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C--C-C=C()readily undergo addition or chaingrowth or simply chain polymerization. Polymerization of such monomers will be discussed in this and several of the subsequentchapters. Chain-growth polymerization,as well as all other typical chain reactions, are fast reactions typified by three normallydistinguishableprocesses,viz., (i) initiation of the chain,. (ii) propagationor growthof the chain, and(iii) termination of the chain. (A fourth process, chain transfer, mayalso be involved.) Theinitiation is usually a direct consequenceof generationof a highly active species R*by dissociation or degradationof somemonomer molecules (M)under the influence of such physical agencies as heat, light, radiation etc., or as a consequenceof dissociation or decompositionof somechemical additives commonly knownas initiators (I): I ~ R* (6.1) Thereactive species R*maybe a free radical, cation, or anion, whichadds itself, if conditions are favorable, to the monomer moleculeby openingthe ~" bondto form a fresh reactive center (radical, cation, or anion center), dependingon the nature of R*. The newreactive center adds to another 435
436
Chapter 6
monomermolecule, M, and the process is repeated in quick succession resulting in addition of many more molecules to the same growing chain at its reactive center to carry on the chain propagation process: R* + M ----+
R-M* ~ R-MM* +riM
,
R_(M)n+IM.
(6.2)
The chain growth is terminated at some stage by annihilation of the reactive center by one or more convenient and appropriate mechanism which depends largely on the type of reactive center (radical, cation or anion), nature of the monomerM, and the overall chemical environment and condition of reaction. In the present chapter, the basic principles of chain polymerizations in which the reactive centers are free radicals will be considered in detail, focusing on the polymerization reactions in which only one monomeris involved. Copolymerizations involving more than one monomerare considered separately in ChaPter 7. Chain-growth polymerizations in which the active centers are ionic are reviewed in Chapter 8.
OVERALL SCHEME POLYMERIZATION
OF
RADICAL
CHAIN
Radical chain polymerization, as noted above, is a chain r,eaction consisting of a sequence of three steps-initiation, propagation, and termination. The initiation step is considered to involve two reactions. The first is the production of free radicals. There are many ways to accomplish this, but the most commonmethod involves the use of a thermolabile compound, called an initiator (or catalyst), which decomposesto yield free radicals. The usual case is the homolyticdissociation of an initiator I to yield a pair of radicals R"
i 2R.
(6.3)
where kd is the rate constant for initiator dissociation. Its magnitude is usually of the order of 10-4--10-6 s-1. (The radical R" is often referred to as an initiator radical or aprimaryradical). The second part of the initiation step involves the addition of the radical R" to a monomermolecule as in
R"
H H I + CH2=C ~ R-CH2--C" I X X
(6.4)
437
Radical Chain Polymerization
Reaction (6.4) maybe abbreviated and generalized R" 4-
M--~M~"
where Mstands for monomerand MI" actually represents RM’, that is, a monomer-ended radical containing, one monomerunit and an end group R. The rate constant for the reaction is kl. Initiation is followed by chain propagation, whichconsists of the growth of MI" by the successive addition of large numbers of monomermolecules. Each addition creates a new radical which has the same identity as the previous one, except that it is larger by one monomerunit. The successive additions may be represented by MI" 4- M k-~P M2"
(6.6a)
MZ" + M--~M3"
(6.6b)
M3" 4- MR--~’->P M4", ....
(6.6c)
or, in general terms, Mn" 4-
(6.6d)
M--~Mn+I"
where kp is the rate constant for propagation. The value of kv for most monomersis in the range 102-104 L/moPs. This is a large c, onstant, much larger than those usually encountered in step polymerization (see Table 5.2). Growth of the chain to macromolecular proportions thus takes place very rapidly. At somepoint, the propagation reaction is terminated due to annihilation of the radical center of the propagating chain. The annihilation of the radical centers occurs by bimolecular reaction between radicals. Tworadicals react with each other by combination (also knownas coupling), H
H
H H
vwwCH2-- C~. + ¯ C-CH2vvwv, ~ vwwCH2-- ~-- C~-CH2vww (6.7) X X X X or, by disproportionation in which a hydrogen radical that is beta to one radical center is transferred to another radical center, resulting in the formation of two polymer molecules-one saturated and one unsaturated (at the end unit):
438
Chapter 6 H
~vwCH2--C-+ X
H
H
-C-CH2vww~ X
v~vCH2--C-H X
H + C=CHwvw X
(6.8) These two different terms by
modes of termination can be represented in general
Mn"
4-
Mn" 4-
Mm" ~ Mn+m Mrn"
~ Mn 4-
(6.9) Mm
(6.10)
Termination can also occur by a combination of coupling and disproportionation. However, since both the reactions result in the formation of dead polymer molecule(s) one can also express the termination step kt Mn" 4- Mm° ~ dead
polymer
(6.11)
where the particular modeof termination is not specified and the overall termination rate constant let is given by kt = ktc q- ktd
(6.12)
Typical termination rate constants are in the range of 106-108 L/tools or orders of magnitude greater than propagation rate constants. The much greater value of kt (whether ktc or ktd) compared to kp does not, however, prevent high molecular weight polymer formation because the concentration of radical species is very small (low value of kd) and because the polymerization rate is dependent on only the one-half power of kt (see p. 443). It is apparent from the above schemeof radical chain polymerization that the initiator fragment originating in the form of radical R" are incorporated as end groups R [see Eq. (6.4)] in the polymer structure, sealing one both ends of the polymer chains. A distinctive feature of radical chain polymerization, in sharp contrast to condensation or step-growth polymerization (cf. Table 5.1), that a partially polymerized system of the former would practically consist of full grown polymer molecules of high molecular weight and the unreacted monomer; no species in an intermediate stage of growth can be isolated. The fact is that the polymer molecules formed in the early stages of the reaction are usually comparable in chain length or molecular weight to those formed at a muchlater stage of the process. It is largely a consequence of the very large difference between kp and kd values that the time needed for the full growth of a polymer molecule is an insignificantly
Radical Chain Polymerization
439
small fraction of the time needed for a measurable overall conversion of the monomer.
RATE EXPRESSION POLYMERIZATION
FOR
RADICAL
CHAIN
Equations (6.3) through (6.12) constitute the detailed mechanism free-radical initiated chain polymerization. According to this scheme, the initiator I first decomposesinto a pair of primary (free) radicals, R’, as Eq. (6.3), the rate of radical generation being then given d[R’]/dt
= 2kd[I]
(6.13)
since for each incidence of decomposition of an initiator molecule, two radicals R" are produced. Each R" then attacks a monomermolecule M to produce a chain radical MI" (which has an R end group, not shown), as in Eq. (6.5). These two steps are characterized by the rate constant kd for the decomposition of the initiator and the rate constant ki for the chain initiation reaction, respectively. Of the two steps, the decomposition of the initiator, whichis muchslower than the initiation reaction, is the rate controlling step. The rate of chain initiation, .R/, will thus be the same as the rate of radical generation given by Eq. (6.13), if there is no wastage the primary radicals R" by side reactions. For practical purposes, however, the rate of initiation is expressed by
wherethe factor f is the initiator efficiency or the efficiency of initiation, representing the fraction of primary radicals (R’), which actually contributes to chain initiation as given by Eq. (6.5). The rate of propagation is the sum of many individual propagation steps [Eqs. (6.6a)-(6.6c)]. It is, however, assumedthat the propagation constant kv is independent of the size or the number of monomerunits in the propagating radical. One can therefore express the rate of propagation by Rp = kv [M] [M’]
(6.15)
where [M] is the monomerconcentration and [M’] is the total concentration of all chain radicals, that is, all radicals of size MVand larger. The termination rates ]~t correspon~ling to the different modes of termination are 2.Rtc = 2~c [M’]
(6.16)
440
Chapfer 6
from Eq. (6.9), R,dfrom Eq, (6.10),
2 2ktd[M’]
(6.17)
and 2~t
: 2~[M’] 2 2: 2(k,
tc q- ktd)[M’]
(6.18)
from Eqs. (6.11) and (6.12). The factor of 2 is used in the above expressions for the simple reason that for each incidence of a termination reaction, two chain radicals disappear from the system. It is important to note that as radicals are generated in pairs, they are also destroyed in pairs. In order to obtain a kinetic expression for the overall rate of polymerization, it is necessary to assume that both kp and kt are independent of the size of the radical. [This assumption is inherent in Eqs. (6.15) through (6.18).] It may be recalled that the same type of assumption was also employed in deriving the kinetics of step polymerization (Chapter 5). There is, however, ample experimental evidence which indicates that although radical reactivity depends on molecular size, the effect of the size vanishes after the dimer or trimer [1].
Problem6.1 According to simple collision theory, the rate constant for propagation may be written as
where ~p is the steric factor, a~ is the cross section of the collision, # is the reduced mass of the colliding pair, Ep is the activation energy for propagation, is the gas constant, and T is the absolute temperature. Showthat the assumption made in free-radical polymerization kinetics that kp is independent of the size or degree of polymerization of propagating radicals can be rationalized in terms Eq. (P6.1.1). Commenton the similar assumption also made for Answer: Since the only effective collisions in propagation will be those of monomerM with the growing end of the propagating radical Mn’, the product ~p~rp should be roughly independent of the degree of polymerization of the radical. Because the chemical nature of the reactive end of the radical is independent of the degree of polymerization, E~ should also be independent of radical size. The factor that remains to be considered is the reduced mass # which will be defined by /z
=
MM,. MM MM.. -k
(P6.1.2)
MM
where MM,. and MM are the masses of the propagating radical and monomer, respectively. Since MM,. >> MM,except in the initial stage, Eq. (P6.1.2) may be written as /z ~ MM (P6.1.3)
Radical Chain Polymerization
441
It maytherefore be concluded that kp should be a constant that is independent of radical size (except in the initial stages of propagation). For mostterminationreactions, the rate constant is determinedby the collision frequencyof radicals (diffusion controlled reactions), and the reduced massdoes not becomeindependentof radical size as in Eq. (P6.1.3). Hencethe assumption that kt is independentof size is usually less valid. Neverthelessthis assumption must be madein order to obtain tractable results. Monomerdisappears by the initiation reaction [Eq. (6.5)] as well by the propagation reactions [Eqs. (6.6a)-(6.6c)]. rate of monomer disappearance, which is synonymouswith the rate of polymerization, is thus given by
dt
_
+
(6.19)
However, the number of monomermolecules reacting in the initiation step [Eq. (6.4)] is insignificant comparedwith those consumedin the propagation step [Eqs. (6.6a)-(6.6c)] for a process producing high molecular weight polymer. Thus, to a very dose approximation, the former can be neglected and the polymerization rate is given simply by the rate of propagation:
diM]-dt
/~ = v[M][M ’] k
(6.20)
This equation is not directly useful for evaluating Rp as it contains a term for the concentration of radicals. Radical concentration~ are difficult to measure quantitatively, since they are very low (,,~ 10- mol/L), and is therefore desirable to eliminate [M’] from Eq. (6.20). In order to this, the steady-state assumption is made that the concentration radicals increases initially, but quickly reaches a constant steady-state value. This can be explained as follows. Whena free-radical polymerization is started, the number of radicals in the system will" increase from zero as the initiator begins to decompose according to Eq. (6.2). The rate of termination reaction will also increase from zero in the beginning because the rates of these reactions are proportional to the square of the total concentration of radicals in the system [Eqs. (6.16)-(6.18)]. Eventually the rate of radical generation be balanced by the rate at which radicals undergo mutual annihilation, and the concentration of radicals in the system will reach a steady value. It can be shownthat in typical polymerizations this steady state is reached very early in the reaction. The assumption that the rate of initiation equals the rate of termination is called the "steady-state assumption." It is equivalent to the following two statements:
Ri = Rt at steady state and
d[M’]/dt
= 0 at
steady
(6.21) state
(6.22)
442
Chapter6
The theoretical validity of the steady-state assumption has been discussed [2] and its experimental validity has been shown in many polymerizations.
Problem6.2 Experimentally, it is found that, except in the very earliest
(and generally negligible) stages of the reaction, the loss of monomeris accounted for quantitatively by the appearance of the polymeric product. Justify on this basis the steady-state approximation that all free radicals present in a polymerizing system are at steady-state concentrations. Answer: Let [M]0 be the initial concentration of the monomer. Monomermolecules that have reacted must be contained either in the propagating radicals or in the polymer (i.e., product molecules). Therefore, the stoichiometry requires that IM]o = [M] + Z ~[P~] + Z ~[ram’] Differentiating
Eq. (P6.2.1) with respect to time and rearranging,
According to experimental observation, dt
-
Therefore,
~n(~)
=
This means that dt
dt
Equation (P6.2.3) represents the steady-state
approximation.
Since the steady state is reached soon after polymerization starts, we can assume without significant error that it applies to the whole course of the polymerization. Substituting /~t from Eq. (6.18) into Eq. (6.21) obtains t~ = 2kt Rearrangement
2[M’]
(6.23)
of Eq. (6.23)
[M’]= (
1/2
(6.24)
tLadical ChainPolymerization
443
and substitution into Eq. (6.20) yields
dt - E = [M] E for the rate of polymerization. Whe~initiation takes place by thermal decomposition of initiator, i.e., Eq. (6.3), substitution for R,/ from Eq. (6.14) gives d[M] d$ --
R,p
(fkg [I]) 1/2 = kp[M]k~j
(6.26)
Equations (6.25) and (6.26) have the significant conclusion that the of polymerization depends directly on the monomerconcentration and on the square root of the rate of initiation. Thusdoubling the rate of initiation or initiator concentration does not double the polymerization rate, but the polymerization rate is increased only by the factor V/~. This behavior is a consequence of the bimolecular termination reaction between radicals. It is further evident from Eqs. (6.25) and (6.26) that the polymerizability a monomerin a free radical polymerization is related to the ratio kp/~/2 rather than to kp alone. This ratio will appear frequently in the relations we develop for radical polymerization. Integrated Rate of Polymerization Expression It should be noted that Eq. (6.26) represents the instantaneous rate polymerization corresponding to [M] and [I] values at any instant. Since these values change with conversion, Eq, (6.26) must be integrated over period of time to determine the overall extent of polymerization. If the initiator decomposesin a unimolecular reaction [cf. Eq. (6.3)], the correspondingrate expression is first order in initiator: -- d[II/dt
= kd[I]
(6.27)
Integration of Eq. (6.27) between [I]0 at t = 0 and [I] at t gives -k~t [I] = [I]oe
(6.28)
444
Chapter 6
Table 6.1 Half-Lives of Initiators Initiator 50°C Azobisisobutyronitrile 74 h Benzoyl peroxide Acetyl peroxide 158 h Lauryl peroxide 47.7 h t-Butyl peracetate Cumylperoxide t-Butyl peroxide Source:Datafrom Refs. 3 and 4.
Half-life at 70°C 100°C 4.8 h 7.2 min 7.3 h 19.8 min 8.1 h 3.5 h 12.5 h
130°C
18 rain 1.7 h 6.4 h
218 h
[For first order reactions, it is often convenient to integrate between[I]0 at t = 0 and [I] = [I]0/2 at t = tl/2, the half-life of the initiator, to obtain t,/e
= (ln2)/ka
.(6.29)
The half-life is thus independent of the initial concentration. It is a convenient criterion for initiator acfivities. Table 6.1 lists the half-lives for several commoninitiators [3,4] at various temperatures.] Substituting Eq. (6.28) into Eq. (6.26) one obtains
[M]-On integrating
-~ (fkd[I]o)
between [M]oatt
- In [M] _ 2 (-~)
1/2
(e -kd)
dt
(6.30)
= Oand [M]att: (@~°)1/~(1-
e-~et/2)
(6.31)
The extent of monomerconversion, p, is defined as
So 1 --p
(6.32) [M]o = [M]/
Therefore, Eq. (6.31) mayalso be written -ln(1-
p)= 2 (~/23
(f[I]°~-x/2(1-
e-kdt/2)
This gives the amount of polymer produced (in terms of the moles of monomerconverted) in time t at agiven temperature. It is also useful for
445
Radical Chain Polymerization
Table 6.2 Reaction Parameters in Radical Chain Polymerization Quantity /{i
Units mol L-I -1 s -1 s
kd
[I] [M’] P~ [M] kp Rt /q
General range of values 10-8 -1° - 10 -6 10-4
_ 10
-1 mol L
10-2 -4 - 10
-1 tool L
10 -7 -9 - 10
mol L-1 -1 8 -1 mol L -I -1 L tool s -1 mol L -1 s -1 L mo1-1 s 12 kp / k: (L mo1-1 $-1)1/2
10-4 -6 - 10 10-1 - 10 102 4 - 10 10-8 -l - °10 106 - 108 10-2 -- 1
determining the time needed to reach different extents of conversion for actual polymerization systems where both [M] and [I] decrease with time. Table 6.2 shows the general range of values of the various concentrations, rates, and rate constants pertaining to the above kinetic scheme. These values are typical of radical chain polymerizations.
Problem6.3 The decomposition of benzoyl peroxide is characterized by a halflife of 7.3 h at 70°C and an activation energy of 29.7 kcal/mol. What concentration (mol/L) of this peroxide is needed to convert 50%of the original charge of a vinyl monomer to polymer in 6 hours at 60°C ? (Data: f = 0.4; k~/k~ -2 = 1.04x10 L/m61-s at 60°C.) Answer: FromEq. (6.29), at 70°C, In 2
In 2 (7.3 x 3600 s)
= 2.638 x 10-~ -1 s
To calculate ka at 60°C, In
r. ] [(2.638 x :tO -~ ~-1)1
From the given value of E~, (29.7 x 103 cal mo1-1) Therefore,
(1.987 cal mo1-1 °K-I) (kd)~0 o = 7.128 x 10-~ -1 s
= 1.495 x 104 °K
446
Chapter 6
Using Eq. (6.33), - ln0.5
for 50% conversion at 60°C,
= 2(1.04
× 10 (7.128 × 10-6 s-l)’/2 [1 - e -(7"12s
(0.4
[I]0)
1/2
× 10-6 s-1)(6
X
× 3600 s)/2]
tool L [I]0 = 3.75 × 10-2 -1
Problem6.4 For a new monomer 50% conversion is obtained in 500 rain when polymerized in homogeneoussolution with a thermal initiator. Predict the time for 50% conversion in another run at the same temperature but with four-fold initial initiator concentration. Answer: Approximating
(1 - e-kat/2)
by karl2, Eq. (6.33) may be written
-ln(1-p) Taking ratio of equations for the runs (same conversion, same rate constants), 1 -- [~1°~(~ t~ t2 = (500
min)/v~
[~102 / [~10,1 = 4
’
= 250 rain
Problem6.5 If a 5% solution of a monomerA containing l0 -4 mol/L of peroxide P is polymerized at 70°C, 40% of the original monomercharge is converted to polymer in 1 h. Howlong will it take to polymerize 90%of the original monomer charge in a solution containing (initially) 10%A and -~ mol/L of peroxide P ? Answer: Approximating (1 -- e -~:~t/2)
-ln(1-p)
by k~t/2,
Eq. (6.33)
becomes
=
where K is a lumped constant, same for both runs. Taking ratio to eliminate If, t = 0.1(ln 0.1/ In 0.6) = 0.45
447
RadicalChai~Polymerization A Note on Termination
Rate Constant
Researchers in the United Kingdomand the United States whopioneered muchof our knowledgeof free-radical polymerizationsused different conventions for termination rate constants. All United States texts and data compilations adhere to the Americansystem while United Kingdomtexts rely on the British method. Thoughthe convention is seldom explicitly specified, it can be usually inferred fromthe particular context. In the British convention, ktc and ktd are defined by --diM’i/at It followsthen that
= ktc[M’] 2 + 2ktdiM’]
d[polymer]/dt---
~]¢,tc[M’] 2 2+ ~td[M’]
(6.34)
(6.35)
since a pair of radicals give rise to onepolymermoleculeif the termination occurs by combination,but two polymermoleculesif the termination is by disproportionation. Onthe other hand, the Americanconvention, whichis followed in this text, uses the followingdefinitions: --d[M’]/dt
=_ 2ktc[M’] 2 -+- 2ktd[M’] 2
(6.36)
and hence, d[polymer]/dt --- ktc[M’] 2 + 2~a[M’] 2 (6.37) The rate constants quoted according to the Americanconventionwill thus be exactly half those measuredby the British system. However,the same conclusions about polymerization rates are reached wheneither usage is adopted because a compensatoryfactor of 2 is present in the kinetic equations that use Americanrate constants and not in those corresponding to the British system. Hence,each conventionis unobjectionable if used consistently but the two cannot be mixed. EXPERIMENTAL DILATOMETRY
DETERMINATION
OF P~:
As Eq. (6.26) shows, polymerization rates depend on the monomerand initiator concentrations. Since these concentrations are knownmost accurately at zero time, it is useful to workwith initial rates of polymerization, as given by o = _ (d[M]~ = lim [M]o- [M] (6.38) k, dt ]0 at-~0 ~ Unlessotherwisespecified all rates mentionedin the followingsections will be initial rates and the superscript and subscript on ~ and (diM]/dr), respectively, in Eq. (6.38) will be dropped.
448
Glhapter6
It is easy to determine the rate of polymerization since, according to Eq. (6.38), it is merely necessary to measure the monomerconcentration [M] a function of reaction time t andthen determine the initial slope of a plot of [M] versus t. Moreover,since such plots are usually sufficiently linear up to about 10-15% monomerdepletion, only one or two experimental points are often adequate. The most obvious and direct way of measuring [M] is to stop the reaction at some predetermined time and then isolate the polymer from the reaction mixture (e.g., by sudden chilling of the reaction mixture followed by drying) in either of two ways: precipitation of the polymer by addition of a nonsolvent or distillation of the monomer.The amount of polymer formed, and hence the amount of monomer consumed at this reaction time, may be determined simply by weighing. The amountof monomerremaining may be determined directly by weighing or calculated from the monomerconsumed. The technique is, however, time consuming and requires the preparation of a new reaction mixture for each experimental point on the concentration-time plot. It is muchfaster and more convenient to measure some physical property of the reaction ~nixture that changes as the polymerization proceeds and that may be related to the concentration of the monomer. Although a numberof suitable physical methodsof analysis are available, dilatometry is most often used in the measurement of polymerization rates. Because the density of a polymer is usually greater than the monomerfrom which it was formed (see Table 6.3), the rate of addition polymerization can be followed by observing the contraction in volume of a fixed weight of monomeras it is polymerized. The sensitivity of the change in volumewith conversion can be increased significantly if the shrinkage in volume is observed in a tube of very narrow diameter. Such a device is called a dilatometer. It can be constructed with a reservoir to contain a sufficient volumeof liquid (to make the total volume change occurring during conversion to be meaningful) and fitted with a capillary tube to make the volume change accompanying the conversion of monomerto polymer readily measurable. The dilatometer maybe constructed in a variety of ways. The principle of operation of a dilatometer maybe seen from the simple apparatus shown Table 6.3 Densities of SomeMonomersand Polymers Density (g/cm3) at 25°C Monomer Monomer Polymer Volume Acrylonitrile 0.800 1.17 Methylacrylate 0.952 1.223 0.940 1.179 Methyl methacrylate Styrene 0.905 1.062 Vinyl acetate 0.934 1.191 1.406 Vinyl chloride 0.919 Source: Datafrom Ref. 5.
change (%) 31.0 22.1 20.6 14.5 21.6 34.4
Rad./cal ChainPolymerization
449
Figure 6.1 Sketch of a dilatometer.
in Fig. 6.1. The total volume of the dilatometer (B to D) is predetermined (e.g., by the difference in weight when empty and when filled with water at a fixed temperature). The monomeror a solution of the monomerin solvent are introduced, along with an initiator, into the apparatus through filling tube A until the liquid is drawnwell up into the capillary tube D and the stopcock B is then closed. The dilatometer is placed in a thermostatic oil bath maintained at the desired reaction temperature and is immersedin the oil so that the capillary tube protrudes from which the volumeshrinkage is to be recorded. As the volumeof liquid increases by thermal expansion, the liquid will rise, fill the capillary tube, and overflow. The excess solution can be removed by wiping the top of the capillary tube with a piece of filter paper. As soon as the solution has come to a thermal equilibrium, the volume of solution will decrease. The change in height of the liquid in the capillary is measured periodically with a cathetometer (a rigidly mounted, vertically sliding telescope) or from the scale on the dilatometer. The rate of poly-
450
Chapter 6
merization can then be determined of the liquid.
from the rate of change in the height
Problem6.6 Show how the rate of a free-radical mined from the measured changes in the capillary dilatometer (Fig. 6.1).
polymerization can be deterliquid height (Ah) in a simple
Answer: Referring to Fig. 6.1, total volume of the dilatometer or the reaction system is V = VBC q- ~rr2h
(P6.6.1)
where VBCis the volume contained in the space from the stopcock B through the bulb C to the entrance to the capillary tube D, r is the radius of the capillary, and h is the length of the capillary or the height of the liquid in the capillary above the entrance. It follows from Eq. (P5.5.1) that the change in volume of the reaction system is proportional to the change in h, as in AV = Y o - V = 7rr2Ah where V0 is the initial volume and V is the volume at time t, given by
(P6.6.2)
V = w,~,~ + w~p + ws~s (P6.6.3) Here w,~, wp, and ws are the weights and v,~, vp, and ~, are the partial specific volumes of monomer, polymer, and solvent, respectively. (For polymerization of the bulk monomer, ws = 0.) To a very good approximation, o (P6.6.4) Wp
Wm
~
--
Wm
0 is the initial weight of monomer. where w m Substituting Eq. (P6.6.4) into Eq. (P6.5.3) and rearranging wm =
V wm o-v~ -- ws~s
(P6.6.5)
Since no polymer is present initially,
the initial volumeis given by (P6.6.6) ~ + ws~ Vo = wm° ,~ Assuming that all the monomeris converted to polymer after a sufficiently long time (t = cx~) when there is no further decrease in h, the final volume (P6.6.7) V~ = w,.~ o + w~~s Equations (P6.6.6) and (P6.6.7) from Eq. (P6.6.5) to yield V -
Voo o
may be used to eliminate
~,~ - ~p (P6.6.8)
On a weight fraction basis, the fractional yield of the reaction, y, may be written as
Y = w,,
-
w,~
(P6.6.9)
Radical Chain Polymerization
451
Then combining with Eq. (P6.6.8) and (P6.6.2), Vo - V = Ah(t_~_) (P6.6.10) Vo - V~ Ah(cc) Utilizing the definition of the initial rate of polymerization [Eq. (5.38)], one may then write (e6.6.11) y [M]o Ah(t) [M]o t Ah(t = cx~) y
=
Since Ah(t = c~) can be calculated (see Problem 6.7), P~ can be determined from the observed decrease in liquid height (Ah) in the capillary of a dilatometer at time t.
Problem6.7 A dilatometer (total volume 49.0 cm3, capillary radius 0.1 cm) was filled with a freshly distilled sample of styrene containing 0.1% (by wt) of 2,2’azo-bis-isobutyronitrile. The dilatometer was placed in an oil bath at 70q-l°C and was immersed in the oil so that the capillary tube protruded. Whenthe volume of the solution began to decrease after coming to thermal equilibrium, the fall in height of the liquid (Ah) in the capillary tube was determined periodically from the scale on the dilatometer. This yielded the following data: Time (s) 300 600 1800 3600 5400 7200
Ah (cm) 0.83 1.68 5.03 10.05 15.10 20.13
Determine the kinetic parameter kp/k~/2 at 70°C, given that f = 0.60 and ka = 4.0x 10-s s-1 at 70°C. [Density (g/cmz) at 70°C: styrene 0.860; polystyrene 1.046] Answer: Initial
volume of styrene (V0) = 49.0 3 at 70°C.
Wt of polystyrene at 100%conversion = Initial gcm-z) = 42.14 g
wt of styrene = (49.0 cm~)(0.860
V~ = (42.14 g) / (1.046 -3) = 4 0. 287 cmz W0 - V~ = (49.0
- 40.287)
or 8.713 3
3) = 277.22 (8.713 cm 2 Ah(t = c~) = (3.143)(0.1
[M]o = (1000
cmaL-1)(0.860 (104 g mo1-1)
gcm -a)"
The yield of polymer (y) can be calculated
cm
-1 8.27moiL from Eq. (P6.6.10)
and the poly-
452
Chapter 6
merization rate (~) from Eq. (P6.6.11) using the observed values of Ah. gives: Time(s) 300 600 1800 3600 5400 7200
% Conversion (y x 100) 0.30 0.62 1.84 3.69 5.55 7.39
/~ x l0 s (tool -1 s -1) 8.40 8.51 8.49 8.48 8.50 8.49
For low degrees of conversion (generally below10%)both [I] and [M], and hence /~, may be assumedconstant. The average value of/~ obtained from the above data is 8.49x10-5 mol L-1 -1. s [I]o = (1 g L-1)/(164 g mol -1) 6.1 -3 mol L-1 FromEq. (6.26), using initial conditions,
[M]0 (Ykd [t]o)) (8.49 × 10-s moll-t -1) s (8.27 molL 0.027 mol
METHODS
OF INITIATION
Equation (6.25) for rate of polymerization is general in that the reaction for the production of radicals [e.g., Eq. (6.3)] is not specified and the reaction rate is simply shownas /?4. A variety of initiator systems can be used and radicals can be produced from them by a variety of thermal, photochemical, and redox methods [3-5]. (The term catalyst is often used synonymouslywith initiator. This is incorrect in the classical sense, since initiator fragments appear as end units [cf. Eq. (6.4)] and the initiator is thus consumed. The use of the term catalyst may, however, be condoned since very large numbers of monomer molecules are converted to polymer for each initiator molecule which is consumed.) Polymerization can also be induced by supplying the initiation energy through irradiation with visible and ultraviolet light, high-energy or ionizing radiation, or by the passage of an electric current. The conversion of a monomerto a polymer will occur through the" normal propagation, termination, and transfer reactions as in free-radical and ionic chain polymerizations (see Chapter 8). Only the initiation processes will be different.
/Lad/ca/Chain Polymerization Thermal Decomposition
453
of Initiators
The thermal scission of a compoundis the most commonmeans of generating radicals to initiate polymerization. The numberof different types of compounds which can be used as thermal initiators is rather limited. Compounds with bond dissociation energies in the range 100-170 kJ/mol are usually suitable. (Others with higher or lower dissociation energies will dissociate too slowly or too rapidly to be useful.) The major class of compoundswith bond dissociation in this range contain the O-Operoxide linkage. There are numerous varieties of compoundsof this type and some are listed in Table 6.4.
Table 6.4 SomePeroxide Initiators for Radical Polymerizations Type Diacyl
Example peroxides
(~ C-O-O-C--~
Temperature (°C) for tl/2 of 10 h 73
0 0 Dibenzoyl peroxide (CH3)3 C-C-O-O--C (CH3) 3 II II 0 0 Diisobutyryl peroxide - CH CH 3 3 I I Dialkyl peroxides
21
115 CH3 CH 3 Dicumylperoxide
Peroxyesters
CH3-C-O-OC (CH3) 3 II O t-Butyl peracetate CH 30
Dialkyl peroxydicarbonates
O CH 3 II II I H-C-O- C-O-O- C-O-C-H I I C2H5 C2H5 Di-sec-butylperoxydicarbonate
102
45
454
Chapter 6
Thermal decomposition is ideally a unimolecular reaction with a firstorder rate constant, kd, which is related to the half-life of the initiator, tl/2, by Eq. (6.29). For academic studies it is convenient to select initiator whoseconcentration will not change significantly during the course of an experiment so that instantaneous kinetic expressions, such as Eq. (6.26), maybe applicable. From experience it seems that an initiator with a tu2 of about 10 h at the particular reaction temperature is a good choice in this regard. This corresponds to a lea of 2×10-5 s -1 from Eq. (6.29). For the peroxide initiators listed in Table 6.4 the required reaction temperatures for 10 h half-life (t~/2) are also shown. It should be noted, however, that the temperature-half-life relations given in Table 6.4 mayvary with reaction conditions, because some peroxides are subject to accelerated decompositions by specific promoters and are also affected by solvents or monomers in the system. Aside from peroxides, the main other class of compounds used extensively as catalysts are the azo compounds. By far the most important memberof this class of initiators is 2,2’-azobisisobutyro-nitrile (AIBN) which generate radicals by the decomposition reaction: CH3
~H3
CH3-C-N--N-C-CH3 CN CN
CH3 -~ 2CH3-C" + CN
N2
(6.39)
The activation energies for decomposition of azo compoundsare similar to those of peroxides and they undergo facile dissociation like the latter, although the azo initiators do not contain a weak bond like the O-O linkage. In spite of the high dissociation energy (,-~ 290 kJ/mol) of the C-N bond, docomposition of AIBN proceeds because the nitrogen which is formed [Eq. (6.39)] is a very stable gas and has a very high enthalpy formation. This initiator has a 10-h t~/2 at-64°C. Azo compoundsare preferred for scientific investigations because the choice of reaction conditions has muchless effect on the behavior of azo initiators and their kg values do not vary with the particular polymerization system as muchas those of peroxides. Initiator
Efiiciency
Initiators are not used efficiently in free-radical polymerizations. This becomes apparent when a material balance is performed on the amount of initiator that is decomposed during a polymerization and compared with the amount that initiates polymerization and thus becomes a part of the polymer formed. The values of f for most initiators lie in the range of 0.3-0.8. The major cause of this low f is wastage of primary radicals in "cage" reactions. When
Radical ChainPolymerization
455
an initiator molecule decomposesforming primary radicals, the radicals are each other’s nearest neighbors for about 10-l° s. During this short interval the primary radicals are surrounded by a "cage" of solvent and monomer molecules through which they must diffuse to escape each other. While in the cage, the radicals can be expected to be colliding on the average once every 10-13 s (the vibrational frequency of a diatomic molecule at reaction temperatures being approximately 1013s-1) and so any reaction can take place. To illustrate, the decomposition of benzoyl peroxide could lead to the following reactions: ~bCOO-OOCq~ ~ (2q~COO’)cage (q~COO’)cage (¢CO0")cage @CO0" + M ~COO" -- ~"
+ M
(2q~COO’)cage ~ (q~COO~ + COs)cage + M ~ ¢COOM" ~ ¢C00" ~ ¢COOM" + COz
(6.40) (6.41) (6.42) (6.43) (6.44) (6.45)
Equation (6.40) represents the primary step of initiator decomposition into two radicals, which are held within the solvent cage (with solvent and/or monomermolecules comprising the cage wall). The radicals in the solvent cage mayundergo recombination [i.e., reverse of Eq. (6.40)], reaction with each other [Eq. (6.41)], reaction with a monomermolecule contained the wall of the cage [Eq. (6.42)], or diffusion out of the solvent cage [Eq. (6.43)]. Once outside the solvent cage, the radicals may react with monomer[Eq. (6.44)] or decompose according to Eq. (6.45)] to yield a radical which may react with monomer. Once one or the other radical leaves the cage, it is extremely unlikely that the pair will encounter each other again. Recombination of the primary radicals [the reverse of Eq. (6.40)] has no effect on the initiator efficiency. Initiation of the polymerization occurs by reactions (6.42), (6.44), and (6.46). The initiator efficiency is decreased by the reaction indicated by Eq. (6.41) since the reaction products are stable and cannot give rise to radicals. This reaction is usually muchmore significant than any other in decreasing the value of f. Since the rate constants for radical-radical reactions are in the range 107 L/mol-s and higher, and the concentration of radicals in the solvent cage is high (,-~ 10 mol/L), there is a reasonable probability that the radical pair in the solvent cage will react as indicated by Eq. (6.41). All initiators suffer cage wastage reactions. For AIBN,for example, f is only 0.6 at 60°C because of these reactions.
Problem6.8 Consider the following schemeof reactions for free-radical chain polymerizationinitiated by thermal homolysisof initiator.with cage effect [6]:
456
~hapter6
I
~ (2R.)
(2R-)
(P6.8.1)
-~
(P6.8.2)
(R-) + ~ --~ (R’)
(P6.8.4)
~
R" + R. R"
+ M k.~
M-
+
M ~
M"
+
M’
~
Q’
(P6.8.5)
M"
(P6.8.6)
M"
(P6.8.7)
V
(P6.8.8)
where (R’) indicates a primary radical within a cage provided by the medium, is the stable product of reaction between a pair of primary radicals within a cage, M" denotes chain radicals having an end group R (derived from initiator), and P a dead polymer molecule; other species are as defined earlier. Reactions (P6.8.2), (P6.8.3), and (P6.8.4) are the alternatives available to a primary radical within cage, namely, reaction with its primary partner, reaction with a monomermolecule contained in the wall of the cage, and diffusion out of the cage. Reactions (P6.8.5) and (P6.8.6) are analogous to (P6.8.2) and (P6.8.3), but refer to the main body the solution, that is, they are reactions which may occur only after (P6.8.4). Neglecting Chain transfer, derive an expression for the rate of polymerization showing the cage effect. Answer: It should be noted that the rate of reaction (P6.8.2), unlike reaction (P6.8.5), first order with respect to [(R’)], since the primary radicals are necessarily formed in pairs in independent cages. It is also knownthat for all practical values of [M], reaction (P6.8.5) is negligible. The net rate of formation of (R’) is thus given d[(R-)]
- 2kd[I] - /¢, [(R.)]- ks [(R.)][M]kn[(R.)]
For a steady state concentration
[(R-)]
of (R.), d[(R’)]/dt
= 0. Therefore,
2ka[I] k~ + kD + k~[M]
(P6.8.9)
If reaction (P5.8.6) is fast, the rate of initiation will be given ~ = kD[(R’)] + k~[(R’)][M] = [(R.)] (ko + k,
(P6.8.10)
Combination of Eqs. (P6.8.9), (P5.8.10), and (5.25) (P6.S.11) -k~ + kD + k,[M] [IIV~[MI ( ~ ) x/2 kD+ k ~ [M] Comparison of Eq. (P6.8.11) with Eq. (6.26) shows thatthe polymerization is reduced by the cage effect. R~ = kp
457
Radical ChainPolymerization For k v >> k~[M]
and kD >> kr,
Eq. (P6.8.11) reduces to Eq. (6.26)
ideal kinetics and negligible cage effect. The initiator efficiency is not an exclusive property of the initiator alone, but it varies to different extents depending on the prevailing condition of polymerization, including the identities of monomerand solvent used. The viscosity of the reaction mediumhas an effect on f. Withincreasing viscosity, the lifetimes of radicals in the solvent cage are increased, leading to greater extents of radical-radical reactions within the solvent cage and hence to a lower value of f. In some cases, f varies with solvent due to the solvent reacting with (scavenging) radicals before the latter can initiate polymerization. The change of initiator efficiency with solvent mayin a few instances be due to solvation of radicals by solvents. The initiator efficiency for any particular initiator mayalso vary depending on the monomerwhich is polymerized. For example, the value of f for AIBNranges from 0.6 to 1.0 in the polymerizations of methyl methacrylate, vinyl acetate, styrene, vinyl chloride, and acrylonitrile, increasing in that order [9]. This is a consequence of the differences in the rates with which radicals add to the different monomers. Experimental
Determination
of f
Several methods can be used for the evaluation of the initiator efficiency. One method depends on the direct analysis of initiator fragments as end groups in the polymer formed compared to the amount of initiator consumed. The use of isotopically labeled initiators such as 14C-labeled benzoyl peroxide and other related peroxides, and 14C-labeled AIBNand asS-labeled potassium persulfate provide appropriate sensitive methods for determining the number of initiator fragments trapped as end groups in the resulting polymers [10,11]. A second method involves measurement and comparison of both polymer production and initiator decomposition. Since reaction environment has a significant effect on initiator decompositionreaction, it is necessary that the measurement of initiator decomposition is done during an actual polymerization. The decomposition of AIBNcan be followed relatively easily by monitoring the evolution of nitrogen. Determination of the number-average molecular weight, and hence the number of polymer molecules formed in a given time, and comparing with the number of radicals produced over the same period (estimated from initiator decomposition) allows a determination of f. This method, however, requires a knowledge of whether termination occurs by coupling or by disproportionation, since the former results in two initiator fragments per polymer molecule and the latter in only one. A third method involves counting of radicals in a system with radical scavengers which stop chain growth rapidly and effectively. The stable free
458
Chap~e~ 6
radical diphenylpicrylhydrazyl (DPPH)has been widely used for this purpose [10,11]. The DPPHradical (purple or deep violet), obtained by oxidation of diphenylpicrylhydrazine with PbO2, reacts with other radicals to form a non-radical adduct (light yellow or colorless): 02N
02 N
NOz(6.47) O2N
~ O2N
The reaction can be easily followed spectrophotometrically because of the color change associated with the reaction. Other radical scavengers have been used in similar counting of radicals [14]. The approach of determining f using radical scavengers is, however, not very useful as the reaction between the scavengers and radicals is often not quantitative. A fourth and probably the most useful method of determination of initiator efficiency is based on the dead-end effect in polymerization technique which is treated in a later section. This technique allows treatment of kinetic data obtained under dead-end conditions to evaluate both the rate constant for initiator decomposition (kd) and the initiator efficiency (f) under experimental conditions. Redox Initiation Manyoxidation-reduction reactions produce free radicals that can be used to initiate polymerization. This type of initiation is referred to as redox initiation or redox catalysis. A prime advantage of redox initiation is that radical production occurs at reasonable rates over a very wide range of temperatures, including 0-50°C and even lower, depending on the particular redox system. This allows a greater freedom of choice of the polymerization temperature than is possible with the thermal dissociation of initiators. This redox initiation can be arranged to proceed quickly under mild reaction conditions and is particularly useful for low and ambient temperature radical polymerizations. A wide range of redox systems, including both inorganic and organic components, either wholly or in part, maybe employed for this purpose. A general redox reaction described by A- B + X ----+ A" + Be + Xe (6.48) can proceed with any molecule AB, provided the reducing agent X is strong enough to split the A-B bond. For practical purposes, the A-B bond in redox systems must be relatively weak and this limits the choice of such materials. Someof the commonredox systems are described below.
459
Radical Chain Polymerization
(a) Peroxides in combination with a reducing agent are a commonsource of radicals, for example, the reaction of hydrogen peroxide with ferrous ion: HOOH + Fe z+ --~ HO" + OH- + Fe 3+ (6.49) Ferrous ion also promotes the decomposition of a variety of other compounds including various types of organic peroxides [4]: ROOR + Fe 2+ 3+ ~ RO" + RO- + Fe (6.50) 2+ 3+ RCOOH -+- Fe ~ RO" q- OH- q- Fe (6.51) +, 2+, 2+, 2+, 3+ Other reductants such as Cu Co Cr V and Ti can be employed in place of ferrous ion in manyinstances. Most of these redox systems are aqueous or emulsion systems. In organic media amines can be used as the reductant [15,16] for redox initiation with acyl peroxides, an examplebeing the combination of benzoyl peroxide and an N,N-dialkyl-aniline. O
O
R
q~-C-O-O-C-q~
+ q~-N-R
O ~
O
4-c-o- + -o-c-4 +
R ~.-N’+ R
Initiation is only by the q~COO"radical because the amino cation radical is not an effective initiator as shownby the absence of nitrogen in the polymer. The rate of initiation by this redox system will thus be given by R./ = k d [peroxide] [amine] (6.53) (Note the absence of factor 2 in this expression.) Substitution of R/in Eq. (6.25) gives t~ = 1/2 kp [M] (kcl[per°xide]2kt [amine])"
(6.54)
as the equation for the rate of polymerization with peroxide-amine redox initiation. Similar procedure may be followed for other redox systems. The decomposition rate constant kd for pure benzoyl peroxide in styrene polymerizations is 1.33x10 -4 s -I at 90°C, while that for the benzoyl peroxide-N,N-diethylaniline redox system is 1.25x 10-2 L/mol-s at 60°C and 2.29x10-3 L/mol-s at 30°C [15]. The redox system thus has a muchlarger decomposition rate. Peroxide decomposition is also accelerated in the presence of transition metal ion complexes such as copper (II) acetylacetonate and ammoniumsalts [17,18]. (b) The combination of a variety of inorganic reductants and oxidants can be used to initiate radical polymerization [4,19], for example, redox systems with persulfates as the oxidant:
460
Chapter 6
-o s-o-o-so + -O S-O-O-SO;+
+ SO- + Fe (6.55) + SO- + S,O(6.56/
2+. Other redox systems include reductants such as HSO~,SO~-, and Fe (c) A combination of inorganic oxidant and organic reductant initiates polymerization, usually but not always by oxidation of the organic 4+, component, for example [20], the oxidation of an alcohol by Ce Ce 4+ -~- RCH2- OH ~ Ce 3+ n t- H+ + RCHOH (6.57) or by V5+, Cr6+, or Mn3+ [21]. Other redox pairs include oxidation of aldehydes and ketones by Ce4+ and V5+ [22], oxidation of thiol compounds such as thioureas, thioglycolic acid, and 2-mercaptoethanol by Fe3+, 4+, Ce BROW-, and $2082- [23,24], and oxidation of oxalic, malonic, and citric acids by permanganate and Mn3+ [25]. Someredox polymerization involve termination by reaction between the propagating radicals and a component of the redox system. Thus in the alcohol-Ce4+ system [Eq. (6.57)], termination occurs according Mn" + Ce 4+ ~ Ce 3+ + H+ + dead
polymer
(6.58)
at high eerie ion concentrations. The propagating radical loses a hydrogen to form a dead polymer molecule with an olefinic end group. The rates of initiation [Eq. (6.57)] and termination (neglecting the usual bimolecular termination mechanism) are given by R4 = kd ICe4+] [alcohol] nt ---- /~ [Ce4+1 [M’] By making the usual steady-state assumption (i.e., the polymerization rate as
(6.59) (6.60) Ri = Rt), one obtains
kd kp [M] [alcohol]
(6.61)
Someredox systems involve direct electron transfer between oxidant and reductant, while others involve the intermediate formation of oxidantreductant complexes. For those redox initiations involving the equil~rium formation of intermediate complexesthat lead to radical formation, derivation of the kinetics follows in a straight forward manner (see Problem 6.9). Problem6.9 The free-radical polymerization of acrylonitrile initiated by the redox system Mna+-cyclohexanol(CH) was investigated [22] in aqueous sulfuric acid in the temperaturerange 30-45°C.The following reaction mechanisminvolving
461
Radical Chain Polymerization
3+ and the alcohol, whose decomposition the formation of a complex between Mn yields the initiating free radical with the polymer chain being terminated by the mutual combination of growing chains was suggested: K ~ complex (a) 3+ + CH k~
(b)
complex
R" + Mn2+ +
(c)
R" + 3+ -- ~ Mn 2+ +
(d)
R"
+ M -~
(e)
M~" + M ~ M,~+I"
(f)
M~" + M,~"
H+
products
MI"
~ polymer
Derive suitable rate expressions for evaluation of rate parameters from initial rates of polymerization.
Rate of Mn3+ disappearance Applying the steady-state
principle to the pfima~ radial R’, z+] k.K [Mn [CH] ko [Mna+] + hi [M] For reaction (a), [complex] K [Mn3+1 [CH]
(P6.9.1)
(P6.9.2)
3+ For total Mn [Mna+]tot
[Mn3+] + [complex] [Mn~+] (1 + K [CHI)
(P6.9.3)
Therefore, d [Mna+]tot dt
a+] d [complex] d [Mn dt dt k,- K [Mna+] ~+] [CH] + ko [R’] [Mn = k,.
ko k~ K [Mn3+]2 [CH] K [Mn3+ [CH] + 3+]
ko[Mn + k, [M]
If ko [Mn~+] >> hi[M], Eq. (P5.9.4) reduces to the form d [Mn~+]tot 3+] [CH] 2k,. K[Mn dt 2k,- g [Mn3+]tot [CH] 1 + K [CH] = 2k~ [Mn3+]tot
(
1 [CI-~
1 K)
(P6.9.4)
462
Chapter 6
The values of K and kr can be computed by plotting (- d [Mn3+]tot / dr) versus a+. From the intercept and the ratio 1/[CH] at constant concentration of total Mn intercept/slope of the plot the rate constant for the unimolecular decomposition of the complex (k~) and its formation constant (K) can be calculated. Rate of polymerization Applying the steady-state principle to the growing chains, i.e., of reactions (d) and (f),
equating the rates
~ k~ JR’] [M] = k, [M’] ~-"
[M’] " (ki JR’] ’/2 [M]) k,
(P6.9.6)
Substituting for [R’] in Eq. (P5.9.5) from Eq. (P5.9.1) and then substituting [M.] ~n Rp = kp [M-] [M], yields p~ = k~, k~/2 (k~ K [Mn3+] [CH])1/2 ~/~ [M]
k:/2
+ [M])1/2
If k0 [Mn3+] >> k~ [M], Eq. (P5.9.7)
(P6.9.7)
can be approximated to the form
I~ = k~ k~/~ (k~ K [CH])~/~ ~/~ [M] The com~osk¢ ~ns[am k~ (k~ / ko ~/~ can be obtained ~om ~h¢ slope of the plot of ~M]~ / R~) versus -~/[CH], if k~ and g are ~own from ~q. (P5.~.5). ~or fitfin~ ¢xpe~mcntal ra~e dam ~q. (P5.11.7) can b¢ conveniently rea~anged to the form
This equation can be used to evaluate rate parameters using the iNtial rate of polymeNzation (~) data that may be obtained ~om the iNtial slope of the conversion vs. time plots. Sin~ k~ and K are obtained from Eq. (P6.11.5), the value of the mmposite constant k~ (k~/k, ~)~1~ can be obtained ~om the inter~pt of a plot of ([M]/~)~ against 1/[Mn ~+] at mnstant ~ncentration of the monomer[M] and the reducing agent [CH]. ~e slope gives the parameter k~/k~/~ while the quotient of intercept and slope yields k,/k~.
Photochemical Initiation Photoinitiation of vinyl polymerization offers significant practical advantages. An obvious advantage is the avoidance of chemical contamination by initiator residues. Moreover, there is a marked convenience to photochemical reactions that appeals to many researchers. Photoinitiation and
Radical Chain Polymerization
463
polymerization can be spatially directed (i.e., confined to particular regions) and turned on or off simply by turning the light source on or off. Moreover, the initiation rates can be controlled by a combination of light intensity, source of radicals, and temperature. Extensive and expanding use is being madeof these advantages in the printing and coating industries. Somemonomersundergo direct photoinitiation and free-radical chain polymerization when exposed to ultraviolet or visible light. For other monomers,a photosensitizer must be added to the system. Photosensitizers are compoundsthat absorb ultraviolet or visible light and then dissociate into free radicals or transfer energy directly to the monomer. Direct
Photoinitiation
Two different types of direct photoinitiation can be recognized. In the first, absorption of light photons (quanta) yields an electronically excited monomer molecule M* : M +
hv
~
M*
(6.62)
which subsequently decomposes to give radical fragments: M* ~ R" + R" (6.63) capable of initiating polymerization of the monomer. Examples of monomersin this category include alkyl vinyl ketones and vinyl bromide both of which dissociate whenirradiated with ultraviolet light by the following reactions: O
O
R-C-CH=CH~ -----> O R-C"
~
R"
CH2=CHBr --~
+
R-C"
+ "CH=CH2
(6.64)
CO
Br"
(6.65) + CH2=CH"
(6.66)
The resultant monoradicals add to the monomerand radical chain polymerization takes place. The second type of initiation mechanism is exemplified by the photopolymerization of styrene or methyl methacrylate. Absorption of light in this case does not result in decomposition of monomermolecules. Instead, it has been suggested [26] that radicals are produced by a complexinitiation mechanism,illustrated for styrene by the following equations: + hv’ Ph-CH=CH2
~
(PhCH=CH2)*
__~PhCH=CH2 t*ph~H-~H2
(6.67) (6.68)
464
Chapter 6
Ph~H -- ~H2 4Ph~HCH2CH2~HPh
PhCH -- CH2 ~ Ph~HCH2CH~HPh (6.69) 4- PhCH : CH2 ~ CH3~HPh 4PhCH = CHCH~HPh
(6.70)
According to this mechanism, the absorption of light produces an excitdd singlet state of the monomerwhich may either fluoresce [Eq. (6.67)] be converted to an excited (and long-lived) triplet st.ate [Eq. (6.68)]. latter maybe regarded as a diradical, that is, oCH2-C(H)X.Attack on the monomerby this diradical ultimately yields two monoradicals [Eqs. (6.69) and (6.70)], which, in turn, initiate polymerization. For both types of direct photoinitiation the rates are proportional to the light intensity and to the extinction coefficient of the monomer(see later). Photosensltization Even if direct light absorption as above does not occur, polymerization can still be initiated if photosensitizers are present that produce free radicals when they absorb ultraviolet or visible light. The same substances that are used for thermal initiation are often used for photosensitization. For example, azo compoundsand peroxides are photosensitizers, and the photoinitiation reaction is the sameas is the thermal initiation process, described earlier in this chapter. However, the photoinitiation can take place at much lower temperatures than in the thermal initiation by the same initiators. Moreover, manyiniti£tors can be used as photosensitizers even though they do not dissociate thermally at convenient rates or temperatures to be useful as thermal initiators. For example, azoisopropane does not dissociate sufficiently rapidly below 180°C to be useful thermal initiator. However,it photodissociates even at low temperatures when irradiated with near-ultraviolet light: (CH3)2CHN
= NCH(CH3)2
+ h~ (3000~
< A < 4000~)
2(CH3)2~H 4- N2 (6.71) Other examples of such photosensitizers include carbonyl compoundssuch as ketones, both aliphatic and aromatic. Aromatic ketones are, however, more useful in commercial practice, since their absorptions occur at longer wavelengthand their efficiency of initiation (quantumyield) is higher. Benzophenone and acetophenone and their derivatives are the most commonly encountered aromatic ketones. Ketones undergo homolysis by one or both (often simultaneously) of two processes- fragmentation and hydrogen abstraction. Fragmentation involves O O O
¢-c-¢’
+ "¢’
(6.72)
while hydrogen abstraction occurs only in the presence of a hydrogen donor (RH):
RadicalChainPolymerization 0 II
¢-c-¢’
hu
465
0 [I RH C (¢--¢’)* ------>
OH
I
¢-C-¢’ + R"
(6.73)
Amineswith abstractable c~-hydrogensare the mostefficient and extensively used hydrogendonors; less efficient donorsinclude alcohols and ethers. The hydrogenabstraction is generally moreefficient than fragmentation and occurs at longer wavelengths(lower energy photons). The relative amounts of the fragmentationand hydrogenabstraction reactions vary dependingon the type of initiator and on the hydrogendonor employed. Similarly photolytic reactions occur with benzoin (I), benzoin ethers (II), benzil (III), and benzil ketals (IV). These and related compounds are extensively used as photoinitiators in commercialpractice, usually in combinationwith hydrogendonors. 0 OH II I
0 OR II I
(I)
(II)
0 0 II II
0 OR II I
(Ill)
I OR (IV)
Dye-sensitized photopolymerizations are of interest in that the spectral range of photoinitiation can be extendedinto the visible region. A variety of dyes such as methyleneblue, thionine, tluorescein, and eosin undergo excitation and the excited dye can interact with an appropriate substanceto produceradicals which, in turn, can initiate polymerizationof the substrate monomer.Dye-sensitized photopolymerizations often comprise redox systems involving electron or hydrogentransfer betweenthe excited dye and the other substance. Anexampleis the methyleneblue-p-toluenesulfinate ion system. Thep-toluenesulfinate ion is oxidized by the irradiated dye to the correspondingradical whichinitiates polymerizationof the monomer:
CH3--~~SO~
~
CH3---~SO
2"
(6.74)
Somedye-sensitized systems appear to proceed by energy transfer from the excited dye D* to another compoundC, D* + C ~ D + C*
(6.75)
466
Chapter 6
Radicals then form by decomposition of the excited state C, C* ~ radicals
(6.76) The net outcomeis that, whereas C* cannot be produced by direct irradiation of C with light of frequency t~, the excitation of C takes place because D* is able to transfer energy to C at a different frequency, ut, which can be absorbed by C. Rate
of
Photopolymerization
In photochemistry, a mole of light quanta is called an Einstein. A mole of light quanta of frequency ~ or wavelength A has energy Nhvh~, or NAvhC/A,where NAyis Avogadro’s number, h is Planck’s constant, and c is the speed of light. The rate of photochemical initiation maythen be expressed as P~ = 2~I~ (6.77) simply by replacing led [I] of Eq. (6.14) with Ia, the intensity of absorbed light in moles (Einsteins) of light quanta per liter per second, and replacing f with d~ for photochemical polymerization. The factor of 2 in Eq. (6.77) is used to indicate that two radicals are produced per molecule undergoing photolysis. The factor of 2 is not used for those initiating systems that yield only one radical instead of two. Referred to as the quantumyield for initiation, ~ is synonymouswith f in that both describe the efficiency of radicals in initiating polymerization. Thus, the maximumvalue of ¢~ is 1 for all photoinitiating systems. An expression for the photopolymerization rate is obtained by combining Eqs. (6.25) and (6.77) to yield P~p = kp [M] (9
I~ / ~)1/2
(6.78)
Problem 6.10 The polymerization of methyl methacrylate (1 mol per liter of solution) is carried out using a photosensitizer and 3130 ~ light from a mercury arc lamp. Direct measurementby actinometry showsthat light is absorbed by the systemat the rate of 1.2x105ergs/L-s. If the quantumyield for chain initiation in this systemis 0.50, calculate the rates of initiation and polymerization.[k~,/k~/2 at 60°C = 0.102 L1/2 mo1-1/2-1/2] S Answer: Energy of 1 photon (hc/A) = (6.63 x -27 er g s) (3 x 1 01 (3.13 x 10-5 cm) -12= 6.35 x 10 erg
467
Radical Chain Polymerization
Energyof 1 mol of light quanta -12 -1) erg quantum = (6.02 x 10~z quanta tool -1) (6.35 10 = 3.82 × 1012 ergs mo1-1 I, = (1.2 × 105 ergs L-ls-1)/(3.82 × 1012ergs tool -1) = 3.14 x 10-8 -1 tool L-is Ri = 2~ar, ---- 2 x 0.5(3.14 × 10-s molL-is-1) ----- 3.14 x 10-s -1 tool L-is 1/~ /~ = (k,/k~/~)
[M] (R,/2)
= (O.102Ll/2mo,-l’2s -1/2) (1.0mol -I) ( 3.14× 10-8mo1 L-is-l) = 1.28 x 10-5 -1 mol L-is Assuming,for simplicity, that the incident light intensity does not measurably vary with thickness of the reaction system, I, will be given by
io = do [A] b
(6.79)
where lo is the incident light intensity, A is the species that undergoes photoexcitation, e is the molar absorptivity (extinction coefficient) of A at the particular frequency of radiation absorbed, and b is the thickness of the reaction system being irradiated. (e usually has units of liter/molcm.) Combination of Eq. (6.77) with Eq. (6.79) yields ~ = 2+ao [A] b (6.80) This can be substituted into the general equation (6.25) for P~o to give P~ ---
/¢p [M]( ~, fl~,Zo -~[Al b ) 1/2
(6.81)
Equation (6.81) indicates that for photopolymerizations P~ is first order in [M], ½-order in light intensity and ½-order in [hi for the case where there is negligible attenuation of the light intensity in traversing the reaction vessel. Whenthe photoexcitation involves monomer,i.e., A is M, Eq. (6.81) becomes 1~ = kp[M] 3/2
(~elo
b~ 1/2
(6.82)
that is, the dependence of Rp on [M] becomes 3/2-order. Abnormal orders in [M] have been found under certain circumstances. An example is the photopolymefization of methyl methacrylate with ketone photoinitiators [27]. For this system the dependence of Rp on [M] drops from first-order [Eq. (6.81)] to ½-order as [M] increases, leading to quenching by the monomer. In simple terms, a quencher (which can be A or M or solvent) undergoes energy transfer with the photoexcited species to dissipate the excitation energy. Quenchingcan be observed if the concentration of A or Mis too high. It leads to a lower than expected dependence of Pqo on the component of the system that acts as a quencher.
The use of Eq. (6.82) assumes that there is negligible attenuation the light intensity in passing through the reaction vessel. This wiIl be nearly true ~only whenthe light absorption is quite low or very thin reaction vessels are employed. For most polymerizations, however, the light absorption will not be negligible and hence the incident light intensity will vary with thickness. From Lambert-Beer’s law, -~ I [A]b = Io e
(6.83)
where ~r is the light intensity at a distance b into the reaction vessel. The light intensity absorbed, Ia, is then given by
= ±o- = ±0 where b now reprrsents the total thickness of the reaction vessel. An expression for the polymerization rate can be obtained by combining Eq. (6.25) with Eqs. (6.77) and (6.84) to
1/2 R~ = kp[M] [.~I°
(1 - ~,e-~[Alb)]
¯
(6.S~)
The light intensities delivered by various light sources are usually known in units such as kcal/s, kJ/s or erg/s, and it is necessary to convert them into the appropriate units of moles (Einsteins) of light quanta per liter per second before use in the above equations. Measurement
of Absorbed
Light
One may avoid the use of Eq. (6.85) and, instead, use Eq. (6.78) [with Ia defined by Eq. (6.84)] by directly measuring /’a in the particular polymerization system (see Problem 6.10). Measurementof light intensity, generally referred to as actinometry, may be performed with chemical, thermal, and electrical actinometers. The thermal and electrical actinometers are generally more convenient to use than chemical actinometers and include semiconductor photodetectors, photomultipliers, and thermocouptes which operate on the principle of converting photon energy to either electrical or thermal energy. The absorbed light intensity Ia is measured by placing an actinometer directly behind the reaction vessel and measuring the differences in light intensity whenthe vesgel is emptycomparedto when it holds the reaction system.
tL~d~calChainPolymerization Initiation
by Ionizing
469
Radiation
High-energy or ionizing radiation can induce chain reaction polymerization of a pure monomer (or a solution of the monomer). Alpha particles, beta rays (electrons), gammarays, or high-velocity particles from particle accelerator can all be used. (Ionizing radiations have particle or photon energies in the range 10 keV-100 meV compared to 1-6 eV for visible-ultraviolet photons.) Practically any monomerthat polymerizes by a free-radical mechanism can be polymerized in this way. Though rapid polymerization of monomers and the cross-linking of polymers by highenergy radiation have been considered as possible manufacturing processes, radiation-induced polymerization has achieved far less commercial success than photochemical polymerization. The reason is the higher costs and safety problems of ionizing radiation sources compared to photochemical sources. Gammaradiation is the most convenient type of high-energy radiation for initiating polymerization because its high penetrating power affords uniform irradiation of the system. Because gammarays are absorbed to the same extent by solids as by liquids, solid monomerscan be polymerized readily. This allows polymerization of manymonomersat low temperatures. The chemical effects of the different types of radiation on molecules are qualitatively the same, though there are quantitative differences. Molecular excitation mayoccur with the subsequent formation of radicals in the same manner as in photolysis, but ionization of a compoundby ejection of an electron is more probable because of the higher energies of these radiations. (For this reason such radiations are termed ionizing radiations.) Thus a compoundC, on excitation, may yield a radical-cation C+" by ejecting an electron, C + radiation -~ C+" + e(6.86) The radical-cation can propagate at the radical and positive centers depending on reaction conditions. It mayalso dissociate to form separate radical and cationic species: C+" ~ A+ q- B" (6.87) The initially ejected electron maybe attracted to the cation A+ with the formation of another radical: A+ q- e- ----* A"
(6.88)
The ejected electron may also be captured by the component C forming an anion C- which may or may not be ex6ited depending on the energy of the electron, and may further dissociate producing radicals and ions:
470
Chapter 6
C + e-
~
C-
-[-B-
~ A"
B- --~
C-
B" -[-e-
(6.89)
(6.90) (6.91)
The high-energy irradiation of either a pure monomeror a solution of a monomergenerates both free radicals and ions. In light of the above discussion, these seem to result more from the gross "damage" sustained by the monomerthan from the selective induction of specific chemical reactions. Becauseof this lack of selectivity, it is not possible to calculate a meaningful quantumyield for radical-induced reactions. Instead, the energy yield is described by a G-value, which is defined by (say, for substance A), G(:/:A)
number of molecules of A formed or consumed xl00 numberof electron-volts of energy absorbed
(6.92)
Since the high-energy irradiation generates both free radicals and ions, either free-radical or ionic chain polymerizations may be induced, the preponderance of one or the other mechanism being dependent on the nature of the monomer,as well as on the temperature, and purity of the reagents. Somemonomerssuch as acrylic esters, vinyl esters, and vinyl fluoride, polymerize only by free-radical mechanisms,while others such as styrene, acrylonitrile, isoprene, apparently polymerize by both radical and ionic types of chain mechanisms.Isobutylene, however, polymerizes only by a cationic chain mechanism.It is usually only at low temperatures that the ionic species are stable enough to initiate polymerization. At ambient or higher temperatures, the ionic species are usually not stable and dissociate to yield radicals. Initiation mayalso be carried out using initiators or other compounds which are prone to undergo decomposition on irradiation. Three distinct phases may be identified in a radiation-induced polymerization. In the first phase, the interaction of radiation with monomer, -16 solvent molecules or other compoundsoccurs within a brief interval of 10 to 10-15 s, resulting in the formation of electronically excited molecules, ions, and electrons. In the second phase, which takes place some 10-14 to 10-1° s after the initial interaction, these products dissociate or react with monomerto yield a set of initiating free radicals and ions. In the third phase occupying the time regime of 10-1° to 10-1 s, these free radicals and ions undergo the normal elementary reactions of initiation, propagation, transfer, and termination characteristic of chain polymerization. The irradiation of a pure monomer gives rise to the simplest initiation reactions, because only one chemical species absorbs the radiation. However,
Radical Chain Polymerization
471
solutions undergo more complicated initial reactions because both the solute and the solvent can absorb radiation energy to produce ions and free radicals. As a useful approximation, one can assume that the fraction of the total energy absorbed by a particular species in solution is proportional to the electron fraction of that species. The electron fraction is defined as the number of electrons contained in that species divided by the total number of electrons in the whole solution.
Problem6.11 If a 0.1 Msolution of styrene in carbon tetrachloride is irradiated to initiate polymerization,whatfraction of the total energyabsorbedby the system will be absorbed by the solvent ? Whattype of species will be the predominant 3] initiating species ? [Styrene density -- 0.905 g/cm3;CC14density = 1.594 g/cm Answer: Basis: 1000 cm~ solution Vol. of styrene (CsHs) ---- (0.1 mol)(104 g mo1-1)/(0.905 -3) ~ = 11.49 cm Assumingadditivity of volumes, Amountof CC14 = (1000cm3 - 11.49cm3) (1.594 gcm-a) -1 / )(154 g tool = 10.2 tool [CCl4]
=
-a 10.2 tool L
The numbersof electrons in styrene and CC14 molecules are 56 and 74, respectively. Therefore, the electron fraction of CC14 in solution is 74 [eel4] 74 [CCl4].q- 56 [CsH8] 74 x 10.2 = = 0.993 74×10.2 + 56×0.1 Thus, 99.3%of the total energy absorbed by the system will be absorbed by the solvent, and hencemostof the initiating ions and free radicals will be derived from the solvent. Thestyrene polymerizationis this case will be initiated predominantly by species such as CCI~, CCI~+, CI’, CC13", etc. eCC h =
The kinetics of radiation-initiated polymerizations follow those of photolytic polymerization in a relatively straightforward manner. The rate of initiation is determinedby the intensity of irradiation and the concentration and radiation susceptibility of the compoundthat decomposesto yield the initiating species (ions and/or radicals). The final expression for the rate
472
Chapter6
polymerizationis, however,determinedby the exact details of the initiation, propagation, and termination steps. l~ree-Radical
Chain Initiation
Themostimportantcharacteristic of the initiation step in radiation-induced free-radical chain polymerizationis the yield of radicals generatedby the absorption of a given radiation dose. This characteristic is quantified by a G-value, defined as the numberof radicals producedfor 100 eV of energy absorbed. This is referred to as GM(R" ) or Gs(R"), dependingon whether the radiation energy is absorbedby the monomer or by the solvent. SuchGvalues have been determined for a numberof commonmonomersby radical scavengingtechniques. Sometypical values are shownin Table 6.5. Froma knowledge of such values the rate of formationof radiation-initiated radicals can be calculated in the samewayas wasdescribed earlier for thermal and photochemicalinitiation. Thus, for the radiation-induced polymerizationof a pure monomer, the rate of formationof initiating radicals is described by d[R’] aM(R’) (dQA~ d~ -- i00 \--~-] where(~A is the energyabsorbedper unit volumeof the reaction systemFor monomer solution, the correspondingexpression is
d[R.]_ dt
100
+
(dQA) 100 J \ dt
(6.94/
The energy absorption per unit volume, QA,and the rate of energy abTable6.5 G-Values(100-eVyields of initiating radicals) in RadiolyticFree-RadicalChainPolymerization Monomer or solvent Styrene Acrylonitrile Methylmethacrylate Vinylacetate Isobutylene n-Hexane Benzene Toluene
GM(R-) or ) Gs(R" (radicals/ 100-eV) 0.66 5.0 6.1 9.6 3.9 5.8 0.66 2.4
Radical Chain Polymerization
473
sorption per unit volume, dQA/dr, are related, respectively, to the dose and dose rates (the terms used by radiation chemists to express energy absorption per unit mass) by the density of the system. Radiation doses are often expressed in a unit called the rad, which is defined as 100 ergs/g. A typical dose rate from a 6°Co "),-ray source wouldbe 106 rads/h or 1 Mrad/h.
Problem 6.12 Consider the irradiation of (a) pure styrene (density = 0.905 g/cma) and (b) 1.0 Msolution of styrene in toluene (density = 0.871 g/era3) at 20°C with 7-rays and a dose rate of 1 Mrad/h. Calculate the rate of initiating radical formationin the twocases. Answer: (a)
dQ A dt
= (l×10 s radh -a)(10z
ergsg-a rad-1)(0.905
g -a)
(6.24 x 10la eV erg-a) (2.78 x 10-4 -1) h s la -a -1 = 1.57 × 10 eV crn s -- (0.66 x 10-2 radicals eV-a) (1.57 = 1.04 x 1034 radicals cm-3 -a s
× 10 la eV
cm-3 -1) s
(b) Assumingadditivity of volumesof styrene (Calls) and toluene (Crt-Is), obtains.by calculation: [CrHa] -- 8.34 mol -1 L Therefore,
d0h = (1 x 10~ tad h-~) (102 ergs g-1 rad-1) (0.871 g -~) dt
(6.24 × 10n eV erg-~) (2.78 x 10-4 -~) hs = 1.51 x 101~ -as eV -1 cm
The numbersof electrons in styrene and toluene are 56 and 50, respectively. Therefore, 56 (1.0 tool -a) ~C~H~= ’56(1.0 tool L-1) -t- 50(8.34 tool -a) =0. 12 eCTI-h = 1.0 -- 0.12 = 0.88 From Eq. (6.94), dt
-- [(0.12)(0.66 x lO-2radicais -1) -q-(0.88)(¢~.4 x (1.51 x 10’~ ~Vcrn-z -a) s TM -~ -~ = 3.31 × 10 radicals cm s
X
lO-~radicals eV-~)]
474
Chapter 6
Ionic
Chain Initiation
The G-values for the initial formation of ion pairs in liquids are in the range 3 to 4. Though this is comparable to the G-values found for free-radical formation, the efficiency of ionic chain initiation is much lower than that of free-radical chain initiation. This is because most of the gegenions (see Chapter 8) formed initially do not separate, but instead undergo mutual charge annihilation. The radiation yield of "free" ions, which .can initiate polymerization depends on the dielectric constant (e) of the medium, higher e promoting the yield of free ions. Thus, in hydrocarbons which have low dielectric constants (e-values 2 to 4), the G-value for "free" ions is only 0.1, whereas alcohols which have e-values in the range 20 to 40 show free-ion G-values of 0.6 to 1.5 and water with e = 78 has a free-ion G-value of about 2.5. Moreover, ionic chain polymerizations are especially sensitive to traces of impurities, and these impurities can exert a strong inhibiting effect.
Problem 6.13 It is observed that styrene that has been dried by distillation from sodium-potassium alloy polymerizes under irradiation about 200 times faster than styrene that has only been subjected to a single conventional distillation. Give a qualitative explanation for this difference. Answer: Ionic chain polymerizations are especially sensitive to traces of moisture and other impurities which can terminate ions. Water and other similar compoundsterminate ions by transferring a proton o~: negative fragment (see Chapter 8) For example, the cationic polymerization of styrene, the cationic chains are effectively terminated by proton transfer to water molecule:
"{" H20 "---’~ -I~Jn i~ CH2R ~-rCH?-CH Dr" IC+
R-~CH2 ~
O+ -~nCH =~
+H3
Styrene monomer,as normally purified by conventional distillation, has sufficient water present (ca 10-2-10-4 M) to prevent ionic polymerization and consequently only radical polymerization occurs. In an extremely dried sample of styrene (as obtained by distillation from sodium-potassium alloy) the polymerization, however, proceeds entirely by cationic propagation. Ionic polymerizations are generally much faster than free-radical polymerizations.
Radical Chain Polymerization
475
By analogy with free-radical polymerizations, Eqs. (6.93) and (6.94) can be used also to calculate the radiation-induced rate of formaIion of initiating positive and negative ions by replacing R" by R+ or R-. Pure Thermal Initiation Many monomers appear to undergo a spontaneous polymerization when heated without the addition of an initiator. In most cases, such polymerizations are due to initiation by the thermal or photolytic homolysis of impurities (including peroxides or hydroperoxides formed due to 02) present in the monomer. Thus, it is observed that most monomers, when exhaustively purified (and contained in exhaustively purified vessels) do not undergo a purely thermal, self-initiated polymerization in the dark. However, some monomershave been unequivocally shown to undergo self-initiated polymerization. Styrene and methyl methacrylate belong to this type of monomer,The rates of thermal, self-initiated polymerizations are much slower than the corresponding polymerizations initiated by the thermal homolysis of an initiator such as AIBN,but are far from negligible. For example, the self-initiated polymerization rates for bulk styrene at 60°C and bulk methyl methacrylate at 70°C are observed to be 1.98x10-~ mol/L-s [28] and 0.21x 10-6 mol/L-s [29]. The extent of self-initiated polymerization must therefore be taken into account in any polymerization study if it is conducted at temperatures at which self-initiation constitutes a significant part of the total initiation process. At very low initiator concentrations, thermal initiation makes an appreciable contribution to the polymerization rate for styrene. The self-initiation mechanismfor styrene polymerization has been established [30]. It involves the formation of a Diels-Alder dimer (V) of styrene followed by transfer of a hydrogen atom from the dimer to a styrene molecule : 2CH2=CH (6.95)
(v) CH3-~:H (6.96) Ph
Ph
476
Chapter 6
The Diels-Alder dimer has not been isolated confirmed by ultraviolet spectroscopy.
but its existence has been
Problem6.14 There is evidence [30] that thermal self-initiated polymerization of styrene maybe of about five-halves order. Showthat this is in agreementwith the established initiation mechanism involving a Diels-Alderdimer formation [Eqs. (6.95) and (6.96)]. Answer: The higher than second-order rate observed for thermal conversion of monomer indicates that Eq. (6.96) is the slow step. Representing the concentration Diels-Alder dimer (V) by [Ell and that of styrene by [M], R, l= k,[DI[M = ki K whereK is the equilibriumconstant for the reaction of Diels-Alderdimerformation [Eq. (6.95)] and ki is the rate constant for the initiation reaction [Eq. (6.96)]. Using steady-state approximation (gi k,[M’l 2 3= kiK[M] [M’] =
a/2 [MI
Substituting this into Eq. (6.20) gives
showingfive-halves order in monomer concentration.
The self-initiation mechanismfor methyl methacrylate appears to involve the formation of a biradical by reaction of two monomermolecules followed by hydrogen transfer from some species in the reaction system to convert the biradical to a monoradical [32]: CH.~ CH3 ~ ~ "C-CH2-CH2-C’I I H-C’CH2"CH2-CI"l (6.97) 2CH2~---.C. COOCH3 COOCH3 COOCH3 COOCH3 COOCH3 CH3
CHz
CH3
The possibility of the diradical itself undergoing propagation to form large chains is very small because a diradical must almost inevitably cyclize at someearly stage in its growth.
Rad/caJ Cha/n Polymerization
DEAD-END
477
POLYMERIZATION
Under normal situations where sufficient initiator concentration is present, the free-radical polymerization of a given monomer solution at a given temperature proceeds until equilibrium is reached at which point the monomer concentration decreases to the equilibrium or critical value [M]e (see later) corresponding to the temperature of polymerization. This represents the maximum possible conversion (Pc) of monomer to polymer at the given temperature and it may be attained if only the initiator molecules do not get depleted during the process to below a minimumrequired to sustain the polymerization. However, in the event of initiato~ concentration used being low and insutficient, leading to a large depletion or complete consumption of the initiator before maximum conversion of monomer to polymer is accomplished, it is quite likely to observe a limiting conversion poo which is less than Pc. This is known as the dead-end effect in radical polymerization. The effect is shown schematically in Fig. 6.2. However, if there is autoacceleration effect or gel effect (see later) leading to a sharp rise in rate of polymerization, viscosity of medium, and degree of polymerization, pure dead-end effect cannot be observed.
1.0
-
(Injection of freshinitiator)
....
o 0.2
o o
0 Time Figure6.2 Schematic representation of dead-end effect in radical polymerization showing a limiting conversion of monomerto polymer (due to initiator concentration used being low and insufficient). Injection of the initiator in adequate amounts in the system at time t] immediately causes formation of more polymers up to a maximumconversion corresponding to the equilibrium monomerconcentration
478
Chapter6
Consider a dead-end polymerization initiated of an initiator. Recalling Eq. (6.33)
\r~t
by the thermal homolysis
I t"~--d) (1 -- e. -kdt/2)
(6.33)
where p is the fractional extent of monomerconversion at time ~ and [I]0 is the initial concentration of the initiator, let p~ be the limiting conversion attained at long reaction times (~ ---~ oc). Equation (5.33) then becomes -ln(1 - p~) = 2kl~lf[I]°l
’l~f
\
(6.98)
Dividing Eq. (6.33) by Eq. (6.98), rearranging, and then taking logarithms of both sides leads to the useful expression In
1 1~(1 )
(6.99)
=-2
A plot of the left side of Eq. (6.99), which is equivalent to the expression in [(ln[M]~ -- In[M]) /ln[M]~ - In[M],)], versus time permits evaluation of kd (see Problem 6.15). Since kd is determined, f can obtained from either Eq. (6.26) or (6.98) if the ratio kp/k~/2" is known from other studies. The thermal dissociation rate constants and activation energy values for several commonlyused initiators are listed in Table 6.6.
Table 6.6 Thermal Decomposition of Initiators Initiator Acetyl peroxide 2,2’-Azobisisobutyronitrile Benzoyl peroxide t-Butyl hydroperoxide t-Butyl peroxide Cumylperoxide
5kd x 10 2.39 0.845 5.50 0.429 3.00 1,56
Theunits of kd are s-i; the units of Edare Ll/mol. Source:Data from Ref. 3.
T°C 70 60 85 155 130 115
Ed 136.0 123.4 124.3 170.7 146.9 170.3
479
Radical Cha/n Polymerization
Problem6.15 Isoprene was polymerized in bulk at several temperatures using AIBNat an initial concentration of 0.0488 mol/L in dead-end polymerization experiments [33]. In every case, the conversion increased with time until a limiting value was obtained beyond which no further polymerization was observed. No autoacceleration effect was observed in this system. The data of fractional degree of conversion (p) with time, including the limiting value of conversion (p~), determined at each temperature are shown in table below: 60°C 70°C Time (h) .p Time (h) 0.054 4 8 16 0.086 6 30 0.167 12 0.220 24 48 72 0.280 30 96 0.315 48 144 0.360 72 240 0.390 96 300 0.390 150 oz 0.390 cxz Source: Data from Ref. 33
p 0.055 0.102 0.180 0.235 0.273 0.310 0.310 0.325 0.325 0.325
80°C Time (h) 2 4 6 8 16 24 48 o~
0.100 0.172 0.202 0.240 0.290 0.305 0.305 0.305
Determine the kinetic parameters kd and (kp / kit/z) fi/2 for isoprene-AIBN system and the activation energy of the initiator dissociation. Answer: The left side of Eq. (6.99) is plotted against time t in Fig. 6_3 using the conversion-time data of the isoprene-AIBN system. The slope of the linear plot yields kd/2, and hence kd, of AIBNin isoprene. (k~, / k~t/~) fl/2 is then calculated from Eq. (6.98). This yields Temperature (°C) 60 70 80
-8. 8.54 x 10 -5 3.08 × 10 -5 9.84x 10
3.27 4.94 8.17
It is possible to calculate f from the above values of (k~/k~tl2)f 112 if k~,/k~ I~ is known from other studies. An Arrhenius plot of the kd values as -Inkd vs. 1/7" yields from the slope, Ed = 29.3 kcal mo1-1.
480
Chapter 6
60 °C
0
I
40
80
I
120
I
160
Time(h) Figure 6.3 Test of Eq. (6.99) for dead-endpolymerizationof isoprene-AIBN systemat different temperatures(Problem6.15). Mathematical treatments have been. developed to extend the deadend polymerization technique to other situations such as polymerizations which are not dead-end, i.e., polymerizations go to completion and also polymerizations involving appreciable induced decompositionof initiator [34,35]. DETERMINATION OF ABSOLUTE RATE CONSTANTS Threedifferent types of rate constantsare of concernin ideal polymerization kinetics describedby Eq. (6.26)--those for initiation (kd), propagation(kp), and termination (k,t). The use of polymerization data under steady-state conditions allows the evaluation of only kd (see Dead,endpolymerization). The ratio kp/k~/2 or k2p/kt can be obtained from Eq. (6.25) since /gp,/{/, and [M] are measurable. However,steady-state data do not allow
Radical ChainPolymerization
481
the evaluation of the individual kv and k~ values. It is necessary to employ non-steady-state conditions to determine these individual rate constants. Non-Steady-State
Kinetics
One of the best means of obtaining individual rate constants using nonsteady-state conditions is photochemical polymerization. The treatment discussed here is essentially that of Flory [31] and Walling [36]. Wehave seen previously that the assumption of steady-state enables one to equate Pv/ to Rt to obtain Eq. (6.24) for radical concentration and hence Eq. (6.25) for the rate of polymerization under steady-state conditions. However,at the very outset of the polymerization, the radical concentration is zero, and a finite time must be required before it reaches the steady-state level. During the non-steady interval, the rate of change of radical concentration is given by the difference of their rates of production and termination -- Ri -- Rt 2= P,4 - 2kt[M’] (6.100) dt In photoinitiated polymerization it is possible to commencethe generation of radicals abruptly by exposure of the polymerization cell to the light source, and the time required for temperature equilibration in an otherwise initiated polymerization can be avoided. The rate of photoinitiation is given by Eq. (6.77) and Eq. (6.100) then becomes d[M’]/dt Since for steady-state
= 2~5Ia
--
2kt[M’] 2
(6.101)
conditions, d [M’]/dt = 0, Eq. (6.101)leads
2e~ra = 9.~ [M.]~
(6.102)
where the subscript s denotes steady-state condition. CombiningEqs. (6.101) and (6.102) one obtains d[M’] dt This equation gives the rate of change of the radical concentration under a non-steady-state condition as the difference in the rates of termination under steady-state and non-steady-state conditions. It is convenientat this point to define a parameter~’s, called the average lifetime of a growingradical under steady-state conditions, as
2) - 2k, ([M’I~ -[~’l
(6.103)
No. of radicals present at steady state No. of radicals disappearingper unit time at steady state
[M-I, - 2k,[M.]~ -- 9.a[M’ls
(6.10~)
482
~hapte~6
Combination of Eqs. (6.105) with Eq. (6.20) "~s -As [M] and (Rp)s are measurable,
at steady-state
yields
kp [M]
by determining
(6.105) -rs one can obtain
from Eq. (6.105), and since kp/k t or kp/kt can be obtained ~om steadystate measurements, both ~p and kt can be evaluat¢d individu~ly. It is the objective of non-steady-state experiments to determine Ts for this pu~ose. Integration of Eq. (6.103) yields
,1
-+
where to is the integration
: constant
such that [M’] = 0 at t =
S~neet~h-’~ = (~/~)t.[(~+ ~) / (~ - ~)], ~om~,~n~ (6.104)
and (6.106)
one may write -1 tanh
(~.107)
Therefore, ~ _ [M’]
_ tanh
(~)~
[M-]~[
The ~ in these equations nation.
may be identified
[.(t
-
(6.~08)
t0)
with the duration
of the i~umi-
Problem6.16 Typical % values determined from photoinitiated
radical chain polymerization with intermittent illumination are in the range 0.1-10 s. Calculate from this the duration of the non-steady-state period and commenton the validity of steady-state approximation made in a typical polymerization study. Answer: [M’]o = 0 at t = 0. Therefore, From Eq. (6.108), [M’] = tanh(t)
to = 0.
For a steady-state condition, assuming, for example, 99.9999%attainment of the steady-state radical concentration, t/~’s = 7. Thus the time required for [M.] to reach its steady-state value is 70, 7, and 0.7 s, respectively, for ~-s values of 10, 1, and 0.1 s. Thus, in the typical polymerization stu.dy the steady-state assumption is valid after a couple of minutes at most.
Now suppose the polymerization
is being conducted
with intermittent
483
Radical Chain Polymerization
illumination, that is, with alternate light and dark periods. At the very beginning the radical concentration [M’] is zero and it builds up in the period of illumination till it reaches a steady-state value [M’]s as shownin Fig. 6.4(a). If the light source is switched on and off and held for long but equal time periods of light (t) and darkness (t~), the radical concentration will alternately build up from zero to [M’]s, the steady-state value, and decay from [M’]s to zero with the repetition of the sequence t and t ~ of illumination and darkness, respectively [Fig. 6.4(a)]. The intensity of illumination is I0 during t and zero during t ~ with short zones of transition in between. The radical concentration during illumination is essentially consis-
O
-= [~]s
t
t~/"
t
>/ .t
t
(a)
Figure 6.4 Schematicrepresentation of variation of chain radical concentration I-M-] over (a) cycles of long illumination period (t) and dark period ~) and (b) cycles of short (intermittent) illumination period (t) and dark period tent with I0, but radicals are present only half of the time in itermittent illumination and hence the average rate of polymerization (~v) observed corresponds to one-half of the rate (P~)s, to be observed for the same intensity on the basis of continuous illumination. Thus for slow blinking, P"v / (P~p)* = 1/2.
484
CJhapter6
Whenthe frequency of blinking is high giving very short but equal light and dark periods [Fig. 6.4(b)], then, even if one starts with [M"] = 0 at the beginning of the first light period, the radical build up [curve OAEin Fig. 6.4(b)] is interrupted by the interception of light before it reaches [M’]s (at point E). [M’] reaches a maximumvalue, say, [M’]I < [M’]s the end of the illumination period (t). The decay of radical concentration from the [M’]I value begins immediately thereafter as the dark period commences.Since the dark period ({) is short, radical concentration does not decay to zero, but drops to a minimumvalue, say, [M’]2 > 0, when it starts rising as. the illumination is on again. With frequent blinking, the concentration of radicals alternates between [M’]I and [M’]2 as the system passes through the end of a light period to the end of a dark period in successive cycles of illumination and darkness [Fig. 6.409)]. With progressive increase in the frequency of blinking the difference [M’]x and [M’]2 will be progressively small and in the limiting case of very fast blinking the radical concentration would reach a constant or plateau value [M’]e below the steady value [M’].,. This constant value [M’]dwould effectively be that which correspgnds to a continuous illumination of intensity Io/2, as only 50%of the irradiation is received by the system. It then follows from Eqs. (6.80) and (6.24) that [M’]c will be proportional to (L/2)1/~. Since the rate of polymerization is proportional to the concentration of radicals [cf. Eq. (6.20)], the average rate of polymerization (~p) for very fast blinking will therefore be proportional to (/0/2) 1/2. In comparison, for steady conditions under continuous illumination (i.e., no blinking), (P~o)s (x 1/2. According to analysis and consideration detailed above for photoinitiated polymerization, it may now be concluded that R.p or [M’] can be varied by varying the frequency of blinking. Under otherwise comparable conditions, the average rate (P’-v) at different flashing conditions with the same L related to the steady-state (P~o)s -and
(P~p)
--
1 2
(for slow blinking) (for very fast blinking)
(6.109) (6.110)
For unequal light and dark periods such that t r = rt, i.e., the dark period is ~" times longer than the period of illumination in all successive cycles (r = 1 for the systems considered above), the general expressions for the relative rates may be written as:
(_P~)~
--
1 (r
+
(for slow blinking)
(6.111)
RadicalChainPolymerization
485 1
- (,. + 1)v,
(for very fast blinking)
(6.112)
Considering, as an example, a case where the ratio r of the length t r of the dark period to the length t of a light period is 3, the relative rate equals 1/4__for slowblinking and 1/2 for very fast blinking. Thusthe averagerate, (Pqo) increases from1/4 to 1/2 of the steady-state rate as the cycle time (time for one light period and one dark period) decreases from a muchhigher value to a muchlower value in comparisonwith the average lifetime of a growingchain (~’s), or as the frequencyof blinking 1/(t -F rt) increases from a muchlower value to a muchhigher value in comparisonwith 1/~s. The mathematicaltreatment of intermittent illumination has been described [37]. As explained above, in relation to Fig. 6.4(b), the radical concentration, after a numberof cycles, oscillate uniformlywith a constant radical concentration [M’]I at the end of each light period of duration and a constant radical concentration [M’]2 at the end of each dark period of duration f~ = ft. Considering first light period, if [M’] = 0 at t = 0, then from Eq. (6.107), t0 = 0; but for [M’] = [M’]2 > 0 at the beginning of light period (t = 0), Eq. (6.107) yields -- to/rs
= tanh -1 ([M’]2/[M’]s)
(6.113)
and hence tanh -1 ([M’]/[M’]s) -- tanh -~ ([M’]2 /[M’]s) = t / ~-s (6.114) At the end of light period t, [M’] = [M’]I [see Fig. 6.4(b)] and Eq. (6.114) becomes ta,nh_ 1 ([M’]I~
_ t&nh-’ ([M’]2~ _ __~
\[M.],J
(6.115)
On the other hand, during the dark period radical decay occurs according to d[M’]/dr’ = - 2kt 2[M’] (6.116) which on integration,
with [M’] = [M’]I at t’ = 0, yields 1 1 -- 2kit’ (6.117) [M’j [M’]I Multiplying Eq. (6.117) through by [M’]s and combiningwith Eq. (6.103), r[M’]s
[M’]s
-t
(6.118)
486
C,]aapter 6
Since t ~ -- z’t and [M’]. = [M’]2 at the end of dark period t t, one obtains fromEq.(6.118), [M’]s
[M’ls
--
(6.119)
Equations (6.115) and (6.119) permit evaluation of the maximum minimumradical concentration ratios [M’]I /[M’]s and [M’]2 /[M’]s forgiven values of ~ (= e / t) and t / rs. The average radial concentration [M’] over a cycle of light and dark periods is given by
Here [M" ] in the first integral covering the peNodof illumination is ~ven by (6.114) and that in the second integal coveNngthe dark period is given by Eq. (6.118). Evaluation of the integrals yields the following expression
[ al:
(6.121) Thus, for a given ratio (r) of dark period to light period, values [M’]/[M’]s or (~) / (Pqo)s may be calculated for different assumed values of t/"r s. A semilog plot of relevant data for r = 3 is shown in Fig. 6.5. The plot shows that the average radical concentration falls from one-half of the steady-state value for fast blinking (low t / ~-s) to one-fourth of the same for slow blinking (large t/~’s), in full conformity with Eqs. (6.111) and (6.112). In order to experimentally determine the "rs value for a particular polymerization system, one interposes a rotating sector or disc in between the system and the source of light. The sector has a portion cut out, which determines the value of r. The steady-state polymerization rate (/~p).__s first measured without the sector present. Then the average rate (P~) measured with the sector present at different (increasing) speeds of sector rotation. The blinking frequency as well as/; and t’ are determined by the speed of sector rotation. The polymerization is conveniently followed by dilatometric technique (p. 329). Thus a numberof rate ratios (P~p) / (P~)s are obtained for a given sector ratio (r) by varying the sector speed and hence t. The rate ratios are then olotted against log t. Alternatively, one can also plot the data as (~) / (R~)o~ since this ratio is related
487
Radical Chain Polymerization
0.55
0.45
0.35-
0.25 0.01
I 0.1
I
I
I
1.0
10
100
1000
t/’r Figure 6.5 Semilog plot of [M’]/[M’]s versus t/% for r = 3. (Adapted from Ref. 39.)
Pt:o / (/~)s through Eq. (6.112). The theoretical curve (e.g., Fig. 6.5) the same r value is placed on top of the experimental curve and shifted on the abscissa until a best fit is obtained. The displacement of one curve relative to the other along the abscissa yields log’rs since the abscissa for the theoretical curve represents (log t - log’rs). (Several experimental variations of the rotating sector method have been used [40,41]. One of these uses a glass tubular reactor surrounded by a metal cylinder having narrow regularly spaced slots through which light shines. Monomeris pumped through the reactor and passes alternately through light and dark regions. The mathematical-treatment [41] is very similar to that described above for the rotating sector method.) Evaluation of % then allows calculation of absolute rate constants kp and ~, making use of Eq. (6.105) relating Ts with k v / kt and of equations and approaches discussed earlier leading to evaluation of the parameter
488
Chapter 6
kp2 / k.t. Table 6.7 lists the k/~ and k,t values and the corresponding activation energies for some common monomers.
CHAIN
LENGTH
AND
DEGREE
OF
POLYMERIZATION It is relevant at this point to examine if the chain length or degree of polymerization (~---~n) of a polymer product could be predicted or calculated from measured rate of polymerization with a knowledge of kinetic constants. Since the number-average degree of polymerization is given by the average number of monomer molecules consumed per polymer molecule, it becomes necessary first to define and obtain an expression for the kinetic chain length. Kinetic
Chain
Length
The kinetic chain length (v) of a radical chain polymerization is defined as the average number of monomer molecules consumed (i.e., polymerized) per each radical which initiates a polymer chain. This quantity will obviously be given by the ratio of the rate of propagation (Rp) to the rate
Table 6.7 Kinetic Parameters in Radical Chain Polymerization Monomer
k~,x10
-3
Ep
AexlO -z
ktxl0
-w
-9 Et
A~x10
Methyl acrylate
2.09
29.7
10
0.95
22.2
Methyl methacrylate
15
0.515
26.4
0.087
2.55
11.9
0.11
Styrene
0.165
26
0.45
6.0
8.0
0.058
Acrylonitrile
1.96
16.2
-
7.8
15.5
-
Vinyl chloride (50°C)
11.0
16
0.33
210
17.6
600
Vinyl acetate
2.30
18
3.2
2.9
21.9
3.7
.... 54.0
1.3
-
-
-
Tetrafluoroethylene (83°C)
9.10
17.4
Ethylene
0.242
18.4
-
1,3-Butadiene
0.100
24.3
12
-
kp and k,t values are for 60°C unless otherwise indicated and have the units of L mo1-1 s -1. Theunits of Ep are kJ/moi of polymerizingmonomer and those of Et are kJ/moi of propagatingradicals. Sourde: Data mostly from Ref. 3.
489
/Lad/ca/Cha/n Polymerization
initiation (P,,/) or to the rate of termination (Rt), sinc~ Pq = Rt under the steady-state conditions. Thus,
v=
= P /Rt
(6.122)
Combiningwith Eqs. (5.15) and (6.18) we
=
kp [M]
(6.123)
Eliminating the radical concentration term [M" ] with ~e help of ~q. (6.15),
-
2~
~
The ~netic chain length is thus inversely dependent on the radial concentration [Eq. (6.123)] or the polymerization rate [Eq. (6,124)]. This is great practi~l signifi~nce .~ it shows that any attempt to incr¢~e the rate of polyme~zation by increasing the radial concentration will be only at the expense of produdng smaller size polymer molecules. Equations (6.123) and (5.i24) are applicable for all ~ses of bimolecular te~ination i~espective of th~ exact mechanism (combination or dispropo~ionation) ~d also irrespectiw of the nature of the initiation process. Thus, for any monomer the ~netic chain length will be independent of whether the polyme~tion is initiated by thermal, redox, or photochemical means, or of the initiator used, if the [M" ] or ~ is the same. For polymerization initiated through radicals, generated by the~al decomposition of initiator, Eq. (6.25) may be combined with Eq. (6.124) to give an alternative expression for ~:
u = ~(fke~)~/~
[I]~/~
Thus a four-fold increase in initiator concentration wouldresult in halving the size of pol~er molecules, though the rate of polymerization [Eq. (6.26)] would be doubled by this change in ~itiator concentration. Problem6.17 In a benzoyl peroxide initiated polymerization of styrene it is desired to double the initial steady rate of polymerization without changingthe initial number-averagedegree of polymerization. Howcould this be achieved by changing only the monomer and initiator concentrations ? Answer: FromEq. (6.26), [M]2[I]~/2---- 2 [M]I[Illl/2 [Mb_/ [M],= 2 [I]ff 2 / [I]~/2
(r6.17.1)
490
Chapter 6
From Eq. (6.125), since there is no change in [M]2/ [I]~/2 = [M]I / [I]11/2 or
[M]2/ [M], ---- [I]~/2 / [I]]/2
From Eqs. (P6.17.1) and (P6.17.2),
[I]2/[I]1
2:1.
Therefore, [M]2/ [M]I= : 1 Mode
of
Termination
The number-average degree of polymerization number of monomer molecules contained in a to the kinetic chain length. If the propagating or combination [Eq. (6.7)], a dead polymer kinetic chain lengths, that is, D---~,~
DPn, defined as the average polymer molecule, is related radicals terminate by coupling molecule is composed of two
= 2v
However, if the termination occurs by disproportionation dead polymer molecule is composed of only one kinetic D--’ff,~
= v
(6.126) [Eq. (5.8)], chain and so,
the
(6.127)
The mode of termination is experimentally determined from the observation of the number of initiator fragments per molecule. This requires the analysis of the molecular weight or the DPn of a polymer sample as well as the total number of initiator fragments contained in the sample.
Problem6.18 For a radical chain polymerization with bimolecular termination, the polymer produced contains on the average 1.60 initiator fragments per polymer molecule. Calculate the relative extents of termination by disproportionation and by coupling, assuming that no chain transfer reactions occur. Derive first a general relation for this calculation. Answer: Let n = number of propagatingchains etc = fraction of propagating chainswhichundergotermination by coupling 1 -- etc = fraction of propagating chainswhichundergotermination by dispropo~ionation b = average number of initiator fragments per polymer molecule formed = et--2-~ 2 + n(1 Total number of initiator fragmentsTotal number of polymer molecules 2 n
Number.of polymer molecules b =
nero~2 + n(1 - e,c)
2 -
(P6.18.1)
491
RadicalChainPolymerization Fromthis, etc = (2b - 2)/b
(1-,,o)
(P6.18.2)
= (2- b)/b
(P6.18.3)
For the givenproblem, Fraction of coupling= (2× 1.50 - 2)/1.50 = 0.75 Fraction of disproportionation= (2 - 1.5)/1.5 = 0.25
If b is the average numberof initiator fragmentsper polymermolecule and etc is the fraction of propagatingchains whichundergotermination by coupling, the two are related [cf. Eq. (P6.18.1)] b = 2/(2
- ere)
(6.128)
The number-averagedegree of polymerization DP,~will then be related to the kinetic chain length u by DPn --
(2)
2 - etc
u
(6.129)
CombiningEqs. (6.124) and (6.129) one obtains DPn =
(2 - tc)
(6.130)
Althoughexperimental data are not available for all monomers,for most monomersthe termination of propagating chains appears to occur predominantlyor entirely by coupling. However,varying extents of disproportionation are observed depending on the monomerand the reaction conditions employed.For example, disproportionation increases whenthe propagating chain radical is sterieally hindered or has morefl-hydrogens available for transfer (see later). Thus, whereasstyrene, methylacrylate, and acrylonitrile undergoterminationalmostexclusively by coupling, methyl methacrylate undergoes termination by both coupling and disproportionation. Theextent of disproportionationincreases as the temperatureis raised, the effect being mostsignificant for sterieally hinderedradicals, In methyl methacrylate, for example,the extent of disproportionation increases from 67%at 25°C to 80%at 80°C[42]. Problem6.19 Usingcarbon-14labeled AIBN as an initiator a sampleof methyl methacrylateis polymerizedat 80°Cto an averagedegree of polymerizationof 1.5 x 103. TheAIBN has an activity (per tool) of 9.1×t counts per minute ina scintillation counter,ff 1.0 g of the poly(methyl methaerylate)showsan activity of 337 counts per minute, determineby appropriate calculation the modeof
492
Chapter 6
termination in methylmethacrylate at 80°C. Answer: Mer weight of methyl methacrylate = 100 Molesof mers in 1.0 g poly(methyl methacrylate) = -2 -1 1 mol of AIBN--= 9.1×107 counts min Therefore 337 counts/min ---- 337/(9.1 × 107) or 3.70 × -6 to ol AI BN --= 7.4 × 10-6 mol chain radicals, since I tool of AIBN gives rise to 2 molesof chain radicals (assuming100%initiator efficiency). Let x fraction of chain radicals terminate by coupling and (1 - x) fraction by disproportionation. Therefore 1 moi of chain radicals give rise to 0.5x + (1 z) or (1 - 0.5z) tool polymer molecules. Hence 10-2 tool D--~ = = 1.5x103 .6 (7.4 × 10 moi) (1 -- 0.5x) x = 0.2 So 20%of the chain radicals terminate by coupling and 80%by disproponionation.
Average
Lifetime
of Kinetic
Chains
The average lifetime (’r) of the kinetic chain is given by the ratio of the steady radical concentration to the steady-state rate of radical disappearance : T --
[M’]_ 1 2kt [M’] 2 2~ [M’] Substituting for [M’] from Eq. (6.123) yields
"r -
(6.131)
(6.132)
For termination by disproportionation [cf. Eq. (6.127)], "r = D---~n / kp [M]
(6.133)
and for termination by coupling or combination,
r = / 9.kp [M]
(6.134)
Problem6.20 Consider the polymerization of styrene in bulk at 60°C initiated by 1 x 10-3 Mbenzoylperoxide. The density of liquid styrene is 0.909 g/cm3 at the reaction temperature. Whatis the average radical lifetime and what is the steadystate radical concentration ? [Data at 60°C: kn (styrene) = 6.0×107L/mol-s; (benzoyl peroxide) = 7.1x10-6 s-x, f = 0.5] Answer: CombiningEq. (6.132) with Eq. (6.125),
RadicMChain Polymerization
493
1/. = 2(ykdkt = 2 [(0.5)(7.1 x -6 s- 1)(6.0 x r L tool-1 s-l) (1 x 10 -3tool L-l)] 1/2 -~ = 0.923 s ~- = 1.1s FromEqs. (6.24) and (5,14), 1/2
[M-]=
r.(o-~)(7.1x lo-~~-’)(1~-~~o l = 7.7x10 -~ -1 tool L
CHAIN
TRANSFER
In manypolymerization systems, the polymer molecular weight is observed to be lower than predicted on the basis of Eqs. (6.126) and (6.127). effect is due to the premature termination of a growing polymer chain by transfer of its radical center to other species, present in the reaction mixture. These are termed chain transfer reactions and may be depicted as Mn" + XA ~ MnX + A" (6.135) where XA may be monomer, initiator, solvent, polymer, or any other substance present in the reaction mixture, and X is the atom or species transferred; ~tr is the chain transfer rate constant. The new radical A’, which results from chain transfer, can reinitiate polymerization by the reaction A" q- M "~ M" (6.136) where kr is the rate constant for addition of monomerto A" leading to chain reinitiation by the process
where kp is the normal prbpagation rate constant. The chain transfer to monomeris negligible for most monomers, but may be significant for some monomers, for example, vinyl acetate, vinyl chloride, and o~-methyl substituted vinyl monomers, e.g., propylene and methyl methacr]late : CH3
I
+
COOCH3
CH3 I ktr,M
CH3
COOCHs
COOCH3
---+
I
.CH2
+
I
7
COOCH~
494
Chapter 6
/gtr, Mis the rate constant for chain transfer to monomer.In general, the rate of transfer to monomeris given by
where
Rtr,M = ktr, M [M] [M’] (6.139) Manyperoxides used as initiators have significant chain ~ransfer reactions. Dialkyl and diacyl peroxides undergo chain transfer due to breakage of the O--O bond, e.g. H
0
0
wwvCH2-C. + R-C-O-O-C-R X
H
0
-~ vwvvCH~-C-O-C-R X
0 + R-C-O"
(6.140)
where ~r,I is the rate constant for chain transfer to initiator. The hydroperoxides are usually the strongest transfer agents amongthe initiators. In general, the rate of chain transfer to initiator is given by /~tr,I = k, tr,I[I] [M’] (6.141) Chain transfer to initiator was earlier referred to as induced initiator decomposition. In some laboratory polymerizations, the solvent itself acts as the chain transfer agent. For example, the chain transfer reaction for vinyl polymerization in CC14can be represented by H
H
vvvwCH2-C" + CCI4 ----> wvwCH2-C.CI + "CCI 3 I X X
(6.142)
wherektr,Sis therateconstant forchaintransfer to solvent. Solvents are normally, notusedin industrial free-radical polymerizations, foreconomic reasons, andthechaintransfer agentsin thesereactions areingredients thatareaddeddeliberately to limitthemolecular weight ofthepolymer. In general, therateof chaintransfer to solvents andaddedchaintransfer agents is givenby atr,s= ~r,sIS] [M’]
(6.143)
Sincechaintransfer stopsgrowing chain, it always results ina lowermolecularweightthanwouldoccurin itsabsence. Theeffectof chaintransfer on therateof polymerization varies, however, anddepends on therelative ratesof thetransfer [Eq.(6.135)] andreinitiation [Eq.(6.136)] compared to thatof thenormalpropagation reaction [Eq.(6.6d)]. Several possible situations thatmaybe encountered aresummarized in Table6.8.Theseare allinstances ofchaintransfer, buttheyareusually givendifferent names, as shown,depending on theneteffects on polymerization, rateandmolecular weight.
Radical Chain Polymerization
495
Table 6.8 Effect of Chain Transfer on Polymerization Rate and PolymerMolecular Weight Process name Normal chain transfer Telomerization Retardation Degradative chain transfer Inhibition
Characteristics
kp >>ktr, kr --- kp kp > kv) and the new radical formed by this reaction reinitiates poorly (kr < kv), with the result that there is a large decrease both in polymerization rate and molecular weight.
496
G~pter 6
Problem 6.21 A vinyl monomerof molecular weight 132 is polymerized by a free-radical initiator in the presence of dodecyl mercaptan(CnH~sSH). The rate of polymerization is not depressed by the mercaptan. The purified polymerhas a sulfur content of 0.02%(w/w)and its DP,, is 450. If 80%of the kinetic chains are terminated by coupling and 20%by disproportionation, what should be the extent of terminal unsaturation of the chains ? A.swer : Molar mass of repeat unit = 132 g mo1-1, Polymerchains = [(450)(132 g mol-a)] Sulfur = (0.02 x 10-~)/(32 g g-atom
D--~,~= 450
In the presence of mercaptan,the following reactions take place [31]: M,~" RS-
+ RSH ~ M~-H + RS. +M ~ RSM" ~ etc. ~ RSM~"
Since the rate of polymerization is not reduced by the mercaptan, the transfer radical RS" evidently reacts readily with monomerto- start a new kinetic chain. Accordingly, it maybe assumedthat for one mol of mercaptan consumed one mol of polymerchains are formedand one mol of kinetic chains are initiated. Therefore 6.25 x 10-6 molesof polymerchains are producedby transfer to mercaptan. Remaining(1.68 x 10-5-6.25 x 10-~) or 1.055 x 10-5 mol of polymer chains result from termination by disproportionation and coupling. Out of every 100 kinetic chains, 80 terminate by coupling to produce 40 polymer molecules and 20 terminate by disproportionation to produce 20 polymer molecules of which10 contain terminal unsaturation [see Eq. (6.8)]. Therefore, terminal unsaturation = (1.055 x 10-5 mol) (10/60) = 1.76x 10-~ mol g-1 Hence (1.76×10-6)(100)/(1.68x10 -5) or 10.5% of polymer chains have a terminal unsaturation.
Degree of Polymerization Equations (6.129) and (6.130) for D---~n apply to free-radical polymerization following ideal kinetics in which termination of the growth of polymeric radicals is accounted for only by mutual reaction of two such radicals. Combining Eqs. (6.122) and (6.129) one may write DPn = 2 --
et:
~ --
znt
where z = (1 -- ere / 2). In Eq. (6.146), Re is the rate of termination chain radicals and zRt is the rate of production of dead polymer molecules by bimolecular termination mechanism, i.e., by combination [Eq. (6.9)]
Radical ChainPolymerization
497
and/or disproportionation [Eq. (6.10)]. (If combination is the sole mechanism, etc = 1 and z = 1/2, while for termination by disproporfionation etc = 0 and z = 1.) Since, as we have seen above, chain radicals can also be terminated by chain transfer reactions, Eq. (6.146) will nowbe amended to include transfer reactions. This can be easily done by redefining DPnas the ratio of rate of polymerization to the rate of formation of dead polymer molecules by all reactions, namely, by the normal bimolecular termination and various transfer reactions. Thus Eq. (6.146) takes the form
zRt + Rtr,M + Rtr,I
+ Rtr, S
zP~ + ktr,M [M’] [M] + ~r,I [M’] [I] + k, tr, S [M’] [S]
(6.147) since at steady state, Rt = R/. Noting from Eq. (6.15) that /~p k v[M] [M’], conveniently rearranged to the form
Eq. (6.147)
1
z_R/ [S] (6.148) ~DPn P~ CM -[- el -[[~] Cs [M---] where CM, CI, and Cs are the chain transfer constants for monomer, initiator, and solvent/chain transfer agent, respectively, defined as the ratio of ~tr for the respective material with a propagating radical to kv for that radical, that is, CM --
]Qr,M
CI - ktr,i
ktr,s
(6.149)
Equation (6.148), often referred to as the Mayoequation, shows the quantitative effect of various transfer reactions on the numberaverage degree of polymerization. Note that the chain transfer constants, being ratios of the respective rate constants for chain transfer (Rtr) to the rate constant for propagation (kp), are dimensionless quantities dependent on the types of both the monomerand the material causing chain transfer as well as on the temperature of reaction. Problem 6.22 Vinyl acetate has a relatively high monomerchain transfer constant (2x10-4 at 60°C). What is the upper limit of molecular weight of poly(vinyl acetate) madeby radical polymerization at 60°C? Answer: The upper limit of molecularweightcorrespondsto the lower limit of (l~--~n)
498
Chapter6
Eq. (6.148). The lower limit of the first, of Eq. (6.148) is 0. Hence, 1 -4 D-’-~---~lmin = CM= 2x10 DP,, = 5,000 M---, = (5,000)(86
g mol-’)
third and fourth terms on the right side
= 4,30,000
g mol-’
Problem6.23 For a solution (density 0.87 g/cma) of 1.0 M styrene and 0.01 Mtea-butyl peroxide in toluene, the initial rates of initiation and polymerization at 60°C are 4.0x10 -11 mol/L-s and 1.5×10-z tool/L-s, respectively. Calculate (a) how often on the average chain transfer occurs per each initiating radical from the peroxide and (b) the molecular weight (assuming coupling termination) of polystyrene produced. Use the following chain transfer constants: C’M = 6.0×10 -5, CI = 8-4x10 -4, and C’s -5 = .1.25x10 Answer: Given -1. [I] =0.01 moll -1, [M] = 1.0 moll -u -1 (Pg) = 1.5×10-z mol L-’ s-’. (/~i) = 4.0×10 mol L -~, s (a) Total rate of chain transfer (l~tr)tot = -~,-,M + i~’,S + P~t,-,I = ktr,M [M’] [M] + ktr,S [M’] [S] + /%,I [M’] [I] -1. Molar mass: styrene = 104 g mol-~; tert-butyl peroxide = 146 g moi [S] = (870 - 0.014x146 - 1.0x104)/92 = 8.31 mol -1 (/{t.)tot/~
= CM + Cs[SI/[M]
+ CI[I]/[M]
= (CM + CS[S] / [M]÷ 6’~ [I] / [M])(/%, (8.31 mol -1) = 6.0x10 -5 + 1.25x10 -5 (1.0 tool -1) + 8.4x
(0.01 mol L-x)] (1.5_x -7 ~ 10 -4 (1.0 tool -1) J \~× 1 -u]
= 0.646 (b) Substituting appropriate values in Eq. (6.148) and noting that z ---- 1/2, s. obtains D-~,~ = 3279 and so ~,~ = 3.41x 10
Problem6.24 Vinyl acetate is polymerized in benzene solution at 60°C using 2,2’-azobisisobutyronitrile(AIBN) as initiator and carbon tetrachloride as chain transfer agent. The initial monomerconcentration is 200 g/L and solution density is 0.83 g/cm3. Select concentrations of initiator and chain transfer agent that will give poly(vinyl acetate) with an initial molecular weight (assuming coupling) of 15,000 and 50%polymerization in 2 h. Neglect chain transfer to initiator in
499
Radical Chain Polymerization
calculations. [Data: ka = 8.45x10-6 s-l; k~ = 2.34x10a Idmol-s; ~ = 2.9x107 L/mol-s; f = 1.0; CM= 2.3x10-~; Cs(benzene)= 1-2x10-~; Cs(CCh)= 1.07 ] Answer: Molecular weights: vinyl acetate 86, AIBN164, benzene 78, CCI~154. [M]0 = (200 g L-1)/(86 g tool -1) -~ = 2.32 mol L Neglectinginitiator mass, [S]benzene= (830 g -- 200g)/(78 g mo1-1)= 8.08 moi -1. Assumingthat chain transfer has no effect on polymerizationrate, Eq. (6.33) can be used. Usingrelevant data and p = 0.5, this equation gives [I]0= 6.16x I0-3 tool-1 L -3x -I ----6.16x10 164 or 1.0 g L FromEqs.(6.125) and(6.126), (~-~,~)o
= k~ [M]o 1/2 (fkdkt
[[]o)
Substituting appropriate values, (~--~.)o = 4340. Desired DP,~ = 15,000/86 or 174. FromEq. (6.148), 1 1 IS]benzene + c~(ccm[S]cc~ q- CM q- Cs(benzene) D’~n -- (~-~)~ .... [Mlo -1 Substituting appropriate values, [S]ccl 4 = 0.0106 tool L = 0.0106 x 154 or 1.63 g -1. L
Determination of Chain ~ansfcr Constants Various methods can be employed, based on the Mayo equation, to determine the values of the chain transfer constants. The following sections review some of these methods. Deterrnlnation
of
CM
A special case of Eq. (6.148) is of interest. Consider polymerization in the absence of a solvent or added chain transfer agent, so that IS] = 0. For steady-state polymerization, Eq. (6.25) can be used to express Pq in terms of P~ as /~ -- kp2 ~ [M]
500
Chapter 6
and Eq. (6.26)
can be rearranged [I]
Substitution
to express [I] --
Rp2kt k i [M]2 f kd
of Eqs. (6.150) and (6.151),
1 + r Fnhi [M]2
CM "-~
(6.151)
and IS] = 0 into Eq. (6.148) CI
hi f
(6.152)
Since Eq. (6.152) is quadratic in ~, the plot of l~n vs. ~ is turned, the e~ent of w~ch varies with the initiator. However, the initial portion of the plot, co~esponding to small ~ values, is linear. By extrapolation of this linear part to ~ = 0 yields CMm the intercept. Moreover, the slope of the linear portion is given by 2zkt/~ [M]2 from which mode of termination or k~/kt may be dete~ined, provided the other is ~own. For AIBN initiator CI is negligibly small; as a result Eq. (6.152) is practically linear in ~ even at higher v~ues of ~.
Problem6.25 The following data of rate of polymerization
and degree of polymerization at low conversion were obtained in bulk polymerization of monomer M (initial concentration 8.3 tool/L) using different concentrations of thermal initiator [ at 60°C: [I]
Calculate
x 102, mol/L /~ x 10a, mol/L-s 0.018 0.005 0.072 0.010 0.280 0.020 1.74 0.050 4.48 0.086 7.80 0.115 13.20 0.15 (a) CM, and
DP~ 8267 5495 3296 1300 714 495 352
(b) k~,/k~t/2. Assumetermination by coupling.
Answer: The plot of 1/~--~,~ vs. P~ (Fig. 6.6) is seen to be linear at low P~ (i.e., first 3 points) according to Eq. (6.154). Therefore the values of the intercept slope are determined from a least-squares calculation using the first 3 data points, yielding CM = Intercept = 6.03×10 -5 and k~2[M]2 = slope
= 12.16
kp/kit 12 = 3.46 x 10-2 L112 mo1-1/2
-1/2 S
Radical Chain Polymerization
~01
32
24
0
/~
8 Rpx 5 10
12
~6
Figure6.6 Plot of Eq. (6.151) for the determination of M(Problem 6. 25). The monomer chain transfer constants are generally small for most monomers-being in the range 10 -5 to 10 -4 (Table 6.9). Chain transfer to monomer places the upper limit to the polymer molecular weight that can be obtained in the absence of all other transfer reactions (see Problem 6.22).
Table 6.9 Monomer Chain Transfer Monomer Acrylamide Acrylonitrile Ethylene Methyl acrylate Methyl methacrylate Styrene Vinyl acetate Vinyl chloride All CMvalues are for 60°C. Source: Data mostly from Ref. 3.
Constants (7 M X 104
0.6, 0.12 0.26 -0.3 0.4-4.2 0.036-0.325 0.07-0.25 0,30-0.60 1.75-2.8 10.8-16.
502
Chapter 6
Determination
of
CI
Several methods are available for the determination of CI. Equation (6.152) can be rearranged and divided through by P~p to yield 1 ~n
CM Rp -)
2zkt kp 2[M]2
q-
ktRp 3CIk~/kd[M]
(6.153)
A plot of experimental data as the left hand side of Eq. (6.153) versus P~p yields a straight line whose slope is ktt{p / (k2p f kd [M]3). The value of CI can be obtained from the slope provided other constants are known, or one can make use of the fact that
ted[M] 3 2--
(6.154)
[MIRp
and use experimentally measured P~p for a given [I] and [M]. When chain transfer to monomer is negligible (CM " 0), rearrange Eq. (6.153) and combine with Eq. (6.154) to yield
~2p2~]
= Ci
[~]
one can
(6.155 /
A plot of the left side of Eq. (6.155) versus [I]/[M] yields a straight line whose slope is CI. Some values of initiator transfer constants are listed in Table 6.10.
Table 6.10 Initiator
Chain Transfer
Initiator 2,2’-Azobisisobutyronitrile Benzoyl peroxide t-Butyl hydroperoxide t-Butyl peroxide Cumyl hydroperoxide Cumyl peroxide (50°C) Lauroyl peroxide (70°C) Persulfate (40°C)
Constants
CI for polymerization of Styrene Methyl metha- Acrylamide crylate 0.091-0.14 0.048-0.10 0.035 0.00076-0.00092 0.063 0.01 0.024 -
All CI values are for 60°C except where otherwise noted. Source: Data mostly from Ref. 3.
0.02 0.02 0.02 0.33 -
0.0026
Radica/Cha/n Polymerization
503
Problem 6.26 Fromthe polymerization data given in Problem 6.25, determine the chain transfer constant of the initiator I for the polymerizationof monomer Mat 60°C. Answer: The value of CM obtained in Problem 6.25 is 6xl0-~. Since it is very small comparedto 1/DP~, Eq. (6.155) can be used to determine Cl. For termination 2) by coupling, z = 1/9. and Fig. 6.7 thus showsa plot of (1/~-~n - ~P~/k~, [M] vs. [I]/[M]. Fromthe slope of the linear plot C’i = 0.066.
Determination
of Cs
A special case of Eq. (6.148) consists of the situation where transfer with the chain transfer agent is most important. In some instances, the solvent itself is the chain transfer agent, while in others it is an added compound.In such a case, the fourth term of the right side of Eq. (6.148) makes the
12 10
0
I
4
t
I
8
t
I
12
i
I
16
I
20
[l]x 3 ~o Figure 6.7 Plot of Eq. (6.155) for the determination of CI (Problem 6.26)
504
Chapter 6
biggest contribution to the determination of DP---n. For determination of Cs the polymerization conditions maybe adjusted so as to considerably @~plify Eq. (6.148). Thus, for a series of measurements one may keep [I]I/’/[M] constant, so the first term on the right side of Eq. (6.148) becomesconstant and also use an initiator for which OI is negligibly small (e.g., AIBN) that the third term becomesnegligible. Under these conditions, Eq. (6.148) takes the form
(6.156) + Cs D~ where (I/~.)0 isthevalue of(I/~) inthe absen~ ofsolvent thechaintransfer agent, andit represents thesumof thefirstthreeterms ontherightsideofEq.(6.148). Theslopeof thelinear plotof (I D/-D-~n) vs.[S]/[M]givesthe measureof ~’S-Figure6.8 showssuchplotsfor severai aromatic solvent as chaintransfer agentsin thepolymerization of styrene. Theplotsdearlyindicate dependence of chaintransfer constants on thechemical structure of chaintransfer agents.
0
5 10
1.5
20
25
Figure 6.8 Effect ofvafious chain ~ansfer agen~ on the degree ofpolyraerization of styrene at 100°C. (Af’terRef. 43)
Radical Chain Polymerization
505
Another method of determining Cs involves dividing the rate expression for transfer [Eq. (6.143)] by that for propagation [Eq. (6.15)] to yield dis]/dt ~,s IS] _ Cs IS] (6.~57) d[M]/dt - kp[M] [M] The value of Cs is obtained as the slope of the line obtained by plotting the ratio of the rates of disappearance of transfer agent and monomerversus
[Sl/[MI. Problem 6.27 In a free-radical polymerization of vinyl chloride the initial monomerconcentration was 1 mol/L and the concentration after 1 h was 0.85 mol/L. Chloroformwas present as a chain transfer agent and its concentration decreased from 0.01 mol/L at time zero to 0.007 mol/L after 1 h. Whatis the chain transfer constant CSfor vinyl acetate/chloroform ? (Neglect chain transfer to monomer, initiator, and solvent.) Answer: For chain transfer and propagationreactions, respectively, - d[S] / dt = knr,S [M’] [S] -d[Ul/dt = ~[M’][M] Dividing and rearranging, d IS] d[M]
[s-T= csIMp-
Integrating betweento and t, \ IS]o,] = CSIn ~ [M]o,] Thisgives, Cs = 1n(0.007/0.01)
ln(O.8~ / 1.o) = 2.19
Chaintransfer reactions, generally viewedas additional reactions disturbing the normal features of radical polymerization, are often advantageous in limiting the growth of polymer chains by design and hence in controlling their molecular weights to desirable ranges. Equation (6.148) can used to determine the concentration of the transfer agent needed to obtain a specifically desired molecular weight (see Problem 6.24). Transfer agents with large Cs are especially useful since they can be used in small ~ concentrations. The transfer constants for a number of solvents/additives for polymerization of styrene, methyl methacrylate, and vinyl acetate are listed in Table 6.11. The data indicate dependence of chain transfer constants on the chemical structure of both chain transfer agents and the monomer.The
506
Chapter 6
Table6.11 Transfer Constants for Solvents and Chain Transfer Agents
Transfer Cs × 104 for polymerization of. agent Styrene Vinylacetate Heptane 0.42 17.0 (50°C) Benzene 0.023 1.2 Toluene 0.125 21.6 Ethylbenzene 0.67 55.2 Isopropyltienzene 0.82 89.9 t-Butylbenzene 0.06 3.6 n-Butyl chloride 0.04 10 n-Butyl bromide 0.06 50 n-Butyl alcohol 1.6 20 Chloroform 3.4 150 n-Butyl iodide 1.85 800 Triethylamine 7.1 370 Di-n-butylsulfide 22 260 Carbontetrachloride 110 10,700 Carbon tetrabromide 22,000 390,000 n-Butyl mercaptan 210,000 480,000 All valuesare for 60°Cunless otherwisenoted. Source:DatamostlyfromRef. 3. CS value is influenced by the nature of the bonds which are broken and formed and the relative stabilities of both radicals Mn" and A" in reaction (6.135). In general, a given transfer agent (XA) is more reactive (Cs is greater) for a reactive radical (Mn") like those in ethylene or vinyl chloride polymerizations than for a resonance-stabilized radical like that of styrene. Similarly, when a given monomeris being polymerized, aliphatic compoundsthat yield tertiary radicals are more effective transfer agents than those that produce secondary radicals, and chain transfer activity is also enhanced by the possibility for resonance stabilization of radical A’. Chain
Transfer
to
Polymer
The previous discussion has ignored the possibility of chain transfer to polymer molecules. However, chain transfer to polymer can occur and it is very significant with very reactive propagating radicals like those in the polymerizations of vinyl chloride, vinyl acetate, ethylene, and other monomersin which there is no significant resonance stabilization. It is also likely to be significant in polymerizations carried to high conversions where the concentration of polymer in the system is relatively high.
507
Radical ChainPolymerization
Chain transfer to polymer results in the formation of a radical site on a polymer chain. Polymerization of monomerat this site produces a polymer with a long branch, for example, X
X Mn"
+ vvvwCH2-Cvww
~
MnH + vwwCH2-C,
vww
x wvwCH2Cwwv
At low conversions the polymer concentration is low and the extent of transfer to polymer is negligible. Thus ignoring chain transfer to polymer in Eq. (6.149) does not present difficulty in obtaining precise values CM,(7i, Cs, as these are determined from data at low conversions. It should be noted that the occurrence of chain transfer reaction (6.158) does not change the number of monomer molecules which have been potymerized nor the number of polymer molecules over which they are distributed. Chain transfer to polymer thus has no effect on DPnand so it is not included in Eq. (6.147). It, however, causes a change in the molecular weight distribution. The distribution becomes broader because the polymers which are already large are more likely to suffer transfer reactions and become yet bigger due to branching. Chain branching normally makes the polymer less crystalline, weaker in mechanical properties, and less resistant to heat, solvents, and chemicals. The effect of chain transfer to polymer thus plays a very significant role in determining the physical properties and the ultimate applications of a polymer. The transfer constant Cp for chain transfer to polymer is not easily obtained as it involves the difficult determination of the numberof branches produced in a polymerization relative to the number of monomermolecules polymerized. There are thus relatively few reliable Cp values available in the literature Cp values are about 10-4 for manypolymers. Flory [44] has derived the equation
to express the branching density Pb as a function of the polymer transfer constant Cp and the extent of reaction p. The branching density Pb is the -4 number of branches per monomermolecule polymerized. For a Cp of 10 and an 80%conversion, one thus calculates from Eq. (6.159) that there will be one branch for every 104 monomerunits polymerized. The extent of branching is greater in polymers, such-as poly(vinyl acetate), poly(vinyl chloride), and polyethylene, which have very reactive propagating radicals. The extent of branching in polyethylene varies considerably depending on the polymerization temperature and other reaction conditions, and may
508
Chapter 6
reach as high as 15-30 branches per 500 monomer units. The branches in polyethylene are of two types: short branches (ca. less than 6 monomer units) and long branches. The long branches are formed by the "normal" chain transfer to polymer reaction [Eqs. (6.158)]. The short branches, which outnumber the long branches by a factor of 20-50, are mostly nbutyl branches. A typical polyethylene, for example, contains five n-butyl branches and one or two each of ethyl, n-amyl, and n-hexyl branches per 1000 carbon atoms. The generally accepted mechanism for the formation of short branching in polyethylene involves a "backbiting" intramolecular transfer reaction in which a radical at the end of the polymer chain abstracts a hydrogen atom from a methylene unit in the same chain (Fig. 6.9). This is a very important process in the free-radical, high-pressure polymerization of this monomer. Branched polyethylene from this process has lower crystallinity than linear polyethylene produced by a low-pressure process and as a consequence it tends to be less rigid and tougher and form clearer films than the latter.
j H -,~CH "CH l"~.CH [ CH 22 /CH2
lntramotecutar chain transfer. (self-transfer)
I
CH2 ,CH2-CH 3 ~CH~" 2CH = CH
~
CH 3 A second I CH isetf-transfer I CH jCH-CH2- CH 3 ~CH 2
I
/.~CH2 H2 H
~ ~CH
~CH 2
/CH-CH2-CH 3
I
Propagation
Propagation
fC, H3 branchL~H 2 ..-..--~
!H 2
CH.CH ~CH~" ~CH2- CH3
CH2 I ~ C.l-I
Ethyt branch
.CH2- CH 3 2- CH ~ Butyt branch
Figure 6.9 Mechanism of ethyl and butyl branching
in polyethylene.
Radical Chain Polymerization Allylic
509
Transfer
Chain transfer to monomerwas described earlier in general terms for vinyl monomers[cf. Eq. (6.138)]. Such reactions are particularly favored with allylic monomerssuch as allylic acetate which have the structure CH~_=CHCH.~Xwith a C-H bond alpha to the double bond described as an allylic C-H. The propagating radical in the polymerization of such monomersis very reactive, while the altylic C-H bond in the monomeris quite weak, resulting in facile chain transfer to monomer: H H I I t,,~. M "~CH2-C"I + CH2=CH-C-H ----* CH~X H! ,~’*CH~-C~H2 + CH~=CH-C. e---~
cr 2x
H "CH2-CH=C
(6.160)
Since the allylic radical which is formed by the transfer reaction has high resonance stability, it is particularly unreactive and does not initiate new chains, with the result that the allylic monomerpolymerizes at abnormally low rates and the degree of polymerization, which is independent of the polymerization rate, is very low (for example, only 14 for allyl acetate). These effects are the consequenceof degradative chain transfer (see Table 6.8) to monomer,also knownas autoinhibition. In this polymerization, the propagation and termination reactions will have the same general kinetic expression resulting in the unexpected dependence of the rate on the first powerof the initiator concentration (see Problem6.28). Problem6.28 Suggest a kinetic schemeto account for the following characteristics of free-radical polymerizationof allylic monomers: (a) P,,p is very lowwith first order dependenc e in initiator concentration. (b) DP, is very low and independent of monomerand initiator concentrations. (c) Deuteratedallylic monomer possessing allylic C-Dbondhas significantly higher/~0 than the normalallylic monomer. Answer: (a) Since the allylic radical formed[Eq. (6.162)] has high resonance stability it does not initiate newchains. Chaintermination occurs predominantlyby chain transfer. At steady state, = /~ - ktr,M [M’I[M] = 0 dt Combinationwith /~p = kl. [M-] [M] leads to Rr -- ktr,M
_ 2fk d ktr,M
(P6.28.1)
0’6.28.2)
510
Chapter 6
For degradative chain transfer, kp > [C], K --
[c]
(P6.30.1)
= ([I]0 - [C])[M] where[I]o is the initial concentrationof the initiator. Rearranging Eq. (P6.30.1), K[M][I]0 [C] -- 1 + K[M]
(P6.30.2)
Therate of initiation is given by
(r6.30.3)
= [c] Combinationof Eqs. (P6.30.2) and (P6.30.3) with Eq. (6.25) t~
=
K
(r6.30.4)
\T,]
Equation (P6.30.4) desc6bes a change in reaction order with respect to monomer from 1.5 to 1 with increasing [M]. Equation (P6.30.4) maybe transfo~ed follows: [M] ~ ~ R~ - k~k.K [I1o + k~k~ [I]o (P6.30.5) 3/~ Equation (P6.30.5) pewits a plot of [M] vs.. [M] to give a straight line such that the quotient of the slope and the intercept is equal to ~.
Degradative Chain Transfer Initiators under ideal conditions wouldcontribute only to chain initiation by dissociation [Eq. (6.3)] into primary radicals (R’). But in certain systems they also contribute to chain termination, partly or exclusively, giving rise to significant deviations from the ideal kinetics (see Problem 6.31). The degradative chain transfer to initiator (I) maybe written M~" -[-I’-~
Mn q- I"
(6.162)
where I" is a radical product from I, inactive or less active than the primary radical R" from I.
514
Chapter 6
Problem 6.31 The degradative chain transfer to initiator (I) may be written k~r,I M~" + I ----* M, + I" where I" is a radical product from I, inactive or less active than the primary radical R- from I. Derive suitable expressions for the rate of polymerization considering (a) an extreme case where chain termination occurs exclusively by the degradative initiator transfer and (b) a more general case where chain termination takes place by simultaneous occurrence of the degradative initiator transfer and the usual bimolecular mechanism. In both cases, assume that the radical I- formed by the chain transfer to initiator I is too inactive to reinitiate polymerization. Answer: (a) For termination of the kinetic chains exclusively by the degradative initiator transfer process, the rate of termination is Rt = ktr,i [M’] [I] Using the steady-state concept for the chain radicals, d[M’] -- Ri - t~t dt
= 2fkd[I]
-- ktr,i[M’][I]
= 0
[M’]= --2fkd kt~,I The rate of polymerization is then given by Rr = k,[MI[M’]
(P6.31.1)
which shows that Rp is independent of initiator concentration but it still first order dependence on monomerconcentration.
retains
(b) Under steady state, the following relationship holds good when chain termination occurs both by the degradative process and the usual bimolecular mechanism: dt
-- 2fkd [I]-
kt,,i
[M’]
On elimination of [M’] by substituting rangement one obtains
[II - 2k, [M.I2 = 0 [M-] = /~p/k~[M] and on further
Equation(P6.~l.~) allows a plot of _R~/[I]
rear-
[~]~vs.P~/[M], anda negative
slope of the linear plot is indicative of termination by the degradativeinitiator transfer reaction in addition to bimolecular termination. Fromthe slope of the plot, the parameter (kt,,i I kp) can be obtained and from the intercept fkd can be calculated, if the kinetic parameter (k~ / ~) for the monomeris known. When ~ becomes independent of [I] for a given [M], Eq. (P6.31.3) is unsuitable for the analysis of the degradative effect and Eq. (P6.31.2) may then be employed.
Radical Chain Polymerization
515
Problem6.32 Nonideal behavior in polymerization
of a given monomer is reflected in the variability of R~/[I] [M]2 at a constant temperature. Derive an equation for R~/[I] [M]2 representing in the most general form the perturbations introduced by primary radical termination and various chain transfer reactions. Neglect, however, the recombination reactions of primary radicals and of radicals formed as a result of chain transfer, as also cross-combination of these types of radicals, all of which are likely to be insignificant except under unusual conditions. Discuss, on the basis of the derived equation, the factors which lead to decreased rate of polymerization. Answer: Omitting the recombination reactions of primary radicals and radicals which result from chain transfer, the following scheme of reactions may be considered: Reaction
Rate
(a) I k--Ka 2R-
2A/~ [I]
(b)
R" + M ~ MF
ki[R’]
[M]
(c)
MI" + M -~. M2" ~ k~ [M’t [MI
(d) Mm"+ M22Y_, Mm+l" (e) Mm"+ Mn* ~-~ 2Polymer 2kt [M’] (f) (g)
Mn" + R" ~ Polymer ktp [M’] [R’] M."
+X~M.+X"
(h) X" + M ~2K, MI" (i)
M,F + X" ~ Polymer
ki~ l [X’] [NI k~, [M’I[X’l
ProceN Production of primary radicals Initiation of polymer chain Propagation Termination of growing chains by mutual deactivation Chain termination by primary radical Chain transfer where X may be monomer,solvent, initiator, or any additive Re-initiation Chain termination by a radical formed due to transfer
In reaction (a), f~ represents the total efficiency of the initiator defined [48] as the fraction of primary radicals that come out of the solvent cage escaping recombination therein and take part in initiation and primary radical termination of growing chains. Evidently f~ should be greater than the conventional f used in ideal polymerization equation (6.26). Application of stationary-state conditions to the concentrations of R’, X" and M" (denoting all radicals of size MI" and larger) leads to the equations: 2y~,kd[I] = ki [R’] [M] + ~, [R’] [M’] k,,. x [M’] IX] = ki, [X’] [M] + k~, [M’] [X’] k, [R’} [MI + k,~ [x.] [M] = 2/~ [M’]2 + k,~ x [M’] IX]
(P6.32.1 (P6.32.2
(P6.32.3 +/% [M’I JR.] + kt~ [M.] [X-] Combining Eqs. (P3.32.1)-(P3.32.3) and simplifying leads to the following equation relating [M’], [I], [M], and IX]:
516
Chapfer 6
--
-
k,=
[M’])
’ (P6.32.4)
The summation in this equation extends for all the ~ansfer-active present in the system. Equation ~6.32.4) can easily be simplified to
kt[M.]
~ _ (1
k~,[M’]~k~[M]
-Z
J k,~[X][M’]~
components
(ra-z -s)
[Note that when both prima~ radical termination and degradative chain transfers are neglected, Eq. (P3.32.5) transforms to Eq. (6.24) for ideal polyme~ation with ~ Nven by Eq. (6.14).] Unless the polymeric chains are ve~ short, one may use the long chain approximation /~ = h~[M’I[M] (P6.32.6) so that we have from Eq. (P6.32.5)
[I][M]2
kt 1 + kikr ) [M]2.]
k~[X]C ~ k,~k~[I] [MI
(P6.32.7)
(
where CX is the transfer constant kt,,x/kp. Equation (P6.32.7) represents in the most general form the perturbations introduced by primary radical termination and chain transfers. The first term on the right side represents the effect of primary radical termination and the second term that of degradation. Evidently, the greater the value of ~p the greater is the decrease in the rate of polymerization. On the other hand, the greater the values of Cx and kt~/ki~, the greater is the perturbation due to the chain transfer. In physical terms, this predicts that the more stable is the radical formed due to chain transfer, the greater is the degradative effect of chain transfer on the rate of polymerization. The degradative chain transfer causes a lower specific rate of initiation, k~, of the newly formed radical compared to that of a primary radical derived from an initiator. Case L No degradative chain transfer The termination of chain radicals occurs by combination with primary radicals and by the normal processes of mutual deactivation. In this case, Eq. (P6.32.7) simplifies R] _ f~kek~ 1 kik~, [M]2,] a[I1 [M] k, 1 + kik~ [M]2,]
(P6.32.8)
517
Radical Chain Polymerization or
- 0.868
,og : ,og
(P6.32.9)
for hnpP~ //¢ik~ [M]2 KK1. Case II. No primary radical termination. The termination of chain radicals occurs by degradative chain transfer and by combination with the resulting radicals besides the normal processes of mutual deactivation. Equation (P6.32.7) can then be written as
_ fkkdk~
(P6.32.10)
[M]" (1
Problem6.33 Reconsider the case of degradative
initiator transfer as described in Problem 6.31 but assume now that the radical I" formed due to chain transfer is capable of reinitiating polymerization. In addition to the normal modes of initiation, propagation, and bimolecula,r termination of chain radicals as in ideal polymerization, other reactions that may follow as a consequence of this degradative initiator transfer are shownin the following reaction scheme: Reaction (a) Mn" + I -~ Mn + I" ktr,I
Rate [M’] [I]
(b) I" + M." ~ Polymer hnl [I’]
[M’]
Process Chain transfer Termination by I"
Reinitiation by I" following transfer Derive an expression for the rate of polymerization and indicate how it can be used to obtain a measure of the degradative initiator transfer from experimental kinetic data. (c)
I" + M ~-~ MI"
kil [I’] [M]
Answer: Degradative effect will be prominent due to the occurrence of reaction (b). In the absence of reaction (b), degradative effect would still be measurable and important due to reaction (c) with kit < k~,. In the absence of other chain transfer reactions (i.e., other than with initiator) and primary radical termination, Eq. (P6.32.7) simplifies to the form (replacing f~ by the conventional f since primary radical termination is neglected):
[i]
[M]--~k~~[I] [Cskt,~[/ [~ 1 + ~k~-~-]2] 2[,1+ (kilk~,) ]/ ktlP~p ~1J
--
fkdk~kt
(P6.33.1)
518
Chapter 6
For (P~/[M]2) > k4 and the reverse reaction in step 2 [Eq. (ii)] is neglected. Assuminga steady state for [M~".... M,,’], d[M." .... M,~’] dt Therefore, °[M,~
kl[M.’I[M.~’] - k2[M." .... M,~’] - k3[M." .... M~’] = 0
= k2 + k3 [M~’][M.~’]
and /~ = ka [Mn" .... M,~-] klk3 2[M’]
(P6.34.1) k2 + k3 where [M-] is the concentration of all chain radicals. For slow translational diffusion, kz >> k2 and Eq. (P6.34.1) then reduces /~ = kl [M’] 2 (P6.34.2) For slow segmental diffusion, k2 >> k3 and Eq. (P5.34.1) then reduces klk3 Rt -- k2 [M’]2 (P6.34.3) The experimentally observed termination rate constant kt thus corresponds to kl and k~k3/k2, respectively, for the two limiting situations.
To ascertain the. effect of conversion on polymerization rate, it is useful to determine the ratio P~ / [M] [I]1/2 instead of percent conversion as it takes into account the chafigeg in- monomerand initiator concentrations with time (or conversion). A plot of P~p / [M] [1] 1/2 versus conversion (Fig. 6.11) show that three stages can be distinguished in some polymerizations. Stage ! involves either a constant rate (IA) or declining rate (IB) with time. Stage H represents the autoaccelerative gel-effect region, while Stage 11I involves either a constant (IIIA)or declining rate (IIIB). Stage I behavior is caused by the opposite effects of the increase in segmental diffusion and decrease in translational diffusion at higher conversions. The increase in segmental diffusion is attributed to the fact that with increasing conversion the polymerization medium becomes a poorer solvent due to the increased polymer concentration. The size of the randomly coiled up propagating radical in solution (referred to as coil) thus becomes smaller, resulting in an effective higher concentration gradient
Radical ChainPolymerization
521
Ilia \
\ Ill II
Conversion(*/.) Figure 6.11 Effect of conversion on polymerization rate. across the coil. Segmentaldiffusion of the radical end out of the coil to encounter another radical therefore increases with conversion. Simultaneously, however, the increasing polymer concentration decreases translational diffusion, as the reaction mediumbecomesmore viscous. At sufficiently high conversion, the polymer radicals are more crowded and entangled with each other leading to an even faster decrease in translational diffusion. Stage IA behavior observed for manymonomersresults when the increase in segmental diffusion is counterbalanced by the decrease in translational diffusion (i.e., kt remains constant). If, however, the initial increase in segmental diffusion is greater than the decrease in translational diffusion, k¢ increases and the polymerization rate decreases producing Stage IB behavior of decrease in/~ /[M] [1] 1/2 with conversion. Moderate Stage IB behavior has been observed in polymerizations of several monomersincluding styrene and methyl methacrylate [53,54]. As polymerization proceeds and viscosity increases, at some point the translational diffusion decreases faster than the increase in segmental diffusion and rapid autoacceleration or the gel effect (Stage II) occurs. When the polymer concentration becomes high enough, the chain radicals become more crowded and entangled with each other. As a result, the rate
522
Chapter 6
of diffusion of the polymer radicals and the frequency of their mutual encounters decrease. The rate of termination thus becomes increasingly slower. Termination involves the reaction of two large polymer radicals whereas propagation involves the reaction of small monomermolecules and only one large radical. High viscosity thus affects the termination reaction much more than the propagation reaction, that is, kt decreases muchmore 1/2 in than kp. The net result in this case is an increase in the ratio kv //~ Eq. (6.26) and hence an increase in the rate of polymerization. Since vinyl polymerizations are exothermic (see later) the increased polymerization rate associated with the autoacceleration effect can cause a temperature rise and faster initiator decomposition, leading to runaway reactions or explosions, if the heat of reaction is not removedefficiently. In Stage II, the kp//c~/2 ratio and the /~p/[M][I] 1/:~ value increase rapidly at first and then taper off as /cv is also affected in the later stages of reaction. At ve~ high conversions, /~p becomessufficiently affected that the /~p/[M] [I] 1/2 begins to level off (Stage Ilia behavior) or decrease (Stage IIIB behavior). Stage IIIB behavior which is much more common than Stage IIIA, is sometimesreferred to as the glass effect. The decrease in polymerization rate can be extremely pronounced and polymerization can end appreciably short of full conversion when the reaction temperature is below the glass transition temperature of the polymerization reaction system [55].
INHIBITION
AND RETARDATION
Somesubstances suppress free-radical polymerization of monomersby reacting with primary radicals or polymerradicals to yield either nonradical products or radicals that are of too low reactivity to undergo propagation. Such polymerization suppressors are called inhibitors or retarders depending on their effectiveness. Inhibitors stop every radical and polymerization is completely halted until they are consumed.Retarders are less efficient and stop only a fraction of the radicals. In this case, polymerization is not halted but it occurs at a slower rate. Figure 6.12 compares these effects on the rate of free-radical polymerization. Polymeriztion is completely stopped by an inhibitor during an induction or inhibition period (curve 2). At the end of this period, whenthe inhibitor has been consumed, polymerization proceeds at the same rate as in the absence of inhibitor (curve 1). A retarder lowers the polymerization rate without an inhibition period (curve 3). Somesubstances exhibit complexbehavior (curve 4). This behavior is not at all uncommon and may be exhibited by a substance that initially acts as an inhibitor but is converted to a product which acts as a retarder after the inhibition period. Impurities present in a monomermay act as inhibitors or retarders and those are usually the cause of the irreproducible polymerization rates observed with insufficiently purified monomers.On the other hand, inhibitors are invariably added to
523
Radical Chain Polymerization
I
2
> 0
Time Figure 6.12 Comparison of conversion-time plots for normal, inhibited,
and retarded free-radical polymerization. Curve 1: normal polymerization; curve 2: inhibition; curve 3: retardation; curve 4: inhibition followed by retardation. commercial monomers to prevent premature thermal polymerization during storage and shipment. These inhibitors are removed prior to polymerization or, alternately, an appropriate excess of initiator may be used to compensate for their presence. The difference between inhibitors and retarders is simply one of degree and not kind. Both are either chain transfer agents or act by addition processes to provide an alternative reaction path to propagating polymer radicals: Monomeraddition M,~"
¯
Chain transfer to XA> Addition to Q
:~
M~+I" MnX + A"
(6.163a) (6.163b)
M,~Q"
(6.163c)
If the new radicals A" and M~Q"do not react readily with monomer, there will be a decrease in the concentration of reactive radicals and a consequent fall in the rate of polymerization. If the rate of reaction (6.163b) or (6.163c) is very much greater than that of reaction (6.163a) the new radicals A" and M,~Q" do not add monomer then high-molecularweight polymer will not be formed and the rate of polymerization will be effectively zero. This is a case of inhibition (see Table 6.8). In retardation
524
Chapter 6
the rate of polymerization is slowed down but not reduced to zero. This occurs (a) if the rate of reaction (6.163b) or (6.163c) is close to that normal propagation reaction (6.163a) and the new radicals A" and M,~Q" not reinitiate (Table 6.8), or (b) if reactions (6.163b) and (6.163c) compared to reaction (6.163a) but the new radicals A" and MnQ"that are formed reinitiate slowly. Quinones are probably the most important class of inhibitors. The following transfer reactions may take place in the presence of quinone:
(6.164) HC-R I -~--CH 2
R
The inhibitor radicals formed in the above reactions are stabilized by resonance to such an extent that they do not start chains and initiate polymerization. They disappear partly through disproportionation (forming quinone and hydroquinone):
o
HO
6 HO (6.165)
0
HO
HO
0
and partly by combining with each other (dimerization) or with new chain radicals. Reaction (6.165) results in the regeneration of one inhibitor molecule per each pair of inhibitor radicals. Therefore this wouldlead to a 2:1 stoichiometry between the number of kinetic chains terminated [such as by reaction (6.164)] and the number of quinone molecules consumed. Disappearance of inhibitor radicals by dimerization wouldlead to a 1:1 stoichiometric ratio. Hydroquinoneand Other dihydroxybenzenes such as t-butyl catechol also act as inhibitors, but only in the presence of oxygen. The inhibiting effect is due to their oxidation to quinone. A large number of other substances are also active inhibitors. These include oxygen, NO(one of the most effective inhibitors, so muchso that some highly reactive monomerscan be distilled
525
Radical Chain Polymerization
only under an atmosphere of NO), aromatic nitro compounds, numerous nitroso compounds, sulfur compounds, amines, phenols, aldehydes and carbamates. Aninteresting inhibitor is molecular oxygen. Being a diradical, oxygen reacts with chain radicals to form the relatively unreactive peroxy radical: M,~- + O2 --4 Mn--O--O" (6.166)
Kinetics
of Retarded
Polymerization
In treating the kinetics of inhibited or retarded polymerization the usual kinetic schemeof initiation, propagation and termination can be used with an added inclusion of the transfer reaction between the chain radical and the inhibitor molecule Z M" + Z ~2~
Z"
(6.167)
For the sake of simplicity it will be assumedthat the inhibitor radicals (Z’) do not initiate new polymer chains and also do not regenerate the original inhibitor molecule by reactions such as Eq. (6.165). In the presence of the inhibitor, the rate of radical termination will be given by Rt = 2~ [M’] 2 + kz [Z] [M’] Since at the steady state, P~ = Rt, one may write 2kt [M’]2 -t- kz [Z] [M’] -- /74 = 0 Substituting
(6.168)
(6.169)
for [M"l from P~p = kp [M] [M’], Eq. (6.169) yields ~ [M]-------~
P~ = 0 + [M]
(6.170)
where Cz is the inhibition constant defined as Cz
-
k~
(6.171)
Twolimiting cases may now be considered: (a) When~ ~ 1, termination of chain radicals will be mostly caused reaction with the inhibitor. The normal bimolecular termination can thus be neglected and Eq. (6.170) reduces
~ [z] Cz
P~ = 0
(6.173)
or, diM] dt -
[M]P~ Rp - Cz[z]
(6.174)
The rate of strongly retarded polymerization is therefore dependent on the first powerof the initiation rate R4. This is in contrast to the polymerization in the absence of inhibitor or Cz Tc (just as liquid does not aggregate into crystals at temperatures above the melting point). In a dynamic equilibrium at To, forward (propagation) and reverse (depropagation or depolymerization) reactions proceed at equal rates. Thus reaction (6.66) should be written more generally (6.187) M ~ Mn+ k@ where ]¢dp is the rate constant for depropagation or depolymerization. Equation (6.15) is then replaced Mn" 1" -I-
diM] Rp - dt - /~p [M] [M’]
-- k,
dp [M’]
(6.188)
The overall effect of temperature on polymerization is complex due to the presence of both propagation and depropagation reactions. Whenthe temperature is initially increased for the polymerization of a monomer, the polymerization rate increases as kp increases. However, at higher temperatures the depropagation rate constant k, dp, which was initially zero, increases and becomes significant with increasing temperature (see Problem 6.38). Finally, a temperature is reached at which the propagation and depropagation rates are equal. This temperature is called the ceiling, temperature, To. So at To, -d[M]/dt -= 0 and, from Eq. (6.188), ]~p [M]e = ~dp, or ]¢p/kdp = g = 1/[Mle (6.189)
534
Chapter 6
-4 6x10
_-
kdp kp[M] e -~/
_ ckp
[M]e’-~~I ,
0
200
400
600
Temperature
Figure 6.14 Variation of kp[M]~ and kdp with temperature for styrene (Problem 6.38).
whereK is the equilibrium constant and [M]e is the equilibrium monomer concentration. One maythus predict that a ceiling temperature will be reached whenkp [M]eequals kdp, regardless of the variations of [M’]. The variations of k~ and ka with temperature will be given by Arrhenius expressions" k~ -- Ap exp(-
E~ / RT)
kd~ = Adp exp(-Edp/
nT)
(6.190) (6.191)
where Ap and Adp are pre-exponential factors and Ep and Edp are the activation energies for propagation and depropagation, respectively; Ep Edp = AHpis the enthalpy change for the overall reaction. It is obviousfromthe abovedefinition Of the ceiling temperaturethat To will dependon the monomer concentration in the system. If polymerization is performed at a temperature T and [M] is greater than [M]e at that temperature, as calculated from Eq. (5:189), then the polymerization wouldproceeduntil [M]falls to the value of [M]e. Conversely,for a given [M]e, a temperature satisfying Eq. (5.189) is the ceiling temperature (To)
Radical Chain Polymerization
535
above which a high-molecular-weight polymer cannot be obtained. The predicted variation of Tc with [M]e can be found by inserting Arrhenius expressions in Eq. (6.189), whence
the
Tc =
zXHp
(6.~9~)
Equation (6.192) shows that there is a series of ceiling temperatures corresponding to different equilibrium monomerconcentrations. For any monomersolution of concentration [Mle there is a temperature at which polymerization does not occur. In fact, for each [M]e there is a corresponding plot analogous to Fig. 6.14 in which kdp = k v [M]e at its Tc. Stated another way, the polymerization of a monomersolution at a particular temperature proceeds until equilibrium is established, that is, until the monomerconcentration decreases to the [M]e value corresponding to that temperature which, in turn, is the Tc temperature corresponding to the particular [M]e. Thus higher monomerconcentrations are required with increasing temperature in order to observe a net production of polymer before equilibrium is reached. There is an upper temperature limit above which a polymer cannot be obtained even from pure monomerat equilibrium. The apparent designation of a singular Tc value, often referred to in the literature as "the ceiling temperature," usually refers to the Tc for the pure monomeror in some cases to that for the monomerat unit molarity. Problem6.38 For pure styrene (density 0.905 g/cm3 at 25°C) calculate ka0 [M]e and k@at different temperatures, and hence determine the ceiling temperature, using the following data [60]: Ap = l0 s L mo1-1 S-I; A@ = 1013 s-l; Ep = 6.5 kcalmol-1; E@= 6.5 + 16.1 = 22.6 kcalmo1-1. Answer: For bulk styrene at 25°C, zL-1) -3) [M]=(1000 cm (0.905 gcm
-1 =8.7mol
L
Assumethat ~]~ = 8.7 mol L-~. The values of k~[M], and kd at any given temperature ~n then be ~lculated from the following expressions: ~(6-5xl0zcalm°l-~) k~ [M]¢ = (10~L mol -~ s -~) [ e~ L(1.987~IV~~K). j (8.7mol
-~)
(P6.38.~) x-1 mo~ [ G~OK -~) (T °K)J (P6.~S.~) ~ = 0°’~ ~-~) ~P[(~.~ Values of G [M],, kd,, and (G [M]~- ka) ar~ ~lculated for different assumed
536
Chapter 6
values of T, starting from roomtemperature (T = 300°K), and these are plotted in Fig. 6.14. The extrapolated curve of (kp [M], ka) cuts the temperature axis at T = 580°K. Therefore, Tc = 580 - 273 = 307°C. Alternatively, since A//p = E~ - Ea = -16.1 kcal tool -1, one obtains from Eq. (6.192), -I) (-16.1 x 103 cal tool
-~) ln[(106 -~ s-1) (8.7mol’-~) /(101~ s(1.987cal°K-1 mol Lmol 1)] = 5S0OK(= 307°c)
An alternative approach to the problem of determining ceiling temperature is based on the recognition of Tc as the temperature at which AGp = 0, and hence from Eq. (6.186),
Tc = AHp/ ASp
(6.193)
where AHp and ASp are the heat and entropy changes under the prevailing experimental conditions. Since Eq. (6.193) contains no reference to the mode of polymerization, Tc is characteristic of the polymer and not of its method of synthesis. For example, the same Tc applies to all polystyrenes of given molecular weight and tacticity, regardless whether they were polymerizedby anionic, cationic, or free-radical initiation. Comparing Eqs. (6.192) and (6.193), one may write ASp = Rln(Ap/ddp)
Rl n[M]e =
AS~ +
Rl n[M]e (6
.194)
where AS’~ is the entropy change for [M]e = 1 mol/L. Therefore, Tc = AHp/(AS~
-t"
Rln[M]e)
(6.195)
This equation implies that at the ceiling temperature (To) the monomer concentration in equilibrium with long chain polymer is [M]e.
Problem6.39 To study the polymerization-depolymerization equilibrium of amethylstyrene, solutions of this monomerin tetrahydrofuran were polymerized [61] at several temperatures using a sodium-naphthalene complexas initiator. The polymerization reaction was allowed to proceed for as long as 2.5 to 65 hours, after whichthe reaction was terminated with water and the polymerprecipitated in methanol, dried, and weighed. The concentration of monomerremaining at equilibrium was obtained from the difference in the original monomer and the polymer formed. The equilibrium concentration values obtained at several temperatures are given below:
537
Radical Chain Polymerization
Time Temperature (°K) (h) 273.2 2.5 7 273.2 5.5 298.2 298.2 22.5 309.2 65 47 320.2 328.2 16 Source: Data from Ref. 61.
Initial monomer Equil. monomer (mol/L) (mol/L) 1.535 0.715 " 0.767 0.737 4.03 2.21 3.44 2.23 5.52 3.50 4.60 4.53 7.57 6.65
Determine the heat of polymerization and the corresponding entropy value. Answer: The data show that solutions with different initial monomerconcentrations give the same equilibrium monomer concentration for each temperature, showing that the equilibrium concentration depends only upon the reaction or ceiling temperature. Equation (6.195) can be rewritten ln[M]~
AHv (
1 )
AS’;
(P6.39.1)
As shownin Fig. 5.15, the given data afford a linear relationship of ln[M], against reciprocal temperature (To = T), in agreement with Eq. (P4.39.1), yielding Slope = AHp/R = - 3.53 × 103 °K AHp= (- 3.53 x 103 °K) (1.987 cal°K-1 mo1-1) ---AS from Eq.(P6.39.1) = 25.0 cal°K-lmo1-1
For polymerization dard states [60],
- 7.0 × 103 cal mo1-1
with the monomer and polymer in appropriate
= T S;
stan-
(6.196)
All conditions for a standard state are fixed except temperature, which is always the temperature of the system. Standard-state properties are therefore functions of temperature only [52]. For equilibrium situation, AGo = 0 and the ceiling temperature may thus be given by T~ : AH~ / AS~ (6.197) Thus the value of Tc really revolves around the actual values of A/-/° and AS° for polymerization. Table 6.13 lists A/-/~, AS~ and calculated values of AG~at 25°C for several olefin and aldehyde polymerization systems. The values of Tc calculated from Eq. (6.197) using AH~ and AS~ values ~5°C, with the assumption that standard enthalpy and entropy changes have no significant temperature dependence, are also shown in Table 6.13. It is
538
Chapter6
Table 6.13 Standard Enthalpies, peratures
Entropies, Free Energies, and Ceiling Temfor Polymerization of Various Monomer-PolymerSystems at 25°C -AS~ -AG~ (cal/deg-mol) (kcal/mol)
Ceiling Temperature (°C) (To = AH~
Monomer
-AH~ (kcal/mol)
Butadiene Ethylene
17.6 21.2
20.5 24
11.5
585
14.0
610
Formaldehyde
7.4
19
1.7
116
Isobutylene
12.9
28.8
4.3
175
Isoprene
17.9
24.2
10.7
466
Methyl methacrylate
13.2
28
4.9
198
a-Methylstyrene
8.4
24.8
1.0
66
Styrene
16.7
25.0
9.2
395
Tetrafluoroethylene
37
26.8
29
1100
Unless otherwise specified, data refer to standard states of pure liquid for the monomer and amorphousor slightly crystalline state for the polymer. ’ Source : C.T. Mortimer, Reaction Heats and Bond Strengths, PergamonPress, NewYork (1962), Chap5; R. M. Joshi and B. Z. Zwolinski, in Vinyl Polymerization, Part I (G. H. Ham,ed.) Dekker, NewYork (1967), Chap. 8; E SI Dainton and K. J. Ivin, Rev. Chem. Soc." (London), 22:61 (1958); T. Ohtsuka and C. Walling, J. Am. Chem.Soc. 88:4167 (1966).
539
Radical ChainPolymerization
seen from Table 6.13 that while A/-/_* has a wide range of values, AS°_ vanes httle between monomers. The range of AS~ values (Table 6.13) from -19 to -28 cal/deg-mol. The reason for the narrow range is that the dominant factor in A.S~ is the loss of translational entropy caused by the large reduction in the number of molecules present, and this factor is relatively constant from system to system. The ceiling temperature is therefore dominated by the magnitude of A_H~. Vinyl monomerswith 1,1° values and hence lower Te than disubstitution generally have lower AH_ the corresponding singly substituted anaffogs. Thus the calculated Tc values of polystyrene and poly(c~-methyl styrene) are 395°C and 66°C, respectively. Solving Eq. (6.195) for [M]e yields in
[M]e - AHp RT~
AS~ R
(6.198)
which shows the equilibrium monomerconcentration [M]e as a function of the reaction or ceiling temperature Te. Equation (6.198) can be used calculate how much monomerwill be in equilibrium with high-molecularweight polymer at any temperature. This information is useful because many monomersare toxic or have offensive odors and it is often necessary to limit their concentrations in their polymers. Table 6.14 shows the monomer concentrations at 25°C for a few monomers.The data do indicate that the polymer obtained in any polymerization will contain some concentration of residual monomeras determined by Eq. (6.198).
Table 6.14
Polymerization-Depolymerization Equilibria
Monomer [Mlc at 25°C -6 Styrene 1 x 10 c~-Methylstyrene 2.2 -9 Methylacrylate 1 x 10 .3 Methylmethacrylate 1 x 10 .9 Vinylacetate 1 x 10 Ethylene Isobutene Source:Datafromvarious sources.
T~ for pure monomer(°C) 310 61 220 400 50
Problem6.40 The standard enthalpy of polymerization (AH~)of vinyl chloride at 25°C is -72 kJ/mol and the standard entropy of polymerization (AS~)can taken to be approximately--100 J/°K-mol. Canthe polymerbe safely used at the
Chapter 6
540
ambient temperature (25°C), in view of the fact that vinyl chloride is carcinogenic Answer: For T~ = 298°K, Eq. (6.198) gives (-72
in [M], =
(8.314
× 103 J mo1-1) J °K-’ mol-’)
(100 J °K-1 mo1-1)
(a00°K) (8.314 J °K-1 mol-’)
= -16.84 or [M], = 4.9×10 -s -1 tool L So only a negligible concentration (< 0.0005 ppm) of monomerwill be in equilibrium with high-molecular-weight polymer at 25°C. If unreacted monomercan be purged from the polymer, no significant concentration will develop thereafter at room temperature because of the polymerization-depolymerization equilibrium.
Problem6.41 If a free-radical
polymerization of 1.0 M solution of methyl methacrylate was being carried out at 100°C, what would be the maximumpossible conversion of the monomerto polymer, that is, till the polymerizationdepolymerization equilibrium is reached ? (Take relevant data from Table 6.13.) Answer: To calculate an approximate value of [M]~, consider the monomerand the polymer in their standard states and assume that there is no significant temperature dependence of enthalpy or entropy of polymerization so that the AH~and AS~ data of Table 6.13 can be used. For Tc = 373 °K, Eq. (6.198) then yields, (-28 cal °K-’ mol-’) (-13.2 x 103 cal mol-’)
in
--
-
(1.987 cal °K-1 mo1-1) (373 °K) (1.987 cal °K-’ mol-’) = - 3.72 [M]¢ = 0.024 mol L-’ Maximum conversion = (1 - [M]~)x 100 97 .6%
Problem 6.42 Using the AHi~and AS~ data for styrene from Table 6.13 calculate kp at 60°C the depolymerization rate constant of polystyrene at 100°C. [Data: = 165 L/mol-s; Ep = 26 kJ/mol.] Answer: From the Arrhenius expression for k~, o (k/~)100 (26 x 103 J mo1-1) [ 1 In (165 L mol-’ s-’) = (~--..~1~ oK-X mol-’)~335°K (kp)100o
l
]
37~°K
= 452 L mo1-1 s-’
For Tc = 373 °K and assuming no significant temperature dependence of enthalpy and entropy of polymerization, so that AH~and AS~ values at 25°C from Table 6.13 can be used, Eq. (6.198) yields (25.0 -a cal °K-1 mol (- 16.7 x 10z cal mo1-1) In [M]~ = + -~) -1) (1.987 cal °K-1 mol (373 °K) (1.987 cal °K-’ tool = -9.95
Radical Chain Polymerization
541
[M]~ ---- 4.77x10 -2 -1 mol L From Eq. (6.189),
kd, = k,[Mh = (452L mo1-1 s-1)(4.77× -2 mo l L-1) = 2.15 x 10-2 -~ s
While for many alkene monomers the position of the propagationdepropagation equilibrium is far to the right under the usual reaction temperatures employed(that is, there is essentially complete conversion of monomerto polymer for all practical purposes), there are some monomers for which the equilibrium is not particularly favorable for polymerization. For example, o~-methylstyrene in a 2.2 Msolution will not polymerize at 25°C and pure o~-methylstyrene will not polymerize at 61°C (see Table 6.14). In the case of methyl methacrylate, though the monomercan be polymerized below 220°C, the conversion will be appreciably less than complete. For example, the value of [M]e at 110°C is found to be 0.139 M [3] which corresponds to about 86%conversion of 1 Mmethyl methacrylate. Since Eqs. (6.195) and (6.196) contain no reference to the of initiation, they apply equally well to ionic and ring-opening polymerizations. Thus the lower temperatures of ionic polymerizations often offer a useful route to the polymerization of many monomers that cannot be polymerized by radical initiation because of their low ceiling temperatures. Though a monomercannot be polymerized above its ceiling temperature, it should not be assumed that a polymer will depolymerize and thus be useless above the ceiling temperature. A dead polymer that has been removed from the reaction media or made at a temperature below Tc will, in fact, be stable and will not depolymerize unless an active end is produced by bond cleavage of an end group or at some point along the polymer chain. Whensuch an active site is produced by thermal, chemical, photolytic or any other means, depolymerization (unzipping) may follow until the monomerconcentration becomes equal to [M]e for the particular temperature. Poly(oz-methylstyrene) with Tc = 61°C and poly(methyl methacrylate) with Tc ~ 165°C exhibit such behavior. For a polymer with this behavior, depolymerization is a valuable method for recovering scrap quantities of the polymer as monomer. The thermal behavior of many polymers, however, is much more complex. Moreover, degradative reactions other than depolymerization often occur at temperatures below the ceiling temperature without yielding major quantities of monomer. It should be noted that Eq. (6.198) gives no information as to how quickly the equilibrium monomerconcentrations will be attained at the ceiling temperature. Polymers may in fact be quite useful above their ceiling temperatures if depolymerization processes are kinematically hindered. For example, poly(formaldehyde) h.as a Tc of 126°C, but the polymer can be made sufficiently stable for melt processing at temperatures above 200°C. This may be achieved by esterifying or etherifying the thermolabile hydroxyl ends of the macromolecule, copolymerizing with small concentrations of ethylene oxide, and using basic additives as stabilizers. The under-
542
Chapter6
lying principle of these expedients is to retard the initiation or propagation steps of chain reactions that could "unzip" the polymer to monomer.
MOLECULARWEIGHT DISTRIBUTION The molecular weight distributions in radical chain polymerization are more complex than those in step-growth polymerization (Chapter 5). This is because radical chain polymerization involves several possible modesof chain termination-disproportionation, coupling, and various chain transfer reactions. The situation is further complicated by the fact that the molecular weight of the polymer produced at any instant varies with conversion due to changes in the monomerand initiator concentrations and in the propagation and termination rate constants. However, at low conversions these kinetic parameters remain approximately constant and the polymer molecular weight does not change with conversion. Molecular weight distributions can thus be relatively easily calculated for polymerizations restricted to low conversions.
Low-ConversionPolymerization Weassume here that the concentrations of monomerand initiator remain essentially constant during polymerization and that any dependence of termination rate constants on polymer chain size and concentration or autoacceleration effects can be neglected. Molecular weight distributions derived under these conditions will not obviously apply to commercial polymers, whose polymerizations are often finished at high conversions. These highconversion polymers mayhave distributions that differ from those calculated here. A later section discusses the size distributions of such polymers. A given monomer-ended radical may add a monomer molecule or undergo chain transfer or termination. The probability that it will add monomer is
P =
/~ P~ + Rtr + Rt
(6.199)
where /~p, /:~tr, and -~tr are the rates of propagation, chain transfer, and termination, respectively. These are given by Rp
=
k v [M] [M’] ntr = ktr,M[M’][M] q- ]~r,I[M’][I] /~t = 2 (ktc q- ktd)[M’] 2
(6.200) q- k, tr,S[M’][S]
(6.201) (6.202)
Note that the effects of any chain transfer agent are included in the term for solvent and that transfer to polymer is not included in the expression for R.tr because such transfer can be significant only at high conversion where sufficient polymer can be present.
Radical ChainPolymerization Termination
543
by Disproportionation
and/or
~ransfer
Wefirst consider the polymerization where each kinetic chain yields one polymer molecule. This happens when the growth of microradical chains is terminated by disproportionation and/or chain transfer (i.e., ktc = 0). The situation here is completely analogous to that for linear, reversible stepgrowth polymerization described in Chapter 5. If we select an initiator fragment at the end of a macromolecule, the probability that the monomer molecule picked up by this initiator radical has added another monomer molecule is P. Continuing in this way the probability that x monomer molecules have been added one after another is px-1 (see p. 347). Since the probability that the radical end of a growing chain has terminated is (1 -- P ), the probability that the macromolecule under consideration consists of essentially x monomerunits is _p~-I (1 -- P). Since such propabilities are equal to the corresponding mole fraction of this size molecule, n~, we have the expression nx = (1
--
P)P~-I
(6.203)
for the number distribution function. The weight distribution function wx is also given by direct analogy to that for linear, equilibrium step-growth polymerization (p. 348)
w~ = x (1 - P)2PX-1
(6.204)
By analogy with l~qs. (5.77), (5.80), and (5.81) we can D--P,~ ----
1/(1 -- P)
DPw = (1
+ P)/(1
DP~/DPn
= 1 +P
(6.205) (6.206)
-
(6.207)
Substituting t~q. (5.199) into l~q. (5.205) and noting that for most addition polymerizations, P~p )) Rtr + /~t (or high-molecular-weight polymer would not be formed),
DPn =
P~ + Rtr + Rt Rv - Rt~ + R~ -/~tr + Rt
(6.208)
Insertion of I~qs. (5.200)-(6.202) into Eq. (6.208) and simplification (noting that ktc = 0) gives
1 DPn
-- CM -]-
CI,--,
-I-
[[MI_~]]
IS]
CS~-~ -1-
2/~d
k~[M]2Rp
(6.209)
which can be easily shownto be identical with lEq. (6.148). A consideration of Eqs. (6.203) and (6.204) indicates that highmolecular-weight polymer (i.e., large DPnand DPw)will only be produced
544
Chapter 6
if 2° is close to unity, i.e., if P~p >> }~tr -I- /~t. Equation (6.207) indicates that the size distribution D--~w/ DPn(also referred to as PDI, the polydispersity index) has a limiting value of 2 as 20 approaches unity. The situation is thus analogous to that for linear step-growth polymerization considered in Chapter 5 [cf. Eq. (5.81)]. There is, however, an important difference between the distributions calculated for equilibrium, bifunctional step-growth polymerization in Chapter 5 and for the free-radical polymerizations with termination by disproportionation and/or chain transfer that are being considered here. Thus p in Eq. (5.81) is the extent of conversion, while 20 in the above equations the probability that a propagating radical will continue to propagate instead of terminating. There is a very important second difference. While the distribution functions in the step-growth case apply to the whole reaction mixture, in the free-radical polymerization this distribution applies only to the polymer fraction of the reaction mixture. Termination
by Coupling
To consider another extreme, suppose that each polymer molecule consists of two kinetic chains, that is, termination occurs only by coupling. Each polymer molecule thus consists of two sequences of units which grew independently and were joined together at their mutual termination. They are analogous to the dichain (f = 2) condensation polymers discussed Chapter 5 (p. 367). Further advantage may be taken of this analogy replacing p by 20, defined as the probability of continuation of either chain from one of its units to the next. Then 1 -- _P is the probability that the i-th unit in the growth of the chain reacts by termination; it is therefore equal to the ratio of terminated to total units. Since two units are involved in each termination step, one can write 1
--
P -
Rt
_
2k¢c
[M’]
Rv + Rt kp[M] + 2ktc[M’]
(6.210)
where ktc is the rate constant for termination by coupling. Substitution of [M’] ----- P~p / kp [M] from Eq. (6.15) into Eq. (6.210) and simplification gives
1_ 1+
(6.211)
Then, since each molecule consists of two chains, the number-average degree of polymerization will be given by [cf. Eq. (6.205)],
_
2 - 2 + (1- 20)
[M]
(6.212)
RadicMChainPolymerization
545
For the weight-averagedegree of polymerization, the_following equation can be shownto be applicable: 2+P D---~, -- 1 -- P (6.213) Hence,
= (2 + P)/2
(6.214)
The ratio in Eq. (5.214) has a limiting value of 1.5 at high polymer molecular weights whenR,p >> Rt and P approaches 1. This is narrower than the distribution producedin the absenceof termination by coupling. Thenumberfraction and weight fraction distributions [63] are readily shownto be n~ = (x - 1)(1 - P)eP~-~ Wx-~ ~127(a~ -- 1) (1 _ p)Z
(6.215) (6.216)
whereeach initiator radical is countedas a unit. [Notethat Eq. (6.216) obtained simply by multiplication of Eq. (6.215) by x/~--~n.] These expressions correspond nearly to Eqs. (5.115) and (5.116) Chapter 5 for dichain polymers(f = 2). Minordifferences occur because the latter contain a single central unit, whereastwo mustbe countedin the present case. Termination by Coupling, and Chain Transfer
Disproportionation
For polymerization wheretermination occurs by all three modes, namely, coupling, disproportionation and chain transfer, one can obtain the size distribution by a weightedcombinationof the abovetwo sets of distribution functions. For example,the weightdistribution can be obtained as w~ = wx(1-P)2P~-I
+-~ l(l_w)x(x_l)(
1 p)apz-2 (6.217)
wherew is the fraction of polymermaterial formedby disproportionation and/or chain transfer reactions [64]. Anexpression for P can be obtained by inserting Eqs. (6.200)-(6.202) into Eq. (6.199) and using the relation [M’] = Rp / kv[M]. This gives 1 p --
i
[I] IS] 2(k, tc q- ~d) + CM~ + Cs~ + k~ 2[M]~ /~
(6.218)
546
Chapter6
The valueof w is givenby 2]¢¢r,M[M’][M]-t- ktr,I ktr,M[M’][M] -1- ktr, CM[M] -{- CI[I] CM[M]q- CI[I]
[M "] [I] -]- ~r,s[M’][S]-1- 2ktd[M’] I[M’][I l 2q- kcr, s[M’][S] q- 2(kt¢ q-ktd)[M’]
d- Cs[S l -{- 2~dP~p/kp2[Ml
q- Cs[S] -b 2(k,
tc q-
(6.219)
To calculate _P and w, and hence wz, from Eq. (6.217)~ from kinetic and theoretical considerations for any polymer system, it is thus necessary to have the values of transfer constants (CM, CI, Cs), 2 /k n, le t, an d
Problem6.43 The bulk polymerization
of methyl methacrylate (density 0.94 g/cma) was carried out at 60°C with 0.0398 Mbenzoyl peroxide initiator [64]. The reaction showed first order kinetics over the first 10-15%reaction and the initial rate of polymerization was determined to be 3.93 x10-4 mol/L-s. From the GPC molecular weight distribution curve reported for a 3% conversion sample, the weight fraction of polymer of D---~ = 3000 is seen to be 1.7x10-4. Calculate the weight fraction from Eq. (6.217) to compare with this value. [Use the following data: CI _~ 0.02; CM = 10-5, fka = 2.7 x 10-6 s-l; kt = 2.55 x 107 L/tool-s; fraction of termination bydisproportionation = 0.85] A~lswer : From Eq. (6.26), [M]2 (fka) [I]
kt
(3.93 x 10-4 tool L-1 2s-1) (9.4 tool L-l) ~ (2.7 × 10-6 S-1) (0.0398 mol
=
-~ = 0.0163 L mo1-1 s
In as much as polymerization rates are measured at less than 10% conversion, it can be assumed that [M] and [I] in Eq. (6.218) are equal to their initial concentrations. Therefore, -~) --1 = 1 + 10 -5 + (0.02)(0.0398 molL -1)/(9.4 molL P +
(2) (3.93 x -4 mol L - ~ s - 1) (0.0163 L tool -1 s -1) 2(9.4 mol L-l)
= 1.0006 P = 0.9994 Since ktd / (kte -}- ktd) -~- 0.85 and knc +ktd ---- kt = -1, 2.55 × 107 L mo1-1 s it follows that kid = 2.167x10 r -~ Lmo1-1 s
547
Radical Chain Polymerization
k:/~d = Ck:/k)C~/~,d) = (0.0163L mo1-1 s-1)(2.55 x 107/2.167 x 107) = 0.0t92L mo1-1 -1 Substituting the appropriate values in Eq. (6.219) yields ~ = 0.871. Therefore, from Eq. (6.217), w3000 = (0.871)(3000)(1 - 0.9994) 2 ~°°°-1 (0.9994) + ½(1 - 0.871)(3000)(3000 - 1)(1 - 3 (0.9994 3°°°-2 = 1.8 × 10-4 -4 (el.) reported value = 1.7 × 10
Problem6.44 Consider a case of free-radical
polymerization where termination involves both disproportionation and coupling of chain radicals but chain transfer reactions can be neglected. Derive an expression for the distribution function for the degree of polymerization of polymer in terms of the kinetic chain length and the ratio of termination by disproportionation to that by coupling [65]. Simplify the expression for two limiting cases where (a) termination is solely by coupling and (b) termination is solely by disproportionation. Answer: Applying the steady-state radicals may be written:
approximation, the rate equation for propagating :r-mer
at - ~ [M][M~-x’]- ~ [M][M.’]- 2~ [M~’][M’]= 0 (P6.44.1) After division by [Mz-l’], followed by rearrangement, Eq. (P6.44.1) yields [M,-] _ ¯ [M,_,’]
k~[M] = (1+ 2k’[[M--M~])-~ k. [M] 9- 2k, [M’] k.
(P6.44.2)
From Eq. (6.123), kinetic
chain length,
~, -- ks [M] 2/% [M-]
(P6.44.3)
Equation (P6.44.2) may thus be written conveniently
An expression for the ratio [M~-] / Nil may be obtained plication of the ratios in (P6.44.4). Thus,
by successive multi-
or
If a~ is defined as the fraction of propagating radicals that have a degree of polymerization z, then, in view of Eq. (P6.44.6), wehave the relationship:
[M.]
(P6.44.7)
Chapter ~
548
Applying the steady-state approximation to the concentration of the smallest propagating radical, [MI"], and to the total radical concentration, [M’], one obtains -- Ri - k~o [M] [M,-] -- 2~ [M~’] [M’] = 0
dt
-- Ri- - 2kt[M’l 2 = 0
dt
(P6.4A.8)
(P6.44.9)
Equation (P6.44.8) may be rearranged [Ml’] = k~ [M] + 2k~ [M-]
(P6.44.10)
and Eq. (P6.44.9) [M’] - 2k~ [M’] Taking the ratio (6.44.3) gives [M~’] [M’]
_
(P6.44.11)
of Eq. (P6.44.10)
2hn [M’] k~ [M] + 2/~ [M-]
to Eq. (P6.44.11)
and combining with
= (1 + u)-~
(P6.44.12)
Substitution of Eq. (P6.44.12) into Eq. (P6.44.7) then yields a~
= -
1 +
(P6.44.13)
This equation represents the distribution of the degree of polymerization of the propagating radicals. The distribution of the degree of polymerization of the polymer will, however, be determined by a, and by the mechanismof termination of the propagating radicals, as shownin the following. The mole fraction of polymer molecules consisting of z mer units will be given by the rate ratio d[P,] / dt d[Pl /dt
n~ -- dips] / dt Z~ d[P~] / dt
(P6.44.14)
where the denominator represents given by dIP]
/ dt = (k,~
the total rate of formation of polymer and is "~ + 2k, d) [M’] z (P6.44.15)
(The factor of 2 appears because two polymer molecules are formed in termination by disproportionation.) To evaluate the numerator in Eq. (P6.44.14) we need only
Radical Chain Polymerization sum the rates of all the reactions in which P~ is formed. These reactions are: Coupling
Disproportionation
M=-i" + M1° ~ P= M=-2" + M2" ~ P~
M=" + Ml" -~ P, + P1 M=" + M2" ~ P, + P2
:
M=_,~"
(P6.44.16) (P6.44.17)
;
+ M~" ~ P~
MI" + Mz-l"
M~" + M,~" ~ P~ + P,~
(P6.44.18)
~ P~
Weshould note that in summingthe rates of the coupling reactions in (P6.44.16) to (P6.44.18), every reaction will be counted twice, with one exception. The one exception is that reaction in which m = x - m = z/2, and such a reaction between like radicals is possible only if the integer z is even. If z is even, then
at = ~,o[M=/2.][M=/~.]+½ ~ /~:o[M._r~.][M,~.]+~/~[M,’][M’] (P6.44.19) where k~ is the coupling termination rate constant for like radicals and k’t~ that for unlike radicals; the factor 1/2 corrects for the addition of each reaction between unlike radicals twice in summingthe coupling reactions (P6.44.16) to (P6.44.18). maybe noted that the rate constant for termination of unlike radicals is twice that for like radicals-a conse~quenceof the relative collision frequencies of like and unlike species - that is, kte = 2ktc. Therefore Eq. (P6.44.19) may be written dt
-- kt~ ~ [M=_,~’] [M,~’] + 2k,d [M=’] [M’]
(P6.44.20)
There can be no combination of like radicals to produce a polymer having an odd numberfor x. Equation (P6.44.20) is therefore generally applicable, i.e., both for even and odd values of x. Substitution of Eqs. (P6.44.7) and (P6.44.12) leads iv 2 1 +
d~
~-~.(1) "~ + -- 1 +
[M’]* (P6.44.21)
m=l
The summation is equal to (n - 1), so we have
Dividing by Eq. (P6.44.15), one finally obtains the mole fraction of polymer of met units, that is, 1
(
~)-=
(z-l)/v
+
Equation (P5.44.23) showsthat the distribution function fo~ the degreeof polymerization of polymer formed by a free-radical chain mechanism,in which chain transfer is absent, depends only on the k~netic chain length andthe ratio of disproportionation to coupling. The plot of n~ vs. x accordingto Eq. (P6.44.23) gives the
550
Chapter 6
number or mole fraction distn’bution of the degree of polymerization. The molecular weight distribution is easily obtained from Eq. (P6.44.23) since M where -Mo is the, molecular weight of the monomer. (a) Case 1: Termination is solely by coupling, i.e., thus reduces to
/eta = 0. Equation (P6.44.23)
Since /2 = /~//~t and P~ >> Rt for most addition polymerizations, easy to see that Eq. (P6.44.24) is equivalent to Eq. (6.215). (b) Case 2: Termination is solely by disproportionation, (P6.44.23) reduces n~
i.e.,
it is
/~, = 0. Equation
=
+ (P6.44.25) 1(~ It is e,hsy to see that Eq. (P5.44.25) is equivalent to Eq. (5,203) when termination is solely by disproportionation (i.e., R~r = 0).
Problem6.45 Show graphically
the number distribution of degree of polymerization for (a) termination by coupling and kinetic chain length (v) values of 300 and 400, and (b) for/2 = 300 and ktd/ktc = O, 0.2, 0.4, 1.0, and Show that there is a value of ~c for which the mole fraction of polymer with DP = z is independent ofkt~/ktc and this value is ~: = /2+ 1. Answer: The functional dependence of the distribution function in Eq. (P6.44.24) for termination solely by coupling is shown in Fig. 6.16(a) for v = 200, 300, and 400. The distribution is seen to become broader at higher values of v. The number distribution of degree of polymerization for v = 300 and different values of ktd/~c is plotted according to Eq. (P6.44.23) in Fig. 6.16(b). It seen that all the distribution curves pass through the same point. This means that there is a value of x for which the mole fraction of polymer with DP = z is independent of ~/ktc. To determine this value of z analytically, Eq. (P6.44.23) may be differentiated with respect to k~d/ktc and equated to zero. This gives
Problem6.46 Derive weight-fraction
distribution of degree of polymerization, wz, from the number fraction distribution, n~; described by Eq. (P6.44.23). Answer: Let N = total number of moles of polymer molecules; M0= molecular weight of monomer; DP, = average degree of polymerization of polymer molecules. Then Number distribution, N~ = n~N Weight of x-mers, W~ = xN~Mo = xn~NMo Total weight, W = N(~-~,~)Mo
Radical ChainPolymerization
2.0 [
551
9 : 200 (a)
1.5
0.5 0
200
/-.00 x
600
800
:2.0
~
~.o ~.5~ o¯5I L/~.~ /
I/-I
0
I
~~~~o.2 ~~o,~ I
I
200
I
I
~00
I
I
600
/0.0
I
800
X
Figure 6.16 Numberdistribution of degree of polymerization (Problem 6.45) (a) termination by combinationfor several values of kinetic chain length (u); distribution for u = 300 and several values of kta/ktc shownon the figure.
Weight fraction
of x-mers, wx -- W= n=
Since DPnis equal at any instant to the ratio of the rate of monomer disappearance to the rate at whichcompletedpolymermolecules are produced,that is, D~,,-- - diM] / dt d[P] / dt Combinationof this equation with Eqs. (6.20) and (P6.44.15) yields DP’--~=
k~, [M]
(k,o + ~,~)[M.]
(P6.46.2)
(P6.46.3)
552
Chapter 6
Substituting for [M-] in this equation from Eq. (6.123) and for ~ from Eq. (6.12) one then obtains -(P6.46.4) DPn = 2v ~ -l(k,t~ + kta’~ Substitution of Eqs. (P6.44.23) and (P6.46.4) into Eq. (P5.45.1) yields weightfraction distribution --
~ - 2~2 1 + ~ (x 1) / ~ + 9.(~d/~o)
(r6.a6.5)
Note that Eq. (P6.46.5) is equivalent to Eq. (6.216) for kta = 0 and P~ >>
High-Conversion
Polymerization
Molecular weight distributions in high conversion polymerizations are not nearly as predictable as those in low-conversion reactions and they also vary with polymerization conditions and from monomer to monomer. The size distributions for high-conversion polymerizations becomemuchbroader than those described above for incremental or low-conversion polymerization. The polymer molecular weight depends on the ratio [M]/[I] 1/2 according to Eq. (6.125). As a polymerization proceeds, [I] usually decreases faster than [M] and the molecular weight of the polymer produced at any instant increases with the conversion. The overall molecular weight distributions for high-conversion polymerizations are quite broad with DPw/~-~n ratio being in the range 2 to 5. Whenautoacceleration or gel effect occurs in polymerization there is even larger broadening. Since autoacceleration results from a reduced termination rate resulting in large increases in the kp/le~/2 ratio, it is always accompaniedby large increases in the average molecular weight and the breadth of the distribution. Thus, DPw/~---~n values as high as 5 to 10 may also be observed when the gel effect is present. If chain transfer to polymer can occur, this will be most significant at higher conversions when the polymer concentration is high. This results in a further broadening of the molecular weight distribution and can lead to D---~o / ~-Pn ratios as high as 20 to 50. This very extensive broadeningoccurs because chain transfer to polymer increases as the polymer size increases and branching caused by chain transfer thus leads to greater branching as polymerization proceeds. Broad molecular weight distributions are usually not desirable from the practical viewpoint since optimum values of polymer properties are usually obtained at specific molecular weights. Addition of multiple charges of initiator and/or monomerduring the course of polymerization is often practiced in commercial polymerization processes to minimize the molecular weight broadening due to change in [M] and [I]. It is, however, more difficult to minimize molecular weight broadening due to the gel effect and chain
Radical Chain Polymerization
553
transfer. Thus, for example, low temperatures minimize chain transfer polymer but maximize the gel effect.
to
POLYMERIZATION
PROCESSES
Free-radical polymerizationsare carried out by a variety of processes .that require different design considerations with respect to recipe of polymerization and physical conditions for the process and process equipment. Generally free-radical polymerizations are carried out by four different processes: (a) bulk or mass polymerization, (b) solution polymerization, (c) suspension polymerization, and (d) emulsion polymerization. Of the four processes, the last two are essentially of the heterogeneous type containing a large proportion of nonsolvent (usually water) acting as dispersion mediumfor the immiscible liquid monomer.Bulk and solution polymerizations are homogeneous processes, but some of these homogeneous systems may become heterogeneous with progress of polymerization due to the polymer formed being insoluble in its monomer(for bulk polymerization) or in the solvent used to dilute the monomer(for solution polymerization). Though all monomerscan be polymerized by any of the various processes, it is usually found that commercial polymerizatio~ of any one monomeris best carried out by one or two of the processes. The laboratory techniques for carrying out polymerizations have been discussed [66,67]. The kinetic schemes described in this chapter will apply to free radical polymerizations in bulk monomer,solution, or in suspension, but the kinetics of emulsion polymerization, to be discussed later, are different. Bulk Polymerization Polymerization in bulk, that is, of undiluted monomer,offers the simplest process with a minimumcontamination of the product. Thus for radical chain polymerization in bulk, the only additive to the monomer is an initiator and that again decomposesand reaches almost vanishing concentration at the end of the polymerization; the process thus results in optically clear polymers such as polystyrene and poly(methyl methacrylate). Bulk polymerization difficult to control, however, due to the characteristics of radical chain polymerization, namely, their highly exothermic nature, the high activation energies involved, and the tendency toward the gel effect, which combine to makeheat dissipation difficult. For dissipation of the heat liberated with progress of polymerization, continuous stirring of the reaction system is essential, but the stirring process and heat dissipation becomeprogressively difficult due to rapid increase in viscosity of the reaction system. The viscosity and exotherm effects which often become more acute due to the phenomenon of autoacceleration or gel effect make temperature control difficult . Local hot spots may occur and this may lead to discoloration, thermal degradation, branching, development of chain unsaturation or even cross-linking, thus giving rise to irreproducible and often inferior product
Chapter 6
554
quality. In the extreme case, uncontrolled acceleration of polymerization rate can also lead to disastrous runawayreactions. Because of the aforesaid problems and disadvantages, bulk polymerization is not used for chain polymerization as muchas for step polymerization. It is, however, used in the polymerization of ethylene, styrene, and methyl methacrylate. The heat dissipation and viscosity problems in such cases are circumvented by two approaches: (i) by carrying out the polymerization to low conversions with separation and recycling of unreacted monomer,as in the high pressure polymerization of ethylene using tubular reactor; and (ii) by accomplishing the polymerization in stages-to low (2030%)conversion in a large stirred reactor and to final conversion in thin layers (either on supports or free-falling streams), as in the preparation acrylic castings from methyl methacrylate monomerand in the manufacture of polystyrene from styrene. Solution
Polymerization
By carrying out the polymerization of a monomerin a solvent manyof the disadvantages of the bulk process can be avoided. The solvent acting as a diluent reduces the viscosity gain with conversion, allows more efficient agitation or stirring of the medium, thus effecting better heat transfer and heat dissipation. Although thermal control is much easier in solution polymerization compared to bulk polymerization, the solution method has its own demerits. The method often requires handling of flammable or hazardous solvents and removal or recovery of the solvent to isolate the polymer after the polymerization is over. The purity of the polymer may suffer due to retention of last traces of solvent in the isolated product. Unless the solvent to be used is chosen with appropriate consideration, chain transfer to solvent may also pose a problem..Solution polymerization is, however, advantageous if the polymer formed is to be applied in solution as in the case of making of coating (lacquer) grade poly(methyl methacrylate) resins from methyl methacrylate and related monomers. Suspension
Polymerization
Suspension polymerization is designed to combine the advantages of both the bulk and solution polymerization techniques. It is one of the extensively employed techniques in the mass production of vinyl and related polymers. Suspension polymerization (also referred to as bead or pearl polymerization) is carried out by suspending the monomer as droplets by efficient agitation in a large mass (continuous phase) of nonsolvent, commonlyreferred to as the dispersion or _suspension medium. Water is invariably used as the suspension mediumfor all water insoluble monomers because of the manyadvantages that go with it. Styrene, methyl methacrylate, vinyl chloride, and vinyl acetate are polymerized by the suspension
555
Radical Chain Polymerization
process. The size of the monomer droplets usually range between 0.1-5 mm in diameter. Suspension is maintained by mechanical agitation and addition of stabilizers. Lowconcentrations of suitable water-soluble polymers such as carboxymethyl cellulose (CMC)or methyl cellulose, poly(vinyl cohol), gelatin, etc., are used as suspension stabilizers. They raise the mediumviscosity and effect stabilization by forming a thin layer on the monomer-polymerdroplets. Water insoluble inorganic compounds such as bentonite, kaolin, megnesiumsilicate, and aluminumhydroxide, in finely divided state, are sometimes used to prevent agglomeration of the monomer droplets. Initiators soluble in monomer,such as organic peroxides, hydroperoxides or azocompounds-oftenreferred to as oil-soluble initiatorsare used. Each monomerdroplet in a suspension polymerization thus behaves as a miniature bulk polymerization system and the kinetics of polymerization within each droplet are the same as those for the corresponding bulk polymerization. At the end of the polymerization process, the monomer droplets appear in the form of tiny polymer beads or pearls and hence, the process is also knownas bead or pearl polymerization. The polymers are filtered, washedprofusely with water to removethe stabilizer as far as practicable, and dried. They, however, usually retain traces of stabilizers besides the residual initiator as contaminants. Heat and viscosity control in suspension polymerization is relatively easy compared to bulk polymerization. Another important advantage of the method is that the polymer product can be obtained directly in spherical bead form (which may subsequently be functionalized to make ion-exchange resins). Problem 6.47 A monomeris polymerized at 80°C (a) in benzene solution and (b) in aqueous suspension in two separate runs, both containing 60 g the monomer (density 0.833 g/cm3) and 0.242 g of a peroxide initiator in a total volumeof 1 liter. If the initial rate of polymerizationfor 1 liter of solution is 0.068 mol/h, whatis the expectedinitial rate for 1 liter of suspension? (Assume that rate constants and the initiator efficiency are samein both cases.) Answer: Let MA= molar mass (g/tool) initiator I. (a) Solution (1 liter):
of monomerA; MI = molar mass (g/mol)
[M], mol/L = 60/MA, I[I],
mol/L = 0.242/M
(b) Suspension(1 liter): (1000 cm3) -z) (0.833 gcm 833 M. M. ~ 1) (0.242 g)(lO00 L mol/L = (MI g mol-1)(60 g/(0.833 -a )
[M], mol/L = [I],
3.36
MI
556
Chapter 6 (Rp)a = -dt d[M]~ ]a = kp(fkd/kt)l/2[Mla[II~a/2
(R~)b = kp (fkd / kt) 1/2 [Mlb[I]~/~ (R=o)b (8 33/MA)(3.36/MI) 1/2 = 51.7 1/~ (R~)a (60/MA) (0.242/MI) (/~)b = 51.7 (0.068 molh-1 L-1) = 3.5 molh-~ L-’ For 1 liter suspension (72 cm3 monomer),rate = 3.5×0.072 or 0.252 mol -1
Emulsion
Polymerization
Emulsion polymerization refers to a unique process employed for some radical chain polymerizations. It involves polymerization of monomersin the form of emulsions. Like suspension polymerization, the emulsion process uses water as a heat sink. Polymerization reactions are thus easier to control in both these processes than in bulk systems because stirring is easier and removal of the exothermic heat of polymerization is facilitated. Emulsion polymerization, however, differs from suspension polymerization in the type and smaller size of particles in which polymerization occurs and in the kind of initiator employed. The process is also quite different from suspension polymerization in its mechanismand reaction characteristics. The emulsion method of polymerization was developed in the United States during the 1940s for the production of synthetic styrene-butadiene rubber when the supplies of natural rubber were cut off during World War II. The.process is now extensively used for polymerizing conjugated dienes such as butadiene and isoprene and also for polymerizing vinyl monomers such as styrene, vinyl chloride, vinyl acetate, acrylates, and methacrylates to produce homopolymersand copolymers. Emulsion polymerization yields a stable water-dispersed product of the polymer in the form of colloidal size particles. Someof the advantages of the method are: (a) thermal and viscosity problems are much less severe than in bulk polymerization; (b) in several applications, such as in the formulation of latex paints, coatings, finishes, adhesives, and floor finishes, the products of emulsion polymerization can be directly used without further separation from the suspending medium; (c) whereas in bulk, solution, and suspension polymerizations, molecular weight of the polymer can be increased only by reducing the rate of polymerization [see Eq. (6.130)], the emulsion polymerization method allows both polymer molecular weight and polymerization rate to be increased simultaneously. Qualitative
Picture
Emulsion polymerizations vary greatly, and no single reaction mechanism accounts for the behavior of all the important systems. Useful insights
557
Radical Chain Polymerization
can be obtained, however, by considering an "ideal" case in which the monomeris nearly insoluble in water and the polymer is soluble in its own monomer.The general effects of experimental variables for such a case are discussed below. The physical picture of emulsion polymerization is based originally on the qualitative picture of Harkins [68] and the quantitative treatment of Smith and Ewart [69] with later contributions by Ugelstad and Hansen [70], Gilbert and Napper [71], Gardon [72], and others [73,74]. The essential ingredients in an emulsion polymerization are water, a monomerwhich is not miscible with water, an oil-in-water emulsifier, and a compoundor compounds (initiator) which produce free radicals in the aqueous phase. Typical proportions (by weight) are monomers100, water 150, emulsifier 2-5, and initiator 0.5, although these ratios mayvary over a wide range. Practical recipes mayalso include small amounts of various other ingredients. Thus an emulsion stabilizer such as carboxymethylcellulose, poly(vinyl alcohol), gelatin, dextrin, etc., may be used to prevent emulsion breakdown with progress of polymerization and a chain length regulator such as mercaptan to control the polymer molecular weight. To minimize fluctuations in surface tension of the emulsion as polymerization progresses, small proportion of a surface tension regulator (usually a long chain fatty alcohol such as cetyl alcohol) is used. Small volumeof a selected buffer solution is added to minimize or eliminate variations of pH of the system due to hydrolysis or other reactions. The emulsion system is usually kept in a well-agitated state during reaction. Before describing a qualitative picture of emulsion polymerization a note on monomersolubility and type of surface active agents is in order. Monomersfor emulsion polymerization should be near~y insoluble in the dispersing mediumbut not completely insoluble. The solubility must be less than about 0.004 mol/L, as otherwise the aqueous phase will become a major locus of polymerization and the system will then not be typical emulsion polymerization..At the same time the monomermust be slightly soluble as this will allow the transport of monomerfrom the emulsified monomerreservoirs to the reaction loci (see later). Surfactants or emulsifiers play an important role in the emulsion process. They are composed of ionic hydrophilic end and a long hydrophobic chain. Examplesare : Anionic detergent Sodium laurate
CHa(CH2)10COO- +
Sodiumalkyl aryl sulfonate
+ CnH2n+l-~O~--SO~1
Na
Cationic detergent Cetyl trimethyl Anionic and cationic
ammoniumchloride detergent
+ ClaHa3N(CH3)3 CI-
molecules may thus be represented
by
558
Chapter 6
-----~- and ----~+, respectively, indicating hydrocarbon chains with ionic end groups. The locations of the various components in an emulsion system will now be considered. Because of the polar end the detergent dissolves in waterthe nonpolar hydrophobic end finding itself in a hostile environment. Thus when a minimumor critical concentration of surfactant is exceeded, the hydrophobic ends collect into aggregates knownas micelles. This is known as critical micellar concentration (CMC).A micelle of anionic surfactant can thus be depicted as a cluster of surfactant molecules ( ----~- ) with the hydrocarbon chains directed toward the interior (see Fig. 6.17)..Since the surfactant concentrations in most emulsion polymerizations exceed CMCby several orders of magnitude, the bulk of the surfactant is in the micelles, the shape depending on the surfactant concentration. At lower surfactant concentrations (1-2%) the micelles are smaller and spherical (20-100 ,~), micelle containing about 50-150 surfactant molecules. At higher surfactant concentrations, micelles are longer and rodlike in shape. Such micelles are 1000-3000 ~ long with diameters approximately twice the length of an emulsifier molecule. Whena relatively water-insoluble vinyl monomer,such as styrene, is emulsified in water with the aid of anionic soap and adequate agitation, three phases result (see Fig. 6.17): (1) aqueous phase in which a small amount of both monomerand emulsifier are dissolved (i.e., they exist in molecular dispersed state); (2) emulsified monomerdroplets which are supercolloidal in size (> 10,000 ~), stability being imparted by the reduction of surface tension and the presence of repulsive forces since a negative charge overcoats each monomerdroplet; (3) submicroscopic (colloidal) micelles which saturated with monomer.This three-phase emulsion represents the initial state for emulsion polymerization. Stage [ Stage I begins (see Fig. 6.17) when a free-radical producing water-soluble initiator is added to the three-phase emulsion described above. The commonlyused initiator is potassium persulfate, which decomposes thermally to form water-soluble sulfate radical ions:
s2o- 0-60oc___+ 2so
(6.220)
The rate of radical generation by an initiator is greatly accelerated when it is coupled with a reducing agent. Thus an equimolar mixture of FeSO4 and K2S208 at 10°C produces radicals by the reaction: $2082-
q- Fe 2+ ~ Fe 3+ q- SO42- -k SO~-
(6.221)
about 100 times as fast as an equal concentration of the persulfate alone at 50°C. (Redox systems are generally used for polymerizations at lower temperatures. Manyof these redox initiator couples were developed for the emulsion polymerization of butadiene and styrene, since the 5-10°C "cold recipe" yields a better rubber than the "hot" 50°C emulsion polymerization.)
Radical Chain Polymerization
559
560
Chapter 6
The sulfate radical ions generated from persulfate react with the dissolved monomermolecules in the aqueous phase to form ionic free radicals SO~-
+ (n
+ 1)M ~ -SO4(M)nM"
(6.222)
Because of the presence of a long hydrocarbon chain carrying an ionic charge at one end, these ionic free radicals will have surface active properties. These soaplike anionic free radicals (represented in Fig. 6.17 as -A---’) behave like emulsifier molecules and because of the existence of a dynamic equilibrium between micellar emulsifier and dissolved emulsifier they can at some stage be implanted in some of the micelles. Once implanted in a micelle, a soaplike anionic free radical initiates polymerization of the solubilized monomerin the micelle. The micelle, thus "stung," grows in size as the solubilized monomeris used up and to replenish it more monomer enters the micelle from monomer droplets via the aqueous dispersion phase. The ’stung’ micelle is in this way transformed into a monomerpolymer (M/P) particle (see Fig. 6.17). Thus in stage I, the system consist of aqueous phase containing dissolved monomer,dissolved soaplike free radicals, micelles, ’stung’ micelles, M/P particles, and monomer droplets. The rate of overall polymerization increases continuously since nucleation of new particles and particle growth occur simultaneously. For the same reason a particle size distribution occurs during stage I. At 13-20% monomerconversion, however, nearly all the emulsifier will be adsorbed on the M/Pparticles and the micelles will disappear. Since new particles mostly originate in micelles, with the disappearance of micelles the nucleation of new M/Pparticles essentially ceases. This marks the end of stage I. Problem 6.48 In the model for emulsion polymerization it is assumed that most of the soaplike free radicals produced in the aqueous phase enters the micelles rather than the emulsified monomer droplets. Howwouldyou justify this assumption? Answer: The assumption that the soaplike free radicals produced in the aqueous phase enters the micelles rather than the emulsified monomer droplets can be justified because of two reasons: (a) Micelles have a muchhigher surface area to volumeratio than the monomer droplets since the former are muchsmaller in size than the latter. Micelles will therefore havea greater probability of receivingthe soap-typeanionic free radicals. (b) The numberof micelles per unit volumeof aqueousphase is muchmore than the numberof monomerdroplets per unit volume, the typical values of these al. numbersbeing 1018versus 10 The numberof free radicals that might be c~iptured by the monomer droplets can therefore be conveniently neglected. The monomerdroplets can thus be considered to serve primarily as reservoirs of monomer.
561
Radical Chain Polymerization
Stage H This stage is characterized by a continued growth of the existing M/P particles and no new particle nucleation. Free radicals enter only the M/P particles where polymerization takes place as the particles are supplied with monomer from the emulsified monomer droplets via the aqueous phase. Stage II is thus featured by a constant overall rate of polymerization as depicted in Fig. 6.18. As explained below, polymerization within a M/P particle can be characterized by alternating periods of activity and inactivity with the growth of a chain radical within the particle occurring in an isolated state unhindered over the active period. This results in a rapid rate of polymerization with a simultaneous generation of very high-molecularweight polymer. Stage III This stage begins when the overall rate of polymerization begins to deviate from linearity and is characterized by nonlinear growth rate with diffusion controlled regime. The nonlinearity may appear as a decrease in rate due to dwindling monomer concentration in M/P particles or as an increase if the Tromsdorff effect is important. The monomer reservoirs will have long since disappeared in stage II and the ratio of monomer to polymer within the particle will have dwindled to the point where the reaction becomes diffusion-controlled. The three stages in an emulsion polymerization system are depicted in Fig. 6.18.
/
y
J
diffusion controtted regime
-7L-~ 60 % StageII : Constantrate of growth--noparticle / /
~
/
.°° 7
~,~ !/I t" ~ zo*~ xo ou-/,
Emulsified monomer -.’"-’y .............. droptets disappear
15 % Stagel : SimuLtaneous particte nucteation and growth Time
.Figure 6.18 Schematic conversion-time curve for emulsion polymerization showmg three stages.
562
Chapter 6
Kinetics of Emulsion Poly~nerization The kinetic analysis here is based on quantitative considerations of the ideal emulsion polymerization systems which have been described qualitatively in the preceding sections. The treatment centers only around stage I and stage II (Fig. 6.18), as no general theory for stage III is available. The treatment applies to styrene-like monomers,meaning those monomerswith low water solubility and those in which monomerand polymer are completely miscible over all ranges of composition. Stage I This is the nucleation period. Ideally, all M/P particles are generated in stage I. The particles grow in volume and adsorb surfactant molecules, resulting in diminution of micelles. If the area occupied by each surfactant molecule is the same on particle and micellar surfaces and the particles are completely covered by surfactant, the combined areas of micelles and particles in unit volume of the reaction mediumwill remain constant.. The particle surface area will grow at the expense of micellar surface area and whenthe total surface area of particles equals the total surface area occupied by the surfactant initially added, all micellar soap will have disappeared and further nucleation will cease. For simplicity of calculations it is assumedthat the volumeof a particle grows linearly with time with rate u, once polymerization has been initiated there. It maybe noted that particles are nucleated at different times during stage I. Hence at time t in stage I, the volume of a particle which is nucleated at ~- will be u (/; -- ~-) if the volumeof the initial micelle negligible. The area of this spherical particle, at,~-, will be at,~-
= [(4~r) 1/2 3u (t - ~_)]2/3
(6.223)
If the rate at which radicals nucleate micelles is constant at v (effective radicals/era 3 aqueous phase/s), then vd~" particles are generated in the time interval dr. The area At of all particles present at time t, is given by the sums of the areas of particles generated from t = 0 onward: At = [(4~)l/Z3u]2/3
"L ~(t ~_)2/3vd~_ =
0.6 [ ( 47r ) l/2 3u]2/3vtS/3
(6.224) If as is the area occupied by unit weight of surfactant, then no mice~es will remain when At = asS, where S is the weight concentration of suffactant. ~us stage I is completed at a time tc such that a~S = 0.6 [(4~) U~ 3u] ~/3vt~/3
(6.225)
It nowremains to calculate v, the rate of nucleation. ~e rate of radical generation per unit volume, ~, by thermal decomposition ~ an initiator is (6.226) ~ = 2NA~kd[I]
563
Radical Chain Polymerization
where NAyis Avogadro’snumber. Nucleation is effected by radicals that enter micelles rather than particles. The fraction of radicals that enter particles rather than micelles maybe taken to be the ratio of the area of all particles to that of the total surfactant/water interface, that is, At / asS. Thus, (6.227) v --- P~ [1 - A, / a~S] Combiningthe foregoing equations one obtains [59]: tc = 0.37 (a~S //~)0.6
/ u0.4
(6.228)
The value of u for a particular system can be calculated ap~ori from knowledge of the monomerconcentration and other monomercharacteristics. In emulsion recipes, typical values [72] are R.r "~ 1012 - 1014 radicals cm-3 s -1, ass "~ 105 cm2/cm3 aqueous phase, u "~ -20 10 cm3 s -1. The number of particles per unit volume of aqueous phase, at the end of stage I is °6 (P~/u) °4 Np = vtc = 0.37(asS) (6.229) This equation indicates that the particle number depends on the 0.6 power of the suffactant concentration and on the 0.4 power of the initiator concentration (since /%r o< [I]). Usual values of Np are 1015 - 1016 per cm3 of aqueous phase.
Problem6.49 Consider the following emulsion polymerization recipe: z) Styrene (density 0.9 g/cm 3) Water(density 1.0 g/cm K2S2Os
Sodiumlauryl sulfate
100 g 180 g 1g 4g
Calculatethe numberof polymerizingparticles per liter of water using the following additional data: surface area per surfactant molecule = 5×10-15 cmZ; rate of volume increase of latex particle = 4×10-20 cmZ/s; ka of K2S2Osat 60°C = -~ s-~. 6xlO Answer: -I Molarmass of sodiumlauryl sulfate = 288 g tool (5 × 10-15 cm~ molecule-1) (6.02 × 10~ -1) molecules tool -~) g tool (288 = 1.05 x 10"t cm2 g-1 ~ L- 1) g)(1000 = 22.22 g L1 3) (180 cm (a~S) °’~ = 1.049 × 10~ em1’~ -°n L S = (4.0
564
Chapter 6 (1.0 g)(lO00 a [I]
L- 1)
L1
= (270 g mo1-1)(180 3) = 0. 0206 to ol
= 2(6x10 -6 s -1)(0.0206 -ls--- 11.488×1017 L
tool L-1)(6.02x102a
-1) tool
(@)o.4= Lr(1488 x 1°’7t’-I J =4.u8 x lO,’ t,-o."
= 1.~9 x 10 ~ -~ L -~ Here L imp~esper liter of aqueous phase.
Stage II Stage II begins when the conversion becomes linear with time (see Fig. 5.18). It is assumed that this coincides with the disappearance of micelles and the cessation of particle nucleation. The number of particles Np in stage II is fixed at the value formed in stage I and given by Eq. (5.229). Rate ofpol)~nerization. Under general conditions employed in emulsion polymerization, a typical value of the rate of generation of free radicals (P~) in the aqueous phase is 1014 per second per milliliter and a typical value of the numberof polymer particles is 10"~5 per milliliter. If all the radicals generated eventually enter M/Pparticles, since the micetles will have already disappeared, the rate of radical entry in a particle will average out to about one every 10 seconds, which means that the free radicals will generally enter the particles singly. Whena soaplike free radical enters a M/P particle, polymerization takes place. However, when another free radical enters the same particle, it terminates the growing chain radical by combining with it. (Calculation using known~ values predicts that two radicals cannot coexist in the same polymer particle and they would terminate mutually within a few thousands of a second.) So the particle, remains inactive till another free radical enters and initiates the polymerization. Thus, if a radical enters a polymerparticle every 10 seconds as calculated above, the particle will grow in alternating periods of actMty and inactivity, each of 10 seconds duration. In other words, each particle will remain active for half of the total time (and inactive for the other half). This situation will be unchanged even if the rate of radical entry into the particle is decreased or increased. This can
R~clicalChainPolymerization
565
3Rrp
Rpp~0
2Rrp
Rpp
~
0
Time Figure 6.19 Effect of rate of radical entry into particle (/~) on rate polymerization per particle (/~). be seen in the bar diagramof Fig. 6.19, wherethe rate of polymerization within a particle,/~o, for variousrates of ~ree radical entry into a particle, Ptcp (which is proportional to rate of radical generation P~r in aqueous phase) is shown. The important feature to observe here is that the total area of active period (shaded) for each P~pcase is the same; consequently the rate of polymerizationper particle is independentof the rate of radical entry. The concepts embodiedin the foregoing discussions are known collectively as the Srnith-EwartTheory,CaseH. The rate of polymerizationin a M/Pparticle, /~p, is given by P~ = k, [M] (~ / NAy)
(6.230)
where [M] denotes the monomerconcentration in the M/Pparticles and ~ the average numberof radicals per particle; -NAyis Avogadro’snumber. Since accordingto the Smith-Ewarttheory, the growingparticle contains a free radical only half the time, that is, ~ = 1/2, the rate of polymerization per particle is p~_
k,[M] 2NAy
(6.231)
If 1~ is constant and the numberof pai-ticles per unit volume, .Np, is constant, then the overall rate of emulsionpolymerizationper unit volume,
Chapter 6
566 Rp, is simply given by diM] dt -
Rp
Np kp [M] = 2NAv
(6.232)
Substituting for Np from Eq. (6.229) gives _k~o[M] (6.233) 2~Av In stage II, then, the rate of polymerization will depend on the 0.6 power of the suffactant concentration and the 0.4 power of the aqueous phase initiator concentration [since ~ is related to the aqueous phase initiator concentration through Eq. (6.226)]. It must be noted that although Eq. (6.233) gives the rate of polyme6zation in stage II, t~e value of [I] appropriate to the ~ term in this equation is that present in stage I when the panicles are formed. If this modelis co~ect, addition of extra initiator during stage II would have no effect on the rate of polymerization. This is evident from Eq. (6.232) in which the rate of polymerization is related only to quantities that are assumed to.be invadant du6ng this pa~ of the process. ~e value of ~ in Eq. (6.230) is of critical importance in dete~ining the rate of polymerization in stage II. Three cases -- designated 1, 2, 3 -corresponding, respectively, to ~ < 0.5, ~ ~ 0.5, and ~ > 0.5 can be distinguished based on the work of S~th and Ewart [69] and others [70-74]. The ~netic treatment given above confo~s to Case 2 (~ = 0.5), which is the predominant behavior for emulsion polymerizations. It occurs when desorption of radicals does not occur or is negligible comparedto the Rp = 0.37 (ass)0.6
Problem 6.50 The experimental value of dynamic concentration of styrene in polymer latex particles under the conditions of constant rate in emulsion polymerization has been found to be 5.2 tool/liter. Assumingthis value to be applicable, calculate the rate of polymerization per liter of aqueousphase in stage II of the reaction of the emulsion polymerization recipe given in Problem 6.49. (Data: kv for styrene af 60°C = 165 L mo1-1s-1.) Answer: FromEq. (6.232), diM] dt
- gpkp[M]/2YAv
mo1-1S -1) 2 (6.02x 1023-I) mol -I = 0.012toolL-~ s HereL-Iimplies perliter of aqueous phase. (1.649
× 1019
t -1)
(165
t
(5.2
-1) mol L
Radical ChainPolymerization
567
rate of radicals entering particles (absorption) and the particle size is too small to accommodatemore than one radical. If radical desorption from particles and termination in the aqueous phase are not negligible, ~ can drop below 0.5 (Case 1). The decrease in ff is larger for small particle sizes and low initiation rates. In large particles, on the other hand, several radicals can coexist, and ~ can be larger than 0.5 (Case 3). Degree of Polymerization. Once inside the M/P particle, agates at a rate rp given by rp
= kp [M]
a radical prop(6.234)
where [M] is the concentration inside the M/P particle. The rate re at which a radical enters a polymer particle in stage II is given by
= / Np
(6.235)
where /~ is the rate of generation of free radicals per unit volume in the aqueous phase [Eq. (6.226)] and Np is the number of M/P particles per unit volume. Equation (5.235) is based on the assumption that all radicals generated in the aqueous phase eventually enters the M/P particles, that is, radical capture efficiency is 1. Since termination reaction takes place as soon as a radical enters an active M/P particle (i.e. in which a polymer chain is propagating), re is also equal to the rate of termination of a polymer chain. Hence the degree of polymerization will be given by DPn --
rp
_ Npkp[M]
(6.236)
assuming, however, that chain transfer of any kind is negligible. Equation (6.236) shows that the degree of polymerization DP,~, like the rate polymerization Pqo [Eq. (6.232)], is directly dependent on the number particles. Thus, unlike polymerization by the bulk, solution, and suspension techniques, that by the emulsion technique permits simultaneous increase in rate and degree of polymerization by increasing the number of polymer particles (Np), that is, by increasing the surfactant concentration, at a fixed rate of initiation. Substituting Eqs. (6.226) into Eq. (6.236) one obtains Np kp [M] DPn -- 2NAvkd [I] The initiator stage II.
(6.237)
concentration here is that which exists at a given instant in
Problem 6.51 A particular emulsion polymerization yields polymer with ~ = 200,000. Howwouldyou adjust the operation of an emulsion process to produce polymer with M~= 100,000 in stage II without, however, changing the rate of
568
Chapter 6
polymerization,particle concentration, or reaction temperature? Answer: According to Eq. (6.237), DPno~ 1/[I], sin~e N is constant. So DP, can reduced to half by adding moreinitiator in stage II so that [I] is doubled. The rate of polymerization[Eq. (6.233)] and the particle concentration [Eq. (6.231)] will not be altered becausethe [I] value whichis operative in these relations is that for stage I. Analternative procedurewouldinvolve addition of chain transfer agents in appropriate concentrations.
The combination of high molecular weight with high polymerization rate is one reason for the popularity of the emulsion technique. Seeded polymerizations can be useful for makinglarge-particle-size latexes by the emulsion technique. Thus a completed "seed" latex may be diluted to give the desirable value of Np particles per liter of emulsion. No additional surfactant is added, so no new polymer particles are formed. Whenmonomeris fed and initiator is added, polymerization occurs in the previously formed particles, so that each one grows as monomerdiffuses into it and is converted.
Problem6.52 A polystyrene latex produced by emulsion polymerization contains 10%by weight of polymerparticles (average diameter 0.20 #m). It is decided grow these particles to a larger size by slowly adding to the latex 2 kg of monomerper kilogram of polymer as polymerization proceeds at 60°C without further addition of emulsifier. Thereaction is to be carried out until all monomer has been added to the reactor and the weight ratio of monomerto polymer has decreased to 0.2. The unreacted monomeris then to be removedby steam stripping. Estimate the’time required for the reaction and the final particle diameter. [Data: k~, at 60°C = 165 L mo1-1s -1. Density: monomer= 0.90 g/cm3; polymer = 1.05 g/cm3; dynamic solubility of monomerin polymer = 0.6 g monomerper gram polymer.] Answer: The time of reaction has to be calculated in two consecutive periods, with zero order in monomer(constant monomerconcentration) until the monomerreserve is exhausted, and then with first order until the desired conversionis reached. Basis: 1000 g latex (900 g water + 100 g polymer) Monomerto be added = 2×100 or 200 g Monomerto be converted = x g
C00_ = 0.2,
Reaction to be stopped when \1--~~
Monomerto be stripped = (200 - 150) or 50
x = 150
Radical Chain Polymerization Monomerconcentration
569
when reaction
is to be stopped is [(50 g monomer)/(104 g mol-1)](1000 s L- 1) (250 g polymer)/(1.05 g -3) + (5 0 g monomer)/(0.90 gc -a) -1 ---- 1.64 mol L Dynamic concentration of monomerin panicles is [(0.6 g monomer)/(104 g mol-~)](1000 -1) (1 g polymer)/(1.05 g -3) d- (0. 6 g m onomer)/(0.90 g c -a ) -~ = 3.56 tool L Let the amount of monomer remaining unconverted at the end of zero-order period be y gram. Therefore, [(y g) / (104 g mol-~)] (1000 a L- 1) -1 = 3.56 tool L [(300 - y) / 1.05] a polymer ÷ (y/ 0 .9 ) cm 3monomer y ---- 112.4 g Numberof particles
(Np’) in 1 kg of original latex:
Initial diameter of particle = 0.2 #m ---- 0.2x10-4 cm Volume/particle = (~r/6)(0.2x10 -4 cm)3 = 4.19×10 -~ 3cm 1 (100 g polymer) Nz~’ -~ = )(1.05 g cm (4.19 x 10-is 3) cm ~ = 22.7 x 10 Rate of conversion in zero-order period is: (22.7 x 101~ particles kg-~)(165L -~ s-~)(3.56 mol -~) N~,’k~,[M]/2NAv = -~) 2 (6.02 x 102a particles mol -Stools-I = 11.1x10 kg -1 (= 4.0x10 -~molh-~ -~) kg Monomerconverted in zero-order period per 1 kg original latex = 200 - 112.4 or 87.5 g (= 0.84 mol). Therefore, Time for conversion ---- (0.84 mol kg-~) /(4.0 x 10-2 tool h-1 -~) kg ~- 21h First-order period From Eq. (6.232),
d* = Integrating and solving for t
=
2 ln([M]0/[M]) NAy
Here Np is the numberof particles per liter of latex. It can be taken, without any significant error, to be equal to the numberof particles in 1 kg of latex, N~,’. Thus, 21n[(3.56 mol -~) / (1 .64 mol L- l)] (6 .02 x ~ part icles tool -~) t = (22.7 × 10is particles L-1(165 L mol-is-~) (3600 s -1) 69 h
570
Chapter 6
Total time= (21 + 69) or 90h Final particle diameter, d: (d/0.2 so,
Other
3 #m)
= ( oo 0.oo g)
=
d=2.7#m
Theories
A number of workers have suggested that emulsion polymerization may not occur homogeneously throughout a polymer particle but either at the particle surface [75] or within an outer monomer-richshell surrounding an inner polymer-rich core [76]. The latter has been referred tO as the shell or core-shell model. The latter model has been proposed to explain the apparent anomaly between the observed constant rate behavior up to about 60 percent conversion, which according to Eq. (6.232) requires [M] to constant, and the considerable experimental evidence which indicates that emulsified monomerdroplets (serving as monomerreservoirs) disappear at 25 to 30 percent conversion and the monomer concentration drops thereafter. According to the core-shell model, the growing particle is actually heterogeneous rather than homogeneous, and it consists of an expanding polymer-rich (monomer-starved) core surrounded by a monomer-rich (polymer-starved) outer spherical shell. It is the outer shell that serves the major locus of polymerization and Smith-Ewart (on-off) mechanism prevails while virtually no polymerization occurs in the core because of its monomer-starvedcondition. Reaction within an outer shell or at the particle surface would be most likely to be operative for those polymerizations in which the polymer is insoluble in its own monomeror under conditions where the polymerization is diffusion-controlled such that a propagating radical cannot diffuse into the center of the particle.
1. J. A. Kerr, "Rate Processes in Gas Phase," Ch. 1 in Free Radicals (J. K. Kochi, ed.), vol. I, Wiley, NewYork,Q973). 2. V. N. Kondratiev, "Chain Reactions,’ Ch. 2 in ComprehensiveChemical Kinet&s (C. H. Bamford and C. E H. Tipper, eds.), vol. 2, American Elsevier, NewYork(1969). 3. J. Brandupand E. H. Immergut(eds.) with W.McDowell,PolymerHandbook, Wiley-Interscience, NewYork(1975).
Radical Chain Polymerizafion
571
4. E. S. Huyser, Free Radical Chain Reactions, Chap. 10, Wiley, New York (1970). 5. E. A. Collins, J. Bares and E W. Billmeyer, Jr., Experiments in Polymer Science, Chap. 5, Wiley-Interscience, NewYork (1973). 6. T. Koenig, "The Decomposition of Peroxides and Azoalkanes," Ch. 3 in Free Radicals (J. K. Kochi, ed.), vol. 1, Wiley, NewYork (1973). 7. G. C. Eastmond, "The Kinetics of Free Radical Polymerization of Vinyl Monomers in Homogeneous Solutions," Ch. 1 in Comprehensive Chemical Kinetics (C. H. Bamford and C. E H. Tipper, eds.), vol. 14A, American Elsevier, NewYork (1976). 8. A. D. Jenkins, J. Polym. Sci., 29, 245 (1958). 9. L. M. Arnett and J. H. Peterson, J. Am. Chem. Soc., 74, 203 (1952). 10. G..Bonta, B. M. Gallo, S. Russo and C. Uliana, Polymer, 17, 217 (1976). 11. K. C. Berger, P. C. Deb and G. Meyerhoff, Macromolecules, 10, 1075 (1977). 12. P. D. Bartlett and H. Kwart~ J. Am. Chem. Soc., 72, 1051 (1950). 13. M. S. Matheson, E. E. Auer, E. B. Bevilacqua and E. J. Hart, J. Am_Chem. Soc., 73, 1700 (1951). 14. T. Sato, M. Abe and T. Otsu, Makromol. Chem., 178, 1951 (1977). 15. K. F. O’Driscoll, P. E Lyons and R. Patsiga, J. Polym. Sci., A3 1567 (1965). 16. S. E. Morsi, A. B. Zaki and M. A. E1-TGayami, Eur. PolyP. J., 13, 851 (1977). 17. P. Ghosh and S. N. Maity, Eur. Polym. J., 14, 855 (1978). 18. C. J. Sahani and N. Indictor, J. Polym. Sci., Polym. Chem. Ed., 16, 2683, 2997 (1978). 19. S.P. Manickam,U. C. Singh, K. Venkatarao and N. R. Subbaratnam, Polymer, 20, 917 (1979). 20. N. Mohanty, B. Pradhan and M. C. Mahanta, Eur. Polym. J., 16, 451 (1980). 21. R. K. Samal, M. C. Nayak and P. L. Nayak, J. Macromol. Sci.-Chem., A12(6), 815 (1978). 22. K. R. Ahmed, L. V. Natarajan and Q. Anivaruddin, Makromol. Chem., i79, 1193 (1978)., 23. G. S. Misra and S. L. Dubey, Z Polym. Sci. Polym. Chem. Ed., 17, 1393 (1979). 24. D. Pramanick and A. K. Chatterjee, J. Polym- Sci. Potym. Chem. Ed., 18, 311 (1980). 25. K. Kaliyamurthy, P. Elayaperumal, T. Balakrishna and M. Santappa, Makrotool. Chem., 180, 1575 (1979). 26. R. G. Norrish and J. P. Simons, Proc. Roy. Soc. (London), A251, 4 (1959). 27. E. A. Lissi, M. V. Encina and M. T. Abarca, J. Polym. Sci. Polym- Ed., 17, 19 (1979). 28. W. D. Graham, J. G. Green and W. A Pryor, J. Org. Chem., 44, 907 (1979). 29. J. Lingnau, M. Stickler and G. Meyerhoff, Eur. Polym. J., 16, 785 (1980). 30. N. J. Barr, W. I. Bengough, G. Beveridge and G.. B. Park, Eur. Polym. J., 14, 245 (1978). 31. P. J. Flory, Principles of Polymer Chemistry, Comell Univ. Press, Ithaca, New York (1953). 32. J. Lingnau and G. Meyerhoff, MacrrmOlecules, 17, 941 (1984). 33. R. H. Gobran, M. B. Berenbaumand A. V. Tobolsky, J. Polym. Sci., 46, 431 (1960). 34. K. E O’Driscoll and P. J. White, J. Polym. Sci., BI: 597 (1963); A3:283 (1965). 35. K. F. O’Driscoll and S. A. McA_rdle,J. Polym. Sci., 40, 557 (1959). 36. C. Walling, Free Radicals in Solution, Chaps. 3-5, Wiley-Interscience, New York (1957).
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37. E Brier, D. L. Chapmanand E. Waiters, J. Chem. Soc., 562 (1926). 38. W. A. Noyes and P. A. Leighton, The Photochemistry of Gases, p. 202, Reinhold, NewYork (1941). 39. M. S. Matheson, E. E. Auer, E. B. Bevilacqua and E. H. Hart, J. Am. Chem. Soc., 71,497(1949). 40. P. Penchev, Mal~omol. Chem., 177, 413 (1976). 41. K. E O’Driscoll and H. K. Mahabadi, J. Polym. Sci. Polym. Chem. Ed., 14, 869~(1976). 42. C. H. Bamford, G. C. Eastmond and D. Whittle, Polymer, i0, 771 (1969). 43. R. A. Gregg and E R. Mayo, Disc. Faraday, Soc., 2, 328 (1947). 44. E J. Flory, J. Am. Chem. Sot., 69, 2893 (1947). 45. C. Walling and L. Heaton, J. Am. Chem. Soc., 87, 48 (1965). 46. E Ghosh and E W. Billmeyer, Advances in Chemistry Series, 91, 75 (1969). 47. P. Ghosh and A. N. Banerjee, J. Polym. S¢i. Polym. Chem Ed., 12, 375 (1974). 48. E C, Deb and G. Meyerhoff, Eur. Polym. J., 10, 709 (1974). 49. G. V. Schulz and G. Haborth, Makromol. Chem., 1, 106 (1948). 50. A. M. North and G. A. Reed, Trans. Faraday Soc., 57, 859 (1961); J. Polym. Sci., A1, 1311 (1963). 51. H. K. Mahabadi and K. E O’Driscoll, J. Polym. Sci. Polym. Chem. Ed., 15, 283 (1977); Macromolecules, i0, 55 (1977). 52. J. M. Dionisio, H. K. Mahabadi, K. E O’Driscoll, E. Abuin and E. A. Lissi, J. Polym. Sci. Polym. Chem. Ed., 17, 1891 (1979). 53. J. M. Dionisio and K. E Driscoll, J. Polym. Sci. Pokym. Chem. Ed., 18, 241
198o). 54. H. K. Mahabadi and A. Rudin, J. Polym. Sci., 17, 180 ,(1979). 55. N. Friis and A. E. Hamielec, ACS Symp. Set, 24, ’Polymerization, ,, 82 " 56. t1976~j . L. ce, J. Am. Chem. Soc., 76, 627 (1954). 57. E R. Mayo and C. Walling, Chem. Revs. 46, 191 (1950). 58. H. W. Melville and L. Valentine, Proc. Roy. Soc. (London), A200, 337, 358 (1950). 59. E D. Bartlett and H. Kwart, J. Am. Chem. Soc., 72, 1051 (1950). 60. E S. Dainton and K. J. Ivin, Qtly. Rev., 12, 61 (1958). 61. H. W. McCormick,J. Polym. Sci., 25, 0. 488 (195" 62. J. M. Smith and H. C. Van Ness, Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, New York (1987). 63. G. V. Schulz, Z. Physik. Chem., B43, 25 (1939). 64. W. B. Smith, J. A. Mayand C. W. Kim, J. Pofym. Sci., A2, 365 (1966). 65. A. M. North, The Kinetics of Free Radical Polymerization, Pergamon Press, New York (1966). 66. J. A. Moore (ed.), Macromolecular Syntheses, Collective vol. 1, WileyInterscience, NewYork (1977). 67. S. R. Sandier and W. Karo, Polymer Syntheses, Academic Press, NewYork, vols. 1 and 2 (1974), vol. 3 (1980). 68. W. D. Harkins, J. Am. Chem. Soc., 69, 1428 (1947). 69. W. V. Smith and R. W. Ewart, J. Chem. Phys., 16, 592 (1948). 70. J. Ugelstad and E K. Hansen, Rubber Chem. Technol., 49, 536 (1970). 71. R. G. Gilbert and D. H. Napper, J. Chem. Soc., Faraday I, 70, 391 (1974). 72. J. L. Gardon, "Emulsion Polymerization," Ch. 6 in Polymerization Processes (C. E. Schildknecht, ed., with I. Skeist), Wiley-Interscience, NewYork (1977). 73. I. Piirma (ed.), Emulsion Polymerization, AcademicPress, NewYork (1982). 74. B. S. Casey, I. A. Maxwell, B. R. Morrison and R. G. Gilbert, Makromol. Chem. Macromol. Symp., 31, 1 (1990). 75. A. Sheinker and S. S. Medvedev, Dokl. Akad. Nauk SSR, 97, 111 (1954). 76. M. R. Grancio and D. J. Williams, J. Polym. Sci., A-I, 8, 2617 (1970).
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EXERCISES 6.1. Whena.peroxide P is heated to 60°C in an inert solvent it decomposes by a first order process and 20%of the peroxide decomposes in 60 min. A bulk monomeris polymerized using this initiator at 60°C, the initial concentration of the letter being 4.0x10 -4 mol/L. What fractions of the monomer and the initiator should remain unconverted after 10 min ? At 60°C, the system parameters are k~/~ = 22.34 L mo1-1, f = 0.8. [Ans. Monomer0.67;. Initiator 0.963.] 6.2. A solution of 100 g/L acrylamide in methanol is polymerized at 25°C with 0.1 mol/L isobutyryl peroxide whose half life is 9.0 h at this temperature and efficiency in methanol is 0.3. For acrylamide, k~/~ -1 = 22 L/mol-1 s at 25°C and termination is by coupling alone. (a) What is the initial steady state rate of polymerization ? (b) Howmuch polymer has been made in the first 10 min of reaction in 1 L of solution ? [Ans. (a) 0.37 g -1 s-l; ( b) 8 9.4 g L-1.] 6.3. A dilatometer which has a 50 cm long capillary (diameter 0.2 cm) has total volume of 50 cmz (including the volume of capillary). The dilatometer was filled with a freshly distilled sample of methyl methacrylate (MMA) containing 0.25 wt% benzoyl peroxide and then immersed in a water bath (at 50°C) so that the capillary tube protruded from the water. Whenthe volume of the solution began to decrease after coming to thermal equilibrium and overflowing the capillary, the fall in liquid level in the capillary was determined periodically from the scale on the dilatometer. This yielded the following data : Time (s) 480 1200 1920 4080 8280 9600
Ah (cm) 1.48 4.09 6.46 13.56 27.24 31.91
Determine the kinetic parameter kp/k~/2 at 50°C, given that f = 0.80 and ka = 1.11×10 -6 s -1 at 50°C. [Density (g/cm a at 50°C): MMA0.893; PMMA
1.160]
[Ans. 0.0948 tool 1/2 L-1/2 -1/2] s 6.4. The polymerization of methyl methacrylate (1.0 Min benzene) is carried out using a photosensitizer and 3130 ,~klight from a mercury lamp. If the quantum yield for radical production in this system is 0.50 and light is absorbed by the system at the rate of 105 ergs/L-s, calculate the rate .of initiation. [Ans. 2.6×10-8 tool L-1 -1] s 6.5. Consider irradiation of pure acrylonitrile (density = 0.81 g/cm~) at 20°C with "/-rays, with a dose rate of 106 rads/h. Calculate (a) the rate of energy absorption and (b) the rate of initiating radical formation per unit volume of the monomer.(100-eV yield of initiating radicals = 5.0) [Arts. (a) 1.4×1016 eV cm-3 s-l; (b) 7,0×1014 radicals -3 s - 1]
574
Chapter 6
6.6. The peroxide (thermal homolysis) initiated polymerization of a monomer follows the simplest kinetic scheme represented by Eq. (6.26). For a polymerization system with [M]0 = 4 mol/L and [I]0 = 0.01 tool/L, the limiting conversion p~ = 0.10. To increase P~o to 0.20, (a) would you increase or decrease IM]0 and by what factor? (b) would you increase or decrease [I]0" and by what factor ~c) would you increase or decrease tlae reaction temperature [Ans. (a) no effect; (b) increase by a factor of 4.5; (c) decrease temperature.] 6.7. One hundred liters of methyl methacrylate containing 10.2 moles of an initiator (ti/2 = 50 h) in solution is polymerized at 60°C. Calculate (a) kinetic chain length in this polymerization and (b) the amount of polymer formed in the first 1 h of reaction. [Data: monomerdensity 0.94 g/cm3; _kp =515Lmo1-1 s-l; kt =2.55x107Lmo1-1 s-l; f =0.3] [~tns. (a) 1397; (b) 70 6.8. Calculate the time needed to convert half of charge of methyl methacrylate (10 g per 100 mLsolution) to polymer using benzoyl peroxide (0.1 g per mL solution) as initiator in benzene at 60°C. What number-average degree of polymerization will be expected initially ? Whatfaction of the initiator will remain unused after 50% conversion of the monomer? [At 60°C, ku = 4.47×10 -6 s-l; k~/kt = 10-~ L/moPs; f = 0.4; termination occurs by both disproportionation (58%) and coupling (42%).] [Ans. 24.7 h; 739; 0.67] 6.9. Initiator 11 has half the half-life that initiator I2 has at 80°C wheninitiator I1 is used for both and all the concentrations are the same. What is the ratio of degree of polymerization for M1 and M2if they are polymerized with initiator I1 and I2, respectively, the ratio of monomerconcentrations being 1:2 and that of initiator concentrations being 1:5 ? It can be assumed that both polymers terminate exclusively by coupling and that the initiator efficiencies are equal. [Arts. 3.16] 6.10. A vinyl polymer with a number-average degree of polymerization of 10,000 was produced by polymerization at 70°C using a peroxide initiator concentration of 4×10-4 mol/L. If 4.0% of the initial monomerpresent was converted to polymer in 60 min, what was the initial monomer concentration? The modeof termination is coupling and the initiator is knownto have a half-life of 1.0 h at 90°C and an activation energy of 30.0 kcal/mol. Assume f = 1.0. [Ans. -1] 6.0 tool L 6.11. Using carbon-14 labeled AIBNas an initiator, a sample of styrene is polymerized to an average degree of polymerization of 1.28×104. The AIBN has an activity of 8.97x107 counts per minute per mol in a scintillation counter. If 5.0 grams of the polystyrene shows an activity of 315 counts per minute, determine the modeof termination of polystyryl radicals. [Arts. Coupling 93%, disproportionation 7%] 6.12. In the bulk polymerization of methyl methacrylate at 60°C with azo-bisisobutyronitrile as the initiator the initial rates of initiation and polymerization are 1.7x10-6 mol/L-s and 8.8x10-4 mol/L-s, respectively. Predict the initial molecular weight of the polymer formed in this system, if the extent of disproportionation is 70%at 60°C. Neglect chain transfer reactions for the calculation. [Ans. 60,800]
Radical Chain Polymerization
575
6.13. Determinethe concentrations (g/L) of initiator (AIBN)and chain transfer agent (n-butyl mercaptan)that will give poly(vinyl acetate) with an initial molecular weight (assuming coupling) of 15,000 and 50%conversion monomer (initial concentration 250 g/L) at 60°Cin 30 rain. [Systemparameters (all at 60°C): k~/k~ = 0.1824 L/mol-s; tl/2 of AIBN= 22 h; f = 1; CS = 481 -1] [Arm.15.24 g L-l; 0.027 g L 6.14. The molecular weight of polymerwhenstyrene is polymerizedin benzeneis 400,000.Withall other conditions the same,addition of 4.23 mg/Lof n-butyl mercaptan decreases the molecular weight to 85,000. Whatconcentration (mg/L)of n-butyl mercaptanwill give a molecular weight of 50,000 (other conditions remaining the same)? -l] [Arm. 8 mgL 6.15. Accountfor the fact that propylene and isobutylene have low reactivity toward radical polymerization, and do not yield high polymersin contrast to monomers such as methyl methacrylate and methacrylonitrile which yield high polymersin radical polymerization. 6.16. Discuss howthe followingfactors wouldinfluence the gel effect: (a) polymer molecular weight; (b) solvent goodness; (c) chain transfer; temperature. 6.17. Modifythe Mayoequation (6.148) to take into accountthe effect of degradative chain transfer on the number-averagedegree of polymerization. For simplicity, assumethat onlythe chain transfer to solvent is degradative(i.e., the newradical formeddoes not initiate polymerization). 6.18. Considera free radical polymerization initiated by 10-3 MAIBN.At 70°C, kd is 4.0×10-5 s -1 and f is close to 0.6. If an inhibitor is to be used to suppress polymerization for an hour, what should be its concentration, if every inhibitor molecule accounts for one primary or monomer-ended radical ? [~ns. 1.73 x 10-4 M] 6.19. Assumethat the various reactions which may be brought about by an inhibiting or retarding substance, represented by Z, maybe reduced to the following simple schemeof three reactions: ktr,z (a) M~-÷ Z ~ Polymer q- Z"
Co)z.+ (c) Z’÷ Z-k-~Z~ Nonradica! products Derive an expression for the rate of consumptionof inhibitor and explain its dependenceon reaction parameters. 6.20. One ldlogramof a 25%Coy weight) solution of acrylamide in water at 27°C is polymerizedadiabatically with a redox initiator. The peak temperature reached is 90°C. Calculate the molar heat of polymerization using the following heat capacity data: monomerand polymer= 0.5 cal/g-°C, water 1.0 eal/g-°C, reactor 0.1 kcal/°C. -1] [Arm.17.4 kcal tool
576
Chapter 6
6.21. Methyl acrylate (1 mol) is polymerized using 0.001 mol succinic peroxide in 1 liter solution in benzene at 60°C. If the polymerization is carried out adiabatically, how much would the temperature rise in 30 min ? [Data (all at 60°C): tl/2 of initiator = 19 h; f = 1; k~/kt = 0.460/_]mol-s; AH~, = - 18.6 kcal/mol] [Ans. 6.0°C] 6.22. A vinyl monomeris photopolymerized in two experiments in which only the temperature is varied. In these experiments, the time to convert 20%of the original charge of monomerto polymer is found to be 30 min at 60°C and 27 min at 70°C. However, when an organic peroxide is used as the initiator, the corresponding times for 20% conversion are 62 min at 60°C and 29 min at 70°C. What is the activation energy for the dissociation of the organic peroxide ? [Ans. 29.7 kcal mo1-1] 6.23. The half-lives of azobisisobutyronitrile at 50°C and 70°C are 74 h and 4.8 h, respectively. What will be the half-life at 60°C? [Ans. 18.1 h] 6.24. In the bulk polymerization of styrene by ultraviolet radiation, the initial polymerization rate and degree of polymerization are 1.3×10 -3 mol/Ls and 260, respectively, at 30°C. What will be the corresponding values for polymerization at 80°C? The activation energies for propagation and termination of polystyryl radicals are 26 and 8.0 kJ/mol. What assumption, if any, is madein this calculation ? [Ans. 4.48×10-z tool L-1 s-l; 896] 6.25. A radical chain polymerization conforming to ideal behavior shows the indicated conversions for specified initial monomerand initiator concentrations and reaction times: z[I]0 x 10 Temperature Reaction Conversion [M]0 (mol/L) (mol/L) time (min) (%) (°C) 0.80 1.0 60 60 40 0.50 1.0 75 70 80 Calculate the overall activation energy for the rate of polymerization. [Ans. 63.8 kJ mo1-1 (= 15 kcal mol-1)] 6.26. The enthalpy and entropy of polymerization of a-methylstyrene at 25°C are -35 kJ/mol and -110 J/°K-mol, respectively. Calculate approximately the equilibrium constant for polymerization at 25°C and 50°C. Comment on the results. [Ans. 2.45, 1.22] 6.27. Calculate/~[M], and kap at different temperatures and hence determine the ceiling temperature for pure methyl methacrylate (density 0.940 g/cm3 at 25°C) using the following data: Ap = 106 L mo1-1 -l, Aa~ = 10az s - I -a. = 82 IO mol (assumed), /~ = 26 kJ tool -~, Edp
[Ans.T~= 488°K] 6.28. Calculate the equilibrium monomerconcentration [M]e for radical polymerization of styrene at 50°C, assuming that A/-/° and AS° are given by values in Table 6.13. Repeat the calculations for 75°C and 125°C. [Ans. 4.23x10-7 mol L-l; 2.98×10-6 tool L-l; 1.0×10-4 -~’] tool L
Radical Cha/_n Polymerizafion
577
6.29. The enthalpy and entropy of polymerization of methyl methacrylate at 25°C are -56 kJ/mol and -117 ld/°K-mol, respectively. For a solution of the monomer(1.0 mol/L), calculate the maximumattainable conversion at (a) 25°C, (b) 120°C and (c) 200°C. [Ans. (a) 99.98%; (b) 95.0%; (c) 6.30. For polymerization of tetrafluoroethylene, AH° and AS° values at 25°C are given as -37 kcal/mol and -26.8 cal/°K-mol. Calculate the ceiling temperature (To) from these two values. Account for the fact that in practice poly(tetrafluoroethylene) is found to undergo fragmentation well below the calculated [Ans. 1380 °K] 6.31. Using the enthalpy and entropy of polymerization data for methyl methacrylate from Table 6.13, calculate the depolymerization rate constant of poly(methyl methacrylate) at 100°C. [Data: kp at 60°C = 515 L/mol-s; Ep = 26.4 k J/moll [Ans. -1] 34.7 s 6.32. If a free-radical polymerization of 1.0 M solution of styrene were being carried out at 100°C, what would be the maximumpossible conversion of the monomerto polymer, that is, till the polymerization-depolymerization equilibrium is reached ? (Take data from Table 6.13.) [Ans. 99.995%] 6.33. What is the maximumbreadth of the size distribution to be expected for a low-conversion polymerization where termination is entirely by coupling ? Howwill each of the following situations alter the size distn’bution (a) chain transfer to mercaptan, (b) chain transfer to polymer, (c) high conversion, and (d) autoacceleration? [Arts. PDI = 1.5] 6.34. Styrene (density 0.90 g/cm3) was polymerized at 60°C with 0.01 Mbenzoyl peroxide as the initiator [W. B. Smith, J. A. May, and C. W. Kim, J. Polym. Sci., PartA2, 4, 395 (1966)]. The initial rate of reaction was obtained as 3.95x10 -s mol/L-s. From the GPCmolecular weight distribution curve reported for a 0.79% conversion sample, the weight fraction of polymer of DP~---- 3000 is seen to be 2.3x10-4. Calculate the weight fraction from theoretical distribution function to compare with this value. [Data: k~/kt at 60°C = 0.00119 L mol [Ans. -4] 2.2 x 10 6.35. MonomerA is polymerized in solution at 60°C using a peroxide initiator I which has half-life of 5.0 h at the same temperature. A 30%conversion of the monomeris obtained in 25 rain when the initial concentration of A is 0.40 Mand the initial concentration of I is 0.04 M. Polymerization of A in an emulsion of 8x 1017 particlesper liter at 60°C yielded a conversion rate of 18.1 mol/h/L when the concentration of A in the particles is constant at 4.0 M. Determine the termination rate constant of A at 60°C. [Ans. 9.73x10 6.36. What happens to (a) rate of emulsion polymerization, (b) number average degree of polymerization, and (c) polymer particle size, if more monomer is added to the reaction mixture during stage II polymerization ? Explain. [Ans. (a)’No change; (b) no change; (c) increases.]
578
Chapter 6
6.37. The rate of emulsion polymerization of styrene at 60°C during the constant rate period (stage II) is 5.6×10 -~ mol/cm3-min and the number of M/P particles is 1.40×10~5 per cm3. Taking kv from Table 6.7, calculate the dynamic concentration of monomerin particles under these conditions. -1] [Ans. 4.8 tool L 6.38. In an emulsion polymerization of isoprene with 0.10 M potassium laurate at 50°C the estimated time required for 100%conversion at steady rate is 30 h. The final latex has 40 g of polymer per 100 mLwith particles of 450 ~, diameter. During stage II, the growing swollen polymer particles contain 20 g of monomerper 100 mL of swollen polymer. Assuming that there is no change in total volume on polymerization, estimate the polymerization rate constant from these data. Assume that the polymer has a density of 0.90 3.g/cm [Ans. 2.4 L tool -1 -1] s 6.39. Consider a typical reactor charge for the production of polymer latex: monomer(s) 100, water 180, sodium lauryi sulfate (surfactant) 4, potassium persulfate (initiator) 1 (all quantities are in parts by weight). What effects do the following changes have on the polymerization rate in stage II ? (a) Using 8 parts surfactant; (b) using 2 parts initiator; (c) using 8 parts surfactant and 2 parts initiator; (d) adding 0.1 part butyl mercaptan (chain transfer agent). [Anz. (a) P~ increases by a factor of 1.52; (b) /~ increases by a factor of 1.32; (c) /~ increases by a factor of 2; (d) /~ unchanged.] 6.40. A 10%(by weight) latex of poly(methyl methacrylate) produced by emulsion polymerization contains particles that average 0.2 mumin diameter. In order to grow the particles to a larger size it is decided to feed 4 kg of monomerinto the latex per kilogram of polymer as polymerization proceeds at 60°C without further addition of emulsifier. The reaction is to be carried on until all monomeris added to the latex and the weight ratio of monomer to polymer has decreased to 0.2. The unreacted monomer is then to be recovered by steam stripping. Calculate the total time that will be required for reaction and the final particle diameter. [Data: kp at 60°C = 515 L mo1-1 s -~. Density: monomer 0.9 g/cm3; polymer 1.2 g/crn 3. Dynamic solubility of monomer in polymer = 0.5 g monomer per gram polymer.] [Ans. 42 h; 0.64/zm]
Chapter Chain Copolymerization INTRODUCTION In the preceding chapter we have considered free-radical polymerizations where only one monomer is used to produce a homopolymer. However, chain polymerizations can be carried out with mixtures of two or more monomersto form polymeric products that contain two or more different structures in the polymer chain. This type of chain polymerization process in which two or more monomers are simultaneously polymerized is termed a copolymerization and the product is a copolymer. It is important to note that the copolymer is not an alloy of two or more homopolymers but contains units of all the different monomersincorporated into each copolymer molecule. The process can be depicted, for copolymerization of two monomers, as MI + M2-----o
MIM2MIM2M2M2MIMIMIM2MIMI
(7.1)
The two monomersenter into the copolymer in overall amounts determinedby their relative concentrations and reactivities. The chain copolymerization may, however, be initiated by any of the chain initiation mechanisms, namely, free-radical chain initiations considered in the preceding chapter, or ionic chain initiations, which will be described in a later chapter. Chain copolymerizations involving more than two monomersare generally referred to as multicomponent copolyrnerizations. For systems of three monomers,the specific term terpolymerization is commonlyused. Chain copolymerization is important both from academic and technological viewpoints. Thus much’of our knowledgeof the reactivities of monomers, free radicals, carbocations, and carboanions in chain polymerization comes from copolymerization studies. The behavior of monomersin copolymerization reactions is especially useful for studying the relation betweenchemical structure and reactivity of monomers. From the technological viewpoint, 579
580
Chapter 7
copolymerization of two or more monomersis an effective way of altering the balance of properties of commercial polymers. While polymerization of a single monomeris relatively limited as to the numberof different products that are possible, copolymerization, enables the polymerscientist to tailormake polymers with specifically desired properties. Thus by variations in the nature and relative amounts of the two monomersin a copolymerization, an almost unlimited number of products with different properties can be synthesized. A notable example of the versatility of the copolymerization process is the case of polystyrene: Polystyrene is a brittle plastic with low impact strength and low solvent resistance. Copolymerization greatly increases the usefulness of polystyrene. Styrene copolymers are useful not only as plastics but also as elastomers. Thus free-radical copolymerization of the hydrocarbon monomerstyrene with 20-35% of the relatively polar monomeracrylonitrile produces a transparent copolymer with increased impact and solvent resistance, while copolymerization with 1,3-butadiene leads to elastomeric properties. On the other hand, free-radical copolymerization of styrene with acrylonitrile and 1,3-butadiene improves all three properties simultaneously. Similarly, although polyisobutylene is elastomeric, the polymer product consisting of saturated hydrocarbon chains cannot be crosslinked by sulfur vulcanization. Cationic copolymerization of isobutene with 1-3 mol%isoprene at very low temperatures yields a polymer with sufficient unsaturation to permit vulcanization by modified sulfur systems. The copolymerdescribed by Eq. (7.1), referred to as st atistical co polymer, has a distribution of the two monomerunits along the copolymer chain that follows somestatistical taw, for example, Bernoullian (zero-order Markov) or first- or second-order Markov. Copolymers formed via Bernoullian processes have completely random distribution of the two monomer units along the copolymer chain and, according to IUPACterminology, are referred to as randomcopolymers. Statistical copolymers are those in which the distribution of the two monomersin the chain is essentially random but influenced by the individual monomerreactivities. The reader is cautioned that the distinction between the terms statistical and random, recommended by IUPAC[1], has generally not been followed in the literature and most references ~ase the term random copotymer independent of the type of the statistical process involved in synthesizing the copolymer. There are three other types of copolymerstructures-alternating, block, and graft. The classification of copolymers according to these structural types and the nomenclature for copolymers have been described previously in Chapter 1. The present chapter is primarily concerned with the simultaneous polymerization of two monomersto produce random, statistical, and alternating copolymers. Graft copolymers and block copolymers are not synthesized by the simultaneous polymerization of two monomers. These are generally
581
Chain Copolymeriza~ion obtained by other types of reactions (see p. 641). BINARY
COPOLYMER
EQUATION
The composition of a copolymer produced by simultaneous polymerization of two monomersis usually different from the composition of the comonomer feed from which it is produced. This shows that different monomershave different tendencies to undergo copolymerization. These tendencies often have little or no resemblance to their behavior in homopolymerization. Somemonomersare more reactive in copolymerization than indicated by their rates of homopolymerization, and some monomers are less reactive. Thus, vinyl acetate polymerizes about twenty times as fast as styrene in a free-radical reaction, but the product in free-radical polymerization of a mixture of vinyl acetate and styrene is found to be almost pure polystyrene with practically no content of vinyl acetate. By contrast, maleic anhydride, which has very little or no tendency to undergo homopolymerization with radical initiation, undergoes facile copolymerization with styrene forming one-to-one copolymers. The composition of a copolymer thus cannot be determined simply from a knowledge of the homopolymerization rates of the two monomers. The simple copolymer model described here, however, accounts for the behavior of manyimportant systems and the entire process is amenable to statistical calculations which provide a good deal of useful information from few data. Thus, it is possible to calculate the distribution of sequences of each monomerin the macromolecule and the drift of copolymer composition with the extent of conversion of monomersto polymer. To predict the course of a copolymerization we need to be able to express the composition of a copolymer in terms of the concentrations of the monomersin the reaction mixture and the relative reactivities of these monomers. In order to develop a simple model, it is necessary to assume that the chemical reactivity of a propagating chain (which may be freeradical in a radical chain copolymerization and carbocation or carboanion in an ionic chain copolymerization) is dependent only on the identity of the monomerunit at the growing end and independent of the chain composition preceding the last monomerunit [2-5]. This is referred to as the first-order Markovor terminal model of copolymerization. Let us consider the case for the copolymerization of two monomers M1and M2. Although copolymerization has been more extensively studied using radical initiation, and radical copolymerization is also more important than ionic’copolymerization, we will consider here the general case without specification as to whether polymerization occurs by a free-radical or ionic mechanism. To generalize, an asterisk(*) will be used-instead of the con-
582
Chapter 7
ventional dot(" ) used in radical polymerization or plus (+) and minus signs used in ionic polymerizations-to indicate the active center of chain growth. Copolymerization of the two monomers M1 and M2 would thus lead to two types of propagating species-one with M~at the propagating end and the other with M~,where the asterisk represents either a radical, a earbocation ion, or a carboanion, depending on the modeof initiation. If it is assumed that the reactivity of the propagating species is dependent only on the monomerunit at the end of the chain (referred to as end or ultimate unit), four propagating species are then possible. Representing the propagating chains simply by their asterisked end units, these propagation reactions can be written as: M~
+
M1
~
M~
(7.2)
M~
+
M2
~
M~
(7.3)
M~
+
M1
~
M~
(7.4)
M~ + M2 k-~ 22 M~ (7.5) where the first subscript on the rate constant refers to the active center of the propagating chain and the second to the monomer.Reactions (7.2) and (7.5) where the reactive chain end adds the same monomerare often referred to as homopropagationor self-propagation. Propagation reactions involving addition of another monomer(Reactions 7.3 and 7.4) are referred to as cross-propagation or cross-over reaction. It is assumed in the above scheme that the reaction is carried out below the ceiling temperature of both the monomersand the various propagation reactions are irreversible. In order to simplify the kinetic formulation of copolymerization it is assumed that a steady state mechanismapplies, in which the concentration of each propagating chain type, that is, the concentration of each of M~and M~, remains constant. This assumption requires that the rate of conversion of M~to M~must equal that of M~to M~, or in mathematical terms k12 [M~] [M2] -- k21 [M~] [MI]
(7.6)
The rates of disappearance of the two types of monomersare given by [see Eqs. (7.2) to (7.5)1
dt
dt
-- kll. [MI] [M1] -}- k21 [M~] [M1]
-
[M2]+ [M;]
(7.7)
(7.S)
It should be noted that the rate of disappearance of each type of monomer is synonymouswith its entry into the copolymer chain.
583
Chain Copolymerization Dividing Eq. (7.7) by Eq. (7.8) and combining the resultant with Eq. (7.6) we obtain
diM1]
_
2]gXlk21 [M~][M1] k12[M2] q- k21[M~][M1]
d [M2]
k21[M~21[M1] q- k22 IMP] [M21
By defining the parameters rl and r2, representing ratios, as rlkl 2 , and r2 --
equation
(7.9)
monomerreactivity (7.10)
and substituting them into Eq. (7.9) after dividing the top and bottom the right side of this equation by k21 IMP] [M2] one finally obtains d[Ml_~!] d[M2]
= [M1] rl [M1] + [M~] [M2] [M~] + r2[M2]
(7.11)
This is the so-called copolymer equation or the copolymer composition equation. The ratio d [M1]/d [M2] in Eq. (7.11), representing the ratio the rates at which the two monomers M1 and M2 enter the copolymer, gives the molar ratio of the two monomerunits in the copolymer (being formed at a given instant), and hence is referred to as the copolymer composition. According to Eq. (7.11), the copolymer composition depends on the concentrations of the two types of monomersin the feed, namely, IMp] and [M2] and the monomerreactivity ratios rl and r2. As defined by Eq. (7.10), the monomerreactivity ratio is the ratio the rate constant for a reactive propagating species adding its own type of monomerto the rate constant for its addition of the other monomer.The monomerreactivity ratio can thus be looked upon as the relative tendency for homopropagation and cross-propagation. The tendency of two monomers to copolymerize is noted by r values between zero and unity. An rl value of zero would mean that M~is incapable of undergoing homopolymerization in the presence of M2. While an r~ value greater than unity means that ~ preferentially adds M1instead of M2, an rl value less than unity means that M~preferentially adds M2. For example, an rl value of 0.5 would mean that M~ adds M2twice as fast as M1. It is evident from Eq. (7.10) that the values of rl and r2 refer to pair of monomers undergoing copolymerization. Thus the same monomer can have different values of ri in combination with different monomers, e.g., acrylonitrile has (rl, r2) values of (0.35, 1.15), (0.02, 1.8), (1.5, and (4.2, 0.05) at 50°C in flee-radical copolymerization with acrylic acid,
584
Chapter 7
isobutylene, methyl acrylate, and vinyl acetate, respectively, each one being designated as M2 and the other monomer, acrylonitrile, as M1.
Problem7.1 The above derivation
of the copolymer composition equation [Eq. (7.11)] involves the steady-state assumption for each type of propagating species. Show that the same equation can also be derived from elementary probability theory without invoking steady-state conditions [6-8].
Answer: Let = Pll
probability that M~will add MI rather than M2, where the first subscript designates the active center and the second the monomer.
P12 = probability
that
M~will add M2 rather
than M1
Since termination occurs rarely in the formation of high polymer, we can neglect it for the purpose of this analysis. This means that Plx + PJ.2 In the same way,
= 1
(PT.l.1)
(P7.1.2) P22 ÷ P21 = 1 Theprobability thatpropagating species M~ addsan M~ unitis equalto therate of thisreaction divided by thesumof theratesof allreactions available to this radical. Thisis theprobability P~Ithatan MI unitfollows an M~ unitin the copolymer.Hence Pll
=
kll [M~][M1]
= rl
[M~]
kl, [M~][Ma]+ k,~ [M~][M2]rl [M~]÷ [Mz]
(P7.1.3)
Similarly, the other probabilities are obtained as P12 = p~l
=
[M2]
n
+ [M~]
[Mx]+ [M2]
p22 = ~’~ [M2] [M~] ÷ r2 [M2]
(P7.1.4) (P7.1.5) (P7.1.6)
Let "~(M1) = number average sequence length of monomer M~, that average number of M~monomerunits that follow each other consecutively in a sequence uninterrupted by M2 units but bounded on each end of the sequence by M2 units. Similarly, 5(M2) = number average sequence length of monomerM2. order to evaluate 5(M~) and 5(M2), it is necessary to determine the distribution of sequence lengths of each monomerin the copolymer.
585
Chain Copolymerization
To determine the distribution of sequence lengths of M1, an M1unit in the copolymer is selected at random. If this unit is part of a sequence of x number of M1units, reaction (7.2) would have been repeated (x - 1) times. Since probability of one such an event is Ply, as shown above, the probability that it occurs (z - 1) times is (Pll) z-1. If the M1sequence is exactly x units long the (x - 1) reactions of M~with M~must be followed by reaction (7.3). placement has the probability P~2 = 1- Pu [see Eq. (P7.1.1)]. It can thus concluded that the probability that the original M~unit was part of a sequence of x such units is PI{-~ (1 - P~I). But the probability that the sequence contains x number of M1 units is also the fraction of all M~sequences which contain x units. That is to say, it is the numberdistn’bution function n~(M1)for M~-sequence lengths : (P7.1.7) nz(M1) = Vii z-l(1 _Pll) = -~ O12 _p11~-x Similarly, units is
the fraction of all M2sequences that contain exactly x number of M~_
n~(M2) = P22~-1 z-1 (1 - P22) = P21 P22 The number average sequence length of M1 is then given by
(P7.1.S)
oo
5(M~) = ~-~n~(M,)
(e7.1.9)
[This is completely analogous to the definition of number average molecular weight M,~ in Eq. (4.3). A number average quantity is always the sum of products values of that quantity times the corresponding fraction of the whole sample which is characterized by the particular value.] Substituting Eq. (P7.1.7) into Eq. (P7.1.9), -~ 5(M1)
= £XPlzPI{ = P~2 (1 + 2P1, + 3Pll ~ + 4P~1a + ......
)
(PT.l.10)
For P~ < 1 which holds in a copolymerization, the expansion series (P7.1.10) is 1/(1 -- Pll) 2 and l~q. (PT.l.10) becomes 1 P12 ~(M1) = (1 - Pll) 2 - P12 = 1 -1-
r1~-~] IMp]
in Eq.
(P7.1.11)
In a similar manner one obtains P21 2 ~(M2) = (1 - P22)
--
P21
1
--
[M~]
1 q- r2 IMp]
(P7.1.12)
The mole ratio of monomers M~and M2 contained in the copolymer is given by the ratio of the two number-average sequence lengths, 5(M~) _ diM1] [M~] (r l [M 1] + [M~]) ¯ (M~) d [M2] [M2] ([M1] -]- r2 [M2])
(P7.1.13)
586
Ghap~er7
whichis exactly the sameresult as Eq. (7.11). Thusthe copolymerequation holds for copolymerizations carried out under both steady-state and non-steady-state conditions providedthat the reactivity of a propagatingspecies is dependentonly on the end unit, depropagationdoes not occur, and high polymeris formed. Equation (P7.1.13) [and also Eq. (7.11)] describes firs t-order Mark ov or t erminal model of copolymerization.
Range of Applicability
of Copolymer Equation
The simple copolymerequation [Eq. (7.11)] has been experimentally verified in innumerable comonomersystems. The equation is equally applicable to radical, cationic, and anionic chain copolymerizations, although the rl and r2 values for any particular monomerpair can be drastically different in the three types of chain copolymerization. For example, for the monomerpair of styrene (M1) and methyl methacrylate (M2) the I and r 2 values a re 0 .52 and 0.46 in radical copolymerization, 10 and 0.1 in cationic polymerization, and 0.1 and 6 in anionic copolymerization. Methyl methacrylate as expected has higher reactivity in anionic copolymerization and lower reactivity in cationic copolymerization, while the opposite is the case for styrene. Thus the copolymer obtained from an equimolar styrene-methyl methacrylate feed is approximatelya 1:1 copolymerin the radical case but is essentially a homopolymerof styrene in cationic copolymerization and a homopolymer of methyl methacrylate in anionic copolymerization. This high selectivity of ionic copolymerizationlimits its practical use. Since, moreover, only a small number of monomersundergo ionic copolymerization (see Chapter 8), the range of copolymer products that can be obtained is limited. On the other hand, almost all monomersundergo radical copolymerization and thus a wide range of copolymers can be synthesized. For any specific type of initiation (i.e., radical, cationic, or anionic) the copolymer composition equation is independent of many reaction parameters. Since no rate constants appear as such in the copolymer equation, the copolymer composition is independent of differences in the rates of initiation and termination or of the presence or absence of inhibitors or chain transfer agents. Thus the same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysisof initiators (such as AIBNor peroxides), photolysis, radiolysis, or redox systems. Under a wide range of conditions the copolymer composition is also independent of the degree of polymerization. The limitation on the above generalization is that the copolymer be of high molecular weight. It may be recalled that the derivation of Eq. (7.11) involved an assumption that the kinetic chains
587
Chain Copolymerization
were long so that initiation and termination reactions could be ignored compared to propagation events.
TYPES OF COPOLYMERIZATION Before measurementsof reactivity ratios are reviewed, it is useful to consider what the absolute magnitudes of these parameters imply. Depending on the values of rl and r2, and of the rlr2 product four types of copolymerizations can be recognized.
Alternating
Copolymerization:
rl = r2 = 0
A zero (or a nearly zero) value for the reactivity ratio means that the monomeris incapable of undergoing homopolymerization and its radical prefers to add exclusively to the other monomer.This leads to alteration of the two monomerunits along the copolymer chain. For rl = r2 = 0, Eq. (7.11) reduces aIM1]
_ 1
(7.19,)
Copolymerization of the two monomerstherefore produces an alternating copolymer (in which the two monomerunits alternate in a regular fashion along the chain) irrespective of the composition of the monomerfeed.
Ideal Copolymerization:
rl = r2 = 1 and rlr2 = 1
A value of unity (or nearly unity) for the monomerreactivity ratio signifies that the rate of reaction of the growing "chain radicals towards each of the monomersis the same, i.e. kll ~ k12 and k22 ~-- k2~ and the copolymerization is entirely random. In other words, both propagating species M~and M~have little or no preference for adding either monomer.The copolymer composition is the same as the comonomerfeed with a completely random placement of the two monomersalong the copolymer chain. Such behavior is referred to as Bernoullian. Free-radical copolymerization of ethylene and vinyl acetate and that of isoprene and butadiene are examples of such a system, but this is not a commoncase. Randommonomerdistributions are obtained more generally in a situation where both types ofradicals have exactly the same preference for the same type of monomeras represented by the relationship
kll k~l -kl~ k~
or r~ --
1 r~.
(7.13)
Chapter 7
588
Equation (7.13) means that k11/k12 and k21/k22 will be simultaneously either greater or less than unity or in other words, that both radicals prefer to react with the same monomer.All copolymers whose ?’1r2 product equals 1 are therefore called Meal copolymers or random copotymers. Most ionic copolymerizations are characterized by the ideal type of behavior.
Problem7.2 Use simple probability concepts to justify the following statement: a value of unity for the product rlr2 signifies that the likelihood that an M1unit in the copolymerchain follows an Maunit is the same as the likelihood that it follows an M2unit.
According to the reaction scheme of the simple copolymer model, M1-Mabonds are formedonly by reaction (7.2). The probability that a propagating species (that is, endingin an M1 unit) adds an Maunit is equal to the rate of this reaction divided by the sumof the rates of all reactions available to this propagating species. This is the probability Pn given by [see Eq. (P7.1.3)]: Pn =
r~ IMp] rl [M~]+ [M21
(P7.2.1)
Similarly, the probability P2a that an M1unit follows is given by [see Eq. (P7.1.5)]: P2~ =
[M1] r~_ [M2]+ [Ma]
an M2 unit
in the polymer
(P7.2.2)
If r~r2 = 1, then Pn and P~ defined above are equal. That is to say, the likelihood that an M1unit follows an M~unit equals the likelihood that it follows an M2unit in the copolymerchain. The absolute values of the probabilities Pn and P2a will dependon the relative concentrations of monomers in the feed, but the equivalence of the probabilities is independent of the feed and copolymer compositions.
For rl = r2 = 1, Eq. (7.11) reduces diM1] _ [M~] diM2] [M2]
(7.14)
which means that the copolymer composition will always be the same as the feed composition. The relative amounts of the two monomerunits in
589
ChMnCopolymeriz~ion the copolymer chain are determined by the relative monomerunits in the feed. For rlr2 = 1, Eq. (7.11) reduces d [M1] diM2]
_ rl
concentrations of the
(7.15)
[M2]
The relative amounts of the two monomerunits along the copolymer chain are thus determined by the relative concentrations of the monomerunits in the feed and the relative reactivities of the two monomers.Thus a very important practical consequenceof ideal copolymerizations is that it becomes progressively more difficult to produce copolymers containing appreciable amounts of both monomersas the difference in reactivities of the two monomersincreases. It should be noted that the term ideal copo~ymerization does not in any sense connote a desirable type of copolymerization. Somecommercially important examples of random free-radical copolymerizations include styrene (rl ---- 0.8)-butadiene (r2 ---- 1.4) for which rlr2 = 1.1 and vinyl chloride (rl ---- 1.4)-vinyl acetate (rg. = 0.65) which rlr2 = 0.9. In these products the proportion of a given monomer in the copolymer depends on the feed concentrations and reactivity ratios [Eq. (7.11)]. Random-Alternating
Copolymerization:
0 < fir2
> 1 and r2 > 1 and r:~ 1,
r2 > 1
An rl-value greater than 1 means that an M{ propagating species would add monomer M1 in preference to M2, and so many units of M1 would successively add to the growing chain until an M2unit happened to add, converting the growing chain from ME type to M~type. Since r2 is also more than 1, the ~ propagating species would then preferentially add manyM2units in succession until an M1 unit happened to add, converting the chain again to the ME type. This process would give rise to a block copo(ymer consisting of long sequences of each monomerin the copolymer chain. With an increase in the value of r, the tendency of each radical to add its own type of monomer would increase and in the limit when both rl and r2 became sufficiently large, the two types of monomerswould simultaneously homopolymerize in each other’s presence. However, such reactivity combinations are not knownin free-radical copolymerizations, but they can be found in other systems. Since there is no established instance of free-radical copolymerization where both rl and r2 are greater than unity, block copolymersby free-radical initiation are thus to be madeby homopolymerization using special techniques. These are discussed toward the end of this chapter. INSTANTANEOUS COMPOSITIONS FEED AND COPOLYMER
OF
The copolymer equation (7.11) can be converted to a more useful form expressing concentrations in terms of mole fractions. Let fl and f2 be the mole fractions of monomersM1and M2in the feed, that is, fl
= 1 -- f2 --
[M,] [M1] d-[M2]
(7.16)
and F1 and F2 be the mole fractions of monomers M1 and M2 in the polymer being formed at any instant, so that (7.17) d[M1] d([M~] + [M2]) CombiningEqs. (7.16) and (7.17) with the copolymer equation (7.11), obtains rifl 2 q- fir2 (7.18) -~ : r~fl ~ d- 2fir2 -t- ~ r2f2 F1
= 1-
F~
=
Chain Copolymerizafion
591
Equation (7.18), which is also called the copotymer equation, gives the mole fraction of monomerM1in the copolymer whose feed contained fl mole fraction of monomerM1. It is more convenient to use than its previous form [Eq. (7.11)]. It should be noted that/71 gives the instantaneous copolymercomposition and both fl and/71 change as the polymerization proceeds. The composition of the copolymeras a function of conversion can be derived by integration of Eq. (7.18). Equation (7.18) may be used to calculate the instantaneous composition of copolymer as a function of feed composition for various monomer reactivity ratios. A series of such curves are shownin Fig. 7.1 for ideal copolymerization, i.e., rlr2 = 1. The term ideal copolymerization is used to showthe analogy between the curves in Fig. 7.1 and those for vapor-liquid equilibria in ideal liquid mixtures. The vapor-liquid composition curves of ideal binary mixtures have no inflection points and neither do the polymercomposition curves for random copolymerization in which rlr~ = 1. Such monomersystems are therefore called ideal. It does not in any sense imply an ideal type of copolymerization. It is evident from Fig. 7.1 that only a small range of feed compositions give copolymers containing appreciable amounts of both components unless monomershave very similar reactivities. Suppose, for example, that it is desired to synthesize an ideal copolymer with 60 mol%M1in a system where z’l --= 0.5. FromFig. 7.1 it is seen that a feed composition of about 75% M1is required. However, since/71 ~ fl, there occurs a drift in monomer composition as copolymer is formed. Therefore copolymer composition changes with conversion. To obtain a constant copolymer composition of 60% M1, it would be necessary to maintain a constant feed composition of 75%, such as by adding fresh M1to the feed. For cases in which rl = r2 = 1, the composition of the copolymer (/71) will always be the same as the feed composition (fl)- For this copolymer system obviously there occurs no drift in composition with conversion.
Problem 7.3 It is desired to form a copolymer from CH~=CHX (M1) and CH2=CHY (M2), containing twice as manyX groups as Y groups. The monomers copolymerizeideally, with M~adding M1twice as fast as M2. Describe the procedure as well as the feed compositionyou might use to makethis polymer. Answer: Since (M~+ M1)reaction is twice as fast as (M~+ Ms)reaction, --- -- kn/ kl2 = 2. For ideal polymerization rlr2 = 1. Therefore, r2 = 0.5 It is desired to haveF1 = 2/3. Todeterminethe correspondingfl it is necessary to rearrange the copolymerequation (7.18) into a form which enables fl to calculated from /;’1 for a given pair of ~1 and-r2 values. Remembering f~ = 1 fl, then from Eq. (7.18), 2 q- flf2 -/7’I(’rl/? -1- 2:1f2q-~’2f~) = ’rlfl
- 1) + :i(I
- - + - /i)
592,
Chapter 7 f12rl (_~1 - 1) + f~2 (1 -.2ivy) + f~ (2F~ - 1) + F~r2 2 - 2 fl + 1)=
f,2 IF, (rl + r2 - ~.) + (1 - ~1)]+ f, [2F,(1 - ~) - 11+ y~r~
(],7.3.1)
This equation is a qua~dratic in fl and can be solved in the usual way. For the calculations required it is necessary to evaluate fl for F1 = 2/3, rl = 2, r2 = 0.5. Equation(P7.3.1) simplifies
2f12+ fl-- 1 -= 0 Only one of the two solutions will be meaningful. Solving, fl = 0.5. (To check the result, substitution of fl = 0.5 into Eq. (7.18) gives F~= 0.667.) Since the copolymerformedis richer in M1as comparedto feed, calculated amountsmust be added to the monomermixture, continuously or periodically, to maintain the compositionat fl = 0.5 as the reaction progresses. Figure 7.2 shows curves for several nonideal cases, that is, where fir2 ~ 1. It is seen that whenboth r I and r2 are less than 1 there exists somepoint on the Fl-versus-fl curve where the copolymer composition equals the feed composition and at this point the curve crosses the line F1 = fl (that is, the diagonal line). At this point of intersection, polymerization proceeds without change in either feed or copolymer composition. Distillation terminology is again borrowed for this instance. Azeotropic copolymerization is said to occur at such points and the resulting copolymers are called azeotropic copolymers. 1.0
0.4 0.2 0
~ 0.2
0./,
0.6
0.8
1.0
Figure 7.1 Copolymerizationdiagrams (without inflection points) showinginstantaneous compositionof copolymer(mole fraction F1) as a function of monomer composition (mole fraction fl) for copolymerswith the values of rl = 1/r~ for ideal copolymerization.
Chain Copolymerization
593
1.0
0.6
.
0.2
0
0.2
0./-.
0.6
0.8
1.0
f~ Figure 7.2 Copolymerizationdiagrams with inflection points showingcomposition of copolymerF~ as a function of monomer composition f~ for the values of the reactivity ratios rl/r~ indicated. Since all azeotropic copolymers must have a point of constant composition, the critical composition (fl)c for the azeotrope can be evaluated by solving Eq. (7.11) with d [M1] / d [M2] = [M~] / [M2] or Eq. (7.18) F1 = fl. Whenthis is done,
_ ([M,]~
(7.~)
1 - r2 (f,)c =(2 - rl -
(7.20)
1-
and
Note that f~ in the above equation is physically meaningful (0 _< f~ 1, r2 > 1 is unknownin free-radical systems, the necessary conditions for azeotropy in such copolymerizations is that rl < 1, r2 < 1 (see Fig. 7.2).
594
Chapter 7
Equation (7.20) predicts the feed composition that would yield invariant copolymer composition as the conversion proceeds in a batch reactor. It should be noted that comonomerratios that are near but not equal to the estimated azeotropic value may also produce copolymers whose compositions are constant for all practical purposes. It is seen from Fig. 7.2 that the permissible range of feed compositions for which this "approximate" azeotropy occurs is greater the closer the two reactivity ratios are to each other.
Problem 7.4 WhenmonomersMI and M2are copolymerized, an azeotrope is formed at the feed ratio of 1 mol of M1to 2 tool of M2. MonomerM1is known not to homopolymerize.Will a polymer formedat 50%conversion from an initial mixture of 4 mol of M1and 6 mol of M2contain more of M1or less of M1than a polymer formed at 1%conversion? Answer: Since M1does not homopolymerize,ra = 0. Azeotropic feed composition, fl = 1/3 = (1 - r~)/(2 - 0 - r2). This gives r2 = 0.5. For a feed composition 0.4 and f~ = 0.6, Eq. (7.18) with rl = 0 and r~ = 0.5 gives F1 = 0.36. Therefore the feed compositionwill drift toward higher fl at higher conversion and hence F1 at 50%conversionwill be greater than _b"l at 1%conversion.
INTEGRATED
BINARY
COPOLYMER
EQUATION
The copolymer equations, Eqs. (7.11) and (7.18), give inst antaneous copolymer composition, i.e. the composition of the copolymer formed from a given feed composition at very low degrees of conversion (approximately < 5%) such that the composition of the monomerfeed may be considered to be essentially unchangedfrom its initial value. For all copolymerizations except when the feed composition is an azeotropic mixture or where rl = re = 1, the comonomer feed and copolymer product compositions are different. The comonomer feed changes in composition as one of the monomerspreferentially enters the copolymer. Thus there is a drift in the comonomercomposition, and consequently a drift in the copolymer composition, as the degree of conversion increases. It is important to be able to calculate the course of such changes.
Problem 7.5 A monomerpair with rl -- 0.2 and r2 = 5.0 is copolymerized beginning with a molar monomerratio [M1]/[M2] = 60/40. Assumingthat the copolymercompositionwithin a 10 mol%conve.rsion interval is constant, calculate instantaneous monomerand copolymercompositions and cumulative average copolymercompositions at 10 mol%conversion intervals up to 100%total conversion. Showthe results graphically as change in composition of the copolymer and the monomermixture during copolymerization.
595
Chain Copolymeriza~ion Answer: In intervalI: fl = 60/(60+40) = 0.60.From Eq. (7.11),El = 0.2308. At the end of interval 1 (i.e.,
after 10 mol%conversion),
M~converted = 2.308 mol M1 remaining ---- 60 - 2.308 or 57.692 mol fl = 57.692/90 = 0.641 _b-’~= 2.308/10----- 0.2308 The residual mixture with fl = 0.641 will be the starting mixture for the interval 2. From Eq. (7.11) then, F1 = 0.2631. Hence at the end of interval 2 (20 tool% conversion), M1 converted = 2.308 + 2.631 = 4.939 tool M1 remaining = 60 - 4.939 = 55.061 mol fl = 55.061/80 = 0.6883 F1 = 4.939/20 = 0.247 The results obtained by proceeding in this way are tabulated below: mol% Conversion Interval (cumulative) FIa ~ f, a 0.23 1 10 0.60 0.23 0.25 2 20 0.64 0.26 0.27 3 30 0.69 0.31 4 0.74 0.37 0.29 40 5 50 0.80 0.45 0.32 0.58 0.37 6 60 0.88 7 70 0.95 0.79 0.43 8 80 1.0 1.0 0.50 9 90 1.0 1.0 0.55 10 0.60 100 1.0 1.0 aInstantaneous value at the beginning of each interval (assumedto be constant withinthe interval). bThis copolymeris really a mixture of different copolymersand, at higher conversions, a mixture of these copolymersas well as someM~homopolymer. The results are shown graphically in Fig. 7.3. Comment:If one makes the conversion interval smaller and smaller, this corresponds to an integration of the copolymer equation (see below).
To follow the composition drift of both the comonomer feed and the copolymer formed requires integration of the copolymer equation. This problem is rather complex. The most convenient approach utilizes a numerical or graphical method developed b} Skeist [9] for which Eq. (7.18) forms the basis. Consider a system initially containing a total of N moles of the two monomers; choose M1 as the monomer in which F1 > f~ (i.e.,
596
Chapter 7
20
40
60
80
100
Conversion(moL°/o) Figure 7.3 Change in the composition mixture during copolymerization.
of the copolymer and the monomer (fx)0 = 0.60, rl = 0.20, r2 = 5.0. (Problem
7.5). the polymerbeingformed contains moreM1than the feed). WhendNmoles of monomers have polymerized,the polymerwill contain FIdNmolesof M1and the feed content of M~will be reducedto (N - dN)(f~ - df~) moles.A material balancefor monomer M~requires that the molesof M~ copolymerized equal the difference in the molesof M~in the feed before andafter the reaction, or fin - (N - aN )(fl - dr1) = FIdN (7.21) which becomes (neglecting the small term dfldN) dN df~ (7.22) ~ = -~l
--
-fl
597
ChainCopolymerization Integration
gives lrI-N-- f(fl)fl° (-~’1-/~’0
dfl
-
(7.23)
where No and (fl)0 are the initial values of M and f~. For given values of rl and r2, the quantities F~ and 1/(F1 -- fl) are computed from Eq. (7.18) at suitable intervals for 0 < f~ < 1. The indicated integration may then be performed graphically or numerically to give the degree of conversion /9 (= 1 -- N/No) required for a change in feed composition from (fl)0 to f~. Through a repetition of this process for suitably chosen values of fl, it is possible to construct the relationship between fl and the degree of conversion p. The average overall copolymer composition for any conversion p can be determined by graphical integration of a plot of F1 versus f~ or from the amounts of residual monomers and those present initially (see Problem 7.6).
Problem7.6 Derive an equation that gives the cumulative or average composition of the copolymer formed at a given overall conversion of the monomers. Answer: Consider a batch polymerization mixture containing initially (N1)o tool of monomer M1 and (N2)o tool of monomerM2. After a fraction p of the initial monomers have been polymerized, the unreacted monomersare, respectively, N1 and N2. The mole fractions of monomersM1 and M2 in the feed after a degree of conversion p are A and f2, the corresponding initial values being (fl), and (f2)0- Then, (N1)o + (N2)o (N1)o = (fl)0No, (N2)0 (f ~)oNo NI = f~(1 - p)No,. Nu = fz(1 - p)No
(P7.6.1)
Since the average mole fraction of M~in copolymer, F~, is the ratio of the number of moles of M~converted divided by the total number of moles of M1 and M2 polymerized in the same interval,
F1 =
(N1)o NI [(N1)0 - N,] + [(N2)o -
Substituting from the above definitions ~11 = (fl)o
(P7.7.1), one obtains
- fl(1 (P7.6.2) P The cumulative average copolymer composition can be calculated in a straightforward manner by entering Eq. (P7.6.2) with the cumulative value of p and the initial value of (f~),0. [As a check, the value of ~ at p = 1 must equal
598
Chapter 7
Equation(7.23) has been integrated to the useful closed form [10]:
(7.9.~) whichrelates the degreeof (overall) conversion(1 N/No) tochanges in the monomer feed composition. Thezero subscripts indicate initial quantities and the other symbolsare given by r2 (1 -"/
= (1 --
rl 9-2)
’
(1 --
(1 - 9-z9-~) 9"1)(1 - r2)
(5 = (1 (2 -- 9"1 -- r2)
(7.25)
It shouldbe noted that there are certain difficulties with the use of Eq. (7.24) for conversion-composition calculations. Thus, singularities occur r: = l, r2 = 1, r: -F r2 = 2, f: = di, and (fl)0 = 0 or (f2)0 all of whichresult in division by zero. Thedifficulties with the reactivity ratios equat to unity can be circumventedby using the special solutions [10] for these two cases as follows: For ?’1 = 1 and r2 ~ 1, Eq. (7.24) becomes
N
11
i:{t(f:)oJ 9"2 1 (fl)o-
1 .] (7.26) I fl-
For rl ~ 1 and r2 = 1, Eq. (7.24) becomes 9" 1
In --
No
B
fl
rl
- 1
[{ }1
J 1
/Sx)0
1 ]
/
(7.27)
Equation (7.24) was formulated so as to make6 equal to the azeotropic composition(f~)c Ice. Eq. (7.20)] for those systemsexhibiting azeotropic
599
Cha/n Copolymerizafion
composition behavior. However, this results in division by zero when rl + r2 = 2. To overcome, this difficulty, the third right-hand term of Eq. (7.24) may be rewritten as [11]: [(fl)0
-- ~]7 (fl)0(2-
-~- -rl r--2} -’+--- --r2- ---- 1
]7
J = £(2 - rl - r2) + - 1
(7.28)
It should be noted, however, that the difficulties with the reactivity ratios can also be circumvented simply by making a small, but for practical purposes insignificant, change in the values of the reactivity ratios. The copolymerization behavior for the cases (fl)0 -- 0, (f2)0 = 0 and (fl)0 = ¢5 which give rise to singularities are not systems of actual interest and so may be ignored. Equation (7.24) or its equivalent has been used to correlate the drift in the feed and copolymer compositions with conversion for a number of different copolymerization systems [10,12,13].
Problem 7.7 A mixture of styrene (M1) and methyl methacrylate 0VI2) polymerized at 60°C with initial composition (fl)0 = 0.80, (f2)0 = 0.20 and polymer obtained by precipitation at appropriate intervals was analyzed. Some of the conversion-composition data so obtained are given below: Oxygen in polymer (Wox), Conversion (we) wt.% wt.% 11.74 8.32 29.32 7.92 46.18 7.61 65.88 7.43 86.37 7.00 Source: Data from Ref. 14.
0.8091 0.8229 0.8391 0.8769 0.9648
With rl = 0.52 and r 2 ~. 0.46, calculate from Eq. (7.24) the changes in instantaneous monomerand copolymer compositions as a function of conversion and compare the results graphically with the above experimental data. Also calculate the cumulative average copolymer composition at different conversions. Answer: The essential procedure for calculating the composition drift with conversion "is that fl is decreased or increased in suitable increments from (fl), to 0 or 1.0. For each value of fl, the corresponding degree of conversion is obtained from Eq. (7.24) and the corresponding instantaneous copolymer composition from Eq. (7.18). With the monomer mixture composition, fl, and the degree of conversion p = 1 - N/No thus known, it is then easy to also calculate cumulative average copolymer composition F1 from Eq. (P7.6.2). For the given monomersystem and feed composition, Eq. (7.18) shows that F1 < fl, i.e., the
600
Chapter7
polymeris richer in M2as compared to the monomer feed; fl is therefore to be increasedin step incrrmentsfrom(fl)0 in the computation. Therelation betweenF1 and the oxygencontent (Woxwt.%)of the copolymer is easily obtained frommassbalance, taking note that each MMA unit in the copolymeraccounts for 2 oxygenatoms. Takingmolar massesof styrene and MMA as 104and 100 g/mol, the followingrelation is obtained: 32 - wo~ 32 + 0.04wo~ To convert weight%conversion(we) of monomers into molefraction degree of conversion(1 - N/No),the followingrelation is readily derived: N [4(fl)0 + 100] 1 No - 1- [~-~-~-]~ j (1-we/100) [Since for the given systemthe differences between(fl)0 and fl are small, 1- N/No ~ we/100and mole fraction conversion nearly equals the weight fractionconversion.] Thecalculated values of fl, F1, and F1 are plotted against molefraction degree of conversionalong with the given experimentaldata in Fig. 7.4. The results for f2 followfromthe relation fl + f~ = 1, andsimilarly for F2 andF2.
EVALUATION OF MONOMER REACTIVITY RATIOS Most procedures for evaluating rl and r2 involve the experimental determination of the compositions of copolymersformed from several different comonomerfeed compositions. These data of corresponding feed and copolymercompositionsare used in conjunction with the differential copolymerequation [Eq. (7.11) or (7.18)]. Copolymerizationsare carried out to as low degrees of conversion as possible (ca. < 5%) in order insure that the feed compositionis essentially unchanged.This is necesSary in order to minimizethe drift of copolymermakeupand consequent errors in the use of the differential equation. The copolymercomposition is determined either directly by analysis of the copolymeror indirectly by analysis of comonomerfeed. While comonomer feed compositions are typically analyzed by high-pressure liquid chromatography(HPLC)or gas chromatography(GC), the copolymercomposition is measured, depending on the type of the copolymer,by elemental analysis, chemicalanalysis, or physical analysis (such as refractive index, IR, UV,NMR,etc.). Though the techniques for analyzing comonomer compositionsare inherently more sensitive than those for copolymer composition,this is offset by the fact that the determination of copolymercomposition by comonomer feed analysis requires the measurementof small differences between large numbers. Various methods have been used to obtain monomerreactivity ratios from the copolymercomposition data. Several procedures for extracting reactivity ratios from the differential copolymerequation [Eq. (7.11)
Chain Copolymerizafion
601
0.6
0,4
0.2
O.Z, 0.6 0.8 0 Degreeof conversion (1-N/N O)
1.0
Figure 7.4 Copolymerization behavior of styrene (M1) and methylmethacrylate (M2) for (f~)o = 0.80, (f2)~ = 0.20, and rl = 0.53, r2 = 0.56. Experimental points oI A are from Problem 7.7.
(7.18)] are mentionedin the following paragraphs. Twoof the simpler methodsinvolveplotting of rl versus ~’~ or fi’l versus Plot of rl Versus 7"2 Also knownas the "methodof intersections," the methodfirst described by Mayoand Lewis[3] has been widely used for computingreactivity ratios from data fitted to the differential copolymerequation. In this procedure, Eq. (7.11) is recast to the form
1-~ ] "’) =[~1L~--]~,] -~
(~~)
~h~pte~ 7
1.0
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1.0
Figure 7.5 Graphical determination of rl and ’r2 according to Eq. (7.30) for the system styrene/methylmethacrylate (M1 = styrene; M2= methyl methacrylate). (After Ref. 3.) or, equivalently, Eq, (7.18) to the form
If one knows experimentally the copolymer composition (/~1) corresponding to a given feed composition (fl) then one can calculate ~’2 values corresponding to various assumed values of rl and thus obtain a straight line plot of rl versus r2. Each experiment thus yields one straight line in the rl -- r2 plane (see Fig.7.5). If this procedure is repeated for different values of F~ and f~, a series of straight lines with different slopes should result. Theoretically, the lines should intersect in a single point corresponding to the actual values of rl and r2. However, because of errors in experimental results, the lines may not pass through a commonpoint and the area of the region in which the intersections occur is assumed to give the best values of rl and
603
Chain Copolymerization
Plot of F1 Versus fl Fineman and Ross [15] rearranged
Eq. (7.18)
(1 - fl)F1 = ----
to the form
(7.31)
fl)2F~j r~ r2
or
G = rlH - r2
(7.32)
where G = X(Y-1)/Y, H = X2/y, X = [M1]/[M2] = fl/(1 :-- f~), and Y d[ M1]/d[M2] = /7 1/(1 /7 1). [s ee Eq (7.16) and (7.17)]. If the term on the left side of Eq. (7.31) or (7.32) can be plotted against the coefficient of rl, a straight line should result, the slope of which is rl and intercept is r2.
Problem7.8 The initial
concentrations of styrene (M1) and acrylonitrile (Mg_) employed in a series of low conversion free-radical copolymerizations are given in the table below together with the nitrogen contents (% N by wt.) of the corresponding copolymer samples produced: [M1] mol/L [M2] mol/L % N in copolymer
3.45 1.55 5.69
2.60 2.40 7.12
2.10 2.90 7.77
1.55 3.45 8.45
Determine r~ and r.~ for the monomerpair by the Fineman-Ross method. Answer: -~ Molar mass of styrene (M~) repeat unit = 104 g mol Molar mass of acrylonitrile %N =
(M2) repeat unit = 53 g mo1-1 (1 -- F1)(14 g -I) tool × 100 F~(104 g tool -1) -1 + )(1 - F1)(53 g tool
which upon rearrangement for F1 gives 1400 - (%N × 53) 1400 + (~oN x 51) Table below gives fl = [M1]/([M~ -t- [M2]) and F~ calculated from %Ntogether with the composite quantities required to make a plot according to Eq. (7.31).
_~ =
0.69 0.52 0.42 0.31
0.6499 0.5800 0.5501 0,5200
f1(2~1 - 1) f~(1 - F1) (I - fl)FI (1 -- fl)2F1 1.0268 2.6688 0.2989 0.8499 0.1319 0.4289 0.0346 0.1863
Chapter 7
604
The data are plotted in Fig. 7.6 from which slope = rl and intercept = -r2. This gives rl = 0.40 and r2 = 0.04. Analysis of the data may also be done by regression analysis.
The best values of r" are obtained from slopes rather than intercepts. While Eq. (7.23) gives rl as the slope, it can be rewritten in form which makes r2 the slope: G/H = -re/n -{- ?’1 (7.33) The experimental composition data are unequally weighted by the MayoLewis and Fineman-Rossplots with the data for the high or low compositions (depending on the equation used) having the greatest effect on the calculated values of rl and r2 [16]. For example, the experimental data obtained at low [M2] in Eq. (7.32) or low [M1] in Eq. (7.33) have the greatest influence on the slope of a line corresponding to these equations. The same set of experimental data can thus yield different (rl, r2) sets depending on which monomeris indexed as MI and which is M2.
1.0 0.8 0.6 0.4 0.2 I
I
1.0
2.0
3.0
Figure 7.6 Plot according to the Fineman-Rossmethod (Problem 7.8).
Chain Copolymerization
60~
Linear least-squares regression can also be applied to a series of experimental values of/’1 and fl to obtain the best values of ~’1 and ~’2 from Eqs. (7.32) and (7.33). This procedure is statistically unsound, however, since Eqs. (7.32) and (7.33) do not meet the statistical requirements linear least-squares computations [16]. Kelen and Tudos [17] refined the Fineman-Ross linearization method by introducing an arbitrary positive constant ot into Eq. (7.34) to spread the data more evenly so as to give equal weighing to all data points. Their results are expressed in the form
where = G/(a
q- H)
(7.34a)
# = H/(c~
-b H)
(7.34b)
rl
Plotting r/ against ~z gives a straight line that yields --r2/a and ~’1 as intercepts on extrapolation to /~ = 0 and # = 1, respectively. The values of a, chosen as a = (HminHmax)1/2, where Hmin and Hmax are the lowest and highest H values, respectively, distributes the experimental data symmetrically on the plot. Even with the Kelen-Tudosrefinement there are statistical limitations inherent in the linearization method. It has been shown[18] that the independent variable in any form of the linear equation is not really independent while the dependent variable does not have a constant variance. The most statistically sound method of analyzing the experimental composition data is the nonlinear methodwhich involves direct curve fitting to the copolymer composition equation. Direct
Curve Fitting
Fromthe slope of the experimental _~1 versus fl plot an estimate of r 1 and ~’2 can be made by comparison with curves based on Eq. (7.18). The best values of r’~ and r’2 can be selected by determining which theoretical curve best fits the data by trial and error. A limitation of the methodis the relative insensitivity of the curves to small changes in ~’1 and r2. The pros and cons. of both the linearization and nonlinear methods have been discussed in detail, along with approaches for the best choice of feed compositions to maximizethe accuracy of the I" 1 and v2 values [17,19,20]. A serious drawback in the use of a differential form of the copolymerization equation [Eq. (7.11) or (7.18)] is the assumption that the composition does not change during the experiment, which is obviously not true. One carries out the polymerization to as low a conversion as possible, but there are limitations since one must be able to isolate a sufficient sample of the copolymer for direct analysis, or, if copolymer analysis is done
606
Chapter 7
indirectly via the change in feed composition, there must be a significantly measurable change in the feed composition. These limitations can be overcome by the use of an integrated form of the copolymer composition equation [18,21]. The change in copolymer composition or feed composition with conversion is measured and the data are curve-fitted to an integrated form of the copolymer composition equation. For example, one method uses Eq. (7.24) relating the degree of conversion (1 N/N o) to changes in the comonomerfeed composition fl or fg.. Experimental data on the variation of feed composition with conversion are plotted as fl or f2 versus (1 -- N/No) to yield curves like those in Fig. 7.4. Using computational techniques one then determines the best values of/’1 and r2 that fit Eq. (7.24) to this experimental curve.
Table 7.1 MonomerReactivity Ratios in Radical Copolymerization Monomer (M1)
Monomer (M2)
rl
r2
T (°C)
Acrylic acid
Styrene Vinyl acetate
0.25 8.7
0.15 0.21
60 70
Acrylonitrile
Acrylamide Ethyl vinyl ether Methylacrylate Methyl methacrylate Styrene Vinyl acetate Vinyl chloride Vinylidenechloride
0.86 0.69 1.5 0.14 0.020 5.5 3.6 0.92
0.81 0.060 0.84 1.3 0.29 0.060 0.044 0.32
40 80 50 70 60 70 50 60
1,3-Butadiene
Methyl methacrylate Styrene Vinyl chloride
0.75 1.4 8.8
0.25 0.58 0.04
90 50 50
Ethylene
Acrylonitrile Tetrafluoroethylene Vinyl acetate
0 0.38 0.79
7.0 0.10 1.4
20 25 130
Maleic anhydride
Acrylonitrile Methyl methacrylate Styrene Vinylacetate Vinylchloride
0 0.01 0.005 0 0
6.0 3.4 0.050 0.019 0.098
60 75 50 75 75 .. (continued)
6O7
Chain Copolymeriza~ion Table 7.1 (Continued) r2
T (°C)
Monomer (Mr)
Monomer (M2)
rl
Methacrylic acid
Acrylonitrile Styrene Vinylchloride
2.4 0.60 24
0.092 0.12 0.064
70 60 50
Methacrylonitdle
Styrene Vinyl acetate
0.25 12
0.25 0.01
80 70
Methylmethacrylate
Styrene Vinyl acetate Vinyl chloride Vinylidene chloride
0.46 20.0 9.0 2.4
0.52 0.015 0.07 0.36
60 60 68 60
Styrene
Ethyl vinyl ether Vinylacetate Vinylchloride Vinylidenechloride
90 42 15 1.8
0 0 0.01 0.087
80 60 60 60
Vinyl acetate
Ethyl vinyl ether Vinyl chloride Vinylidenechloride
3.4 0.24 0.03
0.26 1.8 4.7
60 60 68
DatamostlyfromR. Z. Greenley,"FreeRadicalCopolymerization ReactivityRatios," pp 153-266in Chap.II in PolymerHandbook,3rd ed., (J. Brandrupand E. H. Immergut, eds.), Wileylnterscience, NewYork(1989).
Somerepresentative values of rl and r2 in radical copolymerization for a number of monomerpairs are shown in Table 7.1. These are seen to differ widely. The reactivity ratios obtained in anionic and cationic copolymerizations are given and discussed in Chapter 8. MONOMER AND RADICAL Resonance
REACTIVITIE,
S
Effects
The reactivity of a monomertoward a radical depends on the reactivities of both the monomerand the radical. The reactivities of various monomers can be considered by considering the inverse of the monomerreactivity ratio (l/r). The inverse of the monomerreactivity ratio gives the ratio of the rate of reaction of a radical with another monomerto its rate of reaction with its own monomer: 1/~1 = kl~/kll
(7.35)
608
Chapter 7
Table 7.2 Relative Reactivities (l/r) of Monomers with Various PolymerRadicals Polymerradical (reference) Methyl Vinyl Vinyl Monomer Acrylonitrile methacrylate Styrene Acetate Chloride Butadiene 50 4 1.7 29 Styrene 25 2.2 100 50 Methyl methacrylate 6.7 1.9 67 10 Methylvinyl ketone 1.7 3.4 20 10 Acrylonitrile 0.82 2.5 20 25 Methylacrylate 0.67 0.52 1.3 10 17 Vinylidenechloride 1.1 0.39 0.54 10 Vinylchloride 0.37 0.10 0.059 4.4 Vinylacetate 0.24 0.050 0.019 0.59 Valuesof 1/r calculated fromdata of Table7.1
Values of lit for different monomerpairs having the same monomeras M1 but different monomers as M2 would thus provide a comparison of reactivities of the M2monomers. Table 7.2 shows 1/r values calculated from the data in Table %1. The data in each vertical column show the monomerreactivities of a series of different monomerstoward the same reference polymer radical. (Note that the data in each horizontal row in Table 7.2 cannot be compared; the data can only be compared in each vertical column.) The monomershave been arranged in Table 7.2 in their general order of reactivity. The order of reactivity is approximatelythe same in each vertical columnirrespective of the reference radical. (The exceptions that occur are due to strong alternating tendency of certain monomerpairs.) Table 7.2 and other similar data of relative monomer reactivities indicate that substituents tend to enhance monomerreactivity according to the following order: -C6H5, -CH=CH2 > -CN, -COR > -COOR > --CI > -OCOR, R > --OR The order of monomerreactivities in the above series corresponds to the order of increased resonance stabilization (by the particular substituent) of the radical formed from the monomer.Substituents containing unsaturation are more effective in stabilizing the radicals because of the loosely held 7r-electrons, which are available for resonance stabilization. Resonance stabilization becomesmore significant in radical polymerization when the monomers contain conjugated C-C double bonds as in styrene, 1,3-butadiene, and similar molecules: H H H H H R*+ CH2=C--~ R-CH2-C’~’~’R-CH2-C~ R-CH2-.C~ R-CH2-C
06-6
(7.36)
Chain Copolymerization
609
Substituents such as halogen, acetoxy, and ether are increasingly ineffective in stabilizing the radicals because only the nonbondingelectrons on halogen or oxygen are available for interaction with a radical. Thus styrene has a radical whose resonance stabilization is high (84 kJ/mol) whereas vinyl acetate forms a very unstable radical. The spread in the effectiveness of the various substituents in enhancing the monomerreactivity is about 50-200 fold depending on the reactivity of the reference radical. The less reactive the radical, the greater is the spread in reactivities of the different monomers.The placement of a second substituent in the a-position, as in vinylidene chloride, lends an additive effect, provided steric hindrance does not dominate. As a reactive monomerforms a stable free radical, the radical reactivity will be the reverse order of the series given above. This means that monomerscontaining conjugated systems (styrene, butadiene, acrylates, acrylonitriles, etc.) will be highly reactive monomersbut will form stable and so relatively unreactive radicals. Conversely, nonconjugated monomers (ethylene, vinyl halides, vinyl acetate, etc.) are relatively unreactive toward free radicals but will form unstable and highly reactive adducts. A quantitative comparison of the order of radical reactivities can be obtained by multiplying the 1/r values in Table 7.2 by the appropriate propagation rate constants for homopolymerization (kll). This yields the values of k12 for the reactions of various radical-monomer combinations as shownin Table 7.3. The k12 values in any horizontal row in Table 7.3 give the order of radical reactivities toward a reference monomer.(The data in any vertical columnstill give the order of monomer reactivities, as was the case for the data in Table 7.2). It is seen fromTable7.3 that the order of radical reactivities is essentially the same irrespective of the monomerused as reference. The order of substituents in enhancing the radical reactivity, however, is seen to be the opposite of their order in enhancing monomerreactivity. A substituent that
Table 7.3 Rate Constants (k12) for Radical-MonomerReactions Polymerradical Monomer (M2) Methyl (Reference) Styrene methacrylate Acrylonitrile Butadiene 280 2,060 98,000 Styrene 165 1,130 49,000 Methyl methacrylate 314 515 13,100 Acrylonitrile 413 422 1,960 Methylacrylate 215 268 1,310 Vinyl chloride 9.7 52 720 Vinyl acetate 3.4 26 230 Valuesof k12 calculatedfromdata in Tables6.7 and7.2
Vinyl Vinyl acetate chloride 319,000 230,000 550,000 154,000 46,000 23,000 10,100 2,300
110,000 225,000 187,000 11,000 6,490
610
~]~ap~e~ 7
increases monomerreactivity does so because it stabilizes (and hence makes less reactive) the radical formed from the monomer. A consideration of data in Table 7.3 showsthat the effect of a substituent on radical reactivity is considerably larger than its effect on monomerreactivity. It thus turns out that resonance stabilization is more successful in suppressing radical reactivity than in enhancing monomerreactivity. Thus vinyl acetate radical is about 100-1000 times more reactive than styrene radical toward a given monomer, while styrene monomeris only 50-100 times more reactive than vinyl acetate monomertoward a given radical. These two effects tend to compensate each other as shownlSy the fact that the self-propagation rate constant (kp) for vinyl acetate is only about 16 times that of styrene (Table 6.7). Steric
Effects
The rates of radical-monomer reactions are also dependent on considerations of steric effects. It is observed that most common1,1-disubstituted monomers--for example, isobutylene, methyl methacrylate and methacrylonitrile-react quite readily in both homo- and copolymerizations. On the other hand, 1,2-disubstituted vinyl monomersexhibit a reluctance to homopolymerize, but they do, however, add quite readily to monosubstituted, and perhaps 1,1-disubstituted monomers.A well-known example is styrene (M1) and maleic anhydride (M2), which copolymerize with rl = 0.01 ~’2 = 0 at 60°C, forming a 50/50 alternating copolymer over a wide range of monomerfeed compositions. This behavior seems to be a consequence of steric hindrance. Calculation of k12 values for the reactions of various chloroethylenes with radicals of monosubstituted monomerssuch as styrene, acrylonitrile, and vinyl acetate showsthat the effect of a second substituent on monomerreactivity is approximately additive when both substituents are in the 1- or o~-position, but a second substituent when in the 2- or H-position of the monomerresults in a decrease in reactivity due to steric hindrance between it and the polymer radical to which it is adding. Polar Effects Monomerreactivity cannot be considered independent of radical reactivity and vice versa. One observes enhanced reactivities in certain comonomer pairs and this corresponds to an alternating tendency. Whicheverof the two radicals one might find at the growing chain end, the opposite monomeris always preferred in forming an alternating sequence. This behavior leads to the idea of a positive and a negative charge. Thus, if the radical containing end unit is positively charged, a negatively charged monomeris attracted and vice versa. Whether the addition of a monomerto a growing chain gives rise to a positive or a negative chain end depends on the substituents of the monomer. Thus, electron withdrawing (accepting) substituents, -C6H5,
611
Chain Copolymeriza~ion
-C1, -COOR, -CN, -COCH3, all decrease the electron density of the double bond in a vinyl monomer,whereas electron donating groups, e.g., -C~Hs, -CHa, -OR, -OCOCH3increase the electron density. (The phenyl group -C6H5 can be regarded as an electron acceptor as well as an electron donor. It becomesone or the other by inductive effects.) Thus monomerssuch as vinylidene chloride, acrylic esters, and acrylonitrile are polarized in such a way that the vinyl groups represent the positive part, and the substituents the negative part of a dipole:
CHz~C
tiCe
\ct’-
CH~CH--C-O-CHa
CH~CH-C~N
On the other hand, monomerssuch as styrene or vinyl ethers are polarized in the opposite sense such that the vinyl groups represent the negative part, and the substituents the positive part of a dipole:
~
2~CH
CH2~- CH
C 3 The polarity of any species is independent of whether it is in monomer or radical form for the free radical is a neutral entity. Thus assumingthat the above types of polarization are also possible with radicals, one can understand that a chain end at which there happens to be a structural unit with an electron-withdrawing substituent, prefers a monomerwith an electron-donating substituent and vice versa. Such consideration of polarity explains that, for example, acrylonitrile forms statistical copolymers with methyl acrylate (rlr2 = 1.26), while copolymerization of acrylonitrile with ethyl vinyl ethers leads to alternating structures (fir2 = 0.04). However, the opposite polarization caused by the electron-donating or electron-withdrawing substituents is not the only factor governing the reaction of monomersand radicals in copolymerization. Thus the magnitude of the resonance stabilization and in some cases steric hindrance are important too, and the actual behavior of the monomertherefore results from the overlapping of the three factors.
Problem7.9 Explain the following copolymerization results or observed behaviors considering the influence of resonance, steric, and polar effects on monomer reactivity: (a) Vinyl acetate and vinyl chloride are the most favored copolymerization componentsfor vinyl ethers, but both of themare reluctant to copolymerizewith styrene. (b) Neither maleic anhydride nor diethyl fumarate forms homopolymers but both react with styrene and vinyl ethers to form alternating copolymers. (c) In copotymerization, vinylidene chloride monomeris 2-10 fold more reactive whereas1,2-dichloroethyleneis 2-20 fold less reactive, as comparedto vinyl
612
Chapter 7
chloride. !d) Althoughthe reactivity of 1,2-dichloroethylenein copolymerizationis low, it Js still muchgreater than their reactivity in homopolymerization. 1,2-Disubstituted ethylenes do not homopolymerize. Ans wet: (a) Vinyl ethers have low resonancestabilization. In copolymerizationwith vinyl ethers, one should probably choose those monomerswhich have equally low resonancestabilization, but, if possible, no polarization, or only one of opposit~ sign. Thusvinyl chloride and vinyl acetate, whichhavelow resonancestabilization and also low polarity, should be chosenas copolymerizationcomponentsfor vinyl ethers. Styrene, on the other hand, has high resonance stabilization. A styryl radical therefore does not add a vinyl chloride or vinyl acetate monomer as this wouldlead to the formation of a higher energy radical. (b) Both maleic anhydride and diethyl fumarate do not form homopolymers due steric hindrance.But both react with styrene and vinyl ethers of oppositepolarities which help to overcomesteric hindrance and lead to the’formation of alternating copolymers. (c) The difference maybe attributed to steric hindrance. The effect of a second substituent on monomer reactivity is approximatelyadditive whenboth substituents are in the 1- or s-position. However,a second substituent whenin the 2- or flposition of the monomer results in a decrease in reactivity due to steric hindrance betweenit and the radical to whichit is adding. (d) The steric hindrance betweena fl-substituent on the attacking radical and substituent on the monomer is responsible for the inability of 1,2-disubstituted ethylenes to homopolymerize. The reactivity of 1,2-disubstituted ethylenes toward copolymerizationis due to the lack of fl-substituents on the attacking radicals (e.g., styrene, acrylonitrile, andvinyl acetate radicals).
The Q --
e Scheme
All the above factors controlling monomerand radical reactivities contribute to the rate of polymerization, but in a manner which makes it difficult to distinguish the magnitude of each effect. Attempts to correlate copolymerization tendencies based on these factors are thus mainly of a semiempirical nature and can, at best, be treated as useful approximations rather than rigorous relations. However,a generally useful schemewas proposed by Alfrey and Price [23] to provide a quantitative description of the behavior of different monomersin radical polymerization, with the aid of two parameters, for each monomerrather than for a monomerpair. These parameters are denoted by (~ and e and the method has been called the Q -- e scheme. It allows calculation of monomerreactivity ratios rl and r2 from properties of monomersirrespective of which pair is used. The scheme assumes that each radical or monomercan be classified according to its reactivity or resonance effect and its polarity so that the rate constant
Chain Copolymerization
613
for a radical-monomer reaction, e.g., the reaction of MI" radical with M2 monomer, can be written as kt2 = P1Q2exp(-ele~) (7.37) where P1 is considered to be a measure for the reactivity of radical MI" and Q a measure for the reactivity of monomerM2; e~ and e2, on the other hand, are considered to represent polar characteristics of the radical and monomer,respectively. By assuming that the same e value applies to both a monomerand its radical (that is, el defines the polarities of M1and MI", while eg~ defines the polarities of M~and M2", one can write expressions for kll, k22 and k21 analogous to Eq. (7.37). These can be appropriately combinedto yield the monomerreactivity ratios. Thus for kl~ one can write by analogy to Eq. (7.37), kll = PIQl exp(-elel) (7.38) Therefore, ku Q~ exp[-e~ (el - e2)] (7.39) rl -- k12 -- Q2 Thus the effects of radical activity cancels, and rl can be expressed analytically in terms of parameters independent of the paired interdependence of M1 and M2. (Note that in any ~ven pair of monomers, the monomer cited first is considered as M1and the other as M2.) An expression for r2 is similarly obtained, viz., k~2 Q2 exp[-e2 (e2 - el)] (7.40) r2- k21 -- Q1 Thus rl and r2 can be calculated from Qand e values of monomers forming the pair. Equations (7.39) and (7.40) permit us to calculate Q and e va lu es for single monomers from the values of rl and r2, provided we have one monomerfor which Q and e have been arbitrarily established. Price chose styrene as the standard monomer with the values Q = 1 and e ---- --0.8. One can then calculate the Q and e values of any monomer that has been copolymerized with styrene from the rl and r2 values of the copolymerization of styrene with particular monomer. Knowingthe Q and e values of these various monomers, one can then calculate the Qand e for any monomerthat has been copolymerized with these monomers, that is, where rl and r2 are known. Extensive tabulations of Qand e values for monomersthus exist in the literature. Table 7.4 gives a selection of Q and e values for some of most commonmonomers. As a general rule, monomers with electron-rich double bonds have more negative e values and those that form highly resonance-stabilized radical have higher Q numbers. As noted earlier, Q is a measure for the reactivity of a monomer.However, this reactivity is greater, that is, the readiness of the monomerto undergo reaction forming a radical is greater, the greater the resonance stabilization
Chapter 7 Table 7.4 Q - e Values Monomer e Q Ethyl vinyl ether - 1.17 0.03 Butadiene - 1.05 2.39 Styrene (reference standard) - 0.80 1.00 Vinyl acetate - 0.22 0.03 Ethylene - 0.20 0.01 Vinyl chloride 0.20 0.04 Vinylidene chloride 0.36 0.22 Methyl methacrylate 0.40 0.74 Methyl acrylate 0.60 0.42 Acrylic acid 0.77 1.15 Methacrylonitrile 0.81 1.12 Acrylonitrile 1.20 0.60 Methacrylamide 1.24 1.46 Maleic anhydride 2.25 0.23 Source: Data from R. Z. Greenley, "Q and e Values for Free Radical Copolymerizations of Vinyl Monomersand Telogens," pp 267-274 in Chap. II in Polymer Handbook(J. Brandrup and E. H. Immergut,eds.), 3rd ed., Wiley-Imerscience, NewYork (1989). of this radical. Therefore, Q must also be a measure for the resonance stabilization of the radical formed from the monomer. Using the tabulated Q and e values for any two monomers, one can calculate the ’P1 and r2 values from Eqs. (7.39) and (7.40) for this monomer pair whether or not they have ever been polymerized.
Problem7.10 Calculate the rl and r2 values for the monomerpair styrene(M1)acrylonitrile(M2)
from the tabulated Q and e values.
Answer: From Eq. (7.39), 1.00 r~ = --exp[0.S0(-0.S0 - 1.20)] 0.60 (cf. exptl, rl = 0.29) = 0.336 From Eq. (7.40), 0"60exp[-1.20(1.20 r2 = 1.0----~ = 0.054 (cf.
exptl,
+ 0.8)1 r~ = 0.03)
Until the appearance of the Alfrey-Price necessary to refer relative monomerreactivity
Q -- e scheme, it has been ratios to the particular two-
615
Chain Copolymeriza~ion
component system investigated. By means of two constants Q and e, the Alfrey-Priee scheme enables calculation of reactivity ratios of any vinyl monomer with any other vinyl monomer whose (~ and e parameters are known. The Q--e prediction scheme is not quantitatively reliable. But when regarded as an empirical tool for predicting copolymerization behavior, the Q -- e scheme is of the utmost utility qualitatively, for predicting copolymerization behavior and for obtaining approximate estimates of rl and r2 values.
Problem7.11 Predict the type of copolymerization
behavior that would be expected for the following monomerpairs: (a) Both monomers have low Q values and the e values are of opposite signs (example: ethyl vinyl ether and vinyl chloride). (b) One monomer has a large Q value and the other has a small Q value (example: styrene and vinyl chloride). (c) Both monomers have similar Q values and also similar e values (example: styrene-butadiene). (d) Both monomers have approximately the same Q value and high e values opposite sign (example: styrene-methacrylonitrile). Answer: (a) This condition favors good copolymerization. Both components will occur significant amounts in the copolymer chain. (b) The addition of a radical chain with high resonance stabilization (large Q) monomerwith a small Q value leads from a stable (energy-poor) state to an unstable (energy-rich) state, which on thermodynamic grounds is not very probable. Thus the two monomerswill not copolymerize well. The monomer-polymer composition curves also will deviate widely from the azeotrope line. (c) Since both monomershave similar reactivities and similar polarities, nearly ideal copolymerization will occur. This is also evident from the product of reactivity ratios rx and r 2 expressed by Eqs. (7.38) and (7.39) which give 2 ~exp[-(el - e2)2]. For el --~ e2, rar2 ----- 1 indicating ideal copolymerization. (d) The monomerswill show tendency to alternating addition (inflection point curves). For high e values of opposite signs the value of rlra from Eqs. (7-39) and (7.40) is very small indicating alternating behavior.
SEQUENCE
LENGTH
DISTRIBUTION
The copolymer equation (7.11) describes the copolymer composition only on a macroscopic scale, that is, the overall mole ratio or mole fraction of monomer units in a copolymer sample produced from a comonomer feed. It does not reveal details of molecular level composition or microstructure, that is, the manner in which the monomer units are distributed in the
616
Chapter 7
copolymer. Thus for two monomers M1 and M2, the ratio F1/(1 - F1) gives the overall mole ratio of M1and M2units in the copolymer but no information concerning the average lengths of the -(-M1-)n- and -(-M2-)nsequences in a typical copolymeras illustrated by - M1-M1-M1-M1-M2~-M1-M1-M2-M2-M2-M1-M1-M1
-
where the sequences are underlined. A completely random placement of the two monomerunits along the copolymer chain occurs only for the case rl = r2 = 1. There is a definite trend toward a regular microstructure for all other eases. For example, if r~ > 1, once a propagating species of type M~is formed it will tend to a sequence of M1units. However, there is a random aspect to copolymerization due to the probabilistie nature of chemical reactions. Thus an rl value of 2 does not imply that 100%of all M1units will be found as part of long sequences of M1. Though a very large fraction of M1units will be found in such a sequence, a small fraction of M~units will be randomly distributed. Similar arguments hold for M2 sequences if r2 > 1. The microstructure of a copolymeris defined by the distributions of the various lengths of the M1 and M2sequences, that is, the sequence length distributions. The probabilities or mole fractions nz(M1) and nz(M2) forming M1 and M2 sequences of x are given by (see Problem 7.1 for derivation), nz(M~)
PI F-1Pjt~
nx(M2)
= P~2z-1P~I
(7.41) (7.42)
where the probability (P) values are defined by,
Pll ~-rl[M1] rl[M1] _ "rlfl rill-~ f2 nI- [M2] P12 = rl[M1] [M21 q-[M21_rlflf2 + f2 r2f2 _ P22"- [M~] r2[M2] + ,’2[Mqfl +
(7.43)
P~I = [M]I[M1] + ,’2[M2]_fl fl+
(7.46)
(7.44) (7.45)
Equations (7.41) through (7.46) allow one to calculate the mole fractions different lengths of M~and M~sequences. Such calculations reveal that for a feed composition other than equimolar, thedistribution becomesnarrower for the monomerpresent in lower amount and broader for the monomer present in larger amount. This is a general phenomenonobserved for all sequence distributions.
Chain Copolymerization
617
Problem 7.12 The sequence length distribution for a copolymerization system can be described by the mole fractions of sequences with 1, 2, 3, 4, 5, 6, ...., M1 or M2 units in a copolymer and plotting against sequence length in a bar graph. Describe such distribution for an ideal copolymerization with equimolar feed composition considering two cases: (a) rl = r2 = 1 and (b) x =5, r2 = 0.2. Answer: (a) For the system I =r 2= 1 , fl = 0.5 , Eqs . (7. 43)-(7.46) giv e Pll = P1 P2~ = P~ = 0.50. The values of n~(Ma) calculated from Eq. (7.41) are 0.50, 0.25, 0.125, 0.0625, 0.0313, 0.0156, and 0.0078 for sequences with 1, 2, 3, 4, 5, 6, and 7 M1units, respectively. A bar graph is shown in Fig. 7.7(a). Thus, although the most plentiful sequence is single M~at 50%, there are considerable amounts of other sequences: 25%, 12.5%, 6.25%, 3.13%, 1.56%, and 0.78%, respectively, of dyad, triad, tetrad, pentad, hexad, and heptad sequences. The distra"oution of M2sequences is exactly the same as for M1sequences. (b) For the system r~ = 5, r2= .2 f~ = 0.5. Equations (7.43)-(7.46) PI~ = P21 = 0.8333 and P12 = P220=’ 0.1667. The values of n~(M1) calculated from Eq. (7.41) are 0.167, 0.140, 0.116, 0.097, 0.081, 0.067, and 0.055 for sequences with 1, 2, 3, 4, 5, 5, and 7 M1units, respectively. A bar graph is shownin Fig. 7.7(b). It is seen that the single M1sequences are again the most plentiful but only at 16.7% and the sequence-length distribution is also broader than for rl = r2 = 1 of case (a). There are small amounts of relatively long sequences; 3.2% of 10unit, 1.3% of 15-unit, and 0.4% of 20-unit M1 sequences. The sequence-length distribution for the less reactive M2 monomer,calculated from Eq. (7.42) and shown in Fig. 7.7(b) is seen to be muchnarrower. Single M2units are by far the most plentiful (83.3%) with 13.9% dyads, 2.3% triads, and 0.39% tetrads.
Problem7.13 Consider an alternating
copolymerization with r 1 = ?’2 = 0.1 and fl = 0.5. What percentage of the alternating copolymer structure is made of M~M~ sequence ? Compare the sequence length distribution with that for the ideal copolymer in Problem 7.12(a) which has the identical overall composition. Answer: For the system with rl = r2 = 0.1 and fl = 0.5, Eqs. (7.43)-(7.46) P~I = P22 = 0.0910; P12 = P21 = 0.9090. Therefore, the sequence length distributions for both monomerunits are identical. The single M1and single Mz sequences are overwhelmingly the most plentiful at 90.9% each. Thus the M1Mz sequence comprises 90.9% of the copolymer structure. From Eqs. (7.41) and (7.42) the dyad and triad sequences are 8.3% and 0.75%, respectively, for both and M2. The large difference between this distribution and the distribution in Fig. 7.7(a) for a randomcopolymerhaving identical overall composition clearly indicates the difference between alternating and ideal behavior. The ideal copolymer with an overall composition of F1 = F~ = 0.5- has a microstructure that is very different from that of a predominantly alternating copolYmer.
618
Chapter 7
1.0
1.0
0.8
0.8
nx(M I) ~ nx(M2) ....
c 0.40.2-
2 3 4 5 6 "~ 8 Sequencelength (x)
2 3 4 5 6 7 Sequencelength (x)
(a)
(b)
Figure 7.7 Sequencelength distribution for an ideal copolymerization with (a) r1 = r~ = 1, fl = f~ and (b) ~’1 = 5, r2 = 0.2, fl = f> [In (a) the distribution M2sequencesis not shownas it is the sameas for Mt sequences. In (b) the plots of n~(M2)(---) are shownslightly to the left of the actual sequence length.]
The average sequence lengths ~(M1) and ~(M2) may also be determined from Eqs. (7.41) and (7.42). Wehave already derived these expressions in Eqs. (PT.l.ll) and (P7.1.12): ~(M1) : 1 + ?’I[M1] E(M2) ----
1 -t-
--
r2[M21 [M1]
1 + I ( fl/f2)
(7.47)
_ 1 Jr r2(f2/fl)
(7.48)
The run number, NR of the copolymer is defined as the average number of sequences of either type per 100 monomerunits. Considering, for example, a hypothetical copolymer shown below, in which the sequences are underlined, M2-M1-Mt-M2-M1-M2-M2-M1-Mt-M1-M2-M;-M1-M1-M2-M2-M2-M2-M1-M~ the number of sequences are 10 and there are 20 monomerunits. Hence NR= 50. A larger run number indicates a greater tendency toward alternation. For a perfectly alternating polymer NRis 100.
Chain Copolymerization
619
The rate of sequence formation, dS/dt, regardless of length, is simply the rate at which sequences are ended. Assumingthat the molecular weight of the polymer is fairly large so that chain termination can be neglected, this is given by dS -- k12 [M~I[M2] q- k21 [M~I[MI] (7.49) dt The total rate of polymerization is given by d([M1] q-[M2])
= kll [M~][M1] q- k12 [M~][M2] q- k21 [M~][M1] q- k22 [M~[Mg.]
(7.50)
Elimination of dt by combination of Eqs. (7.49) and (7.50) and use of steady-state approximation [cf. Eq. (7.6)] yields d([Ml] q- [M2]) kll[M1] q- k12[M2] ]~22 [M2] q- /~21 [M1] = + dS 2k12 [M2] 2k21 [M1]
(7.51)
or
d([M1 q-[M21) = 1 q- rl[Ml_ ] q- r2 [M2] dS 2 [M2]2 [M1]
(7.52)
Since the run number is the average number of sequences per 100 monomer units, this maynowbe written as NR = 100 --d([Ml] which after substitution yields
+ [M~])
of Eqs. (7.52) followed by Eqs. (7.47) and (7.48) 2OO
2 q- rl([M1]/[M2])
2O0 -b r2([M2]/[M1])
~(M1) q-
(7.54) Equations (7.47), (7.48), and (7.54) indicate that a knowledgeof [M1] fl), [M2] (or f2), rl, and r~ enables a prediction to be made, not only of the average copolymer composition [from Eqs. (7.11) or (7.18)], also of the average sequence length of each monomer and the average number of sequences of monomerunits per unit length of copolymer. As many significant properties of the copolymers depend on the distribution of monomeralong the chains, the ability to make such predictions from a relatively small amountof experimental data can be very useful indeed.
620
Chapter 7
Problem7.14 Vinyl acetate (3.0 M) is copolymerizedwith vinyl chloride (1.5 M) in benzene solution by adding azobisisobutyronitrile to a concentration of 0.1 Mand heating to 60°C. Calculate for the copolymerinitially formed(a) the probability of formingvinyl acetate and vinyl chloride sequencesthat are 3 units long, (b) the average sequencelengths of vinyl acetate and vinyl chloride in the copolymer, and (c) the run numberof the copolymer. 1 = 0.24, r2 = 1.80] Answer: (a) f~ = (3.0 M)/(3.0 M + 1.5 M) = f2 = 1-0.67 = 0.33 From Eqs. (7.43)-(7.45): Pll = 0.3244, P12 = 0.6756, P~2 = 0.4736, P~I = 0.5264. From Eq. (7.41): n3(M1) = (0.3244)3-~(0.6756) From Eq. (7.42):
nz(M2) = (0.4736)z-~(0.5264)
(b) FromEqs. (7.47) and (7.48): 5(M~) = 1 (0.24)(0.67/0.33) = 1. 48 5(M~) = 1 + (1.80)(0.33/0.67) (c) From Eq. (7.54): Nn = 200/(1.48 + 1.90) =
RATE
OF FREE-RADICAL
COPOLYMERIZATION
In the derivation of copolymer composition equation, Eq. (7.11), considered only the rates of the four possible propagation steps in a binary system. However, the overall rate of copolymerization depends also on the rates of initiation and termination. In deriving an expression for the rate of copolymerization in binary systems the following assumptions will be made [25]: (a) rate constants for the reaction of a growing chain depend only upon the monomerunit at the growing end, and not upon chain length or further composition; (b) steady-state conditions apply both to the total radical concentration and to the separate concentrations of the two radicals; (c) chain termination is by bimolecular radical reaction. By assumption (a) the overall rate of monomerdisappearance is given by [cf Eqs. (7.7) and (7.8)I: d ([Mx] + [M2]) = kll [MI’] [MI] q- ]g21 [M2"] [M1] q- ]g12 [MI’] [M21
+ IMp]
(7.55)
621
Chain CopolTmerizafion
where [M1] and [M2] are concentrations of the two monomers, [MI’] and [M2"] are concentrations of chain radicals ending in M1and M2units, respectively, and k~l is the rate constant for attack of a chain radical ending in Mz unit upon monomerM~,etc. By assumptions (b) and (c) and defining an overall termination rate constant kto, two steady-state assumptions may also be written as ]¢12 [MI’] [M2] ~--- k21 [M2"] [M1] Ri -~ Rt 2~--- 2]et~ ([MI’] ~t. [M2.])
(7.56) (7.57)
where R/ is the overall initiating rate and Rt is the overall termination rate. Solving Eqs. (7.56) and (7.57) simultaneously for [MI’] and [M2"] substituting into Eq. (7.55) we obtain d([M1]-a u [M2]) __ /~/:~(rl[M1] 2 2) + 2[M1][M2]q- r2 [M2] dt -- (2]et~)l/2(r, [Mll/kll ~t_ r2[M2]/k22 )
(7.5s) where rl and r2 are the monomerreactivity ratios given by the propagation rate constant ratios kn/k12 and k2~/k2l, respectively. If the cross-termination rate constant, that is, the rate constant for termination of radical MI" with radical M2-is kfl2, then the steady-state for the total concentration of radicals can also be written as 1~ = Rt = 2~11 [MI’] 2 W 2kt12 [MI’] [M2"] q- 2~22 [M2"] 2 (7.59) If we define mole fractions of the respective radicals as/~ and ~2, that is, ~1
=
[MI’] and ---- i -- = [M2"] [MI’]q-[M2"] [MI’] -F[M2"] (7.60)
then from Eqs. (7.57), (7.59) and (7.60)
R,
- 2 (~11~12
([MI’]-1-[M2"])
2 --
-t-
kt12~1~2
q- k~t22~)
(7.61)
whence ]¢,to
= /gt11~L12 nu ]gt12~l~2 J~- ]¢,t22~/-~
Nowwe define a cross-termination
(7.62)
factor as
¢ = ktl2 / 2(ktll
1/2 k,~22)
(7.63)
622
Chapter 7
to represent the rate constant for cross-terminationrelative to the geometric meanof the rate constants for chain termination of each monomer alone. Its value > 1 is thus indicative of the preference for cross-termination over homotermination.Equation(7.58) then assumesthe following familiar form of the so-called "chemicalcontrol" model: (d[Ml] q- d [M2I) d~:
(rl[Ml] 2 + 2[M~I[M~I+ r2[M212)Pt~/2 (9"1~ [M1]2 1/2 q- 2~brlr2~l~[M1][M2] q- ~2~22[M212)
(7.64) where~t and ~2 represent the termination-propagationrate constant ratios given by ~1 (2k,,t11/"’11)
, ~2 = (2k,
t22
/ k222) 1/2
(7.65)
Equation(7.64) can also be derived from Eq. (7.55) by eliminating radical ¯ concentrationswith the help of twosteady-state assumptionswritten as Eqs. (7.56) and (7.59). Equation (7.64) represents a one-parameter model the copolymerization rate [8] containingthe parameter~b. Statistically, ~b is expectedto equal unity.
Problem7.15 Show that if reaction probabilities
of radicals depend only on encounter rates and are independent of the nature of the radicals, ~ should equal
unity. A rlsw~3,F :
For simplicity consider a reaction mixture in which [MI"] = [M2"]. Since MI" ° radicals with equal frequency and since radicals will collide with M2"and M1 the same applies to M~"radicals, the frequency of M~" - M~’encounters is twice that of MI° -- M~" or M2"-M2"collisions. If the reaction probabilities’depend only on encounter rates, P~12
(/~n P’-tzz) 1/2 -- 2 where
= 2&n [Mx’] -~n ~ /~2 2= 2/~= IMp’]
Thus, ktl2
~ = ~(ktn&~2)~/2 -
Chain Copolymeriza~ion
623
In practice, ¢ can be calculated by inserting experimental copolymerization rates into Eq. (7.64). The values of ¢ thus obtained are frequently greater than unity, and these deviations are ascribed to polar effects that favor cross-termination over homotermination. However, this is not always unambiguous, since the apparent cross-termination factor may vary with monomerfeed composition in a given system [25,26]. It is clear also that termination reactions are at least partially diffusion controlled [27,28]. A dependenceof segmental diffusivity on the structure of macroradicals is to be expected and dependence of diffusion controlled termination on copolymer composition seems reasonable. It is therefore plausible that the value of the overall termination rate constant kt0 in copolymerizations should be functions of fractions (Ft and F2) of the comonomersincorporated in the copolymer. An empirical expression for kt0 has thus been proposed [27]: kt0 = F1]¢,~11 Jr F2/c, t22 (7.66) that represents kto as the average homotermination rate constants weighted on th~ basis of mole fractions F1 and /w2 of the respective monomersin the copolymer; F1 and /w2 can be calculated from the feed composition by the copolymer composition equation [Eq. (7.18)]. Equation (7.58) combination with Eq. (7.66) provides a model for diffusion-controlled reactions with no adjustable parameters (such as ¢ in chemical controlled model). No strong theoretical case can be made for the relationship in Eq. (7.66). It fits some, but not all, of the copolymerization systems to which has been applied. A better fit is often provided by a combined model [29] which uses the parameter ¢ of the chemical control model in combination with an empirical formulation for ~0 related to copolymer composition. The empirical formulation is derived by substituting mole fractions of each monomerfor the radical mole fractions/Zl and h2 in Eq. (7.62) 2 tz2F2 kto = ktl~,Fx 2 + k,t~2F~,F2 + k, (7.67) Combination with Eq. (7.63) then yields ]¢to ---- ktllF12 Jr 2¢(]et11~22)l/2Fl-b-’2 Jr ]¢t22-b-’2 2 (7.68) Equations (7.58) and (7.68) yield the rate of copolymerization, and ¢ be taken from previous studies of the chemical control model, or from an empirical correlation between this parameter and the rlr2 product [27] which is based on the fact that ¢ more or less parallels 1/rxr~ as a measure of the increased preference for cross-termination over homotermination. Direct measurements of ¢ have been obtained [26] by measuring the absolute values of the rates of propagation and termination in pure monomersand in mixtures of various compositions. In the case of styrene-p-methoxystyrene, ¢ = 1, indicating that no polar or other influences favor cross-termination. In most cases, however, cross-termination is
624
Chapter 7
markedly favored, with ¢ varying over a wide range. For styrene-methyl methacrylate, for example, ¢ is 15, while for styrene-butyl acrylate ¢ is 150.
Problem7.16 Bulk polymerization
of styrene in the presence of 1 g/L of AIBNinitiator at 60°C gave a measured polymerization rate of 5.92 mol/Ls. Predict the rate of copolymerization at 60°C of a mixture of styrene (M1) and methyl methacrylate (M2) with 0.579 mole fraction styrene and the same initial concentration of the initiator as in the homopolymerization case. Comparethe rates predicted from chemical control, diffusion control, and combined models with the experimental value of 4.8x10-~ mol/L-s [25]. Use relevant kp and kn values for homopolymerization from Table 6.7 and assume ¢ = 15. [Other data: rl = 0.52, r2 = 0.46; monomerdensity = 0.90 g/cma.] Answer: kll = (kr,)styrene = 165 L mo1-1 -1 ktll --~ (kt)styrene = 6xl0r L tool -1 s-I k2~ = (kp)MMA -1 = 515 Lmo1-1 s kt~ = (kt)MMA = 2.55X107 L mo1-1 -1 For bulk styrene, For styrene -1 mol L
[M] = (1000 cma L-l)(0.90 -1) (104 g tool
g -a)
(M1)-MMA(M2) feed of 0.579 mole fraction
= 8.70
mol L_ 1
styrene,
[M~] =
For styrene homopolymerization [cf. Eq. (6.25)],
1~ =
[M]2 2(5.34 × 10-s mol L-1 s-l) 2 (6 × 107 L mo1-1 -1) (165 L tool -~ s-l) 2 2(8.70 tool L-l)
=
1.66 × 10-7 mol L-1 -1 s
Chemical Control Model For copolymerization, written as
Eq.
d([M1] + [Mz])
dt
(7.64) for chemical control model is conveniently
’
(r1612a~ + 2~rlr~¢S182c~+ r2822
(P7.16.1)
where a = mole ratio of M1 and M2 in feed = 0.579/0.421 = 1.375, rl = 0.52, rz =0.46, /~i = 1-66 x10-7 molL-is-~, ~b= 15
625
Chain Copolymerization 1/2 I2(6 x 107 L tool-’ s-l)] ~1
~ ["
’/ ~ ~ =
TX~g
[
~"
~Ol--~’i"
~l~~i
"~-1~
J
J
1/2 ~--
oi-’ = 13.87
66.39
mol
tool
sl/2 L_1/2 Sill L_,/1
Substituting the values in Eq. (7.16.1), - d( [M,] + [M~] )/dt = 5.~ x 10-~ mol L-1 s-’ Diffusion Control Model Substituting appropriate values in Eq. (7.18), F1 = 0.5624, F1 = 0.4376. From Eq. (7.66), ~o = (0.5624)(6 x 107 L tool -1 s-i) + (0.4376)(2.55 x 107 L mo1-1-1) -1 = 4.49 x 107 L mo1-1 s Equation(7.58) can be conveniently written in the form n112(rl~2 --[- 20~+ "2) [M1] d( [M1] + [M2]) (v7.16.e) (2~)~/~ ~ (r~lk~l + ~1~)~ where a is the mole ratio of M1and M2= 1.375. Substituting appropriate values in Eq. (P7.16.2), - d( [M,] + [M~] )/dt = 12.7 mol L-’ Combined Mode! From Eq. (7.68) with ¢ = 15, ~o = 31.26x107 L mo1-1-1. FromEq. (P7.16.2), - d( [Ml] + [M2] )/dt = 4.8 x 10-~ mol L-1 -i s Comparison (P~)copolym× 105 Chemical control model Diffusion control model Combined model with ¢ = 15 (no parameter) with ~ = 15 Exptl: 4.8
5.4
12.7
4.8
MULTICOMPONENT COPOLYMERIZATION There is considerable interest in multicomponent copolymer systems. An example of terpolymerization, that is, copolymerization of three monomers,
626
Chapter 7
is the radical polymerization of styrene with acrylonitrile and butadiene whichallows muchgreater degree of variation in properties than what can be achievedby binary copolymerizationof styrene with acrylonitrile or with butadiene. Manyother commercialuses of terpolymerization exist. In most of these the terpolymerusually has two monomers present in major amounts to obtain the gross properties desired, with the third monomer in a minor amountfor modification of a special property. Thus ethylene-propylene elastomers have minor amountsof a diene as a third componentto allow the product to be subsequentlycross-linked. The quantitative treatment of terpolymerization is morecomplexthan two-componentcopolymerization though the method is similar. In the copolymerization of three monomersM1, M2, and M3there are three different types of growingchain ends v,~vMl", v, wvM2", and v~wM3". Each of these can react with any of the three monomers of the system, and hence there are nine different chain propagation reactions, as shownbelow: Reaction VWMl"-1- M1 ~ vwMl" VWMl’-}- M2 ~ vwM2" vwM1" q- M3 ~ vwM3" vwM2"~ MI ~ WVMl" wvM2" ~ M2 ~ vwM2" vwM2" q- M3 ~ vwM3" wvM3" nt- M1 ~ vwM1" ~vM3"-~- M2 ~ wvM2" vwM3" q- M3 ~ vwM3"
Rate d[M1]/dt
d
= /ell
[M,’I
d M3]/dt =
d M1]/dt = ]~21 - d ~]/dt = -d iM~]/dt=
[MI’] [M3] [M2"] [MI] [M2"] [M2]
(7.69)
[M2"][Mal
-- d M1]/dt = ~1 - d M~]/dt =
- d M~]/dt=
and six monomer reactivity ratios, r12
w
r21
--
~31 ~
kll k12 k22
k2~ k3~ k~
r13 = ~ kl--~ k22 r23 w r32
~
k23’ k33 k~2 ’
(7.70)
are involved(as well as six terminationreactions). The equations for the rates of monomerconsumptionsare
-d[M1]/dt= kn[MI"][M~] + k21[M2"][M1] + ka[M3"][Mx] (7.71) -d[M2]/dt
= kl2[Ml’][M2]-]-
]g22[M2"][M2]
~-/~32[M3"][M2]
(7.72)
--d[M3]/dt
= kl3[MI’][Ma]
+ k23[M2"][M3]
+ k33[M3"][M3]
(7.73)
627
Chain Copolymerization
As in the case of binary copolymerization, we do not know the absolute values of the radical concentrations [M]I", [M]2", and [M]3", but we can derive the steady-state relationships for these unknownconcentrations. Thus since in steady state, radicals of the type wwvMl" are formedjust as fast as they are converted to types vwvvM2"and vvwvM3",we may write ~12 [MI’] [M2] -Jr- ~13 [MI’] [M3] = k21 [M2"] [M1] q- /g31 [M3"] [MI] (7.74) and likewise for radicals of types vwwM~and vwwMa" : ]g21 [M2"] [M1] q- ]g23 [M2"] [M3]
k12 [MI’] [M2] q- k32 [M3"] [M21 (7.75)
]¢31 [Ma’] [M1] 4- ]¢a~ [M~’] [M~]
k13 [MI’] [M3] q- k23 [M2"] [M31 (7.76)
Combining Eqs. (7.74)-(7.76) with following composition relations:
(7.71)-(7.73)
we can obtain
d[M~] : d[M~] : d[M~] = [MI]-
:
[M~_~]IMpel [MI]-Jr-
q’-Jrr31r23 ~ V31V21 r21r32
[ r12r31
r13r21
+
r12r32
r23r12
÷
/
r32r13- [J
r13’~23
q’r12
-r13 J
+ ÷ /
~
r21
r23 J
~al
~a2
(~.zz) A simpler expression for the terpolymer composition has been obtNned [30] by expressing the steady state with the relationships:
k12[MI’] [M2] = k21[M2"] [M1] k23 [M2"] [Ma] = ka~[Ma’] [Mel k31[M3"] [MI]= k13[MI"] [M3] instead of Eqs. (7.74)-(7.76). The combination of Eqs. (7.78)-(7.80) Eqs. (7.71)-(7.73) yields the terpolymer composition
(7.78) (7.79) (7.80)
628
Chapter 7
d[M1] : d[M2] : diM3]
The conventional [Eq. (7.77)] and simplified [eq. (7.81)] terpolymerization equations can be used to predict the composition of a terpolymer from the reactivity ratios in the two-component systems M1/M2, MlfM3, and Mz/Ma. The compositions calculated by either of the terpolymerization equations show good agreement with the experimentally observed compositions. Neither equation is found superior to the other in predicting terpolymer compositions. Both equations have been successfully extended to multicomponent copolymerizations of four or more monomers [30,31].
Problem7.17 The ternary copolymerization
of a monomer mixture containing 35.92, 36.03, and 28.05 tool% of styrene, methyl methacrylate (MMA)and acrylonitrile (AN) at 60°C for 3.5 h yielded at 13.6 wt%conversion a polymer product which analyzed C 78.6% and N 4.68% (by wt.) [31]. Calculate the initial ternary copolymer composition to compare with the composition obtained by the analysis. Answer: Let the mol%composition of the copolymer be ~, y, and z for styrene (CsHs), MMA(CsHsO2) and AN (C3H3N), respectively. From C and N mass balance andx q- y + z = 100, one obtains x = 45.0, y = 25.6 andz = 29.4. From Table 7.1, Styrene (M1)/MMA(M2) : r12 = 0.52, r21 = Styrene (M1)/AN (M3) : rla = 0.29, rzl = 0.020 MMA(M2)/AN (M3) : r2z = 1.3, r32 = Rewriting Eq. (7.77) A = fl
as d[M1] : diM2] : d[Ma] = A : B : C, where +
+
’r21~’32 ’Y127"32
Yl
d~ -
’f2
9"12 ~’21
-~-
~
629
Chain Copolymerization
T237"12
/’31
one can then calculate for a given starting feed composition,viz., fl, f2, and the copolymercompositions as F1 = A/(A+B+C); F~ = B/(A+B+C); F3 = C/(A+B+C) ]Equation (7.81) can be similarly written and A, B, C defined accordingly. With fl = 0.3592, f2 = 0.3603, f3 = 0.2805, and r values given above, the copolymercompositionis calculated from both Eqs. (7.77) and (7.81). The results are tabulated below: Feed composition Terpolymer composition (mol %) Monomer tool % Found Calcd. from Eq. (7.77) Calcd. from Eq. (7.81) Styrene 35.92 44.7 46.5 46.7 MMA 36.03 26.1 26.3 27.7 AN 28.05 29.2 26.9 25.8
The knowledge of the monomer reactivity ratios for each pair of monomersalso permits the calculation of the size distribution of sequences of units of one kind. Thus if the monomer mixture is made up of the monomersM1, M2, M3, ".. MN,the resulting initial copolymer will consist of sequences of M1, M2, ¯ ¯., and MNmonomerunits. The fraction of all M1sequences which possess x number of M1units will be given by a distribution function [2]: x-1 na:(M1)
[M2] [M1]-ff -TI2
[M1] [M3] q- -7"13
q-
....[MN] rlN
x
[M1] ) (7.82) [M1] q-" [M2] q- [M3] q’-"’" [MN____j] 7"12 7"13 rlN Note that with [MI] = 0 for i = 3,4,.-. (7.41) for the binary system.
N, Eq. (7.82) reduces to Eq.
630
Chapter 7
Problem7.18 Consider the initial fractions units.
of styrene,
terpolymer in Problem 7.17. Calculate the MMA,and AN sequences containing 2 or more monomer
ADsvcer: For a terpolymer Eq. (7.82) becomes
fl fa+--
1+--
?’12
Forx
?’13
r12
~13
= 1 =
1-
=
1-
:1+(:2/?’,~) +(y31,’,~) 0.3592
0.3592 + (0.3603/0.52) + (0.2805/0.29)
= 0.822
Therefore, fraction of styrene sequences with 2 or more styrene units = 1 - 0.822 = 0.178. Similarly, hi(M2)
= 1-
= 0.7345 f~ + f2 + fz r23
Therefore, 0.265.
fraction
of MMAsequences with 2 or more units
= 1 - 0.7345
Again, nl(M3)
= 1-
= 0.9865
s’ +~+S~ ?’32
Fraction
of ANsequences with 2 or more ANunits = 1 - 0.9865 = 0.013.
DEVIATIONS FROMTERMINAL COPOLYMERIZATIONMODEL Thederivation of the copolymercompositionequation [Eq. (7.11)] rests on two importantassumptions-oneof a kinetic nature and the other of a thermodynamic nature. Thefirst is that the reactivity of the propagating species is determinedby the end monomer unit (first-order Markov)and
631
Chain Copolymerizafion
is independent of the identity of the monomerunit which precedes the terminal unit. The second is the irreversibility of the various propagation reactions. Deviations observed from the copolymer composition equation under certain conditions have been ascribed to the failure of one or the other of these two assumptions or the formation of a monomercomplex which undergoes propagation. Penultimate
Effect
The copolymerization behavior of somesystems indicates that the reactivity of the propagating species is affected by the penultimate (next-to-last) unit. The behavior, referred to as the penultimate or second-order Markov behavior, often manifests itself by giving inconsistent values of the monomer reactivity ratios for different monomerfeed compositions. This has been observed in many radical copolymerizations where the monomerscontain highly bulky or polar substituents. Thus in the copolymerization of styrene and fumaronitrile [32], propagating chains rich in fumaronitrile and having styrene as the end unit showgreatly reduced reactivity with fumaronitrile monomer.The effect is explained by steric and polar repulsions between the penultimate fumaronitrile unit in the propagating chain and the incoming fumaronitrile monomer. The mathematical treatment of the penultimate effect [33,34] in a binary copolymerization system involves the use of eight propagating reactions: wwvM1Ml"
+ M1 ~ vwwM1M1Ml"
vwwM1Ml"
+ M2 ~ vvvwM1MiM2"
vwwM~M2" + M1 -~
wwvM2M2Ml"
vvvwM2M2" + M2 ~ vvvvvM~M2M~wwvM2Ml"
+ M1 ~ vvvwM2M1M1"
wvwM2Ml"
+ M2 ~ vvwvM2MiM2"
vvvwM1M2 ¯
+ M~ ~ wwvMiM2Ml"
vvvwM1M2"
+ M2 ~ wwvM~M~M2"
(7.83)
with the four reactivity ratios
(7.84)
632
Chapter 7
Each monomeris thus characterized by two monomerreactivity ratios. One of these represents the propagating species in which the penultimate and terminal monomer units are the same, while the other represents the propagating species in which the penultimate and terminal units differ. The latter monomerreactivity ratios are denoted by prime notations (r~, r~). Following a procedure similar to that used in deriving Eq. (7.11), the copolymer composition equation with a kinetic penultimate effect present is obtained as
(fly + 1) d[M1] diM2]
1 + (r~Y q- 1) -- 1 + r~(r2 + Y) Y(r~ + Y)
(7.85)
where Y = [M~]/[M2]. For the styrene(M1)-fumaronitrile(M2) system, fumaronitrile is incapable of self-propagation (r~ = r~ = 0) and Eq. (7.85) simplifies d[M1] diM2]
_ 1 + r~Y (r~Y + 1)
(7.86) . (r~Y + 1) The experimental copolymer composition data for styrene(M~)-fumaronitrile(M2) give a good fit to Eq. (7.86) with rl ----- 0.072 and r~ : [33], but deviate markedly from the behavior predicted by the first-order Markov model with rl = 0.23. Penultimate effects have been observed in a number of other systems. Amongthese are the radical copolymerizations of ethyl methacrylate-styrene, methyl methacrylate-4-vinyl pyridine, methyl acrylate-l,3-butadiene, and other monomerpairs. The copolymerization data for the styrene(M1)-fumaronitrile(M2) system indicate that there are also effects due to remote monomerunits preceding the penultimate unit. The effect of remote units has been treated by further expansion of the copolymer composition equation by the use of greater number of monomerreactivity ratios for each monomer[34]. However, the utility of the resulting expression is limited due to the large number of variables involved. It should be mentioned that deviations from the terminal (first-order Markov) copolymer equation have also been treated from a thermodynamic viewpoint [35], where the deviations are accounted for in terms of the tendency of one of the monomers(M2) to depropagate (see p. 514). if the concentration of the monomerfalls below its equilibrium value [M2]e at the particular reaction temperature, terminal M2units will be prone to depropagate. The result would be a decrease in the amount of this monomerin the copolymer.
633
Chain Copolymerization COPOLYMERIZATION
AND CROSS-LINKING
If one of the monomersin a copolymerization is a divinyl compoundor any other olefinic entity with functionality greater than 2, a branched polymer can be formedand it is possible for the growing branches to interconnect to form an infinite cross-linked network knownas "gel." Copolymerization of such systems is thus generally analogous to step polymerizations invoMngtriand tetra-functional reactants (see Chapter 5). The cross-linking reactions are not capable in themselves of producing highly branched, finite molecules since gelation occurs before sufficient cross-linking can take place to produce such molecules. At this point the most complex of the molecular species are removedas the insoluble gel fraction. It is useful to be able to predict the conditions under which such gel formation will occur. The criteria for this condition are applicable also to cross-linking of preformed polymers which occurs in radiation induced cross-linking, to vulcanization with addition of other reagents, and to chain-growth and step-growth polymerizations of polyfunctional monomers.
Problem7.19 Consider a sample containing discrete polymer molecules that can be interconnectedeither during further polymerizationor by a separate reaction on the macromolecules.Supposesomeof the molecules are cross-linked by linkages formed between randomly selected monomerunits in them. Showby probability considerations that a sufficient condition for gelation occurs whenthe polymer samplecontains one cross-linked unit per weightaverage moleculeor one cross-link per two polymer chains. Answer: Wechoose a cross-link at random.The probability that the monomer unit on this cross-link resides in a primary molecule containing x monomerunits equals the fraction of all monomer units that are in x-mers. That is, this probability Px is P~----
(P7.19.1) E~%1 where N~ is the numberof x-mer molecules in the sample. However,if Mois the meanformula weight of monomericunits in this sample, -- w~ (P7.19.2) Mo ~1co N~ x wherew~is the weight fraction of x-mersin the sample. If a fraction ’u of all monomer units in the sampleformsparts of cross-links and !hese cross-links are randomlyplaced, then an additional u(x - 1) monomer units mthe x-merare also cross-linked, on the average. In other words,the probability that an arbitrarily selected cross-link is attached to a primarychain whichcontains x monomerunits is w~, and it is expected that u(x - 1) of these, x monomer units are also cross-linked. It maythus be said that the initial, randomlychosen cross-link leads through the primary moleculeand other cross-links to wxu(x- 1) additional primary molecules. P~
~h~p~er7
634
Since x can have any positive non-zerovalue, the expectednumberof additional cross-links y in a moleculethat already contains one arbitrarily chosencross-link is {20 y = u~w,(x-1) = ~[DP~,-~,-w.] = u(DP~,-1) (P7.19.3) whereDP~is the weight-average degree of polymerization of the primary chains in the sample. This molecule can be part of an infinite networkonly if y is at least 1. Thecritical value uc of u for this condition, whichis the condition for gelation, is then given by 1 1 DP~, - 1 DP~, since DP~,>> 1. Since gel~tion occurs whena fraction 1/DP’~of all monomer units is crosslinked, a completelygelled polymersamplecontains at least one cross-linked unit per weight average molecule or one cross-link per two polymerchains.
Cross-linking occurs early or late in the copolymerization depending on the relative reactivities of the two double bonds of the divinyl compound or diene. By the proper choice of a monomerwith two double bonds it is possible to reduce the reactivity of one double bond just enough so that it will not enter polymerization under the same conditions as the other, but can be made to react under more drastic conditions. This leads to postpolymerization cross-linking reactions of which vulcanization reactions are an example. If the two double bonds are well separated in the monomer,the reactivity of one is not affected by the polymerization of the other. Ethylene glycol dimethacrylate and allyl acrylate are examples of divinyl monomersof this type. If, on the other hand, the two double bonds are close enough together that the polymerization of one can shield the other sterically, or if they are conjugated as in 1,3-dienes, a difference in reactivity can be expected. The most notable case in which there is a large drop in reactivity of one group on reaction of the other is in the copolymerization of 1,3-dienes where 1,4-polymerization leads to residual 2,3-double bonds which have lowered reactivity. They are subsequently used to bring about cross-linking as in vulcanization. Divinyl benzene is in the intermediate category with regard to dependency of reactivity of one double bond on the other being reacted. Several different cases can thus be distinguished depending on the type of divinyl monomerin copolymerization. Vinyl and Divinyl Equal Reactivity
Monomers of
Consider the copolymerization of vinyl monomerA with divinyl monomer BBwhere all of the vinyl groups (i.e., the A group and both B groups) have
Chain Copolymerization
635
the same reactivity. Methyl methacrylate (MMA)-ethyleneglycoldimethacrylate (EGDMA),vinyl acetate-divinyl adipate (DVA), and to an extent styrene-p- or rn-divinylbenzene (DVB)are examples of this type of polymerization system. In MMA-EGDMA system, ~H~
CHs
CHs
COOCHa
~OOCH=CH~O~O
the unsaturated groups of EGDMA may be assumed with confidence to be equal in reactivity with the identical group of the MMA monomer. Thus the reactivity of one unsaturated group in EGDMA should not depend perceptibly on whether the other is reacted or not. (DVB,by contrast, is knownto be more reactive than styrene.) Let the initial molar concentrations of vinyl monomerand monomericB groups be [A]0 and [B]0, respectively, and that of divinyl BBbe [BB]0. Thus, [B]0 = 2[BB]0. Since the A and B double bonds are equally reactive, i.e., rl = 9"2 = 1, one obtains from the copolymer equation [Eq. (7.11)], /71 = fl. Thus the molar ratio of B and A groups in the copolymer is simply equal to [B]/[A]. At the extent of reaction p (defined as the fraction of A and B groups reacted), the relative number of various monomericspecies can be listed as follows : Unreacted A~s : [A]0 (1 -- p) Reacted A’s : [A]0 p Unreacted BB’s: [BB]0 (1 -Singly reacted BB’s : 2[BB]0 (1 -- p)p 2Doubly reacted BB’s : [BB]op The number of cross-links is simply the number of BB molecules in which both B groups are reacted and the number of polymer chains is derived in terms of the degree of polymerization DP: Number of polymer chains Total numberof reacted A and B grc~ups = ([A]op
DP + [BloP) /DP
(7.87)
Therefore, Numberof cross-links per chain
p[BBIoDP
([A]o p[B]oDP 2([A]o + [B]o)
(7.88)
636
Chapter 7
At the critical extent of reaction Pc for the onset of gelation, the number of cross-links per chain is ½ (see Problem7.19), whencethe critical extent of reaction at the gel point Pc is obtained as
pc ([A]0 = 2 [BB]0
DP~
(7.89),
in which "DP is now replaced by DP~o since, as shown in Problem 7.19, the appropriate average of DPfor the aforesaid gel condition is DP~o.It is the weight-average degree of polymerization of "primary molecules." The term "primary molecule" is used to designate the linear molecule that would exist if all the cross-links were severed, that is, the polymerchains formed before any crosslinking reactions occurred, In the above problem it may be taken approximately as the weight-average degree of polymerization that would be observed in the homopolymerization of monomer A under the particular reaction conditions. For [A]o ~>> [B]o, Eq. (7.89)reduces Pc ~
[A]o 2[BB]0 DP~
(7.90)
Equation (7.89) predicts that extensive cross-linking occurs during copolymerization of A and BB(see Problem 7.20). The equation holds best for systems containing low concentrations of the monomerBB, that is, at higher gel point conversions where the distribution of cross-links is random; its predictive utility decreases as the concentration of BBincreases. With increasing concentration of BB, Eq. (7.89) predicts gel points at conversions that are increasingly lower than those found experimentally. This behavior has been attributed to the wastage of the BBmonomerdue to intramolecular crosslinking which mayoccur at the expense of cross-linking involving two polymer molecules.
Problem 7.20 Bulk polymerization of methyl methacrylate (MMA)at 60°C with 0.9 g/L of benzoyl peroxide yielded a polymerwith a weight average degree of polymerization of 8600 at low conversions. Predict the conversions of MMA at which gelation would be observed if it is copolymerized with 0.05 mol%of eth}lene glycol dimethacrylate (EGDMA) at the same temperature and initiator concentration as in the homopolymerization case. Answer: Let MMAbe denoted as monomer A and EGDMA as monomer BB. Then [BB]o -- 0.0005
[A]0+[BB]; ’[A]o / [BB]o~ 2000
637
Chain Copolymerization
FromEq. (7.90), with DP-~-~(assumedto be the same as that of the homopolymer) = 8600, ~000 = 0.12 Pc ~-2(8600) So gelation wouldbe observed at about12%conversion of MMA. Problem 7.21 Calculate the conversion at which gelation should be observed in styrene containing 0.14 tool% p-divinylbenzeue (DVB)and 0.04 mol/L benzoyl peroxide initiator at 60°C. Assumefor this calculation that the vinyl groups in both styrene and DVB are equally active and that chain termination occurs solely by coupling. [Data at 60°C : kd = 2.4 x 10-6 s-l; f = 0.4; k~/kn for styrene = -4 L tool -1 s-a.] 4.54×10 Answer: [M] for bulk styrene = 8.65 -1 tool L Kinetic chain length = 8.65
(4.54X 10-4)1/22(0.4 x 2.41 × 10-6)1/2 (0.04)1/2 = 470 D/5~ = 2×470 = 940. For chain termination solely by coupling, -DPw/DP~= (2 + p)/2 (see p. 527). For high polymer, p ~ 1. Therefore, DP~= 1410. Let A ~- Styrene, BB---- DVB.Then [BB]o = 0.0014 [A]o + [BB]o [A]o/[BB]o = 713 713 From Eq. (7.90), p~ -- 2(1410) = 0.253 (~ 25.3%).
Equation (7.89) indicates that gelation can be delayed, that is, the extent of reaction at which gelation occurs can be increased by reducing the concentration of divinyl monomer, by reducing the weight-average chain length (increase initiator concentration or add chain transfer agents), or using a divinyl monomerin which one or both the vinyl groups are less reactive than those in the monovinyl monomer(see later).
Problem 7.22 Howwould the percentage conversion at the gel point change if the styrene-divinyl benzenemixture of Problem7.21 contained additionally a mercaptan chain regulator (Cs = 21) at a concentration of 2x10-4 tool/L?
638
Chapter 7
Answer: In the presence of chain regulator (neglecting other transfer reactions), 1 1 (2 × 10 -4 mol/L) -3 = 1.5x10 + DP~ - 940 (21) (8.65 tool/L) D/5,~ = 645 To determine the proportions of unimolecular (chain transfer) and bimolecular (coupling) termination, let y fraction of molecules be terminated by the former mechanism.Therefore, (1 - y)(940) + y(940/2) = 645, or y ~--ff~/~-ffn is given by a combinationof (1 + p) and (2 p)/2 weighted in proportion to the amountsof umimolecularand bimolecular termination, respectively (see pp. 525-527),that is, DP~/DP,, = 0.63(1+p) +0.37(2 +p)/2 = 1.81 forp~l DP~, = 1.81x645 = 1170 From Eq. (7.90), Pc = 713/(2)(1170) = 0.30 (----30% conversion)
Vinyl and Divinyl Monomers of Different Reactivity A second case in vinyl-divinyl copolymerization is the copolymerization of A and BBin which the reactivities of the vinyl groups A and B are not equal, while the two B groups are equally reactive. If the B groups are r times as reactive as the A groups, they enter the copolymer r times as rapidly and hence the ratio of B and A groups in the copolymer, d [B]/d [A], is d[B]/diAl
= r[B]/[A]
(7.91)
where [A] and [B] are the concentrations of the A and B groups in the monomermixture at any instant. Thus, at the extent of reaction p of A groups, [A] = (1- p)[A]0 and [B] = (1- rp)[B]0, where the subscript denotes initial concentrations. By a derivation similar to the case of vinyl-divinyl monomersof equal reactivity considered above, one then obtains an expression for the critical extent of reaction at gelation as [A]o -t- r [B]o Pc = r2[B]oDP~o
(7.92)
For [B]o 1, r 2 < 1 and r 1< 1 , r 2 > 1 ; (b) ’/’1 < 1,r 2 < 1 a rl > 1, r2 > 1 (rare in free-radical copolymerizations, but found in someionic copolymerizations).] 7.3. A monomer pair with rl = 5.0 and r2 = 0.2 is copolymerized beginning with a molar monomerratio [M~]/[M2] = 30/70. Assuming that the copolymer composition within a 10% conversion interval is constant, calculate instantaneous monomer(f~) and copolymer (F1) compositions and cumulative average copolymer compositions at 10 tool% conversion intervals up to 100%conversion. Showthe results graphically as change in composition of the copolymer and the monomer mixture during copolymerization. 7.4. Ferrocenyl acrylate (FMA)and 2-ferrocenylethyl acrylate flEA) were synthesized and copolymerized with styrene (STY), methyl acrylate (MA), vinyl acetate (VA) [C. U. Pittman, Jr., Macromolecules, 4, 298 (1971)]. The following monomerreactivity ratios were obtained:
FMA FMA FMA FEA FEA FEA
STY MA VA STY MA VA
0.020 0.14 1.4 0.41 0.76 3.4
2.3 4.4 0.46 1.06 0.69 0.074
(a) Which of the above comonomerpairs could lead to azeotropic copolymerization? (b) Predict whether FMAor FEA will have higher kp homopolymerization. (c) Is styrene more reactive or less reactive than FMA toward the FMAradical ? By what factor ? (d) List STY, MA, and in order of increasing reactivity toward the FMAradical and toward the FEAradical. (e) List the STY, MA,and VAradicals in order of increasing reactivity toward the FEAmonomer. [Ans. (a) FEA-MA;(b) k;o(FEA) > ka0(FMA);(c) STY50 times more than FMAtoward FMAradical; (d) STY > MA> VAfor both FMAand FEA x > STY~.] radicals; (e) ~ > MA 7,5.
Considering resonance and polarity effects what type of monomers would you choose to copolymerize with vinyl ethers .9
Chain Copolymerizaffon
~49
7.6. On the basis of Q and e values predict the copolymerization behavior of the following pairs of monomers: (a) Vinyl acetate (Q = 0.03, e = -0.22) and ethyl Vinyl ethers (Q = .0.03, e = -1.17). (b) Styrene (Q = 1.00, e = -0.80) and vinyl acetate (Q = 0.03, e = -0.22). (c) Methyl methacrylate (Q = 0.74, e = 0.40) and acrylic acid (Q = e = 0.77). (d) Styrene (Q = 1.00, e = -0.80) and acrylonitrile (Q = 0.60, e = 1.20). 7.7. Using Q and e values in Table 7.4, calculate the monomerreactivity ratios for the comonomerpairs (a) styrene-butadiene and (b) styrene-methyl methacrylate. Comparethe results with the rl and r2 values in Table 7.1. [Ans. (a) rl = 0.51, r2 = 1.84; (b) "~- 0.51, r2 = 0.46.] 7.8. Predict the sequence length distributions for an ideal binary copolymerization with rx = r2 = 1 for (a) fl = 0.5, (b) f~ = 0.8, and (c) 0.2. Comparethe distribution patterns and commenton the results. 7.9. Comparethe sequence-length distribution (by plotting in a bar graph) in the copolymer from the following monomerpairs with and without azeotrope for [Mx]/[M2] = 10/90: (a) rx = r~ = 0.1; (b) = 5- 0, ’r2 = 0. 2. 7.10. For a random copolymer with rx = 1 and a 50/50 composition, plot of n~(Mx)vs.
prepare a
7.11. When0.7 mole fraction styrene (M1) is copolymerized with methacrylonitrile (M2) in a radical reaction, what is the average length of sequence of each monomerin the copolymer ? (rl = 0.37, r2 = 0.44). [Mns. ~(M1) = 1.9; ~(M2) = 1.2.1 7.12. Acrylonitrile monomer(Mx) is copolymerized with 0.25 mole fraction vinylidene chloride (M2). What fraction of the acrylonitrile sequences contain or more acrylonitrile units ? (rl = 0.9, r2 = 0.4).
[~ns.0.53.] 7.13. Styrene (3.0 M) is copolymerized with methacrylonitrile (1.5 M) in benzene solution by adding benzoyl peroxide to a concentration of 0.1 Mand heating to 60°C. Calculate for the polymer initially formed (a) composition the copolymer, (b) probability of forming styrene and methacrylonitrile sequences that are 3 units long, (c) average sequence lengths of styrene and methacrylonitrile in the copolymer, and (d) the run number of the .] copolymer. [Given: rx = rz = 0.25 at 60°C [Ans. (a) 1 57 mol%, M2 43 mol%; ( b) n a(Mx) =0. 0742, ha (M2) = (c) 5(M1) = 1.50, 5(M2) 1.12.] 7.14. The measurement of bulk copolymerization of styrene 0Vlx) and methyl methacrylate (M2) at 30°C in a feed of 0.031 mole fraction styrene with initiation by photosensitized decomposition of benzoyl peroxide gave a value of 7.11×10 -5 mol L-1 s -x, while homopolymerization of styrene under
650
Chapter 7 the same conditions yielded a polymerization rate of 3.02x10 -5 -1 mol L s -1 [H. W. Melville and L. Valentine, Proc. Roy. Soc., A, 200, 337, 358 (1952)]. Calculate the copolymerization rate from (a) chemical control model [Eq. (7.64)] and (b) combined model [Eqs. (7.58) and (7.68)] to with the.experimental value. Use the homopolymerization rate constants at 30°C for styrene as kp = 46 L mo1-1 s -1 and kt = 8.0×106 L mo1-1 s -1 and for MMAas kp = 286 mol L-~ s -~ -x and k~ = 2.44x107 mol L s -1. The reactivity ratios at 30°C are r~ = 0.485 and r 2 = 0.422. Makethe 3.. comparison using ¢ = 10 and ~b = 13. Monomerdensity = 0.90 g/cm Arts. ~. . °, tool L-1 s-1 Rate of copolymenzauon× 10 Chemicalcontrol Combined model Experimental Eq. (7.64) Eqs. (7.58) and (7.68) ff = 10 ff = 13 if= 10 ff = 13 7.11 6.30 5.71 7.85 7.28
7.15. Methyl methacrylate (M1) and vinyl acetate (M2) constitute a system which the nature of polyradical ends has no discernible effect on the overall rate of termination (i.e., ff = 1). The copolymerization rate data measured for this system at 60°C are given below [G. M. Burnett and H. R. Gersmann, J. Polym. Sci., 28, 655 (1958)]: Mole fraction of M2 in feed, f~ 0.915 0.756 0.645 0.548 0.453 0.325
Rate × 105 (mol -1 s -1) 28.0 29.1 42.4 60.7 78.7 103.9
Calculate the copolymerization rate using the diffusion control model [Eqs. (7.58) and (7.66)] and combined model [Eqs. (7.58) and (7.68)] to with the experimental value. Take the reaction with 0.645 mole fraction vinyl acetate in feed as calibration value to normalize on P~. [Kinetic parameters : rl = 28.6; r~ = 0.035; kll = 589, /~ = 2.9 x 107, k22 = 3600, and kt~2 = 2.1 × 108, all in mol L-x s-~; monomerdensity = 0.90 g/cm3.]
651
Chain Copolymeriza~ion Arts.
f2 0.915 0.756 0.645 0.548 0.453 0.325
Rate×lO5, L tool -1 -1 s Diffusion control Combinedmodel 22.2 21.3 30.8 31.5 42.4 42.4 59.2 60.1 82.5 80.1 113.4 108.3
Exptl. 28.0 29.1 42.4 60.7 78.7 103.9
7.16. The ternary copolymerization of a monomermixture containing 31.24, 31.12, and 37.64 mol%of styrene, methyl methacrylate and vinylidene chloride at 60°C for 16 h yielded at 18.2 wt% conversion a polymeric product which analyzed C 68.66% and Cg 12.07% (by wt) [C. Walling and E. R. Briggs, Am. Chem. Soc., 67, 1774 (1945)]. Calculate the initial ternary copotymer composition to compare with the composition obtained by the analysis. Use monomerreactivity ratio data from Table 7.1. Ans. Feed Monomer Mol% Styrene 31.24 MMA 31.12 Vinylidene chloride 37.64
Found 43.4 39.4 17.2
Terpolymercomposition (tool%) Calcd. IEq. (7.81)1 Calcd. [Eq. (7.77)1 44.3 44.3 41.2 42.7 14.5
13.0
7.17. Predict the initial composition of the terpolymer which would be produced from the radical polymerization of a solution containing acrylonitrile (47%), styrene (47%), and 1,3-butadiene 6% (by mol). [Ans. Mt 36.6%, M252.1%, Ma 11.3% (by mol).] 7.18. (a) Calculate the mole fraction composition of the initial terpolymer which would be formed from the radical polymerization of a feed containing 0.414 mole fraction methacrylonitrile (M1), 0.424 mole fraction styrene (M2), 0.162 mole fraction a-methyl styrene (Ma). (b) What fraction of styrene sequences in this copolymer contain 2 or more styrene units ? [Reactivity ratios: M1/M2: rl = 0.44, r2 = 0.37; M1//VI3: rl = 0.38, r2 = 0.53; M~/Ma: rl = 1.124, r2 = 0.627.] [Ans. (a) F1 = 0.443, Fz = 0.403, Fa o= 0.154; (b) 0.23.] 7.19. What should be the concentration of divinyl benzene in styrene to cause gelation at full conversion of the latter, if styrene were being polymerized under conditions such that the degree of polymerization of the polymer being formed were 1000. Assumethat the vinyl groups in divinyl benzene are equally as reactive as those in styrene. [Ans. 0.05 mol%]
652
Chapter 7
7.20. (a) How much of the divinyl monomer, ethylene glycol dimethacrylate (EGDMA),should be added to methyl methacrylate (MMA)to cause set of gelation at 20% conversion when polymerization is carried out at 60°C in the presence of 0.8 g/L benzoyl peroxide. Homopolymerization of MMAunder the same conditions is known to yield polymer with DPw = 1000. M/VIA and EGDMA can be reasonably assumed to be of equal reactivity. (b) Recalculate the amount of EGDMA for the case where of a chain regulator is used to bring down DP~, to 500. [Ans. (a) 0.25 tool% ; (b) 0.5 mol%] 7.21. Consider the styrene-divinylbenzene system of Exercise 7.19. Recalculate the conversion at the gel point taking into consideration the unequal reactivity of styrene and divinylbenzene (r 1 = 0.3, r 2 = 1.0). [Ans. 2.3 tool%] 7.22. Calculate the conversion for onset of gelation in methyl methacrylate (MMA) containing 0.20 tool% ethylene glycol dimethacrylate (EGDMA) when it polymerized at 60°C in the presence of 0.04 moFLAIBNinitiator. Take into account the fact that the chain termination in MMAhomopolymerization occurs both by. disproportionation and coupling, the ratio being 3:1 at 60°C. [Data: k~/G (for MMA)= 1.04x10 -2 L tool -1 s-~; k,~ = 8.45x10 -~ s-l; f = 0.6; monomerdensity = 0.90 g/cm3.] [Ans. Pc = 0.115.] 7.23. Howwould the percentage conversion at the gel point change if the MMAEGDMA mixture of Exercise 7.22 contained additionally an effective chain regulator (Cs = 21 at 60°C) at a concentration of -4 to ol/L? [Ans. Pc = 0.166.] 7.24. Predict the extent of reaction at which gelation would occur in vinyl acetate (VA)-divinyl adipate (DVA)mixture containing 5 tool% DVAand 0.04 mol/L AIBNinitiator at 60°C. Assumedisproportionation to be the predominant mechanism of chain termination. [Data at 60°C: k~/kt for VA= 0.182 L mo1-1 s -1, ka (for AIBN) = 8.45 x -8 s - ~, f 0. 6, mo nomer de nsity = 0.93 g/cm3.] "~.25. Predict the extent of reaction at which gelation would occur in the following two vinyl-divinyl systems, both containing 1 tool% of the dix;inyl component: (a) styrene-ethylene glycol dimethacrylate and (b) methyl methacrylate-divinyl benzene. Assumethat the reaction conditions for the two systems are such as to yield the same D-Pwof 1000 for the uncrosslinked polymer. Take the r~ and ~’z values from Table 7.1 for the analogous vinyl-vinyl copolymerizations. [Ans. (a) Pc = 0.015; (b) Pc = 0.012.]
Chapter Ionic
8
Chain Polymerization
INTRODUCTION Chain or addition polymerization is knownto occur by several mechanisms other than those involving free radicals discussed in Chapter 6. Prominent among these are ionic mechanisms in which the growing chain ends bear a negative charge (carbanion) or a positive charge (carbonium ion). If growing chain end bears a negative charge (wvc¢~), the polymerization knownas anionic polymerization. If the chain end bears a positive charge (ww~), the reaction is cationic po lymerization process. In general, ionic polymerization can be initiated through acidic or basic. compounds. For cationic polymerization complexes of BF3, AICI3, TIC14, and SnCI4 with water, or alcohols, or tertiary oxonium salts have shown themselves to be particularly active. The positive ions are the ones that cause chain initiation. However, also with HC1, H2SO4,and KHSO4one can initiate cationic polymerization. Initiators for anionic polymerization are alkali metals and their organic compoundssuch as phenyllithium, butyllithium, phenyl sodium, sodium naphthalene, and triphenyl methyl potassium. Unlike free-radical reactions which are not selective (as most olefinic monomersundergo radical polymerization), ionic polymerizations are largely selective and are restricted to monomerswhose structures enhance the stability of the ionic species involved in the process. Cationic polymerization is essentially limited to those monomerswith electron-releasing substituents and anionic polymerization takes place with monomerspossessing electronwithdrawing groups. These are elaborated in a later section. The commercial utilization of cationic and anionic pOlymerizations is rather limited because of the high selectivity of ionic polymerizations compared to radical polymerization, as mentioned above. Ionic polymerizations are also most difficult to carry out and require stringent reaction conditions. Thus, unlike in free-radical polymerizations in which the characteris653
654
C,hapt,er 8
tics of the active centers depend only on the nature of the monomerand are generally independent of the reaction medium,in ionic polymerizations the polarity of the solvent strongly influences the mechanismand rate of ionic polymerization. This can be visualized as follows. Ionic polymerizations, as we shall see later, involve successive insertions of monomersbetween a macromolecular ion and a counterion of opposite charge. The macroion and the counterion form an organic salt which may exist in several forms in the reaction medium. The degree and nature of the interaction between the cation and anion of the salt and the solvent -, a (or monomer)can vary considerably. Considering an organic salt A+B continuous spectrum of ionicities ("Winstein spectrum") can be depicted: AB ~ Covalent bonding (I)
A+B ~--~ A+/B ~-~ -A+IIB Contact Solvent Solvated (tight) separated (loose) ion pair ion pair ion pair (II) (III) (IV)
----~A+
+ BFreesolvated ions (V)
One can visualize a range of behavior from one extreme of a completely covalent species (I) to the other of completely free (and highly solvated) ions (V). The intermediate species include the tight or contact ion pair (II) and the solvent-separated or loose ion pair (III). The contact ion pair has counterion (or gegenion) of opposite charge close to the propagating center (unseparated by solvent). The solvent-separated ion pair involves ions that are partially separated by solvent molecules. In cationic polymerization the chain end is cationic and has a negative counterion, while in anionic polymerization the chain end is anionic and has a positive counterion. Most ionic polymerizations involve two types of propagating species-- an ion pair (H-IV) and a free ion (V) - coexisting in equilibrium with other. The relative concentrations of these two types of species and the identity of the ion pair (that is, whether the ion pair is described as species II, III, or IV), depends on the particular reaction conditions, especially the solvent employed. The nature of the solvent has a large effect in ionic polymerization since the different types of propagating species have different reactivities. In general, propagationrates are higher the morethe rnacroionand its counterion are separated. Loose ion pairs are more reactive than tight ion pairs and free ions are significantly more reactive than ion pairs. In general, more polar media favor solvent-separated ion pairs or free solvated ions. Free solvated ions will not exist in hydrocarbon media, where other equilibria mayoccur between ion pairs and clusters of ions. Although solvents of high polarity are desirable to solvate ions, they cannot be employedfor several reasons. The highly polar hydroxylic solvents
Ionic ChainPolymerization
655
(water, alcohols) react with and destroy most ionic initiators and propagating species. Other polar solvents such as ketones prevent initiation of polymerization by forming highly stable complexeswith the initiators. Ionic polymerizations are, therefore~ usually carried out in solvents of low or moderate polarity such as methyl chloride, ethylene dichloride, and pentane. Thoughionic polymerization resembles free-radical polymerization in terms of initiation, propagation, transfer, and termination reactions, the kinetics of ionic polymerizations are significantly different from free-radical polymerizations. In sharp contrast to free-radical polymerizations, the initiation reactions in ionic polymerizations have very low activation energies, chain termination by mutual destruction of growing species is nonexistent, and solvent effects are much more pronounced, as the nature of solvent determines whether the chain centers are ion pairs, free ions, or both. No such solvent role is encountered in free-radical polymerization. The overall result of these features is to makethe kinetics of ionic polymerization much more complex than the kinetics of free-radical polymerization. Rates of ionic polymerization are by and large muchfaster than in freeradical processes. The higher rate of ionic polymerization is mainly because termination by mutual destruction of active centers, which is prevalent in free-radical systems (see Chapter 6), does not occur in ionic systems macroions with the same charge will repel each other and thus concentrations of propagating species can be much higher in ionic than in free-radical systems. Rate constants for ionic propagation reactions vary but some are higher than those in free-radical systems. This is particularly true in media where the ionic active center is free of its counterion. The high reactivity of ionic active centers, which yields fast propagation rates, also results in a greater propensity toward side reactions and interference from trace impurities. Lowtemperatures favor propagation over competing reactions which cause chain termination. Ionic polymerizations are thus performed often at muchcolder temperatures than those used in free-radical processes, which would be impossibly slow under the same conditions. Ionic polymerizations are not as well understood as radical polymerizations because ionic polymerizations are characterized by a wide variety of modes of initiation and termination. The nature of the reaction media in ionic polymerizations is often not clear since heterogeneous inorganic initiators are often involved. Further, it is extremely difficult in most instances to obtain reproducible kinetic data because ionic polymerizations proceed at very high rates and are extremely sensitive to the presence of small concentrations of impurities and other adventitious substances. Because of the high selectivity and sensitivity of ionic reactions, successful ionic polymerizations must be carried out muchmore carefully than
656
Chapter 8
normal free-radical syntheses, consequently, a given polymeric substance will ordinarily not be producedby ionic initiation if a satisfactory product can be made by less expensive free-radical processes. For example, commercial styrene polymers are all free-radical products, though styrene polymerization can be initiated with free radicals as well as with appropriate anions or cations. However, particular ionic processes are used to make research grade polystyrenes with exceptionally narrow molecular-weight distributions and diblock or multiblock copolymers of styrene and other monomers. In this chapter we will review pure ionic polymerizations-first, anionic polymerizations with someof their specific applications and then the polymerization processes which proceed by a cationic mechanism. Coordination polymerizations that are complex polymerizations having partial ionic character and ring opening polymerizations, manyof which proceed by anionic and cationic mechanisms, will be reviewed in subsequent chapters. IONIC
POLYMERIZABILITY
OF
MONOMERS
As we have noted earlier in Chapter 1, a monomermust have a functionality greater than or equal to 2 in order for polymers to be produced from its reactions. For chain growth polymerizations this functionality can be derived from opening of a double bond or opening of a ring. The most important functional groups that participate in chain-growth polymerizations are the carbon-carbon double bond in alkenes and the carbon-oxygen double bond in aldehydes and ketones. The alkene double bond can be polymerized in chain-growth reactions in which the active site is a free-radical, ion, or carbon-metal bond. (Aldehydes and ketones are not activated by free radicals because of the difference in electronegativity of the C and O atoms. Aldehydes and ketones are polymerized only by ionic or heterogeneous catalytic processes.) The processes whereby a given alkene reacts depend on the inductive and resonance characteristics of the substituent X in the vinyl monomerCH~=CHX.Electron-releasing substituents,
R,
RO-,
R--C~C-
and
---((~)
increase the electron density of the double bond and thus facilitate of a cation, H H
H
H /¢,.;
~"~
¢..;
~+ A+B- ~ ACH2--
+... X
B-
addition
657
Ionic ChainPolymerization
Thus monomers like isobutylene (VI), 3-methylbutene-1 (VII), styrene (VIII), and vinyl ethers (IX) all undergo cationic polymerization. CH3 dR (VI)
(VIII)
(VII)
(IX)
Someof these vinyl monomerscan delocalize the positive charge, and this also facilitates reactions with cations, e.g., in the polymerizationof vinyl ethers: A $ + CH_~-----C 6-R
~ A-CH~--C $ ~ A-CH~--~, :O-R 6-R
(s.3)
The alkoxyl substituent thus allows a delocalization of the positive charge over two atoms--the carbon and the oxygen, and this leads to stabilization of the carboniumion. (If the substituent were not present, e.g., in ethylene, the positive charge wouldbe localized on the single a-carbon atom.) Similar delocalization effects occur with phenyl, vinyl, and alkyl substituents, e.g., for styrene polymerization: H vwwCH.~-- C+
H ~
(8.4) vwwCH~5
Electron-withdrawing substituents -C=N,
--~-R,o
--~-OH
or
decrease the electron density of the double bond and thus facilitate of an anionic species on the double bond. H H \ ~ / I /C = C~ + A+B ~ BCH=--C:-... ~ H X ~
attack
H
+ A
(8.5)
The electron-withdrawing substituents may also stabilize the anion formed by delocalization of the charge, e.g., for acrylonitrile polymerization:
658
Chapter 8 H
H
~--N
C=N:-
(8.6)
The stabilization of the propagating carbanion occurs by delocalization of the negative charge over the oz-carbon and the nitrogen of the nitrile group.
Problem 8.1 Contrary to the high selectivity shownin cationic and anionic polymerization,radical initiators can bring about the polymerizationof almost any carbon-carbondouble bond. Explain, giving reasons.
Radical species are neutral and do not have stringent requirements for attacking the ~r-bond. Moreover,resonancestabilization of the propagating radical occurs with almost all substituents, for example, H wvvvCH2--C" ~-~ ~,~A, I C----N
vvCH2--
H C C=N"
H H v~vvCH2--C" ~ vvvvvCH~--Q :CI" ~1
Radical initiation can thus take place with almost any carbon-carbondouble bond. Problem8.2 Explain whyacrylates and vinyl acetate are not cationically polymerizable. Answer: For efficient cationic polymerization of vinyl monomers it is necessary that the carbon-carbondouble bond be the strongest nucleophile (electron donor) in the molecule. If more than one nucleophilic site e.xists in a monomerand the 7r electron system of the double bond does not represent the most nucleophilic site, the other site(s) maycomplexwith the electrophile (proton, cation, Lewis acid). Thus, for methylmethacrylat.e~
Ionic ChainPolymerization
CH3
CH3 CH2~C
659
~
CH2~C
~----O O
CH~ ~
+CH2--C
+C-O-R O
CH 3
CH 3
CH3 ~
~
CH2~
~-O-R O
C-O-R
CH3
CH3
etc.
In addition, with these monomers the substituent not only preferentially complexes the electrophile but mayeven reduce the nucleophilicity of the double bondby electron attraction. Acrylates (and similarly vinyl acetate) thus do not polymerize cationically. (It maybe noted that vinyl acetate is also not polymerizedby anionic initiators as they attack the acetate linkage. Vinylacetate is polymerizedonly by free radicals.)
Phenyl and alkenyl (-CH=CH2)substituents, although electron-pushing inductively, can resonance stabilize the anionic propagating species in the same manner as a cyano group [Eq. (8.6)]. Monomerssuch as styrene and 1,3-butadiene can therefore undergo anionic as well as cationic polymerization. The applicability of various types of initiation mechanismsto the polymeri½ation of commonolefin monomers is summarized in Table 8.1. We see that isobutene can be polymerized only by cationic initiation, whereas monomers,such as vinyl chloride, methyl methacrylate or acrylonitrile with their electronegative substituents will not yield at all to cationic initiation. Vinyl chloride, however, does not respond to anionic initiation as well. Though halogens can withdraw electrons inductively and push electrons by resonance, both effects are relatively weak. Vinyl chloride thus does not undergo either anionic or cationic polymerization. ANIONIC
POLYMERIZATION
Anionic Initiation The overall reaction in anionic polymerization can be divided into initiation, propagation, and termination steps. While anionic initiators are all electron donors of varying base strengths, the initiator type required for a particular polymerization depends on the ease with which an anion can be formed from the monomerwhich acts as an electron acceptor in anionic polymerizations. In general, the strength of the base required to initiate polymerization diminishes with increasing electronegativity of the substituent on the
660
Chapter 8
Table 8.1 Applicability of Various Types of Initiation Mechanismsto the Polyamerization of Olefin Monomers Olefin monomer Ethylene Propylene
Monomerstructure
Free Cationic Anionic Coordiradical nation
CH2 =CH2
q---CH2 =CHC2H5 ---Isobutene CH2=C(CH3)2 -+ --Butadiene-l,3 CH2 =CH--CH=CH2 qStyrene CH2 =CHPh -t-t-tqVinylchloride CH2 =CHCI ---tMethacrylic esters qCH2 =C(CHa)COOCH3. -t--tVinyl ethers CH2 =CHOR -Acrylonitrile CH2 =CH--CN + -+ + aSymbol+ indicates that the monomer can be polymerizedto high molecularweight polymerbythis formof initiation. CH2 =CHCH3
Butene-1
monomer. The electronegativity following order
of some selected substituents
-CN > -COOR > -C6H5 -----
is in the
-CH=CH2 >> -CH3
Thus the relatively weak sodiu m methoxide (NaOCH3)can polymerize acrylonitrile, which has a strong electronegative substituent (-CN). Vinylidene cyanide carries two -CN groups on the same carbon atom and can be polymerized even by weaker bases like water and amines. Polymerization of nonpolar monomerssuch as conjugated olefins, however, requires initiation by very strong bases like metal alkyls. The two principal anionic initiation processes are (a) nucleophilic attack on the monomer which produces one-ended (monofunctiorml) anions addition of the initiator across the double bond of the monomer[see Eq. (8.5)] and (b) electron transfer by alkali metals that leads two-ended (bifunctional) anions (see later). Nucleophilic
Attack
Initiation takes place by a nucleophilic attack which is essentially addition of a negatively charged entity to the monomer. Examples of some reactive bases which can initiate in this manner are n-C4HgLi, C6HsCH2Li, NaNH2, KNH2, C6HsCH2Na, CH3ONa, and EtMgBr. Alkyllithium compounds, probably the most useful of these initiators, are generally low
Ionic ChainPolymerization
661
melting and soluble in inert organic solvents. Organometallic compounds of the higher alkali metals have moreionic character and are generally insoluble; hence they initiate polymerization by a heterogeneous process. Other initiators of this type include organic compoundsof calcium and barium and Grignard reagents, but these are not used as commonlyas the alkali metal compounds. Alkyllithium compoundsare employed commercially in the polymerization of 1,3-butadiene and isoprene. Initiation proceeds by addition of the metal alkyl, e.g., n-butyllithium, to monomer: Y + C4HgLi
+ CH2=CHY
~ C4Hg-CH2--C:
Li
(8.7)
This type of initiation is knownas monofunctionalinitiation as it produces one active (ionic) site for propagation. Propagation takes place by the addition of monomerto the ionic site: Y C4Hg-CH~--6.’-
Li + + n CH2 =CHY ~ C4H9
---(--- CH2CHY--3/w-~ CH~-- C,: H
+ Li
(8.8)
The extensive use of alkyllithium initiators is due to their solubility in hydrocarbon solvents. A commonexample is n-butyllithium which is usually available as a solution in n-hexane. The C-Li bond is not ionic in hydrocarbon media where the initiator molecules exist as aggregates. Initiation is thus fairly slow in hydrocarbon media. Addition of tetrahydrofuran to this solvent increases the concentration of unaggregated initiator (which is more active for initiation) by forming a 1:1 complex with this compound.Alkyls and aryls of the heavier alkali metals, such as Na and K, are poorly soluble in hydrocarbons because of the greater ionic character of the Na-C and K-C bonds. Alkyllithium initiators yield stereoregular polymersof conjugated dienes if the polymerization is carried out in hydrocarbon solvents. Addition of tetrahydrofuran or other more polar solvents changes the microstructure of the polymers that are produced. Alkyl derivatives of the alkaline-earth metals have also been used to initiate anionic polymerization. Organomagnesium compoundsare considerably less active than organolithiums, as a result of the muchless polarized metal-carbon bond. They can only initiate polymerization of monomers more reactive than styrene and 1,3-dienes, such as acrylic and methacrylic esters.
662
Chapter 8
Styrene and other monomers can be polymerized by potassium amide in liquid ammonia.The dielectric constant of the solvent is quite high 22) and this is one of the ionic systems in which the active centers behave kinetically as flee ions. Initiation involves the dissociation of potassium amide followed by addition of amide ion to the first monomerunit: KNH2 ~NH~
+
K+ + NH~ H CH~=C ~ H~N-CH2--C-
(8.9) H (8.10)
Al-so because of the unusual nature of this solvent, chain transfer to solvent is important in this system (see later). Electron
Transfer
Initiation by electron transfer is based on the ability of the alkali metals to supply electrons to the double bonds. This yields an anion radical and a positively charged, alkali-metal counterion. Initiation maybe effected (a) by direct attack of the monomeron the alkali metal, or (b) by attack on the metal through an intermediate compoundsuch as naphthalene. Both result in bifunctional initiation, that is, formation of species with two carbanionic ends. Allah
Metals
Initiation by direct attack of the alkali metal involves transfer of the loosely held s electron from a Group IA metal atom to the monomer. A radical ion is formed:
Li. + CH~=C, --~ .C~--C.. Li" X
(8.11)
The radical ion may dimerize to give a dianion:
7 Li+ --~Li+-~d-CH2-CH2--~. :-Li+ (8.12) 2 "CH:--C. ± k x The eventual result of the initiation process is thus a bifunctional dicarbanion species capable of propagating at both of its ends.
Ionic Chain Polymerization
663
Free metals may be employed as solutions in certain ether solvents, in liquid ammonia,or as fine suspensions in inert solvents. The latter are prepared by heating the solvent and the metal above the melting point of the metal, stirring vigorously to form an emulsion, then cooling to obtain a fine solid dispersion. The metal may also be used as a free-flowing powder coated on an inert support such as alumina. The polymerization process is heterogeneous if the metal is used as a dispersion and homogeneous if it is in solution. [Not all ammoniasolutions of alkali metals initiate by electron transfer; potassium, for example, is believed to form KNt-I2, which initiates polymerization by addition of amide ion, as shownby Eqs. (8.9) lan’d (8.10). [Historically, the most important application of the electron transfer initiation involved the production of stereoregular diene rubbers by lithium metal initiation. The lithium was used as a fine dispersion with a large surface area to speed up the initiation reaction and the process was carried out in hydrocarbon solvents because polar solvents increase the generally undesired vinyl side chain content of the product polymer.] Alkali
Metal Complexes
Polycyclic aromatic compoundscan react with alkali metals in ether solution to produce monomericradical ions [1]. The reaction involves the transfer of an electron from the alkali metal to the aromatic compound.For sodium and naphthalene, for example,
Na,
+
-
Na+ (8.13)
-"
(x) The radical nature of the anion radical (X) has been established from electron spin resonance spectroscopy and the carbanion nature by its reaction with carbon dioxide to form the carboxylic acid derivative. The equilNrium in Eq. (8.13) depends on the electron affinity of the aromatic hydrocarbon and the donor properties of the solvent. Tetrahydrofuran (THF) is a useful solvent for such reactions. This fairly polar solvent (dielectric constant 7.6 at room temperature) promotes transfer of the s electron from the alkali metal to the aromatic compoundand stabilization of the resultant complex, primarily via solvation of the cation. Sodium naphthalenide is
664
Ghapter 8
formed quantitatively in THF, but dilution with hydrocarbons results in precipitation of sodium and regeneration of naphthalene. The naphthalene anion radical (which is colored greenish-blue) transfers an electron to a monomersuch as styrene to form the styryl radical anion (XI) (¢ = --C6H5): H H H H + ¯ -C~.,-,.TC-CI. ’-I I I
Na
¢)H
(8.34) The styryl radical ion (XI) is shown as a resonance hybrid of the forms wherein the anion and radical centers are alternatively on the or-- and /~--carbon atoms. The styryl radical anion dimerizes to form the dicarbanion (XII) ~ : C--C’/Na + ~ Na + + ":"
J
~-CH~-CH~--~.:"
Na
This initiation process is thus similar to alkali metal initiation in (a). That this reaction occurs is shown by electron spin resonance measurements, which indicate the complete disappearance of radicals in the system immediately after the addition of monomer.The monomerin these systems often has a lower electron affinity than the polycyclic hydrocarbon, but dimerization of the monomericradical anion [Eq. (8.15)] drives the equilibrium reaction (8.14) to the right. Dimerizationof radical centers is highly favored by their high concentrations, typically 10-3-10-2 Mand the large rate constants (106-108 L/mol-s) for radical coupling. (Note that the dimerization occurs to form the styryl dicarbanion instead of :CH2CH~bCH~bCH2:, since the former is muchmore stable.) The styryl dianions are colored red (the same as styryl monocarbanionsformed via initiators such as n-butyllithium). Anionic propagation occurs at both carbanion ends of the styryl dianion: H Na :C-CH2-CH2--
’
Na÷ .:-C-CH2-(-
C : Na+ + (n +,m) ~bCH=CH2 ~
cHqb --CH~ ).
( CH2-CH~b--)-~-~ CU~ ’] +
Anionic propagation is generally muchfaster than free-radical reactions.
665
Ionic ChainPolymerization
Problem8.3 Account for the fact that anionic polymerizations are generally muchfaster than free-radical reactions although the kp values are of the same order of magnitudefor addition reactions of radicals and solvated ion pairs (free macroanionsreact muchfaster). Answer: -9The concentrationof radicals in free-radical polymerizationsis usually about 10 10-7 Mwhile that of propagatingion pairs is 10-4-10-2 Mdependinguponinitiator concentrations. As a result, anionic polymerizationsare 10a-107 times as fast as free radical reactions at the sametemperature.
Termination
Reactions
Anionic polymerizations must be carried out in the absence of water, oxygen, carbon dioxide, or any other impurities that may react with the active ionic centers. Glass surfaces carry layers of adsorbed water which react with carbanions. It is thus necessary to take special precautions, such as flaming under vacuum, to remove this adsorbed water in laboratory polymerizations. The monomeritself should be very pure and free from inhibitors. Polymerization Polymerization")
Without
Termination
("Living
Interest in anionic polymerization grew enormously following the work of Michael Szwarc in the mid 1950s. He demonstrated that under carefully controlled conditions carbanionic living polymers could be formed using electron transfer initiation. With ionic polymerization, as we have noted earlier, there is no compulsory chain termination through recombination, because the growing chains carrying same ionic charges cannot react with each other. Thus in anionic polymerization systems, especially of nonpolar monomerssuch as styrene and 1,3-butadiene, initiated by organometallic compoundsand employing perfectly dry inert solvents such as benzene and tetrahydrofuran, termination or transfer is virtually nonexistent and active chain ends have indefinite lifetimes. Such systems are referred to as living po~mers. Propagation occurs with complete consumption of monomerswhile the propagating anionic centers remain intact because transfer of protons or other positive species from the solvent does not occur.
666
Chapter8
The nonterminating character of living anionic polymerization is evident from the fact that if a reaction system is highly purified so that impurities are absent, the color of the carbanions is observed to persist throughout the polymerization and does not disappear or change even at 100%conversion. After 100%conversion is reached, additional polymerization can be effected by adding more monomer,either the same monomeror a different monomer. The added monomeris also polymerized quantitatively, without any new addition of initiator, and the molecular weight of the living polymer is increased. (There is no reason in theory why chain growth should stop if more and more monomeris added and chain terminators are absent. In practice, however, small amounts of terminators are inevitably produced and chain growth also slows downeventually because of the high viscosity of the system or because the chains becomeinsoluble.) Termination of the living chain can be brought about when desired by introducing suitably reactive materials, such as water, alcohol, or ammonia. The aforesaid features offer fascinating possibilities of building model polymer systems such as monodisperse molecular weight polymers (by controlled addition of monomer), structures with defined end groups (by deliberate termination of a living system with appropriate reagents) and. block copolymers (by sequential addition of two or more monomers). These are discussed more fully in a later section. Termination by Impurities 7Yansfer Agents
and Added
Ionic polymerizations, as noted above, are carried out in an inert atmosphere with rigorously purified reagents and cleaned glassware since trace impurities lead to termination. Anymoisture present terminates propagating carbanions by proton transfer: vvwvCH2--~: q- H20 ---* v~wCH2--6H + HO-
x
t
The hydroxide ion is usually not sufficiently nucleophilic to reinitiate polymerization and the kinetic chain is thus broken. Water is an especially effective chain terminating agent. For example, Ctr,s is approximately 10 in the polymerization of styrene at 25°C with sodium naphthalene. Thus the presence of even small concentrations of water can greatly limit the polymer molecular weight and polymerization rate. Ethanol has a C’tr,S value of about 10-:~. Hence its presence in small amounts would not prevent the formation of high polymer because transfer would be slow; the polymer, however, would not be living.
Ionic ChainPolymerization
667
Oxygen and carbon dioxide from the atmosphere add to propagating carbanions to form peroxy and carboxyl anions:
w~wCH2--
(8.18)
+ O2 ~ wvwCH2--C~-O-(~: X
(8.19)
wwvCH2--C: + CO~_ ---~ w~vCH2--C--C--O:
These anions are normally not reactive enough to continue propagation and tile chains are thus effectively terminated. The peroxy and carboxyl anions usually are finally obtained as HOand HOOC groups when a proton donor is subsequently added to the polymerization system. Polymerswith specific end groups can be prepared by deliberately introducing particular reagents that terminate ("kill") living polymers. Telechelic polymers (that is, polymers with reactive end groups), containing one more end groups with the capacity to react with other molecules, can be prepared in this way. Thus, in the anionic polymerization of butadiene with bifunctional initiators, carboxyl end groups are produced by termination with CO2: Na + :-~-CH=CH-CH2vwwwCH2-CH=CH--
_ 9,
Na + + 2CO2 ~
Na ÷ :O--CCH2-CH=CH-CH~w~vwCH~-CH=CH-CH~--
9, -
+ C-O :
Na
(8.20) Reaction with acid then yields carboxyl-terminated polybutadiene (CTPB). Hydroxyl end groups are provided by termination with ethylene oxide: vvwvC: Li + + CH2--CH2
+ wwvCH2-CH~-CH2-O- : Li w~vCH2-CH~-CH2-OH +
Cn_qH LiOCH3
(s.21) Hydroxyl-terminated polybutadiene (HTPB) can be produced by such reactions. Low-molecular-weight (3000-10,000)versions of such elastomers are used as binders and liquid rubbers, which can be shaped more easily than the conventional high-viscosity elastomers. The liquid rubbers can be vulcanized by reactions of their specific end groups. Hydroxyl-ended
668
Chapter 8
polybutadiene can be caused to grow in molecular size and to cross-link, for example, by reaction with isocyanates having functionalities > 2. Spontaneous
Termination
Living polymers do not live forever and even in the absence of terminating agents decays with time [2]. The most stable of all living anionic systems are polystyryl carbanions, as they are stable for weeks in hydrocarbon solvents. The mechanismfor the decay of polystyryl carbanions on aging, referred to as spontaneous termination, is not completely established. The generally accepted mechanismconsists of hydride elimination : wvwCH2CH~CH~--
,~-:
Na+ ~ w~CH~CH~CH=CH~ + HI"
(xni)
+ Na
(8.22)
followed by abstraction of an a[lylic hydrogen from (XlII) by a carbanion center to yield the unreactive 1,3-diphenylallyl anion (XlV) [3]: wvvvCH2~C :
+ wvwCH2CHq~CH=CH¢ ---* wvwCH2-CH2¢
7. ÷ wvwCH2C¢CH=CH¢
(8.23)
(x_w) The sodium hydride eliminated in reaction (8.22) may also take part hydrogen abstraction from (XIII). Problem 8.4 Lower molecular weights and polymerization rates observed in anionic polymerizationsof polar monomers are attributed to the reactivity of the polar substituents towardnucleophiles, leading to termination and side reactions that are competitive with both initiation and propagation. Explain this behavior considering the case of methyl methacrylate monomer. Answer: Several different nucleophilic substitution reactions are possible with MMA. For example, attack of initiator on monomer by the reaction C, H3 ~ CH2 = C~C-OCH3 + R-Li + + ---*
CH3,Oit CH2-----C--C-R
+ CHzC~: Li (P8.4.1) converts active alkyllithium to alkoxide, whichis’a less active initiator, and MMA to i-propenyl alkyl ketone, which forms less active carbanion than MMA. The polymerizationrate is thus decreased.
669
Ionic Chain Polymerization
There may be a nucleophilic attack by a propagating carbanion on the monomer,by the reaction, CH3 l_ vvvwCH~-- C : Li + + ~OOCHz
CH3 O It I C-- C-OCHz -~
CH2 =
C~H3~__ C~ H3 + ~ C=CH2 + CHaO-: vvvvvCH2mC~ COOCH3
Li
(P8.4.2)
whichagain yields a less reactive methoxideinitiator and an i-propenyl keto end group which also forms a less reactive carbanion than MMA. This reaction lowers the polymermolecular weight and decreases the polymerization rate. A nucleophilic attack mayalso take place intramolecularly resulting in chain termination and formationof less active methoxideinitiator
PolymerizationKinetics The kinetics of anionic polymerization is much more complex than the kinetics of free-radical polymerization. Most of the complications arise from the initiation reactions. Th6variety of initiation possibilities often gives the appearance that each anionic polymerization is unique and that no general kinetic treatment is possible. In polymerizations initiated by alkali metals or insoluble organometallics employedas fine dispersions in organic media, the initiation step occurs at a phase interface while subsequent propagation reactions may occur in a homogeneous medium. The overall kinetics of such heterogeneous initiation/homogeneous propagation reactions are often very complexand specific to the particular systems. Useful generalizations mayhowever be provided by systems in which the initiation and propagation processes are both homogeneous.Such polymerizations are discussed next.
670
Chapter 8
Somecases exist in homogeneousanionic polymerization in which the initiator dissociates completely with quantitative transformation into the active ionic form and does so before any significant amount of propagation has occurred (stoichiometric polymerization). This is the case, for example, if one uses, as initiators, alkali organic compounds (e.g., phenyllithium, butyllithium, or sodium naphthalene) in solvents which have unshared electron pairs (Lewis bases). In this case the alkali forms stable positively charged complexions with the Lewis base, so that the organic residue is negatively charged (carbanion) and an ionic polymerization can be initiated by this carbanion [cf. Eqs. (8.13) and (8.14)]: H + C4HgLI + .~.
~ CH3CH2CH2!:-+ [Li-.--.:O~] H
Li {~
"’@ + :NH 3 ~
IL + 3 i -.--
+ 1 :NH
In the above cases, the polymerization kinetics are so simple that it is useful to classify ionic polymerization kinetics according to whether the initiators are quantitatively and instantaneously dissociated or not. (It should be noted that the term "dissociation" does not denote any special kind of charge separation. Probably one has to regard this dissociation as a separation of ion pairs by solvent molecules, but not a separation in the sense of forming single ions which can move independently from the counterion.) Quantitative of Initiator
and Instantaneous
Dissociation
For a kinetic analysis, the process of anionic polymerization has to be divided into at least three main reactions commonto all types of polymerization, viz., initiation, propagation, and termination. Representing the initiator by -) and a terminating agent by X, the reactions can be written CA(or C+A as
Initiation :
+ CA -1-
M ~ AM- C
(8.24)
671
Ionic ChainPolymerization Propagation :
AM- C + + -F
M -~
AMM- C
(8.25)
AMM- C + + M ~ AMMM- C + (8.26) AM~_IM- C+ -]Termination:
AMzM- C+ (q-
M -~ AMxM- C+ (8.27) X) ~-~ AMzM
(8.28)
(Depending upon the solvent, the propagating ion may behave as a free +, or as both.) Living polymerizaion AMzM-or as an ion pair AMzM-C tions are characterized by the absence of termination (as well as transfer) reactions. In most cases it is also possible to find initiators which are reactive enough to give instantaneous initiation, i.e., ki > kv. This implies that no initiation takes place during the polymerization and the number of chain centers to which the monomermolecules may add reaches its maximum value before potymerizalion begins. Moreover, the number of chain centers does not change during the polymerization because there is no termination step. Denoting the total concentration of anions of all degrees of polymerization by [M-] (the positive counterion + i s n ot s hown for s implicity) and assuming that the initiation reaction (8.24) is not only instantaneous but also complete, one can thus write for living polymerization [M-] = [CA]0
(8.29)
Hence the rate of polymerization is given by P~ ----=
- at -- ]~p[M-][M]
= kp[CA]0 [M](8.30)
Here ]~p should more appropriately be called an apparent rate constant or overall rate constant since both undissociated (ion pair) and dissociated (free ions) species usually exist and their propagation rate constants are different (discussed later). Integration of this pseudo-first-order rate equation gives the time dependence of the monomerconcentration as [M] = [M]sp exp (--/¢~[CA]ot)
= ([M]o -- [CA]o)exp (--kp[CA]ot)
(8.31) where the subscript ’0’ indicates initial value. Note that [M]sp is the monomer concentration at the start of propagation [Eq. (8.25)] and thus equals the original monomerconcentration less the concentration of the initiator CA which is quantitatively reacted. From the experimental measurementof [M] at various times after the polymerization is started and knowing[CA]0, that is the concentration of the initiator in the initial reaction mixture, ]~p may
672
Ch~p~er8
be determined either by Eq. (8.30) or Eq. (8.31). The significance of values of kp will be discussed in a later section. Methods Manyanionic living polymerizations proceed too rapidly to be followed by techniques such as dilatometry. The Stopped-flow technique is useful for studying these fast polymerizations. In stopped-flow, rapid-scan spectroscopy [1,4], separate monomerand initiator solutions are rapidly forced through a mixing chamber (where instantaneous mixing occurs) and then into capillary tube located in a spectrophotometer; flow is stopped and the change in absorbance is measured with time. This method allows one to follow the initiation rate (observing the increase in optical density of propagating species) and/or the polymerization rate (by following the loss of monomer). The polymerization rate can be obtained by short-stopping a polymerizing system by means of a highly efficient terminating agent. All propagating centers are quickly terminated with incorporation (into the polymer) of an end group derived from the terminating agent. In a modified apparatus, the rapidly mixed monomer-initiator solution is forced through the flow tube into a solvent containing a terminating agent (Fig. 8.1). A turbulent flow must prevail in this flow tube (Reynolds number > 10,000) since the chains would show growth times of differing duration with a laminar flow. The end groups in the polymer are analyzed after ~eparation of the polymer from the other componentsof the reaction system. The reaction time is given by the ratio of the capillary volume to the flow rate. Short reaction times from 0.005 to 2 sec can be accurately studied in this manner. The conversion, and hence /~, are obtained by analyzing the quenched reaction mixture for either polymer or unreacted monomer.
Problem8.5 Consider the flow tube for rapid polymerization reactions shown schematically in Fig. 8.1. Let ~ be the volumeof the tube (distance between the mixingjets) and V be the volumeof the total liquid flowing through in time t. Denotingthe total concentration (constant) of polymerchain ends by Eq. (8.29) and the concentration of monomer units in polymerby [M]p derive an expression for monomerconversion as a function of t. .~nswer: The effective polymerizationtime is the sameas the residence time ~- given by Vo (P8.5.1)
Ionic Chain Polymerization
673
Integrating the rate of propagation, given by Eq. (8.30) and assuming[M]sp [M]0for high polymers,that is, high monomer to initiator ratio, one obtains -- ln[M] I = k,[CA]0 t I (PS.5.2) where [M]~ = [M]0 - [M]p. Equation(P8.5.2) is transposedwith the aid of Eq. (P8.5.1) t : in [M]o (~) [M]--’-~----- k, [CAIo~" = k, [CA]o where p is the monomerconversion given by tn{1/(1-,)}
V =
(P8.5.3)
[M]o
Average Kinetic
Chain Length
Because there is no termination step in a true "living" polymerization, the kinetic chain growth is ended only when the monomeris completely consumed. The average kinetic chain length in living polymerization with fast and complete dissociation of initiators, will be given by Monomer molecules consumed [M]sp -- [M] Numberof chain centers [CA]o
_
(8.32)
where [M]sp -" [M]0- [CA]0 (8.33) since the initiator is assumed to be instantaneously and quantitatively reacted. Onsubstitution of [M] from Eq. (8.31), ~, is obtained as a function of time, given by [MIsp-~[ {1 cA]° H
H ~C ~ CH2 H
(b) Conjugationwith the carbocation center helps to disperse the positive charge and tends to increase monomer reactivity. The "effect is particularly strong when
Ionic Chain Polymerization
705
conjugation and electron-donating groups cooperate. On the other hand, substitution of an electron-withdrawing halogen for an ortho or para hydrogen, decreases the monomerreactivity. Thus the reactivity sequence of the styrene derivatives is as follows: H\c//CH2
H\c#CH2
CH3\c//CH2
H\C
OCH 3
~CH2
Cl
Electron-releasing substituents, such as RO-, RS-, and aryl at ortho or para position increase the monomerreactivity.
Problem8.18 (a) Consider the cationic polymerizability of vinyl ethers, cyclic ethers (like tetrahydrofuran), cyclic acetals (like trioxane), and N-vinyl bazole. (b) Whydo these monomersnot copolymerize cationically with olefins like styrene or isobutene ? Answer: (a) In these monomersthe heteroatom is bonded directly to the electron-deficient atom and the respective carboxonium ion and immoniumion are more stable than the corresponding carbocations. These monomersare thus suitable for cationic polymerization : H ’ CH2=C-OR Vinyl ether
__CH2_!
~ H2C=C I
H
H ~
+ O-R
~ ~ --CH2-
+O-R
H --CH2-i+
H --CH2-~
II
(b) As noted above, carboxonium and immonium ions are more stable than the corresponding carbocations. Because of this difference in stability, the above monomerswill not copolymerize cationically with olefins like styrene and isobutene.
706
~hap~er 8
Cationic Initiation Various initiators can be used to bring about cationic polymerization of monomerswhich have electron-releasing substituents. Initiation is brought about by addition of an electrophile to a monomer molecule [cf. Eq. (8.2)]. Compounds used more commonly are the various protonic and Lewis acids. Protonic
Acids
Protonic (Br6nsted) acids initiate cationic polymerization by protonation the olefin : R Rt + H+ A- + CH2 = ~--~ CH3--C A(8.106) However, for polymerization to occur the anion A should not be a strong nucleophile; otherwise it will react with the carbocation to form the nonpropagating .covalent compound CH 3 -- C ~A Thus hydrogen halides are ineffective as initiators of cationic polymerization because of the highly nucleophilic character of halide ions. (Hydrogen iodide, however, shows some tendency to polymerize vinyl ethers, but the polymer yields and molecular weights are low.) Other strong acids with larger and less nucleophilic anions such as sulfuric, perchloric, phosphoric, fluoro- and chlorosulfonic, methanesulfonic and trifluoromethanesulfonic (triflic) acids, initiate cationic polymerization. However,the polymermolecular weights rarely exceed a few thousand. The low molecular weights are because of transfer reactions which are discussed later. Initiation by protonic acids is relatively inexpensive. The major applications of such processes are for reactions of simple olefins like propylene or butenes or olefinic derivatives of aromatics such as coumarone (XV) and indene (XVI). The low polymers of olefins are used as lubricants and fuels while coumarone-indene polymers are employed in coatings and as softeners for rubbers and bitumenes.
707
Ionic Chain Polymerization Lewis Acids
Various Lewis acids are used to initiate cationic polymerization, generally at low temperatures, with the formation of high-molecular-weight polymers in high yield. Lewis acids are halides and alkyl halides of Group III metals and of transition metals in which the d electron shells are incomplete. This is the most generally useful group of initiators and include metal halides such as A1C13,BF3, SnC14, SbC15, ZnC12, TIC14, PC15, and organometallic derivatives, e.g., RA1C12,R2AIC1, R3A1. (Many of the metal halides are familiar to chemists as Fried.el-Crafts catalysts.) A1CI3is the most important Lewis acid for industrial cationic polymerizations. Lewis acids are seldom effective alone; rather they require the presence of trace amounts of water or some other proton donor (protogen) such as hydrogen halide, alcohol, and carboxylic acid, or a carbocation donor (cationogen) such as t-butyl chloride or triphenylmethyl chloride, which, on reaction with the Lewis acid, forms the electrophilic species that initiates polymerization. Thus dry isobutylene is unaffected by dry boron trifluoride but polymerization occurs immediately when trace amounts of water are added. The initiation process for boron trifluoride and water is BFz q- H20 ,~- H+ (BF3OH)(8.107) H+ (BFzOH)- q- (CH3)2C = CHz ~ (CH3)3C + (BF3OH)-
(8.108) Initiation
by aluminumchloride and t-butyl chloride is described by
AICI3 q- (CHa)aCGI ,~(CH3)3C q-
(AIC]4)-
(CHa)3C + (AIC]4)-
(8.109)
--[-
~CH = CHz -~ (CHa)aCCH2CH4(AIC14)(8.110) Because it is the proton or carbocation that initiates the polymerization reaction, the compoundsthat give rise to them are correctly referred to as the initiators, and the Lewis acids as coinitiators [11] (not the other way around, as is commonlydone in the polymer literature). The combination of Lewis acid and proton or cation source is the initiating system. The initiation steps described above can thus be generalized as K L q- IB ~--- -B+(LI) B + (LI)-
q-
M -~
(8.111) +(LI)-
(8.112)
where L, IB, and Mrepresent, respectiVely, the Lewis acid coinitiator, initiator, and monomer.Initiation by the initiating system has the advantage -) that the anion (LI)- is far less over initiation by a Br6nsted acid (H+A nucleophilic than A- [cf. Eq. (8.106)].
708
Chapter8
With certain Lewis acids of higher acid strength such as AICI3 and TIC14autoinitiafion or self-ionization mayoccur. In such cases the initiator and coinitiator are the same, and the initiation is usually represented by 2A1Br3 ~ A1Br~ + (A1Br4)AIBrz + (A1Br4)- + M ~ A1BrzM+ (A1Br4)-
(8.113) (8.114)
However, for polymerizations carried out under most reaction conditions, the moisture content (and/or level of other carbocation or proton donors) is often sufficient for reaction (8.111) so that self-ionization constitutes only a minor propagation of the total initiation process.
Problem8.19 Arrangethe following initiators and coinitiators in the general order of activity for initiating cationic polymerizationof monomers: (a) Initiators: water, acetone, hydrogenchloride, methanol,acetic acid, phenol, and nitroethane. (b) Coinitiators: AICI3, AIR3, AIRCI2and AIR2C1; A1R2CI, AIR~Br, and AIR2I. Answer: The extent of formation of the initiator-coinit/ator complex[i.e., the value of K in Eq. (8.111)] and its rate of addition to monomer [i.e., the value of ki in Eq. (8.112)] generally increase with increasing acidity of the initiator and that of the coinitiator. Thusfor the initiators the general order is HCI > CHzCOOH > O2NC2Hs> C~H~OH> water > methanol > acetone For the coinitiators the order of acidity, and hencethe general order of activity, is AICI 3
> AIRCI2 > AIR2CI > AIR3 and AIR21 > AIR2Br > AIR2CI
It mustbe mentioned,however,that the order of activity of a series of initiators or coinitiators maydiffer dependingon the identity of the other component,monomer, solvent, or the presenceof competingreactions. For example,the activity of boron ha/ides in isobutylene polymerization is observed to be BFz > BCI3> BBr3with water as the initiator, while the order of acidity is BBr3> BCI3> BF3.This is due to hydrolysis of the boronhalides to inactive products increasing in the same order as their acidities.
The effectiveness of a cationogen in initiation depends on carbocation stability in a complex manner. Increased stability of a carbocation formed from the cationogen enhances the initiation, but the carbocation has lower reactivity. Differences in stability of the carbocation formed from the
Ionic ChainPolymerization
709
cationogen compared to the propagating carbocation are also important in determining the effectiveness of a cationogen.
Problem8.20 Give plausible explanation for the following facts. Primary and secondaryalkyl halides are generally ineffective as initiators of cationic polymerization x)f monomerssuch as isobutene and styrene, but t-butyl and cumyi chlorides are effective. Onthe other hand, triphenylmethyl chloride and cycloheptatrienyl (tropylium)chloride are not very efficient in polymerizingisobutylene and styrene but produces rapid polymerization ofp-methoxystyrene,vinyl ethers and N-vinylcarbazole. Answer: Primaryandsecondaryalkyl halides are generallyineffective as initiators of cationic polymerization, because primary and secondaryearbocations are formedtoo slowly and/or in extremelylow concentrations. However,tertiary earbocations such as tbutyl and cumyl(2-phenyl-isopropyl) are sufficiently stable to form but are not morestable than the carbocations derived from their addition to monomers such as isobutene, styrene, or N-vinylcarbazole,so that polymerizationsof these monomers occur. +, and Triphenylmethylhalides and tropyliumhalides ionize to formtrityl, ~3C cycloheptatrienyl (tropylium), CrH~-,carbocations [Eqs. (P8.20.1) and (P8.20.2)], which are too stable to efficiently polymerize less reactive monomerssuch as isobutylene and styrene, but polymerizationofp-methoxystyrene,vinyl ethers and N-vinyl carbazole, whichare morereactive, proceeds rapidly. (C6H5)3CCI ~- (C6H5)3 C+ -1- CI-
(P8.20.I)
+ Ct-
(P8.20.2)
Chlorine, bromine, and iodine act as cationogens in the presence of more active Lewis acids such as trialkyl aluminum., or dialkylaluminumhalide. The initiating species is the haloniumion X+ formed via the equilibrium reaction between Lewis acid and halogen. The polymerization by syncata~ytic systems consisting of an aluminum compound R2AIZ(R = alkyl and Z = alkyl or
710
Chapter 8
halogen) and halogen or an interhalogen compoundare initiated addition of a positive halogen ion to the monomer: ~ X+ R2AIYZ-
XY + R2AIZ
X+ R2A1YZ-
by the (8.115)
R I + CH2 = C ~ X-CH2--CI.
R + R2AIYZ - (8.116)
where X is a halogen atom and Y is either a halogen or a different group. Iodine is unique amongthe halogens in that it initiates polymerization of the more reactive monomerseven in the absence of a Lewis acid. Iodine is not the actual initiator when it is used in the absence of a Lewis acid. Iodine adds to the double bond to form a diiodide that eliminates hydrogen iodide [12]. The hydrogen iodide generated by this process acts as the cationogen with iodine acting as a Lewis acid to form the initiating system. (Hydrogeniodide itself is not an efficient initiator because iodide ion is too nucleophilic) I2
+ CH2~CH ~--I OR
ICH2--cHI I OR
~ ICH=CH I OR
+ HI
(8.117)
(8.118) I2 + HI ~ H+ I~This initiation route is moreefficiently utilized by directly adding a mixture of hydrogen iodide and either iodine or a metal halide such as ZnX2or SnX2to the reaction system. An alternative mechanism has been suggested [13] which postulates formation of ion pair directly from the 1,2-diiodo compoundand/or its reaction with I2: + IICH2-- CHI ~ ICH2--CH=OR
I
(8.119)
OR ICH2~CHI I OR
+ 12 ~
ICH2--CH--OR I~
(8.120)
followed by propagation, + ICH:2CH---OR I~" + CH2
=CHOR ~ + ICH2CH(OR)CH2CH--OR I~ (n =1 or
The halogen initiation
(8.121)
mechanismis not directly confirmed, however.
711
Ionic ChainPolymerization Propagation
of Cationic
Chain
The initiator ion pair (consisting of carbocation and its negative counterion) produced in the initiation step [Eq. (8.112)] proceeds to propagate successive addition of monomermolecules. Considering isobutylene polymerization [cf. Eq. (8.108)], for example, this can be represented + H~CH2C(CH3)2--]~-CH2
C(CH3)2 (BF3OH)- + (CH3)2C=CH2 ÷ (8.122) H-{-CH2C(CH3)2-~+I-CH2-C(CH3) 2 (BF3OH)-
or,ingeneral terms[cf.Eq.(8.116)], HMnM + (LI)- -1- M ~ HMn+I M+ (LI)-
(8.123)
The addition proceeds by insertion of monomerbetweenthe carbocation anditsnegative counterion. The propagation reaction canbe complicated in somecasesdue to the occurrence of intramo]ecular rearrangements causedby hydrideion(H:-) or methide ion(CH3:-) shifts. Polymerizations proceeding withsuchrearrangements are referred to as isomerization polymerizations. The extent of rearrangement during propagation will depend on the relative stabilities of the propagating and rearranged carbocations and the relative rates of propagation and rearrangement. Both these factors favor propagation without rearrangement for monomerssuch as styrene, isobutylene, and vinyl ethers, since these monomerspropagate via reasonably stable carbocations such as benzyl, tertiary, and oxycarbocations, respectively. Extensive rearrangement during propagation, however, occurs for a variety of 1-alkenes. Consider, for example, the polymerization of 3-methyl-l,2-butene. Isomerization occurs by a 1,2-hydride ion shift in the first-formed carbocation (XVII) prior to the addition of the next monomerunit. The rearranged ion (XVIII) is a tertiary carbocation and is more stable than the first-formed carbocation, which is a secondary carbocation. H I + vvvwCH2--C
+ vvvvvCH2-CH2--C(CH3)2
CH(CH3)2 (XVII)
(XVIII)
¯ Thepolymer thuscontains mostly therearranged repeating unit(XIX)but alsosomeof thefirst-formed repeat units(XX)as somenormalpropagation occurs athigher temperatures. Itis observed thattheproduct contains about 70 and100%of (XIX)at polymerization temperatures of -130and -I00°C, respectively.
Chapter8
712 w~wCH2 ~ CH2--
C(CH3)2w~v
vwwCH2--C,
(x x)
H CH(CH3)2
(xx)
Propylene, 1-butene, and higher 1-alkenes yield only oligomers (DP no higher than 10-20) with highly irregular structures due to various combinations of 1,2-hydride and 1,2-methide shifts, proton transfer and elimination, and chain transfer. For example, protonation and ethylation of ethylene are rapidly followed by energetically favorable isomerization: + CH~_~H~ =CH2 ~ CH3-CH2 + HT shift + CHaCH2-CH2-CH2 ---~ CHaCH2-CH-CH~ ~ etc.
H + + CH2
(8.124)
These transformations follow the favorable enthalpy differences between primary to secondary (-22 kcal/mol) and secondary to tertiary (’2_ --33 kcal/mol) carbocations.
Problem8.21 Write equations to show the different
structural units that may result from intramolecular hydride and methide shifts involving only the end unit. Which of the resulting repeating units would be the most abundant? Answer: Five different end units (XXI - XXV)may arise from 1,2-hydride and methide shifts. The first-formed carbocation (XXI) undergoes hydride shifts to form carbocations (XXII), (XXIII), and (XXIV); (XXIII) rearranges to (XXV) methideshift : H + CH2=CH -----,...--.CH2-I CH2CH (CH3) 2
~. I CH2CH (CH3) 2 (XXI)
H.rshift
~
~C
H I+ I CH2CH2CH (CH3) 2 (XXII)
I
H:" shift
CH3 ~
-, CH2CH2CH2]~+H~-shift CH 3
0OClV)
H I ?CH3 shift + CH2CH2-C CH 2 (CH3)
(XXlII)
CH3 H I I + = ~ CH2CH2CH-C CH3
(xxv)
713
Ionic ChainPolyrnerization
The tertiary carbocation (XXIV)is the most stable and hence the repeating units derived from it will be present in the greatest abundance(found 42-51%). The other carbocations are of comparablestability and the repeating units derived from themwill be found in comparablequantities.
Other monomers that undergo isomerization polymerization include 5-methyl-l-hexene, 4,4-dimethyl-l-pentene, 6-methyl-l-heptene, cr-pinene, and vinylcyclopropane. Chain Transfer
and Termination
Termination reactions are harder to define in cationic processes because they are easy to confuse with chain transfer. Termination of chain growth in cationic polymerization may take place in various ways. Many of the reactions that terminate the growth of a propagating chain do not, however, terminate the kinetic chain because a new propagating species is generated in the process. Chain
Transfer
to
Monomer
Chain transfer to monomeris perhaps the most important chain breaking reaction in cationic polymerization. Transfer to monomerinvolves transfer of a fl-proton from the carbocation to a monomermolecule. This results in the formation of terminal unsaturation in the polymer molecule. Since in isobutylene there are two different types of fl-protons, two different unsaturated groups are possible: + H-{--CH2C(CH3)2-]rr-CH2 C(CH3)2 (BF3OH)- + CH2 =C(CH3)2 + (CH3)3C (BF3OH)- + H-[-CH2C(CH3)2-]rrCH2C(CHz)=CH~ + H-{-CH2C(CH3 ) 2 Jl~ CH=C(CH3) 2
(8.125)
Other monomerswhere two different end groups are possible include indene and ot-methylstyrene. For monomerssuch as styrene and ethyl vinyl ether only one type of unsaturated end group is, however, possible. In general terms, chain transfer to monomercan be written + (LI)BMnM
-[-
ktr,M
M ~ Mn+l -t-
+ (L I)-
(8.126)
It should be noted that the kinetic chain is not terminated by this reaction since a new propagating species is generated. Manypolymer molecules are usually produced for each initiator-coiniti~tor species present. The relative rates of transfer and propagation are given by the ratio ktr,M/kp, which is the monomerchain transfer constant C’M. The value of
714
Chapter 8
this constant determines the molecular weight of the polymer if other chain breaking processes are not significant. The larger the value of CMthe lower will be the molecular weight of the polymer [cf. Eq. (6.148)]. Chain transfer to monomeris the principal reaction that limits the polymer molecular weight for most monomers,especially at reaction temperatures higher than about 20°C. Chain transfer, however, is usually suppressed by working at lower temperatures since chain transfer to monomer generally has a higher activation energy. Another type of chain transfer to monomerinvolves hydride ion transfer from monomerto the propagating center [14]: + H-[-CH2C(CHa)2-]n-CH2C(CHa)2(BF3OH)- + CH2=C(CH3)2 CH2 = C(CH3)-CH2(BF3OH)4- H-[-CH2C(CH3)2-]rrCH2CH(CH3)2 (8.127) For isobutylene this reaction is a less likely mode of chain termination compared to proton transfer to monomer[cf. Eq. (8.125)1 since the tertiary carbocation formed by proton transfer is more stable than the allyl carbocation formed by hydride transfer. However, the hydride transfer reaction may account in part for the oligomers obtained in the polymerization of propylene, 1-butene, and other 1-alkenes where the propagation is not highly favorable due to the low stability of the propagating carbocation. The proton transfer and the hydride transfer are kinetically indistinguishable, but one [Eq. (8.125)] results in unsaturated end groups, while the other [Eq. (8.127)] results in saturated end groups. Spontaneous
Termination
Spontaneous termination is a rearrangement of the propagating ion pair and involves regeneration of initiator-coinitiator complexby expulsion from the propagating ion pair; the polymer molecule is thus left with terminal unsaturation. For example, for the system isobutylene/BF~JH20, + H-~CH2C(CH3)2--]w-CH2 C(CH3)2 (BF3OH)H+ (BF3OH)- + H--~-CH2C(CH3)2--}n--n CH2C(CH3)--CH2 (8.128) or, in more general terms, + (LI)BMnM
~t, ~ Mn+l
+
+ B
(LI)-
(8.129)
This type of termination, also referred to as chain transfer to counterion, differs kinetically from chain transfer to monomerin that the latter has a first-order dependence on monomer,whereas chain transfer to counterion is independent of monomerconcentration. Both types of chain transfer have
715
Ionic ChainPolymerization
similarity in not terminating the kinetic chain. The kinetic chain is interrupted, but the initiator-coinitiator complexis regenerated and can initiate new kinetic chains. However, chain transfer to counterion is almost never a dominant termination reaction compared to chain transfer to monomer. Combination
with
Counterion
This process, unlike the above mentioned processes, terminates the kinetic chain. In general terms, the reaction can be represented by BMnM+ (LI)-
~ BMnMLI
(8.130)
This type of termination occurs, for example, in the trifluoroacetic initiated polymerization of styrene [15]: H vvvvvCH2-- C
H
O -;O-CCF3
~
vvvvvCH2--
acid
O
C-O--CCF3 (8.131)
Alternatively, the propagating ion may combine with an anionic fragment from the counterion [16] as in BX3.OH~.(X m halogen) initiated polymerization or terminate by alkylation or hydridation [17,18] when aluminium alkyl-alkyl halide initiating sytems are used.
Problem8.22 Write equations to describe plausible termination reactions in cationic polymerization of isobutylene initiated by (a) BF3.OH2,(b) BCI3.OH2, (c)AlR3/t-butyl chloride, and (d) Al(C2Hs)z/t-butylchloride. Answer: (a) For BF~.H20 initiated polymerization,chain transfer to monomer [Eq. (8.125)] is the major modeof chain breaking with a minor contribution by combination with OH, ÷ H’-[--CH2C(CH3)2--~
CH2
C(CH3)2
(BF3OH)-
H--[--CH2C(CH3)2--]-a--, CH2C(CH3)2OH -b
(P8.22.1)
(b) Termination in the BCI3.H20initiated polymerization of isobutylene (and styrene) occurs almost exclusively by combinationwith chloride, +
H--[---CH2C(CHz)2--]a--~ CH2C(CHz)2 (BCI3OH)H--[--CHzC(CH3)2--]-~--~ CH2~(CH3)2CI+ BCI2OH(P8.22.2)
716
Chapter 8
The differences betweenthe reactions (P8.22.1) and (P8.22.2) are explained the order of bond strengths: B-F > B-O > B-CI. Thus, chloride ion easily transfers from the counterion to terminate the propagatingcenter, while fluoride ion is inactive towardtransfer. (c) Besides chain transfer to monomer,combinationwith counterion is also important whenaluminumalkyl-alkyl halide initiation systems are used. Termination occurs by alkylation, that is, transfer of an alkyl anion to the propagatingcenter: +
vvwvCH2--C(CH3)2 (R3AICI)’~’CH~-C(CHa)2R
+ R2AIC1
(P822.3)
(d) Terminationby hydridation, that is, transfer of a hydride ion from the alkyl anion to the propagatingcenter, occurs in preference to alkylation whenthe alkyl aluminumcontains/3-hydrogens: +
vv~vCH~-C(CHa)~ [(CHaCH2)aAICI]vvvwCHzCH(CHa)2 + CH~=CH~ + (CHaCH2)~AICI
Chain
T~ansfer
to
(P8.22.4)
Polymer
Several chain transfer to polymer reactions are possible in cationic polymerization. Transfer to cationic propagating center can occur either by electrophilic aromatic substitution (as in the polymerization of styrene as well as other aromatic monomers)or hydride transfer. Short chain branching found in the polymerizations of 1-alkenes such as propylene may be attributed to intermolecular hydride transfer to polyr~er. The propagating carbocations are reactive secondary carbocations that can abstract tertiary hydrogens from the polymer:
+ vvvvvCHz--CR
n t-
H I vvwvCHz--Cvww ~
H
R H
vwwCH2-- CR + I H
vvvwCH2-- Cvv~v I R
(8.132)
This reaction and the corresponding intramolecular transfers [Eq. (8.124)] are responsible for the production of only low-molecular products from 1alkenes. For example, reaetion (8.133) produces a relatively stable tertiary carbocation from a more reactive propagating secondary carbocation.
717
Ionic Chain Polymerization H
H vwvvCH2C[[ + (BF3OH)CH~
vvwvCH2---C-CH 2 vvwv ~ CH3 CH~v
vvvvvCH2--CH2-- CH3 + wwvCH~ + (BFaOH)-
(8.133)
CH3
Other
Transfer
and Termination
Reactions
Various transfer agents (denoted here by TAor S) present as a solvent, impurity, or deliberately added to the system can bring about termination of the growing polymer chain by transfer of a negative fragment A-. In general terms, the reaction can be represented by BMnM+ (LI)-
ktr,S
+ TA ~ BM,~MA
+ T+ (LI)-
(8.134)
where the term ktr,s as in Chapter 6, is used to denote the rate constant for chain transfer to solvent or any other transfer agent. Water, alcohols, acids, anhydrides and esters have varying chain transfer properties. When present in sufficient concentrations, these play the dominantrole in termination. Termination by these compoundsinvolves the transfer of HO, RO, or RCOO anion to the propagating carbocation, e.g., + vvvvvCH2--C(CH3)2
(BF3OH)-
w~CH2--C(CH3)2OH
+ H20
+ + ( BFzOH)-
(8.135)
Nucleophilic reagents such as water, alcohol (often with KOH), ammonia, and amines, are often used in excess to quench a cationic polymerization. This is typically carried out after complete or maximum conversion has been reached.
Problem8.23 Explain howthe following substances act as inhibitors or retarders in cationic polymerization: water, tertiary amines, trialkyl phosphines, and pbenzoquinone. Answer: Water,whenpresent in very small concentrations,acts as an initiator and initiates polymerizationin combinationwith a coinitiator (e.g., SnCI4). However,in larger concentrations, it inactivates the coinitiator (such as by hydrolysis of SnCI4) competessuccessfully with monomer for the initiator-coinitiator complexto form
718
Ohapter 8
the oxoniumsalt, whichis too unreactive in protonatingoleflns becausethe basicity of the carbon-carbondouble bondis far less than that of water: SnCI4 + H20 ~- SnCI4.OH2 H,_~ (H30)+ (SnCI4OH)Terminationcan also occur by proton transfer to water, e.g., 4vvwvCH2--C(CHz)2 + H20 ~ vv~vCH=C(CHz)2 + +
(P8.23.1) (P8.23.2)
or OH-transfer to carbocation, e.g., +
~,~¢H~-C(CH3h (BF3OH)- + H~O wvvvCH~C(CHa)~OHq- + ( BFaOH)(P8.23.3) + + H (BFaOH)- + HzO ~ (HaO) (BFaOH)(P8~.3.4) In the presenceof considerable amountsof water, reaction (P8.23.4) takes place preference to addition of monomer.This explains the decrease in polymerization rate causedby water in higher concentrations.Alcoholsand acids similarly function as inhibitors or retarders. Tertiary aminesand trialkyl phosphinesreact with propagatingchains to form stable cations that are unreactive to propagation: + + (LI)BM~M + :NR3 ~ BMnMNRa(LI)(P8.23.5) This causes inhibition or retardation. p-Benzoquinone acts as an inhibitor by receiving proton from the carbocation and/or initiator-coinitiator complex:
+
©
2 vvvwCH2 CH¢ CCl3CO~" + O~ + ~ 2 vvvvvCH=CHq~ + HO~
~O
~
÷ =OH + 2CCIzCO[
(P8.23.6)
Kinetics Unlike free-radical .and homogeneousanionic syntheses of high polymers, cationic polymerizations cannot be fitted into a generally useful kinetic frameworkinvolving fundamental reactions like initiation, propagation, and so on. This is because of the complexity of the cationic initiation, the uncertainty concerning the extent of ion-pair formation [cf. Eq. (8.1)] at the propagating chain end, and the possibility of the reaction being heterogeneous as the initiator is often only partially soluble in the reaction medium.
719
Ionic ChainPolymerization Ions
and Ion
Pairs
Electroneutrality demands that carbocations always be accompanied by counterions. The distance between the carbocation and counterion is important because it largely determines species reactivity. Dependingon the distance between the charged particles, which in turn is determined by the intrinsic properties of the ions and experimental conditions, a continuous spectrum of ionicities exists as depicted earlier by Eq. (8.1). Free earbocations can exist only under the purest conditions in the absence of even traces of moisture. In the absence of moisture, high polymerization rates can be obtained and the energy of activation is close to zero. Free ions exist in ’)’-ray radiation-induced bulk polymerizations of certain olefins, for example, o~-methylstyrene, fl-pinene, cyelopentadiene. However, in the majority of cationic polymerization systems reported in the literature, the propagating species are probably associated ion pairs. Thoughthe accurate definition of system ionicity in terms of actual species in solution and their concentration is almost impossible, an order of magnitude of free-ions and ion-pair concentrations can be obtained provided simplifying assumptions are made (see Problem 8.28). Figure 8.6 illustrates, for example, the complicated equilibria [19] in initiation by alkyl halides which are widely used as initiators in combination with eoinitiator such as aluminum alkyl halides or aluminumhalide Lewis acids. Each carbocation can initiate polymerization or remove an alkyl (ethyl) group from the counterion to produce a saturated hydrocarbon, REt, and a more acidic Lewis acid. The propagating cation can also terminate by the same process to produce ethyl-capped polymers and new Lewis acids. Thus, even though the coinitiator used is diethylaluminum chloride there may be major contributions to the polymerization from ethylaluminum dichloride or aluminumchloride. Both the initiation and propagation processes are, moreover, influenced by equilibria between various degrees of association of the active center and its eounterion. As a minimum,it is necessary to consider the existence of solvent-separated ion pairs, and free solvated ions. A simplified scheme [20] is shownin Fig. 8.7. The existence of contact (associated) ion pairs [as in Eq. (8.1)] is neglected in this scheme because the dielectric constants of the solvents usually used for cationic polymerizations are high enough (9-15) to render concentrations of intimate ion pairs negligible compared to those of solvated ion pairs. The observed kv in these simplified reactions will thus be composedof contributions from the ion pairs and free solvated ions :
=
+
-
±
where o~ is the degree of dissociation of ion pairs into free solvated ions, the respective rate constants being k~ and k~-. In media of low polarity,
720
Chapter 8
RC[ +AIEt2Cl
~ R+(AtEt2C|2) l
RCI+ AlEtCt 2 )~R+(AtEtCI3
I
RCt + AlCt 3 )~ R+CALC[4
- ~ RM+(AtEt2(:;12 REt 2 + AIEtCl I ~M RM+(AIEtC[3
)-
~ Polymer
-’-
)-
~ Polymer
:3 REt + AICI ~ RM+(A[CI.4)
-
M ~ Polymer
R= Atky[ or Aryt groups Et = CH3CH 2 -M = Monomer(styrene) Figure 8.6 Equilibria in initiation by aluminumhalides and alkyl halides. (After Ref. 19.)
Solvent B+//(LI)"+M separated ion pairs Sqlvated free ions
B++ (LI)-+M
~ BM+//{LI)
~ BM++ (LI)-
- ~ ~ M+// M
~ ’-~-M++ M
(LI)’-
(LI)-
~ Po[ymer
~ Polymer
Figure 8.7 A simplified reaction schemefor initiation and propagationin cationic polymerization. (After Ref. 20.)
like bulk monomer,the k~+ values for cationic olefin polymerizations are of the order of 106-109 L/mol-s, as comparedto k~" values of the order of 103-105 L/mol-s for anionic polymerizations under more or less equivalent conditions. (Carbocations are thus significantly more reactive than carban-
721
Ionic ChainPolymerization
ions under similar conditions.) In general, both lop+ and ]e~ will decrease with increasing solvent polarity since more polar solvents tend to stabilize the initial state (monomerplus ion or ion pair) at the expense of the transition complex (in which the monomeris associated with the cation and the charge is dispersed over a larger volume). The /ev+ values are generally at least 100 times as great as the corresponding]ep:t: figures for olefin monomers. Simplitled
Kinetic
Scheme
It is clear from the above discussions that deriving a general kinetic scheme for cationic polymerizations is rather unrealistic. Nevertheless, we shall postulate a conventional polymerization reaction scheme based upon the chemistry given in the earlier sections and show where its inherent assumptions are questionable in cationic systems. An ideal reaction scheme is shown below: Pre-initiation equilibrium: L q- IB ~ B+ (LI)(8.137) Initiation:
B+ (LI)-
Propagation:
+ (LI)BMnM
+ M --~
Termination:
+ (LI)BMnM
-~ BMn+ILI
(8.140)
+ (LI)BMnM
k~r,M + M ~ Mn+l + + (L I)-
(8.141)
Transfer:
+ M --~ + (L I)BMn+IM+ (LI)-
(8.138) (8.139)
where L, IB, and M are as defined earlier on p. 707. The scheme is greatly oversimplified to begin with, because we have ignored the existence of equilibria between free solvated ions and ion pairs of various degrees of intimacy. So all the rate constants that are listed are actually composite values [cf. Eq. (8.136)] which will val~j with the nature of the medium and counterion. The observed ]¢p values, moreover, can vary with the total concentration of reactive species because of the tendency of organic ion pairs to cluster in the more nonpolar environment, and the reactivity of aggregated and individual ion pairs is not generally equal. If we ignore all these important complications we can write the following expressions for the rates of initiation (R4), propagation (R~), termination (/~t), transfer to monomer(/~tr,M): R4 = ki (K [L] [IB])[M] +] P~ = ]~p [M] [M
(8.142) (8.143)
722
Chapter8 +] -]~t = ]¢.t [M
(8.144)
Rtr,M = /¢tr, M[M+] [M] + where [M+] represents ~2n=I[BMn_IM oc (LI)-], that is, it is concentration of propagating chains of all sizes irrespective of of association with counterions. It is necessary to invoke the steady state assumption d [M+]/dt= O) to make the model mathematically tractable. assumption, +1 ----[M
and
4=
Kki [L] [IB] [M] ~ Kkikp 2ILl [IB] [M]
/a
(8.145) the total their state (P~ = Rt, With this (8.146) (8.147)
Thus cationic polymerizations show a first order dependence of/~o on P~/ or initiator concentration in contrast to radical polymerizations which show a one-half-order dependence of _/?.p on R/. The difference is a consequence of their basically different modes of termination. Termination is second order in the propagating species in radical polymerization but only first order in cationic polymerization.
Problem8.24 Derive expressions for cationic polymerization rate for the following three cases: (a) an added chain transfer agent terminates the kinetic chain [Eq. (8.134)]; (b) the rate-determiningstep in the initiation processis the forward reaction in Eq. (8.111); and (c) the coinitiator L or initiator IB is present large excess. Howwouldthe order dependenceof the polymerization rate change if either monomer or any of the componentsof the initiating system is involved in solvating the propagatingspecies. Answer: (a) Reaction (8.134) becomesthe termination reaction when+ (LI)- i s unable t initiate newchains (as in the case of a moreactive agent present in considerable amounts).In that case, at steady state,
/~ = ~+P~r,s whichyields [M+] = Kk, ILl [IBI [M] kt -b ktr,S IS] FromEq. (8.143), Kk, k, 2[L] [IB] [M]
ta +t,,r,s [sl
723
Ionic ChainPolymerization
Applyingsteady-state approximation [M+I-- kl ILl [IBI / k, Hence P~ = kl kp ILl [IB] [M] / k, Thus ~ has one order dependenceon [M] instead of 2 order as in Eq. (8.147). (c) If L is present in large excess P~ = k [IB] [M] +] where k is a composite constant. Since [M
= [m] [M]2 / Thus/~ is zero order in L. Similarly, if IB is in excess, P~ will be zero order in IB. If monomer is involved in solvating the propagatingspecies, the/~ will show higher than 2 order in monomer. If L or IB is involvedin solvating the propagating species, the propagationrate is then dependenton the concentration of L or I]3, while initiation is first order in both L and IB [cf. Eq. (8.142)]~thus resulting higher than first order dependencefor P~ on L or IB.
Even whenconditions are scrupulously controlled, the kinetics of cationic polymerization are rarely simple. Water is highly reactive towards organic cations and if present as initiator, any excess will terminate polymer chains. Excess water may also destroy the coinitiator in some cases, or compete successfully with monomerfor the initiator-coinifiator complex (see later). The kinetic influence of water is thus complicated. In some systems, the initial rate of polymerization increases with concentration of water at low concentrations and becomes independent as this concentration increases. Such behavior has been reported for the polymerization of isobutene in dichloromethane initiated by titanium tetrachloride and water [21]. In other systems, the initial rate of polymerization mayrise to a maximumand then decline with increasing concentrations of water. Such behavior has been observed in the SnC14/H20initiated polymerization of styrene in carbon tetrachloride [22]. Degree
of
Polymerization
If the molecular growth is controlled by chain transfer to monomer,which is more likely than the case in which termination reactions limit the size of the macromolecule, then
D °n = / Rtr,M= /
r,M
(S.14S)
724
Chapter 8
Whenchain breaking involves spontaneous termination [Eq. (8.129)] and chain transfer to chain transfer agent or solvent S [Eq. (8.134)], in addition to chain transfer to monomer [Eq. (8.126)] and combination with the counterion [Eq. (8.130)], the concentration of the propagating species remain unchanged (assuming relatively small amounts of TA such that the coinitiator is not inactivated), and the polymerization rate is still given by Eq. (8.147). However, the degree of polymerization is decreased by these other chain breaking reactions and is given by
DP,~=
Rp
(s.149)
Rt q- Rts q- Rtr,M q- Rtr, s
Substituting expressions for the rates given earlier, and rearranging
1 D P,, -
a, qkv[M] kp
Is] q- CM+ Cs[M]
(8.15o)
where CMand (7 s are the chain transfer constants for monomerand chain transfer agent defined by ktr, M/kv and k, tr,S/k v, respectively. Equation (8.150) is the cationic polymerization equivalent of the previously derived Mayoequation [Eq. (6.148)] for radical polymerization. Problem8.25 In studies of the low temperature polymerization of isobutylene using TiCI4as coinitiator [21] the following results were obtained at -35°Cfor the effect of monomer concentration on the avearage degree of polymerization : 0.667 0.333 0.278 0.145 I 0.059 [C4H8] (mol/L) 6940 4130 2860 DP,, 2350[ 1030 Fromthese data, evaluate the rate constant ratios ktr/kp and kt/kp Answer: Since spontaneoustermimition (chain transfer to counterion) is never a dominant termination reaction comparedto chain transfer to monomer,the second term in Eq. (8.150) can be neglected. Further, ignoring the presenceof any chain transfer agent (S), Eq. (8.150) can be approximated D P. k~ [M l
+CM
Figure 8.8 shows a plot of 1/DPnvs. 1/[C4Hs]. The slope gives kt/k~ = 5.0x10-5 tool L-1. -4. From the intercept, CM= k.t~,M/kp = 1.1xl0 Problem8.26 In studies similar to those in Problem 8.25 but performed over a range of temperatures, the following values were found [21] for the intercepts
Ionic Chain Polymerization
725
of plots of 1/(DP.) vs. 1/[C4H8]: t(°C) 103/Dp~
+18 4.37
-14 --35 0.50 0.098
--48 0.027
Evaluate from these data the difference in activation energy betweenchain propagation and chain transfer to monomer. Answer: Expressingthe rate constants by the Arrheniusexpression Intercept
-- kt, _ (At,’~ e(~_F~)/t~r
where/~ and Nt are the actNation energies for propagation and transNr, r~p~tively; A~and At~ are the respective pre-exponential Nctors. TaNnglogarithms ln(Inter~pt) = ln(At~/~) N - N~ RT Figure 8.9 showsa plot of In(Intercept) vs. lIT. Fromthe slope of the finear plot, ~ - Nt~ = (5.1x10~ °K)(1.987 cal mol-~ °K-~) = 10.1x10a -x. cal tool
10 8
1
0
4
|
1
8
12
I
16
20
-1) 1/[C4H8](L rno~ Figure 8.8 Plot of 1/D_P,,vs. ]/[M]. (Problem8.25.)
Chapter 8
-2
3.6 (1/T) 103 (oh-~) Figure 8.9 Plot of In (intercept) vs. 1/T. (Problem 8.26.)
Validity
of Steady-State
Assumption
The steady-state assumption that is helpful in simplifying the analysis of free-radical kinetics is not valid in many, if not most, cationic polymerizations, which proceed so rapidly that steady-state is not achieved. Some of these reactions (e.g., isobutylene polymerization by A1C13at -100°C) are essentially complete in a matter of seconds or minutes. Even in slower polymerizations, the steady-state may not be achieved if P~/ > Rt. The expressions given above can only be employed if there is assurance that steady-state conditions exist, at least during someportion of the overall reaction. Steady state is implied if/~ is constant with conversion, except for change~ due to decreased monomerand initiator concentrations. A more rapid decline in R:v with time than what is expected or an increase in Pup with time would signify a nonsteady state. Thus manyof the experimental expressions reported in the literature to describe the kinetics of specific cationic polymerizations are not valid since they are based on data where steady-state conditions do not apply. Another consideration in the application of the various kinetic expressions is the uncertainty in some reaction systems about the solubility of the
Ionic ChainPolymerization
727
initiator-coinitiator complex. Thus failure of the usual kinetic expressions to describe a cationic polymerization mayoften be an indication that the reaction system is actually heterogeneous.
Absolute
Rate
Constants
The determination of the various rate constants (ki, kv, kt, kes, ktr) for cationic chain polymerization is muchmore difficult than in radical chain polymerization (or in anionic chain polymerization). It is convenient use P~p data from experiments under steady-state conditions, since the concentration of propagating species is not required. The Rv data from non-steady-state conditions can be used, but only whenthe concentration of the propagating species is known.For example, the value of ]¢p is obtained directly from Eq. (8.143) from a determination of the polymerization rate when [M+] is known. The literature contains too many instances where [M+] is taken equal to the concentration of the initiator, [IB], in order to determine kv from measured Rv. (For two-component initiator-coinitiator systems, [M+] is taken to be the initiator concentration [I]3] when the coinitiator is in excess or the coinitiator concentration [L] whenthe initiator is in excess.) Such an assumption holds only if R~> P~ and the initiator is active, i.e., efficiency is 100%.Using this assumption without experimental verification maythus lead to erroneous results. Because the expressions for D.Pn do not depend on either steadystate reaction conditions or a knowledgeof [M+], it is more convenient to calculate the ratios of various rate constants from D.Pndata than from data. However,the use of DP,~data, like the use of R,p data, does require (if the Mayoequation is used) that one employs data at low conversions where reactant concentrations have not changed appreciably. Most values of kv and other rate constants reported in the literature are questionable for several reasons. First, there is ambiguity, as discussed above, about the concentration of the propagating species. Second, the calculations of various rate constants and kinetic parameters are often carried out without adequate substantiation of reaction kinetics and mechanisms. The kinetics, for example, may deviate from Eq. (8.143) and then there is the big question of howto interpret any obtained rate constants in view of the knownmultiplicity of propagating carbocation species. Thus, the kinetic expressions given above are written in terms of only one type of propagating species-usually shownas ion pair. This is incorrect, since both ion pairs and free ions are simultaneously present in most systems of cationic polymerization, usually in equilibrium with each other (see Fig. 8.7). Thus the correct expression for the ~ate of any step in polymerization (viz., initiation, propagation, termination, and transfer) should include sep-
728
Chapter 8
arate terms for the respective species.
contributions
of the two types of propagating
Problem8.27 The term k~ in Eq. (8.143) is only an apparent or overall propagation rate constant, (k~). Showhow it could be related to the propagation rate constants k~+ and k~: of the free ions and ion pairs. Suggest methods of obtaining individual k~+ and k~ values. AEISWeF :
Taking into account the contributions rate may be written as
of free ions and ion pairs the propagation
Rr = k~+ [M+]free [M] q- k~ [M+ (LI)-] [M] (P8.27.1) where [M+]free and [M+ (LI)-] are the concentrations of free ions and ion pairs, respectively. From Eq. (8.143), P~ = k~ [M+] [M] (P8.27.2) where [M+] is the total concentration of cationic ends (comprising free ions and ion pairs). From Eqs. (P8.27.1) and (P8.27.2), k~ = k~+ [M+]free + k; +[M+ (LI)-] (P8.27.3) [M+]free + [M (LI)-] Individual k~+ and k~ values can be obtained by experimental determination of individual concentrations of free ions and ion pairs by a combination of conductivity and short-stop experiments. While conductivity directly yields the concentration of free ions (that is, only flee ions conduct), short-stop experiments yield the total concentration of ion-pairs and free ions. For mostly aromatic monomersthe total concentration of ion pairs and flee ions may also be obtained by UV-visible spectroscopy, assuming that ion pairs show the same UV-visible absorption as free ions since the ion pairs in cationic systems are loose ion pairs (due to large size of the negative counterions).
One of the most often encountered errors in reported k~. values is their assignment of apparent or overall rate constant k~ as k~:. This can be erroneous since even small concentrations of free ions with their high value of kp+ can have a significant effect on the propagation rate constant. The overall rate constant k~ is related to k~+ and k~ (see Problem 8.28)
k°p
= ak+~ + (1-
a)k~
(8.151)
Ionic Chain Polymerization
729
or k°p = k~ + k~ Kid/2
/[M+] 1/2
(8.152)
where o~ is the degree of dissociation and gd the dissociation constant of the propagating ion pair, and [M+] is the total concentration of propagating cationic ends (both free ions and ion pairs). One can thus safely equate kv with k~ only for systems where [M+]/Ka --" 103 - 104 or larger (see Problem 8.28). Problem8.28 Consider styrene polymerization by triflic (trifluoroethanesulfonic) acid in 1,2-dichloroethane at 20°C where Ka is 4.2x10-z mol/L[23]. For experimentsperformed(using stopped-flowrapid scan spectroscopy) at a styrene concentration of 0.397 Mand acid concentration of 4.7x10-3 Mat 20°C, the maximum concentration of cationic ends (both free ions and ion pairs) was found -4 M, indicating that the initiator efficiency is 0.030. At 20°C, to be 1.4×10 k~= is reported [23] to be 12. k27t (a) Whatis the ratio of free ion and ion pair concentrations (b) Whatwouldbe the relative contributions of free ions and ion pairs to the overall propagationrate ? (c) Howmuchwouldbe the error in assigning the overall rate constant kg as k~ Answer: (a) For ion-pair dissociation equilibrium, vvvvvM+ (LI)- ~ vv~vM+ + (LI)ga = [M+]free[(LI)-] [M+]pair
(P8.28.1)
+] _ a2 [M (1 -- 0
(P8.28.2)
wherea is the degree of dissociation of ion-pair and [M+] is the total concentration of cationic ends ([M+]free÷ [M+]pair) Thus, c~ [M+]free = [M+lfre~ +] [M -- [M+]free = 1 -- a [M+]pair SolvingEq. (P8.28.2) for c~, ~ = (Ka/2[M+]) [(1 + 4[M+]/Kd) 1/2
--
(P8.98.3)
l]
Substituting for c~ in Eq. (P8.28.3) fromEq. (P8.28.4) yields (1 + 4[M+] / gd)1/2 - 1 [M+]fre~
[M+]p~r - 1 + (2[M+]/K.) - (1 +4[M+]/K.)I/2
(P8.28.4)
(P8.28.5)
This equation showsthat the fraction of free ions decreases rapidly at higher values of [!vI+]/Ka (dimensionless). Thusfree ions constitute approximately99,
730
Chapter8
90, 62, 27, 9, 2, 1, and 0.3%of the propagating species at [M+] / Ka values of 0.01, 0.1, 1, 10, 102, 10z, 104, and105, respectively. For the given experimentalcondition, [M+] = 0.030(4.7x10-a tool L-1) = 1.41x 10-4 -a tool L [M+]/Ka= (1.41x10 -4 tool L-1)/(4.2×10 -r tool L-a) = 336 FromEq. (P8.28.5), [M+]free/[M+]pair-= 0.056. That is, free ions constitute 5.6%of the propagating species. (b) To obtain a relation betweenk~, +, and k~, Eq. (P 8.27.1) can bewritten as k~[M+][M] = kv +a[M*][M] +j + IM] k~(1 - a)[M whichyields k~ = o~k~ + + (1(P8.28.6) If a 99 RAIX2 + TiCIz + HPT 97 RNa + TiCI3 90 RNa + TiCI4 90 RLi + TiCI4 90 R~Zn + TiClz 65 R~Zn + TiCI3 + Amine 93 R = alkyl, (acac) = acetylacetonate,X halogen, HPT.= hexamethylphosphorictriamide, CsH~= cyclopentadienyl. Source:Data fromRef. 3.
744
Chapter 9
Table 9.2 Influence of the Transition the Stereoregularity
Metal on
of Polypropylene
bTransition metal compound Stereoregularity (%) TiCI4 48 TiBr4 42 TiCIa, c~, 7, or 6 80-92 TiCI3, fl 40-50 ZrCI~ 55 73 VCI3 VOCI3 32 VCI4 48 CrCIa 36 The organometallic compoundis AI(C2H~)3in each case. Source: Data from Ref. 3.
Table 9.3 Influence on the Stereoregularity
of R group of AIRa of Polypropylene
Stereoregularity R TIC13 C2H5 79.4 n-CaH7 71.8 74.5 i-C4H9 C~H5 65.4 C4H1~ 64.0 59.0 C16Haz Source: Data from Ref. 3.
(%) TiCI4 47.8 50.9 30.0 26.2 16.2
Nature of the Catalyst One first assumed that polymerization with Ziegler-Natta catalysts, such as aluminum-alkyls plus halides, works by a simple ionic mechanism. Since single aluminum alkyls normally cause anionic and titanium halides a cationic chain reaction (Chapter 8), the two components of the initiator should neutralize each other and only the excess one over the other should be active. If this were true, then either one of the components alone should be able to initiate the polymerization of ethylene or propylene, but this is not the case. A simple anionic or cationic mechanism can therefore not explain the polymerization with Ziegler-Natth catalysts. The nature of the Ziegler-Natta catalyst systems is still a subject of debate. One fact, however, does appear to be certain, especially about the
Coordination Addition Polymerization
746
insoluble catalyst systems-the true catalysts are not simple coordination adducts formed from the original metal halide and aluminum alkyl. A critical "aging" period for the catalyst is often needed before it achieves its highest activity, and complexreactions occur during this period. These reactions probably include an initial exchangeof substituent groups between the two metals to form transition metal-carbon bonds by exchange reactions such as those shownin Eqs. (9.1)-(9.3): AIRs + TIC14 ,~- R2AIC1 + RTiCls
(9.1)
R2A1C1 + TiCI4 ~ RA1CI2 + RTiC13
(9.2)
A1R3 + RTiC13 ~ R2AICI + R2TIC12
(9.3)
These organotitanium halides are unstable and can undergo reductive decomposition processes, such as shown in Eqs. (9.4) and (9.5): RTICI~ ~ R" + TiCI~
(9.4)
RzTiClz
(9.5)
~ R" + RTiC12
(Note that TIC13 can also be used as an initial catalyst componentin place of TiCI4.) Further reduction mayoccur yielding TIC12: RTiCI2 ~ TIC12 + R" RTiCl3 --~ TiCl~ d- RCl
(9.6) (9.7)
In addition, TiCl3 may be formed by the equilibrium: TIC14 -I- TIC12 ~ 2TiCla (9.8) For heterogeneous catalysts, the reactions are more complicated than implied by these equations. Radicals formed in these reactions may be removedby combination, disproportionation, or reaction with solvent. While such reactions undoubtedly occur in catalyst formation, it is not known to what extent and the aging process certainly requires more clarification. However, the analogous vanadium-containing systems are soluble and maywell be represented fairly accurately by reactions similar to those shown in Eqs. (9.1)-(9.5). In contrast to the heterogeneouscatalyst, the soluble catalysts appear to have well-defined structures. For example, the soluble catalyst system generated from triethyl aluminumand bis(cyclopentadienyl)titanium dichloride has been shown by elemental and x-ray analysis to have a halogen-bridged
746
Chapter 9 C2H 5
Ct Ti
C5H5
/
~Cl
~C2H 5
structure (I). In all these systems, one of the most important steps is the reduction of the transition metal to a low-valency state in which the metal possesses unfilled ligand sites. These low-valency transition metal species are believed to be the real catalysts or precursors of the real catalysts. Evolution
of the Titanium-Aluminum
System
Since the original discoveries of Ziegler and Natta there have been literally thousands of different combinations of transition and Group I-III metal components, often together with other compoundssuch as electron donors, studied for use in alkene polymerizations. However, the major interest in this chapter will be on the titanium-aluminum systems, more specifically, TiCI3 with AI(C2Hs)2C1 and TiCI4 with Al(C2Hs)3-probably the studied systems. It will be therefore useful to review the evolution of the titanium-aluminum catalyst systems starting with the original system used by Ziegler. The original catalyst used by Ziegler for ethylene polymerization was obtained in situ as a precipitate on mixing the components TIC14 and AI(C2Hs)s in a hydrocarbon solvent. This mixture was then used directly for initiating polymerization. Recognizing that the major product of the reaction of the two catalyst components was ~-TiCIa (brown in color), Natta explored various methods of performing it outside the polymerization system, for example, by reduction of TIC14 with hydrogen, aluminum, and various alkylaluminum compounds, including AI(C~Hs)2C1.The stereospecificity producedby these early catalyst systems was low, yielding polymerswith only about 20-40% isotactic content. There was a dramatic improvement with stereospecificity increasing to 80-95%whenthe or-, ~-, or "/-crystalline form of TiCla (all violet in color) was used directly. The efficiency or activity of these early catalyst systems was, however, low. The term activity, as it is used in most .literature references, refers to the rate of polymerization, and is often expressed in terms of kilograms of polymer formed per gram of catalyst. Because of low activity, substantial amountsof catalyst were needed to achieve acceptable yields of polymer, and
CoordinationAddition Polymerlza~ion
747
the spent catalyst had to be removedfrom the finished product. The catalyst activity was enhanced by various ball-milling and heat treatments of the catalyst componentsbefore and after mixing. (Ball-milling not only increases the surface area but also facilitates reactions between the componentsof the catalyst.) However,the activity was still low in comparison to the present catalyst systems, with considerably less than 1%of the Ti being active in polymerization. Subsequent generations of catalysts involved large increases in activity without sacrificing stereospecificity. The effective surface area of the active component is increased by more than two orders of magnitude by impregnating the catalyst on a solid support such as MgC12or MgO.As an example, a typical TiCla-AIRacatalyst yields about 50 to 200 g of polyethylene per gram of catalyst per hour per atmosphere of ethylene, whereas as muchas 200,000 g of polyethylene and over 40,000 g of polypropylene per gram titanium per hour may be produced using a MgC12-supportedcatalyst; thus eliminating the need for the costly step of removingcatalyst from the product. Suchcatalyst systems are often referred to as high-mileagecatalysts. Stereospecificity of the catalyst is kept high (> 90-98%isotactic dyads) by the presence of electron-donor additives such as ethyl benzoate. Thus, a typical recipe for a present day superactive high-mileage catalyst system involves initial ball-milling (mechanical grinding or mixing) of magnesium chloride (or the alkoxide) and TIC14followed by the addition of AI(C2Hs)3, an organic Lewis base being usually added in each of the steps of catalyst preparation [4]. High activity is very important from the commercial point of view not so muchfor the savings in the amountof initiator required but for eliminating the expensive task of initiator removal from the polymer product.
MECHANISMOF ZIEGLER-NATTA POLYMERIZATION Despite the tremendous amount of research that has been done in this area [1,2,5,6] the true mechanismof Ziegler-Natta polymerization is not entirely clear. It is generally agreed that heterogeneous polymerization occurs at localized active sites on the catalyst surface. The organometallic componentis believed to activate the site by alkylafion of a transition metal atom at the surface. Of the various mechanisms that have been proposed, the two that are most generally accepted are the so-called monometallic and bimetallic mechanisms[2,3], the former being favored in heterogeneous processes. In both processes, the monomeris pictured as being incorporated into a polymer by insertion between a-transition metal atom and the terminal carbon of the coordinated polymer chain. These two mechanisms are separately discussed in later sections.
748
Chapter 9
Coordination catalysts perform two functions. First, they supply the species that initiates the polymerization. Second, the fragment of the catalyst aside from the initiating portion has unique coordinating powers. The catalyst fragment, acting as gcgcnion or countcrion of the propagating species coordinates with both the propagating chain end and the incoming monomerso as to orient the monomerwith respect to the growing chain end and bring about stere0spccific addition. So the polymerization can bc considered as a concerted multicentered reaction. Mechanism of Stereospecific
Placement
Manydifferent mechanismshave been proposed to explain the usual isotactic placement obtained with coordination initiators [7]. Figure 9.1 depicts a general situation for an anionic coordination polymerization with isotactic placement. In this mechanismthe polymer chain end has a partial negative charge and the Catalyst fragment G (gegenion or counterion) has a partial positive charge. (A cationic coordination polymerization wouldinvolve a similar mechanismexcept for reversal of the signs of the partial charges,) The generally accepted mechanismfor stereospecific polymerization of ot-olefins and other nonpolar alkenes is a ~r-complexation of monomerand transition metal in G (utilizing the metal’s d-orbitals), followed by a four-center anionic coordination insertion process in which monomeris inserted into a metal-carbon bond. To elaborate further, the catalyst fragment G (containing transition metal) is coordinated with both the propagating chain end and the incoming monomermolecule. The latter is thus oriented and "held in place" by coordination during addition to the polymer chain. Coordination between the catalyst fragment G and the propagating center is broken simultaneously with the formation of bonds between the propagating center and the incoming monomerunit and between the initiator fragment and the incoming monomerunit. Propagation thus proceeds in the four-center cyclic transition state by the insertion of monomerbetween the catalyst fragment G and the propagating center. The insertion reaction has both cationic and anionic features. There is a concerted nucleophilic attack by the incipient carbanion polymer chain end on the oz-carbon of the double bond of the monomertogether with an electrophilic attack by the cationic counterion (G) on the alkene electrons. The catalyst fragment acts essentially as a template or mold for the orientation and isotactic placement of incoming successive monomer units. Isotactic placement occurs because the initiator fragment forces each monomerunit to approach the propagating center with the same face. This mechanism is referred to as catalyst site control or enantiomorphicsite control.
749
Coordination Addifion Polymerization
.H H x ,H
,H
H, :
"’C /= C
R
%H IH C -- CC’:=a H H C -- C’~’: ..... ~÷ G
Figure 9.1 Mechanism for anionic coordination polymerization with isotactic placement. Bimetallic
and Monometallic
Mechanisms
A numberof structures have been proposedfor the active species (sites) in Ziegler-Natta catalyst systems. The diversity of the proposedspecies arises from the numerous products that have been observed or can be postulated in the interaction of the two componentsof a Ziegler-Natta system[see Eqs. (9.1)-(9.8)]. Theproposedactive species fall into either of two general categories: monometallicand bimetallic [8-10] depending on the numberof metal centers. The two types can be illustrated by the structures (II) and (III) for the active species fromtitanium chloride alkylaluminumcomponentssuch as TIC14or TIC13with A1R 3 or A1R2C1. R
i/Cl
(R)Cl~ ,..,R.. /R(Cl)
Ti.";At
(R)Ct/ "’Ct’"
(n)
\R(Ct)
CI/I
(In)
750
Chapter 9
Structure (II) represents a bimetallic species that is the coordination complex of titanium and aluminum compoundsarising from the interaction of the original catalyst components[cf. Eqs. (9.1)-(9.8)] with exchange of R C1 groups. The placing of R and C1 groups in parentheses indicates that the exact specification of the ligands on Ti and A1 cannot be made. The identity and the number of ligands attached to each metal center may vary from one catalyst to other depending on the components and their relative amounts. Structure (HI) of a typical monometallic species represents active titanium site at the surface of a TiCI3 crystal. The titanium atom shares four chloride ligands with its neighboring titanium atoms and has an alkyl ligand (incorporated through exchange of alkyl from the alkylaluminum chloride) and a vacant orbital Bimetallic
Mechanism
Accordingto the bimetallic theory [8] the truly active catalysts are complexes that have an electron-deficient bond, e.g., Ti-.-C.--AI in (II). The bimetallic mechanisminvolves propagation in which growth occurs at two metal centers of the bridge complex as shown in Fig. 9.2(a). The mechanismis similar to that shownin Fig. 9.1 except for the detailing of the structure of the catalyst fragment G. It is suggested that the nucleophilic olefin forms a 7r-complex [Fig. 9.2(b)] with the ion of the transition metal and, following a partial delocalization of the alkyl bridge, is included in a six-membered ring transition state [Fig. 9.2 (c)]. The monomeris then incorporated into the growing chain between the AI and the C, thereby regenerating the complex. For steric reasons, the =CH2group of the incoming monomer points into the lattice and the CH3group to one side. The chain growth always takes place from the metal end (like hair from its root) and the process thus leads to an isotactic polymer. While a limited amount of experimental evidence does lend support to the bimetallic concept, major objections were voiced by Ziegler, who was of the opinion that like dimeric aluminumalkyls the Ti-A1 complex is not likely to be the effective catalyst agent. Other more recent work also favors the second and simpler alternative, the monometallic mechanism. Monometallic
Mechanism
Majority opinion nowfavors the concept that the d-orbitals in the transition element are the mainsource of catalytic activity and that chain growth occurs at the Ti-alkyl bond, which acts as the polymerization center, the function of the aluminum alkyl being only to alkylate TiCI3. The monometallic mechanism presented below are mainly based on the ideas of Cossee and
CoordinationAddition Pol~rnerization
~C,~ CH3
~ CH ~_.~.~.’G 3
6"CH 2
.,,.
(a)
751
>+i’"""
"’""At
÷~++ ""’AtT~: i"
"’-At< "°(:t°° i Ano+ther sequence I I o’f monomer Qddi’kion
CH3 I ..~.....CH ,CH 2 :
"CH2-CH 3
(c) oO
o° °O°¢l.¯
CHIn I CH 2 I
CH-CH 3I CH2 I CH-CH3 I ..CH 2 (e)
>Ti:i"’"
"".’At
T~"" ""’:~,~> ktr,M. Equations (P9.4.1) and (P9.4.2) then reduce to C~ ~ C* and R~ = kp C* [M]. Thus at high [M], becomes proportional to [M] and DP,~ becomes independent of all polymerization variables.
Adsorption Models As early as 1956Erich andMark[17] pointed out that since most ZieglerNatta catalyst systems were heterogeneousin nature, it wasmost likely
Coordination Addition Polymerization
765
that adsorption reactions were involved in such polymerizations. Since then adsorption processes have featured in many kinetic schemes. A number of reaction schemes have been proposed based on the assumption that the polymerization centers are the adsorbed metal alkyl species. It is assumed that monomer and metal alkyl are reversibly adsorbed on to the surface of a crystalline transition metal halide and that chain propagation occurs between the adsorbed metal alkyl and monomer. In this regaxd the Rideal rate law and the Langmuir-Hinshelwood rate law for adsorption and reaction ’ on solids assume importance (see Problem 9.5).
Problem9.5 Considering reaction between A and B catalyzed by a solid there are two possible mechanismsby which this reaction could occur. The first is that one of them, say A, gets adsorbed on the solid surface and the adsorbed A then reacts chemically with the other component B which is in the gas phase or in solution and is not adsorbed on the surface. The second mechanismis that both A and B are adsorbed, and the adsorbed species undergo chemical reaction on the surface. The reaction rate expression derived for the former mechanism is the Rideai rate law and that for the second mechanism is the Langmuir-Hinshelwood rate law. Obtain simple derivations of these two rate laws. Aaswer: Both the Rideal and Langmuir-Hinshelwood rate laws are based upon the Langmuir adsorption equation, which is applicable for gas-solid as well as liquid-solid systems where diffusion of the sorbate to the solid surface is not rate limiting (generally true). The basic assumption of the Langmuir adsorption is that adsorption occurs at adsorption sites and all these sites are equivalent. For gas-solid systems, the rate of adsorption, r~, of the gas A is proportional to the gas pressure, PA, and the numberof vacant sites, i.e., ~’a = kapA (rl,~ -- hA)
(P9.5.1)
where no is the total number of adsorption sites and nA is the number of sites which are occupied by molecules of A. The rate of desorption, on the other hand, is postulated to be ra A
= kan
(P9.5.2)
At equilibrium these rates are equal and one obtains kapA/ka nA = no (1 + kapA/kd) Defining the fraction of adsorption sites covered by A as 0~ = hA~noand the equilibrium constant for the adsorption equilibrium as KA = ka/ka, the above equation reduces to KAPA OA A ---- 1 +KAp
(P9.5.4)
766
Chapter 9
The term 0A in Eq. (P9.5.4) represents the fraction of total adsorption sites occupied by A. If there are two kinds of molecules, A and B, which are competing for the adsorption sites, one modifies Eq. (P9.5.4)
OA =
KAPA 1 + KA B ÷ KBp
(P9.5.5)
KB PB 1 + KAp A + B KBp where PA and PB are the partial pressures of A and B. ff there is a gas molecule A2 which is adsorbed in the dissociated Eq. (P9.5.4) is modified OB =
(P9.5.6) form, A, (P9.5.7)
OA = KA (Kd PA~) 1/2 1 + KA(K,ipA~)a/2
where K~ is the dissociation equil~rium constant of Equations (P9.5.4)-(Pg.5.7) are applicable for gas-solid adsorption. For liquidsolid adsorption, the partial pressures PA, PB, and PA~ in these equations are replaced by concentrations [A], [B], and [A2], respectively. (a) If the reaction takes place between the adsorbed gas A and the other component B in the gas phase, the rate of reaction is given as RA~ = ks[S]0ar ~ where ks is the surface reaction rate constant and IS] is the concentration of adsorption sites. Substituting Eq. (P9.5.4) into Eq. (P9.5.8) gives Rideal rate law as PAPS RAB = ksKA[S] 1 + K (P9.5.9) ApA For liquid-solid
systems, the corresponding rate law is [A][13] RAB = ks KA IS] 1 + KA [A]
(I’9.5.10)
(b) If bothA and B are adsorbed beforethe chemical reaction occurs, the rate ofreaction is givenas RAB = ks 0A 0S IS] (P9.5.11) Substituting for 0A and 0s from Eqs. (P9.5.5) and (P9.5.5) one obtains Langmuir-Hinshelwood rate law [18] as k, K KB [S] PAPS RAB = (1 +KApaA +KBPB)I/2 (P9.5.12) The corresponding equation for liquid-solid KA Ks [S] [A] [B] 2RAB --¯ ks (1 +KA[A] +Ks[B])
systems is then (P9.5.13)
CoordinafionAddition Polymerization
767
The situation for stereoregular polymerization is quite similar to the cases discussed in Problem9.5, if it is postulated that the dimeric alkylaluminum molecules are adsorbed on TIC13sites to give rise to polymerization centers by the following equilibrium process: (A1R3)2 -[- Active site ~ Polymerization center (PC) (9.23) One is now in a position to apply Eqs. (P9.5.9) and (P9.5.10) stereoregular polymerization. The rate so obtained will be applicable in the stationary zone because steady-state conditions are assumedin deriving Eqs. (P9.5.9) and (P9.5.10). Equation (P9.5.9) is applicable when the PC with the monomermolecules which exist in the mediumof the reaction mass. In this case one has -~ool -- ksx [S] 0AI2R6 [M] (9.24) where [M] is the monomerconcentration in the bulk of the reaction mass and /~1 is the rate under the assumption. Substituting for 0AI2R~ by comparison with Eq. (P9.5.4) one obtains KA [A2] P~ol = ksl [S] [M] 1 + KA [A2]
(9.25)
where KAis the adsorption equilibrium constant and [A2] the concentration of the alkylaluminum dimer. If Henry’s law is assumed for the dissolution of the gaseous monomer in the solution, then
[M] = HpM whereHis the Henry constant and PM is the partial
(9.26) pressure of the
monomer. Equation (9.25) then becomes
K.~[A~] Rool = ks1 [S] HpM1 + KA[A2]
(9.27)
Equations (9.25) and (9.27) are the Rideal rate laws for the Ziegler-Natta polymerization. If the polymerization centers react with the adsorbed monomermolecules then the Langmuir-Hinshelwood rate equation [Eq. (P9.5.13)] should used and one would obtain the rate expression in the stationary zone as KA KM[S] [A2] [M] 2Roo2 = (1 ks2+KA[A2] +KM[M])
(9.28)
where KMis the adsorption equilibrium constant for the monomer. Equations (9.27) and (9.28) have been experimentally verified and values of KMand KAdetermined. Someresults [5,19] are shown in Table 9.5.
768
Chapter 9
Table 9.5 Experimental Values of Adsorption Constants in Langmuir-H_inshelwood and Rideal Rate Laws Temp. Catalyst system (°C) TiCI4 + AIEt3 32 44 57
K A (L/mol) 280 170 60
K M (L/too 0 -
TiCIa + AIEta 50 21.2 VCI3 + AIEta 40 40-60 R: Rideal; L-H: Langmuir-Hinshelwood. Source: Data from Refs. 5 and 19.
0.163 6-7
Rate law used R-type R-type R-type L-H type L-H type
For polymerization in the presence of donor-type impurities such as COS, CS2, H20, H~S, a general rate equation of the following type has been used [20]:
kp KMKAIs] [A2] [M]
~ /~
= (1
q-
KA[A2]
q-
KM[M] q-
KD [D])
(9.29)
where KD is the equilibrium sorption constant and [D] the concentration of donor impurities. Equation (9.29) is identical with Eq. (9.28) except the term KD[D] which is added to the denominator to take into account the donor molecules competing with other species for the sorption sites.
Problem 9.6 Show that under conditions
where KM 1), which are in qualitative agreement with experimental observations. The above model based on the Cossee-Arlman mechanismdoes not, however, confirm precisely to all the kinetic features of Ziegler-Natta polymerizations.
Average
Degree
of polymerization
The average degree of polymerization at a given time can be found from the following general relation DP,~ =
Numberof monomermolecules polymerized in time t Numberof polymer molecules produced in time t
(9.47)
The number of polymer molecules polymerized can be obtained by integrating the rate of polymerization. The denominator can, however, be obtained only if the transfer and termination rates are known.If Rt denotes the sum of these rates, then DPn
=
f~ R~dt (9.48) [C*]t + fo* Rtdt where [C*]~ is the concentration of the polymerization centers at time t. One can apply Eq. (9.48) for the stationary state to find DPn.At the stationary state, P~ and -f~t arc both constant and Eq. (9.48) can thus written as 1 /~,~o [C*]~ (9.49)
DPn -
In Eq. (9.49), the contribution to the integrals from the transition zone has been ignored for simplicity. For long durations of time, the second term in right side of Eq. (9.48) tends to zero, and the equation reduces
(9.50)
CoordinationAddition Polymerization
779
To be able to evaluate DPn one has to know the termination and transfer processes. For propylene, for example, these can be described by Eqs. (9.9)-(9.12). The corresponding rates are given Transfer to monomer: Transfer to A1Etz: Spontaneous transfer:
Rtr,M = ktr,M [C*I[M] = a ,A[C*I[AI = [c*l
(9.51) (9.52)
Natta and Pasquon [12] have confirmed this equation experimentally. Transfer agents like H2 may be specifically added to reduce the’molecular weight. The polymers produced by Ziegler-Natta polymerization normally have very wide molecular weight distributions. The polydispersity index PDI (= Mw/M,~)is 5-20 for polyethylene and 5-15 for polypropylene. The cause of the wide dispersity is not precisely known. Someworkers believe that the propagation reaction becomesdiffusion controlled after a few percent conversion and it is this which is responsible for the large dispersity. Some other workers believe that the rate constants are dependent upon the molecular size. Concluding
Remarks
In this section several empirical rate expressions for Ziegler-Natta polymerizations have been presented and attempts to model the polymerization have been described. It is found that several models could be proposed to explain the same rate equations. Ziegler-Natta polymerization systems have been shown to be very complex, and the model of a fixed geometric center that has a defmableidentity and activity invariant with time is far too simplistic. Since most Ziegler-Natta catalyst systems have centers of widely different activities and geometric locations, only limited general agreement of such a model with the observed kinetic behavior or good agreement only in specific conditions could be expected.
SUPPORTED
METAL
OXIDE
CATALYSTS
Oxides of a variety of metals on finely divided inert support materials initiate polymerization of ethylene and other vinyl monomersby a mechanism that is assumedto be similar to that of heterogeneous Ziegler-Natta polymerization; that is, initiation probably occurs at active sites on the catalyst surface [2]. Unlike the traditional Ziegler-Natta two-componentcatalyst systems, the supported metal-oxide catalysts are essentially one-component systems. Amongthe metals that have been investigated for these catalyst
780
Chapter 9
systems are chromium, vanadium, molybdenum~nickel, cobalt, niobium, tantalum, tungsten and titanium. Typical supports include alumina, silica, and charcoal. The most active catalyst is chromiumoxide [7]. Silica (SiOg.) or aluminosilicates (mixed SiO2/Al203) are used as the support material. The sUppv~rt is sometimes modified with titania (TiOg.). The chromiumoxide (Cr IO3) catalyst was originally developed by Phillips Petroleum Company and is referred to as Phillips catalyst. Other metal oxide catalysts were developed primarily at Standard Oil of Indiana, the best known among them being the molybdenumoxide (MoV/O3)catalyst. Catalysts are prepared by one of two methods. The support material is impregnated with the metal ion, then heated in air at a high temperature to form the metal oxide. Alternatively, when the support material is an oxide such as alumina, the two oxides are coprecipitated and dried in air. In such case the catalyst is activated by treatment with a reducing agent such as hydrogen, metal hydride, or carbon monoxide. The function of the support appears to be more than simply providing a large surface area. Sometype of interaction must occur between the metal oxide and support because the oxide alone behaves differently. The supported chromium oxide catalysts can be prepared by impregnating a silica-alumina support with a solution of chromium ions or by coprecipitating the oxides. The preferred impregnating solutions contain dissolved Cr(NO3)3.9H20or CrO3 in nitric acid because catalysts made from chromiumchlorides or sulfates retain some of the anions after calcination. The solid mixture of chromium-silicon-aluminum compounds is calcined in dry air at 400-700°Cor higher to obtain the desired oxide. This probably results in the reaction of surface hydroxy groups in the support material with CrO3 to form chromate (IV) and dichromate (V) species:
o o O=Cr-O- Cr =O OH OH CrO3~, I ~ H2 0 -Si-O -Si
0/ N Ot I
-Si-O-
Si-
(iv)
~
+
~
0 0 t ~ -Si-O-Si-
(v)
The supported chromium oxide catalysts can be activated by carrying out the heat treatment of the .catalyst in a reducing atmosphere of CO, H2, or metal hydride or treatment with AiR.3 or AI(OP,)3. Poisoning the catalyst occurs in the presence of such materials as water, oxygen, or acetylene. Supported molybdena catalysts are prepared by impregnating alumina with ammonium molybdate, calcining in air at 500-600°C to form the oxide,
CoordinationAddition Polymerization and reducing in hydrogen at 430-550°C. Other reducing agents such as CO, SO2, or hydrocarbons can also be used, but hydrogen is preferred. The optimum catalyst contains from 5 to 25% molybdena dispersed on the surface of the support, and polymerization reactions are carried out at 130-325°Cin the presence of an inert solvent. The polymerizations on supported metal oxide catalysts can be carried out by three different processes: solution polymerization, suspension polymerization, and gas-phase polymerization. The solution polymerization occurs in solvents in which the polymer remains dissolved, e.g., cyclohexane. In a continuous process, solvent, monomer,and the catalyst suspension are fed into an agitation vessel at the same rate as the polymer solution is leaving the vessel. At high yields, the polymer can be precipitated out of the specific solvent and there is no need to remove the catalyst. The solvent and unreacted monomerare recycled. The suspension process is quite similar: One takes mixtures of hydrocarbons as solvents, in which the polymer is formed as an insoluble, filterable suspension. Gas phase polymerization may be described as another suspension process in which the monomer,without mixture of solvents, is polymerized directly out of the gas phase. The catalyst is continuously injected into a vertical reactor as gaseous monomeris circulated through the system. Only a small percent of the monomeris polymerized per pass. The polymerization temperature lies below the softening point, and the polymer exists in the reactor as a fine powder, which has the properties of a fluid with regard to its rheologicai behavior. Ethylene is the most important monomerused with supported metal oxide catalysts. In fact, muchof the high-density polyethylene is nowmanufactured this way. Unlike Ziegler-Natta catalysts, which give rise to polymer having primarily saturated end groups, the supported metal oxides yield polyethylene with approximately equal amounts of saturated and unsaturated chain ends. The supported metal oxides, however, are not as active as Ziegler-Natta catalysts, and they do not give rise to a high degree of stereoregularity. Propylene forms partially crystalline polymer, but higher 1-alkenes give amorphous product.
Polymerization
Mechanism
The difference in polymerization mechanism between one-component metal oxide catalysts and traditional Ziegler-Natta two-componentcatalysts seems to exist only in the initiation stage, while the mechanismof continued propagation of polymer chain has manycommonfeatures for all the catalyst systems based on transition metal compounds. Thus most studies of the chromiumoxide catalyst system, for example, deal either with the nature
782
Chapter 9
of the species on the catalyst surface or with the nature of the species responsible for polymerization. Such studies have shown that the formation of a surface chromate takes place by reaction of CrO3with silanol surface groups of the support, as shown by Eq. (9.55), and reduction of this surface chromate by ethylene or hydrogen or carbon monoxide results in the formation of a low-valence chromium center:
O/ \O I I -Si-O-Si-
CH2=CH2 + CO orH2 0"-~
o/Cr\o I
I
Jr
Oxidation products
-Si-O-Si-
The details of initiation mechanismare not understood. There is little doubt, however,that the reaction is a surface catalyzed process requiring the monomerto be adsorbed onto the catalyst surface. Initiation is believed to involve the formation of a metal-carbon ~-bond followed by coordination of an incoming monomermolecule and subsequent insertion into the metalcarbon bond. A mechanism proposed for the formation of the if-bond between the metal and alkyl fragment [26] is shownin Fig. 9.8. The radicals formed in the initiation reactions mayalso participate in the alkylation of the transition metal: M~= + R" ---,M~U
(9.56)
Twogeneral mechanismshave been proposed to explain the formation of polymers with precipitated catalysts: (a) the bound-ion-radical mechanism and (b) the bound-ion-coordinate mechanism. The bound-ion-radical mechanism involves chain growth in a chemisorbed layer of monomermolecules initiated by radicals or ion-radicals bound to the surface of the catalyst, while the coordinate mechanisminvolves chain growth from a complex ionic center in the catalyst. Bound-Ion-Radical
Mechanism
The catalyst is assumed to adsorb monomeron its surface, the first layer being held in a special and uniform fashion [Fig. 9.9(a)]. Initiation occurs when an adsorbed monomeris polarized sufficiently by some constituent on the catalyst surface to convert it to an ion (or a radical or an ion-radical pair) bound to the surface [Fig. 9.9(b)]. Propagation follows along
783
CoordinafionAddition Polymerization
M~I_ I /El
CH2=EH
M~CH= CH /H ¯ 22
ICH2 =CH2
~ 2
M~
CH=CH jr]
M~n
CH2= CH2_.E] M..~ ~CH2-CH 3
+
+ H’
+ CH2=CH"
I
CH2=CH
M~CH2CH3
CH2=CH" Figure 9.8 Mechanismfor the formation of g-bond between the metal and alkyi fragment. (After Ref. 26.) surface [Fig. 9.9(c)] and the polymer chain is eventually terminated and desorbed from the surface, being replaced by fresh monomer. The chain termination may be caused by transfer with monomer or spontaneous transfer or detachment from the surface. The surface layer lines up the monomersso that a polymer with molecular regularity is obtained. In bound-ion-radical mechanismfor ethylene polymerization, initiation can be either through a chemisorbed ethylene molecule (Fig. 9.9) a chemisorbed hydrogen atom. With ethylene as initiator, polymerization occurs simultaneously at two sites, each associated originally with the ends of the double bond in the ethylene molecule adsorbed on an active dual site. With hydrogenas initiator, polymer growth occurs only at one site. In either case, an organometallic bond is formed. The important steps for the polymerization process with the adsorbed hydrogeninitiation are illustrated in Fig. 9.10. Polymerization is initiated by an adsorbed hydrogen atom attaching to a neighboring adsorbed ethylene. Propagation occurs in the adsorbed layer, with the growing chain adding as an ion-radical to a neighboring adsorbed ethylene. Transfer occurs by shift of a hydrogen atom to a neighboring adsorbed monomeror spontaneously to a vacant surface site. In the absence of poisons, termination occurs only by reaction with a chemisorbed hydrogen,which frees a dual site suitable for readsorption of ethylene. With ethylene initiation, the growing polymer is attached at each end (Fig. 9.9) and is converted to single attachment by transfer or termination at one of the ends.
Chapter 9
(a)
(b)
(d)
(c)
Figure 9.9 Bound-ion-radicalmechanismfor polymerization on a catalyst surface showing(a) adsorbedmonomer; (b) initiation; (c), (d), etc., propagation. Ref. 27.)
k~p
Propagation ~i~. ~ Transfer with monomer
M ktr’.---~
Spontaneous transfer
~
Termination
Polymer CH2-CH
-H
+
Polymer
+ Po[ymer
Figure 9.10 Polymerization in adsorbed layrr by adsorbed hydrogen initiation. (After Ref. 28.)
785
Coordination Addition Polymerization
Problem9.11 Metal-oxide catalyzed polymerization of ethylene was carried out in benzene solution in a stirred autoclave with a suspension of hydrogen-reduced molybdena-alumina catalyst [27]. The pressure was maintained nearly constant by repressuring the autoclave with ethylene as it was consumedin the polymerization process. Temperatures of 200-275° were studied. The ethylene concentration in solution was controlled by adjusting the pressure (in the range 625 to 1000 psi) at any particular temperature. The ethylene uptake rate (rate of pressure drop dP/dt) was measured as a function of the catalyst amount (Wear) and ethylene concentration in solution (calculated from ethylene partial pressure) [C~H4]s different, tmperatures. The experimental data plotted as (dP/dt)/(weat vs. [C2H4]sproduce good fit to straight lines whoseslopes decrease at higher temperatures. Further, at higher temperatures, the plot of (dP/dt)/Wcatvs. IC~rhl, fits to straight lines passing through the origin. Derive suitable expressions to explain the aforesaid experimental results, considering that the polymerization takes place in an adsorbed layer of ethylene with initiation by adsorbed hydrogen and transfer and termination processes as illustrated in Fig. 9.10. Answer: It is seen from Fig. 9.10 that chemisorbed ethylene disappears in initiation, propagation, and transfer with monomer.Therefore, dP/dt = k~ [C2I-h],
[H], + (k~ + ktr,
M)[C2H4]~,[Polymer],
fP9.11.1) where [C2H4], is the concentration of ethylene in the concentration of adsorbed hydrogen and ~[Polymer]~ (bound to the surface). Under steady-state conditions, initiation and disappear by spontaneous transfer and state,
adsorbed layer, [H]~ is the that of all growing chains the growing chains arise termination. Thus at steady
/~ [H]= [C2H4]= = (ks + /~[H]=) E.[Polymcr]. or
E,~[Polymer].
= ki [H]. [C2H4]. / (k, + kt [H].)
(P9.11.2)
Substituting in Eq. (P9.11.1), dP/dt = k, [C2H4].[H]. 1 + k. ÷ k~ [H]. [C2H,].
(Pg.11Z)
At low concentrations of ethylene, [C2I-I4],, = KE [S,~] [C2I"I4]s (P9.11.4) where KE is the Langmuir adsorption equilibrium constant, [C~_H4]~is the equilfl> rium concentration of ethylene in solution, and [S~] is the concentration of active dual sites (at which ethylene can be adsorbed with two-point adsorption). [C2H4]~,
Chapfer 9 in turn, is related to the partial pressure of ethylene, PE, in the gas phase by [C2I-I4]s
= K, pE
(P9.11.5)
where Ks is the equilibrium constant for saturation. Substitution of Eq. (P9.11.4) into Eq. (P9.11.3) yields, (dP/dt)
(P9.11.6)
[C2H& which simplifies to
(dR~dr) -- KE k, [H]° + B [C2H4]s (P9.11.7) [S~] [C2H4]s where B is a complexfunction of the various equilibrium and rate constants. Since [S~] is proportional to the Weightof the solid catalyst, a plot of (dR~dr)/(Wcat [C2FI4]s) vs. [C~H4]s should yield a straight line at each temperature, as observed experimentally. Since termination and spontaneous transfer become more important at higher temperatures, the value of the slope B would decrease at higher temperatures. If B is small, Eq. (P9.11.7) simplifies (dP/dt)
[S ~] = KEk, [H] ~ [C~ H4]s (P9.11.8) Thus, a plot of (dP/dt)/Wcat vs. [C2I-I4], at higher temperatures should fit straight lines passing through the origin, as observed experimentally. Note: If ethylene initiation is considered, instead of hydrogeninitiation, the growing polymer is attached at both the ends and is converted to a single attachment by transfer or termination at one of the ends. The equations describing polymerization take exactly the same form as in the case of initiation by hydrogen but are complicated by extra terms dealing with interconversion of the polymer growing from one or both ends.
Problem9.12 Derive an expression for the average degree of polymerization corresponding to the reaction scheme assumed in Problem 9.11. Predict from this relation how the molecular weight of the polymer would be affected by (a) increased amount of catalys t, (b) increased amount of hydrogen adsorbed on the catalyst, (c) increased ethylene concentration, and (d) increased temperature. Answer: The average degree of polymerization is determined as the sum of all the chain growth reactions divided by all the chain transfer and termination reactions: DP~
=
k~ [C~H4]~ E,[Polymer]~ {ktr,M [C2H4]a + ks + kt [H]a} E,[Polymer],
The sum of the growing polymer chains
~,~[Polymer]~
cancels
(P9.12.1) out, and the
CoordinationAddition Polyraerization
787
reciprocal of the simplified DP~becomes -+ DP,~ kp /% [C2H4], Substituting Eq. (P9.11.4) into Eq. (P9.12.2), one obtains
(P9.12.2)
1 = ktr,___~M + k, + 1~ IS], (P9.12.3) DP,~ k, k, KE [S;] [C2H41, Thus the molecularweight should increase slightly with the increased amount of catalyst or increased ethylene concentration, and decrease with an increase in hydrogenadsorbed on the catalyst. (These predictions are in accord with the experimentalobservation.) Becausek~ and [C2I-I4]~ are muchlarger than k, and kt [H]~, especially at lower temperatures, Eq. (P9.12.3) simplifies 1 "~ ktr,M (P9.12.4) k~ DP,~ Expressing the rate constants in the Arrhenlusform, 1 AtoM [AE~ - AEtrM] (P9.12.5) DP,~ = ~exp --R~ ’ J Ordinarily theenergy ofactivation fortransfer withmonomer, AEtr,M, would be greater than the energy of activation for propagation, AEp;so the molecular weight should decrease with increasing temperature.
Bound-Ion-Coordination
Mechanism
The coordinate mechanism is based on earlier proposals that describe the organometallic growth reactions of ethylene with aluminum alkyls alone. The reaction is considered anionic because the negative end of the olefin coordinates with an organometallic complex in the surface. Olefm molecules are inserted one at a time between the metal ions in the complex and the alkyl chain to extend the chain by two carbon atoms (see Fig. 9.11). This mechanismis more satisfying in that the ion pair never becomes widely separated. Addition at an electron-deficient bond bridging the metals in the organometallic complex has also been proposed. In either case, the crucial step in the process is the addition of a monomer molecule held in a fixed orientation at the instant of reaction. This feature is responsible for the stereospecificity of the polymer and can also account for the high rate of reaction, since oriented sorption of the monomercan greatly reduce the activation energy necessary for the propagation step.
Chapter 9
788
~ (b)
(c)
--CH2CH
x
~
CHXCH2CHX
~
~
- - CH2 CHXCH 2 CHX CH2 CHX ~
Figure 9.11 Bound-ion-coordinationmechanismfor polymerization on a catalyst surface with growth from a single active site and replenishment of monomer from the liquid phase. Consecutivepropagation steps are represented in (a), (b), (c). (After Ref. 29.)
Problem 9.13 The coordinate and bound-ion-radical mechanismsalthough apparently quite dissimilar, have manyfeatures in common. If, in the bound-radical hypothesis, the surface involved decreases to the limiting case of three points of contact, the two mechanismswouldappear to be quite similar [28]. Explain this similarity by applyingthe idea of growthon the surface, used in the bound-radical hypothesis, to the coordinate mechanism,considering a surface with only three points of contact. Answer: The schemeis illustrated in Fig. 9.12. The growingpolymermoleculeis in the form of an organometalliccompound at position 1, and adsorbednext to it at positions
~oordin~onAcl~a’~ionPoly~neriza~ion
789
2 and 3 is an olefin molecule. The growing end of the polymer is transferred to the olefin molecule giving a new organometallic compound in position 3. The adsorption of a new olefin molecule in the free positions 1 and 2, followed by transfer of the organometallic compoundback from 3 to 1 in a mannersimilar to the original olefin addition step, then gives an organometalliccompound in the original position but two monomer units longer. This increase can continue back and forth along that portion of the surface that has the proper geometry.Similarity betweenthe surface-coordinate mechanismshownin Fig. 9.12 and the coordinate mechanism shownin Fig. 9.11 is easily seen.
ZIEGLER-NA’I’EA
COPOLYMERIZATION
Randomcopolymers of ethylene and ot-olefins (1-alkenes) can be obtained with Ziegler-Natta catalysts, the most important being those of ethylene and 1-butene (LLDPE) and ethylene with propylene (EPM or EPR EPDM).Representative reactivity ratios are presented in Table 9.7. It is seen from these values that ethylene is much more reactive than tiigher alkenes, and the ratios vary with the nature and physical state of the catalyst. In most instances, rlr2 is close to unity. HeterogeneousZiegler-
C--C C
Figure9.12Idea of growth on surface applied to the coordinate mechanismin the case of a surface consisting of three points of contact. (After Ref. 30.)
790
Chapter 9
Table 9.7 Representative Reactivity Ratios (r) in Ziegler-Natta Copolymerization Monomer 1 Monomer 2 Catalyst ~ Reaction type b rl Ethylene Propylene TiCIa/AIR3 15.72 H C 33_36 TiC14/AIR3 H 5.61 VCI3/AIR3 VCI4/AIR3 C 7.08 Ethylene
1-Butene
Propylene
1-Butene
VCla/AIRa VC14/AIR3
r2 0.110 0.032 0.145 0.088
H C
26.96 0.043 29.60 0.019
VCI3/A1Ra H VCI4/A1Ra C ’~R = C6H~.a;t’H = heterogeneous;C = colloidal. Source:Data from Ref. 2.
4.04 0.252 4_32 0.227
Natta catalysts generally yield a wide range of copolymer compositions, possibly because different active sites maygive rise to different reactivity ratios, or because of the encapsulation of active sites leading to decay of activity. A more homogeneous polymer composition is obtained with soluble Ziegler-Natta catalysts, particularly if monomer composition is carefully controlled to remain relatively constant during polymerization. Commercially important examples of ethylene-propylene copolymer made by this process are EPM(EPR),which contains about 60 parts ethylene to 40 parts propylene, and EPDMwhich is prepared with small amounts of nonconjugated diene to facilitate cross-linking. Typical dienes are ethylidene-norbornene, dicyclopentadiene, and 1,4-hexadiene. Cross-linking of EPM(EPR)is accomplished with peroxides. Both EPM(EPR)and EPDMelastomers have excellent ozone resistance by virtue of having no unsaturation as an integral part of the backbone. A number of block copolymers prepared with Ziegler-Natta catalysts have been reported; however, in most cases the compositions may include significant amounts of homopolymer. The Ziegler-Natta method appears to be inferior to anionic polymerization for synthesizing carefully tailored block copolymers. Nevertheless, bock copolymers of ethylene and propylene (Eastman Kodak’s Potyallomers) have been commercialized. Unlike the elastomeric random copolymers of ethylene and propylene, these are high-impact plastics exhibiting crystallinity characteristics of both isotactic polypropylene and linear polyethylene. They also contain homopolymersin addition to block copolymers.
CoordinationAddition Polymerization METALLOCENE-BASED
Z~_,GLER-NATI’A
7~I CATALYSTS
In contrast to the great successes of Ziegler-Natta catalysts in commercial production of linear polyethylene and isotactic polypropylene and higher cx-olefin polymers, efforts to achieve in-depth knowledgeof the catalysis have not been as successful and manyfundamental questions relating to this process have remained unanswered despite decades of intensive research. A central difficulty is that these catalysts are heterogeneousand function in a ternary gas-polymer-catalyst or liquid-polymer-catalyst system. Ziegler-Natta catalysts, in addition to being heterogeneous, with respect to the number of phases present, are also he, terogeneous with respect to the constitution of the active sites. Multiple sites, each having a different structure and reactivity, are often present and none may be considered to have been characterized completely [31]. More recently, however, homogeneousolefin polymer catalysts have been developed. Although these catalysts are by no means simpler, the fact that much of the chemistry of interest occurs in solution makes possible the application of powerful analytical methodssuch as nuclear magnetic resonance (NMR)spectroscopy and the catalysts can thus be related to the available enormous database of organometallic model compounds and reactions. The first homogeneousZiegler-Natta catalyst was discovered independently by Breslow[32] and Natta [33] in 1957. The catalyst, b/s(cyclopentadienyl)titanium dichloride (Cp2TiC12, Cp = r/S-cyclopentadienyl) activated with alkylaluminum chloride (AIR2CI) exhibited a low polymerization activity for ethylene (~104 g polyethylene/mol Ti-h-atm) and none for propylene. It was found later that small amountsof water increased significantly the activity of the catalyst. The reaction between water and aluminumalkyls was shown to produce alumoxanes. In 1980 Kaminsky and coworkers [34] used oligomeric methyl alumoxane (MAO)with Group IVB metallocene compoundsto obtain ethylene polymerization catalysts having extremely high activities. For instance, a polyethylene productivity of 9.3 x 106 g polyethylene/mol Ti-h-atm is obtained with Cpg.TiC12/MAOat 20°C and 9x107 g polyethylene/mol Zr-h-atm with Cp2ZrCI2/MAOat 70°C. However, these catalysts are non-stereospecific, producing only atactic polypropylene because of the symmetric feature of their active centers. In the early 1980s Brintzinger and coworkers [35,36] synthesized racemic ethylene-bridged bis (indenyl) zirconium dichloride, Et(Ind)xZrC12, racemic ethylene-bridged bt~(4,5,6,7-tetrahydroindenyl)zirconium dichloride, Et(H4Ind)2ZrC12, as well as their titanium analogues, Et(Ind)2TiC12 Et(H4Ind)2TiCl~, which have both meso-and racemic configurations. The Et(Ind)2ZrC12 and Et(H4Ind)2ZrCl2 catalysts activated with MAO catalyzed the stereospecific polymerization of propylene showinghigh productivities. It was the first time that the isotactic polyolefins were made by homoge-
792
Chapter 9
neous Ziegler-Natta polymerization. This finding was immenselysignificant as it demonstrated stereochemical control of the chiral ansa-indenyl ligands (Latin ansa, a handle) on migratory insertion of a vinyl monomer.In contrast, the meso-Et(Ind)2TiCl2/MAOsystem, as predicted, produced only atactic polypropylene. Since then a large group of ansa-metallocene compounds have been developed, each of them having unique catalytic activity and stereospecificlty. These homogeneousmetallocene-based catalysts are of theoretical significance in studies of Ziegler-Natta polymerization. Comparedto conventional heterogeneous Ziegler-Natta systems in which a variety of active centers with different structures and activities usually coexist, homogeneousmetallocene-based catalysts give very uniform catalytically active sites which possess controlled, well-defined ligand environments [37]. Consequently, the polymerization processes in homogeneoussystems are often more simple, and kinetic and mechanistic analyses for these systems are greatly simplified [38]. The metallocene catalysts have been under development for 20 years. Nowadays,there is no doubt that the breakthrough for a technical realization of these catalyst systems has been achieved. This is evident from the announcement of "single-site" catalysts (SSC) by different companies. the core of SSCtechnology are catalysts that permit olefins to react only at single sites on the catalyst molecules. This technology affords unprecedented control over reactivity, and can produce polymers with marked advantages in properties and process conditions. These catalysts are being used to produce tail0r-made high performance polyolefins. Metallocene catalysts now offer possibilities to create novel polymers which have never been produced by conventional Ziegler-Natta catalysts. The recently developed hybrid thermoplastic polyolefins which cover a broad range of products with almost any combination of stiffness/impact are a notable example [39].
Catalyst Composition The main component of homogeneous Ziegler-Natta catalyst systems, the catalyst precursor, is the Group IVB transition metallocenes (titanocenes, zirconocenes, and hafnocenes), which are characterized by two bulky cyclopentadienyl (Cp) or substituted cyclopentadienyl (Cpr) ligands. Twosimple examples of these metallocenes are shownin Fig. 9.13. These molecules have (~2v symmetry. The two Cp rings in the molecules are not parallel and the Cp2Mfragment is bent back with the centroid-metal-centroid angle (0) about 140° due to an interaction with the other two tr bonding ligands [401. The chiral ansa-metallocenes, that is, metallocenes with two Cpr ligands arranged in a chiral way and connected together with chemical bonds by
793
Coordination Addifion Polyraeriza~ion
CP2TiCt 2
CP2 2 Hf (CH3)
Figure9.13 Structures of two metallocenes with C’2~ symmetry. a bridging group were first synthesized by Brintzinger and coworkers [35]. The molecular structures of the two famousBrintzinger catalysts, Et(Ind)2ZrC12and Et(H4Ind)2ZrC12, havingindenyl (Ind) and tetrahydroindenyl (H4Ind) ligands connected with ethylene (Et) bridging groups, depicted in Fig. 9.14. A large numberof ansa-metallocenes have since been synthesized by changing the transition metals (Ti, Zr or Hf) and substituents on the Cprings, as well as the bridging groups. Among a wide variety of Cpligands investigated, the most commonlyused are methylcyclopentadienyl (MeCp),pentamethylcyclopentadienyl (MesCp),indenyl (Ind), tetrahydroindenyl (H4Ind), and fluorenyl (Flu) ligands, while commonly used bridging groups are ethylene (Et, -CHg.CH2-),dimethylsilene [Me2Si,(CH3)2Si=],isopropylidene [i-Pr, (CH3)2C=],and ethylidene (CH3Ch=).
Ct "" Zr--.~ Ct !
E’t(Ind)2 ZrCt2
Zrc Et t2 (H41nd)2
Figure9.14 Structures of Brintzinger catalysts [35].
794
Chapter 9
CH 3
/
CH3\
Pn
Al/ \
I
/
Linear CH~
CycUc
K,
(
Figure 9.15 Possible structures of MAO [41]. The steric interaction of the Cp type ligands surrounding the active metal center with incoming monomerplays a key role in the stereoselectivity of polymerization with metallocene catalysts. Changingthe steric structure of the ligands in the metallocenes leads to changes in steric structures of polyolefin products. The bridging group, which provides a stereorigid conformation for the complex, also dictates the distance between the transition metal atom and the ’Cp ligands and the bending angle 0, thus influencing catalyst activity and stereospecificity (isotactic, syndiotactic, and atactic). Poly(o~-olefins) of any type of stereospecificity can obtained simply by tailoring the stereorigid metallocene (catalyst precursor), basically according to the local symmetxy. While Group IVB transition metallocenes are the main component of homogeneousZiegler-Natta catalyst systems, the most important cocatalyst which activates them is MAO.Before the discovery of the MAO cocatalyst, the homogeneousZiegler-Natta catalyst Cp2TiCI2 was activated with alkylaluminum chloride which led to poor catalyst activity. The use of MAO cocatalyst raised the catalyst activity by several orders of magnitude. MAO is formed by hydrolysis of trimethylaluminum (TMA). As the water source, AI2(SO4)a hydrates are used in order to prevent contamination of MAO from other metal [41]. MAOia an oligomer with 6-20 [-O-AI(Me)-] repeat units. A higher degree of oligomerization of MAO provides a beneficial effect to the catalyst activity. The exact structure of MAO,however, remains a puzzle. While earlier research suggested that MAO might exist in a linear and/or a cyclic form (see Fig. 9.15), later investigation based on 27A1 NMRspectroscopic studies indicated that there appears to be no logical structure for MAO with
CoordinationAddition Polymerization
795
~z > 4, in which all aluminumatoms simultaneously achieve a coordination number of 4. A possible structure as proposed by Suganoet al [42] is shown in Fig. 9.16. The Active
Center
The true active species in metallocene-MAOsystems are believed to be metallocene alkyl cations, i.e., cationic do 14-electron complexesof the type [Cp2M(R)]+ (M = Ti, Zr, Hf). As shown below, the formation of the catalytically active .complexinvolves a series of reactions betweenmetallocenes and MAO [43]. For the halogen-containing metallocenes, a rapid alkylation of metallocene by MAO takes place first, and the active species arises from a methyl transfer reaction between the metallocene alkyls and MAO. Starting from Cp2ZrCI2,for example, the first step of the reactions after mixing the metallocene with MAOis the complexation and alkylation of the former with the latter: Cp2ZrC12 q-- [AI(CH3)-O]n ~ Cp2ZrCI2"[AI(CH3)-O]n CpzZr(CH3)CI AIn(CH3)n_IOnCI ~- Cp2Zr(CH3)CI’[AIn(CH3)n-a’OnCI] In a subsequent alkylation, Cp2Zr(CH3)CI
Cp2Zr(CH3)2is formed:
+ MAO~ CpzZr(CH3)2
+ [Aln(CH3)n-I-OnCI]
The alkylated metallocene, Cp2Zr(CH3)2,further reacts with MAO,forming a compound(A) that features the structural element Zr-O-AI:
CompoundA is believed to be the active’species in the metallocene/MAO systems. Since the Zr-O bond has a polar character and could be ionic in nature, compoundA possibly exists in two different states that are in
796
Chapter 9
equilibrium:
~ + ...O-(’Al-O’~n __ Cp~ZrLR
+ ~ I Cp2(R)Zr L At (CH3)O-
/O’~’At-O~’n I Cp~ Zr\R J
Themetallocenealkyl cation (at one side of the equilibrium) mightbe the true active center. A homogeneous catalyst can be madeas a "single-site," that is, only a single type of active center is present in a homogeneous system,underproper conditions. A "single-site" stereospecific catalyst [44] can producepolymers with sharp melting transitions (Tin) and markedlynarrowmolecularweight distribution (M~/Mn< 2). Polymerization
Mechanism
Therole of the active species in the polymerizationof ce-olefins by homogeneousZiegler-Natta catalysis is nowwell established. Thecationic metallocene alkyls havea strong tendencyto coordinate with olefin molecules, the latter being a weakLewisbase. Oncean olefin coordinatesto the metallocenealkyl, the insertion of the olefin into the alkyl-metalbondwouldthen proceedreadily. Thedriving force for this insertion is the energygained in the transformation of M-Rand M-(C=C)bonds into M-Cand C-R bonds (M= Ti, Zr or Hf; R = alkyl, C=Cis olefin). The insertion leads to the formation of a newdo alkyl complexwhichcan coordinate and then insert another olefin molecule.Successiveoccurrenceof this cycle leads eventually to a polymer. Figure 9.17 showssuch an insertion mechanismby Kaminsky and Steiger [45] for ethylene polymerization with Cp2ZrCI~/MAO.
Figure 9.16 A proposedstructure of MAO with coordination numberof 4 [42].
CoordinationAddition Polymerization
797
I 0 ~A~ ~
0 ~A~ ~
+ CH2-~-CH2
~
I
O--Al--
\ I..o~Zr--CH~.... Ate_
H--- CH--CH 2 [ CH2--Polymer chain
0 ~AI-~ n "~Zr___ClTl.~ I
.AI~
, ~ ’ --CH-,--Polymer CH2--CH2 " chain
Figure 9.17 Kaminsky’smodel for ethylene polymerization [45]. A monometallic mechanism was proposed by Corradini and Guerra [46] in which the active center is a metal-carbon bond and the propagation consists of two stages: the coordination of the olefin to the active site, followed by insertion into the metal-carbon bond through a c/s opening. The + complex. In addition to active species in this model is the cationic Cp2MR aromatic Cp ligands of the precursor metallocenes, an incoming monomer molecule and a growing polymer chain are also coordinated to the metal in the stage preceding monomerinsertion.
Kinetic Models Ewen’s Model The first kinetic model for propagation in homogeneoussystems was proposed by Ewen[47], assuming that the propagation took place as shown in Fig. 9.18. This scheme, shown for Cp2Ti(IV) polymerization of propylene, is representative of the kinetics for all of the polymerizations with Group IVBmetallocenes. In the scheme, species 1 and 4 represent coordinatively unsaturated Ti(IV) complexes that are-formally o 16-electron p seudotetrahedral species, species 2 represents the interacting catalyst/cocatalyst combination, while intermediate 3 is shown with the monomercoordinated
798
Chapter 9
km
CP2TiR2+Cxkc~ (2)
/
CH=CH~ (3)
C’: [-AI.(CH3)-O-]n ~ CP2Ti~ CH2?H_FI +C CH3 Figure 9.18 Ewen’skinetic model[47]. at a molecular orbital. The three non-Cp ligands occupy a commonequatorial plane with the growing chain held between two lateral coordination sites accommodating an unidentified non-Cp anion (Rt) and the monomer. Under pseudo-first-order conditions, the rate of polymerization can be expressed as P~ (9.57) ] ---- kobs[C3H6][MT][C where and
]gobs = kpKcKM/(1 + KM[C3H6] + Kc[C]) KM[C3H6] + Kc[C] 5,7. The principal factor determining the magnitude of the free-energy change is the existence and extent of ring strain. Ring strain is a thermodynamicproperty caused by either forcing the bonds between ring atoms into angular distortion or by steric interaction of substituents on the ring atoms. It is the release of ring strain by polymerization that provides the principal driving force for the polymerization of cyclic monomers.Considering the thermodynamic relation AGlc = AHlc - TASte, where T is the temperature (°K), one notes that AHlc is the major factor in determining AGtc for the 3- and 4-memberedrings, while AStc is very important for the 5- and 6-membered rings. For larger-sized rings the enthalpy and entropy factors AHlc and ASlc contribute equally. As ,might be expected from considerations of ring strain, the most reactive monomersare usually those containing 3- or 4-memberedrings. Fiveand six-memberedrings are virtually free of angle strain; however,torsional strain arising from conformational eclipsing of C-H bonds is the major factor responsible for the lower thermodynamicstability of cyclopentane relative to cyclohexane. Incorporation of heteroatoms into the ring influences ring stability in waysthat are not always predictable. Minor perturbations in the physical conditions and chemical structure can have a markedeffect in causing the sign of the free-energy change to be in favor or against polymerization. Thus, whereas 5-memberedcyclic ethers such as tetrahydrofuran exhibit negative free-energy change and are consequently polymerizable, the five-memberedcyclic esters (7-butyrolactone) exhibit positive free-energy change and are not polymerizable. In contrast, 6-memberedcyclic ethers do not polymerize while the corresponding cyclic esters do. With other cyclic systems such as imides and anhydrides both 5- and 6-memberedrings are polymerizable. Cyclic ethers, which exhibit ring strain similar to that encounteredin cycloalkanes, exhibit the following order of reactivity in terms of ring size: 3 > 4 > 8 > 7 > 5 > 6. For rings of all sizes the presence of substituents decreases the thermodynamicfeasibility for polymerization. Substitution in the ring tends to
812
Chapter 10
make the free-energy change more positive, thereby decreasing polymerizability. Thus, whereas tetrahydrofuran is polymerizable, 2-methyl tetrahydrofuran is not. Since both AHts and ASlc are negative, AGlc becomes less negative with increasing temperature. Above some temperature (the ceiling temperature) AGtc becomes positive, and polymerization is no longer favorble. Ceiling temperatures are often quite low in ring-opening polymerizations compared with vinyl polymerizations, particularly where fiveor six-membered rings are involved. Although ring-opening polymerization is thermodynamically favored for all cycloalkanes except the 6-memberedones (see Table 10.2), polymerization of cycloalkanes has been achieved in practice only in very few cases, almost exclusively with cyclopropane derivatives--and only oligomers are obtained. This shows that a favorable thermodynamicfactor alone does not guarantee actual polymerization of a cyclic monomer.Since polymerization requires a kinetic pathwayfor the ring to open, kinetic factors should also be favorable for polymerization to occur. The cycloalkanes do not have a bond in the ring structure that is prone to attack by an initiator. This is in marked contrast to the cyclic monomerssuch as lactones, lactams, cyclic ethers, acetals, and manyother cyclic monomersthat have a heteroatom in the ring that provides a site for nucleophilic or electrophilic attack by an initiator species, resulting in initiation and subsequent propagation. These monomersthus polymerize because both thermodynamic and kinetic factors are favorable. POLYMERIZATION
MECHANISM
AND KINETICS
The overall process of ring-opening polymerization of cyclic compoundscan be schematically represented by the reaction: A--B A--B
)z
~ --(--A-B---~
,
(10.2)
Two main differences from the two other general methods of preparing linear polymers--condensation and addition polymerizations--can be emphasized. First, in contrast to condensation reactions, ring-opening polymerization does not result in the loss of small molecules. Second, unlike olefin polymerization for which the loss of unsaturation is a powerful driving force, ring-opening polymerization does not involve a loss of multiplebonding enthalpy. Ring-opening polymerizations are primarily initiated by ionic initiators (including coordinate ionic) as well as initiators that are molecular species, e.g., water. This later class of initiators are generally only effective for the more reactive cyclic monomers.Ionic initiators are usually more reactive and typically are the same as those described previously for the cationic and anionic polymerizations of monomerscontaining carbon-carbon and carbon-oxygen double bonds.
813
Ring-Open’.mgPolymerization
Mechanisms of ring-opening polymerization vary according to monomer type and initiator, but in most instances they fit one of the two general forms : 1. Monomeris attacked by some ionic or coordination species (designated X*) at the functional group (designated G) that causes ring opening. This is followed by the attack of the ring-opened monomeron another cyclic unit, and so on:
x ® o*
(-’q
etc.
e.g., anionic polymerization of lactones with initiation
®
(10.3)
by methoxideion:
9 ~ + O/’C\R ~ CH30-CO-R-OCH30 -CO -R-O-CO-R-O(10.4) The typical anionic ring-opening polymerization involves the formation and propagation of anionic centers. Reaction proceeds by nucleophilic attack of the propagating anion on monomer. 2. Monomeris attacked by X* to form a coordination species (most frequently a cation) that undergoes reaction with a second monomermolecule to open the ring, and so on, CH30-
(10.5)
X-- OvwwOww~O~ etc. e.g., cationic polymerization of ethylene/mine:
Most cationic ring-opening polymerizations of cyclic ethers involve the formation and propagation of oxonium ion centers. Reaction involves the nucleophilic attack of monomeron the oxonium ion, e.g., for 1,2-epoxides (oxiranes) : cn 3-c~-°Xc~i2 / CH3CH~CH2 + HA ~ CH3CH-z--_CH2
)
~ A + ~H /HO-CH2~
H~O CHa A- CH~_
(10.7/
Ionic ring-opening polyerizations show most of the characteristics described in Chapter 8 for cationic and anionic polymerizations of vinyl monomers.Thus they show effects of solcent and counterion, propagation by different species (covalent, ion pairs, and free ions), and association phenomenaanalogous to those discussed in Chapter 8.
814
Chapter 10
While ionic or coordination compounds are used most commonly to initiate ring-opening poymerization, molcular compounds(water, alcohols, amins, etc.) are also used. In the latter cases, the initiator (XY)serves open the ring, then polymerization prceeds by step growth. ~ ~ XwwvG--Y ~ XwwvGvvwvG--Y ~ etc., (10.8) For example, polymerization of e-caprolactam to nylon-6 is carried out by heating the monomerin the presence of 5-10% water to temperatures of 250-270°C: O II (CH2)5/
~NH ~ HO2C(CH2)sNH2 ( 2)~.-NNH HO2C(CH2)5NHCO(CH2)5NH2 --~
etc.
(10.9)
The nature of the growth processes shown above [Eqs. (10.3)-(10.9)] bears a superficial resemblance to that in chain polymerization, namely that only monomeradds to the growing chains in a propagation step and species larger than monomerdo not react with each other. However, this is not necessarily the case. Epoxide polymerization under anionic conditions, for example, exhibits characteristics of both step growth and chain growth depending on choice of initiator. Lactams may polymerize by a combination of step-growth and chain-growth processes with a single initiator. The classification of a ring-opening polymerization as a chain or step polymerization can be made on the basis of two criteria: (a) the experimentally observed kinetic laws that describe polymerization and (b) the relationship between polymer molecular weight and conversion. The second criterion marks the major distinction between step-growth and chain-growth polymerizations. High-molecular-weight polymer is formed throughout the course of a chain-growth polymerization in contrast to the slow build-up of polymer molecular weight in step-growth polymerization. Most, but not all, ring-opening polymerizations behave as step polymerizations in that the polymer molecular weight increases relatively slowly with conversion. The rate constants for ring-opening reactions of cyclic monomers,such as ethers, amines, amides, esters, and siloxanes have values muchcloser to those for the reactions of step polymerization (e.g., amidation and esterification) than for chain polymerization (viz., addition of radical, carbocation, or carboanion to C=C). However, irrespective of whether a particular ring-opening polymerization is a step reaction or a chain reaction with respect to molecular weight build-up, its kinetics are usually described by equations resembling those of chain-growth polymerization since only monomeradds to growing chains [see Eqs. (10.3)-(10.9)]. As explained earlier, many ring-opening polymerizations are also complicated by the occurrence of polymerizationdepolymerization equilibria. Various situations will be described in this chapter.
815
Rin~-OpeningPolymerization
Anionic Polymerization Reaction
of Epoxides
Characteristics
The anionic polymerization of epoxides such as ethylene and propylene oxides can be initiated by hydroxides, alkoxides, oxides, and metal alkyls and aryls, including radical-anion species such as sodiumnaphthalene. Thus, -, e.g., K+(ButO-), involves the polymerization of ethylene oxide by M+A initiation : /O\ H2C~CH2 + M+A followed by propagation: A-CH2CH20-M
+ ~ A-CH2CH20-M
(10.10)
+ + H2C--CH2 ~ + A- CH2CH2OCH2CH20- M
( i0. I 1
which may be generalized as + + H2C--CH2 ~ Aff--CH2CH20)nCH~CH20-M A_(_CH~CH20~(n+---I)12H~CH~O- + ( 10.12) A number of initiators can cause epoxide polymerization to proceed through anionic coordination mechanism. These initiators include adducts such as Zn(OCHa)~and ([Zn(OCHa)2]2.[C2HsZnOCHa]6) derived action of dialkylzinc with alcohol, a ferric chloride-propylne oxide adduct C1Fe[OCH(CH3)CH~CI]2 (referred to Pruitt-Baggen ini tiator) andmetatporphyrin derivatives of zinc, aluminum, and manganese. Propagation in these systems involves a concerted process in which the epoxide monomer is inserted into a metal-oxygen bond: (10.13)
w~vCH2CH20,~CH 2 ~ wwvCH2CH2OCH2CH20 /
\
This propagation reaction can be visualized as involving the formation of an incipient alkoxide anion on cleavage of the oxygen-metal bond in the propagating chain--hence the name anionic coordination. Many anionic coordination polymerizations proceed with stereochemical consequences. Polymer molecular weights are low for anionic polymerizations of propylene oxide (< 5000) since polymerization is severely limited by chain transfer to monomer.Chain transfer to monomercan take place by proton abstraction from the methyl group attached to the epoxide ring:
816
Chapter 10 O
CH3 wwvCH2--
I
+
CH-O-Na
q:n
+ wwvCH2--CH--OH
+ CH~-CH~CH2
~
/o\ (10.14)
+ H2C--CH-CH~’Na
Chaintransfer to monomer is muchlessprevalent forpolymerizations withmostof theanioniccoordination initiators. Muchhighermolecular weights arethuspossible in thesepolymerizations. Forexample, molecular weightsof theorderof 105 arereported forpropy]ene pol~eH~tion by an initiator derived ~omdipheny]tin sulfide andbis(3-dimethylaminopropy])zin
Kinetics Most epoxide polymerizations have the characteristics of living polymerizations, that is, the ability to polymerize successive monomercharges forming block copolymers. The expressions for the rate and degree of polymerizations are essentially those used in living chain polymerizations (see Chapter 8). The polymerization rate is given by Rp = ]~;[M-I[M] (10.15) where k~ is the overall apparent rate constant and [M-] is the total concentration of all living anionic propagating centers (free ions and ion pairs); [M] is the concentration of monomer. The decrease of poymerization at time t in the reaction is given by the concentration of monomerthat has reacted divided by the initial initiator concentration :
DPo = ([M]0- [M]t)/[I] where [M]0 and [M]t are the monomerconcentrations
(10.16) at times 0 and t.
Problem 10.1 The polymerization of ethylene oxide was studied by Gee et al. [3] in solution in 1,4-dioxane, catalyzed by solutions of sodiumin a small excess of a simple alcohol, ROH.(An excess of alcohol is added to increase the solubility of the catalyst.) Their experimentssupport the suggestionthat there is no termination reaction and that both the ion pair, RO-Na*,and the ion, RO-, are catalysts. Derive a simple expressionfor the rate of polymerizationunder the experimentalconditions. Answer: Makinga simplifying assumptionthat all the polymerization steps have the same bimolecular rate constant, that is, k~- or k~, de.pending on whetherfree ion or ion pair is involved,
= [ak,; + (1- a)k~] [M-][C_¢I%O](1’10.1.1)
~~
Rin~-Openin~Pol~meriza~ion
where[M-] is the total concentration of all anionic propagatingcenters and ~ is the degree of dissociation. So long as the degreeof ionization remainsconstant, no error will be introduced by using an overall rate constant k~ in place of [~k~- -t- (1 - o0k~]. Moreover, [M-]can be replaced by Co, the total initial alkoxide concentration. Thus, (mO.l.~) i% = ~[C~H,O] where (P10.1.3) k; = ak; + (1- a)k~ Note: A series of proton exchangereactions (see later) arise from the presence excess alcohol. If these exchangereactions are muchfaster than the polymerization, the effect on the kinetics of polymerizationwill be negligible unless the alcohol addeddiffers markedlyin acid strength from the polyether alcohols formedby the exchangereactions.
Polymerization of epoxides occurs readily under the influence of strong bases in both protic and aprotic solvents, propagation involving stepwise growth of alkoxide ions. Dimethyl sulfoxide (DMSO)is the most useful of the dipolar aprotic solvents and shows a marked ability to solvate cations (especially +) whilst l eaving a nions e ssentially u nsolvated. A s a consequencenucleophilic reactivity of anions is greater in solvents such as DMSO. There is a special interest in the use of metal alkoxides in DMSO because of a+ rapid proton transfer leading to equilibria of the type ButO-K + CHaSOCHa ~K CHsSOCH~_K+ + ButO H (10.17) Methyl sulfinyl carbanion (CHsSOCH~) has been given the trivial name dimsyl ion and is involved in the majority of the base-catalyzed reactions in DMSO, in spite of the fact that the equilibrium lies far to the left (K = 1.5 x 10-7). The equilibrium of reaction (10.17) is established quickly and even though the dimsyl ion is present in very low concentrations, it is orders of magnitude more reactive than the t-butoxide ion [4]. Chemical analysis of the lower molecular weight polymers produced by polymerization of epoxides with metal alkoxides in DMSO shows that sulfur is present [5] in low concentrations (< 0.4 percent) and this would arise from initiation involving DMSO, that is, pre-initiation [Eq. (10.17)] followed by CH3-~-CH~’K
o
+ + + H2C~CH2 ~ CH3-.S,
CH2CH~CH20-K
6
Propagation involves the reaction
/o\
CH~oCH~CH2-CH~O-K+
+ H2C~CH 2
--~
+ CH3~CH2(CH2CH20)~K
818
Chapter10
followed by successive monomeradditions which are assumdto be kinetically indistinguishable and have the same rate constant
Problem10.2 Polymerization of ethylene oxide with potassium tert-butoxide in DMSO was followed [5] by conventional dilatometry, using special procedures to eliminate zero time errors consequenton rapid initiation reactions. Givenbelow are someof the data obtained for this systemat 50°C: -1 Concentration, mol L Initial rate (Rr z) × 10 Expt. MonomerInitiator ×103 mol L-1 -1 s 1 3.14 6.84 9.61 2 3.43 7.81 6.51 3 3.45 1.36 0.99 4 4.81 7.30 7.50 5 2.42 7.60 5.00 6 1.54 7.90 3.65 Calculate an estimate .of the apparent rate constant for propagation. Whichof the systems given in the table wouldyield the highest molecular-weightpolymer at 90%conversion ? Answer: Beside the metal oxide, dimsyl ions formed by reaction of metal alkoxide with DMSO [Eq. (10.17)] take part in the initiation of polymerization. Withpotassium as gegenionboth alkoxide and dimsyl ion pairs are completelydissociated in DMSO at salt concentrations less than 0.1 M[5]. The initial rate of polymerizationmay be given by the expression[cf. Eq. (10.15)]: R°~ = -d[Ml/dt Io = k~,PP [M]o [ButO-K+]o (P10.2.1) The values of k~PPcalculated for the six cases from Eq. (P10.2.1) are 0.23, 0.24, 0.21, 0.21, 0.27, and 0.30 L mo1-1s-~, -~ yielding an averagevalue of 0.24 L tool -1. S
Accordingto Eq. (10.16), the highest molecularweight at a given conversion will be obtainedfor the case whichhas the highest value of the [Monomer]/[Initiator], that is for expt. 3 with [Ml0= 3.45 tool L-~ and [I]~ = 1.36x10-~ molL-1, giving -1 L (0.90)(3.45 mol = 2286 DP~ = -z -1) (1.36 x 10 tool L The polymerization of unsymmetrical epoxide such as propylene oxide involves the possibility of two different sites (at carbons 1 and 2 or o~ and/9) on the epoxide ring for the nucleophilic ring-opening reaction. Two different propagating species are then possible, one involving the alkoxide of a primary alcohol [Eq. (10.20)] and the other that of a secondary alcohol [Zq. (10.21)1:
819
Ring-Opening Polymeriza¢ion CH3
vww-CH-CH2-O-K + (10.20) vw~vO-K + + CH3-CH--CH 2 vwwCH2-CH--O-K + (10.21) CH3 However,the polymer has a predominantly head-to-tail structure with propagation occurring almost exclusively by attack at the fl-carbon-the less sterically hindered site [Eq. (10.21)], that is, an SN~attack. Exchange
Reactions
Epoxide polymerizations taking place in the presence of protonic substances such as water or alcohol are always accompaniedby exchange reactions. The presence of water or alcohol is often necessary in polymerizations initiated by metal alkox/des and hydroxides in order to produce homogeneoussystem by solubilizing the initiator. In the presence of alcohol the exchangereaction R-(--OCH2CH2-),n-O-Na + + ROH,---~ R-(-OCH2CH2-)rrOH
+ RO-Na + (10.22)
between a propagating chain and the alcohol is possible. Similar exchange reactions are also possible between the newly formed polymeric alcohol in Eq. (10.22) and other propagating chains: R-(--OCH2CH2--)n-OH + R-xt-OCH2CH2--)wrO-Na + ,~R-{-OCH2CH2--)~-O-Na + + R-(--OCH2CH2--)m-OH
(10.23)
Since these reactions leave the total ion concentration unchanged, they cannot affect the observed overall rate if equal reactivity of all ions can be assumed. (The exchange reactions thus appear equivalent to chain transfer reactions, but they are not. Any polymeric alcohol formed via exchange is not dead but simply dormant since all alcohol and alkoxide molecules in the reaction system are in a dynamic equilibrium.) The alcohol will, however, affect the molecular weight and since each alcohol molecule contributes equally with an initiator species to determining the numberof propagating chains, the number-average degree of polymerization will be given by [cf. Eq. (10.i6)] DPn - [I]
+.[ROH]
(10.24)
This counts each initiator and alcohol molecule as a potential chain. The exchange reaction places an upper limit on the polymer molecular weight for polymerizations performed in the presence of alcohols or other
Chapter 10
820
protonic solvents. Polymerizations initiated by alkoxides and hydroxides in aprotic polar solvents do not have this limitation and so also polymerizations initiated by other initiators such as metal alkyls and aryls and the various coordination initiators, since the latter initiators are soluble in aprotic solvents such as benzene or tetrahydrofuran. However, the addition of alcohol or other protic substance is useful for control of polymer molecular weight. Equation (10.24) can be used to calculate the amount of added alcohol or other substance required to achieve a desired molecular weight.
Problem10.3 Discuss the effect of exchangereaction on polymerizationsinitiated by metal alkoxides in alcoholic solution, for the eases wherethe addedalcohol is (a) equally acidic, (b) moreacidic, and (c) less acidic than the polymericalcohol formedby the exchangereaction. Whatwouldbe the result of the use of HCIor RCOOH in place of ROH(or H20)? Answer: (a) The exchangereaction will occur throughoutthe course of the polymerization, if the acidities of the two alcohols are approximatelythe same.The polymerization rate will be unaffected while the molecularweight will decrease [Eq. (10.24)], but the molecular weight distribution (MWD) will be Poisson. (b) If the added alcohol ROHis muchmore acidic than the polymeric alcohol, most of it will undergoreaction with the first-formed propagatingspecies R’OCH2CH20-Na+ + ROH -~ R’OCH2CH2OH+ RO-Na-~ (P10.3.1) ÷ before polymerization begins. Since ROH is more acidic, reinitiation by RO-Na wouldbe usually slower, resulting in a decreased polymerization rate and a broadeningof the molecular weight. (c) For the case in whichROH is less acidic than the polymericalcohol, the rate of polymerization will be relatively unaffected during most of the polymrization and exchangewill occur in the later stages of reaction with a broadeningof the MWD. Whenprotonic compoundssuch as HCIor RCOOH take part in the exchange reaction, the result is not exchange,as occurs with ROH (or H20), but inhibition or retardation, since an anion such as C1- or RCOOpossesses little or no nucleophilicity. Reinitiation does not occur or is very slow and the polymeric alcohols are no longer dormantbut are dead. Both the polymerization rate and polymermolecular weight thus decrease along with a broadening of the polymer molecular weight.
Cationic
Polymerization
of Cyclic Ethers
Propagation in the cationic polymerization" of cyclic ethers is generally considered as proceeding via a tertiary oxonium ion, for example, for the polymerization of 3,3-b/s(chloromethyl) oxetane (R = CH2C1):
Pdng-OpeningPolymeriza¢ion
:O
wwvOCH2CR~.CH2-O N ,
--~ R R
+ R
R
A~
"R
where A- is the counterion. ~e a-carbon of the oxo~umion is electrondeficient bemuseof the adjacent positively charged o~gen. Propagation is a nucleophilic attack of the o~gen of a monomermolecule on ~e a-carbon of the oxoniumion. A vafie~ of initiator systems of the ~pes used in the ~tionic polymerization of alkenes (Chapter 8) can be used to generate the terfia~ oxonium ion p~oagating species. Strong protonic acids such as sul~ric, tfifluoroacetic, fluorosulfonic, and tfifluoromethanesulfonic (triflie) acids initiate pol~eri~tion via the initial formation of a seeond~ oxonium ion: R R (10.26) H+A + O~ ~ H~ R A ~ R which reacts with a second monomermolecule to form the tertia~ oxonium ion: A~
R
R
N~
R (~0.~
This type of initiation is limited by the nucleophilici~ of the anion A-derived from the acid. For acids other than the ve~ strong acids, such ~ fluorosulfonic and triflic acids, the anion is su~ciently nucleophilic to compete with monomer for either the proton or seconda~ and tertia~ oxonium ions, and consequently, only ve~ low,molecular-weight products are possible. Water, often present as impuri~, ~n also reduce the molecular weight significantly since its nucleophilicity allows it to competewith monomerfor the oxonium ions. Lewis acids such as BFa and SbCIs, initiate polyme~zation of cyclic ethers. Used almost always in conjunction with water or some other protogen, Lewis acids form an initiator-coinitiator complex [e.g., BFa.H;O, H+(SbCI~)-], which acts as a proton donor in an initiation sequen~ similar to Eqs. (10.26) and (10.27). Under ce~ain conditions, polyme~zations of cationic cyclic ethers show the characteristi~ of living polymerizations in that the propagating species are long-lived and narrow MWDs are obtained. The rate and degree of polymerizations are then given by expressions pre~ously described [Eqs. (10.15) and (10.16)]. Living polyme~zations occur when inflation is fast relative to propagation and there is an absence of te~ination processes. Such conditions are found for polymerizations initiated Mth a~lium (I) and
822
Chapter 10
1,3-dioxolan-2-ylium (III) salts containing very stable counterions such AsF~-, PF~-, and SbCI~-. These initiators are obtained either in situ or as isolable salts; for example, O -4aCCI + SbC15 ----+
O q~C+(SbCI~)
(i) ~3C+(SbF6)
-
+ O~O (II)
~ q~3CH
(10.28)
H + O~O (SbFr)
(10.29)
(III)
where qb = phenyl group (-C6H5). Reaction (10.29) involves hydride abstraction which is facile with 1,3-dioxolane (II). Transfer reactions may occur by a variety of reactions, some of which are analogous to those in the cationic polymerization of alkenes. Chain transfer to polymer is a commonmode by which a propagating chain is terminated. The reaction (Fig. 10.1) involves nucleophilic attack by the ether oxygen in a polymer chain on the oxoniumion propagating center (the same type of reaction that is involved in propagation) to form the tertiary oxonium ion (IV). Subsequent nucleophilic attack on (IV) by monomer yields (V) and regenerates the propagating specie s. The kinetic chain is thus unaffected and the overall effect is an exchange of polymer chain segments with a broadening of the MWDfrom the narrow MWDfor a living polymerization. Intramolecular chain transfer to polymer (but not intermolecular transfer), which becomes progressively more important at lower monomerconcentrations, results in the formation of cyclic oligomers, that is, the chain ends in (V) are connected to each other. Termination also occurs to varying degrees by combination of the propagating oxonium ion with either the counterion or an anion derived from the counterion; for example,
wwvOCH2CH2-;~"-~IA (BF3OH)-
~ vwwOCH2CH2OCH2CH2OH + BF3 (10.30)
Transfer of an anion from the counterion occurs to varying degrees depending on the stability of the counterion. Thus, counterions such as (PF6)and (SbC16)- have little tendency to bring about termination by transfer of a halide ion, while counterions of aluminum and tin show appreciable transfer tendencies; others such as (BF4)- and (FeC14)- are intermediate in behavior. Termination may also occur by chain transfer with a deliberately added chain transfer agent. Hydroxyl and amine end groups are obtained by using, respectively, water and ammoniaas chain transfer agents.
Ring- OpeningPolymerization
T~N"~
823
"(CH2)z’ ~ ÷ j(CH2)4""~ ~ ¢,,,.,., . ~ O ( C H ~)4"-O (C H o),’.-(IV;" ~ ~(C H2)4"~
~
,.,,.,,,~O(CH2)4--O(CH2)~-O(CH2)4"""
+ ~A_’-(CH2)4""~
(v) Figure 10.1 Terminationby chain transfer to polymerin cationic polymerization of tetrahydrofuran. Kinetics The rate equations that describe the cationic ring opening polymerizations of cyclic ethers take several forms. Somepolymerizations, where there is little or no termination, can be described by kinetic expressions similar to those used in living polymerizations of alkenes (see Chater 8), for example, Pqo = kp[M][M*] (10.31) where [M*] is the total concentration of propagating oxonium ions of all sizes. Reversible ring-opening polymerizations that take place without termination are described in a different manner. However, a treatment similar to that for other reversible polymerizations such as those of alkenes (pp. 532-541 ) is applicable. The propagation-depropagation equilibrium can thus be expressed by kp . . Mn + M = M (10.32) n which is analogous to Eq. (6.187). The rate of polymerization is given by the difference between the rates of the propagation and depropagation reactions : P~ = -d[M]/df~ = kv[MI[M* ] -- kd:o[M*] (10.33) At equilibrium, the rate of polymerization is zero and Eq. (10.32) thus becomes kp[M]e = kdp (10.34) where [M]e is the equilibrium monomerconcentration, as in Eq. (6.189) for equilibrium alkene polymerization considered in Chapter 5. The derivations
824
Chapter10
given there for [M]e and ceiling temperature Tc as a function of AS° and °, viz., Eqs. (6.195) and (6.198) are also applicable to the present AH system. Combination of Eqs. (10.33) and (10.34) gives the polymerization as
- dN]/dt = kp[M*]- N]e)
(lo.a5)
which can be integrated to yield
where [M]0 is the initial monomerconcentration. Equations (10.33) and (10.35) ~n be used to dete~e the propagation rate constant. The equilibrium monomerconcentration [M]e is obtained by direct analysis or as the intercept of a plot of polymefi~tion rate versus initial monomerconcentration (see Problem 10.4). ~e polymerization data are then plotted, in accordance with Eq. (10.36), ~ the left side of ~at equation versus time to yield a staright line where slope is k~[~]. Since [M~] for a living pol~er can be obtained from measurements of the number-average molecular weight, one can determine the propagation rate constant.
Problem10.4 (a) The kinetics of polymerization of tetrahydrofuran was studied -, as initiator [6] with the use of triethyloxoniumtetrafiuoroborate, (C2Hs)aO+BF~ and dichloromethaneas solvent. Conversionversus time was measuredat 0°C with initial catalyst concentration [I]0 = 0.61 x 10-2 mol/Land monomer concentration [M]0varying from 3 to 9 mol/L. The initial rates, P~, determinedIrom these data are given in Table A. (b) In another series of experiments, all with [M]0 = 6.1 mol/L and [I]0 3.05x10-2 mol/L, the monomerconversion (p) was measured as a function time (t) and the numberaverage molecular weight (M~)was determined yielding the data given in Table B. Table A -~ [M]0, mol L 9.15 8.00 7.00 6.10 5.00 4.06 3.05
/~, mol L-1 rain -~ 0.00930 0.00820 0.00680 0.00500 0.00350 0.00170 0.00037
Table B t, min 24 48 84 162 210 398
p 0.085 0.207 0.310 0.443 0.490 0.565
M~ 1405 2795 4078 -
Determine(a) the equilibrium monomerconcentration and (19) the propagation rate constant kp at 0°C.
825
PJn~- Openin~ Polymerization Answer: (a) The polymerization (P10.4.2). Initiation
proceeds in the manner shown in Eqs.
R
(P10.4.1) and
R
ISoIF¯
R)O
(P10.4.1)
+ R--O
Propagationldepropagation R-OCH2CH2CH2CH2-+O_~
(P10.4.2)
BF 4 In these equations, ki, kr, and kap are the specific rate constants of initiation, propagation, and depropagation reactions, respectively. The data of column 2 arc plotted against the data of column 1 in Fig. 10.2. From the intercept at /~ = 0, [M]~ = 2.65 mol/L. (b) Monomerconversion,
p --
[M]0
or [M] = [M]0(1 - p) (P10.4.3)
With [M]~ = 2.65 mol/L and [M] calculated from Eq. (P10.4.3), the left side Eq. (10.36) is evaluated and plotted against t in Fig. 10.3. The slope gives k~[M*] = 9.5×10-3 -1. rain Assumingthat the termination of the cationic polymer chain is brought about by the addition of water, the polymer has the formula C2Hs(OCH2CH2CH2CH2)=OH and molcular weight = 46 + 72x. For M~= 1405, DP,~ = x =
1405 - 46
= 19 72 Similarly, for Mn = 2795, DP,~ = 38 and for Mn = 4078, DP, = 55. Since for the living polymerization, DP,~ will be given by DP,~ = ([M]o - [M])/[M*], [M*] can be calculated from [M] and DP,~. With [M]0 = 5.1 tool/L, this yields p 0.085 0.207 0.310
[M], mol/L 5.58 4.84 4.21
DP,~ 19 38 56
[M*], mol/L -2 2.74 x 10 -2 3.31 x 10 -2 3.37 × 10 Since the value of [M*] is nearly constant at monomer conversions p > 0.20, it may be assumed with fair approximation that the initiator is completely reacted. Since k~[M*]= 9.5x 10-a, as obtained above, (9.5 x 10-3 -1) min k; = (3.37×10 -2 -1) tool L = 0.28 Lmo1-1 min -~ (_= 4.7×10 -3 -~s-~). Lmol
Chapter 10
826
10
’, 6
x
I
0
2
6
6
8
10
FM30mol/L
Figure 10.2 Determination
of the equilibrium monomer concentration [M]e rate (/?.p) versus initial monomerconcentration ([M]0) data. (Problem
from initial
10.4.)
2.0
0
Figure 10.3 10.4.)
I 40
I I 80 120 Time,rain
i 160
I ,, 200
Plot of Eq. (10.36) for the determination
of kp[M’]. (Problem
827
Rin~- Openin6Polymerizafion
The availability of reliable kinetic and thermodynamic data is far less for ring-opening polymerizations than for step and chain polymerizations. However, a comparison of the available data on propagation rate constants clearly reveals the general similarity of ring-opening and step polymerizations. For various oxirane, oxetane, tetrahydrofuran, and 1,3-dioxepane polymerizations, kv is in the range 10-1-10-a L/mol-s [791. These values can be compared to the corresponding values for step and chain polymerizations (Tables 5.3 and 6.7). The kv values for cyclic ether and acetal polymerizations are seen to be close to the rate constants for polyesterification and muchsmaller than those for various chain polymerizations. Degree of Polymerization The quantitative dependence of the degree of polymerization on various reaction parameters has been described [10,11] for an equilibrium polymerization involving initiation. Suppose that we had an initiator XYwhich brought about the polymerization of a cyclic monomerM in accordance with the following equilibria: [XMY] XY ifM ~ XMY, (10.37) Ki -- [XY][M] XMY q--
M ~ XM2Y,
XM2Y + M ~ XM3Y, XMnY q-M ~ XMn+IY ,
Kp-
[XM2Yl (lO.38)
[XMY] [M]
Kp- [XM2Y] [XM3Y] [M (10.39) l Kp-
[XM,,+Cv] (10.40)
[XMnY][M ]
where XYis the initiator (which can be both ionic or nonionic), M the monomer, and Ki and Kv the equilibrium constants for initiation and propagation, respectively. One obtains the following expression for [XMnY]: n-1 [XMnY] = Ki [XY] [M] (Kv[M]) (10.41) By summing [XMnY] over all species from n = 1 to n = c~, one obtains the total concentration, [N], of polymer molecules of all sizes as IN]
= E XMnY --
Ki[XY] [M] (10.42) 1- K~[M] Similarly, one can obtain by summation the total concentration of monmer segments incorporated into the polymer ~:hain. Denoting this quantity by [W], one has
Chapter 10
828 o~
Ki [XY] [M] 2 (1K~,[M]) ,~=1 The average degree of polymerization DP,~is given by W/N: 1 [W] DPn IN] 1 - Kp[M] The initial concentration of monomer[M]0 is clearly given by
[w] = Z ~[x~v] =
[M]o
(10.44)
= [M] + [W] K,[X~] [,]
{1
+ (1
S~])~}
= {1 + The initial
(10.43)
concentration of initiator
(10.45) [XY]~is Nven by
[xv]0= [xv] + [XY]1 + (1 ---~p[M]) = [XY] {1 + Ki[MI~-ff,,
(10.46) } Combinationof Eqs. (10.44) through (10.46) yields the following (otherwise obvious) relationship: [M]0 -- [M] DP,~ = [XY]0- [XY] (10.47) The quantities [XY] and [M] in the foregoing equations represent the equilibrium concentrations of unreacted initiator and unreacted monomer. The various relationships derived above show the dependence of the degree of polymerization on the initial nd equilibrium concentrations of monomerand initiator and on the equilibium constants Ki and Kr~. The polymer molecular weight increases with decreasing Ki and [XY]0 and increasing Kp and [M]0. The quantities that are experimentally measurable are [XY]e, [M]e, [XY]0, [M]0, and DPr~. To evaluate the constants Kp and Ki one might proceed as follows: Kp is obtained from Eq. (10.44) using the experimen{ally determined values of [M] and DPn; Ki is obtained from Eq. (10.45) using the experimentally determined values of [M], [XY], and DPn. Problem10.5 The experimentaldata available in the literature on the equil~rium polymerization of caprolactam (CL) are of the type: a knownmole ratio m H20to CLis charged in a vessel; the vessel is brought to a definite temperature and polymerization is carried out to equih"orium. Whenequilibrium is reached, the value of DP,~and [M] (or conversion p) are determined.
829
Rin~-Openin~ Pol~merizafion
Two sets of data [11] obtained over a sufficiently wide range of variables (temperature and initiator concentration) are given below: Temp. (°C) 221.5
Run m DP, p 1 0.060 0.9390 120 2 0.192 0.9359 60 253.5 0.060 0.9210 100 1 2 0.132 0.9188 60 ° values for the initiation and propagation steps of the equiDetermine the AH librium polymerization of caprolactam. Answer: The polymerization of caprolactam is accompanied by a volume contraction; therefore, the use of concentration units of moles per kilogram is preferred over the application of moles per liter. It is also necessary to be able to compute [M]0 and [XY] from the initial mole ratio m. This is accomplished from the following relationship : [XY]0 = (1000m)/(18m [M]00
[Mlo = [M]~ [Xy]oo ~
+ 113)
rxvl = 8.85 -
(P10.5.1) 0.1594[xY1o
(P10.5.2)
where the molecular weight of H20 is 18 and that of CL is 113; [M]0o is equal to the moles per kilogram of pure caprolactam (= 8.85) and [XY]00 is equal to the moles per kilogram of pure water (= 55.5). From a set of values of DP,~, p, [XY]0, and [M]0 the constants Ki and K v can be computed by the following steps (a) [M] is calculated from [M] = [M]0(1 (b) Kv is calculated from Eq. (10.44): (DP, - 1) gp - [M] ~-P. (c) [XY] is calculated from Eq. (10.47): [XY] = [XY], [MIo - [M] DP, (d) Ki is calculated from Eqs. (10.46) and (10.47): K = [XY]o-[XY] = [M]0-[M] [XY] [M] DP, [XY] [M] [It should be noted that in the theory outlined above leading to Eqs. (10.44)-(10.47), the presence of cyclic oligomers has not been taken into consideration. They are present in the equilibrium mixture of caprlactam polymerization to the extent of at most 5%.] ° values can be calculated from- the equilibrium constant values at The AH several temperatures. Only one set of values for [XY]0, [M]0, [M], and DP, is necessary in principle to calculate the equilibrium constants; however, both sets at each temperature may be taken to determine the constancy of Ki and K~. The
Chapter10
830 values are T1 = 221.5°C (-= 494.5°K) Run 1 Ki =0.0023 Kp = 1.855 Run 2 K~ =0.0027 Kp= 1.787 Average Ki =0.0025 Kp = 1.821 Fromvan’t Hoff’s equation,
T2 = Run 1 Run 2 Average
253.5°C (= 526.5~K) Ki =0.0025 Kp= 1.430 Ki =0.0031 K~= 1397 Ki = 0.00285 K~ = 1.4135
In (K,)2 _ AH° (T~_ (Ki)I R \ TIT2
or
ln(0.002SS [(526.- 494.5) 0.00:50/(1.987tool-1 °K
Solving, AH~= 2118 cal/mol. Similarly, from K~ values, AH~= -4095 caYmoL Thus, the results obtained are ° = 2118 cal/mol CL + H~O ~ H(CL)OH AH H(CL)OH + CL ~ H(CL)~OH AH° = -4095 cal/mol H(CL),,OH + CL ~ H(CL)~+~OH
Polymerization
of Lactams
Lactams are cyclic amides formed by the intramolecular amidation of amino acids. The polymerization of lactams [Eq. (10.48)] O C (CH2)/m-----~-~NH
~ -{--NH(CH~)mmCO--]-n--
(10.48)
can be initiated by bases, acids, and water. Initiation by water (see Problem 10.5), referred to as hydrolytic polymerization, is the most often used method for industrial polymerization of lactams. Anionic initiation is preferred when polymerization is done in molds to directly produce objects from monomer.Cationic initiation is, however, not useful because the conversions and polymer molecular weights are significantly lower. Hydrolytic
Polymerization
Hydrolytic polymerization [12,13] of e-caprolactam to form nylon-6 [m = 5 in Eq. (10.48)] is carried out commercially in both batch and continuous processs by heating the monomer in the presence of 5-10% water to temperatures of 250-270°C for periods of 12 hr to more than 24 hr. In the first step, the lactam is hydrolyzed to e-aminocaproic acid:
(CH2) 5" \NH + H20 ~ H2N(CH2)sCO2H (M) (W)
(10.49)
831
Ring-OpeningPolymerization This is followed by step polymerization of the amino acid with itself w,,wCOOH
+ H2NHwvw ~ vvvwCONI+av~+
(Sn)
H20 (10.50)
(W)
(Sn+.0
(Sr~)
and initiation of ring-opening polymerization of lactam by the amino acid, in which the COOH group of the amino acid protonates the lactam followed by nucleophilic attack of amine on the protonated lactam: OH -OOCRNH-(CORNH-~CORNH~
+ H R ,--
(sn)
(M)
HO0 CRNH-(CORNH-)-n+ 1-C0 RNH2
(S,~+l)
(10.51)
The propgation process follows in the same manner. The initial ring-opening [Eq. (10.49)] and subsequent propagation steps [Eqs. (10.50) and (10.51)], which include both condensation and stepwise addition reactions, constitute the principal mechanismof the polymerization and may be represented by the following three equilibria: [$1]
M+ w Sn
+ Sm ~ Sn+m
M + Sn
q-
W
~ Sn+l
K2- [Sn+m][W]
g3- [Sn+I]
(10.52)
(10.53) (10.54)
Employingthe usual simplifying assumption, that the reactivity of the end groups are equal and independent of the chain length of the respective molecules, K2 my be expressed as K~- [Sn+~][W] [sd[sl]
(10.55)
and it becomes obvious that Ka = K~Ku (10.56) Applyingthe principle of equal reactivities one can write a more generalized expression for K~ = [NHCO][W]
(10.57)
and since [NH2] = [C00H] = [S],
= [waco][w]/[s]’-
(lo.5s)
Chapter 10
832 where
[NH2] = Concentration of amino end groups [COOH]= Concentration of acid end groups [NHCO]= Concentration of amide linkages [S] = Concentration of polymeric chains Values for the equilibrium constants, K1,/(2, and K3, may be calculated from Eqs. (10.52), (10.58), and (10.56), respectively, by substituting various terms in these equations with quantities that are experimentally obtainable. Kinetics The significant quantities upon which the formulation of kinetic equations may be based are the concentrations of caprolactam (M), polymeric chains (S), and amide groups in linear chains (Z). Neglecting amide groups cyclic oligomers, the relationship between these quantities is given by [Z]
= 1 -[M]-
[S]
(10.59)
from which it follows that d[Zl/dt
= -d[Ml/dt
- diS]/dr
(10.60)
Werecall that the three principal chemical equations for the considered mechanism[cf. Eqs. (10.52)-(10.54)] where Ring opening (RO) M
+
W~
(10.61)
Po~condensath)n(PC) Sn
-t-
Sn+,~
Sm
+ W, K2 = k2/k-~
(10.62)
or, in general, NH2 (S)
+ C00H (S)
~-
NHCO (Z)
+ H20 (W)
Polyaddition (PA) Sn + M ~ Sr~+~,
K3 = k3/k-3
(10.63)
(s) The kinetic equations representing the contribution of the individual reactions are RO: -d[Ml/dt
= kl
([M][W]
- [S1]/K1)
(10.64)
833
t~ng-Open~ngPolyrneHzaf~on PC: d[sl/dt
"--
/gl
([MI[W] -- [S1]/K1)
-- k2 [S] { [S] [W](1-[M]K2IS] PA: -d[M]/dt
= k3[S] {[M] -- (1 -- [S1]/[S])
Since [Wl = [W]o - [S], it follows that -d[M]/dt -- kt {[M] ([W]o- IS]) q-/~3[S]
{[M] --
--[SI]/Kt}
(1 -[S1]/[S])/K3}
- 1¢1 {[M] ([Wlo -- Is]) -- [Sll/K1}
(10.67)
(10.68)
Since it has been assumedthat the reactivities of all carboxyl and amino groups are equal (that is, independent of the chain length of the molecule), the equations derived for linear macromolecules may also be applied to aminocaproic acid (S0. For this case, Eqs. (10.52)-(10.54) may be written as M + W ~ S1, Sn + S1 ~ Sn+l + W, M + S1 ~ $2 The following rate equation may then be written for St : dt
-- kl{[Ml([W]o -- [S])
(10.69) Note that in the last term of this equation, it has been assumed for the sake of simplicity that [S2] ~ [$t]. The set of differential equations comprising Eqs. (10.67)-(10.69) suitable for the evaluation of experimental data of [M], [S1, and [$1], obtained as a function of time, for the estima!ion of values for kt, k2, and
Anionic
Polymerization
Strong bases as alkali metals, metal hydrides, metal araJdes, and organometallic compoundsinitiate the polymerization of a lactam. The initiation involves the formation of a lactam anion, e.g., for caprolactam with a metal:
(CH2)~
\NH + M ~ (CH2)5’
+ + ½H 2 (10.
70)
834
Chapter 10
or with a metal derivative
(
+ 2)5--NH
+ B-M
~
/C\ (CH2)~N-M
+ +
BH (10.71)
The lactam anion (VI) reacts with monomerin the second step of the initiation process by a ring-opening transamidation [Eq. (10.72)]:
9 /c\ (CH2)5~N-M
,o, + HN--(CH2)5
Slow
+ (CH2)s--N-CO(CH2)~-N-M (VII) The primary amine anion (VII), unlike the lactam anion (VI), is stabilized by conjugation with a carbonyl group and therefore this reaction is energetically unfavorable and very slow. For the same reason, (VII) highly reactive and, once it is formed, it undergoesa rapid proton-abstraction reaction with a caprolactam monomerproducing an imide dimer (VIII), N-caproylcaprolactam, and regenerating the lactam anion [Eq. (10.73)]. O
(CH2)~N-CO(CH2)5-N(VII)
+
+ (CH2)5--NH
Fast
O (CH2)f-"N-
CO (CH2)sNH 2 + (CH2)(~NN-M (VIII)
+ (10.73)
This lactam anion attacks the carbonyl group attached to the nitrogen in the N-acyllactam (VIII), as shownin Eq. (10.74), followed by fast proton exchange with monomer[Eq. (10.75)] to regenerate the lactam anion and the propagating N-acyllactam (X). The imide dimer (VIII) has been isolated and is the actual initiating species for the onset of polymerization [14]. The slowness of reaction in Eq. (10.72) accounts for the occurrence of an initial induction period of low reaction rate in lactam polymerization. The imide dimer is necessary for polymerization because the amide linkage in the lactam is not
835
Ring-OpeningPolymerization
sufficiently reactive (i.e., not sufficiently electron deficient) towardtransamidation by lactam anion [cf. Eq. (10.72)]. The presence of the exo-carbonyl group attached to the nitrogen in N-acyllactam (VIII) increases the electron deficiency of the amide linkage. This increases the reactivity of the amide ring structure toward nucleophilic attack by the lactam anion [Eq. (10.74)]. Propagation follows through a sequence of reactions similar those shownin Eqs. (10.74) and (10.75).
,9 (CH2)s
O
~ N- +
+ (CH2)5/-~N-CO(CH2)sNH2
(viii)
O (10.74)
~N-GO(GH~)5--N~-GO(GH~.)s-NH~
(IX)
0
0
/\ M* (CH2)g-~N-CO(CH2)5--N~-CO(CH2)5-NHg. (IX)
+ (CH2)5~NH
,o, /\ C (CH2)~N-CO(CH2)~-NHCO(CH2)5-NH~
(x)
C / \ + (CH2)g~N-M
(10.zs)
It may be noted that the propagating center in the above reaction mechanism is the cyclic amide linkage of the N-acyllactam. Monomerdoes not add to the propagating chain; it is the monomeranion (lactam anin), often referred to as activated monomer, which adds to the propagating chain. The rate of propagation depends on the concentrations of lactam anion and N-acyllactam, both of which are determined by the concentrations of lactam monomer and base. Addition
of N-Acyllactam
The use of strong base alone for aninic polymerization of lactam is limiting. As noted previously, the polymerization is characterized by induction periods and, moreover, only the more reactive lactams, such as e-caprolactam and 7-heptanolactam (~-enantholactam), readily undergo polymerization, while the less reactive lactams, 2-pyrrolidinone, and 2-piperidinone, are
836
Chapter 10
are much more sluggish. Both these limitations are overcome by forming an imide by reaction of lactam with an acylating agent such as acid chloride or~ anydride, isocyanate, and others. Thus, e-caprolactam is readily converted to an N-acylcaprolactam (XI) by reaction with an acid chloride [Eq. (10.76)]. The N-acyllactam can be synthesized in situ by this reaction preformed and then added to the polymerization system. O (CH2)5~NH
O + RCOCI
--~
(CH2)~---2N-CO-I~ (XI)
+ HCl (10.76)
Initiation consists of the reaction [Eq. (10.77)] of the N-acyllactam with activated monomer(lactam anion) followed by fast proton exchange with monomer [Eq. (10.78)]. Species (XII) and (XIII) correspond species (VII) and (VIII) for polymerization in the absence of an lating agent. The acylating agent achieves facile polymerization of many lactams by substituting the slow reaction in Eq. (10.72) by the faster reaction in Eq. (10.77). Induction periods are thus eliminated, polymerization rates are significantly increased, and lower reaction temperatures can be used. Polymerizations in the presence and absence of an acylating agent are often referred to as assisted (or activated) and nonassisted polymerizations, respectively. O
O
(CHe)5~N-M
+ (CH2)s---N-CO-R O
(CH2)5~N-CO(CH2)5--N=--CO-R
(10.77)
(xIr)
O
O
(CH2)5~N-CO(CH2)5--Nz--CO-R O (CH2)(-\N-CO(CH2)5-NH--CO--R (XIII)
+ (CH2)5//NXNH O + + (CH?)5/-NN-M (10.78)
Propagation follows in the same manner as for propagation of species (VIII) through sequence of reactions similar to those in Eqs. (10.74)
Ring- OpeningPolymerization
837
(10.75) except that the propagating chain has an acylated end group instead of an amine end group. The rate of assisted lactam polymerization is dependent on the concentration of base and N-acyllactam, which determine the concentrations of activated monomerand propagating chains, respectively. The degree of polymerization increases with conversion and with increasing concentration of monomeror decreasing N-acyllactam concentration. These characteristics are qualitatively similar to those of living polymerizations, but lactam polymerizations seldom are living [15,16].
REFERENCES 1. H. R. Allcock,/. Macromol.Sci. Re, vs. Macromol.Chem.,C4, 141 (1970). 2. H. Sawada, Thermodynamicsof Polymerization, Chap. 6, Marcel Dekker, NewYork (1976) 3. G. Gee, W.C. E. I-Iigglnson, and G. T. Men:all, J. Chem.Sac., 1345(1959). 4. A. Ledwithand N. R. Mcfarlane, Proc. Chem.Soc., 108 (1964). 5. C. E. Bawn,A. Ledwith, and N. Mcfarlane, Polymer, 10, 653 (1969). 6. D. Vofsi and A. V. Tobohky,J. Polym.Sci., Part A, 3, 3261(1965). 7. J. C. W. Chien, Y.-G. Cheun, and C. E Lillya, Macromolecules, 21, 870 (1988). 8. E Mijangosand L. M. Leon, J. Poem.Sci. Polym.Lett. Ed., 21,885 (1983). 9. S. Penczekand P. Kubisa, "Cationic Ring-OpeningPolymerization: Ethers," Chap. 8 in ComprehensivePolymer Science, Vol. 3 (G. C. Eastmond, A. Ledwith,S. Russo, and P. Sigwalt, eds.), PergamonPress, London(1989). 10. A. V. Tobolsky,J. Polym.Sci., 25, 220(1957); 31, 126(1958). 11. A. V. Tobolskyand A. Eisenberg, Y. Am.Chem.So¢, 81, 2302 (1959); 82, 289(1960). 12. G. Bertalan, L Rusznak, and E Anna, Makromol.Chem., 185, 1285 (1984). 13. H. Sekiguchi, "Lactams and Cyclic Amides," Chap. 12 in Ring Opening Polymerization, Vol. 2, (K. J. Ivin and T. Saegusa, eds.), Elsevier, London (1984). 14. H. K. Hall, Jr., J. Am.Chem.Soc., 80, 6404(1958). 15. M. Kuskova,J. Roda, and J. Kralicep, Makromol.Chem., 179, 337 (1978). 16. J. Sebenda, ’~knionic Ring-OpeningPolymerization: Lactams," Chap. 35 in ComprehensivePolymerScience, Vol. 3 (G. C. Eastmond,A. Ledwith, S. Russo, and E Sigwalt, eds.), PergamonPress, London(1989).
EXERCISES 10.1. Salts of carbazoleare excellent initiators for ethyleneoxide polymerization, giving living polymersof prdieted molecularweights. Fromconductivity measurements at 20°C, th dissociation constant of carbazylpotassium(NK)was found [E Sigwalt and S. Boileau, J. Polym. Sci. Polym. Syrup., 62, 51 (1978)] to be 7.0×10-9 in THF, 1.1xl0 -5 in THF+[2.2.2]cryptand and 7.5× 10-2 in hexamethylphosphoramide (HMPA).,(a) Calculate the fraction
838
Chapter 10
of flee ions in the thre cases with NKconcentration 10-3 mol/L. (b) Calculate the molecular weights of polyethylene oxide initiated by NKin the three cases at 90%conversion of the monomerof initial concentration 1.4 mol/L. (c) What is the number of initiator residue per molecule of the polymer formed ? [Ans. (a) THF0.1303, THF+[2.2.2] 0.11, HMPA 0.99; (b) 55,440; (c) Oneinitiator residue per molecule.] 10.2. The initiation of ethylene oxide polymerization by sodium naphthalene involves direct addition of the monomerto the radical anion and reduction of the adduct by sodium naphthalene producing a dianion. Suggest two tests to support this mechanism. 10.3. Consider the following monomersand initiating systems: (a) Monomers:Propylene oxide, trioxane, oxacyclobutane, a-pyrrolidone (’7butyrolactam), a-piperidone ((5-valerolactam, and ethyleneimine. (b) Initiating
system: n-C4HgLi, H20, BF3 + H20, NaOC2Hs,H:~SO4.
Which initiating system(s) can be used to polymerize each of the various monomers ? Show the mechanism of each polymerization by chemical equations. 10.4. Explain why the polymerization of an epoxide by hydroxide or alkoxide ion is often carried out in the presence of an alcohol. Discuss how the presence of alcohol affects both the polymerization rate and the degree of polymerization. 10.5. Explain the following observations: (a) Anionic polymerization of propylene oxide is usually limited to producing a relatively low-molecular-weight polymer. (b) A small amount of epichlorohydrin gretaly increases the rate of polymerization of tetrahydrofuran by BF3 even though epichlorohydrin is much less basic than tetrahydrofuran. (c) The addition of small amounts of water to the polymerization of oxetane by BF3 increases the polymerization rate but decreases the degree of plymerization. (d) In the presence of an acylating agent, the anionic polymerization !actams occurs without an induction period. 10.6, In an equilibrium polymerization of e-caprolactam initiated by water at 220°C, [I]0 = 0.352 mol/L, [M]0 = 8.79 mol/L, and [M]~ = 0.484 tool/L, DP,~ = 152. Calculate the values of/~i and Kp at equilibrium. [Ans. 2.51×10-3; 2.07] 10.7. An equilibrium polymerization of tetrahydrofuran is carried out with an initial monomerconcentration [M]0 = 12.1 mol/L, [M]~ = 2.0 x 10-3 mol/L. Calculate the initial polymerization rate if [M], = 1.5 mol/L and/~ = 1.3x10-2 l_Jmols. What is the polymerization rate at 20%conversion ? [Ans. (Rr)0 = 2.76x10-4 tool/L-s; Ph0 = 2.13×10-4 mol/L-s.]
Appendix
1
Conversion
SI
UNITS
AND CONVERSION
Physical quantity Length Mass Time Force Pressure Energy Power
Name of SI unit Meter Kilogram Second Newton Pascal Joule Watt
Physical quantity Length Mass Force
Customary unit in. lb dyne kgf lbf 2dyne/cm
Pressure
of Units
atm mm Hg lbf/in. 2 or psi
FACTORS
Symbol for SI unit m kg s N Pa J W
SI unit m kg N N N -2 Pa or -2 Pa or -2 Pa or -2 Pa or
Nm N-m Nm Nm
Definition of SI unit Basic unit Basic unit Basic unit kg m s -2 (= J -I) kg m-1 s -2 (= N -2) kg m2 -2 s kg m2 s -a (= J -1) To convert from customary unit to SI units multiply by -2 2.54 x 10 -1 4.535 923 7 x 10 -s 1 x 10 9.806 65 4.448 22 -1 1 x 10 1.013 25 × 105 1.333 22 x t02 a6.894 76 × 10
839
840 SI
Appendix I UNITS
Physical quantity Energy
ml’ea
AND CONVERSION
Customary unit erg Btu ft-lbf cal eV 2in. 2ft
FACTORS
SI unit J J J J J 2m -~ m
To convert from customary unit to SI units multiply by -7 1 x 10 1.055 056 x 103 1.355 82 4.187 -19 1.602 × 10 -4 6.451 6 x 10 -2 9.290 304 x 10
Viscosity
alb/ft "~) poise (dyne s/cm
-a kg m kg m~1 -1 s Nsm-2
1.601 846 3 x 10 -1 1 x 10
Viscosity, kinematic
Stoke (cme/s)
m2 $-1
10-4
Ibf/ft dyne/cm
-1 Nm -1 Nm
14.59 -3 10
Density
Surface tension
Additional
Conversion
Units
1 ~. = 10-8 cm = 10 -1° m
1 kgf/cm ~ ~ = 9.807 x 104 N/m
1 atm =76cm Hg (at 0°C) = 14.696 psi 1 eV = 1.602 x 10-12 erg 1 #= 10 -4cm = 10 -8 m
1 t-IP = 550 ft lbf/s = 2545 Btu/h = 746 W °C= °F t (1.8t+32) t ° F = (5/9)(t
- ° C
Appendix
2
Fundamental
Constant
Constants
CGS system
Acceleration of gravity (g) (standard value) Normal atmospheric pressure Volume of 1 mole of ideal gas at at 1 atm and 0°C Avogadro’s number Atomic mass unit Universal gas constant (R) Boltzmann costant (k)
S! system
-2 980.665 cm s
-2 9.8066 m s
-2 1,013,250 dyne cm
1.01325 x l0 s 2N m
22.4136litre -1 6.0220 × 1023 mole 1.6604 × 10-24 g
22.41136 × 10-3 m3 -1 mole z~ -1 6.0220 × 10 mole
1.9872 cal deg-1 -1 mole -is 1.3807 × 10 erg deg-1 -1 molecule
Faraday constant
1.6604 × 10-27 kg 8.3143 J deg-1 -1 mole -23 1.3807 × 10 J deg-1 -~ molecule -1 96,487.0 Coulombmole
6.6262 × 10-2~ ergs
6.6262 × 10TM Js
2.99792 × 10rooms--1 4.80325 × 10-l° esu
2.99792 × 10s -1 ms -19 1.60219 × 10 Coulo’mb
Proton rest mass
9.1095 × 10-2a g 1.67265 × 10-24 g
9.1095 × 10-31 kg 1.67265 × 10-27 kg
Neutron rest
1.67482 × I0 -24 g
1.67482 × 10-27 kg
Planck constant (h) Velocity of light in vacuum (c) Electronic charge (e) Electron rest mass
mass
Source: E. R. Cohenand B. N. Taylor, J. Phys. Chem.Ref. Data, 2 663 (1973). 841
Index
Absolute rate constants, determination of, 480 Acetophenone, 464 Actinometry, 468 Addition polymerization, 11 Addition polymers, table of, 12 Aging, 32 AIBN, 454 Alfin catalysts, 742 Al|ylic transfer, 509 Alternating copolymers, 7, 580 Amorphous state, 43 Anionic polymerization, 659-753 alkali metal initiation, 662-664 block copolymers, 699-703 copolymerization, 695-669 degree of polymerization, 673, 676-680 excess counterion effect, 686-690 experimental methods, 672 kinetic chain length, 670-682 kinetics, 669-676 living polymers, 665, 676 polydispersity index, 680, 681 reaction media, 682
Ansa metallocenes, 793 Arborols, 416 Arithmetic mean, 230, 237 Atactic isomer, 74 Atactic polymer, 74 Atactic polypropylene, 52 Athermal mixing, 145 Athermal solvent, 175 Atomic mass unit, 5 Autoacceleration effect, 477, 518-522 Autoinhibition, 509 Autoinitiation, 708 Avrami equation, 88 Azeotropic copolymer, 592 Azeotropic copolymerization, 592 Azeotropic feed composition, 592 Beer’s law, 468 Benzophenone, 464 Bernoullian distribution, 580, 587 Bernoullian model, 82 Bernoullian statistics, 76-82 Bifunctional initiation, 701, 702 Bisphenol-A, 201 Block copolymerization, 590, 641-644 843
844 Block copolymers, 7, 580 coupling agents, 702 star-shaped, 703 Boiling point elevation, 240 Bondrotation, angle of, 45, 46, 47 Branch units, types of, 380 Branched polymer, 21 Branching, 71 Branching probability, 374, 376 Brintzinger catalysts, 793 Bulk polymerization, 553, 554 Butane, potential energy of, 46 n-Butyllithium, 661, 664, 700 Cage of solvent, 455 Carboxyl-terminated polybutadiene, 667 Carother’s equation, 331, 371 Cationic polymerization, 704-755 absolute rate constants, 727-731 chain termination, 713, 718 chain transfer, 713-718 copolymerization, 735 degree of polymerization, 723-725 kinetics, 718-723 Lewis acid, 707 molecular weight distribution, 732-734 propagation, 711-713 protonic acid initiation, 706 steady-state assumption, 726 Ceiling temperature, 533-541 Cellulose, 4 Chain length, 488-490 Chain polymerization, 11 Chain termination: by combination, 437 by disproportionation, 437, 438 mode of, 490 Chain transfer, 435, 493-510 constants, 499-510 effect on DP,~, 96-499 to monomer, 493, 494
Index [Chain transfer] to polymer to solvent, 494, 495 Chemical potential, 141 Cis conformation, 44, 46, 47 Cloud point curve, 192 Cohesive energy, 199 Coiled conformation, 51 Coiled polymer molecules, 59 Cold drawing, 34, 35 Colligative properties, 159 Combination, chain termination by, 13, 491, 492 Combinatorial entropy, 145 Compact molecules, 179 Condensation polymerization, 313-424 branching, 366 breadth of MWD,351 dosed system, 333 control of molecular weight, 338 cross-linking, 369 degree of polymerization, 330 equilibrium consideration, 332 molecular weight distribution, 347, 367 multichain polymer, 366 nonlinear polymer, 366 nonstoichiometric A-A plus B-B, 355 open driven system, 334 recursive approach, 394-415 stoichiometric A-Aplus B-B, 353 type I, 314 type II, 314 Condensation polymers, table of, 19, 20 Configurational entropy, 145 Configurational isomerism, 67, 72 ¯ Configurations, 44, 67 Conformational changes, 44-58 Conformations, 44, 48, 49, 50, 51 gauche, 45, 47 in crystals, 53
Index [Conformations] planar cis, 44, 46, 47 planar trans, 45 Constitutional isomerism, 67-71 Coordination catalysts, see Ziegler-Natta catalysts Coordination polymerization, see ZieglerNatta polymerization Copolymer equation, 586 Copolymerization, 579-646 composition equation, 590-600 effect of cross-linking, 633-640 multicomponent, 625-629 penultimate effect, 631, 632 rate of, 620-625 sequence distribution, 615-619 types of, 587-590 Copolymers, 7, 8 Coupling, termination by, 544-546, 550 Critical branching coefficient, 374 Critical solution temperature, 197 Critical temperatureof miscibility, 190, 193 Cross-linked polymer, 21 Cross-linking, 23, 369 oxidative, 32 Cross-propagation, 582 Cryoscopy, 240 Crystallinity of polymers, 83 Crystallites, 90 Curing, 27 Dead-end polymerization, 477-480 DeGennes theory, 123 Degradative chain transfer, 509, 513 Degree of polymerization, 6, 233, 488, 489 effect of temperature, 531 Dendrimers, 416 Dendritic polymers, 416-424 Dendritic unit, 417
845 Depolymerization, 533 Diblock copolymers, 7 Dicarbanion, 664 Diels-Alder dimer, 475 Diffusion coefficient in bulk polymers, 125 Diglycidyl ether, 201 Dilatometer, 448, 449 Dilute solution viscometry, 285-295 nomenclature, 287 terminology, 286 Diol, cleavage of, 69 Diphenylpicrylhydrazyl radical, 458 Dispersion forces, 206 Disproportionation, 491, 492 termination by, 14, 543-547 Dissymmetrycoefficient, 274, 283, 284 Dissymmetry method, 281 Dissymmetry of scattering, 272 Doolittle equation, 108 DPPHradical, 438 Drawing, 34 Dyad, 77 Ebulliometry, 240 Eclipsed conformation, 44, 46, 47 Eclipsed state, 44, 46 Elastomers, 27-29 Emulsion polymerization, 556-569 constant rate, 561 detergents, 557 kinetics of, 562, 568 qualitative picture of, 551-561 End groups, 6 End-group analysis, 240 End-to-end distance, 58 Epoxy curing, 29 Epoxy resins, 29 Excess Rayleigh ratio, 265 Excluded volume, 65, 178, 179 theories of, 177-181 Excluded volume parameter, 182
~d~ Expansion factor, 185, 215, 217 Extinction coefficient, 467 Fibers, 27-29 Fiducial mark, 289 Fineman-Ross method, 604 First moment, 235 First-order Markov, 580, 581 First-order transition, 91, 92 Fisher projections, 75 Flory constant, 213, 214 Flory-Fox equation, 214, 215, 217 Flory-Huggins equation, 156 Flory-Huggins model, 150-159 Flory-Huggins theory, 145, 150-159 modification of, 168-176 Flory-Krigbaum theory, 176-178 Flory parameter, 213 Flory temperature, 186 Fold period, 86 Fold plane, 86 Fox equation, 119, 120 Free-draining coil, 210 Free-draining molecule, 210 Freely jointed chains, 58-61 Free volume, 121 theory of, 103-106 Freezing point depression, 240 Functionality, 9 Gauche conformation, 45, 46, 47, 48 Gaussian coils, 214 Gaussian distribution, 213 Gegenion, 654 Gelation process, 370 model for, 383, 384 molecular size distribution in, 384 recursive approach for, 399--415 Gel effect, 477 Gel-permeation chromatography, 295-302 apparatus, 297
[Gel-permeation chromatography] calibration, 298, 300 column used, 299 experimental arrangement, 296 universal calibration, 300, 302 Geometrical isomerism, 72 G~bs free energy, 185 Glass transition temperature (Tg), 89-120 effect of branching, 114 effect of copolymerization, 117 effect of cross-linking, 115 effect of diluents, 116 effect of molecular weight. 112 factors affecting Tg, 98-120 relation with T.~, 102, 103 secondary, 91 theoretical treatment, 103-107 Glyptal resin, 32 Graft copolymerization, 644-646 Graft copolymers, 580 Hafnocenes, 792 Hagen-Poiseuille equation, 291 Hansen parameter, 206-210 H-bonding group, 204 HDPE, 22 Head-to-head linkage, 67-71 Head-to-tail linkage, 67-71 Heterotactic triad, 79 High-conversion polymerization, 552 High-density polyethylene, 22 High-mileage catalysts, 747 High-performance polymers, 20 High-speed membrane osmometer, 252 Hildebrands, 202 Hole theory, 111 Homopropagation, 582 Hyd_ride elimination, 668 Hydride ion shift, 711 Hydrodynamic volume, 304 Hydrogen bond; 57
847
~ndex Hydroquinone, retardation by, 524 Hydroxyl-terminated polybutadiene, 667 Hyperbranched polymers, 416-424 applications of, 421-424 by polycondensation, 418-419 generations of, 420, 421 synthetic approaches for, 420 Ideal copolymers, 588, 591 Ideal solution, 173 Ideal solvents, 215 Impermeable coil, 211 Induced dipoles, 148 Induction period, 522 Inherent diluent, 99 Inherent viscosity, 287 Inhibition, 522-527 kinetics of, 525 Inhibition constant, 525 table of, 529 Inhibition period, 522 Inhibitors, 522 Initiator chain transfer constant, 502 Initiator efficiency, 454-458 determination of, 457 Initiator-monomer complex, 512 Initiators, 452--460 thermal decomposition of, 478 Instantaneous copolymer composition, 594 Interaction energy, 148, 185 Interaction parameter, 149, 159-168 critical value of, 189 from osmometry, 255 from osmotic pressure, 163 from vapor pressure, 161 from virial coefficient, 167 Intermittent illumination, 483 Intraparticle interference, 272 Intrinsic viscosity, 212, 214, 215, 287 measurement of, 289 Ionic chain polymerization, 653-735 polymerizability of monomers, 656-659
Ionizing radiation, 469 initiation by,469 Iso-free-volume state, 105 Isomefization polymerization, 711 Isomers, 67 Isotactic form, 53, 55 Isotactic polymer, 74-76 Isotactic polypropylene, 53, 55, 56 Isotactic triad, 79 1-UPACnomenclature, 37
Kelen-Tudos method, 605 Kevlar, 34 Kinetic chain length, 488-490 Kinetic energy correction, 292
Ladder polymers, 25 Lambert-Beer’s law, 468 Lamellae, 86 Lattice theory, 145, 146 LCST, 197, 198 LDPE, 22 Lifetime of radical, 481, 492 Light scattering method, 216, 262 end-to-end distance from, 276, 280 instrumentation of, 282 radius of gyration from, 276 Zimmplots, 278-283 Limiting viscosity number, 287 Linear polymer, 21 Living polymers, 665, 676 London forces, 206 Long-range interactions, 215 Low-conversion polymerization, 542 Low-density polyethylene, 22 Maltese cross pattern, 87, 88 Mark-Houwinkconstants, 215, 290 Mark-Houwinkequation, 176, 215 Mark-Houwink-Sakurada equation, 215 calibration, 288 Maxwell model, 110
848 Mean field approximation, 152, 156 Mean square end-to-end distance, 214 Me-an square radius of gyration, 214 Melt viscosity, dependence on chain length, 122 Melting temperature (T,~), 101-102 factors affecting T,,~, 101-102 relation with Tg, 102-103 Membrane osmometer, 248 Membrane osmometry, 240 Mer, 2 Meso placement, 76 Metallocene catalysts, 791-803 active center, 795, 796 catalyst composition, 792-795 chain transfer, 801, 802 Chien’s model, 798-801 Ewen’s model, 797, 798 kinetic models, 797 polymerization mechanism, 796, 797 Methylalumoxane cocatalyst, 794, 795 Metallocenes, 792 Methylalumoxane, 794, 795 MHSconstants, 304 Miscibility of polymers, 192 Molar attraction constants, 200, 201 Molar mass, 5 Molecular weight, 5 Molecular weight averages, 230-239 determination of, 239-306 in terms of moments, 235-238 Molecular weight determination: by cryoscopy, 243-244 by ebulliometry, 242-243 by end-group analysis, 240-242 by membrane osmometry, 244-257 by vapor pressure osmometry, 258-261 Monodisperse polymer, 235 Monofunctional initiation, 700
/~dex Monomerchain transfer constant, 499-501 Monomerreactivity ratios, 600 table of, 606-607 Monomer, 1, 2 Multiblock copolymers, 7 Network polymer, 22 Newmanprojections, 46 Newtonian flow, 291 Nomenclature of polymers; 37 Nondraining molecule, 210, 212 Nonsteady-state kinetics, 481 Normalized distribution, 231, 237 Norrish-Smith effect, 518 Nuclear magnetic resonance, 76 Nucleophilic attack, 660--662 Number-average molecular weight, 231 Numberdistribution, 231, 236 Nylon, 35, 36, 39, 40 hydrogen bonds in, 57 Oil~soluble initiators, 555 Oligomer, 2 Opalescence, 190 Optical activity, 73 Osmometry, 244-257 practical aspects, 250-257 Osmotic pressure, 163, 240, 245 reduced, 255 Ostwald viscometer, 289, 291 Oxidative cross-linking, 32 Partial molar G~bs free-energy change, 142 Partial molar property, 140, 141 Particle scattering factor, 277 Pentaerythritol, 26 Perturbation theories, 182 Pert_urbed dimension, 186-188 Phase equilibria, 176 in polymer solvent mixtures, 188-198
Index Phenol-formaldehyde resins, 28 Phenylenediamine, 26 Photochemical initiation, 462-468 Photoinitiation, 462-468 Photopolymerization, 466-468 rate of, 466 Photosensitization, 464, 465 Photosensitizers, 464-466 Planar trans, 46, 47 Plastic, 5 Plastics, 27-29 Polyamide, 33 Polybenzimidazopyrrolone, 25 Polybutadiene, isomers of, 70 Polycaprolactam, 38 Polychloroprene, isomers of, 71 Polycondensation reaction, 314 Poly(dimethyl siloxane), Polydispersity index, 235 Polyester resin, unsaturated, 30 Polyesterification, 319-330 acid-catalyzed reaction, 319, 320, 323-325 kinetic parameters, 329 uncatalyzed reaction, 320-321 Polyethylene: crystal structure of, 54 orthorhombic, 54 zigzag form, 49 Poly(ethylene terephthalate), Poly(hexamethylene adipamide), 39-40 Polyimide,26 Polyisobutylene: conformations, 50 Newmanprojections, 50 Polyisoprene (c/s), 102 (trans), 102 isomers of, 71 Polymer coils, 181 Polymerization processes, 11,553-569 Polymerization-depolymerization equilibrium, 532-541
849 Poly(methyl methacrylate), NMRspectra of, 81 Poly(p-phenylene), Poly(phenylene oxide), Polypropylene: atactic form, 52 isotactic form, 53, 55, 56 Newmanprojections, 52 syndiotactic form, 55 Polyspiroketal, 26 Polyurethane, 31 Poly(vinyl acetate), hydrolysis of, 69 Poly(vinyl alcohol), cleavage of, 69 Poly(p-xylylene), Poor solvent, 176, 185 Positional isomerism, 67-71 Post-gel relations, 392-394, 408-415 Prepolymers, 27, 369 Primary radical, 426 Primary radical termination, 511, 512 Primary radicals, recombination of, 455 Primary termination, 511 Pseudoasymmetrie carbon, 73 Pseudochiral carbon, 73 Pyromellitic dianhydride, 25, 26 Q- e schem~ 612-615 Quantum yield, 464 Quencher, 467 Quinone, 524 Radiation-induced polymerization, 469-474 free-radical chain initiation in, 472, 473 initiation of, 469-472 ionic chain initiation in, 474 Radical chain polymerization, 435-570 catalysts for, 452
850 [Radical chain polymerization] dilatometry for, 447-454 experimental, 447--452 initiation in, 452-454 integrated rate of, 443, 444 rate of, 441 Radical reactivity, 609 Radical-monomer reactions, 607-611 polar effects, 610 resonance effects, 607 steric effects, 610 Radius of gyration, 60, 71 Ramanscattering, 263 Random copolymers, 7, 580, 588 Random-alternating copolymerization, 589 Random polymer coil, 275 Raoult’s law, 147, 150 Rate of polymerization, effect of temperature, 527-530 Ratio of moments, 237 Rayleigh equation, 263 Rayleigh ratio, 262, 264 Reactivity of functional groups, 315 Real polymer chains, 61-66 Recursive method, 394-415 for linear step-growth, 395-398 for nonlinear step-growth, 399-415 Redox catalysis, 458 Redox initiation, 458-462 Reducedvariables shift factor, 110 Reduced viscosity, 287, 292 Relative viscosity, 287, 292 Relaxation processes, 121-126 Relaxation time, 123 Repeating unit, 3 Reptation model, 123-126 Resin, 5 Retardation, 522-527 kinetics of, 525 Retarders, 522 Rigid-rod polymer, 276
Index Ring-opening polymerization, 809-837 addition of N-acyllactam, 835-837 anionic polymerization, 833--835 assisted polymerization, 836 cationic mechanism of, 820-823 degree of polymerization, 827-830 exchange reactions, 819, 820 hydrolytic polymerization, 830-833 kinetics, 816-818, 823-826 lactams, 830-837 mechanism, 812-837 nonassisted polymerization, 836 polymers made by, 810 RMSdistance, 60 RMSend-to-end distance, 276, 280 RMSradius of gyration, 276 Rotational isomeric states, 62 Run number, 618, 619 Saw horse projection, 46 Scattering factor, 275 Second moment, 236 Second-order Markov, 580 Second-order transition, 91, 92 Secondvirial coefficient, 180, 254 Semicrystalline polymers, 90 Semiladder structure, 26 Sequence length distribution, 615-619 Shift factor, 110 Short-stopping of polymerization, 672 Silicones, 38 Single-site catalysts, 792 Size of polymer, 58 Skeist equation, 598 Sodium naphthalenide, 663 Solubility behavior, 198-209 of alternating copolymers, 205 Solubility parameter, 199-210 of mixtures of liquids, 205 Solution polymerization, 554 Solvent chain transfer constant, 503-506
85I
Index Specific viscosity, 212, 287 Spherical polymer, 276 Spherulites, 87-89 Spiro-polymers, 26 Spontaneous termination, 668 Staggered conformation, 46, 47 Starburst, 416 Statistical copolymer, 580 Steady-state assumption, 441 Step polymerization, 15-18 Step-growth polymerization, 313-424, see Condensation polymerization Stereoisomerism, 52, 73-82 Stereoisomers, 73 Steric parameter, 63 Stoichiometric imbalance, 339-347 Stopped-flow technique, 672, 674 termination reactions, 665-669 Stress-strain behavior, 35 Styragel, 296 Supported metal oxide catalysts, 779-790 bound-ion coordination mechanism, 787-788 bound-ion radical mechanism, 782-787 polymerization mechanism, 781, 782 Suspended-level viscometer, 291 Suspension polymerization, 554, 555 Syncatalytic system, 709 Syndiotactic form, 55, 74 Syndiotactic polypropylene, 55, 56 Syndiotactic triad, 79 Tacticity, 74--82 by NMR, 78-82 Telechelic polymers, 667 Terpolymerization, 579 Tetrablock copolymers, 7 Tetrad, 77
Tetraminobenzene, 25 Thermal initiation, 475 Thermal transitions, 89-120 thermodynamics of, 810--812 Thermoplastic elastomers, 699, 701 Theta conditions, 172, 185, 214 Theta solutions, 169 Theta solvent, 66, 185, 215, 254 Theta state, 175 Theta temperature, 169-175 Titanocenes, 792 p-ToluenesuLfinate, 465 Torsional mobility, 98 Trans conformation, 45, 49 Triad, 77-79 Triblock copolymers, 7 Tromsdorff effect, 518 Turbidity, 266, 267 Type I condensation, 314, 347, 353, 359 Type I! condensation, 314, 347, 353, 354 Ubbelhode viscometer, 289, 291 UCST, 197, 198 Unimolecutar micelles, 422 Unnormalized distribution, 237 Unperturbed dimension, 184, 186-188, 218 Unsaturated polyester, 30 Unzipping, 541 Urea-formaldehyde resins, 28 Valence angle model, 61 van Laar model, 145-150 Vapor-phase osmometry, 258-261 practical aspects, 259 Vapor pressure, relative, 161 Vapor pressure lowering, 240 Vapor pressure osmometry, 257 Vinyl acetate, 4 Vinyl esters, 27
852 Virial coefficients, 165 Virial equations, 166, 248 Virial expansion, 168 Viscoelastic behavior, 93-94 Viscometry, 285-295 Viscosity: intrinsic, 212 of polymer solutions, 211-219 of suspensions, 211, 212 specific, 212 Viscosity-average molecular weight, 286-288 Viscous flow, 292 Volumeexclusion, 184 Vulcanization, 23 WAXSmethod, 83, 85 Weight-average molecular weight, 234 Weight distribution, 234, 236 Wide-angle x-ray scattering, 83 WLFequation, 107-110 Woodequation, 119, 120 Ziegler-Natta catalysts, 742-755 catalyst composition, 742 high-mileage, 747 metallocene-based systems, 791 titanium-aluminum systems, 746 Ziegler-Natta polymerization, 741-803 adsorption models, 764-773 anionic coordination, 748 bimetallic mechanism, 749, 750 catalyst site control, 748 catalysts, 742-755 cationic coordination, 748 copolymerization, 789-790 degree of polymerization, 778, 779 enantiomorphic site control, 748 kinetic models, 760-764, 773-778 kinetics, 755-778 mechanism, 747-755 monometallic mechanism, 749-751
Index [Ziegler-Natta polymerization] stereoregulation, 754 stereospecific placement, 748 Zimmplots, 278-283 Zirconocenes, 792
