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he£N ~ 1 and g ~ l/sinh(Z + P) in dilute solutions, we may approximate the excess of end points with respect to the bulk solution as pe -1 = big -1) ~ coth 2 + P -1 pe=bg
semidilute dilute
sinh
[1.6.11a] [1.6.11b]
— d
11
J.M.H.M. Scheutjens, G.J. Fleer, J. Phys. Chem. 84 (1980) 168; G.J. Fleer, M.A. Cohen Stuart, J.M.H.M. Scheutjens, T. Cosgrove, and B. Vincent. Polymers at Interfaces. Chapman and Hall, 1993. 21 A.N. Semenov, J. Bonet Avalos, A. Johner, and J.-F Joanny, Macromolecules, 29 (1996) 2179; A.N. Semenov, J.-F. Joanny, and A. Johner. Polymer adsorption: Meanfield Theory and Ground state Dominance Approximation in: Theoretical and Mathematical Models in Polymer Research. Academic Press 1998.
INTERACTION BETWEEN POLYMER LAYERS
1.25
The factor b is a normalization constant, which ensures that the excess number of end points in the adsorbed layer equals the excess number of chains; it is defined through b\(g-l)dz
= Ug2 -l)dz for semidilute solutions and similar (without the term -1) for
dilute systems. We do not consider the precise value of b , suffice it to note that b is of order unity. In order to see the effect of chain ends on the interaction force, the GSA description as discussed in the previous sections has to be extended to include the end points. This was done by Semenov et al. 1 '. The disjoining pressure /7e(h) due to the ends was related to the end-point concentration
serve that the position of the maximum shifts to higher h values. This signals the approach to the critical region. The height of the maximum increases monotonically with the adsorption energy. This can be understood from the fact that the adsorbed amount and, hence, the number of end points is an increasing function of the effective adsorption energy. To stabilize particles with homopolymers one should, therefore, use strongly adsorbing polymer. 1.7c Strong overlap In figs. 1.12,13 a number of plots is collected similar to fig. 1.8c under various conditions. The attractive part of the interaction energy (h < hQ ) is plotted on a doublelogarithmic scale for three values of the bulk concentration cph (fig. 1.12a), the chain length JV (fig. 1.12b), the effective adsorption energy Axs (fig- 1.13a), and the solvency X (fig. 1.13b). The first thing to notice is that for narrow gaps only the adsorption energy has an effect; for small h the curves for different
INTERACTION BETWEEN POLYMER LAYERS
1.31
Figure 1.12. Numerical SCF data for the attractive part of Ga in the range h 0.3 . It is interesting to note that this linear dependence breaks down near the critical condition. To examine the critical region, as well as the depletion region, we also present an enlarged view (-0.1 < Axs < 0.1 ) of the same data in fig. 1.25b. Note the difference in absolute values of the interaction energy in the two figures (more than a factor of 100). Only on this scale is the attraction in the depletion range visible. In the first approximation we expect the depletion minimum for strong repulsion to follow G a (0) = 2[Qa(0)-Qa{oo)] =-2i2 a (~)~ 2L , due to the tail in the profile in the complete SCF profile, caused by fluctuations of chain conformations not included in the box model. For 11
G.J. Fleer, J.M.H.M. Scheutjens, Colloids Surfaces 51 (1990) 281.
INTERACTION BETWEEN POLYMER LAYERS
1.73
H < 1 this box model systematically overestimates the interaction energy. This is because the model does not allow for interpenetration of the chains, which is a poor approximation for a theta solvent. Indeed, a brush in a theta solvent gives a softer repulsion than predicted by the box model. As H = 1 corresponds to 2L ~ 60 , we note that the shallow minimum in the interaction curve shown in fig. 1.37a is outside the range of fig 1.37b. 1.1 lh Soft depletion In sees. 1.8-9 we discussed the effect of free polymer on a dispersion of hardspheres. Quite generally, we found that polymer induces a weak attractive interaction between the colloidal particles, the strength and range of which depend on the concentration of the polymer and the coil/sphere size ratio a la. In figs. 1.34-36 we saw that particles carrying tethered polymer repel each other. We now consider briefly the mixed case of colloidal particles with grafted polymer on their surfaces, dispersed in a solution of free polymer molecules. We suppose that the grafted chains (length JV, grafting density a) and the free polymer (chain length P) are chemically identical. In fig. 1.38 we present a measure for the thickness of a polymer brush immersed in a polymer solution in which P = N = 500 . The thickness is a strong function of both the concentration of the free chains and the grafting density of the tethered chains. Above we have seen that, upon overlap of stretched chains, they relax to less stretched conformations. We can apply the same argument to explain why the brush thickness decreases upon an increase in the concentration of the free chains. The free chains try to penetrate the brush and therefore increase the chain crowding. The response is a collapse of the swollen brush. The symbols in fig. 1.38 indicate the point where the polymer concentration in the (initial) brush (without outside polymer) equals the polymer concentration in the polymer solution. At those points, the osmotic pressure in the polymer solution equals that of the (initial) brush. The fact that the symbols are in the steepest part of the drop in brush thickness strengthens the argument. At very low grafting density, the (initial) tethered polymer layer has no stretched chains and free chains do not alter the thickness. Up to 9 = 10 a brush immersed in the melt,
Figure 1.38. The average position (first moment) of the free end of a brush with chain length JV = 500 and B = dN as indicated, as a function of the polymer volume fraction 14) have fixed charges and charge distributions along the chain, whatever the pH, and are therefore sometimes called 'quenched' polyelectrolytes. Many different kinds of backbones occur: all-carbon (vinyl, allyl) chains, polytesters), poly (ethers), poly (saccharides), poly(peptides), as well as poly(imines) where the charged group is itself part of the backbone. Some backbones are hydrophilic, such as those in poly(saccharides), but most are hydrophobic and the corresponding molecules would not dissolve if they would not carry a sufficient number of charges.
POLYELECTROLYTES
2.3
Copolymers, which have more than one kind of monomer (in particular, monomers with and without dissociating groups), should also be mentioned. For this category, the maximum charge that a molecule can acquire is, of course, determined by the chemical composition. Many of the polyelectrolytes discussed here owe their very existence to synthetic polymer chemistry. This is not to say, though, that nature does not produce polyelectrolytes. Many naturally occurring polysaccharides produced by plants, bacteria or animal cells are polyelectrolytes. One of the best-known natural polyelectrolytes Is DNA, which contains in-chaln phosphate groups as chargeable sites, and its close relative RNA is, of course, also a polyelectrolyte. Finally, polypeptides and proteins often carry charged groups and can thus be defined as (very complicated) polyelectrolytes. Since the structure and physicochemical behaviour of many proteins has rather special features, these molecules will receive attention in a chapter especially devoted to them (chapter 3). In this chapter, we shall first discuss how charge and countercharge In a polyelectrolyte in solution are distributed (the electrical double layer), and we consider the proton exchange equilibria from which the charges originate (2.2). We then take a look at molecular shapes (conformations) and the way these are influenced by the charge (2.3) for free chains in solution, end-grafted chains, and gels. Section 2.4 deals with the viscosity of polyelectrolyte solutions and sec. 2.5 with polyelectrolytes in external electrical fields (conductivity, electrophoresis and dielectric properties). Finally, we discuss in sec. 2.6 the solubility of polyelectrolytes and the formation of complexes in mixtures of polyelectrolytes of opposite charge. 2.2 Polyelectrolyte electric double layers 2.2a Polyelectrolytes: why are they charged and how is the charge distributed? In solution, polyelectrolytes can acquire a charge on the chain by two mechanisms: (i) ions from the solution can bind to them and/or (ii) surface groups can dissociate. For instance, as discussed in sec. 2.1, polyamines can pick up protons to form positive -NHg groups and from polyacids, protons can desorb to form negative, say, -COO ~ or -OSOg groups (we ignore other than simple ions; in particular, adsorption of ionic surfactants will not be considered here). For all the charge formation processes, the driving force is of a chemical or entropical origin, determined by the Gibbs energy difference between the bound and free state, just as with the dissociation of low-M molecules. In processes of type (i) the process is entropically unfavourable, whereas for those of type (Ii) it is entropically driven. Electric forces always oppose the charge formation; in fact, all processes come to an end when the counteracting electric forces cancel any further charging. Then, equilibrium is attained. At equilibrium the Gibbs energy is at a minimum and negative. Electric double layers around polyelectrolytes form spontaneously. It is
2.4
POLYELECTROLYTES
typical for polyelectrolytes that the equilibrium state is also determined by the degree of swelling. The spontaneous charge separation leads to the creation of a chain charge and an equal but opposite countercharge. When the solution contains low-M electrolyte, the latter consists of an excess of counterions and a deficit of co-ions. This negative adsorption of co-ions leads to the expulsion of electroneutral electrolyte, the so-called Donnan exclusion. In salt-free solutions the countercharge only contains counterions; in that case, there can be no Donnan exclusion. All of this is basically not different from the charging principles for hydrophobic colloids, see sec. II.3.2. Quantitative differences with double layers on flat plates and macroscopic spheres may come forward because of the way the chain charge is distributed. The issue is connected to the question as to whether it is allowed to treat the double layer charge as smeared out, which would allow for mean-field interpretations, such as the PoissonBoltzmann distribution for the diffuse part and Bragg-Williams type analyses for the non-diffuse part. As long as a polyelectrolyte chain may be considered as a long charged cylinder with macroscopic radius a, one can assign a surface charge density (7° to it and treat the countercharge by one of the models discussed in chapter II.3 for macrobodies. Anticipating the arguments below, it is at least likely that the outer side of the countercharge obeys PB statistics, i.e. it can be described as a diffuse double layer according to Gouy and Chapman. In figs. II.3.14 and 15, we showed that for the diffuse parts cylindrical double layers assume an intermediate position between flat and spherical ones. As intuitively expected, the larger xa, where a is now the radius of the cylinder, the more similar spherical, cylindrical and flat double layers are. However, a is often not so large that this picture is allowed over the entire electric double layer. For further discussion, it makes sense to divide the countercharge into two parts, an outer or diffuse part and an inner, non-diffuse part. The diffuse part is readily defined as that part where ion size effects are negligible, where charges may be considered smeared out, and where binding is solely caused by electrostatic attraction (zey/(r) per ion of valency z at distance r from the axis of the cylinder). In the nondiffuse part these premises no longer hold. Because of the proximity to the chain, specific ( = non-electrical) binding can usually not be ignored. The specific phenomena depend on the nature of the charged groups and on their positions along the chain. The nature effect is nothing else than the specific binding, which gives rise to the familiar lyotropic sequences (sec. IV.3.9i). However, the position effect is new. For instance, for charged groups residing on sidechains (as in polymethacrylates), it is possible for ions to accommodate between the charges whereas polyelectrolytes with all charges on the backbone (as in poly-imines) do not have this option. As positioning of ions between and outside charges can follow different patterns, interesting lyotropic sequences may be expected, beyond those generally observed for macroscopic solid surfaces. According to general experimental experience with macroscopic surfaces, plots of the diffuse (~ electrokinetically or stability-wise active) charge density ad ~ (7ek as a
POLYELECTROLYTES
2.5
function of a° start as a straight line under 45° where a^ = -o° , to level off to a plateau where further increase of a° does not lead to further enhancement of a^ . See, for instance, figs. II.3.63 and 4.13, for f and cf* , respectively. The diffuse charge density rarely exceeds a few |iC cm"2 . The meaning of the plateau is that a situation has arisen in which any further added charge on the surface is compensated by a countercharge in the non-diffuse part. This non-diffuse part was generally called the Stern part of the double layer, charge densityCT1, with a° + a1 + a^ = 0 because of electroneutrality. Obviously, in this respect double layers around polyelectrolytes resemble Gouy-Stern double layers. At this stage it is necessary to introduce the term ion condensation. This term is typical for polyelectrolyte science, and stands for the binding of (counter)ions to the charged chain. In the literature the term is used in various ways, for instance in the interpretation of experiments to account for the fraction of counterions that do not contribute to osmotic pressure, conductivity etc., or, in theory, in which models for the process of condensation are developed. Theories and the various experimental observations may, or may not, agree. The term is well established in the domain of polyelectrolytes and has the proper resonance. It is not appropriate to speak indiscriminately of 'bound' and 'free' ions, because diffuse ions are also bound in a thermodynamic sense. Hence, we shall continue to use the term condensation in this chapter as a general term for ions that are so strongly bound to (or captured by) the chain that they are osmotically, electrokinetically or conductometrically inactive, irrespective of the reason for the condensation (electric and/or specific). According to this definition, condensed ions and Stern ions are identical. History has led to differentiation between the terms, because the founding fathers of polyelectrolyte theory (Fuoss, Katchalsky, Oosawa, Manning...) were unfamiliar with the much older Stern model; on top of this came the independent development of theories. Typically, in polyelectrolyte theory (Oosawa, Manning...) two-state models have been put forward on purely electrostatic principles. We shall return to these in sees, b and c below. Description in terms of Bragg-Williams type approaches, as in Stern theories including specific binding, appears to be virtually absent in polyelectrolyte literature. As a result, in most polyelectrolyte elaborations, there is little room for ion-specificity interpretations. On the other hand, Stern and condensation theories both predict the formation of a plateau in the cfi ( a° ) relationship, as mentioned before. In order to finally arrive at theories for polyelectrolyte configurational statistics, it appears unavoidable to use a coarse-grained description of the polyelectrolyte chain and the electric double layer surrounding it. Following most of polyelectrolyte theory, the complicated polyelectrolyte molecular structure is modelled as a charged cylinder characterized by just two parameters: its radius a and its surface charge density a°. All details at length scales below the radius a are lumped into the effective parameters a and a°. Sometimes an even further simplification is used and the polyelectrolyte chain is modelled as a line charge with a linear charge density of v = 2naa° . Following
2.6
POLYELECTROLYTES
most of polyelectrolyte literature, a Stern layer to account for ion-specific binding is not taken into account. Instead, the double layers are described by the non-linear PB equation only, assuming all counterions are outside of the cylinder of radius a that models the polyelectrolyte chain. As mentioned, even in such purely electrostatic models, there is a plateau in the 0^(0°) relationship. This is the effect that is usually referred to in the polyelectrolyte literature as (counter)ion condensation. The basic idea, stemming from Imai and Ohinshi11, but elaborated by Oosawa21 and Manning31, is that upon charging the chain above a critical chain charge, the resulting potential near the chain becomes so high that any additional charge is compensated for by an electrostatically captured counterion. The simplified two-state models of Oosawa and Manning (based on the PB equation) predict that, in the limit of vanishing concentrations of both electrolyte and polyelectrolyte, o^fcr0) plots (or equivalents thereof, such as plots of the polyelectrolyte osmotic pressure versus the chain charge v) should consist of an initially linear part, which discretely breaks off into a plateau at the critical chain charge. This discrete limiting behaviour is sometimes referred to as the Manning limiting law. Indeed, for this special limiting case, the solution of the full PB equation does exhibit a mathematical discontinuity at a well-defined critical chain charge. In contrast to the simplified models however, it does not predict a distinct 'break' in, for example, the osmotic pressure as a function of the chain charge. Nevertheless, the existence of a universal critical chain charge for polyelectrolytes and the concept of counterion condensation have been very important in polyelectrolyte modelling to help develop approximate theories for polyelectrolyte properties. In the next subsection, we therefore discuss in some detail both the Oosawa two-state model and the full PB approximation for cylindrical double layers of strong polyelectrolytes without added electrolyte. Next, the case of added electrolyte is treated, again assuming strong polyelectrolytes. For weak polyelectrolytes, charges are determined by adsorption/dissociation equilibria. A final paragraph considers in detail the important case of proton exchange equilibria for linear polyelectrolytes. 2.2b Cylindrical electric double layers without added electrolyte To begin, we assume that the overall polyelectrolyte configuration is at least locally rod-like and study the cylindrical double layer in the PB approximation. While in practice there will always be some amount of electrolyte present, its presence may be neglected if the total number of co-ions is negligible as compared with the total number of counterions. Roughly speaking, this is the case when the concentration of added electrolyte is small as compared with the total polyelectrolyte monomer concentration,
11
N. Imai, T. Ohinshi, J. Chem. Phys. 30 (1959) 1115. F. Oosawa, Polyelectrolytes, Marcel Dekker (1971). 31 G. S. Manning, J. Chem. Phys. 51 (1969) 924. 21
POLYELECTROLYTES
2.7
a situation that is certainly not uncommon in practice. Polyelectrolyte electric double layers in the absence of added electrolyte are also important from an historical and theoretical point of view, since they have played an important role in the development of the theory of counterion condensation, one of the central concepts in polyelectrolyte modelling. A distinct difference with the case of excess added electrolyte is the absence of a well-defined bulk concentration of ions that can be used as a reference point (defining the zero of the electrostatic potential). Instead, models for electric double layers in the absence of added electrolyte depend on the definition of a certain volume to which the counterions are confined. That is, they are so-called cell models. In practice, the volume of the cell is related to the concentration of charged objects (colloids, polyelectrolytes). This reflects the physical effect that diluting the charged objects dilutes the counterions, and hence affects the electric double layers. Oosawa two-state model As mentioned, in the limit of vanishing concentration of both electrolyte and polyelectrolyte, the solution of the cylindrical PB equation exhibits a mathematical discontinuity at a critical chain charge. Simplified two-phase models for this limiting case, based on the PB equation, have been developed by Oosawa (loc. cit.) and Manning (loc. cit.). Their main virtue is that they clearly demonstrate the physical mechanism that leads to (electrostatic) counterion condensation. Below, we first discuss the Oosawa two-phase model. Following, we introduce the exact solution of the cylindrical PB equation in the absence of added electrolyte. Finally, we compare with experimental data for polyelectrolyte osmotic pressures. The Oosawa two-phase model provides a simple way to estimate the magnitude of the fraction /
of free counterions. The remaining fraction of counterions, ( 1 - / ) , is
assumed to be electrostatically captured or condensed into a cylindrical region close to the chain, of radius a (the polyelectrolyte chain itself is viewed as a line charge). The free counterions are assumed to move around within a cylindrical region a < r < R. The value of the radius R is set by the volume fraction (p of chains, which is approximated by (p = a2/R2
[2.2.1]
The geometry of the Oosawa two-phase model (which is a cell model) is illustrated in fig. 2.1. Without loss of generality, the strong polyelectrolyte is assumed to be negatively charged and to have a constant charge density of -v elementary charges e per unit length ( v is positive). Of course, both the counterion concentration and the electrostatic potential y/ are continuous functions of the distance r to the line charge at the centre of the cylinder. In the two-state model, the continuous distributions are approximated by bimodal distributions. The condensed counterions inside the cylinder
POLYELECTROLYTES
2.8
Figure 2.1. a) Geometry for the Oosawa two-phase model. Condensed counterions move in the inner cylinder of radius a. Free counterions move in the volume bounded by the inner and outer cylinders of radius R. b) Relation between the potential t//[r) arising from a line charge of strength -Jv and the potential difference Ayr in the Oosawa two-phase model. Note that the point of zero potential has not been defined in this graph. of radius a are assumed to have a constant concentration c cond , and the free counterions in the cylindrical region between a and R are assumed to have a constant concentration c free , given by the average values: C
free-TT-^T JVAv 7taz _
' 2 - 2 -21
1 (l-J)v
Like the counterion distribution, the electrostatic potential y/ is assumed to be bimodal: the electrostatic potential inside the cylinder of radius a is y/a and the potential in the cylindrical region between a and R is y/R . The distribution of the counterions over the two regions is then governed by a Boltzmann factor involving the difference in the electrostatic energy of the counterions: c
free cond
c
=
_J__ 1 ^ e xp(-eAiy/kT) ! " / {0) is the potential on the chain's backbone at a particular degree of charging 0 (9= a° /o^ax )• It is quite customary to express experimental data on proton binding in terms of pKeff as a function of a or (1 - a). pK eff =pK + ApK
[2.2.42]
In the above mean-field approximation, ApK =
_ J ^ L JcTlnlO
[2.2.43,
In the Debye-Hiickel limit of low charge densities, the potential t//° is proportional to the charge density <j°, hence to 8. The shift is therefore linear in the dissociation. Hence, ApK = ~e6, with ~e defined in terms of the charge parameter x, as follows:
Figure 2 . 6 . pK e f f a s a function of 8 a t v a r i o u s c o n c e n t r a t i o n s of NaNO 3 , a s indicated in t h e figure; (a) for t h e p o l y b a s e poly (dimethylaminoethyl methacrylate) (0=1- a) a n d (b) for t h e polyacid poly (acrylic acid) [6= a).
POLYELECTROLYTES
2.19
x Ko0ra) ~ rfglnlO KjOra)
L
where Ko and K{ are the zeroth- and first-order Bessel functions of the second kind, respectively. An example is shown in fig. 2.6 for the protonation of polydimethylaminoethyl methacrylate at various concentrations of added salt. Since the above expression is based on various assumptions, such as the absence of correlation effects (mean-field assumption) and a constant double layer capacitance (Debye-Hiickel limit), deviations from linearity are likely to occur as soon as these assumptions do not hold any longer. Indeed, non-linear ApK plots are often observed in experiments, and can be represented in the form of a series expansion: ApK = W+e'02 + ...
[2.2.44]
Examples of the latter are given in fig. 2.7a and b, where the full (non-linear) PB equation was used to fit the data. At this point, we should also mention the Henderson-Hasselbalch (HH) equation [1.5.2.34], an empirical equation introduced as a generalization of [2.2.37]:
pH = pK + nlogf-^-J
[2.2.45]
Figure 2.7. a. Degree of protonation as a function of pH for hyaluronic acid at various concentrations of monovalent salt, as indicated. Experimental results are denoted by symbols. Solid curves are fits to the PB equation for a cylinder (radius 1 nm, charge spacing 1 nm and intrinsic pK = 2.75). b. Titration curves plotted as versus 1 — 0 (degree of protonation) for polylDL-glutamic acid) at two concentrations of monovalent salt. Experimental results arc denoted by symbols. The dashed and solid curves are for a PB model with cylinder radius 0.5 nm; dashed curve: flexible chain model (charge spacing 0.7 nm): solid curve: rigid rod model (charge spacing 0.5 nm). (Redrawn from (a) R.L. Cleland, J.L. Wang and D.M. Detiler, Macromolecules 15 (1982) 386; (b) D.S. Olander, A. Holtzer, J. Am. Chem. Soc. 90 (1968) 4549, with fits from M. Ullner, B. Jonsson, Macromolecules 29 (1996) 6645.
2.20
POLYELECTROLYTES
where pKgff and n are an effective deprotonation constant and a parameter accounting for the polyelectrolyte effect, respectively. This equation appears to work quite well for many cases as is best checked by making a 'Henderson-Hasselbalch plot' (pH versus log(cr/l-«)), which should be linear. Comparison with [2.2.35] suggests that if the HH equation applies, the change in pK must scale as (rt -l)log(a/l- a) , which is not justified by theoretical arguments. An illustration follows in fig. 2.12. An alternative method sometimes introduced in the literature is to use the Donnan capacitance. The idea is that the space in the neighbourhood of the chain has a welldefined 'inner' potential given by the Donnan model, and that it is this potential that modifies the proton binding and conversely. This approach may be adequate for strongly branched molecules, gel-like polymer particles or brushes, which have an inner region that is large compared with the Debye length. We shall use that approach in sec. 2.3e. For linear chains such a region does not really exist, and the Donnan approach is less appropriate; indeed, the linear dependence of the capacitance on ionic strength predicted by the Donnan model is usually not found in experiments with linear chains. When the distance between proton binding sites on the chain becomes smaller, the interaction between them becomes stronger, and at some point (when the interaction energy becomes of order kT or more) we can no longer assume weak coupling. That is, the distribution of charges along the chain is no longer entirely random. For this case, rather than separating the Helmholtz energy in an ideal entropy term and an averaged energy term, we must weigh all possible configurations of charges along the chain with their respective interaction energies. A useful approximation is to rewrite the Helmholtz energy F({Sj}) of a molecule with a specified distribution of protonated and deprotonated sites {Sj} in terms of a cluster expansion: F
(<si>) = - Z / ' i s 1 + X V i s J i=l
i<j
+
X Lijksisjsk + -
[2.2.46]
i<j c"] and £ < ! K .
1 , no condensation is expected. Note the logarithmic scale: [//] varies by a factor of 10 3 . The [TJ] values are easily a factor of 10 2 higher than those for the corresponding uncharged polymers because of the chain expansion. As expected, [rj] increases with M and with K~1 : the lower the electrolyte concentration, the more extended the chain is. In the low salt limit, the values for extended rods are approached. To the left, at high c s a l t , the polyelectrolyte effect is suppressed and (9 conditions are approached. Here, the polyelectrolyte behaves as a non-draining Gauss-type coil. The drawn curves are based
11 21
R.M. Davis, W.B. Russel, Macromolecules 20 (1987) 518. H. Yamakawa, M. Fujii, Macromolecules 7 (1974) 128.
POLYELECTROLYTES
2.51
on the hydrodynamic theory by Yamakawa and Fuji11, combined with earlier work for such chains by Odijk21 and Fixman and Skolnick31. For theoretical background, see sec. 2.3c. We note that this reasonably accounts for the experimental trends. Key factors are chain stiffness (or for that matter, persistence length) and the excluded volume. As a trend, thermodynamic quantities are more easily accounted for than hydrodynamic ones. More to the quantitative side, it appears that [77] is, as a first approximation, proportional to M 1/2 . For a variety of systems this has been observed, for instance for poly( a -L-glutamic acid) in NaCl solution and various values of cNaC14), for poly(mono methyl itaconate) in organic solvents at various degrees of neutralization51, for sodium poly(acrylate) in aqueous NaBr solutions and at different degrees of dissociation6 and for oligo- and poly(methylmethacrylates) in acetonitrile, n-butylchloride and benzene71, where a lower slope than 1/2 was found for the low M samples. This proportionality is theoretically predicted by the familiar Stockmayer-Fixman equation81 [ti]/M1/2 = Ko+O.5l0oBM1/2
[2.4.11]
Here, B is a second virial coefficient, &0 is the Flory (or Flory-Fox) constant introduced in [2.4.7] and Ko is also a constant (independent of M ), which equals (r2\3/2
K =0
° °^r~
l2 4 121
--
where (r^ is the r.m.s. end-to-end distance under 0 conditions. Equation [2.4.11] works well if the chain is not too expanded. A plot of \rj\lM1^2 as a function of M 1 / 2 (a Stockmayer-Fixman plot) helps to assess the (hydrodynamic) virial coefficient. Intrinsic viscosities of polyelectrolytes typically depend on the electrolyte concentration c s , on the line charge and on the way this charge is distributed. As a first approximation for c s » c , one may expect [rf\(c ) to scale as c~ 1 / 2 . This scaling will hold when the polyelectrolyte behaves as a coil, expanded by intramolecular repulsion. A quick scan of the formulas for electric interaction Gibbs energies shows these to scale with c~1/2 provided / or ff11 are constants. Deviations from the c~ law are A expected for electrostatic ( \j/ and/or cfi are not constant but will regulate) and H. Yamakawa, M. Fujii, loc. cit. T. Odijk, J. Polym. Sci. Polymer Phys. Ed. 15 (1977) 477; Polymers 19 (1978) 989. 31 J. Skolnick, M. Fixman, Macromolecules 10 (1977) 944; M. Fixman, J. Skolnick, ibid. 11 (1978) 863; M. Fixman, J.Chem.Phys. 76 (1982) 6346. 41 M. Satoh, J. Komiyama, and T.Iima, Coll. Polym. Sci. 258 (1980) 136. 51 L. Gargallo, D. Radic, M. Yazdani-Pedram, and A. Horta, Eur. Polym.J. 25 (1989) 1059: also see Eur. Polym. J. 29 (1993) 609 for other solvents. 61 1. Noda, T. Tsuge, and M. Nagasawa, J. Phys.Chem. 74 (1970) 710. 71 Y. Fujii, Y. Tamai, T. Konishi, and H. Yamakawa, Macromolecules 24 (1991) 1608. 81 W.H. Stockmayer, M. Fixman, J. Polym.Sci part Cl (1963) 137. 21
2.52
POLYELECTROLYTES
conformational reasons (for high chain charges, the molecule assumes a rather rod-type conformation, see sec. 2.3). By way of illustration we give a few illustrations, emphasizing the c j 1 / 2 part and accompanying deviations.
Figure 2.24 Electrolyte concentration dependence of the intrinsic viscosity for NaPAA in NaBr solutions of concentration cs (moldm"3) . Given is the parameter B in [2.4.11]. The degree of dissociation is indicated. (Redrawn from Noda et al. loc. cit.) Figure 2.24 illustrates the expected trends for a weak polyelectrolyte. The data are plotted in terms of the parameter B in the Stockmayer-Fixman equation. This parameter is independent of M and has the dimensions of intrinsic viscosity, i.e. of a reciprocal weight concentration (in these experiments, decilitres per gram). One may expect B to consist of an electric and a non-electric part, which according to the figure, are linearly additive: B
= B non-el +B el
B e l = const •f{a)cl1/2
I2-4-13! [2.4.14]
where /(a) is a function of the degree of ionization. It appears that Bnon.ei is independent of c s and a ; this must be an intrinsic macromolecular parameter. The function J(a) is essentially a measure of the relation c^ia0) . As is always found, upon increasing a° further increases of a become gradually less active in increasing cfi (or the 'active' fraction). The trends of fig. 2.24 appear to be rather representative; they have also been reported (in less detail) by Satoh et al. (toe. cit.) for poly(a-L-glutamic acid) in NaCl.
POLYELECTROLYTES
2.53
Figure 2.25. Ion specificity in the intrinsic viscosity of Na poly(styrene sulphonatc) as a function of the electrolyte concentration. Measurements at non-zero shear (/ = 1000 s"1) . Redrawn from Jiang etal. 11 . Figures 2.25a and b are meant to illustrate the lyotropic effects for a strong polyelectrolyte solution. These measurements have been carried out as a function of the shear rate y . The intrinsic viscosity increases somewhat with decreasing y but maintains the same ionic specificity, of which the trends are typical. For instance, these have also been observed by Cohen and Priel 2 ', though at lower c s . The differences between the different counterions reflect their specific binding to the chain; increased binding leaves less charge in the diffuse {i.e. interaction-active) part. So, it is seen that the binding increases from z + = 1 to z + = 2 and for fixed z + , according to Li + < Na + < K+ and Mg 2+ < Ca 2+ < Ba 2 + . This is the familiar sequence for sulphate groups; it is a.o. reflected in the c.m.c. of dodecylsulphate micelles31 and in the surface pressure of Gibbs monolayers of the corresponding surfactants 41 . 2Ad The dilute and semidilute range Now we are considering intermolecular hydrodynamic interactions. For a variety of polyelectrolytes, the reduced viscosity as a function of c passes through a maximum, as sketched in fig. 2.22. The higher the c s , the more suppressed this maximum is. Examples include Na-pectinate in NaCl51, poly(n-butyl-4-vinylpyridinium) bromide in
11
L. Jiang, D.H. Yang, and S.B. Chen, Macromolecules 34 (2001) 3730. J. Cohen, Z. Priel, Macromolecules 22 (1989) 2356. P. Mukerjce, K.J. Mysels, Critical Micelle Concentrations of Aqueous Surfactant Systems, U.S. Natl. Bureau Standards, 36 (1971). 41 See the references in sec. III.3.10b. 51 D.T.F. Pals, J.J. Hermans, Rec. Trau. Chim. 71 (1952) 433. 21
2.54
POLYELECTROLYTES
NaCl, poly(2-vlnyl pyridine) in HCl-solutions in ethyleneglycol and triethylamine11, Napoly(vinyl sulphate) probably in NaCl or NaBr2), and Na-poly(styrenesulphonate) in saltfree31 and salt-containing media41. Figure 2.26 gives an illustration for the last-mentioned system by Cohen and Priel. In fig. 2.26a the position of the maximum is independent of M~5xlO~ 6 g ml"1 , which more or less corresponds to the overlap concentration c* . Added electrolytes lower the maximum, make it less distinct and move it to higher c . This last trend is about linear, with c (max)/ c s =4±0.5 and 77inc (max) also linear with M , and the steeper the lower c s is. The theoretical interpretation, offered by the authors, centres around this equation n J2r2 ^ i n c — ^
12-4.15]
Figure 2.26. Reduced viscosity as a function of polymer concentration for Na-neutralized poly (styrene sulphonate). (a) Influence of M at fixed, low electrolyte concentration (4xlO~ 6 M); (b) Influence of c s at fixed M = 16,000 . In fig. (a) the drawn curves are meant to guide the eye; in fig. (b) the dashed curves are theoretical. Redrawn from Cohen and Priel, loc. cit.
11 21 31 41
H. Eisenbcrg, J . Pouyct, J Polym. Sci. 13 (1954) 85. D.F. Hodgson, E.J. Amis, J. Chem. Phys. 9 1 (1989) 2635. H. Vink, Polym. 3 3 (1992) 3711. N.Imai, K. Gekko, Biophys. Chem. 4 1 (1991) 31.
POLYELECTROLYTES
2.55
with the screening now determined by K2 =4;rt R (c n + 2c.) 0
\ P
s
[2.4.16]
/
because the polyelectrolyte and the indifferent electrolyte both contribute; a h is the hydrodynamic radius. This equation was derived for extended chains, but Hess and Klein" obtained a very similar result for spherical coils. Hence, it is apparently not discriminative. In fact, apart from a numerical factor this equation contained the effective counterion charge z 4 , where z is defined as the number of counterions compensating the line charge, i.e. it is a measure of the diffuse, or mobile part of the countercharge. The factor z 4 also occurs in a paper by Antonietti et al.2), to be discussed below. That this factor does not occur in [2.4.16] stems from the formalism, according to which the structure factor S(q) is related to an 'exclusion radius' determined by K . It is also noted that the dependence o n e is a function of the cs I c ratio. Equation [2.4.15] can at least semi-quantitatively account for the trends in fig. 2.26: 77inc as a function of c passes through a maximum; this maximum increases with M via a h (for an extended chain it is linear) and gets lower with increasing c s . Even the slope cs(max)/ c s = 4 agrees with [2.4.15 and 16]. Equation [2.4.15] is, of course, more specific than the virial expansion [2.4.3]; in fact, this contribution has to be added to [2.4.12], hence the A in the l.h.s. of [2.4.15]. It is, on the one hand, gratifying that such a simple equation represents the data well over the given c range. On the other hand, one cannot infer too much from it about specific polyelectrolyte properties, such as the persistence length and the (counter) charge distribution.
Figure 2.27. Reduced viscosity increment for poly(Na-styrene sulphonatc) microgels in salt-free solutions. The molecular weight of the parental solution increases in the direction of the arrow. Degree of sulphonation 70%. Drawn curves, theory. (Redrawn from Antonietti c.s., loc.cit.}
11 21
W. Hess, R. Klein, Adv. Phys. 32 (1983) 173. M. Antonietti, A. Briel and S. Forster, Macromolecules 30 (1997) 2700.
2.56
POLYELECTROLYTES
Antonietti et a l . ' ' have presented another illustration of the same nature. These authors studied the rheology of branched polyelectrolytes, viz. cross-linked poly(styrene sulphonates) in electrolyte and salt-free solutions. So, the polyelectrolyte molecules behave as microgel particles. Below c*p there is no M -effect anymore, as would be the case for impenetrable spheres; but above c* , r][ac decreases with c just as in the r.h.s. of fig. 2.26. For this part of the curve, the authors derived an equation, which just as with the previous example consisted of the series expansion [2.4.3] plus an additional term, somewhat more elaborate than [2.4.15], but with the factor z 4 made explicit. Figure 2.27 gives an illustration. This double logarithmic plot shows that the theory can account satisfactorily for the results. Data below the predicted maximum are not available, but in analogy to fig. 2.26 a decline with decreasing c must be anticipated. For a gel the molecular mass is not so easily definable, the more so as the parental polymers (from which the gel particles were synthesized) were polydisperse. However, the trend is indicated by the arrow. This trend is reflected in the intrinsic viscosity, which in this direction increases from 0.044 via 0.052 to 0.090 dm 3 g"1 for the parental microgels, whereas the fitted values for the intrinsic viscosity and Huggins constant ku are, in this order, 0.139, 0.143 and 0.182 d m 3 g - 1 and 0.2, 0.6 and 0.9 , respectively. So, one accounts semiquantitatively for the trends.
Figure 2.28. Huggins constant for the same solution of K poly(styrene sulphonate) as in fig. 2.23.
Finally, fig. 2.28 gives an illustration of the salt effect on the Huggins constant, which displays a striking minimum between high values at low and high ionic strengths. To the left, 0 -conditions are approached. These minima result from an interplay of direct intermolecular contributions to the stress, the ensuing coil compression and the attractions appearing near 0-conditions. The authors discuss this in more detail, but 11
M. Antonictti, A. Briel and S. Forster, loc. cit.
POLYELECTROLYTES
2.57
the final quantitative answer still has to come. For further interpretations, see". Viscometry has also been invoked to monitor conformational changes and counterion specificity features. By way of illustration, we refer to the frequently discussed21 phase transition, which occurs as a function of pH in solutions of poly(methacrylic acid), but not with poly(acrylic acid). Figure 2.12 already gave an illustration. Sugai et al.3> confirmed these transitions for poly(ethacrylic acid) in NaCl and at various temperatures, and Klooster et al. 4) studied these for poly(acrylic acid) in methanol (MeOH) and found the occurrence of the transition to be ion-specific: for or > 0.1, it does not occur in LiOCH3 (as in aqueous solution of the Na-salt), whereas it is found in NaOCH3 . There appears to be more room for viscometric studies of ion specificities. In particular, the effects of higher valence cations like La3+ and Th 4+ deserve attention since it is known that, at the proper pHs these ionic species hydrolyze and give rise to superequivalent adsorption (sec. IV.3.9J) For polyelectrolytes, the phenomenon has been reported51. 2.5 Polyelectrolytes in electric fields Just as with low M electrolytes and particulate colloids, polyelectrolyte solutions can be subjected to an electric field, the response of the system acting as a tool to extract information. Three familiar techniques are electrokinetics (electrophoresis in particular), dielectric studies and conductometry. Experiments can be carried out in DC or AC. Electrophoresis is usually done in DC, dielectric investigations mostly in AC, with the aim of scanning the various relaxation ranges (dielectric spectroscopy). Conductometry is preferentially carried out in DC, but AC data are automatically produced as a side effect of dielectric spectroscopy: the (measurable) complex impedance consists of a real (resistive) part yielding the conductivity spectrum K(co) and an imaginary (capacitive) part giving a>£0£{a>), see [II.4.5.13] and sec. II.4.8a. These two quantities are related to each other through the Kramers-Kronig relations. The interpretation of the obtained electrometric data is cumbersome because a number of physical phenomena participate and interfere; for many of these no sufficient theory is available. For instance, the conduction mechanism differs substantially among the dilute, semi-dilute and concentrated regimes and may depend in a complex way on the presence of added electrolyte. In this section, some attention will be paid to the issue
11
J-L Barrat, J.F. Joanny, Adv. Chem. Phys. XCIV(1996) 1, I. Prigogine, S.A. Rice. Eds. Already in 1974 H. Okamoto, and Y. Wada cited 30 references, sec J. Polym. Sci. Polym. Phys. 12 (1974) 2413. 31 S. Sugai, K. Nitta, N. Ohno, and H. Nakano, Colloid Polym. Sci. 261 (1983) 159. 41 N.T.M. Klooster, F. van der Touw. and M. Mandel, Macromolecules 17 (1984) 2070. See for instance M. Drifford, J.P. Dalbiez, M. Delsanti, and L. Belloni, Ber. Bunsengesellsch. Phys. Chem. 100 (1996) 829. 21
2.58
POLYELECTROLYTES
of electrometrically bound counterions {= counterions that in electrometry appear not to move freely). Apart from the question as to how these are bound (electrostatically condensed, chemically or still otherwise associated), one of the issues is whether different electrometric techniques yield identical answers (are electrophoretically and conductometrically bound counterions identical?). Accepting that there is no established overall theoretical picture, it is sometimes helpful to compare electrometric properties of polyelectrolytes with those of low M electrolytes, on the one hand, and with particulate colloids on the other. One typical illustration is that the conductivity of a polyelectrolyte of JV charged monomers and its compensating counterions is always lower than that of the JV monomers free in solution. Apparently this is the result of counterion immobilization by the chain. Another line is the interpretation of the slip plane for solid particles and the application to polyelectrolytes. We shall address this issue first. 2.5a The issue of electrokinetic binding Although polyelectrolytes, together with their countercharge, are electroneutral, they move in an electric field, i.e. they exhibit electrophoresis. The occurrence of this phenomenon implies charge separation: upon moving, the polyelectrolyte may entrain part of the countercharge, but not all of it. Which part? The issue has a micromechanical origin. Upon tangential movement of a liquid (especially water) with respect to a solid, a thin, adjacent layer of this water is stagnant, meaning that it does not move with respect to the solid; in electrophoresis the stagnant water moves with the solid. In streaming potential experiments, it remains stationary with the particles constituting the porous plug. Countercharges captured in stagnant layers behave as if they are electrokinetically bound. The phenomenon is widespread; it is observed for inorganic solids, polymer latices, hydrophobic and hydrophilic surfaces, surfactant micelles, ... Hence, it presumably also occurs with polyelectrolytes, either with coils as a whole or with individual chains. Questions coming to mind include: (i) what is the origin? (ii) how can the phenomenon be experimentally detected? and (iii) can we state something about its magnitude? (i) According to present day insight, the origin has to be sought in the water structure adjacent to hard walls1'21. Mostly as a result of the repulsive part of the intermolecular interactions, this leads to the familiar stacking: oscillations of the molecular density pN{z) that peter out over a very few molecular diameters. This picture is in line with the generality of the phenomenon; it should apply to liquids adjacent to any surface that is hard (impenetrable) on the molecular scale. It is even observed for some L-L interfaces31, should not occur for clean water-air phase boundaries, but must be expected for fluids
11
J. Lyklema, S. Rovillard, and J. de Coninck, Langmuir 14 (1998) 5659. J. Lyklema, Oil Gas Set Technol. 56 (2001) 41. 31 A.M. Djerdjev, J.K. Bcatty and R.J. Hunter J. Colloid Inter/act Sci. 265 (2003) 56. 21
POLYELECTROLYTES
2.59
adjacent to polyelectrolytes. The structure formation leads to an increase of the tangential viscosity in the adjacent liquid that, because of the strongly cooperative nature of viscous flow, becomes so strong that phenomenologically speaking the layer behaves as if it were stagnant.
Figure 2.29. Relation between the electrokinetic and surface (- or line) charge, both expressed in the same units Cm" 2 or Cm- 1 . Tan a = / e k .
(ii) For particulate colloids, micelles, etc., the electrokinetically bound charge can be determined by simultaneously measuring the surface charge a° and the electrokinetically free charge crek . The latter can be inferred from £ potentials, using GouyChapman theory, of which the application is safe because the electrokinetically free part of the countercharge more or less coincides with the diffuse part of the double layer. Measurement and interpretation of f -potentials have been described in detail in chapter II.4. Figure 2.29 sketches the relationship between the two types of charges as it is usually found. At very low surface or line charge this charge equals the electrokinetic one (negligible fraction of countercharge in the stagnant layer), but upon increasing the surface or line charge, 0 , t P
r
. =0.5, Na+
meaning that 50% of the charge transport is accounted for by the counterion and 50% by the macro-ion. When a increases, t decreases because a fraction of the Na+ ions Na +
is bound to the chain, and therefore moves to the anode, together with the 11
H. Vink, Macromolec. Chem. 183 (1982) 2273.
POLYELECTROLYTES
2.65
polyelectrolyte. For larger a , t + even becomes negative, i.e. t > 1. This means that the polyelectrolyte does more than its share in the conduction; it even carries its counterparts in the wrong direction. The phenomenon is not unique; it is also observed for micelles and charged colloids in dilute electrolyte.
Figure 2.31 Concentration dependence of K - K{cp = 0) for poly(diallyl dimethyl ammonium chloride) (PDADMAC) over three c p ranges and for different molecular masses: O, Mn = 12,000; • 22,000; • 72,000; • 170,000 gmol" 1 . (Redrawn from Wandrey and Hunkclcr, toe. cit.)
Figures 2.31 and 32 stem from a review by Wandrey and Hunkeler11, containing much experimental information. In fig. 2.31 the average distance between the charges on the chain is 0.5nm , so the line charge ve = 3.2xlO~6 juC cm~' . As these charges reside at the periphery of the ally! groups (a five-member ring with an N(CH3);j; at its end), the backbone can be interpreted as well as a cylinder. If the radius a is ~ 0.6 nm C. Wandrey, D. Hunkeler, Study of Counterion Interactions by electrochemical Methods in Handbook of Polyelectrolytes and their Applications, S.K. Tripathy, J. Kumar, and H.S. Nalwa, Eds. Vol. 2 chapter 5. American Scientific Publ. (2002).
2.66
POLYELECTROLYTES
Figure 2.32. Molar conductivity A of Na poly(styrene sulphonate). Influences of molar mass and NaCl concentration: T = 20°C. Key: O, no added salt: V, 1CT6 (5xlCT 6 in (c)); • , 2xlO~ 6 ; D, 4xlO~ 6 ; • , 10~ 5 ; A, 2xlO~ 5 ; A, 5 x l 0 ~ 5 ; O, 10~ 4 M. The (number-average) molecular mass (in g/monomol ) is indicated. (Redrawn from C. Wandrey, loc.cit.; data points below 10 6 monomol"1 deleted.)
(depending on the radial positions of the allyl groups), this cylinder has a surface charge 1000 kg/mol. The effect of molar mass in orthokinetic flocculation can be related to the time-dependent thickness of the adsorbed polyelectrolyte layer, in the same way as discussed in sec. 1.12.e; it is more complicated, though, because salt also influences the relaxation processes in the polymer layer21. 2.7b Stabilization enhancement Highly charged polyelectrolytes have the ability to adsorb strongly to charged surfaces such that the effective charge of the covered particle reverses. Moreover, the adsorption of weak polyelectrolytes (which is of course sensitive to pH) often shows considerable hysteresis upon cycling the ionic strength. For example, when 90% hydrolyzed polyacrylamide (effectively a copolymer of 90% acrylic acid and 10% acrylamide) adsorbs onto cationic latex from 0.5 M NaCl, the adsorbed amount is much higher than when adsorption takes place from 0.002 M NaCI. However, if adsorption is allowed to take place at 0.5 M salt, after which the ionic strength is lowered to 0.002 M, an intermediate adsorbed amount results, which is definitely higher than the one obtained upon adsorption at 0.002 M 31 . Meadows et al. called this 'enhanced adsorption,' and noticed that enhanced adsorption makes colloidal particles much more stable than particles prepared by the usual procedure (adsorption at low ionic strength). Similar enhancement effects occur upon cycling the pH41. The stabilizing effect of dense and strongly adsorbed polyelectrolyte layers is very effective indeed. Meadows found a tenfold increase in critical flocculation concentration for particles with enhanced adsorption. 2.8 General references 2.8a IUPAC recommendation Conductometric Analysis of Polyelectrolyte Solutions. Prepared for publication by H. van Leeuwen, R.F.M.J. Cleven and P. Valenta, Pure Appl. Chem. 63 (1991) 1251. 11
G. Durand-Piana, F. Lafuma, and R. Audcbert, J. Colloid Interface Sci. 119 (1987) 474; L. Eriksson, B. Aim, and P. Stenius, Colloids Surf. A70 (1993) 47. 21 Y. Adachi, T. Matsumoto, and M.A. Cohen Stuart, Colloids Surf. A207 (2002) 253. 31 J. Meadows, P.A. Williams, M.J. Garvey, and R. Harrop, J. Colloid Interface Sci. 139 (1990) 260. 4) J.G. Gobel, N.A.M. Besseling, M.A. Cohen Stuart, and C. Poncet, J. Colloid Interface Sci. 209 (1999) 129-135; C.W. Hoogendam, A. de Kcizer, M.A. Cohen Stuart, and B.H. Bijsterbosch, Langmuir 14 (1998) 3825.
POLYELECTROLYTES
2.83
2.8b Other references Aut. Div. International Symposium on Macromolecules, under auspices of IUPAC, Butterworth (1970). (Contains contributions on polyelectrolytes; old, but not dated, containing papers giving the then state of affairs.) J.-L. Barrat, J.-F. Joanny, Theory of Polyelectrolyte Solutions, in Adv. Chem. Phys. XCIV (1996) 1-66. (Review, 125 refs., emphasizing theory from a physical angle of incidence.) Polyelectrolytes in Solution and at Interfaces, J. Barthel, H. Dautzenberg, D. Horn and W. Oppermann, Eds., Ber. Bunsengesell. 100 Nr. 6 (1996). (Proceedings of the Symposium Polyelectrolytes Potsdam '93'. Containing 62 papers on polyelectrolytes in solution and at interfaces.) M. Borkovec, B. Jonsson and G.J.M. Koper, Ionization Processes and proton Binding in Polyprotic Systems: Small Molecules, Porteins, Interfaces and Polyelectrolytes, in Colloid and Surface Set 16 (2001), E. Matijevic, Ed., Kluwer/Plenum, 99-339. (Very detailed review on electric double layers in various systems, 390 refs.) H. Dautzenberg, W. Jaeger, J. Kotz, B. Philipp, C. Seidel and D. Shtcherbina, Polyelectrolytes; Formation, Characterization, Application, Carl Hanser, Miinchen (1994). S. Forster, M. Schmitz, Adv. Polymer Sci. 120 (1955) 51. M. Mandel, Polyelectrolytes, in Encyclopaedia of Polymer Science and Engineering, 2nd ed., H.F. Mark, N.M. Bikales, C.G. Overberger, and G. Mendes, Eds., Wiley, Vol. 11 (1988) 739. (Extensive review, 314 refs, covering the entire field. Although some features are nowadays better understood, this review still serves as an excellent introduction into the field.) M. Mandel, T. Odijk, Dielectric Properties of Polyelectrolyte Solutions, in Ann. Rev. Phys. Chem. 35 (1984) 75-108. (Review of the state of affairs indicating the many problems that have to be addressed.) T. Radeva, Ed., Physical Chemistry of Polyelectrolytes, Detcher (2001). K.S. Schmitz, Macroions in Solution and Colloidal Suspensions, VCH, New York (1993). Handbook of Polyelectrolytes and their Applications, S.K. Tripathy, J. Kumar and H.S. Nalwa, Eds., Am. Scientific Publishers 2002. (Three volumes: 1. Polyelectrolytebased Multilayers, Self-assemblies and Nanostructures; 2. Polyelectrolytes, their Characterization and Polyelectrolyte solutions; 3. Application of Polyelectrolytes and Theoretical Models.)
2.84
POLYELECTROLYTES
C. Wandrey, D. Hunkeler, Study of Polyion Counterion Interaction by electrochemical Methods, (2002).
3
ADSORPTION OF GLOBULAR PROTEINS
Willem Norde, Jos Buijs and Hans Lyklema 3.1
Introduction
3.2
Structure of globular proteins
3.3
3.2a
Conformational entropy
3.4
3.2b
Interactions that determine the 3D structure of proteins in aqueous solution
3.3
3.4
3.1
3.4
Adsorption of globular proteins from aqueous solution onto (solid) surfaces
3.10
3.3a
3.11
Adsorption kinetics
3.3b
Relaxation at interfaces
3.17
3.3c
Driving forces for protein adsorption
3.19
Adsorption-related structural changes in proteins
3.23
3.4a
How to measure structural properties of adsorbed proteins
3.24
3.4b
General trends
3.30
3.5
Adsorbed amount and adsorption reversibility
3.37
3.6
Influence of some system-variables on protein adsorption
3.40
3.7
3.6a
Protein and sorbent charge
3.40
3.6b
Hydrophobicity
3.41
3.6c
Protein structure stability
Adsorption at fluid interfaces
3.42 3.42
3.7a
Review of some general trends and techniques
3.43
3.7b
Some illustrations
3.45
3.8
Competitive protein adsorption and exchange between the adsorbed and dissolved states
3.52
3.9
Tuning protein adsorption for practical applications
3.55
3.10
General references
3.58
This Page is Intentionally Left Blank
3 ADSORPTION OF GLOBULAR PROTEINS WILLEM NORDE, JOS BUMS AND HANS LYKLEMA
3.1 Introduction This chapter may be considered as a sequel to chapter II.5. Chapter II.5 deals with the adsorption of relatively simple polymers and polyelectrolytes, whose molecules are built up of identical units. In solution, such molecules are rather featureless, having a flexible coily structure, and their adsorption behaviour has been well-modeled. In the present chapter we will discuss the more complicated biopolymers, which are often made up from a variety of monomeric units. For example, proteins are polymers of some twenty-two different amino acids. Because of the variation in physical-chemical properties-mainly in polarity and electrical charge, between the constituting amino acids, protein molecules are ampholytic, are more-or-less amphiphilic, and assume complex three-dimensional structures. As a result, the adsorption of biopolymers is more intricate than that of the simpler polymers treated In chapter II.5. Knowledge of the adsorption behaviour of biopolymers has progressed over recent decades but a unified predictive theory is still far away. However, the discussion of the principles of biopolymer adsorption may start from general trends observed for the adsorption of the simpler polymers, and, in particular, polyelectrolytes. Some main features of polyelectrolyte adsorption may be summarized as follows: (a) When a flexible polymer molecule adsorbs, its conformatlonal entropy is reduced. Hence, for adsorption to occur spontaneously (parts of) the polymer molecule should be attracted by the sorbent surface. Even if the attraction per adsorbing segment of the polymer is only weak the whole polymer molecule may adsorb tenaciously, because many segments adsorb. (b) A flexible, highly solvated polymer molecule typically adopts a train-loop-tall conformation in the adsorbed state, as depicted in fig. II.5.1. The extension and the density of the loops in the adsorbed layer are determined by the solubility of the polymer. A high loop-density is reached only with poor solvents. (c) Because of their polar ionic groups polyelectrolytes are usually well soluble in water. Also, mainly owing to intramolecular electrostatic repulsion, they adsorb with relatively little loop formation in a rather flat conformation.
Fundamentals of Interface and Colloid Science, Volume V J. Lyklema (Editor)
© 2005 Elsevier Ltd. All rights reserved
3.2
PROTEIN ADSORPTION
(d) More often than not, sorbent surfaces are electrically charged and they may electrostatically attract or repel polyelectrolytes. Even in the case of electrostatic repulsion the polyelectrolyte may still adsorb, namely if non-electrostatic attraction of segments outweighs the electrostatic repulsion. For example, polyelectrolytes containing hydrophobic apolar groups may adsorb readily on a (hydrophobic) surface under electrostatically unfavourable conditions. (e) Polyelectrolyte adsorption is strongly affected by the ionic strength. At elevated ionic strengths, charge-charge interaction may be effectively screened and the polyelectrolytes' behaviour approaches that of an uncharged polymer. The pH, which often controls the charge on the polyelectrolyte, and sometimes, that on the sorbent surface, influences polyelectrolytic adsorption in a similar way, at the pH where the polyelectrolyte attains a low charge density it adsorbs in a relatively thick, loopy layer, which is not sensitive to ionic strength variation. (f) In line with paragraphs c, d and e, the variation of the adsorbed amount of polyampholytes (macromolecules containing both anionic and cationic groups) as a function of pH, passes through a maximum at the isoelectric point. The pH-dependent adsorption profile flattens with increasing ionic strength. Polysaccharides, polynucleotides, and unfolded protein molecules that all attain extended structures in aqueous solution, adsorb according to the patterns mentioned above. However, globular protein molecules may deviate strongly from (some of) these principles. The polypeptide chains of globular proteins, to which enzymes, immunoproteins and most transport proteins belong, are folded into a denser structure and, as a rule, contain different structural elements such as a-helices and (3sheets as well as more unordered parts. The architecture of a globular protein is complex and heterogeneous, and highly specific for each type of protein. When interacting with an interface the protein structure may change. The kind of rearrangements depends in a complex way on the interaction with the sorbent surface. Because of the structure-specificity, the adsorption behaviour will differ between different protein species. Consequently, a general theory predicting globular protein adsorption is not to be expected but, based on the advances made during the last few decades, some general principles have been unraveled. Studies of the interaction between proteins and interfaces may help understanding of the mechanism that determines the 3D structure of protein molecules. In addition to this academic interest, protein adsorption has a high practical impact. Examples can be found in biomedical engineering, enzyme immobilization in bioreactors, drug targeting and -delivery, and its use in stabilizers in dispersions in foodstuffs, pharmaceuticals and cosmetics, etc. Conformational changes in protein molecules, which have consequences for their biological functioning, are the most intriguing and challenging aspects of protein adsorption, both from a theoretical and an applied point of view. This matter will be
PROTEIN ADSORPTION
3.3
discussed extensively in sec. 3.4. To understand the behaviour of proteins at interfaces we first have to discuss the main types of interaction that determine protein structure in (aqueous) solution. 3.2 Structure of globular proteins. Proteins are co-polymers built from some 20-22 L-a-amino acids linked together into a linear polypeptide chain. The polypeptide backbone consists of repeating identical peptide units. The structure of a peptide unit is presented schematically in fig. 3.1. Peptide units may interact through H- bonds (C=O ... H-N-) or with other adjoining hydrogenbonding entities, e.g., water molecules. Two of the three bonds in the peptide unit are free to rotate, whereas the C-N bond, shaded in fig. 3.1, is fixed because of its partial double-bond character represented by mesomerism. The side-groups, R, R', ... are specific for the type of amino acid. They vary in size, polarity, and charge. Depending on the distribution of the polar and apolar residues, the protein molecule is more or less amphiphilic and this is one of the reasons why they can be surface active. Some side groups contain cationic groups, others anionic groups. This makes the protein belong to the polyampholytes. Just as an essentially infinite number of words can be written by using the twenty six letters of the alphabet, an endless number of different polypeptides may be formed, characterized by a given sequence of amino acids. This sequence, the so-called primary structure of the protein molecule, rules the interactions in the molecule as well as those between the molecule and its environment. These, in turn, determine the spatial organization, i.e., the three-dimensional (3D) structure adopted by a protein molecule in a given environment. Within the 3D structure, different levels of organization may be distinguished, referred to as the secondary, tertiary, and quaternary structures. The secondary structure is the spatial arrangement of the polypeptide backbone, ignoring the side groups. The tertiary structure refers to the overall topology of the polypeptide chain, and the term, 'quarternary structure' is used for the non-covalent association of independent tertiary structures.
Figure 3.1. Structure of a peptide unit in a polypeptide chain. Two of the three bonds are free to rotate whereas the shaded bond is fixed.
3.4
PROTEIN ADSORPTION
In globular proteins the polypeptide chain folds into a dense structure in which the packing reaches volume fractions of 0.70-0.80. In such compactly folded conformations, the rotational freedom of the bonds in the polypeptide backbone (and side chains) is highly restricted. Such low-conformational-entropy structures are only thermodynamically stable if they are supported by interactions whose the net effect is sufficiently favourable to compensate for the low conformational entropy. Globular protein molecules in an aqueous environment have a few characteristic features: a. They are more or less spherical or ellipsoidal, with dimensions of the order of a few, to a few tens, of nanometers. b. Apolar amino acid residues tend to be accommodated in the interior of the molecule where they are shielded from contact with water. c. Almost all charged groups reside at the exterior of the protein molecule. Charges buried in the low dielectric interior occur as ion pairs. 3.2a Conformational entropy When apolar side groups are rejected from water to form the hydrophobic core of a protein molecule, part of the polar polypeptide backbone is pulled along into the interior. There, because of the absence of water molecules, the peptide units form hydrogen bonds among each other, which stabilizes the ordered structures of the polypeptide backbone. The best known secondary structures occurring in globular proteins include the a-helix and the fS-sheet. Schematic representations of these structures are shown in fig. 3.2. In distinction to a random polypeptide conformation, where two of the three bonds of a peptide unit are free to rotate, all three bonds in cc-helices and (3-sheets are blocked from rotation. This involves a reduction in conformational entropy of 2Rln2 = 11.53 J K"1 per mol of peptide units. Thus, if a polypeptide consisting of 100 amino acids (corresponding to a molar mass of ca. 10,000 Da) folds from an unordered (coily) conformation into a globular protein containing 50% of ordered structure, this goes at the expense of 580 J K^mol" 1 , which, at 300 K, yields an increase in Gibbs energy of 174kJmol~ 1 . Taking into account the restriction in the degrees of freedom of the side groups, the total increase in Gibbs energy upon folding of such a polypeptide may be in the range of a few hundreds of k j per mol. 3.2b Interactions that determine the 3D structure of proteins in aqueous solution Hydrophobic interaction Dehydration of apolar amino acid residues is the main driving force for polypeptide chains to fold into a compact globular conformation. To establish the contribution to the stabilization of a compact structure (taking the completely unfolded, hydrated conformation as the reference state) the distribution of all the amino acid residues and their individual hydrophobicities must be known. The distribution may be obtained
PROTEIN ADSORPTION
3.5
Figure 3.2. Ordered secondary structure elements in polypeptdide chains, (a) a- helix; (b) antiparallel |3- sheet; (c) parallel |3- sheet. from solving the 3D structure (by, e.g., X-ray diffraction and/or NMR) and the individual hydrophobicities can be expressed as the Gibbs energy of partitioning the amino acid between a non-polar medium and water. In this way, it has been inferred that the Gibbs energy of dehydration is about -9.2 kJnm~ 2 per mol 1 '. Based on an empirical relationship between the change in the water-accessible area upon folding and the molar mass of the polypeptide, and assuming that 60% of the interior of the folded protein molecules is made up of apolar amino acid residues21, the compact globular structure of a protein of molar mass 10,000 Da, is stabilized by a Gibbs energy of about SOOkJmor 1 at 25°C. Electrostatic interactions Proteins acquire their charge by (de)protonation of ionic groups in the side groups of the amino acid residues and the a -carboxyl group and a -amino group of both
11 21
F.M. Richards, Ann. Rev. Biophys. Bioeng. 6 (1977) 151. B. Lee, F.M. Richards, J. Mol. Biol. 5 5 (1971) 379.
3.6
PROTEIN ADSORPTION
terminal amino acids. Most of these charged groups are located at the aqueous periphery of the globular protein molecule, whereas in the unfolded conformation, depending on the primary structure, the charged groups are more or less homogeneously distributed over the fully hydrated expanded coil. The Gibbs energy of dissociation, AdissG , of a proton from any particular group can be split into a chemical ('chem') and an electrical ('el') term A
diss G = A diss G chem + A diss G el
I3-2- * 1
The chemical term contains the intrinsic contribution to the dissociation, and the electrical term the additional electrical work to remove the proton from the charged site to infinity (where the electric field strength is zero). In the simple case where all titratable groups belong to one and the same class Q0 = azFN
[3.2.2]
where Qo is the total charge of the sample, N the number of titratable groups, and a the degree of dissociation11. For the dissociation constant K diss the following expressions apply
p K diss=p H + i °g : 4r
l3-2 31
'
and AG° = -RTlnK d i s s
[3.2.4]
Combining [3.2.1], [3.2.3] and [3.2.4] yields pH = 0.434 AdissGc°hem + AdissGe°l _ j F RT
j B
^
[3 2 5 ]
a
It should be realized that A diss G° is a function of a ; at a high degree of dissociation, when the surface has attained a negative charge density and, consequently, a high negative potential, it requires more electrical work to remove a proton from the surface. The quantity AdissG°[ is often expressed as diss el =_2WE0_ RT F
=
_2WazN
[3.2.6]
in which W is the so-called electrostatic interaction factor. It depends primarily on the dielectric constant and the ionic strength of the medium. In differential form, [3.2.6] may be written as
The titration behaviour of polyelectrolytcs has been discussed in sec. 2.2d.
3.7
PROTEIN ADSORPTION
^ ^ - = -0.868 WzN + 0.434 da all-a)
[3.2.7]
M L °434 dg>0 zNFa(l-a)
[3.2.8]
or 0.868^ F
The quantity d p H / d Q 0 reaches a minimum value for a = 0.5 which is reflected by an inflection point in the titration curve for Qo versus pH. Proteins contain more than one class of titratable groups. Different classes j of groups are titrated in distinct pH regions. By way of example, the number of titratable groups, together with their intrinsic pK°-values for the protein ribonuclease (RNase), are given in table 3.1. For systems containing more than one class of titratable groups [3.2.8] has to be modified into *& = ^ dg>0 FljJVjZjajd-aj)
0.868 ?L F
[3.2.9]
and the differential titration curve, d p H / d g 0 versus QQ (or versus pH) displays more than one minimum, as is shown for RNase in fig. 3.3. Adsorption of ions other than protons can also lead to charging of the surface, provided that the adsorption is specific. The term, 'specific' implies that the adsorption
Table 3.1. Titratable groups and their intrinsic dissociation constants (pK°'s) in ribonuclease. Group
Number
pK°
Group
Number
pK°
a -carboxyl
1
3.75
e -amino
10
10.2
(5-, y -carboxyl
10
4.0-4.7
phenolic OH
3
10.0
imidazole
4
6.5
3
inaccessible
a -amino
1
7.8
4
> 12
guanidyl
Figure 3.3. Differential proton titration curve for bovine pancreas ribonuclease in 0.05 M aqueous solution. (Redrawn from W. Norde, J. Lyklema, J. Colloid Interface Sci. 66(1978) 266.)
3.8
PROTEIN ADSORPTION
Figure 3.4. Schematic picture of a globular protein molecule in solution. Shaded areas indicate hydrophobic regions. Charged groups originate from (de)protonation of amino acid residues (+/-) and from specific ion adsorption ( ©/© )• The dashed envelope iindicates the slip plane. Within this envelope the charge is Q e k . The compensating diffuse charge is not drawn.
Figure 3.5. Proton charge Qo and electrokinetic charge S e k of the same RNase as in fig. 3.3. The point of zero charge (p.z.c.) and isoelectric point (i.e.p.) are indicated. (Redrawn from W. Norde, J. Lyklema, J. Colloid Interface Sci. 66 (1978) 277.)).
forces are partly non-electric so that these ions can overcome the repelling electric potential at the surface and, by their adsorption, even increase the surface electric potential. In practice, often the electrokinetic charge @ek is measured, which results from both (de)protonation of amino acid residues and specific ion adsorption. This situation is depicted schematically in fig. 3.4. Figure 3.5 shows Q0(pH) and gek(pH) for RNase. The charge associated with specific adsorption of ions other than proteins is given by ( 9 e k - Q 0 ) . The difference between the point of zero charge (p.z.c.) and isoelectric point (i.e.p.) is a measure of the extent of specific adsorption. The protein charge is neutralized by countercharge. The electrical part of the Gibbs energy of a given charge-distribution can be evaluated as the reversible, isothermal, and isobaric work of charging the system. This is given by
Gel= J 9=0
y/'dQ'
[3.2.10]
PROTEIN ADSORPTION
3.9
where y/' is the electrostatic potential at the surface and Q' is the charge of the protein molecule during the charging process. To solve [3.2.10] a model for the charge distribution is required that relates y/ to Q . Some of such models are presented in chapter II.3. Away from the isoelectric point, where the protein surface contains a significant excess of negatively or positively charged groups, the charge may be thought of as being smeared out and the Gouy-Stern model may be applied. At, and near the isoelectric point, a model accounting for discrete charge effects is required to yield realistic results. Assuming a smeared-out distribution, and complete penetration without restraint of counterions in the expanded, unfolded polypeptide, the Donnan model may be a reasonable choice. The difference between the Gibbs energies for the compact and unfolded conformations, determines the stability of the one conformation relative to the other. It may be clear that, in the isoelectric region, a homogeneous charge distribution resists unfolding, whereas the opposite is true away from the isoelectric point. Values for the difference in Gibbs energies between the globular and the unfolded states are typically in the range of a few tens of k j per mole of protein, the effect becoming smaller at higher ionic strength. If ions reside in the interior of the protein they do so in pairs, and do not contribute significantly to the potential. In the unfolded state, such ion pairs are disrupted. Disruption of ion pairs is electrostatically unfavourable, but this effect is more or less compensated by hydration of the isolated ionic groups. For this reason, together with the fact that protein molecules usually contain no more than a few ion pairs, ion pair formation does not contribute much to the (de)stabilization of a compact protein structure. Lifshits-Van der Waals interaction Lifshits-Van der Waals interactions arise from forces between fixed and/or induced dipoles. For isolated molecules they decay steeply with the separation distance between the interacting dipoles, scaling as r"6 . Folding of the polypeptide chain into a compact protein involves the loss of Lifshits-Van der Waals interactions between units of the polypeptide and water molecules but, at the same time, such interactions are formed within the protein molecule and between water molecules. This is the Archimedes principle, discussed in sec. 1.4.6b. Quantitatively, the overall effect is not well understood for proteins. Because of the relatively high packing density in globular proteins, Lifshits-Van der Waals interactions are likely to promote a compact structure. The difference between the Hamaker constant of a protein and pure water points in the same direction. However, because of the opposing contributions of disruption and the creation of contacts, the net contributions of Lifshits-Van der Waals interaction to the stabilization of the protein structure is relatively small. Hydrogen bonds In the fully hydrated unfolded state, peptide units and some other moieties in the
3.10
PROTEIN ADSORPTION
amino acid side groups interact with water molecules through hydrogen bonds. When the protein folds into a compact structure, many of these bonds are broken and, instead, intramolecular hydrogen bonds are created in the protein molecule, and hydrogen bonds between water molecules. Peptide units dominate intramolecular hydrogen bonding, and determine the unique and fixed structures of helices and (3 sheets. Although hydrogen bonding is essential for maintaining ordered structures in the protein's Interior, its net contribution to the stabilization of the protein conformation is not particularly clear. Model studies1 2) suggest that peptide-water hydrogen bonds are more favourable than peptide-peptide and water-water hydrogen bonds. This would imply that hydrogen bonding (weakly) favours the unfolded conformation. However, hydrogen bonding between peptide units that, by the action of other factors (e.g., hydrophobic interaction) are forced into the non-aqueous inner parts of the protein, strongly stabilize ordered structures. Bond lengths and angles When the polypeptide chain folds into a tightly packed structure the bond lengths and angles may be more or less distorted. This could oppose stabilization of the globular protein structure by several kJ per mole31. In summary, the protein structure and structure stability is determined by various interactions inside the protein molecule, between the protein and water, and between the water molecules. These interactions compete with each other. As a result, the one structure is usually only some tens of kJ per mole more stable than the other. Hydrophobic interactions and the conformational freedom of the polypeptide chain play the leading parts. Both are mainly of entropic nature. Hence, the resulting protein structure is the outcome of an entropy battle between the polypeptide chain and water. Because of this marginal thermodynamic stability, none of the other factors influencing protein folding is unimportant. Consequently, even subtle changes in the environment of the protein, e.g. pH, ionic strength, ionic specificity, temperature, or additives, may cause structural transitions in the protein. In view of this, it is not surprising that most proteins, under most conditions, change their structure when adsorbing from solutions onto an interface. 3.3 Adsorption of globular proteins from aqueous solution onto (solid) surfaces The overall protein adsorption process is schematically depicted in fig. 3.6. Several steps or stages, indicated by the numbers in fig. 3.6, may be distinguished:
11
G.C. Kresheck, I.M. Klotz, Biochemistry 8 (1969) 8. W. Norde, Adv. Colloid Interface Sci. 25 (1986) 267. 31 M. Levitt, Biochemistry 17 (1978) 4277. 21
PROTEIN ADSORPTION
3.11
Figure 3.6. Schematic presentation of the protein adsorption process. Further explanation is given in the text. (1) transport from the bulk solution Into the subsurface region from where it is (2) attached at the surface. After initial adsorption the protein may (3 and 3*, etc.) relax at the sorbent surface. Relaxation may involve a fast surface-induced conformational change, but a slow spreading to optimize protein-sorbent interactions is also a very general phenomenon. Protein molecules may desorb from the sorbent surface (4, 4*, 4**). Obviously, the rate-constant of desorption is the smaller when the adsorbed protein molecule has reached a greater extent of relaxation. After desorption, the protein molecules (back in solution), may or may not (completely) regain their original native conformation. If not, the solution will eventually contain structurally perturbed protein molecules that may re-adsorb with an affinity different from the native ones. In this chapter we shall discuss all these aspects of the overall adsorption process in some detail, with special attention to adsorption-related conformational changes. In sec. 3.9 the chapter will conclude with some remarks on sorbent surface modification in order to adapt protein adsorption for practical applications. 3.3a Adsorption kinetics The rate of adsorption comprises two consecutive steps, (a) transport of the molecules to the interface and, (b), attachment at the sorbent surface. These steps will be considered separately and combined thereafter to derive an equation for the overall rate of adsorption. Transport towards the sorbent surface. The basic mechanisms of transport are diffusion and convection. The latter may be by laminar or turbulent flow. When the protein adsorbs, the subsurface region of the
3.12
PROTEIN ADSORPTION
solution becomes depleted and a protein concentration gradient is built up. This causes a flux J of protein molecules from the bulk solution towards the subsurface region. Under steady state conditions the flux is given as J = ktr(cb-ca)
[3.3.1]
where k^. is a transport rate constant, which depends on the transport mechanism and the dimensions and orientation of the protein molecules, and c b and cs are the protein concentrations in the bulk solution and the subsurface zone, respectively. In static systems, where the transport is by diffusion only, k^ may be approximated by [D/nt)l/2 in which D is the diffusion coefficient of the protein in bulk solution and t is the time1'. Clearly, the flux reaches a maximum value when cs = 0, that is, when attachment at the interface is much faster than transport to the subsurface region. This is the case when there is no activation energy for attachment, and in the initial stage of the adsorption process when there is no limitation of surface area available for adsorption.
Figure 3.7. Identification of ka and fcd .
Exchange at the interface. A simple situation is depicted in fig. 3.7. The protein molecules attach at, and detach from, the sorbent surfaces. This gives two fluxes from the subsurface region to the surface: one forward, dr/dt\+ , and one backward, dr/dt\_ , where the adsorbed amount r may be expressed in mass per unit of sorbent area. The net adsorption rate is given by, d/7dt = d/7dt| + -d/7dt|_
[3.3.21
The forward flux scales as cs and is proportional to the fraction (1 - 0] of sorbent surface area that is unoccupied with adsorbed protein. Hence, d/7dt| + =k a (l-0)c s
[3.3.3]
in which fca is the attachment rate constant. For the simple case that the adsorbing
11
For a general discussion and derivation, see sec. I.6.5e.
PROTEIN ADSORPTION
3.13
molecules do not change their sizes and shapes, as in fig. 3.7, the degree of surface occupancy 9 is defined as 77 .T 6 ^, where T"681 is the adsorbed amount when the sorbent surface is saturated with protein. For adsorption-induced conformational changes, as happens with most proteins and other (bio)polymers, the relationship between F and 6 is more complicated, and will be discussed later. The value of fca is lowered by any barrier for attachment, e.g., electrostatic repulsion, or hydration effects. A repulsive barrier may be created or reduced by the pre-adsorbed protein molecules and, hence, ka may vary with 0 and, therefore, with time. For the backward flux we can write
^j
= *d*
[3.3.4]
where kd is the detachment rate constant. In the course of the adsorption process, 6 increases and eventually a dynamic equilibrium (steady state) is reached, for which cb = cs = c
, the equilibrium concentration in solution. The equilibrium is character-
ized by fca(l-0)ceq =
fcd0
[3.3.5]
Assuming that d 77 d t_ is exclusively determined by kd and 6, the rate of adsorption off-equilibrium is still given by ka (1 - 0)c , so that ^
= ka(l-0)(cs-ceq)
With dT/dt
[3.3.6]
= J . Combining [3.3.1] and [3.3.6] gives
^ -
;b'Cef
dt
1
|
[3.3.7,
1
Polymers, including proteins, usually adsorb with a high affinity for the sorbent surface, characterized by an extremely high value of the adsorption equilibrium constant K (= ka/kd). For physical reasons, ka cannot attain extremely high values, and hence fcd must be very small. The reason for the almost infinitely low polymer desorption rate has been discussed in chapter II.5. High affinity adsorption isotherms (see fig. II.2.24) have the property that, below adsorption saturation, c is extremely low (usually below detectability). When reaching saturation, which is reflected by the (semi-)plateau in the isotherm, c (6) increases steeply and approaches c b . It follows that, upon approaching saturation, dF/dt drops strongly. This is reflected by a sharp transition in the curve for F(t) often observed for (bio)polymers. A typical example is given in fig. 3.8. Away from saturation, where c
= 0 , [3.3.7] may be rewritten as
3.14
PROTEIN ADSORPTION
Figure 3.8. Typical example of polymer adsorption kinetics.
c
b/rmax_
dO/dt
1 ,
ku
1
[3.3.8]
fca(l-0)
If fcjj. « ka(l-ff), dO/dt or, for that matter, dF/dt are determined by transport from the bulk to the subsurface region, independent of 0. This permits direct derivation of k^ from the initial linear part of the isotherm. If kb » ka (1 - 9), a condition that is probable when there is a barrier for attachment at the surface or when the surface is covered to some extent, dF/dt is determined by the rate of attachment, and hence, depends on 8. The value of ka(6) may be derived from F(t), using approximation [3.3.8]. So far, the discussion has been based on the oversimplified model shown in fig. 3.7. However, it is a rule rather than an exception that biopolymers, including proteins, adapt their conformations as a result of relaxation at the interface. This phenomenon is illustrated in fig. 3.9, where the native conformation is denoted, the 'N state' and the adapted, perturbed conformation the 'P state'. The rate-constant for relaxation is kT and those for desorption from the N state and P state, kd N and kd p . It follows that
d#M ^ f =
fc
a,Ncsa-8N-0P)-
kdN0N - kT9N
[3.3.9]
and d(9p
[3.3.10]
Figure 3.9. Adsorption and desorption of protein molecules followed by transition from the native (N) state to the perturbed (P) state. After desorption of a molecule in the P state the molecule may, or may not, return to the N state.
PROTEIN ADSORPTION
3.15
In the steady state, where dF/dt = 0 , k a V ^ N - ^ e q =fcd,N^N+
fc
d,P^P
I3-3-11'
In general, kdN *kdp. Now, contrary to the simple situation of fig. 3.7, the rate of desorption is not a unique function of the desorption rate constants but it also depends on 6P / 0^ . This ratio changes in the course of the adsorption process. As a result of surface relaxation it is expected that fcd p < kd N . The smaller the kd p / fcdN ratio, the larger the fraction of perturbed molecules in the steady state is. If kd p approaches zero, the adsorbed layer eventually consists of molecules that are all perturbed. It goes without saying, that when adsorption induces conformational changes in the protein, the expression for dF/dt is much more complicated than the one given in [3.3.7]. The adsorption kinetics are even more complicated when the increase in area per protein molecule ('footprint') due to spreading at the sorbent surface is taken into account. Let the molecular area of N state molecules be a N , and of P state molecules a p , with a p / aN = a r > 1. The maximum number of molecules in the N state per unit sorbent surface area is No , and in the P state it is JV. It follows that JV0 = aTN, and N o a N = 1. Further, 0N = nN / JV0 and 0V =np/N0, where n is the number of protein molecules in the adsorbed state. Hence, dft, -jf =
fc
a,Ncs(1-^N-aA)-'cd,N%x/(ar-%.ep)
I 3 - 3 - 12 !
in which /(a r ,# N ,i9 p ) takes into account the fact that the area-enlargement involved in the N —» P transition reduces the probability for other molecules to undergo the transition later. When a r = 1, _f (ar, #N, £?p) = 1 and it decreases for larger values of a r , the more so, the higher is the surface occupancy, {0N + 0p). Similarly, ^
= kr0Nx/(ar,0N,0p)-kdp0p
[3.3.13]
The steady state evolving from this model is given by k 0 a,NV- N
-aA)ceq
=k
d,fA
+fc
d,P0P
[3.3.14]
which is equivalent to [3.3.11] because (1-# N -ar8p) and (1-# N -&p) in the respective equations are the covered fractions of the sorbent surface. Both 0N and 6>p are expressed in number of adsorbed molecules per fixed number of sites per unit surface area. It means that (#N + 0p) is proportional to the adsorbed mass per unit surface area, F. This model explains the remarkable phenomenon of transient adsorption of polymers which has sometimes been reported. If fcdp 1 and the rates of attachment and spreading are of comparable magnitude, (#N + 0p) and, hence, F would pass through a maximum in the course of the adsorption process.
3.16
PROTEIN ADSORPTION
Figure 3.10. Sketch of excluded area for the deposition of molecules according to the random sequential mode.
Most theories for (blo)polymer adsorption, including proteins, start from the models presented above. Other models proposed to describe the kinetics of (bio)polymer adsorption include the random sequential adsorption (RSA) model11. In this model it is assumed that the molecules arrive randomly at the sorbent surface and that they stick where they hit. A subsequently arriving (spherical) molecule cannot be accommodated within the dashed areas around pre-adsorbed molecules, as illustrated in fig. 3.10. Clearly, the fraction 0 of the surface which is available for adsorption is a function of the degree of coverage, 0, of the surface by the adsorbate. For hard sphere molecules, 0=rmR2 (where n is the number of molecules per unit surface area, and R is the radius of the sphere. The RSA theory produces the following functionality
^=«p{ 2 -^ + i^ + i I n a - f l ) + -}
[3 3 151
--
which can be developed into 0(0) = l-46> + ^ 3 -6^+2.4243 ft + ....
[3.3.16]
K
Figure 3.11. Surface area available for the adsorption of spherical molecules in a random sequential mode. The drawn curve obeys [3.3.15], the other ones [3.3.16] with two, three or four terms of the expansion. 11
P. Schaaf, J.C. Voegel, and B. Senger, Ann. Phys. 23 (1998) 1.
PROTEIN ADSORPTION
3.17
The third term of the r.h.s. of [3.3.16] accounts for the overlap of the dashed areas in fig. 3.10, the fourth term for the double overlap, etc. Figure 3.11 shows curves for 0(9). In the kinetics according to the RSA model, the uncovered surface area (1 - 9) is replaced by
1), and the degree of spreading will be affected by the protein flux, because a neighbouring site may already be occupied by a newly arriving molecule before the previously adsorbed molecule is given the time to relax. This results in less spreading, which is reflected in a higher value of r 6 ^ with increasing flux. The adsorbed layer may become heterogeneous with respect to the conformational states of the protein population. Molecules arriving at an early stage find sufficient area available for spreading, whereas this is much less the case for the molecules that arrive when the surface is already crowded.
Figure 3.13. Relaxation of protein molecules, adsorbed on silica. Surface area occupied per adsorbed IgG molecule as a function of the time required to fill the surface. (Based on data of M.G.E.G. Bremer, Immu.noglobu.lin Adsorption on Modified Surfaces, PhD thesis, Wageningen University, The Netherlands (2001).)
When the surface area occupied per adsorbed molecule (derived from / ^ a t ) is plotted vs. Tj (calculated from the flux), a curve is given, as shown in fig. 3.13. For Tt = 0, spreading is completely inhibited and the corresponding area may be compared with the dimensions of the native molecule. Extrapolation to constant r 8 ^ , where full relaxation is reached, allows estimation of the relaxation time. Thus, relaxation times in the range of tens- to thousands- of seconds are inferred for globular proteins. There is strong experimental evidence11 that at interfaces, as in solution, the conformational change of globular protein molecules is a distinctly co-operative, rather than a gradual process. It implies that the intermediate part of the curve in fig. 3.13 reflects the co-existence of native (N) and spread (P) molecules at the interface. Assuming a two state transition N —> P , the rate of spreading can be expressed as,
11
T. Zoungrana, G.H. Findenegg, and W. Norde, J. Colloid Interface Sci., 190 (1997) 437.
PROTEIN ADSORPTION ^
= -(cscN
3.19 [3.3.18]
where ks , the spreading rate constant, is determined by the activation Gibbs energy AG^ of the N —> P transition as
in which h is Planck's constant. Fitting the experimental curve to [3.3.18] yields estimates for ks and, hence, AG^ . For globular proteins, typical values for ks are in the range of lO^-lO" 1 s" 1 , and for AG+ some tens of kT . 3.3c Driving forces for protein adsorption In this section, the main contributions to protein adsorption on a smooth, rigid surface will be discussed. These contributions originate from (a) redistribution of charged groups (ions) when the electrical double layers around the protein molecules and the sorbent surface overlap, (b) dispersion forces between the protein and the sorbent material, (c) changes in the hydration of the sorbent surface and the protein, and (d) structural rearrangements in the protein molecules. Although these interactions are discussed separately, they are by no means independent of each other. Their actions could be synergistic or antagonistic. Redistribution of charged groups. As a rule the surfaces of the protein molecules and the sorbent are electrically charged, and surrounded by counterions and co-ions, together constituting the countercharge that neutralizes the surface charge. The surface charge and the countercharge together form an electrical double layer. Models for the electrical double layer are discussed in chapter II.3 and their interaction in chapter IV.3. There, it has been explained that the Gibbs energy Gcd required to invoke a charge distribution can be calculated as the isothermal, isobaric reversible work o° G c d = J y/° A 33 and A22 > A33 , and hence -A12(3) > 0 , so that AadsGdi < 0 , which implies attraction between 1 and 2. The Hamaker constant for interaction across water is ca. 6.5xlO~ 21 J for globular proteins, (l-3)xlO~ 19 J for metals and (4-12) xlCT21 J for synthetic polymers1'21. Based on these data, and applying [3.3.24] and [3.3.22], for a spherical protein molecule of radius 3 nm at a distance of 0.1 nm from the sorbent surface, AadsGdi at room temperature amounts to 6-1IRT per mol at a metal surface, and to 1-4 RT at a polymeric surface. Clearly, these estimates are semi-quantitative. Obtaining more accurate estimates requires more detailed knowledge of the system's parameters, such as Hamaker constants, sizes and shapes of the protein molecule and the sorbent material. Hydration changes Polar molecules attract water molecules, mainly through hydrogen bonding. They compete successfully with hydrogen bonds between the water molecules, so they are readily soluble in water. Apolar groups do not offer the possibility of a favourable interaction with water and therefore they are expelled from an aqueous environment. This is the hydrophobic effect. The water molecules at an interface of apolar material are strongly oriented so as to form as many hydrogen bonds as possible to other water molecules, as none can be formed with the apolar material. This reduces the entropy of the water adjacent to apolar compounds. 11
S. Nir, Progr. Surface Set 8 (1977) 1.
21
J . Visser, Adv. Colloid Interface Sci. 3 ( 1 9 7 2 ) 3 3 1 .
3.22
PROTEIN ADSORPTION
Protein molecules contain both polar and apolar groups. As discussed in sec. 3.2, for globular proteins in aqueous solution the apolar parts tend to be hidden inside the molecule, whereas the exterior is mainly polar. Other interactions and/or geometrical constraints interfere with these tendencies. Hence, although it is mainly apolar, the heart of the protein contains polar groups as well, and apolar groups occupy parts of the aqueous periphery of the molecule. However, water-soluble non-aggregating protein molecules do not have pronounced apolar patches at their surfaces. The surfaces of (model) synthetic sorbent materials are usually less complex than protein surfaces, but natural surfaces may also be rather heterogeneous. When the surfaces of the protein molecules and the sorbent are predominantly polar it is likely that some hydration water is retained between the sorbent surface and the adsorbed protein layer. However, if (one of) the surfaces are (is) apolar, dehydration would stimulate protein adsorption. The contribution from changes in hydration to the Gibbs energy of adsorption may be estimated from the partitioning of model compounds between water and a nonaqueous medium. It is thus estimated that dehydration of an apolar surface lowers the Gibbs energy by 10-20 mJ m~2 . In the case of a protein of 30,000 Da and an adsorbed mass of 1 mg m~2, this corresponds, at room temperature, to AadsGh d r ranging between -120 RT and -240 RT per mole of protein. It evidently indicates that apolar dehydration outweighs the contributions from overlapping electrical double layers and Van der Waals forces. Rearrangements of the protein structure When a protein molecule makes intimate contact with the sorbent surface, on one side of the molecule the aqueous environment is replaced by the sorbent material. As a consequence, intramolecular hydrophobic interaction becomes less important as a structure-stabilizing factor; i.e., apolar parts that were buried in the interior of the dissolved molecule may become exposed to the sorbent surface without making contact with water. Because hydrophobic interaction between amino acid side groups in the protein's interior support the formation of secondary structures, such as a-helices and |3 -sheets, a reduction of this interaction destabilizes such structures. A reduction in the a-helix and/or |J-sheet- content is, indeed, expected to occur only if peptide units released from these structures can form hydrogen-bonds with the sorbent surface, as is the case for oxides (e.g., glass, silica and metal oxides), or with surfaces retaining residual water molecules at the sorbent surface. Then, the decrease in secondary structure may lead to an increased conformational entropy of the protein. This may favour the adsorption process by tens of RT per mole of protein. If, in the non-aqueous protein-sorbent contact region, it is not possible for the peptide units to form hydrogen bonds with the sorbent surface, as is the case for hydrophobic surfaces, adsorption may induce the formation of extra intramolecular peptide-peptide hydrogen bonds, thereby promoting the formation of a-helices and/or p -sheets. Thus, whether adsorp-
PROTEIN ADSORPTION
3.23
tion on a hydrophobic surface results in an increased or decreased order in protein structure, depends on the subtle balance between energetic and entropic interactions. To summarize, it is concluded that protein-sorbent interaction is a complex phenomenon, comprising various subprocesses operating simultaneously. For example, hydrophobic interaction between the protein and the surface requires close contact between the two, which may be optimized by structural rearrangements in the protein. This may involve increased or decreased flexibility along the polypeptide chain. At hydrophilic surfaces, increased conformational freedom is expected in adsorbed protein molecules. Based on these considerations we arrive at the following 'rules of thumb'. Because of favourable dehydration, essentially all proteins adsorb on hydrophobic surfaces, even under electrostatically adverse conditions. With respect to hydrophilic surfaces, distinction may be made between proteins having a strong internal coherence ('hard' proteins) and those with a weak internal coherence ('soft' proteins). The hard proteins adsorb only if they are electrically attracted, whereas in the soft proteins the surfaceinduced conformational entropy gain is large enough to cause adsorption on a hydrophilic, electrostatically repelling surface. 3.4 Adsorption-related structural changes in proteins While searching for explanations of the clotting of blood, in the 1950s Leo Vroman discovered that water-repellent surfaces became water-wettable after contact with plasma. Later he discovered that some, but not all, of the proteins involved in blood clotting were adsorbed to hydrophobic surfaces. Together, these observations allowed him to propose that, 'globular proteins which can open easily will do so when they see a hydrophobic surface, and will turn themselves inside out to paste themselves with their fatty hearts onto that surface'11. About twenty years later Norde performed an extensive thermodynamic analysis of the protein adsorption process. This study confirmed that human plasma albumin changes its conformation when it adsorbs at polystyrene surfaces2'. This adsorption process was entropically driven, and part of the entropy gain originated from the conformational changes in the proteins31. Indications that proteins might change their conformation when they adsorb to air/ water and oil/water interfaces have been reported since the early part of last century. Information on the conformational state of proteins at the air/water interface was obtained by studying interfacial pressures and tensions using, for example, the Langmuir trough (III.3.3) and the Wilhelmy plate (III. 1.8a) techniques. Reviews cover-
11
L. Vroman, Blood, The Natural History Press (1968) 63. W. Norde, J. Lyklema, J. Colloid Interface Sci. 66 (1978) 257, 266. 31 W. Norde, J. Lyklema, J. Colloid Interface Sci. 71 (1979) 350. 21
3.24
PROTEIN ADSORPTION
ing this early work have been written by Chessman and Davies11, and Cumper and Alexander2'. For proteins adsorbed at the solid/liquid interface, information on the surface area per molecule can be derived from adsorption isotherms. However, without insight into the surface pressure or the geometry of the adsorbed protein layer, interpretation of plateau values in terms of conformational changes of adsorbed proteins becomes rather presumptuous. In one study, using infrared spectroscopy to analyze the bound fraction, the observed conformational changes of several proteins were so small that the authors felt it necessary to report that, 'caution must be exercised in interpreting the available surface area per adsorbed molecule as an indication of changes in conformation upon adsorption' 3). Generally, structural properties of proteins are either described by the energy that is required to unfold their natural state or by the relative location of all atoms in the folded structure. The folded structure is discussed in sec. 3.2. In the 1970s some experiments were performed to measure directly one of the structural properties of proteins in the adsorbed state. Structural elements of adsorbed proteins were investigated by using spectroscopic techniques, such as circular dichroism (CD), nuclear magnetic resonance (NMR), electron spin resonance (ESR), and fluorescence spectroscopy, while microcalorimetry was used to obtain thermodynamic information on the adsorption process. Reviews of this early work have often reported moderate changes in the protein structure, although the measurements were not sensitive enough to establish the type and extent of the adsorption-induced conformational changes4 5). From the late 1970's sophisticated experimental evidence became available that proved the extent of adsorption-induced structural changes to range from none to substantial denaturation of the proteins upon adsorption. A few decades of gathering experimental evidence has led to a number of general trends that relate the various physical and chemical properties of the protein/sorbent system with adsorption-induced structural changes. Nevertheless, a comprehensive theory with predictive value that describes the extent and rate of adsorption-induced structural changes in the proteins remains a challenge for the future. 3.4a How to measure structural properties of adsorbed proteins The development in experimental techniques has made it feasible to probe directly the conformational features of proteins in the adsorbed state. Not only have new and/or more sensitive instruments been developed, but more sorbent surfaces have also become available that interfere less with the measurement techniques. 11
D.F. Chessman, J.T. Davies, Adv. Protein Chem., 9 (1954) 439. C.W.N. Cumper, A.E. Alexander, Rev. Pure Appi Chem.. 1 (1951) 121. 31 B.W. Morrissey, R.T. Stromberg, J. Colloid Interface Set 46 (1974) 152. 41 W. Norde, Adhesion and Adsorption of Polymers, part B (1980) Plenum Publishing Corp. New York. 51 M.E. Soderquist, A.G. Walton, J. Colloid Interface Set. 75 (1980) 386. 21
PROTEIN ADSORPTION
3.25
Most of the techniques for measuring structural properties of proteins at interfaces are based on experimental methods that provide information on the structural properties of proteins in solution. For example, CD is a successful technique for measuring the secondary structure of proteins in aqueous surroundings. In 1974, McMillin and Walton constructed a cell that contained a stack of quartz disks to provide an optically transparent cell with enough protein layers to generate a reasonable signal11. However, difficulties with scattering and the alignment of the quartz plates made the researchers return to solution studies of desorbed proteins21. Finally, the technique regained much interest after it was shown that a suspension of small, nanometer sized colloidal particles covered with proteins generated high quality CD spectra3 . The most important approaches for determining structural properties of adsorbed proteins are based on spectroscopic methods that rely on the interaction of biopolymers with electromagnetic radiation (1.7.3), using techniques such as fluorescence-, NMR, infrared, and CD spectroscopy. Infrared and CD spectroscopy are mainly used to quantify the average amount of a -helical and (3 -sheet structures. As carbonyl groups on the protein backbone are involved In specific H-bonds in secondary structure elements, the wavelength at which infrared radiation is absorbed is slightly shifted. Circular dichroism occurs because secondary structure elements in proteins absorb left- and right- hand circularly polarized light slightly differently in the UV and far UV region. Infrared spectroscopy has a higher sensitivity for measuring changes In P -sheet structures, while CD has a higher sensitivity for quantifying a-helical structures. A major advantage of CD over infrared spectroscopy is that the spectroscopic signal is not affected by the presence of water. Fluorescence spectroscopy can generate information on the local surroundings and the solvent accessibility of fluorescent groups such as tryptophan residues or haem groups in proteins. Furthermore, fluorescence anisotropy and time-resolved fluorescence decay measurements provide information on the rotational mobility of adsorbed proteins, whereas fluorescence recovery after photo bleaching (FRAP) can be used to measure the lateral mobility. To date, applications of NMR in protein adsorption studies are rare51. Its use is limited to relatively small proteins for which complete 'H, 13C, and 15N assignments of the native structure are known. NMR spectroscopy can also be used in combination with hydrogen-deuterium exchange (HDX) experiments to probe the solvent accessibility of exchangeable hydrogens in the protein structure, because the NMR signal disappears when protein hydrogens are exchanged with deuterium atoms from solution. This type of HDX can be used to probe parts of the protein structure that are in contact with the sorbent
11
C.R. McMillin, A.G. Walton, J. Colloid Interface Set 48 (1974) 345. A.G. Walton, M.E. Soderquist, Croat. Chem. Acta 53 (1980) 363. 31 A. Kondo, S. Oku, and K. Higashitani, J. Colloid Interface Set 143 (1991) 214. 41 W. Norde, J.P. Favier, Colloids Surf. 64 (1992) 87. 51 K.Wuthrich, Acta Crystallogr. D51 (1995) 249. 21
3.26
PROTEIN ADSORPTION
surface and are thus less accessible for the deuterated solvent1'21. To characterize adsorbed proteins in terms of the energy or enthalpy involved in the stabilization of the protein structure, one can employ differential scanning calorimetry (DSC) and hydrogen-deuterium exchange in combination with mass spectrometry (HDX-MS). In DSC one measures the difference in specific heat as a function of the temperature between a sample with and without proteins. With such experiments one can derive the enthalpy and temperature of the transition between a folded and unfolded, or otherwise perturbed, conformation of proteins. In HDX-MS, one monitors the exchange between amide hydrogens on the protein backbone and protons in solution. When amide hydrogens are involved in hydrogen bonding in the secondary structure elements, their exchange rates decrease considerably. The time scale of such an exchange process is usually much larger than that used to study the solvent accessibility of exchangeable hydrogens located on the outside of the protein structure. By measuring the deuterium incorporation as a function of time, the protein is exposed to a deuterated solvent. With mass spectrometry, information is revealed on the folding/ unfolding equilibrium. This folding/unfolding equilibrium, in turn, is related to the Gibbs free energy that stabilizes the folded conformation of a protein. Compared to the spectroscopic techniques, DSC and HDX-MS monitor more general aspects of the conformational state of (adsorbed) biomolecules. Additionally, both techniques also provide information on the heterogeneity in the structural populations. Besides these techniques, most of the methods that can be used to characterize surfaces and adsorbed monolayers (III.3.7) also yield indirect information on the conformational state of proteins. For example, neutron reflectivity, ellipsometry, and
Figure 3.14. Atomic Force Microscopy images (0.75 um x 0.7 um ) of human plasma fibronectin measured in the intermittent-contact mode (Courtesy of M. Bergkvist). On the lefthand side, fibronectin is adsorbed at a hydrophilic mica surface, and on the right-hand side on a hydrophobic surface created by silanisation of silica with dichlorodimethylsilane11. 11 21
D.G. Gorcnstein, Z. Santago-Rivcra, and D.A. Keire, Polym. Mater. Sci. Eng. 71 (1994) 261. H. Nagadome, K. Kawano, and Y. Terada, FEES Letters 317 (1993) 128.
PROTEIN ADSORPTION
3.27
reflectometry can be used to study the average density and thickness of an adsorbed protein film, while imaging techniques such as scanning force microscopy (SFM) can be used to generate information on the dimensions that a protein assumes in the adsorbed state. By way of illustration, in fig. 3.14 an AFM image is given for the adsorption of fibronectin on two different surfaces. Fibronectin is a large flexible protein that is stabilized by intermolecular ionic interactions to form a compact structure. Upon altering the solution conditions the structure can revert to a more expanded state, thereby exposing previously hidden domains, for example cell-binding sites. Upon adsorption to hydrophilic surfaces, fibronectin often adapts an elongated structure, whereas on hydrophobic surfaces the compact structure predominates. The difference in morphology is explained by the interaction between fibronectin and the negatively charged groups on the hydrophilic surface that interferes with the stabilizing interaction between the protein domains. Finally, adsorption-induced conformational changes, as well as the influence of the sorbent surface on conformational transitions in the protein molecules, may be inferred from proton titration studies2'3'41. By way of example we present some results for the adsorption of a-lactalbumin (aLA ). To that end in fig. 3.15, proton titration curves for aLA in solution and adsorbed on negatively and positively charged polystyrene particles are presented. The curves for the dissolved and the adsorbed states differ over a wide pH-range. The shifts upon adsorption reflect the influence of the electric field caused by the charges on the polystyrene surface on the pK-values of the titratable groups of the aLA molecules. Figure 3.16 shows the titration behaviour in the pH-region where the carboxyl groups are protonated. The curve for aLA in solution comprises a region reflecting the translation from the holo- to the apo-state. The non-electric Gibbs energy, A holo ^ apo G°, associated with that transition can be
Figure 3.15. Proton titration curve for a -lactalbumin in solution ( ) and on negatively (A) and positively (o) charged polystyrene particles. T = 25°C; electrolyte, 0.05 M KC1. (Redrawn from W. Norde, F. Galisteo Gonzalez, and C.A. Haynes, Polym. Adv. Technol. 6 (1995) 518).
11
M. Bergkvist, J. Carlsson and S. Oscarsson, J. Biomed. Mater. Res. (2002). C.A. Haynes, E. Sliwinsky, and W. Norde, J. Colloid Interface Set 164(1994) 394. 31 F. Galisteo, W. Norde, Colloids Surfaces B4 (1995) 389. 4 ' W. Norde, F. Galsiteo Gonzalez, and C.A. Haynes, Polymers for Adv. Technol. 6 (1995) 518. 21
3.28
PROTEIN ADSORPTION
Figure 3.16. Titration of carboxyl groups in a -lactalbumin. The drawn curve refers to the protein in aqueous solution, the upper clashed curve to the protein, adsorbed on negatively charged polystyrene particles. T = 25°C; electrolyte, 0.05 M KC1. (Redrawn from W. Norde, F. Galisteo Gonzalez, and C.A. Haynes, loc. cit.)
derived according to l A
G
2 303
holo^apo ° = -
NmaxRT\[pK(a.po)~pKihol0))da
[3.4.1]
0
with pK = pH + log[ — - 1
[3.4.2]
where K is the dissociation constant of the carboxyl groups, iVmax the total number of carboxyl groups in the oeLA molecule, and a their degree of dissociation. Hence, Aj^^ a p o G° for aLA in solution may be evaluated from the shaded area in fig. 3.16. It is estimated to be ca. -3 RT per mole of aLA . Proton titration calorimetry data, presented in fig. 3.17, reveal an endothermic holo to apo-state transition of ca. + 18 RT per mole of protein. It follows that, at room temperature, the transition is
Figure 3.17. Isothermal proton titration enthalpy of a -lactalbumin in solution (•) and adsorbed on negatively charged polystyrene particles (A ). T= 25°C ; electrolyte, 0.05 M KC1. (Redrawn from W. Norde, F. Galisteo Gonzalez, and C.A. Haynes, loc. cit.)
PROTEIN ADSORPTION
3.29
driven by an entropy gain of about 0.17 kJ K"1 mol" 1 . Remarkably, the structural transition is virtually absent when aLA is adsorbed on the polystyrene surface. It demonstrates that the structural properties of aLA are very sensitive to the local environment. In this special case of aLA it implies that adsorption causes (a) spontaneous transition to the apo-state, (b), spontaneous transition to a new conformation from which the apo-state is no longer accessible, or, (c), stabilization of the native structure such that the apo-state is no longer favoured at low pH. All the above-mentioned techniques require specific characteristics of the type of interface that can be studied. For spectroscopic techniques, these solid surfaces should not interfere with the spectroscopic signal of interest. Furthermore, for adsorption studies a selection mechanism is required to obtain experimental signals that originate only from the adsorbed proteins. Besides this selectivity, the signal sensitivity can also be a problem, as going from proteins in solutions to proteins adsorbed at a twodimensional surface means that the possibilities for concentrating the sample are limited. Because of these requirements, studies of the conformational state of proteins are restricted to a limited number of available sorbent surfaces. In fluorescence and infrared spectroscopy one can selectively excite adsorbed proteins by using an evanescent wave that is created by total internal reflection of a lightbeam within an optically transparent material [1.7.10.a]. The evanescent wave penetrates the solution to a depth that is roughly half the wavelength of the radiation used. Two prominent techniques based on this principle are total internal reflection fluorescence (TIRF) (see sees. II.2.5c and III.3.7c, iv) and attenuated total reflection-fourier transform infrared (ATR-FTIR) spectroscopy (sec. II.2.5.C). Another advantage of using total reflection is that the polarization of the evanescent wave can be controlled easily, allowing investigation of the spatial orientation of adsorbed molecules. Techniques that utilize evanescent waves require optically inert and smooth surfaces that resemble Fresnel surfaces. For example, silica interfaces as present in oxidized silicon wafers, silicon crystals, polished glasses, and quartz in fluorescence or infrared studies. These silica surfaces can be modified easily by silanization. Self-assembled monolayers (SAM), or Langmuir-Blodgett films (sec. III.3.7a) can be used to obtain a wide range of surface characteristics. The smoothness of most of these above mentioned surfaces also makes them suitable for studies with microscopic techniques such as SFM. For infrared spectroscopy, adsorption can also be studied on polymeric material that is generally spin- or dip-coated on silicon, germanium, or zinc selenide crystals. Another way to apply common biochemical techniques which are used to characterize protein structures in solution, and are suitable for proteins in the adsorbed state is to utilize nanometer-sized colloidal particles. Because of the small size, the lightscattering is very low. At the same time, the small diameter of the particle provides a relative large surface area per sample volume, which benefits the sensitivity in measurements, using for example CD, DSC and NMR spectroscopy. Ultrafine particles of teflon, polystyrene, silica, and titanium oxide have been used successfully.
3.30
PROTEIN ADSORPTION
3.4b General trends To perform their biochemical functions, many proteins fold in specific well-defined and highly ordered structures. The folded conformations of globular proteins reach atomic packing densities, expressed in volume fractions, between 0.7 and 0.8. In such a compact structure the rotational mobility along the polypeptide chain is severely restricted, which implies that it has a low conformational entropy. This low entropy is balanced by hydrophobic and Coulomb interactions, the possibility of forming intramolecular hydrogen bonding in secondary structure elements, and interactions between fixed and induced dipoles. The net result is often a compact folded protein that is marginally stable, with stabilization Gibbs energies in the order of a few- to a few tens of kJ per molar quantity, see sec. 3.2. One should note that for a protein with a stabilization Gibbs energy of 15 kJ/mol, one out of 500 is unfolded, and that folding and unfolding processes often occur within fractions of seconds. Thus, although the structures of globular proteins are described as compact and well-defined, this structure is not static. The protein structure is readily disrupted if, for example, electrostatic interactions change by varying the pH in solution. In the same way, protein structures can be affected by adding organic solvents that affect the Van der Waals interactions and the solvation or by adding molecules that compete for the interactions, such as the chaotropics sodium dodecyl sulphate (SDS) and guanidine hydrochloride. Strength of Interaction: Hydrophobic interactions As mentioned before, the same type of interactions that drive the adsorption of proteins to interfaces are the ones determining the structure of proteins. Logically, a stronger interaction between a protein and a sorbent surface is expected to increase the probability and the extent of adsorption-induced structural changes. For example, when proteins adsorb to hydrophobic surfaces, dehydration of the hydrophobic surfaces is the main driving force and, at the same time, hydrophobic interaction is an important force that keeps the polypeptide chains tightly folded. In the adsorbed state the protein/sorbent interaction can be increased by having parts of the hydrophobic core of the protein exposed to the hydrophobic sorbent, leaving more hydrophilic parts of the protein in a more flexible, and thus entropically favourable conformation. Many studies have proved that structural changes are more substantial when globular proteins adsorb to hydrophobic surfaces compared to hydrophilic surfaces. For example, early TIRF studies demonstrated that the conformation of fibronectin is not affected when it is adsorbed onto hydrophilic silica but it is affected when the surface becomes more hydrophobic11.
11
J.D Andrade, V.L. Hlady, and R.A. van Wagencn, Pure Appl. Chem. 56 (1984) 1345.
PROTEIN ADSORPTION
3.31
Strength of interaction: Electrostatic interactions A tendency similar to that above has been observed with respect to electrostatic interactions, i.e., the stronger the attraction, the larger is the extent of structural changes1 . A similar observation was made by Larsericsdotter et al., who used DSC to show that, for the adsorption of lysozyme and ribonuclease-A at hydrophilic surfaces, strong electrostatic attraction leads to high affinities whereby the protein adsorption is accompanied by a reduction in the denaturation enthalpy. Shielding the electrostatic interaction by increasing the ionic strength reduces the affinity, and the adsorptioninduced reduction of the denaturation enthalpy is diminished . Another electrostatic contribution that can affect the protein structure in the adsorbed state is the net charge density in the interfacial layer (see also sec. 3.3c). In solution, most proteins unfold when the net charge density increases, for example at low or high pH values or at low ionic strengths. If proteins adsorb to charged surfaces the interplay between charged groups, including co-adsorbed low molecular weight ions, will affect the balance between the electrostatic interactions within the protein. It is generally observed that the maximum amount of protein is adsorbed when the solution pH is close to the isoelectric point of the protein. A study in which the amount of secondary structure of monoclonal antibodies adsorbed at silica surfaces was monitored while the electrostatic interactions involved were systematically varied, revealed a clear correlation between the reduction in adsorbed amounts when the pH is shifted away from the isoelectric point and the reduction in secondary structure3'. Structural stability of proteins Conformational changes in proteins not only result from the strong interaction between a protein and a surface but can also be seen as driving forces for adsorption41. This was inferred from experiments in which protein adsorption was monitored on hydrophilic surfaces under conditions where the proteins were electrostatically repelled by the sorbent. Under these conditions, the only driving force for adsorption is generated by a total increase of the entropy of the adsorbed proteins. It was also observed that only proteins having a relatively low structural stability adsorb under these otherwise adverse adsorption conditions. This led in sec. 3.3 to the introduction of the notions of 'soft' and 'hard' proteins. Proteins that adsorb to hydrophilic surfaces under electrostatic repulsive conditions are classified as soft proteins whereas proteins that do not adsorb under those conditions are considered hard proteins . Elegant studies on the conformation of mutants and the wild-types of T4 lysozyme'.6) 11
A. Kondo, F. Murakami, and K. Higashitani, Biotech. Bioeng. 40 (1992) 889. H. Larsericsdotter, S. Oscarsson, and J. Buijs, J. Colloid Interface Set 237 (2001) 98. 31 J. Buijs, J.W.Th Lichtenbelt and W. Norde, Langmuir 12 (1996) 1605. 4) W. Norde, J. Lyklema, J. Colloid Interface Sci. 71 (1979) 350. 51 W. Norde, J. Lyklema, J. Biomater. Sci. Polymer 2 (1991) 183. 61 P. Billsten, M. Wahlgren, T. Arnebrant, J. McGuire and H. Elwing, J. Colloid Interface Sci. 175 (1995) 77. 21
3.32
PROTEIN ADSORPTION
and carbonic anhydrase II11 adsorbed on nanometer-sized silica particles revealed that the extent of structural changes was inversely related to their stabilization Gibbs energies in solution. The nature of structural changes, however, was different between the two proteins. T4 lysozyme lost part of its secondary structure upon adsorption, while for carbonic anhydrase II the secondary structure is unaffected, but the protein adopts a more open conformation which is thermally destabilized compared to the protein in solution. The examples above prove that protein stability is an important factor that determines the extent of structural changes. At the same time, no clear relationship between the stability of a protein in solution and the extent of structural changes has been found. Apparently, the structural flexibility of a protein needs to be defined in more detail before such a relationship with predictive value can arise. It is repeated that one should distinguish between adsorption-induced changes that result from strong interactions between the protein and the sorbent surface, and structural changes that result from an adsorption process in which structural rearrangements are prerequisites for adsorption to take place. Surface coverage A number of CD studies, using nanometer-sized silica particles as the sorbent surface, demonstrated that the extent of structural changes was larger when the surface coverage was less 2 ' 3 '. Apparently, the adsorbed proteins need space for structural changes to take place. This phenomenon was also observed for protein adsorption at the air-water interface, where the biological activity of an adsorbed protein monolayer was stabilized by increasing the surface pressure 4 '. A theoretical approach to this phenomenon has been given in equation [3.3.12]. From this equation it is clear that the extent of adsorptioninduced conformational changes in proteins is a function of the adsorption kinetics, i.e., the faster a surface is covered with proteins, the lower is the probability that the proteins will undergo structural rearrangements. The strength of interaction also plays an important role, as it has been observed that the adsorbed amount F passes through a maximum in the course of adsorption, because adsorbed proteins spread at the expense of the total number of proteins attached to a surface. Time-dependency of the structure of adsorbed proteins In general protein adsorption is irreversible, implying that, as a rule, the interactions between a substrate and proteins increase with contact times. It is generally 11
P. Billsten, U. Carlsson, B.H. Jonsson, G. Olofsson, F. Hook and H. Elwing, Langmuir 15 (1999) 6395. 21 A. Kondo, S. Oku and K. Higashitani, J. Colloid Interface Set 143 (1991) 214. 31 W. Norde, J.P. Favier, Colloids Surf. 64 (1992) 87. 41 A. Tronin, T. Dubrovsky, S. Dubrovskaya, G. Radicchi and C. Nicolini, Langmuir 12 (1996) 3272.
PROTEIN ADSORPTION
3.33
accepted that when proteins adsorb they do so tenaciously, because of the large number of segment contacts that can be established between them and the surface. In turn, conformational changes in the protein structure are generally thought to be responsible for increasing the number of contact points, leading to protein adsorption process models that do not allow for conformationally changed proteins to desorb spontaneously1 2). These models are supported by the often observed reduction in protein activity at longer contact-times with the substrate, and by several studies that show that proteins slowly lose secondary structure in the adsorbed state. Unfortunately, little is known about the factors that determine the overall rate of conformational changes. Adsorption isotherms of IgG and fibronectin on hydrophilic and hydrophobic substrates, obtained either by direct addition or successive addition of proteins, clearly demonstrated that conformational changes occur more rapidly on hydrophobic surfaces31. Another observation is that structurally less stable and soft proteins not only have a higher tendency to undergo structural changes upon adsorption but the structural changes occur also more readily41. Moreover, structurally less stable proteins that adsorb with high affinity to surfaces show a higher irreversibility in adsorption and, for those proteins that do desorb, the extent of refolding is lower than observed for structurally stable proteins5'6'71. These observations indicate that rearrangements in the proteins' structure occur faster under adsorption conditions that lead to a large extent of structural changes, as intuitively expected. Besides the slow structural rearrangement, a rather rapid change in the structure is also observed when the first proteins adsorb . This effect can be explained by the lack of steric hindrance for spreading on the surface. See sec. 3.3 Recent stopped-flow fluorescence spectroscopy and anisotropy measurements9 revealed clearly distinct stages for protein structural rearrangements. Specifically, the conformational changes of a -lactalbumin adsorbed on polystyrene particles occur with rate constants of 50 s"1, 8 s' 1 and 0.001 s" 1 . Following the time-dependence of the (3 -sheet content of adsorbed antibodies to silica surfaces, using FTIR spectroscopy, clearly showed that both the relatively low amounts of structure for proteins that were adsorbed in the initial phase and the slow reduction in the [3 -sheet content after longer adsorption times (see fig. 3.18)10).
11
M.E. Soderquist, A.G. Walton, J. Colloid Interface Sci. 75 (1980) 386. I. Lundstrom, H. Elwing, J. Colloid Interface Sci. 136 (1990) 68. 31 U. Jonsson, I. Lundstrom and I. Ronnberg, J. Colloid Interface Sci. 117 (1987) 127. 41 B. Singla, V. Krisdhasima and J. McGuire, J. Colloid Interface Sci. 182 (1996) 292. 51 A. Kondo, J. Mihara, J. Colloid Interface Sci. 177 (1996) 214. 61 W. Norde, J.P Favier, Colloids Surf. 64 (1992) 87. 71 W. Norde, C.E. Giacomelli, Macromolecular Symposia 145 (1999) 125. 81 A. Tronin, T. Dubrovsky, S. Dubrovskaya, G. Radicchi and C. Nicolini, Langmuir 12 (1996) 3272. 91 M.F.M. Engel, C.P.M. van Mierlo, and A.J.W.G. Visser, J. Biol. chew... 277 (2002) 10922. 101 J. Buijs, J.W.Th. Lichtenbelt, and W. Norde, Langmuir 12 (1996) 1605. 21
3.34
PROTEIN ADSORPTION
Figure 3.18. The fraction of amino acid residues in adsorbed antibodies that adopt a (5 -sheet structure (closed circles), and the adsorbed amount (open circles), as a function of the adsorption time. Both the adsorbed amount and the percentage P -sheet structure were obtained with ATR-FTIR. The data presented were obtained when IgG molecules adsorb to a hydrophilic and negatively charged silica surface created by oxidation of a cylindrical crystal made of silicon. The crystal was surrounded by a solution containing 50 jig/ml of a monoclonal IgG with an isoelectric point of 5.8, and 5 mM acetate buffer at pH 5. In the native state, roughly 60% of the amino acids are involved in a p -sheet structure. (Redrawn from J. Buijs et ai., loc. cit.}
Structure of adsorbed globular proteins As might be apparent from the paragraphs above, the final structure of a protein in the adsorbed state is the result of the interplay between many factors. Even if all the interactions between a protein and a surface, including intramolecular interactions, that determine the protein stability, are fully characterized, the problem remains that the structure of the adsorbed protein will depend on the adsorption time and on the interactions with neighbouring proteins. Furthermore, structural alterations can appear on various structural levels. For example, in fig. 3.14 an example is shown where fibronectin is adsorbed in a more elongated structure when it is adsorbed on a negatively charged hydrophilic mica surface, whereas the structure is more compact when adsorbed on a hydrophobic surface. At the same time fig. 3.14 shows that fibronectin only changed its conformation when adsorbed to hydrophobic surfaces. Most probably, the contradiction between these data is based on the differences in structural properties that were probed using different measurement techniques. The first study utilized SFM, which can be used to monitor changes in the tertiary structure, while the second study was performed with TIRF, which is sensitive to local changes involving the relocation of a couple of amino acid residues. An interesting aspect of studies of adsorption-induced changes is that very few
PROTEIN ADSORPTION
3.35
investigators report a complete unfolding of adsorbed proteins. Cases of the absence of structural changes are reported, but they are definitely outnumbered by studies that indicate partial unfolding of globular proteins upon adsorption. At hydrophobic surfaces, some proteins even increase their content of secondary structure elements121 or one type of ordered structure may be converted into another. Both the conversion from a -helix to (3 -sheet structure31 and vice versa 451 have been observed. These results are noteworthy in view of the relatively low stabilization Gibbs energies of the protein structure in solution, where a small disruption in the structure often results in complete unfolding. One should note, however, that most techniques employed to study protein structures at interfaces only monitor average properties. This implies that the results obtained mean either that each protein is partially unfolded to some extent, or that a fraction of the adsorbed molecule is strongly unfolded while another fraction is in its native conformation. Some studies claim that the proteins adopt a well-defined structure similar to the intermediate structures created by local energy minima in the folding pathway of proteins in solution61. Nevertheless, measurements using techniques that provide information on the structural heterogeneity of the protein structure in the adsorbed state, such as DSC and HDX, generally show that structures of adsorbed protein molecules are perturbed differently. Also, with other methods, such as FRAP that is used to monitor the two-dimensional diffusion of adsorbed proteins, it has been observed that one population of BSA molecules, adsorbed to various polymeric materials, is mobile, while another population is immobile. The difference in mobility between populations was ascribed to the distribution of protein conformations, established in the early stage of adsorption71. Even for proteins that show no change in average structure upon adsorption, a more heterogeneous structure can be observed. For example, lysozyme adsorbed to silica surfaces has been subjected to a broad range of techniques to assess its structural properties, such as CD, DSC, TIRF, FTIR, and HDX-MS. These studies revealed that lysozyme does not undergo significant structural alterations when adsorbed to silica in compact monolayers. Nevertheless, the results from DSC, TIRF, and HDX studies indicate that the conformation of lysozyme is rather heterogeneous. This heterogeneity fits well into the models that allow structural rearrangements as long as space is available for the proteins to spread; whereas for proteins that adsorb at a later stage, the spreading is inhibited by spatial restrictions (sec. 3.3b). 11
E.J. Castillo, J.L. Koenig, J.M. Anderson, and J. Lo, Biomater. 5 (1984) 319. M.C.L. Maste, W. Norde, and A.J.W.G. Visser, J. Colloid Interface Set 196 (1997) 224. 31 C.E. Giacomelli, W. Norde, Biomacromolec. 4 (2003) 1719. 41 J. Buijs, W. Norde, and J.W.Th. Lichtenbclt, Langmuir 12 (1996) 1605. 51 A.W.P. Vermeer, C.E. Giacomelli and W. Norde, Biochim. Biophys. Ada 1526 (2001) 61. 61 P. Billsten, U. Carlsson, B.H. Jonsson, G. Olofsson, F. Hook, and H. Elwing, Langmuir 15 (1999) 6395. 71 R.D. Tilton, C.R. Robertson, and A.P. Gast, J. Colloid Interface Set 137 (1990) 192. 21
3.36
PROTEIN ADSORPTION
To illustrate the complexity of adsorption-induced changes in protein structures, an example will now be given of how the structural stability of various segments of myoglobin is affected by adsorption on silica particles. The results were obtained using HDX-MS, a technique that is sensitive to the stability of secondary structure elements in a protein, as the exchange-rate between amide hydrogens in the protein and deuterium atoms in solution is dramatically slowed if the amide hydrogens are involved in hydrogen bonding. In this study, the hydrogen/deuterium exchange process was followed as a function of the exchange time. After the exchange process, myoglobin was cleaved enzymatically, and the deuterium incorporation into four fragments, covering 90% of the sequence, was monitored using mass spectrometry11. Structurally, myoglobin is a 153 residue, tightly folded protein with a haem group that is bound noncovalently in a hydrophobic pocket. Myoglobin contains an extremely stable core, located at the C-terminus and linked to a part of the N terminus, while the centre part of the sequence, surrounding the haem group, is less stable. Upon adsorption to silica, the myoglobin segment located in the middle of the myoglobin sequence, and close to N terminal fragments are destabilized (see fig. 3.19). Although the structural stability of the segment around the haem group did not change upon adsorption, this structure became clearly more heterogeneous. Interestingly, for the N terminal fragment, comprising residues 1-29, two distinct and equally large conformational populations were
Figure 3.19. The structure of myoglobin in solution (left), and adsorbed at silica particles (right). The structural stability is indicated in terms of grey scales and is based on the average folding/unfolding equilibrium of four segments comprising residues 1-29, residues 30-69, residues 70-106, and residues 107-137. The structure is taken from S.R. Hubard, W.A. Hendrickson, D.G. Lambright and S.G. Boxer, J. Mol. Biol. 213 (1990) 215, and the grey scale ranges from 16 kJ/mol (light) to 32 kJ/mol (dark). Upon adsorption, only the structural stabilities of the C- and N-terminal parts are reduced whereas the a -helices close to the haem group are unaffected.
11
J. Buijs, M Ramstrom, M. Danfelter, H. Larsericsdotter, P. Hakansson and S, Oscarsson, J. Colloid Interface Set 263 (2003) 441
PROTEIN ADSORPTION
3.37
observed. One of these populations has a stability similar to that in solution (~ 23 kj/mol) whereas the other population is highly destabilized upon adsorption (—11 kj/mol). From these results it is clear that, even within one protein, the structures of parts are differentially affected by adsorption. Some parts of the protein and a part of the population are highly destabilized upon adsorption whereas other parts are only affected in their structural heterogeneity.
3.5 Adsorbed amount and adsorption reversibility Protein molecules may form numerous contacts with a sorbent surface (as synthetic polymers can). Although data are very limited, there is experimental evidence for such multi-contact adsorption1'. Multiple contacts probably lead to high-affinity adsorption of the whole protein molecule. Plateau-values of the adsorbed amount F corresponding to full coverage of the sorbent surface are reached at a very low protein concentration in solution c and the region in which F depends on c is limited to values very near the /"-axis. Dilution of the sorbate in the bulk phase creates a transient difference in the chemical potential of the sorbate at the interface and that in solution. This chemical potential difference is then eliminated by spontaneous desorption of the sorbate. For high-affinity adsorption, desorption is difficult, if discernible at all, because in the c regime where F is below its plateau value the protein concentration may well be below the detectable limit. Furthermore, when equilibrium is established at such low protein concentrations, where the protein concentration gradient between the subsurface region and the bulk solution is so small that, according to [3.3.1], the transport of protein molecules into the bulk solution is extremely slow. Occasionally, protein adsorption isotherms are reported whose initial rising part deviates from the /"-axis. However, upon dilution, F(c ) rarely (if ever), follows the same path backwards, thereby making the ascending and descending branches of the isotherm distinguishable. As a rule, it is found that dilution only leads to partial desorption, if at all, even when the observation time greatly exceeds the relaxation time of the protein at the sorbent surface2'31. Desorption upon dilution is minimal, especially at hydrophobic surfaces. Such hysteresis indicates a prohibitively high barrier for (further) desorption. The system has two (meta)stable states, one on the ascending branch and the other on the descending one, each being characterized by its local minimum in Gibbs energy. The fact that the adsorption and desorption isotherms represent different metastable states, implies that a physical change has occurred in the system between adsorption and desorption. 11
B.W. Morrissey, R.T. Strombcrg, J. Colloid Interface Set 46 (1974) 152. H.P. Jennissen, in Surface and Interfacial Aspects of Biomedical Polymers, Vol. 2 J.D. Andrade, Ed., Plenum (1985) 295. 31 W. Norde, C.A. Haynes, ACS. Symp. Series 602 (1995) 26.
3.38
PROTEIN ADSORPTION
Despite the irreversible nature generally observed for protein adsorption, many authors interpret their experimental data using theories that are based on reversible thermodynamics. The most common example is the calculation of the Gibbs energy of adsorption, AadsG , by fitting the (ascending) isotherm to the Langmuir equation or variations thereof121. It is, however, questionable whether the adsorption or desorption isotherm should be used for that purpose. Another approach sometimes encountered involves calculation of the Gibbs energy of adhesion, AadhG , using A
adh G = rsp - r™ - rpw
I3-5-1'
where y is the interfacial tension of the interface indicated by the superscripts. AadhG is the reversible work (at constant temperature and pressure) to form a protein (p)/ sorbent (s) interfaces at the expense of sorbent (s)/solution (ix>) and protein (p)/solution (u>) interfaces31. Equation [3.5.1] essentially corresponds to our [III.5.1.1] for the initial spreading tension. For further analysis, see sec. III.5.2; it is noted that the interfacial tensions may change with time. It is not clear how AadhG relates to AadsG, since the latter quantity is determined not only by creation and rupture of phase boundaries but also includes other contributions such as those resulting from electrostatic interaction and protein (and sorbent) structural rearrangements. The error involved in treating protein adsorption as a reversible process may be approximated by calculating the entropy production due to the irreversibility (reflected by the hysteresis) of the process. In a closed system, the entropy change associated with any process can be written as AS = ASe + ASj
[3.5.2]
where ASe is the reversible entropy exchange between the system and its surroundings, and ASj is the internally produced entropy. For a reversible process, AS{ = 0, but for an irreversible process ASj > 0 . According to Everett41, AadsSj can be calculated from the hysteresis loop, as the closed loop integral between the ascending and descending branches of the adsorption isotherm A
adsSi=RJ ^ f d l n c p
[3.5.3]
where r* is the adsorbed amount at the upper closure point of the hysteresis loop. The integral of [3.5.3] may be evaluated as the shaded area indicated in fig. 3.20. Regrettably F(c ) is not usually known in the very dilute region (i.e., at very negative
11
T. Mizutani, J.L. Brash, Chem. Phartn. Ball. 36 (1988) 2711. E.C. Moreno, M. Krcsak and D.I. Hay, Biofouling 4 (1991) 3. 31 C.J. van Oss, Biofouling 4 (1991) 25. 4) D.H. Everett, Trans. Faraday Soc. 50 (1954) 1077. 21
PROTEIN ADSORPTION
3.39
Figure 3.20. Adsorption ( —t) and desorption ( D transition at pH of maximal stability.
PROTEIN ADSORPTION
3.47
Figure 3.24. Two-dimensional equations-of-state at the air-water interface for adsorbed monolayers of five proteins and PVA (M = 42.000 ). The concentrations, c, of the solutions from which the monolayers were made (given in g d m " ' ) are indicated. Discussion in the text (courtesy, J. Benjamins). number. The thermodynamic stability given refers to thermal denaturatlon, but conformatlonal alterations upon adsorption probably follow a different path, so the conformatlonal stability may also be different. Figure 3.24 contains n{F) curves for five different proteins, including the uncharged polymer poly(vlnyl alcohol) for the sake of comparison. In these experiments it was measured by the Wilhelmy plate technique, and r was obtained ellipsometrically on the same interface.
3.48
PROTEIN ADSORPTION
The first notable feature is that data points obtained at different values of c all collapse to one 'mastercurve'; surface pressures are fully determined by F, and not by the concentration in solution needed to obtain these surface concentrations. Stated differently, for these adsorbed monolayers the n{F) relationship is unique for each protein and so we may ask whether it makes sense to speak of a 2D equation of state. The second observation is that, for all five proteins, the first 0.7-1.1 mg m~2adsorbed do not contribute measurably to the surface pressure. This is a typical protein feature, which is not exhibited by the random and heterodisperse polymer PVA. For spread monolayers, the TI(F) curves are rather different (results not shown) but the horizontal initial parts persist. These parts coincide with the initial steep rise in the isotherm, F(c). In this part of the isotherm the adsorbing molecules have the entire surface at their disposal; they can complete any conformational adjustment during the time it takes to carry out an ellipsometry measurement (ca. 10 min.). If one is interested in the occurrence, and rates, of re-conformation on much shorter time scales, dynamic measurements have to be carried out. Indeed, such processes have been observed with relaxation times of a few seconds up to a few minutes. There is some correspondence between the length of the very low n range; for more rigid molecules, it is longer. Lysozyme being the top, lower for the albumins, still lower for the structurally relatively 'weak' caseins down to virtually zero for the fully structureless and heterodisperse PVA. Semiquantitative computations with the ideal 2D equation of state (n = RTF, with F in moles m" 2 ) show that, in these initial parts, K is indeed very low; the pressure starts to build up when this layer is completed and lateral interaction sets in. This lowpressure part was also studied optically for lysozyme by Ericson et al.1'. For proteins like the albumins the plateau adsorption passes through a maximum around the i.e.p., similar to that at SL interfaces (fig. 3.22), and for the same reason. The different rates of unfolding are also reflected in the dynamic surface tension. In fig. 3.25, this tension is given as a function of the relative expansion rate of a surface,
Figure 3.25. Dynamic surface tensions obtained by the overflowing cylinder technique for 0.25 gdm~ 3 solutions of p-casein, [3lactoglobulin, ovalbumin and lysozyme. Temperature 25°C. (Redrawn from Van Kalsbeek and Prins, loc. clt.).
11
J.S. Ericson, S. Sundaram, and K.J. Stebe, Langmuir 16 (2000) 5072.
PROTEIN ADSORPTION
3.49
Figure 3.26. Apparent interfacial shear viscosities at the water-n-tetradecane interface. A, myosin; B, lysozyme; C, K-casein; D, gelatin; E, Na-caseinate; F, a s -casein; G, (5casein; H, P-lactoglobulin and I, a-lactalbumin. (Redrawn from E. Dickinson, J. Chem. Soc. Faraday Trans. 94 (1998) 1657.)
as measured by the overflowing cylinder technique described in sec. III.3.7e and illustrated in fig. III.3.73. These data have been obtained by van Kalsbeek and Prins1'. With increasing expansion rate, all the curves tend towards the surface tension of water but the 'weaker' casein can unfold far more rapidly than lysozyme, and hence take segments to the interface at a rate that is more compatible with the rate of expansion. Hence, with this protein the dynamic tension remains below the static tension over the entire range studied. Long term interfacial viscosity changes are shown in fig. 3.26. Plotted are the apparent surface shear viscosities at the water-n-tetradecane interface. Adsorption takes place from the aqueous phase, which contains 10~3 weight % of the protein at neutral pH. The method for obtaining the apparent shear viscosity was not reported, but two conclusions can be drawn. First, 77 continues to increase over tens of hours, i.e., long after adsorption has been completed. This increase must be caused by structural changes at the interface, the lateral interaction between the adsorbed protein molecules being an important characteristic. Secondly, there are dramatic differences between the relatively rigid globular proteins and the rather random caseins, the former group displaying values that are higher by several orders of magnitude. One interpretation is that the rigid spheres can acquire a much higher packing density, perhaps with some cross-linking. An additional feature is that, in several cases, the proteins can form 2D gels, which may exhibit rupture: when that occurs, a kind of slip viscosity is measured. The corresponding interfacial dilational properties exhibit the same trend with respect to the protein specificity but the
H.K.A.I, van Kalsbeek, A. Prins, in Food Emulsions and Foams, Interfaces, Interactions and Stability. E. Dickinson and J.M Rodriquez Patino, Eds., Royal Soc. Chem (London ) (1999), 91.
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PROTEIN ADSORPTION
difference between them is less1'21. The inference of these observations is that the adsorbates behave like a 2D gel, with their strength depending on the nature of the protein; several protein molecules unfold to a greater extent at oil-water interfaces than during heat-denaturation in aqueous solution3 . Our last illustration, fig. 3.27, combines at least three important features. It relates the interfacial rheology to the surface pressure, different non-aqueous phases are compared, and the experiments have been carried out conscientiously. The reported rheological characteristic is the interfacial dilational modulus, K£. This quantity can be obtained by several methods, either by an oscillatory technique, using [3.7.1] to obtain Kg', or by a monotonous expansion, yielding Kg directly. The data reported stem from experiments with the dynamic drop tensiometer, described in connection with fig. HI.3.72. They have been compared to those from the barrier-andplate method (essentially a longitudinal wave technique) and were found to be very similar at given n. (For the sake of simplicity we use the symbol Kg ). The matter of the identity of results from different techniques is a separate problem, and is not generally solved. The three different non-aqueous phases are air (as in figs. 3.24 and 3.25), n-tetradecane (as in fig. 3.26), and triacylglycerol, which is a sunflower-seed oil, an important fluid for the food industry, and has useful properties as a solvent. The purity of this oil was improved (e.g., by silica extraction) and verified (by surface tension measurements) to ensure the absence of surface-active admixtures. The monolayers are formed by adsorption. As a result, n and Kg depend on the adsorption time, but for the n{F) relationship there exists a time-independent mastercurve (fig. 3.24). As the moduli also collapse into a protein-specific mastercurve at different solution concentrations, it makes sense to plot K^ as a function of n. Thus, the adsorption time is eliminated as a variable. Another matter is the frequency a> of the measurement. The higher is co, the more elastic is the behaviour, i.e., the more the first term on the r.h.s. of [3.7.1] dominates. The figure only gives data at 0.1 Hz. One would intuitively expect Kg to increase with n, and for low n this is indeed observed. For an ideal monolayer the slope should be unity, but experimental moduli are higher than that. At higher n 's, Kg increases less than linearly, and even diminishes. (3 -Casein exhibits a more capricious behaviour than its more rigid globular counterparts. Generally, the behaviour in triacylglycerol (which may be a better solvent for hydrophobic and/or even hydrophilic parts of the protein molecules) is more unequivocal than for air and tetradecane, in that the curves consist of two linear parts, even for the unruly p-casein. A kind of scaling is suggested, with at least the solvent 11 F.J.G. Boerboom, A.E.A. de Groot-Mostcrt, A. Prins and T. van Vliet, JVeth. Milk Dairy J. 50 (1996) 183. 21 A. Williams, A. Prins, Colloids Surf.. A114 (1996) 267. 31 J. Lefebvre, P. Relkin, in Surface Activity of Proteins. S. Magdassi, Ed., Marcel Dekker (1996), p.181.
PROTEIN ADSORPTION
3.51
Figure 3.27. Modulus as a function of the interfacial pressure for the indicated proteins in three non-aqueous phases. Temperature 25°C, frequency of drop oscillation 0.1 Hz. BSA = bovine serum albumin, BLG = bovine lactoglobulin. (Same source as fig. 3.24.) quality of the protein parts for the oil as one of the parameters. The inference is that the descending branch is caused by reconformation or collapse; it is certainly not a result of desorption. Formation of a second adsorbed layer is also unlikely, because there is no reason why this would reduce Kg . Experiments like those above can suggest ideas for further theoretical and experimental studies. One could think of optical investigations in conjunction with the rheol-
3.52
PROTEIN ADSORPTION
ogical ones which, In turn, may be extended by looking in more detail at the influence of
OJ12).
For reasons other than merely academic, this type of study has enormous practical relevance. Several of the proteins discussed here are milk constituents and are relevant in the preparation of food products: See the examples in chapters 7 and 8, and the book by Dickinson and Rodriguez Patino, mentioned in the General References, sec. 3.10. Other interest stems from interfacial enzymatic reactions, whose time dependence can be followed from surface pressure and surface rheology studies. By way of illustration we refer to studies from the group of Nitsch on lipase31 and catalase41 an investigation by de Roos and Walstra51 on the loss of activity of the enzymes lysozyme and bovine chymosin owing to adsorption on emulsion droplets, and a review by Panaiotov and Verger61. There is no need to state that this is a challenging area where significant developments may be expected. 3.8 Competitive protein adsorption and exchange between the adsorbed and dissolved states Protein adsorption is generally highly irreversible with respect to variation of the concentration in solution. Nevertheless, proteins can easily be desorbed by surfaceactive molecules that compete for the interaction sites, such as surfactants or other protein species. By studying protein adsorption from plasma, Vroman and co-workers observed that the adsorbed protein layer was rather dynamic. They observed that more abundant and smaller proteins adsorb first, because the transport to the sorbent is quicker. Proteins that have a higher affinity for the sorbent surface then slowly replace these adsorbed proteins7'81. For plasma proteins adsorbing to hydrophilic surfaces, HSA adsorbs first and is then followed by IgG, fibrinogen, fibronectin, Hageman factor, and high-molecular weight kininogen. This cascade of competitive protein adsorption is generally called the Vroman effect. As surfaces with an abundance of albumin tend to be less thrombogenic than those coated with fibrinogen or IgG, controlling the protein Also see, J. Benjamins, E.H. Lucassen-Reijnders, Surface Dilational Rheology of Proteins Adsorbed at Air-Water and Oil-Water Interface in Proteins at Liquid Interfaces 7 (1998) 34184. 21 M.A. Bos, T. van Vliet, Interfacial Rheological Properties of Adsorbent Protein Layers and Surfactants: a Review,. Adv. Colloid Interface Sci 91 (2001) 43-71. 31
W. Nitsch, R. Maksymiw, and H. Erdmann, J. Colloid Interface Sci.. 141 (1991) 322 R. Maksymiw, W. Nitsch, J. Colloid Interface Sci. 147 (1991) 67. 51 A.L. de Roos, P. Walstra, Colloids Surf. B6 (1996) 201. 61 I. Panaiotov, R. Verger, Enzymatic Reactions at Interfaces; Interfacial and Temporal Organization of Enzymatic Lipolysis in Physical Chemistry of Biological Interfaces, A. Baszkin, W. Norde, Eds. (see sec 3.10) ch. 11. 71 W.G. Pitt, K. Park, and S.L. Cooper, J. Colloid Interface Sci. I l l (1986) 343. 81 L. Vroman, A.L. Adams, J. Colloid Interface Sci. I l l (1986) 3 9 1 . 41
PROTEIN ADSORPTION
3.53
adsorption cascade from blood proteins is a crucial aspect of producing nonthrombogenic biomaterials. Logically, most research dealing with competitive protein adsorption has long been focused on the above-mentioned proteins to a variety of surfaces 1 ' 2 ' 34 '. As a general trend, the displacement of proteins is strongly related to their affinity for the interface. For example, human serum albumin (HSA) adsorbed to hydrophilic silica can be partly replaced by fibrinogen, whereas HSA adsorbed at hydrophobic methylated silica surfaces prevent any displacement or further adsorption of fibrinogen or IgG. A similar result was obtained when trying to replace fi -casein and fragments thereof with (3-lactoglobulin. If (}-casein is adsorbed to a methylated silica surface, no further adsorption of, or replacement by, (5 -lactoglobulin occurs. However, when the hydrophobic C-terminal half of p -casein is cut off, (3 -lactoglobulin easily replaces the hydrophilic, N-terminal half of P -casein, with adsorption kinetics similar to those for (5-lactoglobulin adsorption to a bare methylated silica surface. Thus, strong hydrophobic interactions, originating from a hydrophobic substrate or a hydrophobic protein surface, diminish the displacement of adsorbed proteins by proteins from solution. As illustrated in fig. 3.6, a requirement of adsorption reversibility is that not only can the molecules attach to and detach from the surface, but detachment should lead to their original structure. The extent of structural perturbation of adsorbed protein molecules depends on various parameters such as the hydrophobicity of the sorbent surface, the structural stability of the protein, the charge contrast between the protein and the sorbent surface and, not least, on the degree of coverage of the sorbent by the protein (see sec. 3.4). Accordingly, the structure of the exchanged protein molecules and, hence, the reversibility of the adsorption process, may be affected by the same variables. Unfortunately, very little attention has been given to this issue so far. Only a few papers have considered protein refolding after exchange from a (solid) surface. Below, some trends emerging from the few systems studied, are presented. They deal with the hard protein, lysozyme and the soft protein, serum albumin, exchanged at hydrophobic and hydrophilic colloidal particles. Samples of exchanged protein were obtained by incubating an excess of protein in a colloidal dispersion for a period of about 16 hours. As reported for various systems, 56 ' 71 after 16 hours essentially all protein molecules have been on and off the sorbent surface. The supernatant solutions may contain different populations of protein molecules with respect to the number of 11
A. Baszkin, MM. Boissonnade, Am. Chem. Soc. Symp. Sen 602 (1995) 209. B.K. Lok, Y.L. Chang, and C.R. Robertson, J. Colloid Interface Sci. 91 (1983) 2104. 31 M. Malmsten, B. Lassen, Colloids Surf. B4 (1995) 173. 41 T. Nylander, N.M. Wahlgren, J. Colloid Interface Sci. 73 (1994) 151. 51 V. Ball, P. Schaaf, and J.C. Voegel, in Surfactant Science Series 75. M. Malmsten, Ed., Marcel Dekker (1998) p. 453. 61 J.L. Brash, Q.M. Samak, J. Colloid Interface Sci. 65 (1978) 495. 71 J.C. Voegel, N. de Baillon, and A. Schmitt, Colloids Surf. 16 (1985) 289. 21
3.54
PROTEIN ADSORPTION
Figure 3.28. CD spectra (left) and DSC thermograms (right) of native BSA (drawn curve) and BSA exchanged from polystyrene surfaces (dashed). Aqueous solution, 25°C, pH 7. (Redrawn from W. Norde, C.E. Giacommelli, J. Biotechn. 79 (2000) 259.) times they have been exchanged at the surface. As they could not be separated, the experimental data are averaged over these populations. Changes In structural properties of the exchanged protein are probed by monitoring the thermal stability, and the secondary structure. By way of example, fig. 3.28 shows CD spectra and DSC thermograms for BSA in solution, before adsorption and after release from polystyrene surfaces. The homomolecular exchange of BSA at polystyrene clearly provokes a change in the secondary structure. The shifts in the CD spectra indicate the formation of (3-sheet structure at the expense of an a-helix. The structural alteration is most pronounced when exchanged with a lower adsorbed amount, corresponding to a lower protein concentration in solution. As discussed in sec. 3.3b, adsorption from a low proteinconcentration solution allows more time for adsorbed molecules to relax at the sorbent surface before neighbouring patches are occupied by protein as well. Hence, the degree of spreading, i.e., the structural perturbation, is higher at lower protein concentration, and this is reflected in the exchanged molecules. The DSC data are in line with the CD results. The thermogram of the exchanged BSA molecules deviates from that of native BSA, the more so the smaller is the adsorbed amount. Exchanged BSA is more thermostable and the heat-induced transitions occur over a wider temperature range. A broader transition region could well be caused by a heterogeneous protein population with molecules of different thermostabilities. Similar results have been reported for BSA exchanged at other hydrophobic sur-
PROTEIN ADSORPTION
3.55
faces, i.e., those of silver iodide11, and Teflon21. Formation of (3-sheet structures is often associated with intermolecular aggregation. Aggregation between exchanged BSA molecules is indeed observed, and intermolecular hydrogen bonding invoking aggregation through pi -sheet formation3'4' may cause the increased thermostability. In contrast with the hydrophobic sorbent surfaces, mentioned above, homomolecular exchange at hydrophilic silica surfaces neither leads to a modification in the secondary structure of BSA, nor to a change in the thermal stability, at any degree of surface coverage. Still, in the adsorbed state the BSA molecules have different structural characteristics, but upon release from the hydrophilic surface the protein molecules fully regain their original native structures '. Lysozyme, a hard protein, recovers its native conformation after being exchanged, 2)
irrespective of the hydrophobicity of the sorbent surface . Thus, if from the limited number of experimental data, a trend may be inferred, it would be the following: a less stable protein conformation, a more hydrophobic sorbent surface, and adsorption from protein solutions of lower concentrations, promote conformational changes that, at least partly, persist after desorption by a homomolecular exchange process. Consequently, for a given protein, to avoid irreversibility and loss of biological activity associated with interfacial exchange, a hydrophilic sorbent and a high degree of surface coverage should be selected. 3.9 Tuning protein adsorption for practical applications In various applications it is desired that proteins should be in the adsorbed state. For example, in emulsions, foams and other dispersions, adsorbed proteins may be used to stabilize the dispersed particles against coalescence and, possibly, disproportionation. For more information, the reader is referred to chapter 8. In other applications, the adsorbed proteins have to be biologically active. This requirement holds, e.g., for immobilized enzymes in bioreactors and biosensors, immunoproteins in ELISA devices and other diagnostic test kits, and for proteinaceous farmacons in drug targeting systems. As a rule, in order to retain biological activity, the structural integrity of the protein should not be perturbed too much upon binding at the surface. In other cases, where surfaces are brought into contact with protein-containing fluids, the adsorption of proteins at these interfaces should be avoided as much as possible. Adsorption of proteins from (biological) fluids is generally considered to be the first event in the biofouling process. Subsequently, bacterial and/or other biological cells (e.g., blood platelets, erythrocytes) deposit on the adsorbed protein layer. Adsorption-induced conformational changes in the protein molecules usually enhance the 11
T. Vermonden, C.E. Giacomelli and W. Norde, Langmuir 17 (2001) 3734. W. Norde, C.E. Giacomelli, Macromol. Symp. 145 (1999) 125. 31 V.J.C. Lin, J.L. Koenig, Biopolymers 15 (1976) 203. 41 R.J. Jakobsen, F.M. Wasacz, Appl. Spectrosc. 44 (1990) 1478. 21
3.56
PROTEIN ADSORPTION
interaction with the cells. After deposition, microbial cells multiply, forming so-called biofilms. Adhesion of blood platelets at surfaces of cardiovascular implant materials may lead to thrombus formation. Biofouling causes great problems in areas as diverse as biomedicine (implants, catheters, artificial kidneys, contact lenses, teeth, and dental restoratives, etc.), food processing (heat exchangers, separation membranes, etc.) and the marine environment (ship hulls, desalination units, etc.). Knowledge of the mechanism of protein adsorption provides a few clues to control the process, for example by adapting the charge and hydrophobicity of the sorbent surface and the protein molecules, and by selecting environmental conditions such as pH, ionic strength, or temperature. However, practical applications often do not allow much freedom of choice. The composition of a natural fluid is a pre-set condition, and only the surface properties of a (synthetic) material contacting the fluid can be chosen to some extent. Mutatis mutandis, the same is true for immobilized enzymes and immunoproteins in bioreactors and bio- and immunosensors. Moreover, most natural fluids contain a mixture of proteins. Selection of a combination of surface properties with respect to, e.g., charge and hydrophobicity may involve a low adsorption affinity for one protein but a high adsorption affinity for another. A generic approach to influence the magnitude of the interaction between a protein molecule (and also other macromolecules and particles) and a sorbent surface is to manipulate both the long- and short-range interaction forces by grafting soluble polymers or oligomers onto the sorbent surface. Thus, the application of oligomers of ethylene oxide (EO) on polystyrene surfaces leads to the retention of the enzymatic activity of adsorbed a-chymotrypsin, whereas this activity is lost in the absence of such pre-adsorbed oligomers. The short EO chains prevent the enzymes' making intimate contact with the polystyrene surface, without hampering adsorption. As a result, the stress exerted by the sorbent surface on the protein molecule is less, so that the protein's structural integrity, and hence its biological functioning, is less perturbed, as shown in fig. 3.29. Another interesting example is the steering effect of pre-adsorbed polyethylene-oxide (PEO) molecules on the orientation of consecutively adsorbed IgG molecules. IgG molecules are anisotropic, and by realizing proper spacing between the adsorbed PEO molecules the IgG molecules can be forced into the desired orientation at the sorbent surface, i.e., with their antigen binding sites exposed to the solution in which antigens have to be detected. According to this sieving principle, the immunological activity per molecule of IgG adsorbed on a polystyrene surface could be doubled11. By far the greatest part of the recent research on modifying surfaces by grafting
" M . G . E . G . Bremer, Immunoglobulin Adsorption on Modified Surfaces, Wageningen University, the Netherlands, ch. 7 (2001).
PhD Thesis,
PROTEIN ADSORPTION
3.57
Figure 3.29. Temperature dependency of the specific activity of a-chymotrypsin in solution (o), adsorbed on polystyrene (A) and on polystyrene covered with octaethyloxide chains (•). pH = 7.1. (Redrawn from W. Norde and T. Zoungrana, Biotechnol. Appl. Biochem. 28 (1998) 133.)
soluble polymers aims at the prevention of protein adsorption and/or adhesion of biological cells". Because the natural habitat of proteins and biological cells is an aqueous medium the polymers used must be well-soluble in water. In most cases, PEO is used. Sometimes the use of polysaccharides, e.g., dextrans, is reported. The efficacy of the grafted polymers in reducing protein adsorption depends primarily on two characteristics of the polymer layer: (i) the grafting density and, (ii) the extension Into the solution. Despite controversy In the literature data, some trends emerge. As expected, protein adsorption decreases with increasing grafting density of the polymer. Also, as a rule, protein repellency increases with increasing length of the grafted polymer chains. At a grafting density where the separation distance between neighbouring polymer molecules is smaller than twice the radius (of gyration) of the polymer molecule, the grafted polymer chains have to stretch out into the solution. The polymer layer is said to attain a 'brush' conformation. The brush conformation determines the efficacy of protein repulsion. More specifically a few more trends may be mentioned. In the case of a not-too-thick polymer layer and relatively large protein molecules, long range dispersion forces may cause accumulation of protein molecules at the outer edge of the polymer brush. Furthermore, a higher brush density is required to resist adsorption of
11 E.P.K. Currie, W. Norde, and M.A. Cohen Stuart, Adv. Colloid Interface Sci. 100-102 (2003) 205.
3.58
PROTEIN ADSORPTION
Figure 3.30. The influence of the adsorption of BSA by the PEO grafting density and chain length: 700, 445 and - - 148 EO monomers. (Redrawn from ".)
smaller protein molecules. Currie et al.11 reported an even more complex interaction between proteins, i.e., bovine serum albumin (BSA), and PEO brushes. The results of that study are shown in fig. 3.30. At relatively low grafting densities long PEO chains in a brush stimulate BSA adsorption. However, with increasing grafting densities, the adsorption gradually decreases. This result can only be explained by assuming an attractive interaction between the PEO chains and the protein molecules which, in some unknown way, is determined by a combined effect of the length of the PEO chains and the grafting density. These results are supported by data on protein-polymer brush interaction forces, obtained by Norde and Gage21 and by Leckband's group3'41. They report an activation energy up to a few tens of kT for protein (i.e., streptavidin) molecules to penetrate into a PEO brush. However, when by applying a compressive load the activation energy barrier is surpassed, PEO-streptavidin contacts are stabilized by 1-2 kT. It seems that steric and osmotic forces are involved in rejecting proteins from polymer-brushed surfaces, but more subtle interactions such as the conformationdependent hydration of the EO units may be decisive with respect to whether the PEO's layer is protein resistant or not51. Theories describing these phenomena are currently under development. 3.10 General references Physical Chemistry of Biological Interfaces, A. Baszkin and W. Norde, Eds., Marcel Dekker (2000).
11 E.P.K. Currie, J. van der Gucht, O.V. Borisov, and M.A. Cohen Stuart, Pure Appl. Chem. 71 (1999) 1227. 21 W. Norde, D. Gage, Langmuir,20 (2004) 4162. 31 N.V. Efremova, S.R. Sheth, and D.E. Leckband, Langmuir 17 (2001) 7628. 41 S.R. Sheth, N.V. Efremova, and D.E. Leckband, J. Phys. Chem. B104 (2000) 7652. 51 M. Morra, Poly(ethylene-oxide) Coated Surfaces in Water in Biomaterials Surface Science, M. Morra, Ed., John Wiley (2001) ch. 12.
PROTEIN ADSORPTION
3.59
J.P. Brash, P.W. Wojciechowski, Interfacial Phenomena and Bioproducts, Marcel Dekker (1996). (Includes various applications of proteins at interfaces.) Colloidal Biomolecules, Biomaterials and Biomedical Applications, Surfactant Science Series 116, A. Elaissari, Ed., Marcel Dekker (2003). T.E. Creighton, Proteins: Structures and Molecular Properties, 2nd ed., W.H. Freeman (1993). (Textbook) Food Emulsions and Foams, Interfaces, Interactions and Stability, E. Dickinson and J.M. Rodriguez Patino, Eds., Roy. Soc. Chem. (London) (1999). (Role of proteins in stabilizing emulsions and foams, dynamics of proteins at fluid interfaces.) E. Dickinson, Adsorbed Protein Layers at Fluid Interfaces: Interactions, Structure and Surface Rheology, in Colloids Surf. B15 (1999) 161-176. (Review, includes rheology and competition with surfactants.) Food Colloids, E. Dickinson, Ed., Curr. Opin. Colloid Interface Sci. 8 (2003) 346421. (Update, contains various aspects of proteins at interfaces.) C.A. Haynes, W. Norde, Coilloids Surfaces B2 (1994) 517. (Review, emphasizing thermodynamics of protein adsorption.) V.N. Izmailova, G.P. Yampolskaya and Z.D. Tulovskaya, Development of Rebinder's Concept on the Structure-Mechanical Barrier in the Stability of Dispersions, Stabilized with Proteins, in Coll. Surf. A160 (1999) 89-106. (Paper with a review character; emphasis on the mechanical strength of proteinaceous adsorbates.) Y. Lvov, M. Mohwald, Protein Architecture: Interfacing, Molecular Assemblies and Immobilization Biotechnology, Marcel Dekker (1999). (State of the art on protein immobilization, emphasizing biotechnological and biomedical applications.) F. MacRitchie, Chemistry at Interfaces, Academic Press (1990). (Textbook) F. MacRitchie, Proteins at Interfaces in Adv. Protein Chem. 32, G.B. Anfinsen, J.T. Edsall and F.M. Richards, Eds., Acad. Press (1978) 283-326. (Protein adsorption and its effect on biological activity.) F. MacRitchie, Spread Monolayers of Proteins, Adv. Colloid Interface Sci. 25 (1986) 341. (Review, 122 references.) Biopolymers at Interfaces, 2nd ed., M. Malmsten, Ed., Surfactant Science Series 110 Marcel Dekker (2003). (Contains 30 chapters on principles, techniques and applications.) W. Norde, Adv. Colloid Interface Sci. 25 (1986) 267. (Review, 178 references.)
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4
ASSOCIATION COLLOIDS AND THEIR EQUILIBRIUM MODELLING
Frans Leermakers, Jan Christer Eriksson and Hans Lyklema 4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Introduction
4.2
4.1a
Aqueous solution amphiphiles
4.2
4.1b
Hydrophile-lipophile balance (HLB)
4.6
4.1c
Critical micellization concentration (cm.c.)
4. Id
Surfactant packing parameter
4. le
Phase diagrams
4.7 4.14 4.16
Classical thermodynamics
4.18
4.2a
Thermodynamics of small systems
4.20
4.2b
The mass action model
4.22
4.2c
Implication for molecular modelling
4.24
4.2d
Fluctuations in micelle sizes
4.27
Molecular modelling
4.29
4.3a
Molecular simulations
4.30
4.3b
Self-consistent field (SCF) theory
4.31
4.3c
Quasi-macroscopic models
4.42
SCF for (spherical) non-ionic micelles
4.47
4.4a
4.49
Micelles at and above the c.m.c.
4.4b
Structure of C p E 5 micelles
4.53
4.4c
Trends for various micellar characteristics
4.56
4.4d
Quasi-macroscopic approaches to non-ionic micelles
4.59
4.4e
Pluronic micelles
4.61
SCF for (spherical) ionic micelles
4.64
4.5a
Micelles at the c.m.c. in various salt solutions
4.66
4.5b
Radial profiles
4.69
4.5c
Chain length dependence
4.72
4.5d
Specific ion effects
4.73
4.5e
Quasi-macroscopic approach to ionic micelles
4.75
Linear growth of micelles
4.76
4.6a
Phenomenological model for rod-shaped micelles
4.77
4.6b
SCF theory of infinitely long linear micelles
4.80
4.6c
The endcap energy
4.83
4.6d
Persistence length of wormlike micelles
4.85
4.6e
Second c.m.c. for ionic surfactants
4.86
Biaxial growth of micelles
4.88
4.7a
Thermodynamic stability of infinite bilayers
4.89
4.7b
Finite size disks
4.91
4.7c
Homogeneously curved surfactant bilayers
4.93
4.7d
On the thermodynamic stability of vesicles
4.96
Interactions between parallel lamellar surfactant layers
4.101
4.8a
Undulation forces between bilayers
4.102
4.8b
Intrinsic interactions between surfactant bilayers
4.104
4.8c 4.9
Liquid crystalline phases
Applications of the modelling
4.107 4.107
4.9a
Binary non-ionic ionic surfactant systems
4.108
4.9b
Solubilization of apolar compounds
4.113
4.10
Kinetic aspects of surfactant solutions near the c.m.c.
4.11
Outlook
4.118 4.120
4.12
General references
4.121
4 ASSOCIATION COLLOIDS AND THEIR EQUILIBRIUM MODELLING FRANS LEERMAKERS, JAN CHRISTER ERIKSSON AND HANS LYKLEMA
In this chapter we consider amphiphilic molecules in a solvent. Amphlphiles are (usually) short chain molecules that have two distinct sides. One moiety of the molecule dislikes the solvent, the other part favours it. When water is the solvent these moieties are called hydrophobic and hydrophllic, respectively. As a result of these interactions, the molecules associate and form objects of mesoscopic size, which are classically called association colloids. Without the process of self-assembly of amphiphiles into association colloids, interface and colloid science would not nearly be as challenging and significant as it is. The association of the hydrophobic (apolar) parts of the amphiphiles gives the driving force for the assembly (hydrophobic bonding). These fragments form the cores of such aggregates. The hydrophilic (polar) sides of the amphiphilic molecules accumulate at the water-core interface, forming the corona. The formation of the corona eventually counteracts the association process, and when finite objects are formed these are known as micelles. Micelles are prominent members of the colloid family and they typically introduce a large interfacial area to a system. Micelles are thermodynamically stable and it is possible to apply the powerful machinery of statistical thermodynamics to describe their self-assembly. The goal of such analyses is to understand such features as the micelle size, shape, the (in)stability against dilution and the influence of various physicochemical parameters in relation to the molecular architecture, as well as the solvent properties. In this chapter we will review the fundamental aspects of association colloids with a focus on the understanding of the underlying physicochemical phenomena. We cannot review all aspects of association colloids because the huge volume of experimental literature, the many implications to countless applications and the detailed modelling of generic and molecular-specific issues simply defy condensation into one coherent and concise text. Here we choose for an approach that largely relies on self-consistent field modelling. We like to show that, within one set of approximations, it is possible to cover a wide range of properties of these interesting systems. In particular, we will elaborate on the way in which modern computational methods can help to gain a better understanding of association colloids. Computer modelling cannot be regarded as the Fundamentals of Interface and Colloid Science, Volume V J. Lyklema (Editor)
© 2005 Elsevier Ltd. All rights reserved
4.2
ASSOCIATION COLLOIDS
end point of investigations. We therefore also pay close attention to various aspects of analytical quasi-macroscopic approaches. 4.1 Introduction Amphiphilic self-assembly introduces (liquid) hydrophobic domains in an aqueous solution. The sizes and shapes of the micelles depend strongly on the nature and concentration of the surfactant and other physicochemical conditions (pressure, temperature, ionic strength, additives) and determine in large the many applications. The use of amphiphiles in, for example, food processing or as a lubricant probably dates back to the beginning of mankind. The link between the physical properties and the molecular structure is much more recent. The term "micelle" dates back to McBain who referred to it in a Faraday Discussion remark" in a General Discussion on colloids and their viscosity (!). Early on the shape of small micelles was disputed, partly as a result of interpretational problems with X-ray data, but nowadays spherical micelles are considered as the prototypes for surfactant aggregates. Besides McBain, Hartley21, Debye31, and Stigter41, many others have in the early stages contributed to their understanding. In this connection it may also be mentioned that monolayers of surfactants at waterair interfaces have served as models for determining various parameters important for micellization. Recall Benjamin Franklin's seminal spreading experiments of oil on Clapham Lake (introduction of chapter III.3) and assessing molecular areas from j'(logc) curves for Gibbs monolayers (c.f. sec III.4.6d). 4.1a Aqueous solutions of amphiphiles Amphiphiles can hardly be discussed without explicit reference to the solvent in which they are dispersed. In order to have stable micellar structures, the solvent should be selective in the sense that it should be poor for one part of the molecule and good for the other. Self-association of surfactants in apolar media results in so-called reverse micelles with a polar core and apolar corona. These systems are close to water-in-oil microemulsions. More specifically, it is possible to tune the solvent selectivity, and thus the micellar structures, by using supercritical solvents. Space does not allow us to visit these systems (see e.g.51 for micellization in non-aqueous and mixed solvents). In this chapter the main focus is on aqueous systems. The hydrogen bonding capabilities of water makes it a highly associative liquid. 11
J. McBain, Trans. Faraday Soc IX (1913) 99. G.S. Hartley, Aqueous Solutions of Paraffin Chain Salts, Hermann (1936). 31 P. Debye, J. Phys. Coll. Chem. 53 (1949) 1; Ann N.Y. Acad. Set 51 (1949) 573. 41 D. Stigter, Rec. Trav. Chim. 73 (1954) 593; J.Th.G. Overbeek, D. Stigter, Rec. Trau. Chim. 75 (1956) 1263. 51 J. Eastoe, A. Dupont, and D.C. Steytler, Current Opin. Coll. Interf. Set 8 (2003) 267. 21
ASSOCIATION COLLOIDS
4.3
Molecules, or parts of them that are not able to take part in this hydrogen bonding network, are likely to be rejected by water. That is why oil and water do not mix. The hydrogen atoms in hydrocarbon molecules or tails are too strongly bonded to the carbon atoms to take part in hydrogen bonding. Hydrocarbon tails are therefore excellent entities to make the hydrophobic parts of surfactants. The longer the tails, the stronger the demixing with water and the stronger the driving force for micelle formation. In other words, the Helmholtz energy of mixing hydrocarbons in water is very unfavourable. It amounts to an unfavourable exchange energy of order kT per -CH 2 unit. There are many names associated with subsets of amphiphiles. Such names reflect some feature of the molecular structure or some physical property they represent or are coupled to a typical application. The name "surfactant" refers to the ability to adsorb strongly onto many surfaces while reducing the interfacial tension. Nowadays the keyword surfactant is used as a generic term. However, there are many other molecules that are surface active but which are not amphiphiles; homopolymers adsorb strongly onto almost any interface (see chapter II.5) and ions to (charged) mercury surfaces. If amphiphiles are used as a means to solubilize apolar compounds in an aqueous medium, they may be named emulsifier or they are called foaming agent if they stabilize thin liquid films. Surfactants are wetting agents when promoting, for example, the spreading of crop protection agents on leaves. If the surfactant is used to stabilize apolar particles in water (or a polymer matrix), the term compatibilizer is sometimes used. Amphiphiles are known to increase the solubility of other organic substances in water. Certain sub-classes of surfactants also have dedicated names. Substances that co-adsorb, or co-micellize, and in this way promote the activity of the surfactant, are called linkers, or, when in aqueous solution, hydrotopes. A class of its own is the set of lipid molecules, which are the main components of biological membranes. Molecules that have a hydrocarbon tail and a hydrophilic head group are the classical examples of a micelle-forming surfactant. When the head group is charged, we have the sub-class of ionic surfactants. Ionic surfactants are among the most prominent surfactants in aqueous media. We distinguish cationic and anionic surfactants. Sodium dodecyl sulfate (NaDS) or (sodium lauryl sulfate) is the best-known anionic surfactant. This surfactant is almost always polluted by dodecylalcohol, which is its hydrolysis product. Cetyltrimethylammonium bromide (CTAB) is a typical example of a cationic surfactant. We will see below that such micelles are strongly dependent on added indifferent electrolyte and that the kind of counterion is also relevant in these systems (see table 4.1). The phase diagrams of surfactants may differ significantly depending on the hydrophilicity or size of the counterion. Zwitterionic surfactants have both a negative and a positive charge in the head group. These are less sensitive to added salt. A snapshot of the structure of a small ionic micelle, as generated by molecular
4.4
ASSOCIATION COLLOIDS
Figure 4.1. a) Computer (MD) generated snapshots of an ionic micelle composed of cesium pentadecafluorooctanoate significantly deviating from the spherical structure". The dark spheres are the C-units (the fluor atoms are omitted, that is why one can "look through" the structure; the CH2 unit is somewhat more polar than the CF2 one), the light spheres are the oxygen of the carboxylic head group, the counterions (Cs) are dark gray spheres, b) MD snapshot of a spherical non-ionic micelle composed of C 12 E 6 surfactants21. The core is made up of densely packed alkyl tails (black, space-filling spheres). The lighter gray hairs are the EO fragments forming the corona. Water molecules are not shown, c) Schematic cross-section of a Na-dodecylsulphate micelle. The large spheres with a minus sign are the OSOg groups; the compensating countercharge is indicated by + and - signs, d) Schematic cross-section of a nonionic micelle, the core of densely packed alkyl chains are thin line parts, the ethylene oxides are the fat line parts. dynamics simulations, Is given in fig. 4.1a. In principle, we are interested in the average behaviour of surfactant assemblies and therefore it is always dangerous to discuss snapshots. Apart from this, we may be amazed at this stage about the complexity of the molecular assembly and the apparent importance of fluctuations (chain conformations, micelle shape, etc.). From the above, it follows that a CH2 group is a classical (but not the only) hydrophobic building unit. On the other hand, an oxygen atom in a larger molecule can 11 21
S. Balasubramanian, S. Pal, and B. Bagchi, Current Sci. 82 (2002) 8456. F. Sterpone, C. Pierleoni, G. Briganti, and M. Marchi, Langmuir 20 (2004) 4311.
ASSOCIATION COLLOIDS
4.5
accept a H-bond from water and is a typical hydrophilic unit. It is possible to combine these two in a regular fashion. The methyleneoxide (MO) chain -(CO-) n , where the Hatoms around the C are dropped for convenience, is the first member. Ethyleneoxide (EO) chain -(CCO-)n is the second; the propylene oxide (PO) chain -(C[CH3]CO-)n , where the CH3 branches off from the main chain, is the third compound. These homopolymers are unable to form micellar-like objects on their own because the amphiphilicity on the monomer length scale is insufficiently expressed. In this series, only the EO member mixes readily with water. The other two are not miscible in all proportions with water. A detailed understanding of this is still missing. Apparently the dimensions of the water H-bonding network "match up" with ethyleneoxide, but not sufficiently well with the other two. With this information, it is possible to design non-ionic surfactants. Combining sufficiently long aliphatic (hydrocarbon) tails and EO head groups leads to surfactants, which are nowadays available in high purity and with high homodispersity. The general constitution is C n E x , where E stands for EO. Results for these systems from before the 1970s should be regarded with some caution because at that time the products were rather polydisperse, especially with respect to the EO parts. When both n and x values are very small, we have weak surfactants. A typical example for a reasonably strong surfactant is for n = 12, x = 6 . I n this case, the lengths of the apolar and polar parts are about equal. A computer-generated example of the spatial structure of a spherical micelle composed of the C 12 E 6 surfactants is given in fig. 4.1b. Again, this example may serve to sharpen our intuition about these molecular aggregates. In this chapter our attention will be focused on strong surfactants, i.e. surfactants that form micelles at low surfactant concentrations. The schematic drawing of fig. 4. Id is derived from fig. 4.1b. Of course there are many polymeric amphiphiles, e.g. Pluronics, which have PPO as the apolar and EO as the polar moiety. The diblock copolymers are the polymeric analogues of the classical surfactants, but there are many other options. For example, one can have amphiphilic side chains also known as polysoaps. There exist protein molecules, such as caseins that have emulsifying properties. They have a rather apolar domain, but also a polar one, and further contain a conformationally disordered fragment that is highly solvated. This shows that amino acids can also serve as the surfactant building blocks. Polysaccharides are yet another class of water-soluble compounds. Linking aliphatic tails to a short string of these molecules leads to environmentally friendly, biocompatible amphiphiles ["sugar surfactants"). Surfactants based on n-alkyl chains generally form micelles for which the core is densely packed, c.f. fig 4.1b. In this case, the dimension of the apolar part of the surfactant molecule is a fundamental property. For this reason, it is evident that relatively small deviations from the linearity, which leads to more compact but less regularly packed tails, may have important consequences for self-assembly. We may consider a given polar head group connected to various isomers of a given apolar
4.6
ASSOCIATION COLLOIDS
constituent. The chain can be branched, it can be split into two or more subchains connected to the head, etc. The micelles composed of these isomers will differ noticeably and systematically. For example, when two ionic surfactants are coupled by a short bridge {spacer) at the position of the head groups, we have twin surfactants also called gemini. The name was coined by Menger et al.1'. In recent years the study of gemini surfactants has seen increasing interest, because it was shown that the micellization properties can be nicely varied by, for instance, controlling the length of the spacer. With the spacer, one can insert an extra steric contribution to the packing of head groups in the corona region. For overviews see refs. 23) . This again points to the fact that molecular structure is important for self-assembly. Alkyl chain lengths on the order of C16 or longer occur frequently in nature, as in lipid molecules. One then has to be aware of the fact that densely packed layers of these molecules will not necessarily be in a liquid-like state at room temperature. If linear, they can give rise to liquid-crystalline ordering. Unsaturated and branched segments in the chain will frustrate crystallization, and thus the degree of saturation is yet another parameter that should be taken into account, especially when fatty acid or mono or di-glyceride molecules are considered. An interesting, and in biological systems relevant example, is the possibility of semirigid molecules in which connected C5 and or C6 rings are grouped together, such as in cholesterol and steroids. Such molecules may have polar and apolar substituents. When the polar ones are predominantly on one face of the molecular plane and the apolar ones on the other side, we obtain facial amphiphiles that form aggregates of finite size that are distinctly different from the micelles that are discussed below. The above set of variables that are relevant for amphiphilic molecules is by no means complete, but we trust that the examples given suffice to indicate the vast scope. 4.1b Hydrophile-lipophile balance (HLB) From the above, it is clear that one can, at least in principle, generate series of surfactants in which the apolar part (usually called the tail(s)) and the polar part (usually called the head) systematically vary in size. This is particularly possible for the nonionic polymeric amphiphiles. Within a series, it is possible to rank them according to the polar/apolar ratio or the hydrophile/lipophile balance (HLB value). The empirical HLB notion was developed by William C. Griffin41 in 1949 who proposed to compute the HLB value as the molecular weight percent of the water-loving portion of the surfactant divided by 5. Experience showed that if a surfactant has an HLB = 1, it is very oil-soluble, however a surfactant with an HLB = 15 is water-soluble. Surfactants
11
F.M. Menger, C.A. Littau, J. Am. Chem. Soc. 113(1991) 1451. R. Zana, Adv. Colloid Interface Set 97 (2001) 205. 3 R. Zana, in Novel Surfactants: Preparation. Applications and Biodegradability, K. Holmberg, Ed., Marcel Dekkcr (1998) 241. 41 W.C. Griffin J. Soc. Cosmet. Chem. 1 (1949) 311. 21
ASSOCIATION COLLOIDS
4.7
with an HLB = 1-3 may be used to mix unlike oils, that water-in-oil emulsions can form with surfactants that have an HLB = 4-6, that one can compatibilize small particles in oil using surfactants with HLB = 7-9, that surfactants with HLB = 7-10 may be used to form self-emulsifying oils, that blends of surfactants in the range HLB = 8-16 can be used to make oil-in-water emulsions, that detergent solutions require surfactants with HLB = 13-15 and that surfactant blends with HLB = 13-18 may be used to solubilize oils (and form microemulsions) in water. It is also very useful to know that for making oil-in-water emulsions, the combination of the oil and the suitable HLB value changes from HLB = 6 for vegetable oils, HLB = 8-12 for silicone oils, HLB = 10 for petroleum oils and HLB = 14-15 for fatty acids and alcohols. In conclusion, the HLB notion has been, and still is11, quite useful for formulation purposes. However, the HLB value does not directly relate to the efficiency to form micelles, and for modelling purposes the HLB value is not a prominent quantity.
4.1c Critical micellization concentration (c.m.c.) Experience has shown that micelles only form above a threshold concentration, often referred to as the critical micellization concentration (c.m.c), which is for any surfactant system the most characteristic physical quantity. The lower the c.m.c, the more efficient the surfactant is to adsorb onto various surfaces. For applications in which the presence of micelles is needed, one obviously should choose a concentration above the c.m.c. The issue of sharpness of the c.m.c. will receive detailed attention below. The appearance of a c.m.c. is easily explained borrowing the ideas of macroscopic phase separation of, for example, oil and water, which also gives a rough estimate of the c.m.c. To first order, the surfactants are at low concentrations kept in solution as freely dispersed molecules because the translational entropy can (over)compensate the unfavourable local interactions the tail has with the solvent. With increasing concentration, the translational entropy per chain diminishes and, at a (fairly) well-defined point, it becomes more favourable to form a dense phase of surfactants. Obviously, the fact that objects of finite size are formed proves that such a phase separation model is flawed and more sophisticated models have to be introduced. Anticipating these extensions we nevertheless note that one can easily show, for instance, using the Flory-Huggins (FH) theory, that the maximum solubility (binodal) of oils in water (strong segregation) decreases exponentially with the chain length of the oil IV in line with experimental findings21. Below (see table 4.1) we will see that the c.m.c. indeed has this trend, proving the fact that the demixing of tails and water is crucial for determining the c.m.c. More importantly, we may use the FH theory to find our first estimate of the c.m.c.
11
X.F. Li, H. Kunieda, Curr. Opin. Coll. Interf. Sci. 8 (2003) 327. P.J. Flory, Principles of Polymer Chemistry, Cornell University Press (1953); C. Tanford, The Hydrophobic Effect. Formation of Micelles and Biological Membranes, 2nd ed. Wiley and Sons Inc. (1980). 21
4.8
ASSOCIATION COLLOIDS
The shortcomings of the simplistic phase separation model should not only be attributed to the fact that in the FH theory the solubility characteristics of the head groups are not included. Indeed, it is possible to set up a more elaborate FH-like theory for copolymers and also introduce interaction parameters for the head groupwater contacts, as well as for the head group-tail contacts. Such extended FH theory will also predict some trend of the c.m.c. as a function of the head group properties. Although such an approach is useful because the c.m.c. is reasonably accurately predicted, the theory remains fundamentally wrong. In such a simplistic phase separation picture (oil-water demixing), the chemical potential of the oil is an increasing function of the oil concentration only in the onephase regions. In the two-phase region the chemical potentials are fixed to the binodal values. Above the c.m.c. (corresponding to the two-phase region in oil-water systems), association colloids of finite sizes are formed, which has many important consequences. One of them is that the chemical potential of the surfactant is no longer fixed, but continues to increase with the micelle concentration. The key property that fundamentally changes the above picture is that the aggregates that are formed do not grow to macroscopic size but remain mesoscopic. There are stopping mechanisms, which limit the growth to be discussed, in more detail below. As finite size effects turn the step-wise phase transition into an apparent first-order transition, it is quite obvious that the sharpness of the micelle formation depends on the number of monomers in the micelle and the distribution over micelle sizes. One other consequence is that classical phenomenological thermodynamical arguments are not enough to understand micelle formation. This means that we should carefully consider how to properly use classical thermodynamic arguments in relation to the special model notions invoked. (i) Determination of the c.m.c. As c.m.c.s are characteristic properties of surfactant solutions, which indicate when micelles start to form, it is important to measure them. Such measurements can only be carried out with satisfactory precision when the c.m.c. is sufficiently defined, i.e. provided that a well-defined surfactant concentration exists above which micelles suddenly appear when the concentration is increased. When there is such a sharp c.m.c, a variety of physical properties, measured as a function of increasing surfactant concentration, show a break at the c.m.c, these breaks often coincide within experimental error. Figure 4.2 gives an illustration. We shall now briefly discuss these methods. One of the most obvious ways to probe micelle formation is to shine light on them because the scattering increases strongly with the volume of the scatterer (chapter 1.7). The shorter the wavelength of the light, the more details one can see. That is why Xrays or neutrons are better equipped to obtain insight into the internal structure of the micelles than visual light. Dynamic light scattering may be used to find the hydrodynamic or diffusion radius of the micelles. When the form factor and the structure factor are both playing a role in scattering experiments, one would prefer to construct a
4.9
ASSOCIATION COLLOIDS
Figure 4.2. Schematic figure for the dependence of some physical measurables on the surfactant concentration near the c.m.c. On a log T,p.{Nl}
The implication of [4.2.5] is that, at equilibrium, the Gibbs energy continues to be simply given by c
G
= X'"iJVi i=l
[4 2 71
- '
ASSOCIATION COLLOIDS
4.21
There is no excess Gibbs energy associated with the formation of micelles. This result is completely in line with the macroscopic thermodynamics for homogeneous systems. The extra term introduced in [4.2.3] thus does not, and should not, influence the Gibbs energy in the system. We note that the small system approach does not presuppose the presence of micelles of a particular size or shape. It anticipates, however, and this should follow from any statistical mechanical model, that there is a distribution in size (and shape). For any of these aggregates it must be true that there is no excess Gibbs energy associated with its presence, i.e. e = 0 . It is known that the micellar size (distribution) depends on a variety of factors, such as the nature of the surfactant, the temperature and the presence of additives that may be absorbed in, or repelled by, the micelle. This means that generally e is a function of p , T and the chemical potentials. However, as at equilibrium e is always equal to zero, from the e d V term no information can be obtained regarding the dependence of micellar properties on ambient conditions. To that end, models have to be developed. We note that in general we should expect that the average micelle size will be inversely related to the number of micelles in the system. This means that the Gibbs energy should also have a minimum with respect to the average micelle size. It is possible to split the Gibbs energy into a bulk part G b , referring to the solution in which the micelles are embedded and a part that can be attributed to the micelles Ga, i.e. G = Ga + G b . The total excess number of surfactants associated with micelles may be found if the bulk concentration of surfactant (i.e. outside the micelles) can be determined because the excess is counted with respect to a reference system, which fills the entire volume by the (dilute) bulk solution containing only monomers. The same applies to the other components and material balance gives N{ = N? + JVb for each component.
Because the volume work
does not enter
in the excess
thermodynamic potentials, the difference between the Gibbs and Helmholtz cases vanishes. Starting once again from [4.2.3], we may write c
Fa = Ga = ^ /ijJVf + EAf
[4.2.8]
i=l
where we have retained deliberately the EA/~ contribution to unravel more about its properties. Here we notice that the molecules in the bulk do not contribute to e. The value of e is the Gibbs energy that is in excess due to the presence of micelles. Normalizing the excess Gibbs energy by the number of micelles gives ga =
=Y//inf +£
[4.2.9]
where n? = N?IA/~ is the average excess number of molecules associated with one micelle. We may also refer to this as the most probable size of the micelle. Now E can be identified as the (excess) grand potential
4.22
ASSOCIATION COLLOIDS c
£ = ga - ^T nffii
[4.2.10]
i=l
At constant pressure and temperature we can write c
c
c
de = dg* - £ ^dnf - £ nf d/i, = - £ nf d//t i=l
i=l
[4.2.11 ]
i=l
which is the Gibbs-Duhem equation for micellization. It resembles Gibbs' law for adsorption. When we have a two-component system where surfactant {surf) is dissolved in water, we can assume that the chemical potential of the solvent is nearly constant so that the Gibbs law becomes (9^-)
=- 0 . Recalling the stability condition [4.2.6] we use [4.2.12] and find that 3// surf / 3yl/< 0. Again in words, this says that in a closed system the chemical potential of the surfactant must go down with an increasing number of micelles. Let us next switch our attention from the closed isobaric system at constant T , where the Gibbs energy is minimized, to the open system. The grand potential is the characteristic function of the system in which all chemical potentials are fixed. In such a system both the micelle concentration, i.e. the number of micelles Af per unit volume, and the aggregation numbers (including the distribution) are variables, which the system may use to minimize its grand potential. The minimum of this grand potential should have the value zero in order to be consistent with the analysis in the closed system. In general, the thermodynamics of small systems becomes especially useful when it is applied to the interpretation of experiments. It also turns out to be of utmost importance for analysis of results of simulations or computations on micelles. 4.2b The mass action model A customary way to describe micelle formation is to consider the equilibrium between freely dispersed surfactants, usually called monomers and referred to by Xj, with micelles composed of g surfactants, X . In this approach, one assigns a chemical potential to the g -micelle, and the total number of surfactants in the system is split up into a contribution of the monomers Nsm and a contribution present in the micelles g x JVs( ,, i.e. N surf = Ns(1) + g x JVs( j . This equation is easily generalized to a range of micelle sizes. Ignoring for the moment the size distribution, the equilibrium may be expressed by gXx^±Xg
[4.2.13]
ASSOCIATION COLLOIDS
The equilibrium constant K
4.23
relates the micelle concentration to the monomer
concentration
K = J ^ i =^ L 9
^
9
[4.2.14]
0, we infer that em is a decreasing function of ,usurf. At the same time, g = rigurf must be an increasing function of // surf , and thus e must be a decreasing function of g = n surf , to have stable micelles. Hence, the stability condition in the constrained system is given by — Sflnax • For each of them, there exists the equilibrium of [4.2.13], gXj ^ Xg . At equilibrium, AGg = fig -g/^ = 0 . We may identify AGg as the excess grand potential for the g -micelle. To distinguish this quantity from the most likely grand potential as obtained in the SCF theory and considered so far, we will refer to it as £2(g). Similarly, as done with e, we may split Q up as £2(g) = Qra(g) + kTlnip where
a)
or
tester ^ t e r =-ln(l-/a)
[4.3.10]
Of course, this ideal lattice gas pressure will not be appropriate at large values of Ja and [4.3.10] should be replaced by (i2°)ster /kT = ( l - / a ) " 2 , which follows the simulation results for hard disc pressures in 2D rather accurately even at relatively high values of Ja . We mention once more that we must include extra terms if the head group is charged (of electrostatic origin) or oligomeric (elastic-free energy of stretching of the head group). Such contributions will be discussed separately below. The micelle size distribution is, for given surfactant length t, given by
*>m(9)-exp U ^ ? -
[4.3.11]
The shallow minimum of the total i2° in fig 4.8a leads, even on a logarithmic scale, to a sharp maximum in 0.5 and, depending on the molecular weight, the system has a solubility gap. The surfactants that rely on the EO part of the molecule to have micelles that are soluble in water are correspondingly sensitive to the temperature. Likewise, the solubility of the PPO chain is temperature sensitive. As a result the most important parameter to control the micellization of EO-based surfactants is the temperature. The micellization for the
J)
R. Nagarajan, loc.cit.: D. Blankschtein, et ai. Loc. clt.: J.C. Eriksson, et at, Loc. cit.
4.48
ASSOCIATION COLLOIDS
family of non-ionic surfactants is a very weak function of the ionic strength. Only at relatively high ionic strength do electrolytes affect the solvent quality of the ethylene oxide part of the chain. In this chapter, we choose to construct an SCF model for which the united CH2 atoms determine the discretization length. The simple reason for this is that the alkyl chain may also be modelled using these entities. Using these united atoms allows one, in principle, to account accurately for the chain architecture. We use a model pioneered by Barneveld11 for EO-containing and PO-containing surfactants that has fewer parameters than the two-state model, but still captures the main temperature characteristics (c.m.t, c.p.t). The generic features of micellization can easily be illustrated by a very primitive model, cf sec. 4.3b ad (i). However, eventually one needs to be molecule specific. The challenge for the near future is, of course, to choose parameters and molecular architectures such that the results can be generalized. One of the problems for a realistic molecular model is dealing with the water phase. Water is an associative fluid that forms via relatively strong and many H-bonds small water clusters that dynamically break and form. This complexity is beyond reach for models that are targeted to describe association colloids. At present we can only advance via ad hoc water models. Below we will discuss SCF results with spatial resolution in two dimensions, and for such a coordinate system we need (for the time being) to be less ambitious. In short, we will model water to be composed of a cluster of W units that occupy five sites (one central surrounded by four others). In addition, we allow for discrete amounts of free volume. Free volume is implemented as units called V that occupy one lattice site each. For details about this model, we refer to appendix 1. The alkyl-EO non-ionics are modelled as(Cg)1[C]n_[[(O)1(C)2]x(O)j. Here we choose to introduce the united atom level of description with the C 3 pointing to the terminal methyl group and the O representing oxygen. The terminal O represents the alcohol group. We will model the methyl group to be a bit more hydrophobic than the methylene units and therefore set %C W= 1 • 1 a n d Xc w = 1 ^ • The overall solubility parameter for an ethyleneoxide unit should be such that it is soluble in water. Typically it turns out that one should choose a negative value and use the Ansatz that this parameter is inversely proportional to the temperature Xow = /£ow'300)-22fi where %ow(300) = -0.6 is the value at room temperature. In passing, we note that in the literature there exists a two-state model to deal with the temperature dependence of non-ionics2'. We will not discuss this approach here. An important parameter that drives the demixing of the heads and the tails is the repulsion between O and C for which we choose Xoc = %oc = ^ • The exact value of this parameter is uncertain; this value becomes important when the
1
' P.A. Barneveld, The Bending Elasticity of Surfactant Monolayers and Bilayers, PhD thesis Wageningcn University (1991). 21 P. Linse, M. Bjorling, Macromolecules 24 (1991) 6700.
ASSOCIATION COLLOIDS
4.49
Table 4.2. The Flory-Huggins interaction parameters used in the SCF analysis of the non-Ionic surfactant system at T = 300 K X
ca
c
O
W
V
ca c o w
0
0.5
2
1.5
1.5
0.5
0
2
1.1
2
2
2
0
-0.6
2.5
1.5
1.1
-0.6
0
2.5
2
2.5
2.5
0
V
1.5
bilayer is normally compressed. Bilayers under compression will be discussed in sec. 4.8. To make the set of FH interaction parameters complete, we mention that with respect to the Interaction with the free volume the O is treated as W , i.e. Xyo = 2.5 , and the mixing energy between methylene and methyl groups is set to j
cc
= 0.5 .
Below all lengths are made dlmenslonless by normalization to the characteristic size of the lattice cell for which a value of I = 0.2 nm Is used. The surface tension (grand potential per unit area) is given in dimenslonless units kT 112 . This implies that y = 1 corresponds to 100 mN/m. The tabulated set of FH interaction parameters is relatively large and admittedly to some extent ad hoc. We have used the comparison with the more detailed modelling to estimate most of the parameters, but they still should be regarded as adjustable. We may judge the quality of the set by their consistency with respect to the predictions that result from it and to the comparison of the results with experiments. One should realize, though, that the MD or MC simulations typically include even more parameters In their force fields. Similarly, in analytical models the number of parameters is not small either. We have to live with this. We note that the present free-volume model has approximately twice the number of input parameters as compared with the more primitive incompressible model of sec. 4.3b (i). However, as we will see, this set suffices to deal both with the whole set of non-Ionics, including the Pluronics and related compounds, as well as mixtures of these components. Finally, this parameter set is sufficient to predict the adsorption of the surfactant at the air-water interface without the need to introduce additional parameters (space does not allow us to illustrate this).
4.4a Micelles at and above the c.m.c. We will now discuss in some depth the state of the art of SCF modelling of non-ionic surfactants of the C n E x type, for which we choose three representatives (n,x) = (10,6), (12,5), and (14,4). Later we will also discuss other members of this surfactant family. This set of three surfactants has been selected because all three surfactants have the same number of carbons and as compared with the (12,5), the (10,6) has one more O
4.50
ASSOCIATION COLLOIDS
Figure 4.9. SCF results for three C n E x surfactants, (n,x ) = (10,6), (12,5) and (14,4). a) The translationally restricted (standard state) grand potential as a function of the aggregation number, b) The bulk concentration of the freely dispersed surfactants (monomers) as a function of the aggregation number of the micelles, c) The total volume fraction of surfactant in the system as a function of the monomer volume fraction. The arrows point to the theoretical c.m.c. of the surfactant system, d) The relative size distribution ag/g as a function of the average aggregation number g . The open circles in panels a and b represent the system, which coexists with infinitely long cylindrical micelles to be discussed in sec. 4.6b.
and the (14,4) has one less O unit. Hence, the overall molecular weights of the three components are similar. Nevertheless, the three surfactants are remarkably different in their association behaviour as is known experimentally11. We may refer to fig. 4.1b to a detailed MD-generated snapshot of a non-ionic micelle. Here we will be Interested not in snapshots but in the average micellar properties. Any SCF analysis of micellization starts by analyzing £m(g) as a function of the aggregation number. These functions are given in fig. 4.9a. Typically, £m(g) has a positive slope at very small values of g (dotted line), there exists a part with a negative slope (drawn line), and subsequently there may again be a part with a negative slope (again dotted). As explained, only the sections with negative slopes correspond to micelles that are macroscopically stable. The maxima in the curves correspond to the smallest micelles that are stable. We will refer to these micelles as the ones corresponding to the theoretical c.m.c. " R.G. Laughlin, The Aqueous Phase Behavior of Surfactants, Academic Press (1994).
ASSOCIATION COLLOIDS
4.51
For the surfactant with the largest head group (10,6), there is an aggregation number above which em is negative. We argued above that the physically realistic values for this quantity should be positive, but we have dotted the continuation of the curve towards the negative values. The two other curves do not reach negative values, but develop a minimum in £m{g) • This minimum signals the upper limit of the size of spherical micelles that is thermodynamically stable. This minimum also tells us that the micelle concentration cannot increase further. For these systems we need to consider alternative aggregate shapes. In fig 4.9b we present the volume fraction of the freely dispersed surfactants (monomers) that coexist with micelles with aggregation number g . We note that the chemical potential of the surfactant is (in first order) given by the logarithm of this volume fraction and hence one can interpret the figure also as the chemical potential of the surfactant versus g . It follows from [4.2.19] that there is a direct relation between em and the chemical potential. According to [4.2.19], when £m(g) decreases, ^ s u r f (g) increases and vice versa. Again, we have used a solid line for those parts that are physically significant and dotted the irrelevant parts. Consistent with the idea of a c.m.c, the smallest stable micelles are found at the minimum of the (monomer) chemical potential curve. We will see that other definitions of the c.m.c. may be given. To elaborate on an alternative measure of the c.m.c, we present in fig. 4.9c the relation between the overall surfactant concentration, computed by [4.2.22], i.e. (^ = s cs 2 x 10~3 ), and coexisting with spherical vesicles. undulation entropy. We may now estimate the vesicle size of the C 1 4 E 4 surfactant system of the previous section. Assuming that a renormalized grand potential of e^ ~ 10 kT can be compensated by translational entropy, we find using kc = 4 kT , fc = - 4 kT , and a = 3 , vesicles with a size of order R ~ 150 nm. It will be clear that for a surfactant system with a significantly higher mean bending modulus, the Gauss bending modulus must be sufficiently negative to keep the vesicles to a mesoscopic size.
(i) Charged bilayers Stable vesicles are expected when the mean bending modulus is of order kT and the Gauss bending modulus is sufficiently negative, or -2fcj < k2 2 0 . These mechanical parameters not only depend on the surfactant architecture, but also on the physicochemical conditions. We will illustrate this for the CTAB surfactant system. In fig. 4.37 we present the curvature energy of CTAB surfactant vesicles over one decade in ionic strength, i.e. 10"3 <
