J. Chem. SOC., Faraday Trans. 1, 1982, 78, 11 17-1 126 Seeded Emulsion Polymerizations of Styrene The Fate of Exited Free Radicals BY BARRY C. Y. WHANG, DONALD H. NAPPER,* MATTHEW J. BALLARD AND ROBERT G. GILBERT Departments of Physical and Theoretical Chemistry, University of Sydney, New South Wales 2006, Australia AND GOTTFRIED LICHTI Australian Atomic Energy Research Establishment, Sutherland, New South Wales 2232, Australia Received 7th May, 1981 The kinetics of the seeded emulsion polymerization of styrene at different particle number concentrations and different initiator concentrations have been studied. The results were analysed using a theoretical treatment that incorporates the possibilities of both the re-entry ofexited free radicals into the latex particles and the cross-termination in the aqueous phase of exited free radicals by free radicals generated through initiator decomposition.The results exclude the possibility of complete re-entry of exited free radicals into the latex particles for the initiator concentrations studied. They strongly support the occurrence of significant cross-termination in the aqueous phase of the exited free radicals with free radicals generated by initiator decomposition. This is in accordance with the known rapidity of cross-termination reactions compared with the corresponding self-termination reactions. It was also shown that the rate of entry of free radicals into each latex particle increases with decreasing particle number at constant initiator concentration. The radical capture efficiency was, however, relatively insensitive to the particle number concentration. The overall polymerization rate was found to be a complex function of the number concentration of latex particles; this is because this overall rate is itself a complicated function of the rate coefficients for entry, exit, etc.each of which may be individually a simple function of number concentration. Such behaviour reflects significant deviations from Smith-Ewart case 2 kinetics that occur in these sysems, rather than deviations from the general Smith-Ewart kinetic scheme. Previous studies'. of seeded emulsion polymerizations of styrene showed that free- radical exit (desorption) could play an important role in determining the kinetics of polymerization. In those studies, however, for all except very low initiator concen- trations, the exit rate was only a small fraction of the rate of entry of free radicals into the particles.Consequently, the results cast little light on the importance of the re-entry of exited free radicals into the latex particle^.^-^ The role of radical re-entry can be explored by increasing the relative importance of the exit rate and/or varying the number concentration of the seed latex particles. The former can be accomplished in two different ways: first, by the use of relatively small seed latex particles, since it was shown previously1 that the exit rate coefficient ( k ) is inversely related to the latex particle size; secondly, by the reduction of the initiator concentration so that the entry rate coefficient (p) is decreased.l In what follows, the results of these types of experiments are presented. The experiments highlight the importance of cross-termination of exited free radicals in the aqueous phase.They also confirm that the rate of emulsion polymerization is not always 11171118 SEEDED EMULSION POLYMERIZATION directly proportional to the number of latex particle^.^ An explanation for this type of behaviour in terms of the precepts of the Smith-Ewart theorys is proposed. EXPERIMENTAL The preparation and characterization of the monodisperse polystyrene seed latex have been described in detail previously.' Its mean particle radius was 38.3 nm, comparable to that of latex R 12/ 150 reported previously. mote that the latex designations R 12/ 150 and R 12/ 17 1 were inadvertently interchanged in table 1 of ref.(l).] The dilatometric method for measuring the rate of polymerization at 50 O C has also been detailed elsewhere.' Results are presented only for those systems that exhibited no particle nucleation as determined by electron microscopy. We note parenthetically that the induction period was found to increase significantly with increasing particle number concentration. Values for the contraction factor, the propagation rate constant and the equilibrium concentration of monomer in the latex particles were determined previously.' THEORETICAL TREATMENT OF EXPERIMENTAL DATA SLOPE A N D INTERCEPT METHOD FOR MODELS INCORPORATING RADICAL RE-ENTR Y AND C ROSS-TER MI NATION We have previously1 presented a rigorous theoretical analysis of the approach to a steady state in an emulsion polymerization for interval I1 that is accurate provided that the average number of free radicals per particle (A) does not exceed 0.5.This treatment (which did not take re-entry specifically into account) must of course only be used in such a limit and cannot be extrapolated to values of A greater than 0.5.' This analysis permits values to be obtained forp and k from the slope of the steady-state rate line and its intercept. This analysis did not, as already stated, include the possibility of re-entry of radicals that had exited from the latex particles. In what follows, we incorporate the possibilities of re-entry and cross-termination into the model so that it is possible in this case to transform measurements of the steady-state slope (a) and intercept (b) into values of p and k .Note that the intercept can be either negative (as in chemically initiated seeded systems1) or positive (as in relaxation studies2). We have shown previously1 that this treatment, which we term the 'zero-one' approximation (since only particles containing 0 or 1 free radicals are considered), is valid if the termination rate coefficient c % k,p so that the average number of free radicals per particle is not large ( A < 0.5). The kinetic equations incorporating the possibility of re-entry and cross-termination are -- dNo - - (PA 4- akA)No 4- (PA 4- akii+ k)Nl dt where N , is the relative population of particles containing n free radicals (normalized so that No+ Nl = 1 and thus A = Nl), pA is entry rate coefficient in the absence of exit and a is the exited free-radical fate parameter.The fate parameter a is formally defined such that akfi is equal to the change in the entry rate coefficient arising from the Occurrence of exit. Thus its numerical value is restricted to the range - 1 < a 6 1. A value of a = + 1 would imply total re-entry of exited free radicals into the latex particles whereas a value of a = - 1 would imply that exited free radicals underwentWHANG, NAPPER, BALLARD, GILBERT A N D LICHTI 1119 complete cross-termination in the aqueous phase with entrant free radicals generated as a result of initiator decomposition. Values of a between these two extremes would imply that both re-entry and cross-termination in the aqueous phase could contribute to radical loss from the aqueous phase, as indeed could self-termination.More than one physical interpretation of such intermediate values for a is thus possible (see below). Eqn (1) and (2) may be derived by considering the kinetic equations governing the concentrations of aqueous-phase free radicals arising from (i) initiator decomposition and (ii) exit; these kinetic equations incorporate both self- and cross-termination of these species in the aqueous phase. Eqn (1) and (2) are then obtained by invoking the steady-state approximation for both types of aqueous-phase free radicals. Note that one physical interpretation of a = 0 is the absence of re-entry whence eqn (1) and (2) assume the form discussed previously. Eqn (2) can be re-written as: where f = -2ak, g = -2pA-(1 - a ) k , h = pA and we approximation in the aqueous phase.Integration of eqn (3) leads to the result where p - q6ert 1 -beyt Nl = (3) will adopt the steady-state (4) During interval 11, when the concentration of monomer is essentially constant, the fractional conversion x is given by t x = A J N,(t)dt where A = k, N, CM/nrNA, k, is the propagation rate constant, N, is the number of seed latex particles, CM is the monomer concentration in the particles, n f is the number of moles of monomer initially present and NA is Avogadro's constant. Eqn (5) shows clearly that at long times the time independent slope (a) of a plot of x against t is Aq so that q = B,,, where the subscript ss denotes the steady state. The intercept of this plot is given by b = lim [A(q--p)/y]ln {e;:-q - tdcn = [A(q -P)/Yl In (6/[6 - 11).(6) The expressions derived above permit a and b to be calculated given values for A , pA, k, a and Nl(t = 0). What is required, however, is to be able to calculate p A and1120 SEEDED EMULSION POLYMERIZATION k given values for a, b, A , a and Nl(t = 0). This inversion can be accomplished after some tedious algebra, the results being where k = A In F/2ab (7) P A = G k G = [2aa2+A(1 -a)a]/A(A--2a) (8) F = 0.5+{[2G+(l -a)+4aN1(t = 0)]/2[4G2+(a- 1)2+4G(a+ 1)]4). and Eqn (7) is clearly inapplicable if a = 0. The relationship k = [AN,(? = 0) - U] ( A - 2a)/Ab (9) must then be employed in conjunction with eqn (8) and the appropriate value of G.l RESULTS AND DISCUSSION R AD1 C AL RE-EN TRY The foregoing theoretical analysis enables kinetic data for the approach to the steady state to be analysed for different assumed values of a.Acceptable values for a can be ascertained by determining whether they predict realistic values for k and p A . Values of p A are found to be relatively insen'sitive to the assumed value for a and so provided the calculated value for p A does not exceed the experimentally determined rate of production of free radicals, p A is not a very discriminating parameter. Fortunately, at least at lower initiator concentrations, k is a discriminatory parameter, 150 50 100 150 so 100 time/min FIG. 1 .-Fractional conversion against time curves for seeded emulsion polymerizations: curves 1, 2 and 3 correspond to particle number concentrations of 3.0 x 10l6, 1.5 x 10'6 and 0.75 x 10l6 dm-3, respectively. Initiator concentrations: (a) 1.3 x 10-2, (b) 1.1 x 10-3, (c) 1.0 x 10-4 and (d) 1.2 x rnol13rn-~.WHANG, NAPPER, BALLARD, GILBERT A N D LICHTI 1121 being quite sensitive to the chosen value for a.Two criteria exist for the acceptability of k values: first, the values of k calculated at different particle number concentrations and different initiator concentrations must be identical, within experimental error; secondly, the absolute magnitude of this constant value for k measured for chemically initiated systems must agree with the value obtained by other independent methods (e.g. relaxation studies2). Fig. 1 displays the fractional conversion against time curves for seeded emulsion polymerizations of styrene.These were obtained at three particle number concentra- tions and at four different initiator concentrations lying in the range 10-5-10-2 mol dma3 potassium peroxydisulphate. The exit rate constant was measured independently by relaxation studies on a seeded emulsion polymerization of styrene initiated by prays2 The results were interpreted using the theory set out above. In relaxation studies, the entry rate is very small after removal of the initiating source. As a result, there are insufficient free radicals for cross-termination in the aqueous phase to occur (see below) and so the appropriate value of a was assumed to be + 1 (i.e. complete re-entry). The result so obtained, k = (2.6k0.4) x s-l, is in fair agreement with the value [( 1.4 f 0.4) x s-l] expected from previous measurements' on different latices. This latter value for k was computed using the size dependence TABLE CALCULATED VALUES OF pA AND k FOR DIFFERENT VALUES OF a pA/10-3 S-1 k/io-3 s-1 A,, a = + l a=O a = - 1 a = + l a=O a = - 1 111 N C /mol dm-3 / 1OI6 dm-3 1.2x lo+ 1.0 x 10-4 1.1 x 10-3 1.3 x 2.9 0.06 1.5 0.13 0.72 0.20 3.0 0.10 1.5 0.17 0.76 0.27 2.9 0.15 1.4 0.27 0.79 0.28 3.1 0.27 1.6 0.28 0.77 0.38 0.18 0.47 1.1 0.29 0.58 1 .o 0.9 1 1.2 2.4 2.1 3.1 4.0 0.25 0.26 0.63 0.67 1.4 1.5 0.39 0.41 0.76 0.81 1.3 1.4 1.2 1.3 1.5 1.7 2.9 3.2 2.6 2.8 3.7 4.0 3.5 4.9 mean standard deviation 20 10 12 8.1 6.6 3.3 3.9 6.9 6.7 8.2 3.6 8.6 4.9 14 3.5 3.6 4.1 3.1 2.9 2.2 5.6 2.6 4.7 4.4 5.6 3.0 3.8 1.1 1.9 2.2 2.8 1.8 1.9 1.6 3.5 1.9 3.6 3.3 4.3 2.6 2.5 1 .o k from relaxation studies = (2.6f0.4) x s-l.determined from previous studies. Some variation in the value of k would be expected for latices of the same size if the particles incorporate differing amounts of a soap that functions as a chain-transfer agent.' An analysis of the rate curves shown in fig. 1 for three different values of a, using the theory detailed above, is presented in table 1. The values of the average number of free radicals per particle in the steady state (ass) were all significantly less than 0.5. The values of k calculated for a = + 1 are clearly not constant. Moreover, the absolute values calculated for this value of a from these chemically initiated studies are significantly larger than the value of k measured for this latex at 50 *C using relaxation 37 FAR 11122 SEEDED EMULSION POLYMERIZATION kinetics. For both these reasons, the model with a = + 1, which corresponds to complete re-entry of exited free radicals, can be eliminated as a possible model describing these seeded styrene emulsion polymerizations in the presence of aqueous- phase initiator.Such systems are closely analogous to interval I1 of an ab initio polymerization. In contrast to the results obtained for a= + 1, the results for a = - 1 seem totally acceptable, both on the basis of the constancy of k and also in terms of its absolute magnitude. Indeed, the mean value obtained using a = - 1, k = (2.5+ 1.0) x s-l, is in remarkably good agreement with the relaxation value of k = (2.6 f 0.4) x s-l, although the large standard deviation associated with the former result suggests that such excellent agreement may well be fortuitous.The consistent results obtained with a = - 1 imply that for styrene, essentially complete cross-termination of the exited free radicals occurs in the aqueous phase by free radicals generated as a result of initiator decomposition. This would be in accord with the known8 rapid rate ofcross-termination of free radicals compared with the respective rates of self-termination. Typically, cross-termination rate constants are one or two orders of magnitude larger than those for self-termination. The enhanced rate of cross-termination may be a consequence of differences in the polarity of the two free-radical specie^,^ as well as the steric hindrance accompanying head-to-head linkage in self-termination.Note that the two free radical species in these studies are chemically quite different, the exited one being CH,=c-C6H, and the other SO,- or an oligomeric derivative thereof. Note that in the foregoing discussion we have assumed by analogy with copolymerization systems that low molecular weight free radicals cross-terminate more rapidly than they undergo self-termination. Unfortunately, although it is possible to exclude the model with a = + 1 (i.e. complete re-entry), it is more difficult to distinguish between values of cc = 0 and a = 1. The values of k calculated with a = 0 are reasonably constant and their mean value is k = (3.8 s-l; although large, this value is not totally incompatible with the relaxation result (2.6 x s-l).One simple interpretation of a = 0 would be that one half of the exited free radicals undergo cross-termination in the aqueous phase whilst the other half re-enter the latex particles. Other interpretations of a = 0 are, however, possible : e.g. the occurrence of complete self-termination in the aqueous phase of the exited free radicals, although this seems to be less likely on chemical An additional, and quite probable, interpretation of a = 0 is that the latex radical capture efficiency is low while cross-termination in the aqueous phase is very rapid. An exited free radical would then undergo essentially instantaneous cross- termination on entry into the aqueous phase which (because of the high rate of mutual-termination among aqueous-phase free radicals originating directly from the initiator) would have a negligible effect on p A .The foregoing results show that for the seeded emulsion polymerization of styrene in the presence of added initiator, complete re-entry of exited free radicals does not occur. The results suggest that significant cross-termination of the exited free radicals by free radicals generated by initiator decomposition takes place in the aqueous phase. 1.1) x DEPENDENCE OF THE RATE OF POLYMERIZATION O N THE NUMBER OF SEED LATEX PARTICLES The Smith-Ewart case 2 corresponds to Hss = 4. If case 2 kinetics are operative, the rate of polymerization would be directly proportional to the number concentration (E,,) of latex particles, as ass is independent of p, k and c.As van der Hoff has pointed out, the results of experiments are not always in accord with this simple model. Smith,loWHANG, NAPPER, BALLARD, GILBERT A N D LICHTI 1123 TABLE 2.-RATE OF POLYMERIZATION AS A FUNCTION OF THE NUMBER CONCENTRATION OF LATEX PARTICLES Nc tiss/ 1 0l6 dmd3 [I]/mol dm-3 NC/lOl6 dmW3 = 1 . 2 ~ 10-5 1 . 0 ~ 10-4 1.1 x 10-3 1.3 x 3.0k 0.1 0.18 0.30 0.44 0.84 1.5 f 0. I 0.20 0.25 0.39 0.44 0.75 & 0.05 0.14 0.21 0.22 0.29 C Q8 rate exponent vo. 2 j q . 2 q . 5 Bovey et aZ.ll and van der Hop2 have all reported experiments in which the rate was not directly proportional to the number of particles. Such results would be expected if A,, # f so that the value of A,, depends upon p, k and c ; in particular, p may then be a function of Nc so that the direct proportionality between rate and f l c would be lost.Table 2 presents values of Nc ass, which is proportional to the rate of polymerization, for different values of Nc over the range of initiator concentrations studied. Also presented in the table are values of the exponent y in the equation rate cc x[ obtained from the appropriate log-log plot. At low initiator concentrations when A,, is small, the exponent is only ca. 0.2. As A,, increases with the initiator concentration so does the exponent, reaching a value of ca. 0.8 for the highest initiator concentration studied. For the small particle size used in these experiments, it was not possible to achieve fi,, = 4; the initiator concentrations required to achieve this value of A ~ , induced particle coagulation.It should be stressed that the rate of polymerization of a system obeying Smith-Ewart kinetics is only directly proportional to the number of latex particles for case 2 kinetics (i.e. R,, = i), Deviations from an exponent of unity may well reflect deviations from the value of A,, = 4. At low initiator concentrations, the radical capture efficiency would be expected to approach 100% (see below). Under these conditions the total rate of entry of free radicals into latex particles Ncp would be constant, i.e. p a (RJ. Moreover, at low as,, fi,, = p/(2p+_k) - p / k , as k >> p.l Thus n,, would be inversely proportional to gc and the product NcnSs would be independent of Xc. Thus, for small nSs values and high radical capture efficiencies, the polymerization rate would be independent of the number of particles at constant initiator concentration.The exponent of Nc in the rate equation would then be zero. However, as R ~ , increases to 9, the exponent should increase towards unity. This is qualitatively what was observed in these studies. We conclude that deviations from unity in the exponent of xc do not necessarily reflect deviations from the general Smith-Ewart-type kinetics, merely deviations from Smith-Ewart case 2 kinetics. These deviations arise in part from variations in the radical capture efficiency and thus in p. Smithlo originally proposed that these deviations were a consequence of the inability of monomer to diffuse sufficiently rapidly from the droplets to the polymerizing particles to sustain propagation.This explanation seems unlikely in light of Flory's calc~lation~~ that monomer diffusion is comparatively rapid in these systems. 37-21124 SEEDED EMULSION POLYMERIZATION TABLE 3 .--FREE-RADICAL ENTRY RATES AT DIFFERENT PARTICLE NUMBER CONCENTRATIONS (a= -1) [I]/mol dm-3 = Nc/ 1 0l6 dmP3 1 . 2 x 10-5 1.0 x 10-4 1.1 x 10-3 1.3 x 3.0 f 0.1 0 . 1 4 0.23 0.78 1 . 9 1.5 f 0.1 0.38 0 . 4 9 1 . 2 2.8 0.75 k 0.05 0 . 9 4 0.97 2.2 3.9 TABLE 4.-RADICAL CAPTURE EFFICIENCIES AS A FUNCTION OF PARTICLE NUMBER CONCENTRATION (a= - 1) NebA - knss)/ l OI3 dm-3 s-l capture efficiency (%) IIl/mol RC/1Ol6 dm-3 = dm-3 1.2 x 10-3 1.0 x 10-4 1 . 1 x 10-3 1.3 x 10-2 1.2 x 10-5 1.0 x 10-4 1 . 1 x 10-3 1.3 x 10-2 3.0k0.1 0.41 0.69 2.3 5.9 21 3 1.2 0.3 1.5 +_ 0.1 0.58 0.73 1.7 4.5 29 3 0.9 0.2 0.75 +_ 0.05 0.68 0.74 1.7 3.0 34 3 0.9 0.2 RADICAL CAPTURE EFFICIENCIES In what follows, we will adopt the value a = - 1.As noted above, however, the calculated values of p A are relatively insensitive to the assumed value of a (see table 1). Table 3 displays the values of the average rate of free radical entry per particle (PA - kfi,,) at different particle number concentrations. Lower particle number concentrations could not be investigated because of the occurrence of nucleation in the seeded systems. It is clear that the larger the particle number concentration, the smaller is the rate of free radical entry per particle. Table 4 shows that the overall rate of entry of free radicals into the latex particles, Nc(PA - kfiss), is relatively insensitive to the particle number concentrations at a given initiator concentration.The overall radical capture efficiency, calculated as described previously,' is a sensitive function of the initiator concentration; efficiencies varied in these experiments from 0.3 to 21% as the initiator concentration decreased from 1.3 x mol dm-3. The efficiency was relatively insensitive to the particle number concentration over the four-fold range of concentration studied. This observation is in accord with the predictions of the theory of Hawkett et aZ.14 Briefly, since most of the bimolecular termination of free radicals generated by initiator decomposition occurs in the aqueous phase, the presence of the latex particles has virtually no influence on the radical capture efficiency, at least over the range of particle concentrations accessible in these studies.to 1.2 xWHANG, NAPPER, BALLARD, GILBERT A N D LICHTI 1125 CONCLUSIONS The results of these studies on the seeded emulsion polymerization of styrene rule out the occurrence of complete re-entry of exited free radicals. The data are best fitted by a model that assumes almost complete cross-termination of exited free radicals in the aqueous phase by the free radicals generated as a result of decomposition of the initiator. This is in accord with the known rapidity of cross-termination reactions compared with the corresponding self-termination reactions. It is also shown that the average rate of entry of free radicals into individual latex particles increases with decreasing particle number concentration at constant initiator concentration.The overall radical capture efficiency was, however, relatively insensitive to the particle number concentration over the range studied. These results may be quite simply interpreted as arising from moderately extensive termination taking place in the aqueous phase. Finally, it was found that the rate of polymerization was a complex function of the number concentration of latex particles. This is because this rate is, from the general Smith-Ewart kinetic scheme presented in this paper, seen to be a known but fairly complex function of quantities such as p A , a, etc. Each of these latter are simple functions of Nc, or at least can be represented in terms of straightforward kinetic equations involving various types of aqueous-phase free radicals.Thus the behaviour of the rate of polymerization as Nc is varied reflects deviations from Smith-Ewart case 2 kinetics (nss = i), rather than deviations from the general Smith-Ewart kinetic scheme or the onset of diffusion control of the propagation step. LIST O F SYMBOLS a b C 2 k R k n, = slope of steady-state rate plot (s-l) = intercept of steady-state rate plot = first-order (with respect to particles) bimolecular termination rate constant = concentration of monomer in the latex particles (mol dm-3) = initiator concentration (mol dm-3) = exit rate coefficient (s-l) = propagation rate constant (dm3 mol-1 s-l) = number of moles of monomer initially present = average number of free radicals per particle = steady-state value of A = Avogadro’s constant (mol-l) = relative population of particles containing n free radicals = total number of seed latex particles = number concentration of seed latex particles (dm-3) = time (s) = exited free-radical fate parameter (- 1 < a < 1) = free-radical entry rate coefficient (s-l) = free-radical entry rate coefficient in the absence of exit (s-l).(s-Y We thank the ARGC for financial support of these studies and AINSE for a post-doctoral fellowship for G. L. ; M. J. B. acknowledges the award of a Sydney University post-graduate scholarship. We thank the Electron Microscope Unit of the University of Sydney for their generous provision of facilities.1126 SEEDED EMULSION POLYMERIZATION B. S. Hawkett, D. H. Napper and R. G. Gilbert, J. Chem. Soc., Faraduy Trans. I , 1980, 76, 1323. S. W. Lansdowne, R. G. Gilbert, D. H. Napper and D. F. Sangster, J. Chem. SOC., Faraduy Trans. I , 1980,76, 1344. J. Ugelstad and J. K. Hansen, Rubber Chem. Technol., 1976, 49, 536. J. W. Vanderhoff, in Vinyl Polymerization, ed. G. E. Hamm (Marcel Dekker, New York, 1969), vol, 1, part 2, chap. 1. D. C. Blackley, Emulsion Polymerization (Applied Science, London, 1975). W. V. Smith and R. H. Ewart, J. Chem. Phys., 1948, 16, 592. D. T. Birtwistle and D. C. Blackley, J. Chem. SOC., Faraday Trans. 1, 1981,77, 413. H-G. Elias, Macromolecules (Plenum, New York, 1977), vol. 2, p. 7. 1979). * M. J. Bowden, in Macromolecules, ed. F. A. Bovey and F. H. 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