, 1 Si 1,3-Dimethyldisiloxane 3 CH3.1 SiH20,l SiH2 1,1,3,3-Tetramethyldisiloxane 4 CH3.1 SiHO, 1 SiH Octamethylcyclotetrasiloxane 8 CH3.4 SiO N-Methylpyrrolidone 1 NMP Trichlorofluoromethane 1 CC13F Tetrachloro-1.2-difluorethane 2 CC12F Dichlorofluorome thane 1 HCCL2F
Perfluorohexane 2 CF3.5 CF2,l CF
Example
o\
wl w
Main Group Number
45
45
45
45
45
46
46
46
46
46
46
47
47
48
48
Main Group
“CCLF”
“CCLF”
”CCLF”
“CCLF”
“CCLF”
“CON”
“CON”
“CON”
“CON’
“CON”
“CON”
“OCCOH”
“OCCOH”
“CH2S”
“CH2S”
“CH2S”
“CH3S”
“C2H402”
“C2H502”
“CON( CH2)2”
“CONCH3CH2”
“CON( CH3)2”
“CONHCH2“
“CONHCH3”
“CONH2”
“CCL2F2”
“CCLF3”
“HCCLF2”
”CCLF2”
“HCCLF”
Sub Group
103
102
101
100
99
98
97
96
95
94
93
92
91
90
89
Sub Group Number
1.3863
1.6130
1.8952
2.1226
2.4054
2.6322
2.8589
1.9637
2.1905
1.4515
2.6243
2.1721
1.9670
1.8174
1.6493
Group Volume (Rk)
47.098 46.090
1.060
60.053
1.592 1.368
61.051
70.069
71.077
72.085
58.059
1.904
1.812
2.120
2.428
1.488
59.067
44.033
1.248 1.796
120.914
104.459
86.469
85.461
67.471
Sub Group Molecular Weieht
2.376
2.100
1.828
1.648
1.416
(Qk)
Surface Area
1-Chloro- I .2.2,2-tetrafluoroethane 1 CF3. 1 HCClF 1,2-Dichlorotetrafluoroethane 2 CCIF2 Chlorodifluorome thane 1 HCCIF3 Chlorotrifluorornethane 1 CClF3 Dichlorodifluoromethane 1 CC12F2 Acetarnid 1 CH3.1 CONH2 N-Methylacetamid 1 CH3.1 CONHCH3 N-Ethylacetamid 2 CH3.1 CONHCH2 N.N-Dimethylethylacetamid 2 CH3.1 CON(CH3)2 N.N-Methylethylacetamid 2 CH3,l CONCH3CH2 N.N-diethy lacetamid 3 CH3.1 CON(CH2)2 2-Ethoxyethanol 1 CH3.1 CH2,l C2H502 2-Ethoxy-1-propano1 2 CH3.1 CH2.1 C2H402 Dimethylsulfide 1 CH3.1 CH3S Diethylsulfide 2 CH3.1 CH2.1 CH2S
Example
4
w
VI
4
9$
b
h
C4H3S
C4H3S
49
50
SO
50
Morpholine
Thiophene
Thiophene
Thiophene
C4H3S
Morph
“CHS”
48
“CHZS”
Sub Group
Main Group Number
Main Group
108
107
106
105
104
Sub Group Number
2.5241
2.6908
2.8569
3.4740
1.1589
(Rk)
Group Volume
1.580
1.860
2.140
2.796
,748
(Qk)
Surface Area
82.125
83.133
84.140
86.110
45.082
Sub Group Molecular Weight
Diisopropylsulfide 4 CH3,l CH. 1 CHS morpholine 1 Morph Thiophene 1 C4H4S 2-Methy lthiophene 1 CH3.1 C4H3S 2.3-Dimethylthiophene 2 C H 3 , l C4H2S
Example
B
b ‘ci
00
wl w
Appendix II
539
Table 2: UNIFAC group interaction parameters for prediction of vapor-liquid equilibria at temperature between 250 and 425 K. (Hansen et al., 1991) I “CH2” 1 “CH2”
1 “CH2” 1 “CH2”
1 “CH2” 1 “CH2”
1 “CH2” 1 “CH2”
1 “CH2”
I “CH2” 1 “CH2” 1 “CH2”
1 “CH2” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “CXC” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C” 2 “C=C”
1 “CH2” 0 5 “OH” 986.5 9 “CH2CO” 476.4 13 “CH20” 251.5 17 “ACNH2” 920.7 21 “CC1” 35.93 25 “ACCI” 11.44 29 “CH3SH” 184.4 33 “Br” 479.5 37 “CICC” 4.189 41 “COO” 387.1 45 “CCLF” -5.869 49 Morpholine 216.1
2 “CZC” 86.02 6 “CH30H” 697.2 10 T H O ” 677 14 “CNH2” 391.5 18 “pyridine” 287.7 22 “CC12” 53.76 26 “CN02” 661.5 30 “furfural” 354.5 34 “C-C” 298.9 38 “ACF” 125.8 42 “SiH2” 450.4 46 “CON” 390.9 50 Thiophene 92.09
3 “ACH” 61.13 7 “H20” 1318 11 “CCOO” 232.1 15 “CNH” 255.7 19 “CCN” 597 23 “CC13” 24.9 27 “ACNO2” 543 31 “DOH” 3025 35 “Me2SO” 526.5 39 “DMF’ 485.3 43 “SiO” 252.7 47 “OCCOH” 553.3
4 “ACCH2” 76.5 8 “ACOH” 1333 12 “HCOO” 507.0 16 “(C)3N” 206.6 20 “COOH” 663.5 24 “CC14” 104.3 28 “CS2” 153.6 32 “I” 335.8 36 “ACRY” 689 40 “CF2” -2.859 44 “NMP” 220.3 48 “CH2S” 187
1 “CH2” -35.36 5 “OH” 524.1 9 “CH2CO” 182.6 13 “CH20” 214.5 17 “ACNH2” 749.3 21 “CCI” -36.87 25 “ACC1” 100.1 29 “CH3SH” 0 33 “Br” 183.8 37 “CICC” -66.46 41 “COO” 48.33 4s “ C C L F 0 49 Morpholine 62.56
2 “C=C” 0 6 “CH30H” 787.6 10 T H O ” 448.8 14 “CNH2” 240.9 18 “pyridine” 280.5 22 “CC12” 58.55 26 “CN02” 357.5 30 “furfural” 262.9 34 “C-C” 31.14 38 “ACF” 359.3 42 “SiH2” 0 46 “CON” 200.2 50 Thiophene 0
3 “ACH” 38.81 7 “H20” 270.6 11 “CCOO” 37.85 15 “CNH” 163.9 19 “CCN” 336.9 23 “CC13” -13.99 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 179.0 39 “DMF” -70.45 43 ‘ S O ” 0 47 “OCCOH” 268.1
4 “ACCH2” 74. 15 8 “ACOH” 526.1 12 “HCOO” 333.5 16 “(C)3N” 61.11 20 “COOH” 318.9 24 “CC14” -109.7 28 “CS2” 76.3 32 “I” 0 36 “ACRY” -52.87 40 “CF2” 449.4 44 “NMP” 86.46 48 “CH2S” -617
540
Appendix I I
3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH” 3 “ACH”
3 “ACH”
4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2” 4 “ACCH2”
1 “CH2” -11.12 5 “OH” 636.1 9 “CH2CO” 25.77 13 “CH20” 32.14 17 “ACNH2” 648.2 21 “CCI” -18.81 25 “ACCI” 187.0 29 “CH3SH” -1 0.43 33 “Br” 261.3 37 “CICC” -259.1 41 “COO” 103.5 45 “CCLF’ -88.11 49 Morpholine -59.58
2 “C=C” 3.446 6 “CH30H” 637.3 10 “CHO” 347.3 14 “CNH2” 161.7 18 “pyridine” 4.449 22 “CC12” -144.4 26 “CN02“ 168 30 “furfural” -64.69 34 “C-c“ 0 38 “ACF” 389.3 42 “SiH2” 432.3 46 “CON” 0 50 Thiophene -39.16
3 “ACH” 0 7 “H20” 903.8 11 “CCOO” 5.994 15 “CNH” 122.8 19 “CCN” 212.5 23 “CC13” -231.9 27 “ACN02” 194.9 31 “DOH” 210.4 35 “Me2SO” 169.9 39 “DMF” 245.6 43 “SiO” 238.9 47 “OCCOH” 333.3
4 “ACCH2” 167 8 “ACOH” 1329 12 “HCOO” 287.1 16 “(C)3N” 90.49 20 “COOH” 537.4 24 “CC14” 3 28 “CS2” 52.07 32 “I” 113.3 36 “ACRY” 383.9 40 “CF2” 22.67 44 “NMP” 30.04 48 “CH2S” 0
1 “CH2” -69.7 5 “OH” 803.2 9 “CH2CO” -52.1 13 “CH20” 213.1 17 “ACNH2” 664.2 21 “CCI” -114.1 25 “ACCI” -21 1.8 29 “CH3SH” 393.6 33 “Br” 210.0 37 “CICC’ -282.5 41 “COO” 69.26 45 “ C C L F 0 49 Morpholine -203.6
2 “C=C” -113.6 6 “CH30H” 603.2 10 T H O ” 586.6 14 “CNH2” 19.02 18 “pyridine” 52.8 22 “CC12” -111 26 “CN02” 3629 30 “furfural” 48.49 34 “C-C” 0 38 “ACF’ 101.4 42 “SiH2” 0 46 “CON” 0 50 Thiophene 184.9
3 “ACH” -146.8 7 “H20” 5695 11 “CCOO” 5688 15 “CNH” 49.29 19 “CCN” 6096 23 “CC13” 80.25 27 “ACN02” 4448 31 “DOH” 4975 35 “Me2SO” 4284 39 “DMF’ 5629 43 “SiO” 0 47 “OCCOH” 421.9
4 “ACCH2” 0 8 “ACOH” 884.9 12 “HCOO” 197.8 16 “(C)3N” 23.5 20 “COOH” 87.23 24 “CC14 -141.3 28 “CS2” -9.451 32 “I” 259.0 36 “ACRY” -1 19.2 40 “CF2” 0 44 “ N M P 46.38 48 “CH2S” 0
Appendix
5 “OH” 5 “OH” 5 “OH”
5 “OH” 5 “OH” 5 “OH” 5 “OH”
5 “OH” 5 “OH” 5 “OH” 5 “OH“
5 “OH” 5 “OH”
6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H”
6 “CH30H” 6 “CH30H” 6 “CH30H” 6 “CH30H”
II
1 THY 156.4 5 “OH” 0 9 “CH2CO” 84 13 “CH20” 28.06 17 “ACNH2” -52.39 21 “CC1” 75.62 25 “‘ACCI” 123.5 29 “CH3SH” 147.5 33 “Br” 133.4 37 “ C I C C 225.8 41 “COO” 190.3 45 “CCLF’ 72.96 49 Morpholine 104.7
2 “C=C“ 457 6 “CH30H” -1 37.1 10 “CHO” -203.6 14 “CNH2” 8.642 18 “pyridine” 170 22 “CC12” 65.28 26 “CN02” 256.5 30 “furfural” -120.5 34 “C-C” 727.8 38 “ A C F 44.78 42 5 H 2 ” -817.7 46 “CON” -382.7 50 Thiophene 57.65
3 “ACH” 89.6 7 “H20” 353.5 11 “CCOO” 101.1 15 “CNH” 42.7 19 “CCN” 6.712 23 “CC13” -98.12 27 “ACN02” 157.1 31 “DOH” -318.9 35 “Me2SO” -202.1 39 “ D M F -143.9 43 ‘ S O ” 0 47 “OCCOH” -248.3
4 “ACCH2” 25.82 8 “ACOH“ -259.7 12 “HCOO” 267.8 16 “(C)3N” -323 20 “COOH” 199 24 “CC14” 143.1 28 “CS2” 488.9 32 “I” 313.5 36 “ACRY” 74.27 40 “CF2” 0 44 “NMP” -504.2 48 “CH2S” 0
1 “CH2” 16.51 5 “OH” 249.1 9 “CH2CO” 23.39 13 “CH20” -128.6 17 “ACNH2” 489.7 21 “CCI” -38.32 25 “ACCI” -25.25 29 “CH3SH” -17.50 33 “Br” 106.3 37 “CICC” 33.47 “COO” 165.7 41 “COO” -52.1 49 Morpholine -59.4
2 “C=C” -12.52 6 “CH30H” 0 10 ‘ T H O ” 306.4 14 “CNH2” 359.3 18 ”pyridine” 580.5 22 “CC12” -1 02.5 26 ”CN02” 75. I4 30 ”furfural” 0 34 “C-C” 0 38 “ACF” 48.25 ’‘ SiH2” 0 42 “SiH2” 0 50 Thiophene 46.01
3 “ACH” -50 7 “H20” -181 11 “CCOO” -10.72 15 “CNH” -20.98 19 “CCN” 53.28 23 “CC13” -139.4 27 “ACNO2” 0 31 “ D O H -119.2 35 “Me2SO” -399.3 39 “DMF” -172.4 “SiO” 0 43 “SiO” 0
4 “ACCH2” 44.5 8 “ACOH” -101.7 12 “HCOO” 179.7 16 “(C)3N” 53.9 20 “COOH” -202.0 24 “CC14” 44.76 28 “CS2” -3 1.09 32 “I” 212.1 36 “ACRY” -5.224 40 “CF2” 0 “NMP 0 44 “NMP” 37.63
541
542
Appendix II
7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20” 7 “H20’ 7 “H20” 7 “H20” 7 “H20” 7 “H20”
8 “ACOH” 8 “ACOH”
8 “ACOH” 8 “ACOH” 8 “ACOH” 8 “ACOH”
8 “ACOH” 8 “ACOH”
8 “ACOH” 8 “ACOH” 8 “ACOH” 8 “ACOH” 8 “ACOH”
37 “CICC” 0 41 “COO” -197.5 45 “ C C L F 0 49 Morpholine 407.9
2 “CZC” 496.1 6 “CH30H” 289.6 10 T H O ” -1 16.0 14 “CNH2” 48.89 18 “pyridine” 459 22 “CC12” 370.4 26 “CN02” 220.6 30 “furfural” 188 34 “C-C’ 0 38 “ACF’ 0 42 “SiH2” -363.8 46 “CON” 835.6 50 Thiophene 0
3 “ACH” 362.3 7 “H20” 0 11 “CCOO” 72.87 15 “CNH” 168 19 “CCN” 112.6 23 “CC13” 353.7 27 “ACNO2” 399.5 31 “DOH” 12.72 35 “Me2SO” -139 39 “DMF” 319 43 “SiO” 0 47 “OCCOH” 19.6
4 “ACCH2” 317.6 8 “ACOH” 324.5 12 “ H C O O 0 16 “(C)3N” 304 20 “COOH” -14.09 24 “CC14” 497.5 28 “CS2” 887.1 32 “I” 0 36 “ACRY” 160.8 40 “CF2” 0 44 “NMP’ 452.2 48 “CH2S” 0
1 “CH2” 275.8 5 “OH” 451.6 9 “CH2CO” -356.1 13 “CH20” -162.9 17 “ACNH2” 119.9 21 “CCI” 0 25 “ACCI”
2 ‘‘C=C’’ 217.5 6 “CH30H” -265.2 10 “CHO” -271.1 14 ”CNH2” 0 18 “pyridine” -305.5 22 “CC12” 0 26 “CN02”
3 “ACH” 25.34 7 “H20” 401.8 11 “CCOO” 49.4 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02”
4 “ACCH2” 244.2 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 408.9 24 “CC14” 1827 28 “CS2”
691.5 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 494.2 45 “CCLF” 0 49 Morpholine 0
0 30 “furfural” 0 34 “C- C” 0 38 “ A C F 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 1005
0 31 “DOH” 487.1 35 “Me2SO” 0 39 “DMF” 0 43 ‘ S O ” 0 47 “OCCOH” 0
8484 32 “1” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP’ 459.0 48 “CH2S” 0
1 “CH2” 300 5 “OH” -229.1 9 “CH2CO -195.4 13 “CH20” 540.5 17 “ACNH2” 243.2 21 “CCI” 325.4 25 “ACCI” 133.9 29 “CH3SH” 0 33 “Br” 0
Appendix II
9 “CH2CO”
9 “CH2CO” 9 “CH2CO“ 9 “CHZCO” 9 “CH2CO” 9 “CH2CO”
9 “CH2CO” Y “CH2CO”
9 “CH2CO” 9 “CH2CO” Y “CH2CO”
Y “CH2CO” 9 -’CH2CO”
10 T H O ” 10 “CHO”
10 T H O ” 10 T H O ” 10 T H O “
10 “CHO“
10 “CHO” 10 T H O ” 10 T H O ” 10 T H O ” 10 ‘ T H O ” 10 “CHO” 10 “CHO”
1 “CH2” 26.76 5 “OH” 164.5 9 ”CH2CO” 0 13 “CH20” -103.6 17 “ACNH2” 6201 21 “CCI” -191.7 25 “ACCI” -1 19.8 29 “CH3SH” 46.28 33 “Br” 245.2 37 “CICC’ -34.57 41 “COO” -18.8 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 42.92 6 “CH30H” 108.7 10 T H O ” -37.36 14 “CNH2” 0 18 “pyridine” 7.341 22 “CC12” -130.3 26 “CN02” 137.5 30 “furfural” -163.7 34 “C-C“ -246.6 38 “ACF” 0 42 “SiH2” -588.’) 46 “CON” 0 50 Thiophene -162.6
3 “ACH” 140.1 7 “H20” 472.5 11 “CCOO” -213.7 15 “CNH” -174.2 19 “CCN” 481.7 23 “CC13” -354.6 27 “ACN02” 548.5 31 “DOH” 71.46 35 “Me2SO” 44.58 39 “DMF” 41.7 43 “SiO” 0 47 “OCCOH” 37.54
4 “ACCH2” 365.8 8 “ACOH” -133.1 12 “HCOO” -190.4 16 “(C)3N” -169 20 “COOH” 669.4 24 “CC14” -39.2 28 “CS2” 216.1 32 “I” 53.59 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” 505.7 5 “OH” 529.0 9 “CH2CO” 128 13 “CH20” 304.1 17 “ACNH2” 0 21 “CCI” 751.9 25 “ACC1” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 172.4 41 “COO” -275.5 45 “CCLF” 0 49 Morpholine 0
2 “CXC” 56.3 6 “CH30H” -340.2 10 T H O ” 0 14 “CNH2” 0 18 ”pyridine” 0 22 “CC12” 67.52 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ A C F 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 23.39 7 “H20” 48.08 11 “CCOO” -110.3 15 “CNH” 0 19 “CCN” 0 23 “CC13” -483.7 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “ D M F -268.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 106 8 “ACOH” -155.6 12 “HCOO” 766.0 16 “(C)3N” 0 20 “COOH” 497.5 24 “CC14” 0 28 “CS2” 0 32 “I” 117.0 36 “ACRY” -339.2 40 “CM” 0 44 “NMP” 0 48 “CH2S” 0
543
544
Appendix II
11 “CCOO” 11 “ C C O O 11 “CCOO”
11 “CCOO” 11 “CCOO” 11
“ccoo”
11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO” 11 “CCOO”
12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO” 12 “HCOO”
1 “CH2” 114.8 5 “OH” 245.4 9 “CH2CO” 372.2 13 “CH20” -235.7 17 “ACNH2” 475.5 21 “CCI” -34.74 25 “ACCI” 442.4 29 “CH3SH” 0 33 “Br” 18.88 37 “CICC” -275.2 41 “COO” 560.2 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 132.1 6 “CH30H” 249.6 10 “CHO” 185.1 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 108.9 26 “CN02” -81.13 30 “furfural” 202.3 34 “C-C” 0 38 “ACF’ 0 42 ”SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 85.84 7 “H20” 200.8 11 “CCOO” 0 15 “CNH” -73.5 19 “CCN” 494.6 23 “CC13” -209.7 27 “ACN02” 0 31 “DOH” -101.7 35 “Me2SO” 52.08 39 “DMF” 85.33 43 “SiO” 0 47 “OCCOH” 151.8
4 “ACCH2” -170 8 “ACOH” -36.72 12 “HCOO” -241.8 16 “(C)3N” -196.7 20 “COOH” 660.2 24 “CC14” 54.47 28 “CS2” 183 32 “I” 148.3 36 “ACRY” -28.61 40 “CF2” 0 44 “NMP’ 0 48 “CH2S” 0
1 “CH2” 329.3 5 “OH” 139.4 9 “CH2CO” 385.4 13 “CH20” -234.0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 24.28 29 “CH3SH” 103.9 33 “Br” 0 37 “CICC” -1 1.4 41 “COO” -122.34 45 “CCLF’ 0 49 Morpholine 0
2 “CXC” 110.4 6 “CH30H” 227.8 10 ‘THO” -236.5 14 “CNH2” 0 18 “pyridine” -233.4 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 18.12 7 “H20” 0 11 “CCOO” 1167 15 “CNH” 0 19 “CCN” -47.25 23 “CC13” -126.2 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 308.9 43 “SiO” 0 47 “OCCOH” 0
4 ”ACCH2” 428.0 8 “ACOH” 0 12 “HCOO” 0
16 “(C)3N” 0 20 ”COOH” -268. I 24 “CC14” 179.7 28 “CS2” 0 32 ‘‘1’. 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
Appendix I1 ~~
13 “CH20“ 13 “CH20” 13 “CH20” 13 “CH20” 13 “CH20”
13 “CH20” 13 “CH20” 13 “CH20” 13 “CH20” 13 “CH20”
13 “CH20” 13 “CH20” 13 “CH20“
14 “CNH2“ 14 “CNH2” 14 “CNH2”
14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “ C N H 2 14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “CNH2” 14 “CNH2”
1 “CH2” 83.36 5 “OH” 237.7 9 “CH2CO” 191.1 13 “CH20” 0 17 “ACNH2” 0 21 “CC1” 301.1 25 “ACCI” 134.8 29 “CH3SH” -8.538 33 “BT” -202.3 37 “CICC” 240.2 41 “COO” 417 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 26.5 1 6 “CH30H” 238.4 10 T H O ” -7.838 14 “CNH2” -78.36 18 “pyridine” 213.2 22 ”CC12” 137.8 26 “CNO2” 95.18 30 ”furfural” 0 34 “c‘-C” 0 38 “ACF” -273.Y 42 “SiH2” 1338.0 46 “CON” 0 SO Thiophene 0
3 “ACH” 52.13 7 “H20” -314.7 11 “CCOO” 461.3 15 “CNH” 251.5 19 “CCN” -1 8.5 1 23 “CC13” -154.3 27 “ACN02” 0 31 “DOH” -20.11 35 “Me2SO” 128.8 39 “DMF’ 254.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 65.69 8 “ACOH” -178.5 12 “HCOO” 457.3 16 “(C)3N” 5422 20 “COOH” 664.6 24 “CC14” 47.67 28 “CS2” 140.9 32 “I” -149.5 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S“ 0
1 “CH2” -30.48 5 “OH“ -242.8 Y “CH2CO” 0 13 “CH20” 222.1 17 “ACNH2” -200.7 21 “CCI” 0 25 “ACCI” 30.05 29 “CH3SH“ -70.14 33 “BT” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF“ 0 49 Morpholine 0
2 “C=C“ 1.163 6 “CH3OH” 431.7 10 T H O “ 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02“ 0 30 “furfural“ 0 34 c C” 0 38 “‘ACF” 0 42 “SiH2” 464.4 46 “CON” 0 50 Thiophene 0
3 “ACH” 44.85 7 “H20” -330.4 11 “ccoo” 0 15 “CNH” -107.2 19 “CCN” 147. I 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” 0 35 “ M e 2 S O 0 39 “DMF’ -164.0 43 “SiO” 275.9 47 “OCCOH” 0
4 “ACCH2“ -242.8 8 “ACOH” 0 12 “HCOO“ 0 16 “(C)3N” 41.11 20 “COOH”
“
~
0
24 “CC14” -99.81 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
545
546
Appendix II
15 “CNH” 15 “CNH” 15 CN H ‘I
”
15 “CNH” 15 “CNH”
15 “CNH” 15 “CNH”
15 “CNH” 15 “CNH” 15 “CNH” 15 “CNH” 15 “CNH” 15 “CNH”
16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N” 16 “(C)3N”
1 “CH2” 65.33 5 “OH” -150 9 “CH2CO” 394.6 13 “CH20” -56.08 17 “ACNH2” 0 21 “CCI” 0 25 “ACCl” -18.93 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” -38.77 45 “ C C L F 0 49 Morpholine 0
2 “C=C” -28.7 6 “CH30H” -370.3 10 “CHO” 0 14 “CNH2” 127.4 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 c-C” 0 38 “ACF” 570.0 42 “SiH2” 448.1 46 “CON” 0 SO Thiophene 0
3 “ACH” -22.31 7 “H20” -448.2 11 “CCOO” 136 15 “CNH” 0 19 “CCN” 147.1 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 0 43 ‘ S O ” -1327.0 47 “OCCOH” 0
4 “ACCH2” 223 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” -189.2 20 “COOH” 0 24 “CC14” 71.23 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” -83.98 5 “OH” 28.6 9 “CH2CO” 225.3 13 “CH20” -194.1 17 “ACNH2” 0 21 “CCI” 0 25 “ACC1” -181.9 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 ‘‘C=C’’ -25.38 6 “CH30H” -406.8 10 “CHO” 0 14 “CNH2” 38.89 18 “pyridine” 0 22 “CC12” -73.85 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF’ -196.3 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -223.9 7 “H20” -598.8 11 “CCOO” 2889 15 “CNH” 865.9 19 “CCN” 0 23 “CC13” -352.9 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “ D M F 22.05 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 109.9 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -262.0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CHZS” 0
“
Appendix I1
17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2” 17 “ACNH2”
1 “CH2” 1139 5 “OH” -17.4 9 “CH2CO” 450.3 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 287 25 “ACCI” 617.5 29 “CH3SH” 0 33 “Br” 0 37 “ClCC” 0 41 “COO” -89.42 45 “CCLF” 0 49 Morpholine 0
2 “CZC” 2000 6 “CH30H” -118.1 10 “CHO” 0 14 “CNH2” -15.07 18 “pyridine” 89.70 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 ”C-c” 0 38 “ A C F 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH”
1 “CH2” -101.6 5 “OH” -132.3 9 “CH2CO” 29.1 13 “CH20” -156.1 17 “ACNH2” 117.4 21 “CCI”
2 “C=C” 47.63 6 “CH30H” -378.2 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” -35 1.6 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF -158.8 42 “SiH2” 0 46 “CON” 0 50 Thiophene -136.6
3 “ACH” 31.87 7 “H20” -332.9 11 “CCOO” 0 15 “CNH” 0 19 “CCN” -169.7 23 “CC13” -1 14.7 27 “ACN02” 2845 31 “DOH” 0 35 “Me2SO” 0 39 “ D M F 0 43 “SiO” 0 47 “OCCOH” 0
247.5 7 “H20” -341.6 11 “CCOO” -294.8 15 “CNH” 0 19 “CCN” -281.6 23 “CC13” 0 27 “ACN02” -139.3 31 “DOH” -136.9 35 “Me2SO” 0 39 “ D M F -334.4 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 762.8 8 “‘ACOH” -253.1 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” -396.0 24 “CC14” 822 28 “CS2” 0 32 “1” 0 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S” 0
~
18 “pyridine” 18 “pyridine” 18 “pyridine” 18 “pyridine”
18 ”pyridine” 18 “pyridine” 18 “pyridine” 18 “pyridine” 18 “pyridine”
18 “pyridine” I X “pyridine”
I8 “pyridine” I X “pyridine“
0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” -60.78 37 “CICC” 160.7 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
4 “ACCH2” 49.8 8 “ACOH” -341.6 12 “HCOO” 554.4 16 “(C)3N” 0 20 “COOH” -153.7 24 “CC14” -205.3 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
547
548
Appendix I1
19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN” 19 “CCN”
19 “CCN” 19 “CCN” 19 “CCN” 1 Y “CCN”
19 “CCN” 19 “CCN”
20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 TOOH” 20 “COOH” 20 “COOH” 20 “COOH” 20 “COOH”
1 “CH2“ 24.82 5 “OH” 185.4 9 “CH2CO” -2873 13 “CH20” 38.81 17 “ACNH2” 777.4 21 “CCI” 4.933 25 “ACCI“ 4.624 29 “CH3SH” 0.4604 33 “Br” -62.17 37 “CICC” 55.77 41 “COO” 120.3 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 40.62 6 “CH30H” 162.6 10 ‘THO” 0 14 “CNH2” -157.3 18 “pyridine” 134.3 22 “CC12” -152.7 26 “CN02” -515 30 “furfural” 0 34 “C-C” -203 38 ‘*ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -22.97 7 “H20” 242.8 I 1 “CCOO” -266.6 15 “CNH” -108.5 19 ”CCN” 0 23 “CC13” -15.62 27 “ACN02” 0 31 “DOH” 177.5 35 “Me2SO” 0 39 “DMF’ -151.5 43 “SiO” 0 47 “OCCOH” 16.23
4 “ACCH2”
1 “CH2 315.3 5 “OH” -151 9 “CH2CO” -297.8 13 “CH20” -338.5 17 “ACNH2” 493.8 21 “CCI” 13.41 25 “ACCI” -79 08 29 “CH3SH” 0 33 “Br” -95 37 “ C I C C -11.16 41 “COO” -337 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 1264 6 “CHSOH” 339.8 10 T H O “ -165.5 14 “CNH2” 0 18 “pyridine” -313.5 22 “CC12” 44.7 26 “CN02” 0 30 “furfural” -208.9 34 “C-C” 0 38 “ A C F 0 42 “S1H2” 0 46 “CON” -322.3 50 Thiophene 0
3 “ACH” 62.32 7 “H20” -66.17 11 “CCOO” -256.3 15 “CNH” 0 19 “CCN” 0 23 “CC13” 39.63 27 “ACN02” 0 31 ”DOH” 0 35 “Me2SO” 463.6 39 ” D M F -228.0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2”
-138.4 8 “ACOH” 0 12 “HCOO” 99.37 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -54.86 28 “CS2“ 230.9 32 “I” 0 36 “ACRY“ 81.57 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
89.86 8 “ACOH“ -1 1.0 12 “HCOO” 193.9 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 183.4 28 “CS2” 0 32 “I” 228.4 36 “ACRY” 0 40 “CF2” 0 44 “NMP“ 0 48 “CH2S” 0
Appendix I1 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCL” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI” 21 “CCI”
22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12” 22 “CC12”
549
1 “CH2” 91.46 5 “OH” 562.2 9 “CH2CO” 286.3 13 “CH20” 225.4 17 “ACNH2” 429.7 21 “CCI” 0 25 “ACCI” 153.0 29 “CH3SH“ 59.02 33 “Br” 344.4 37 “CICC” -168.2 41 “COO” 63.61 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 40.25 6 “CH30H” 529 10 ‘ T H O ” 47.51 14 “CNH2” 131.2 18 “pyridine” 0 22 “CC12” 108.3 26 “CN02” 32.73 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 4.68 7 “H20” 698.2 11 “CCOO” 35.38 15 “CNH” 0 19 “CCN” 54.32 23 “CC13” 249.2 27 “ACN02” 86.2 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 122.9 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 519.1 24 “CC14” 62.42 28 “CS2” 450.1 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “ C H 2 S 0
1 “CH2” 34.01 5 “OH” 527.6 9 “CH2CO” 82.86 13 “CH20” -197.7 17 “ACNH2” 0 21 “CCI” -84.53 25 “ACCI” 223.1 29 “CH3SH” 0 33 “Br” 315.9 37 “CICC” -91.8 41 “COO” -96.81 45 “CCLF’ 0 49 Morpholine 0
2 ‘*C=C” -23.5 6 “CH30H” 669.9 10 ‘THO” 190.6 14 “CNH2” 0 18 “pyridine” 587.3 22 “CC12” 0 26 “CN02” 108.9 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 121.3 7 “H20” 708.1 11 “CCOO” -133 15 “CNH” 0 19 “CCN” 258.6 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 215 39 “DMF” 0 43 ‘ S O ” 0 47 “OCCOH” 361.1
4 “ACCH2” 140.8 8 “ACOH” 0 12 ‘ ~ ~ ~ 0 0 7 3 0 16 “(C)3N” -1 41.4 20 “COOH” 543.3 24 “CC14” 56.33 28 “CS2” 0 32 “I” 177.6 36 “ACRY” 0 40 “CF2” 0 44 “NMP’’ 0 48 “CH2S” 0
550
Appendix I1
23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13” 23 “CC13”
24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14” 24 “CC14”
1 “CH2” 36.7 5 “OH” 742.I 9 “CH2CO” 552.1 13 “CH20” -20.93 17 “ACNH2“ 0 21 “CCI” -157.1 25 “ACCI” 191.1 29 “CH3SH” 0 33 “Br” 0 37 ”CICC” 111.2 41 “COO” 255.8 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 5 1.06 6 “CH30H” 649.1 10 “CHO” 242.8 14 “CNH2” 0 18 “pyridine” 18.98 22 “CC12” 0 26 “CN02” 0 30 “furfural” -64.38 34 “C-C” 0 38 “ACF’ 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH”
288.5 7 “H20” 826.7 11 “CCOO” 176.5 15 “CNH” 0 19 “CCN” 74.04 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 363.7 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 69.9 8 “ACOH” 0 12 “HCOO” 235.6 16 “(C)3N” -293.7 20 “COOH” 504.2 24 “CC14” -30.1 28 ”CS2” 116.6 32 “I” 86.4 36 “ACRY“ 0 40 “CF2” 0 44 “NMP” -35.68 48 “CH2S” 565.9
1 “CH2” -78.45 5 “OH” 856.3 9 “CH2CO” 372 13 “CH20” 113.9 17 “ACNH2” 898.2 21 “CCI” 11.8 25 “ACCI” -75.87 29 “CHSSH” 0 33 “Br” 146.6 37 “CICC” 187.1 41 “COO” 256.5 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 160.9 6 “CH30H” 709.6 10 T H O ” 0 14 “CNH2” 261.1 18 “pyridine” 368.5 22 “CC12” 17.97 26 “CN02” 490.9 30 “furfural” 546.7 34 “C-C” 0 38 “ACF” 215.2 42 “SiH2” 0 46 “CON” 0 50 Thiophene 108.5
3 “ACH” 4.7 7 “H20” 1201 11 “CCOO” 129.5 15 “CNH” 91.13 19 “CCN” 492 23 “CC13” 51.9 27 “ACNOZ” 534.7 31 “DOH” 0 35 “Me2SO” 337.7 39 “DMF” 498.6 43 “SiO” 233.1 47 “OCCOH” 423.1
4 “ACCHZ” 134.7 8 “ACOH” 10000 12 ”HCOO” 351.9 16 “(C)3N” 316.9 20 “COOH” 63 1 24 “CC14” 0 28 “CS2“ 132.2 32 “I” 247.8 36 “ACRY” 369.5 40 “CF2” 0 44 “NMP’ 0 48 “CH2S” 63.95
Appendix I1
25 “ACCI” 25 “ACCI” 25 “ACCI” 25 “ACCI” 25 “ACCI“ 25 “ACCI”
25 “ACCI” 25 “ACCI” 25 “ACCI” 25 “ACCI” 2.5 “ACCI” 25 “ACCI” 25 “ACCI”
26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 ”CN02” 26 “CN02” 26 “CN02” 26 “CN02” 26 “CN02”
1 “CH2” 106.8 5 “OH” 325.7 9 “CH2CO” 518.4 13 “CH20” -25.15 17 “ACNH2“ 334.9 21 “CCI” -129.7 25 “ACCI” 0 29 “CHSSH” 0 33 “Br” 593.4 37 “CICC” 0 41 “COO” -71.18 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 70.32 6 “CH30H” 612.8 10 “CHO” 0 14 “CNH2” 108.5 18 “pyridine” 0 22 “CC12” -8.309 26 “CN02” 132.7 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -97.27 7 “H20” -274.5 11 “CCOO” -171.1 1.5 “CNH” 102.2 19 “CCN” 363.5 23 “CC13” 4.2266 27 “ACNO2” 2213 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 434.1
4 “ACCH2” 402.5 8 “ACOH” 622.3 12 “HCOO” 383.3 16 “(C)3N” 2951 20 “COOH” 993.4 24 “CC14” 248.4 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” -209.7 48 “CH2S” 0
1 “CH2” -32.69 5 “OH” 261.6 9 “CH2CO” -142.6 13 “CH20” -94.49 17 “ACNH2” 0 21 “CCI” 113 25 ”ACCI” 132.9 29 “CH3SH” 0 33 “Br” 10.17 37 “ C I C C 10.76 41 “COO” 248.4 45 “CCLF” -218.9 49 Morpholine 0
2 “C=C” -1.996 6 “CH30H” 252.6 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” -9.639 26 “CN02” 0 30 “furfural” 0 34 “C-C” -27.7 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 4.565
3 “ACH” 10.38 7 “H20” 417.9 11 “CCOO” 129.3 15 “CNH” 0 19 “CCN” ,2827 23 “CC13” 0 27 “ACN02” 533.2 31 “DOH” 139.8 35 “Me2SO” 0 39 “DMF” -223.1 43 “SiO” 0 47 “OCCOH”
4 “ACCH2” -97.05 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -34.68 28 “CS2” 320.2 32 “I” 304.3 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
n
551
552
Appendix II
27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACNO2” 27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACN02” 27 “ACNO2” 27 “ACN02” 27 “ACN02” 27 “ACNO2”
28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2” 28 “CS2”
1 “CH2” 5541 5 “OH” 561.6 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 134.9 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC’ 0 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 “C=C”
1 “CH2” -52.65 5 “OH“ 609.8 9 “CH2CO” 303.7 13 “CH20” 112.4 17 “ACNH2” 0 21 “CCI” -73.09 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC -47.37 41 “COO” 469.8 45 “CCLF’ 0 49 Morpholine 0
2 “C=C’ 16.62 6 “CH30H” 914.2 10 ‘THO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12”
0
6 “CH30H” 0 10 “CHO” 0 14 “CNH2” 0
18 “pyridine” 0 22 “CC12” 0 26 “CN02” -85.12 30 “furfural” 0 34 “C-C” 0
38 0 42 0 46 0 50 0
“ACF” “SiH2”
39 “DMF” 43 “SiO” 0
“CON”
47 “OCCOH” 0
4 “ACCH2” -127.8 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0
20 “COOH” 0 24 “CC14” 514.6 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
Thiophene
0
34 0 38 0 42 0 46 0 50 0
0 0
26 “CN02” 277.8 30 “furfural” 0
3 “ACH” 1824 7 “H20” 360.7 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO”
“C-c
3 ‘*ACH” 21.5 7 “H20” 1081 11 “CCOO” 243.8 15 “CNH” 0
19 “CCN” 335.7 23 “CC13” -26.06 27 “ACN02” 0
31 “DOH”
0
35 “Me2SO” 0
“ACF “SiH2” “CON” Thiophene
39 “ D M F 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 40.68 8 “ACOH” 1421 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 40.71 28 “CS2” 0 32 “I” 292.7 36 “ACRY” 0 40 “CF2” 0
44 “NMP” 0 48 “CH2S” 0
Appendix I1
29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH” 29 “CH3SH”
30 “furfural” 30 “furfural”
30 “furfural” 30 “furfural”
30 “furfural” 30 “furfural”
30 “furfural” 30 “furfural” 30 “furfural” 30 “furfural” 30 ”furfural” 30 “furfural” 30 “furlural”
1 “CH2” -7.481 5 “OH” 461.6 9 “CH2CO” 160.6 13 “CH20” 63.71 17 “ACNH2” 0 21 “CCI” -27.94 25 “ACCl” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO’ 0 45 “CCLF” 0 49 Morpholine 0
2 “C=C“ 0 6 “CH30H” 448.6 10 ‘ T H O ” 0 14 “CNH2” 106.7 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 ”ACF” 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 0
3 “ACH” 28.41 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 161.0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 31.66 39 “DMF” 78.92 43 “SiO” 0 47 “OCCOH’ 0
4 “ACCH2” 19.56 8 “ACOH” 0 12 “HCOO” 201.5 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 1004 48 “CH2S” -18.27
1 “CH2” -25.31 5 “OH” 521.6 9 “CH2CO” 317.5 13 “CH20” -87.31 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “ C l C C 0 41 “COO” 43.37 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 82.64 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CNO2” 0 30 “furfural” 0 34 ”C-c” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 157.3 7 “H20” 23.48 11 “CCOO“ -146.3 15 “CNH” 0 19 “CCN” 0 23 “CC13” 48.48 27 “ACN02” 0 31 “DOH” 0 35 “Me2S.O” 0 39 “ D M F 0 43 “SiO” 0 47 “OCCOH” 0
4 ‘;9CCH2” 128.8 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 570.6 24 “CC14” -133.2 28 “CSY 0 32 “I” 0 36 “ACRY” 0 40 “CM” 0 44 “NMP” 0 48 “CH2S” 0
553
554
Appendix II ~~
31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH” 31 “DOH”
32 “1” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I” 32 “I”
32 “I”
~
~
29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 347.8 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 0 6 “CH30H” 240.8 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 481.3 30 “furfural” 0 34 “C-C” 0 38 “ACF“ 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 0
3 “ACH” 221.4 7 “H20” -137.4 11 “CCOO” 152 15 “CNH” 0 19 “CCN” 169.6 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 417.2 39 “ D M F 302.2 43 “SiO” 0 47 “OCCOH” -353.5
4 “ACCH2” 150.6 8 “ACOH” 838.4 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” -262.0 48 “CH2S” 0
1 “CH2” 128 5 “OH S01.3 9 “CH2CO” 138 13 “CH20” 476.6 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 68.55 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 0 6 “CH30H” 431.3 10 ‘ T H O ” 245.9 14 “CNH2” 0 18 “pyridine” 0 22 ”CC12” 40.82 26 “CN02” 64.28 30 “furfural” 0 34 “C-C” 0 38 “ACF’ 0 42 “SiH2” 0 46 “CON” 0 SO Thiophene 0
3 “ACH” 58.68 7 “H20” 0 11 “CCOO” 2 1.92 15 “CNH” 0 19 “CCN” 0 23 “CC13” 21.76 27 “ACN02” 2448 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCHZ” 26.4 1 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 616.6 24 “CC14” 48.49 28 “CS2” -27.45 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP’ 0 48 “CHZS” 0
1 “CH2” 139.9 5 “OH” 267.6 9 “CH2CO” 135.4 13 “CH20” 9.207 17 “ACNH2” 192.3 21 “CCI” 0 25 “ACCI” 0
Appendix I I
33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br“ 33 “Br”
33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br” 33 “Br”
34 “C-C”
34 “C-c” 34 “C-C” 34 “C-C’ 34 C- C” “
34 “C-C“ 34 “C-C” 34 “C-C” 34 “C-C” 34 “C-C“ 34 ”C-c“
34 “C-C” 34 “C-C”
1 “CH2” -31.52 5 “OH” 72 1.9 9 “CH2CO” -142.6 13 “CH20’ 736.4 17 “ACNH2” 0 21 “CCI” -262.3 25 “ACCI” -185.3 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” -195.1 45 “CCLF” 0 49 Morpholine 0
174.6 6 “CH3OH” 494.7 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 42.71 22 “CC12” -174.5 26 “CNO2” 125.3 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
1 “CH2” -72.88 5 “OH” 68.95 9 “CH2CO” 443.6 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 2073 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 “C=C” 41.38 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 174.4 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -154.2 7 “H20” 0 11 “CCOO” 24.37 15 “ C N H 0 19 “CCN” 136.9 23 “CC13” 0 27 “ACNO2” 4288 31 “DOH” 0 35 “Me2SO” 32.9 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 1112 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 5256 24 “CC14” 77.55 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
3 “ACH” 0 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 329.1 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” -1 19.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14’ 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
555
0 .‘H0330., LP 0 ,,0!S.7 Eb PO8‘8‘ m a . , 6s 0 L.OSzaVIV..SE 0 ‘‘Hoa.. 1E 0 ,,ZON3V7:.LZ 0 .‘€I3377 EZ IE‘ZP,,N33.. 61 0 ,,HN3,, Sl SSLI “0033.>11 9‘9% uOZHv L 9‘EZluH3V>*E
L.OSZaVInSE “OSZaINY,, SE
“OSZaVIn SE ‘.OSZaPlY,>SE ‘,OSZaVI.? SE ..oszaPl3. SE “OSZ~PlY.> SE ‘.OSZawV,>SE ,.oszaVIY,, SE .,oszawY.>SE “OSZaVIn SE ..OSZaVIY,. SE
.,OSZW.7 SE
Appendix 11
37 “ClCC” 37 “ClCC” 37 “ClCC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “CICC” 37 “ClCC” 37 “CICC” 37 “CICC”
38 “ACF“ 38 “ACF’ 38 “ACF“ 38 “ACF’ 38 “ACF” 38 “ACF” 38 “ A C F 38 “ACF” 38 “ACF” 38 “ACF” 38 “ACF” 38 “ACF’ 38 “ACF’
1 “CH2” 47.41 5 “OH” 738.9 9 “CH2CO” 40.9 13 “CH20” -217.9 17 “ACNH2” 0 21 “CCl” 383.2 25 “ACCl” 0 29 “CH3SH” 0 33 “Br” 0 37 “ClCC” 0 41 “COO” 730.8 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 124.2 6 “CH30H” 528 10 “CHO” 183.8 14 “CNH2” 0 18 “pyridine” 281.6 22 “CC12” 301.9 26 “CN02” 379.4 30 “furfural” 0 34 “C-C” 631.5 38 “ACF’ 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 395.8 7 “H20” 0 11 “CCOO” 611.3 15 “CNH” 0 19 “CCN” 335.2 23 “CC13” -149.8 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 255 43 ‘ S O ” 0 47 “OCCOH” 0
4 “ACCH2” 419.1 8 “ACOH” 0 12 “HCOO” 134.5 16 “(C)3N” 0 20 “COOH” 898.2 24 “CC14” -134.2 28 “CS2” 167.9 32 “I” 0 36 “ACRY” 837.2 40 “CF2” 0 44 “NMP” 26.35 48 “CH2S” 2429
1 “CH2” -5.132 5 “OH” 649.7 9 “CH2CO” 0 13 “CH20” 167.3 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 ‘‘CXC“ -131.7 6 “CH30H” 645.9 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 159.8 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 c-C” 0 38 “ACF” 0 42 ”SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -237.2 7 “H20” 0 11 “CCOO” 0 15 “CNH” -1 98.8 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” -157.3 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 116.5 20 “COOH” 0 24 “CC14” -124.6 28 “CS2” 0 32 “1” 0 36 “ACRY” 0 40 “CF2” -117.2 44 “NMP” 0 48 “CH2S” 0
‘I
557
558
Appendix II
39 “DMF’ 39 “DMF” 39 “ D M F 39 “DMF” 39 “DMF” 39 “DMF” 39 “ D M F 39 “DMF” 39 “DMF” 39 “DMF’ 39 “DMF’ 39 “DMF’ 39 “DMF”
40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2” 40 “CF2”
40 “CF2” 40 “CF2” 40 “CF2”
1 “CH2” -3 1.95 5 “OH” 64.16 9 “CH2CO” 97.04 13 “CH20” -158.2 17 “ACNH2” 343.7 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” -7 1 33 “Br” 0 37 “CICC” -137.7 41 “COO” 72.31 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 249 6 “CH3OH” 172.2 10 “CHO” 13.89 14 “CNH2” 49.7 18 “pyridine” 0 22 “CC12” 0 26 “CNO2” 223.6 30 “furfural” 0 34 “C-C” 6.699 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -133.9 7 “H20” -287.1 11 “CCOO” -82.12 15 “CNH” 0 19 “CCN” 150.6 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” -191.7 35 “Me2SO” 136.6 39 “DMF’ 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2”
1 “CH2” 147.3 5 “OH” 0 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CC1” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF’ 111.8 49 Morpholine 0
2 “C=C” 62.4 6 “CH3OH” 0 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ A C F 185.6 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 140.6 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF’ 55.8 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
-240.2 8 “ACOH” 0 12 “HCOO” -116.7 16 “(C)3N” -185.2 20 “COOH” -97.77 24 “CC14” -186.7 28 “CS2” 0 32 “I” 0 36 “ACRY” 5.15 40 “CF2” -5.579 44 “NMP” 0 48 “CH2S” 0
Appendix II ~ _ _ _ _ _ _
41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO” 41 “COO”
42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “S1H2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2” 42 “SiH2“ 42 “SiH2”
1 “CH2” 529 5 “OH 88.63 9 “CH2CO” 123.4 13 ”CH20’‘ -247.8 17 “ACNH2” -22.1 21 “CCI” 182.2 25 “ACCI” 956.1 29 “CH3SH” 0 33 “Br” 627.7 37 “CICC” -198 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 “C=C” 1397 6 “CH30H” 171 10 T H O ” 577.5 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 305.4 26 “CN02” -124.7 30 “furfural” -64.28 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 317.6 7 “H20” 284.4 11 “CCOO” -234.9 15 “CNH” 284.5 19 “CCN” -61.6 23 “CC13” -1 93 27 “ACN02” 0 31 “DOH” -264.3 35 “Me2SO” -29.34 39 “DMF’ -2X.65 43 “ S O ” 0 47 “OCCOH” 122.4
4 “ACCH2” 615.8 8 “ACOH” -167.3 12 “HCOO” 145.4 16 “(C)3N” 0 20 “COOH” 1179 24 “CC14” 335.7 28 “CS2” 885.5 32 “I” 288.1 36 “ACRY” -53.91 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” -34.36 5 “OH” 1913 9 “CH2CO” 992.4 13 “CH20” 448.5 17 “ACNH2“ 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “ C C L F 0 49 Morpholine 0
2 “c‘=C” 0 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 961.8 18 ”pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 787.9 7 “H20” 180.2 11 “CCOO” 0 15 “CNH” 1464 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH“ 0 35 “Me2SO“ 0 39 “DMF” 0 43 “SiO” -2 166 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP“ 0 48 “CH2S” 0
559
560
Appendix II
43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO” 43 “SiO”
44 “NMP’ 44 “NMP’ 44 “NMP” 44 “NMP” 44 “NMP” 44 “NMP” 44 “NMP’ 44 “NMP’ 44 “ N M P 44 “NMP” 44 “NMP” 44 “ N M P 44 “NMP”
1 “CH2” 110.2 5 “OH” 0 9 “CH2CO” 0 13 “CH20” 0
17 0 21 0 25 0 29 0 33 0 37 0 41 0 45 0 49 0
“ACNH2” “CCI” “ACCI” “CH3SH”
2 “C=C” 0 6 “CH30H” 0 10 “CHO” 0 14 “CNH2” -125.2 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0
“Br”
“CICC”
34 “C-c” 0 38 “ACF’ 0
“COO” “CCLF” Morpholine
42 “SiH2” 745.3 46 “CON” 0 50 Thiophene 0
1 “CH2” 13.89 5 “OH” 796.9 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2”
2 ‘‘C=C’’ -16.11 6 “CH30H” 0 10 “CHO” 0 14 “CNH2”
0
0
21 “CCI” 0 25 “ACCI” 161.5 29 “CH3SH” -274.1 33 “Br” 0 37 “CICC -66.31 41 “COO” 0 45 “ C C L F
0
18 “pyridine” 22 0 26 0 30 0 34
“CC12” “CN02”
“furfural” “C-C”
0
38 “ACF” 0 42 “SiH2” 0
46 “ C O N
0
0
49 Morpholine 0
50 Thiophene 0
3 “ACH” 234.4 7 “H20” 0 11 “CCOO” 0 15 “CNH” 1604 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “ M e 2 S O 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2”
3 “ACH” -23.88 7 “H20” 832.2 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” -1 96.2 27 “ACN02” 0 31 “DOH” 262 35 “Me2SO” 0 39 “DMF’ 0 43 “SiO”
4 “ACCH2” 6.214 8 “ACOH” -234.7 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH”
0
0
47 “OCCOH” 0
0
8 “ACOH” 0
12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14 70.81 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 ~ ~ 2 ’ 7 0 44 “ N M P 0 48 “CH2S” 0
0
24 “CC14” 0
28 0 32 0 36 0 40 0 44
“CS2” “I”
“ACRY” “CF2” “NMP”
48 “CH2S” 0
Appendix II 45 “CCLF’ 45 “CCLF” 45 “CCLF” 45 “CCLF” 45 “CCLF’ 45 “CCLF” 45 “CCLF” 45 “ C C L F 45 “CCLF” 45 “CCLF” 45 “CCLF’ 45 “CCLF” 45 “CCLF’
46 ‘TON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON” 46 “CON”
1 “CH2” 30.74 5 “OH” 794.4 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0 1 “CH2” 27.97 5 “OH” 394.8 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CCl” 0 25 “ACCI” 0 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 0 4s “ C C L F 0 49 Morpholine 0
2 ‘‘C=C’’ 0
6 “CH30H” 762.7 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02“ 844 30 “furfural” 0 34 “C-c” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0 2 ‘‘C=C’’ 9.755 6 “CH30H” 0 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0
46 “CON” 0 50 Thiophene 0
3 “ACH” 167.9 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACNO2” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 ‘ S O ” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “‘ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” -32.17 44 “NMP” 0 48 “CH2S” 0
3 “ACH” 0 7 “H20” -509.3 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” -70.25 24 “CC14” 0 28 “CS2” 0 32 ‘*I” 0 36 “ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
561
562
Appendix I1
47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH” 47 “OCCOH”
48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S” 48 “CH2S”
1 “CH2” -11.92 5 “OH” 517.5 9 “CH2CO” 156.4 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 2.5 “ACCI” 7.082 29 “CH3SH” 0 33 “Br” 0 37 “CICC” 0 41 “COO” 101.2 45 “ C C L F 0 49 Morpholine 0
2 “C=C” 132.4 6 “CH30H” 0 10 T H O ” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” -I 94.7 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” -86.88 7 “H20” -205.7 11 “CCOO” -3.444 15 “CNH” 0 19 “CCN” 119.2 23 “CC13” 0 21 “ACN02” 0 31 “DOH” 515.8 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” -19.45 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 3.163 28 “CS2” 0 32 “I” 0 36 “ACRY“ 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
1 “CH2” 39.93 5 “OH” 0 9 “CH2CO” 0 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” 0 25 “ACCI” 0 29 “CH3SH” 6.971 33 “Br” 0 37 “CICC” 148.9 41 “COO” 0 4.5 “CCLF” 0 49 Morpholine 0
2 “C=C” 543.6 6 “CH30H” 420 10 “CHO” 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12” 0 26 “CN02” 0 30 “furfural” 0 34 “C-C” 0 38 “ACF“ 0 42 “SiH2” 0 46 “CON” 0 50 Thiophene 0
3 “ACH” 0 7 “H20” 0 11 “CCOO” 0 1.5 “CNH” 0 19 “CCN” 0 23 “CC13” -363.1 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO”
4 “ACCH2” 0 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -11.3 28 “CS2” 0 32 “I” 0 36 *‘ACRY” 0 40 “CF2” 0 44 “NMP” 0 48 “CH2S” 0
a
39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
Appendix II ~~
-~
49 Morpholine -61.2 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine 45, Morphoiine 49 Morpholine 49 Morpholine 49 Morpholine 49 Morpholine
50 Thiophene 50 Thiophene 50 Thiophene
50 Thiophene
SO Thiophene SO Thiophene 50 Thiophene
SO Thiophene SO Thiophene
SO Thiophene SO Thiophene
SO Thiophene
SO Thioohene
I ”CH2” -23.61 5 “OH” -61.20 9 “CHZCO” 0 13 “CH20” 0 17 “ACNHZ” 0 21 “CCI” 0 25 “ACCI” O 29 “CH3SH” 0 33 “Br” O 37 “CICC” 0 41 “COO” 0 45 “CCLF” 0 49 Morpholine 0
2 ”C=C“ 161 I 6 “CH’3OH” -89 24 10 T H O “ 0 14 “CNH2” 0 18 “pyridine” 0 22 “CC12“ 0 26 “CN02” 0 30 “lurfural” 0 34 “C-C” 0 38 ”ACF” 0 42 ”SiH2“ 0 46 “CON“ 0 SO Thiophcnc 0
3 “ACH” 142.9 7 “H20” -384.3 I I “CCOO” 0 1.5 “CNH’’ 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 “DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “ S i O 0 47 “OCCOH” 0
4 “ACCH2” 274. I 8 “ACOH” 0 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” 0 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S” 0
1 “CH2” -8.479 5 “OH” 682.5 9 “CH2CO” 278.8 13 “CH20” 0 17 “ACNH2” 0 21 “CCI” O 25 “ACCI” 0 29 “CH3SH” O 33 “Br” 0 37 “ClCC” 0 41 “COO” 0 45 “CCLF’ 0 49 Morpholine 0
2 “C=C“ 0 6 “CH70H” 597 8 10 T H O ” 0 I4 “CNH2” 0 18 “pyridine” 221 4 22 “CC12” 0 26 “CN02“ 176 3 30 “furfural” 0 34 “C-C” 0 38 “ACF” 0 42 “SiH2” 0 46 “CON“ 0 SO ’I’hiophene 0
3 “ACH” 23.93 7 “H20” 0 11 “CCOO” 0 15 “CNH” 0 19 “CCN” 0 23 “CC13” 0 27 “ACN02” 0 31 ”DOH” 0 35 “Me2SO” 0 39 “DMF” 0 43 “SiO” 0 47 “OCCOH” 0
4 “ACCH2” 2.845 8 “ACOH” 810.5 12 “HCOO” 0 16 “(C)3N” 0 20 “COOH” 0 24 “CC14” -79.34 28 “CS2” 0 32 “I” 0 36 “ACRY” 0 40 “CF2” 0 44 “ N M P 0 48 “CH2S”
Note all group-interaction parameters that do not exist are set to zero. Interactions between the same group are equal to zero.
0
563
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
Appendix I11 Table 1: Trivalent phosphorus antioxidants. Structure
CAS registrv number
Trade names
126523-78-41
TNPP
689.1
131570-04-41
Phosphite 168
646.9
(.?806-.?4-6]
Weston 618
733.0
126741-53-71
Ultranox 626
604.7
Sandostab P-EPQ Irgafos P-EPQ
M,
1035.4
566
Appendix III
Table 2: Major commercial hindered amine stabilizers. Structure
k>."CHzf,.
HN$&H21
CAS registry number
Trade names
M,
152829-07-91
Tinuvin 770
480.1
(82451-48-71
Cyasorb UV-3346
1600 (average)
[63843-89-01
Tinuvin 144
685.0
[64022-57-71
Mark LA 55
608.9
[81406-61-31
Hostavin TMN 20
350.6
[61269-61-23
Spinuvex A-36
[420.7]
11
Appendix 111
567
Table 3: Major commercial hindered phenolic antioxidants. Structure
Chemical name
lb,, HO
\
CHzCHzCOCHz
C
CAS registry Trade names number
tetrakis [methylene [6683-19-8] (3.S-di-terr-butyl-4hydroxyhydrocinnamate)] methane 2.2'methylenehis(4-methyM-terthutylphenol)
[119-47-1]
M,
Irganox 1010
1177.7
Cyanox 2246
340.5
[41484-35-9] lrganox 1035 642.0
9
2,6-di-tert-butyl4-methylphenol
[128-37-0]
Butylated hydroxytoluene ( B W
220.4
[1843-0.?-4]
Topanol CA
544.8
[2082-79-31
Irganox 1076 530.9
C"3
H,C-CH-CH
N J - 1.6-hexame thylene-bis-3(3,s-di-tcrt-butyl4-hy droxypheny l) propionamide
568
Appendix 111
Table 3: (continued) Structure
Hpc3H%\
Chemical name
/ F H \ / OH
CAS registry Trade names number
4,4'-Butylidenebis- [85-60.91 (6-rert-butyl-3me thylphenol)
Santowhite powder
[40601-76-1] Cyanox 1790
M, 382.6
699.9
[27676-62-61 Good-rite 31 14 784.1
R = -CH
[341.?7-09-21 Good-rite 3125 1042.4
[1709-70-21
HO$
S
q OH
4,4'-711iobis(2-fert- 196-69-51
but yl-5-methylphe-
nol)
Ethanox 330 Irganox 1330
775.2
Santonox R
358.0
Reactivity in Molecular Crystals Edited by Yuli Ohashi Copyright @ K d a o r h a Ltd .Tokyo. 1999
Subject Index
ABS plastics 27.317 Activity 82 Activity coefficient 82,93,276 - Combinatorial contribution 95 - Estimation methods 94 - Free volume contribution 95 - Molar 86 - Molecular structures 375 - Residual contribution 95 - Volume fraction 86 - Weight fraction 86 Additive Degradation 370 High molecular mixtures 466 Identity 359 Ionogenic 50 List of 405 Migration rates from polyolefins 452 Reference compound 462 Uselevel 359 Used in plastics 48,380 Adhesive 405 Aging effect 457 Aldol condensation 413 Aliphatic diamines 331 - Chemical stability 332 - Reaction with olive oil 332 - SFC/FID analysis 332 Amino resins 34 Amorphous polymer structure, generation of 142 Analysis - GUMS 415 - Sensory 415 - Mixture of migrants 465 Analytical methods - Calibration 308 - Calibration graph 326 - CEN standard format 311,317 - Chemical derivation 326,329,333 - Confidence bounds 309 - Confirmation 310,318,327,336 - Cost efficiency 313 - Development 306 - Generally agreed methods 313,315 - In-house validation 313 Limit of detection 308,318,325,334 - Micro-disitillation 329 - Practicality 313 ~
Pre-validation 306.313 Precision 308 - Procedures 462 - QM-method 306 Regression line 326 - SML-method 306,317 - Solutions of the diffusion equation 6 - Stability check 310.333 Standard addition procedure 326. - Standard error of estimate 308 - Standard error of procedure 308 - Validation of 302 - Workability 310 - Test report 312 Antiacids 63 Antioxidant 54 - Chain-breaking 55 - Hydroperoxide decomposing 57 Ap-values 456 Aroma barrier 424 Arrhenius equation 248 Atactic 18 -
-
~
~
BADGE 13,319 Barrer’s equation 213 Barrier - Functional 113,438,466 - Layer 407 BCR project ‘Monomers’ 315 BgVV 291,317,319,337 Bifunctional monomers 319,331. Binding agent 43 - Inmolten form 43 - Formation by chemical reaction 43 - Microcrystalline wax 44 - Plastic dispersion 44 - Solution 43 Bisphenol A diglycidyl ether - Confirmation 321 - Ethanolysis products 320,325 - Half-life time 321 - Hydrolysis products 320,325 - Massspectrum 323 - QMmethod 321 - Selective MS-MS analysis, 324 - SMLmethod 321 Blooming 54
570
Subject Index
Carcinogens 365,366 Catalyst 16.405 Cavity, in polymer (see “Holes” in polymers) Carbonyl compounds - a$ unsaturated 414 Cellulose, regenerated 41 CEN TCl94/SC1 313,315 Chain - Branching 18 - Configuration 18 Chapman-Enskog equation 159 Chemical potential 79 - Excess 83 Chromatography - Gas(GC) 410 - High performance liquid (HPLC) 457 Coating, temperature resistant 45 Code of Federal Regulations 359,365 Compliance testing 292,300,334 Compositional analysis of plastics 292,341 Condensation process 21 1 Consumption factor (CF) 362 Convection 183 Copolymer 12 - Block 12 - Graft 12 - Ethylene 23 Council of Europe 406 Crank-Nicholson discretization scheme 223 Crosslinker 14 Crystalline polymer 20, 127. 142, 153
Daily diet 361 Daily intake 361 - Acceptable (ADI) 362,400 - Estimate 362 - Tolerable (TDI) 400 Degradation process, - Melt degradation 53 - Photo-oxidation 53 - Thermal degradation 53 - Thermal oxidation 53 Degradation products 5 Dehydrating agent, for PET 64 Delaney Clause 365 Density of polymers 20 Desorption - Counter current column, in a 409 - CUNeS 270 Detection limit 400 Diameter of molecules 255 Diels-Alder condensation 411 Dietary cocentration 362,365.366 - Predictable 364 - Upper-bound 365 Diethyleneglycol 335 Diffusion - Activated process 130
Activated zone 128 From an infinite thick layer 192-194 - One sided from an infinitely thin layer 192 - Resistance to 217 - Two sided from a finitely thick layer 195 - Two sided from an infinitely thin layer 191 Diffusion activation energy 128, 132 - Intermolecular 129 - Intramolecular 129 - Reference 448 Diffusional jump 128, 145 - Back 144 - Frequency 131 - Length 131.140 Diffusion coefficient - Adjustable coefficients 130, 133,136 - Alkanes in polyethylene 173 - Alkanes. self-diffusion 178 - Calculated versus experiment 146,151, 154 - Dependence from molecular weight 450 - Effective 289 - Einstein equation 1413 - Estimation 256,374,435 - Inaer 171 - lntradiffusion 172 - Mutual 170. 172.177 - Organic compounds in LDPE 265 - Paraffins in paraffin 176 - Plastic specific parameter-values in polyolefins 448 - Polyolefins 451 - Rates 131,147 - Refined equation for 448 - Self-diffusion 133. 134. 139 - Solvent dependence 283,421 - Styrene i n polystyrene 436 - Tracer 172.179 - Upper bond value 446 - Upperlimit 435 - Water,in 1x0 - Zero penetrant concentration, at 138 Diffusion coefficient models - Ab initio 125. 141,147 - Atomistic 126 - Classical approach 126, 152 - Computational approach 141,152 - Correlative 133, 135 - First principles 126, 132, 141 - Free-volume 133. 152 - General equation for plastics 175 - Heuristic 125,447 - Limm and Hollifield 447 - Liquids 176 - Microscopic 126, 130, 140 - Molecular 128 - Molecular dynamics 141,145,153 - Molecular statistical 129,137 - Pace and Datyner 131 - Reference equation 172 -
-
Subject Index Semi-predictive 133 Vrentas and Duda 134,139,152 Diffusion equation 221 - Boundary conditions 222,232 - Comparison of solutions 197 - Cylindrical coordinates 234 - Discretized 228 - Initial condition 221 - Spherical coordinates 234 - Two dimensional 235 Diffusion in polymerlliquid systems 199-208 - General solution of equation 201,206 - Influence of food 208 - Simplified solution 206 - Simplified solution for infinite thickness of polymer 207 - Solution based on error function 201 Diffusion, types - Anomalous 127,149 - Fickian 127, 138 Directive - Ceramic 398 - Framework 394.396,419 - MEG and DEG 405 - Migration tests, for 394 - Monomers 394 - Nitrosamines, draft 405 - Regenerated cellulose film 398 - Vinylchloride 405 Dirichlet boundary conditions 222,228
Regenerated cellulose film 398,405 European project - AIR2-CT93-1014 344 - FAIR-CT984318 347 - SMT4-CT9C2129 353 Euler forward-difference scheme 222 EVA-copolymers 23 EVOH-copolymers 23 Evaporation process 211 Excess functions 96 Extraction 287 - Organic solvents, with 409 - Techniques 409
-
-
-
Eigenmodes 226 Einstein-Smoluchowski equation 159 Elastomers 19 Electrolytic conductivity 253 Energy - Activation, for diffusion 128, 129, 131, 169 - Cohesive, density 90 - Density of interaction 165 - Molar interaction 90 Enthalpy 79 Excess, of mixing 95 - Mixing, of 81 Entropy 79 - Excess, of mixing 95 Epichlorohydrin 328 - Hydrolysis 330 - Half-life time 331 Micro-distillation 329 Epoxy coating 319 Epoxy lacquer 328 Equilibrium conditions 288 Equilibrium state 80 Error function 193 EU Directive 90/128/EEC 291,300,313.445 - 94162lEEC 336 Ceramics 398 - Framework 396 ~
~
~
~
571
Fat simulant - ~ ~ 3 04027 - Oliveoil 402 - Sunfloweroil 402 Fat test 402 - Alternative 404 FDA 337 - Consumption factor 338 - Dietary intake 338 - Threshold-of-Regulation 337,341 Fick’s second law 187,367 - Polymerlfood system 368 Flux 184 - Divergence 186 Flow temperature 19 Food - Classification 360 - Conditions of use 361 - Distribution factor 362,364 - Exposure to packaging 7,363 - Polarity 420 - Purity 396 - Quality 3 - Testing protocols for packaging 361 Food packaging legislation 291 Food simulants 290,361 - Chemical reaction with migrants 333 - Ethanol 290 - Iso-octane 290 - Olive oil 292. - Solubility in polymer 290 - Triglycerides 290.333, - Volatile solvents 290 Free energy 79 - Excess 83 Free enthalpy 79 Free radical 11,66 Free-volume, in polymers 95. 134, 138. 143,152 - Diffusion models 133, 139. Functional barrier plastics 338 - Acryliclayer 343 Barrier properties 343 - Black box approach 340 - Corelayer 340 - Efficiency 339 ~
572
Subject Index
Lag time 339,343 Mathematical model 339 - Model contaminants 340 - Multi-layer structure 339,343 - On paper and board, 343 - Permeation 338,343 - PVDClayer 343 - QM/SML relationship 340 - Recycling specific substances 340 - Surrogates 340 - Test procedures 339
Plastic and simulant. between 456 - Sources 4 Internal energy 79 Isotactic 18 Lacquer 43 Coating 319 Lagrange interpolating condition 232 Leaks in package (see pores) Legislation - European Community 7 - Plastics 7 Lennard-Jones temperature 255
-
-
-
Gas - Ideallaw 84 - Perfect 80 Gas permeability measurement - By sorption 250 - Permeation in a gas stream 251 - Permeation in a sealed container 250 Gibbs free energy (see free enthalpy) Glass transition temperature, of polymer 19,20, 126 Glassy polymers 127, 141 - Diffusion in 136 Global odor 426 Global sensory analysis 409 Group - Contribution 89 - Contribution method 90 - Functional 89 Hagen-Poiseuille equation 253 HAS-photoantioxidants 59,465 Heat - Conduction of 184. 187 - Equation 190 - Solution in polymer 25 - Stabilizers 62 Henry’s - Constant 87 - Law 81,240 Hildebrand correction 166 HIPS-polymers 27 Holes in polymers 133. 138,143 - Affinity and saturation constants. of Homologous series 88. 161 Hydrogen bond 17 Hydroperoxides 59
137
Inhibitor 15 Initiator 14 Ink 405 - Off-odor 426 Ionomer 26 Interaction 4 - Packaging and food, between 407 - Polymers and foodstuffs, between 445
Mass Balance 202,432,434 - Molecular relative 89 - Transfer categories to food 371 - Transfer coefficient 370 - Transfer from liquid (food) into polymer 202 - Transfer from polymer into liquid (food) 203 - Transfer, influence of diffusion in food 208 - Transport 4 Mass spectrometer 410 - Electro-spray-ionization(ESI) or API ion source 462 Mathematical modeling 292.337, Microcrystalline waxes 44 Micro-distillation 329 Migrants - Acrylonitrile 291 - Analytical procedures 300 - Bisphenol A 291,325 - Butadiene 291 - Diffusion 289 - Ethylenediamine 291 - Molecular weight 287 - 1-Octene 291 - Specific migrant 306 - Vinylchloride 291 - Volatility 292 - Volatilization. 319 MIGRATEST Lite 468 Migration 4 - Additives to foods, of 373.378,453,459 - Alternative test 296,404 - Amount to food 383 - Analytical determination 296 - Antioxidant. of 366,369 - Area-related QM 293,322,328 - BHT from polyolefins 369 - Categories 370 - Carcinogenic monomers, of 393 - Control factors 287 - Control methodologies 291 - Data, calculated and experimental 375.378, 454 - Decision tree 372 - Dimensionless curve 296 - Direct measurement 296 -
Subject Index Effect of flavor components 371 Enhanced by full immersion 456 - Equilibrium 293 - Estimation 432 - Food and food simulating solvent, to 369 - Frompolymer 289 Indirect assessment 292 - Intopolymer 289 - High temperature 371 - Level 366 Limits 291 - Limits, regulatory 435 - Low temperature, at 370 Mass balance 293 - Maximumamount 207 - Migration potential 292 Modeling 7.8,374,375 - More severe test 296,297 - Nitrosamines in rubber 405 - Overall 402,404 - Pitfalls 457 - Plastic constituents 287 - Polymedfood system 367 - Polymer additives. of 369 - Prediction, 294.368 - QM 291.300.316.334 - Ratc 9 - Rates. for additives from polyolefins 452 Semi-direct test 297 - Specific 402 - Study 370 - Styrene 370 Swelling, with 218 - Test, accelerated 441 - Test, conditions 403 Test principles 287 - Testing 7 - Total mass transfer 292 - Toxicological parameters 291 Viny! chloride 405 - Worst case 370 - Worst case, estimate 374 Migration modeling - Laminate, polymeric glues, varnish 467 - Software 468 Mixt boundary conditions 231 Modern food packaging applications 336 Monoethyleneglycol 335 Monomer 1 0 , l l - Residual 407
-
-
573
Solution of the diffusion equation 6. 137
-
-
-
-
~
-
-
-
~
Nernst diffusion layer 209 Nernst's law 81 Nucleation - Heterogeneous 21 - Homogeneous 21 Numerical instability 224 Numerical mathematics 466 Numerical methods
Odor compounds Identification 411 - Separation 411 Odor threshold 407,409,413 - Absolute 410,415 - Determination 414 - Relative 422 Off-flavors 7,407 - Overlapping 409 - Styrene 442 Off-odors 407 - Coatedpapers 411 - PE.in 413 - Sources 407 Oil absorption 463 Olefin oxidation products 414 Olfactometer 420 Optimization criteria 4 Organoleptic characteristic 396 Overall migration fat test 297 - Accelerated test 298 - Analytical tolerance 297 - CENstandards 297 - High temperature fat test 299 - Majorproblems 297 - Rapid extraction test 298 - Substitute fat test 299 -
Packaging - Conditions of use and testing 361 - History 411 - Minimization 4 - Requirements 4 Packaging waste 336 Partition - Effects 370 - Function, translational 167 - Multilayer structure 467 - LDPE/octanol 278 - Octanollwater 278 Partition coefficient 5, 82, 89, 209.288.370,375, 420.433 - Aqueous ethanol 280 - Aromas in polyolefiniwater systems 279 - Estimation 100,111,114 - Estimation using Unifac 100 - LDPEkleaning agents 281 - LDPE/ethanol (methanol) 265 - LDPEkkin creme 281 - Non-ideal solutions 84 - Polymedliquid 199 - PS/milk 280 - Solvents/food 421 PBT plastics 30 Permeability 240 - Coefficient 240,242-246.257
574
Subject Index
Coefficients in laminates 284 Coefficients in LDPE 263 - Convertion factors 241 - Measurement 252 - Package 248 - Parameters 247 - Solvent dependence 277 - Total package 248 - Tube 251 Permeation 4.7 - In a gas stream 251 - In a sealed container 250 - Steady state 240 - Through a membrane 240 - Time dependence 250 Peroxides 15 PET plastics 30 Phenol - hindered 66 - Polynuclear 70 Phosphites 57 Photoantioxidant 59 Phthalates 52 Plastics 1 - Degradation 53 - Processing 49 - Processing stabilizers 57 Plastic dispersions 44 Plastics directive 291,300,315 Polyamide 31,331 Polybutene-1 25 Polybutylene terephthalate 30 Polycarbonate 31,325 Polycrystallinity 20 Polyester - Thermoplastic 30 - Unsaturated 35 Polyethylene 21 Polyethylene terephthalate 30,335.338 Polyisobutene 25 Polymer 17 - Crystallisation 20 - Distribution of different chain length 19 - Orientedstate lY - Primarystructure 17 Polymer, biodegradable 41 - Polysaccharides 41 - Polyesters 42 Polymer, containing fluoride 33 Polymer reaction 13 Polymer swelling 290 Polymerization 11 - Addition 11 - Condensation 12 - Ionicaddition 11 Polymethylmethacrylate 32 Poly(4-methylpentene-l ) (P4MPl) 25 Polyoxymethylene 33 Polyolefines 290 Polypropylene 23 -
Polystyrene 26 - Volatile substances 428 Polysulfone 33 Polyurethane - Crosslinked 36 - Foam 37 - Linear 36 Polyvinylchloride 28 Polyvinylether 34 Polyvinylidenechloride 29 Pores in package 253 Potential energy constant 255 Pouch method 273 Practical Guide 445 Principle - Additive 89 - Inertness, of 396 Product 4 Propylenediamine 333 Protection of public health 365 QM/SML ratio 293 Diffusion model 294 - Influence of layer thickness 293,295 - Influence of partition coefficient 293,295 - Influence of polymer type 294 Quality I - Assurance 4 - Preservation 2 - Reduction 420 - Requirements 3 Quantity - Extensive 79 - Intensive 79 - Maximum permitted (QM) 445 - Specific 79,88 Quinone methode 68 -
Radical former 16 Raoult's law 80,276 Rate - Chemical reaction 187,218 - Constant, reaction 370 - Penetration 421 Ratio food volume to polymer volume 367 Raw material - Fossil 10 - Renewable 10 - Residual 407 Recommendation 393 Recycled material 405 Recycling plastics 7.337 - BgVVstatement 337 - Challenge test 344 - Cleansing efficiency 344 - Closed-loop 344 - Contaminants 337 - Direct food contact 337
Subject Index ILSI guidelines 344 Migration model 347 - Post consumer PET 344 Recycling process 345 - Safety/quality assurance 338 Solid-phase condensation 345 Surrogates 344 Reference collection 320 Reference compound class 161 Refillable plastic bottle. 349 Compliance testing 350,353 - Inertness test 350 - Misuse 350 - PET 349 - Re-migration 350 Regulation 365 - Food contact materials 445 - Harmonizing law 393 Residue limit 400 Resolution Colorants 406 Ink.draft 406 Ion exchange resins 406 - Paper and board. draft 406 - Polymerisation aids 406 - Varnishes 406 Restriction criterion 306.308.316.325.335 Retention indices - Method 90 - Molecular 111 Retention time 412.415 Rubbery polymer 126. 144 Diffusion in 128 -
-
-
-
-
-
-
Sackur-Tetrode equation 167 Safety margin 4,446 SAN plastics 27,317 SBpolymer 27 Scalping 4 Scavenger, acid 63 Scientific Committee for Food (SCF) 396 Selective ion monitoring (SIM) 412 Selective methods 462 Sensorial evaluation, global 410 Sensory - Methods 7 - Specific descriptors 408 - Threshold 416.420 Self-diffusion - Gas 168.170 Liquids 177 Separation chromatographic 462 Shelf-life 2,439.440 Silicone, starting material 40 Simulants for migration tests 404 SML/QM correspondence 445 Sniffing 410, 414 Solubility 420,423425 - Coefficient 87,240,255 -
575
Hansen parameter 93 Parameter 91-93 Solution - Athermal 83 - Ideal 80.276 - Non-ideal 84 - Regular 83,91 - Regular, theory 90,96 Sorption - Constant (see solubility coefficient) - Curves 270 - Modeldual 270 - Penetrant 136 - Theory 137 Specific migration 297 Specific migration limit (SML) 400,291,300, 3 16,334 Stabilizer - Heat, for PVC 62 - Hindered amine (HAS), for heat 465 - Organotin 75 Standard - chemical potential 80 - pressure 79 Standard methods 313 - BADGE 3,319 - Carbonyl chloride 325 - CEN ENV 13130 standards 314 - Epichlorohydrin 328 - Ethylenediamine 331 - Hexamethylenediamine 331 - Vinylchloride 314 Standardization 404 Starting material 11 Steam distillation 409 Stochastic process 132, 140, 149 Stokes-Einstein equation 160, 175 Storage - Temperature 420 - Time 420 Siructure - Data of polymers 126 - Increment 89,111 Styrene copolymer 27 Suhstitution tests. conditions 403 Surface to volume ratio 329 Symbol, for - Labelling 396 - Material 396 Syndiotactic 18 Synoptic document 400 Swelling front 218 -
-
Taste - Description 409 - Ethylbenzene 430 - Styrene 430 - Threshold 421 Temperature
576
Subject Index
Reference 167 Standard 167 Test liquid - Ethanol 402 - Isooctane 402 - Media 403 Thermal conductance 183 Thermoplastics 10 Thermoset 18,34 Threshold - Absolute 420 - Air, in 414 - Concentration 438 - Level 424, - Limits 409 - Relative 422,423 - Relative, of odor and taste 422 Threshold of regulation 7,365,366 Time lag 215-217 Time steps 225 Toxic effect - Acute 365 - Chronic 365 - Noncarcinogenic 365 Toxicity testing 401 - Long term 365,401 - Mutagenesis studies 401 - Short term 365 - 90-daystudy 401 Transamidation 333 Transport - Energy 183 - Momentum 183 - Process 183 Trouton’s rule 166
Valence bond 17 - Primary 17 - Secondary 17 Validation 302,334 - Alternative approach 313,334 - Collaborative trial 302,313 - Critical difference 305.318 - Inter-laboratory study 303 - I S 0 5725,303 - Performance characteristics 302 - Probability level 305 - Reduced test scheme 334 - Repeatability r 303,308,334 - Reproducibility R 303 - Statistical tools 303 - Validation parameters 302 - Variance 304 Van der Waals forces 17 Vapor pressure - Estimation 112 - Saturated 80 Viscosity 183 Volume - Fraction 86 - Polymermolar 87 - Reference 167 W-values 112.116 Weight fraction 85 Worst case scenario 292,347,446
UNIFAC 90 - Calculations for liquids 99
Ziegler-Natta catalysts
-
-
-
-
Calculations for polymers 97 Limitations 109 UVabsorber 61
12
