J . Chem. SOC., Furada-v Trans. I , 1982, 78, 2129-2145 Effects of Chain-transfer Agents on the Kinetics of the Seeded Emulsion Polymerization of Styrene BY GOTTFRIED LICHTI? AND DAVID F. SANGSTER AINSE and the Australian Atomic Energy Research Establishment, Sutherland, New South Wales 2232, Australia A N D BARRY C. Y. WHANG, DONALD H. NAPPER* AND ROBERT G. GILBERT Departments of Physical and Theoretical Chemistry, The University of Sydney, New South Wales 2006, Australia Receiued 14th August, 1981 The kinetics of the seeded emulsion polymerization of styrene have been studied in the presence and absence of the chain-transfer agents carbon tetrachloride and carbon tetrabromide. Initiation was achieved by both a chemical initiator (potassium peroxydisulphate) and irradiation with prays.The latter permitted relaxation studies to be performed. A combination of 7-ray initiation, relaxation and particle size distribution studies allowed the fate of the exited free radicals generated in the presence of carbon tetrabromide to be determined. Cross-termination in the aqueous phase was found to be operative in pray initiated systems when the free radical concentration in the aqueous phase was relatively high. In contrast, re-entry of the exited free radicals into the latex particles was found to be important in relaxation studies when the free radical concentration in the aqueous phase was comparatively low. These results show that the exited free radical fate parameter can vary between - 1 and + 1. The exit rate coefficient was found from relaxation measurements to increase linearly with increasing concentration of chain-transfer agent; this result is consistent with a diffusion/transfer mechanism for exit.The increase in the exit rate coefficient paralleled the increase in the chain-transfer constant for the additives : CBr, > CCl, > styrene. On the other hand, the efficiency of exit from the latex particles of free radicals formed by chain transfer follows the inverse order: CBr, < CC1, < styrene. This order may well reflect the relative reactivities with monomer of the low-molecular-weight free radicals formed by atom abstraction. As expected from the increase in exit rate coefficient, the presence of carbon tetrabromide reduced the rate of polymerization of chemically initiated systems.At high initiator concentrations, for which the average number of free radicals per particle i was ca. 0.5, the rate reduction was small but increased monotonically with increasing concentration of carbon tetrabromide. This shows that any effect of carbon tetrabromide on the propagation rate constant was small in these studies. At lower initiator concentrations, however, a much larger reduction in rate was observed, as expected theoretically for values of i < 0.5. The rate in this case did not decrease monotonically with increasing concentration of carbon tetrabromide but passed through a minimum. This minimum was caused by the enhanced rate of entry of free radicals into the latex particles counterbalancing the rate reduction arising from the increased exit rate.The increase in the entry rate in the presence of carbon tetrabromide was explained by the production of hydrophobic free radicals by chain transfer in the aqueous phase and/or a colloidal contribution to the measured entry rate. In principle, chain-transfer agents should not influence the kinetics of the free radical polymerization of monomers in homogeneous bulk or solution systems, although they do reduce the molecular weight of the polymer formed. We have recently reported1 that under certain heterogeneous conditions, such as those pertaining to emulsion t Present address: I.C.I. Australian Central Research Laboratories, Ascot Vale, Victoria, Australia. 21292130 SEEDED EMULSION POLYMERIZATION OF STYRENE polymerizations, a chain-transfer agent may significantly reduce not only the molecular weight of the polymer formed but also the rate of polymerization.This reduction in rate was shown' to arise, at least in part, from the breakdown in the extent of compartmentalization of the free radicals in the latex particles. The presence of the chain-transfer agent promoted the exit (desorption) of free radicals from the latex particles. In what follows, we present quantitative data, obtained from seeded kinetic studies of the emulsion polymerization of styrene, on the role of chain-transfer agents. The results cast light upon the fate of the exited free radicals generated in the presence of chain-transfer agents and especially upon the influence of the free radical concentration in the aqueous phase. They also show that chain-transfer agents can influence the rate of entry of free radicals into the latex particles. Inter aka, our results show that the exit rate coefficient is linearly dependent on the concentration of added chain-transfer agent.This finding is consistent with a diffusion/transfer mechanism for the exit of oligomeric free radicals, a result which is also suggested by previous studies on the dependence of the exit rate coefficient on particle size.2 The planning and interpretation of experiments involving exit of free radicals in emulsion polymerization systems is particularly complex, owing to the plethora of mechanisms which must be taken into account: organic free radicals entering into, propagating within and exiting (desorbing) from the latex particles, and hetero-termi- nation and re-entry (into the latex particles) of oligomeric free radicals in the aqueous phase.Thus a unique interpretation of, for example, a single dilatometric kinetic run is impossible, since so many rate coefficients are involved that many sets of apparently physically reasonable values may fit the data. In addition, refinements such as changing the concentration or nature of the initiator are (when considered alone) only of limited help, since (for example) the rate coefficients for entry and aqueous-phase hetero- termination will then be altered. In order to resolve this problem, we first employ a large range of experimental procedures, as follows. (i) For initiation, we use both a chemical initiator of varying concentrations and y-radiolysis.With both techniques we obtain the rate of approach to steady state for Interval I1 of a seeded styrene emulsion polymerization system; for the y-radiolysis studies, we also obtain the rate of relaxation after removal from the radiation source. (ii) In addition to obtaining rate data from the overall kinetics (followed dilatometrically)2*3 we also use data on the time evolution of the particle size di~tribution.~ (iii) Studies are carried out varying the nature and concentration of initiator and also the nature and concentration of chain-transfer agent. The data obtained using the above experimental methods are then interpreted by the following means. (i) We may reasonably assume that while the rate coefficient for exit will vary with the nature and concentration of chain-transfer agent (since the process seems to be diffusion/transfer controlled),2 it should be invariant to the nature and concentration of initiator.(ii) We may interpret the complexities of the fate of oligomeric radicals in the aqueous phase by a recent theory5 which enables the kinetics of aqueous-phase hetero-termination and of re-entry into the latex particles to be expressed in terms of a single parameter. This parameter will depend on the nature of the oligomeric species (i.e. on the nature and concentration of the chain-transfer agent) and on the nature and concentration of the aqueous-phase initiator. (iii) With the two preceding simplifications, we derive a treatment which permits a unique set of internally consistent rate coefficients to be obtained.LICHTI, SANGSTER, WHANG, NAPPER AND GILBERT 2131 EXPERIMENTAL As stated above, all studies were carried out using seeded latex systems in Interval 11.The seeds employed were two monodisperse polystyrene latices (labelled R17/5 and R007f 15) which were prepared and characterized as described ea~1ier.l.~ For this characterization, the mean particle radius in both latices was determined to be ca. 48 nm by both electron microscopy and sedimentation velocity. The concentration of particles in these studies was ca. 5 x 10l6 particles dm-3. The polymerization rate was found dilatometrically. All studies were carried out at 50 O C . THEORETICAL FRAMEWORK Prior to presenting our experimental results, we give a brief outline of the theory which will be used for their interpretation; details have been presented el~ewhere.~.~ Consider the kinetics of an Interval I1 seeded system.The overall rate of formation of polymer is given by: where x is the fractional molar conversion of monomer, N , is the concentration of latex particles, C, is the concentration of monomer within these particles, k , is the propagation rate coefficient and ri is the average number of free radicals per particle, which will be determined by the values of the rate coefficients for free radical entry ( p ) , exit ( k ) and any other microscopic events which need to be taken into account. Since x is observable directly (e.g. as in our dilatometric experiments), it can be seen that one way of determining ti is to know C , k,. This would then give information which could be used to determine the values of p and k , and in particular the dependence of these parameters on such controllable variables as the nature and concentration of the initiator, etc.However, a major problem which arises is that (at least for styrene systems of the type studied here) small errors in the value of C M k p , and hence of ti, can lead to errors of orders of magnitude in the derived values of p or k . Thus one needs either an accurate value of C,k, for a given system or an alternative means of determining ti. In styrene systems of the type studied here, it has been well established' that ri cannot exceed 0.5 in Interval 11. In such a system, to determine ti from values of p, k , etc. it is sufficient to determine the (time-varying) values of No and N , , which are defined as the relative numbers of latex particles containing zero or one free radical, respectively. One has by definition No + N , = 1, and thus ri = N , .The requisite rate equation for determining N , is: -- dN1 - p ( 1 - N , ) - ( p + k ) N , . dt Note that p is an effective rate coefficient for the entry of free radicals into the latex particles and must incorporate all relevant aqueous-phase processes; p itself will thus in general depend on ri. Aqueous-phase processes which need to be considered are ( a ) entry of species originating directly from aqueous-phase processes, (b) re-entry of oligomers which have exited from latex particles into the aqueous phase and (c) aqueous-phase hetero-termination of these exited oligomers before they undergo re-entry, this hetero-termination being specifically with an entity which would otherwise have entered a particle as in (a).It has been shown5 that one may write:21 32 SEEDED EMULSION POLYMERIZATION OF STYRENE where pA is the free radical entry rate coefficient from process (a) above and a is a dimensionless ‘fate parameter’. One has - 1 ,< a < 1 , and a can be written as a function of the rate coefficients for processes (b) and (c) above (and also processes such as direct production of free radicals from initiator and aqueous-phase bimolecular homo-termination of these). In this formalism, complete re-entry of exited free radicals into latex particles is characterized by a = + 1, whereas complete hetero- termination in the aqueous phase corresponds to a = - 1 .Such cross-termination is postulated to occur between exited free radicals and free radicals (or derivatives thereof) generated by process ( a ) above. Note that the general formulation encom- passed by eqn (1) and (2) incorporates various theoretical refinements suggested by other workers in this field,6 at least as far as a description of systems where fi cannot exceed 0.5 is concerned. We emphasize that extensive experimental studies have shown this last requirement to be met for the present A complete kinetic description of the system would thus be furnished by a knowledge of the dependences of pA, a and k (as well as k, and C,) on the experimentally controllable parameters : the size and nature of the latex particles, the nature and concentration of the initiator and the nature and concentration of any chain-transfer agent.In the present studies, we keep the size and nature of the latex particles fixed. The other controllable variables will be expected to affect the microscopic rate parameters as follows. (i) One expects pA to depend only on the nature and concentration of the initiator I ; we denote this dependence by pA(1, [I]). (ii) One expects the exit rate coefficient k to be dependent on the nature and concentration of any chain-transfer agent T (since it is controlled by diffusion and transfer); we denote this by k(T, [TI). (iii) The fate parameter a may depend on all the controllable variables, since, for example, the rate coefficient for hetero-termination will depend both on the initiator and on the exiting species; we write a (I, [I], T, [TI).(iv) Both k , and C, may depend slightly on the nature and amount of chain-transfer agent. In addition to the time variation of the fractional conversion x, another experimental observable is the time evolution of the particle size distribution : n( V, t), the relative number of particles with volume V at time t. This quantity will be determined by p and k ; the governing equations have been presented previ~usly.~ The object of the present study is to obtain values for the rate parameters pA, a and k , or rather, to show how they depend on the controllable variables. This will enable us to make deductions concerning the mechanisms governing the microscopic processes.The above-mentioned plethora of rate coefficients requires careful data analysis in order to obtain unique values for the desired quantities. Detailed discussions of the means of effecting this are given in the sections on the individual sets of experiments. However, important general assumptions which are relevant to mention at this point are as follows. (i) We assume that the presence of the chain-transfer agent does not significantly affect the value of k , CM at the concentrations employed here. This will be justifed in a later section. For k,, we have assumed (where required) a value of 258 mol-1 s-l dm3, as obtained from previous studies on these latex systems.2 (ii) In Interval I1 of a seeded system, fi goes from ri = 0 at time t = 0 to some steady-state value which we denote by tiss.From eqn (l), one may readily write down fi,, as a specific function of pA, a and k (see below). Now, as indicated by extensive studies of similar systems,3 we assume that for systems where initiation is by y-radiolysis, fiss = 0.5 in the absence of chain-transfer agent, i.e. when I = y and [TI = 0. Assuming then that k, CM is essentially unchanged by the presence of chain-transfer agent, for y-radiolysis in the presence of chain-transfer agent we may then obtain ti,, (or indeed ti at any time) simply by comparison of the rate in the presence of chain-transfer agent with that in the absence of chain-transfer agent.LICHTI, SANGSTER, WHANG, NAPPER AND GILBERT 21 33 The data which we have at our disposal are thus as follows. (a) For y-radiolysis, the steady-state value of ri in the radiation cavity, ti,, (I = y); note that because of experimental limitations, we cannot readily either alter the intensity of the radiation ( i e .for y-radiolysis, [I] = constant) or find the time dependence of approach to steady state within the radiation cavity. (b) For y-radiolysis experiments, the relaxation of the system after removal from the cavity, i.e. in the absence of initiator. Note that we are able to obtain an absolute value of ri through assumption (ii) given above. (c) For chemically activated systems (all with persulphate initiator of varying concentrations) we are able to obtain the time dependence of the fractional conversion, including the rate of approach to steady state, with varying initiator concentration; we may denote this x(t, I = C, [I]). This must be 'normalized' (by means which wilI be discussed later) in order to determine 2.Note that because of experimental limitations, we are able to extract only two meaningful pieces of data from a given x(t) curve: the slope of the straight line portion (i.e. the steady-state value) and the intercept that it makes with the t = 0 axis, expressing the rate of approach to steady state ; under unfavourable circumstances, the errors involved in the value of the intercept may be so large as to render this quantity unusable. 0.14 0.12 2 0.10 r 53 2 0.08 > c - 3 c 0 .- 5 0.06 it" 0.04 0.02 0 20 40 60 80 100 time/ m in FIG. 1.-characteristic kinetic curve for relaxation measurements on latex R17/5 in the absence of chain transfer agents.An illustration of typical kinetic data is given in fig. 1. This is for y-radiolysis initiation both inside and outside the radiation cavity. After an approach to steady state which is too rapid to observe experimentally, the x(t) curve inside the cavity shows a constant polymerization rate. The sample is then rapidly removed from the cavity, and the system then relaxes with a measurable transient decay to a final period of constant rate. This particular experiment was for polymerization in the absence of chain-transfer agent; further typical raw data curves (including those in the presence of chain-transfer agent) may be found in ref. (1).2134 SEEDED EMULSION POLYMERIZATION OF STYRENE RESULTS AND DISCUSSION We first discuss the data obtained from relaxation studies.Table 1 lists the values of the three measured quantities for such a system, as discussed in points (a) and (b) in the preceding section: the steady-state rate inside the cavity, the steady-state rate outside the cavity and the intercept of the out-of-cavity steady-state line; note that we present these data as rates, this being the quantity which is measured. These rates TABLE 1 .--~-RADIOLYSIS RESULTS IN THE PRESENCE AND ABSENCE OF CHAIN-TRANSFER AGENTS (SEED LATEX R17/5) steady-state rate/ min-l lo3 x intercept additive % added (w/w) in-cavity out-of-cavity out-of-cavity nil CBr, CBr, CCl, CCI, CCl, CCI, nil 3 6 1 3 6 10 3.6 1.3 20 2.3 0.29 4.5 1.6 0.27 2.1 3.4 1.2 16 3.6 1.3 14 3.7 1 . 1 13 3.7 1 . 1 8.9 TABLE 2.-KINETIC RESULTS FOR SEEDED (R17/5) EMULSION POLYMERIZATIONS OF STYRENE INITIATED BY )'-RAYS nss 0 3 6 0.50 0.3 1 0.22 are then converted to ii values, using the rate in the absence of chain-transfer agent to give ii,, = 0.5 and thus a normalizing factor, as given in assumption (ii) in the preceding section. Some typical ti values are shown in table 2, with CBr, as chain-transfer agent. ANALYSIS OF D A T A FOR CARBON TETRABROMIDE Using the values of ii in table 2, we wish to obtain the value of the exit rate coefficient k .This apparently requires that appropriate values of pA and a are also known. We resolve this problem as follows, using both the out-of-cavity and in-cavity results, with the condition (as set out in the previous section) that although pA and a will be different inside and outside the cavity, the value of k must be the same. We consider first the out-of-cavity results: the slope and intercept of the curve. From eqn (1) and (2) we may then use these to obtain pA and k as functions of a; the precise equations required for this have been given previ~usly.~ Values of pA and k are given in table 3 and in fig.2, for data obtained with 3 and 6% added CBr,. Note that the values of pA in table 3 refer to the rate of entry of thermally generated free radi~als~9~ after the system has withdrawn from the cavity. Secondly, we consider the in-cavity results. Since we are unable to observe the rateLICHTI, SANGSTER, WHANG, NAPPER AND GILBERT 21 35 TABLE 3.-cALCULATED VALUES OF THE ENTRY AND EXIT RATE COEFFICIENTS FOR DIFFERENT VALUES OF THE FATE PARAMETER COMPUTED FROM Y-RADIOLYSIS RELAXATION DATA 3% ( W W ) CBr, 6% (w/w> CBr4 a PA/ 10-4 s-1 k / 10-3 s-1 pA/10-4 s-1 k/10-3 s-1 - 1.0 -0.5 0 + 0.5 + 1.0 3.4 4.2 3.2 5.2 2.8 6.7 2.2 9.7 0.67 20 4.2 5.7 4.0 7.2 3.7 9.6 3.0 15 0.96 35 6 4 2 16 12 8 4 0 -1 0 ff FIG.2.-Calculated values for the exit rate coefficient for various values of the fate parameter: (a) 3% CBr,; (b) 6% CBr,; curves 1 and 2 refer to the in-cavity and relaxation methods, respectively. The dashed lines define the lower and upper bounds for k estimated from the precision of the data points.2136 SEEDED EMULSION POLYMERIZATION OF STYRENE of approach to steady state, we know only the steady-state rate, i.e. fi,,, which we use as follows. From eqn (1) and (2) in the steady state (when dN,/dt = 0, N , = is,) we obtain: PA( - 2, k = (1-a+2afiS,)' (3) The value of p A in eqn (3) (which of course will be different inside and outside the cavity) was found for in-cavity conditions from the time evolution of the particle size distribution, as described previ~usly,~ in the absence of chain-transfer agent.The experimental details have been given el~ewhere.~ For in-cavity conditions in the absence of chain-transfer agent, we have ii,, = 0.5. Since this implies that akii,, < p A , the analysis of the particle size evolution data given in ref. (4) is straightforward (in the absence of chain-transfer agent). We thus obtain pA (I = y) = (2.740.8) x s-l. From this value and from eqn (3) we may then determine k as a function of a for our in-cavity data.The results are shown in fig. 2. Since k must be the same for both in-cavity and out-of-cavity data (for a fixed concentration of chain-transfer agent), even though the values of p A and a will be different, fig. 2 allows us to establish the value of k and the value of a under the two different conditions. The ranges of k values given by the two methods overlap only in a relatively narrow zone (see fig. 2). The values of k obtained with 3 and 6% carbon tetrabromide present were (1.6f0.5) x low2 and (3.2k0.6) x lo-* s-l, respectively. These values will be discussed below. It is also apparent from fig. 2 that inside the radiation cavity the exit fate parameter is negative and lies in the range - 1 .O d a < - 0.75, irrespective of the concentration of carbon tetrabromide. This is in accord with the value of a = - 1 obtained previously5 for similar systems in the absence of carbon tetrabromide but initiated by potassium peroxysulphate.In contrast, the results obtained outside the cavity suggest that a is positive and lies in the range 0.75 < a < 1 .O, again irrespective of the concentration of carbon tetrabromide. The foregoing results suggest that the value of a changed from ca. - 1 for systems in the radiation cavity to ca. + 1 for polymerization outside the cavity. The former value corresponds to almost complete cross-termination of the exited free radicals in the aqueous phase whereas the latter value corresponds to almost complete re-entry. This change in the value of a we attribute as being due to the decrease in the concentration of free radicals in the aqueous phase when the system is removed from the radiation source.As shown in table 3, the background thermal entry rate coefficient ( p A ) is very small outside the cavity so the value of p (= p A - kii) would be negative if a = - 1 .O. This is physically unacceptable because a negative entry rate coefficient has no meaning in the context of eqn (2). This apparent anomaly is explained by a breakdown of the various assumptions concerning the relative magnitudes of the various rate coefficients for production and termination of free radicals in the aqueous phase used to derive eqn (1) and (2). We see from the foregoing results that, in the cavity, the high concentration of free radicals in the aqueous phase results in the exited free radicals being annihilated almost completely by cross-termination.This we ascribe to the known rapidity of cross-termination reactions compared with the corresponding self-termination reaction^.^ The enhanced rate of cross-termination, typically one or two orders of magnitude, may be a consequence of the differences in polarity of the exited free radical species (presumably -CBr,) and the initiating species (presumably -OH or an oligomeric derivative thereof).* Stated differently, in the presence of a chemical initiator or for initiation by y-rays,LICHTI, SANGSTER, WHANG, NAPPER A N D GILBERT 21 37 the rate of production and concentration of free radicals in the aqueous phase is high and the exited free radicals undergo rapid cross-termination in the aqueous phase.In relaxation studies, the concentration and rate of production of free radicals in the aqueous phase fall rapidly to comparatively low values. The exited free radicals are then more likely to undergo re-entry into the latex particles than to cross-terminate in the aqueous phase. These results suggest that for styrene the value of a can vary from + 1 to - 1 according to the concentration and rate of production of free radicals in the aqueous phase. ANALYSIS O F D A T A FOR CARBON TETRACHLORIDE When carbon tetrachloride was added to the styrene it was found that the calculated values of k were relatively insensitive to the assumed value of a. It was therefore adequate to calculate k using the slope-intercept method2* applied to the relaxation data with a = + 1 (see table 1).Note also that we have previously presented both relaxation results3 and approach to the steady-state data2 for the seeded emulsion polymerization of styrene that were interpreted using an exited free radical fate parameter equal to zero. From the present studies, the values of a that should have been used previously are + 1 and - 1, respectively. Fortunately, the differences in the numerical values that would be obtained using a = 0 and the correct values for a lie within the precision of the data for almost all of the experiments reported. [CC141 / 10 mol d ~ n - ~ [CBr4],’10 rnol d ~ n - ~ F CC14 7 CBr4 FIG. 3.--Ef€ects of different concentrations of chain transfer agents on the exit rate coefficient for latex R17/5: (a) carbon tetrachloride; (h) carbon tetrabromide.EXIT RATE OF FREE RADICALS FORMED FROM CHAIN-TRANSFER AGENTS Having extracted the rate coefficients for exit from the radiolysis experiments, we will now discuss their variation with the amount and type of chain-transfer agent. The exit rate coefficients from relaxation studies in the presence of differing amounts of the chain-transfer agents carbon tetrachloride and carbon tetrabromide are displayed in fig. 3. These results were obtained as described above using a = + 1. As shown in table 4, the chain-transfer rate constant for carbon tetrachloride is2138 SEEDED EMULSION POLYMERIZATION OF STYRENE TABLE 4.-TRANSFER, SOLUBILITY AND EXIT DATA FOR THE SYSTEMS STUDIED transfer % chain-transfer rate constant free radicals water solubility agent /dm3 mol-l s-l escaping /mol dm-3 styrene 1 .4 ~ 2 4 x 10-3 carbon tetrachloride 2.3 0.5 5 x 10-3 carbon tetrabromide 9.5 x 104 0.003 7 x 10-4 approximately two orders of magnitude larger than that for transfer to the monomer styrene; that for chain transfer to carbon tetrabromide is approximately seven orders of magnitude greater than that for transfer to rn~nomer.~ The results presented in fig. 3 show that the exit rate coefficient increases linearly with increasing concentration of both carbon tetrachloride and carbon tetrabromide. This result is consistent with a diffusion/transfer mechanism for the exit process, as is also suggested by the dependence of the exit rate coefficient on particle size;2 two important cautions with regard to this result will however be mentioned below.Note also that, at comparable molar concentrations in the latex particles, the increase in the exit rate coefficient produced by carbon tetrabromide is approximately forty times that produced by carbon tetrachloride. This may be attributed qualitatively to the greater chain-transfer rate coefficient for CBr, compared with that for CCl,. More low-molecular-weight free radicals are generated in the presence of CBr, than in the presence of CCl,, and some of these escape from the latex particles into the aqueous phase. One caveat with regard to a simplistic diffusion/transfer mechanism for exit is as follows: the increases in the exit rate coefficient induced by CBr, and CCl,, while linear in the concentration of these substances, are not, however, commensurate with those expected if the probability of exit of the free radicals produced by transfer to these chain-transfer agents was the same as that for free radicals generated by transfer to monomer.This is illustrated by the following calculation. The mean interval between successive chain transfers to monomer is l/ktr, , C,, where ktr, is the rate constant for chain transfer to monomer and C, is the concentration of monomer in the latex particles. Setting ktr, dm3 mol-l s-l and C, = 5.8 mol dm-3,27 trans- fer to monomer is calculated to occur once every 12 s. An exit rate coefficient k = 1.6 x lop3 s-l (see fig. 3) in the absence of chain-transfer agents implies that an exit event occurs at average intervals of I l k = 625 s.This corresponds to ca. 2% of the free radicals generated by transfer to monomer actually escaping from the latex particles. By way of comparison, consider a seeded emulsion polymerization of styrene containing 3 % carbon tetrabromide. The rate constant for chain transferlo ktr,cHr, = 9.5 x lo4 dm3 mol-l s-l implies that ca. 520 chain-transfer events occur every second. This assumes that the carbon tetrabromide is distributed equally between the emulsion droplets and the particles and that chain transfer to monomer can be ignored under these conditions. The measured exit rate constant k = 1.6 x lop2 s-l corresponds to an exit event occurring once every 63 s. Accordingly, only ca. 0.003% of free radicals generated by chain transfer to carbon tetrabromide actually escape from the latex particles.This is only approximately one seven- hundredth of the probability of exit of free radicals generated by transfer to monomer. The linearity of the data in fig. 3(6) implies that this probability remains constant as the concentration of carbon tetrabromide increases. A corresponding calculation for = 1.4 xLICHTI, SANGSTER, WHANG, NAPPER A N D GILBERT 21 39 carbon tetrachloride shows that ca. 0.5% of the free radicals generated by chain transfer underwent exit from the latex particles. This is only one-quarter of the value observed for styrene but one hundred and fifty-times greater than that calculated for carbon tetrabromide (see table 4). The results demonstrate clearly that the rate of chain transfer by the propagating chains is only one of the factors governing the observed exit rate coefficient. Several other factors might be expected to be important in determining the value of k : (a) the relative solubilities of the low-molecular-weight free radical species in both the aqueous phase and the swollen latex particles; (b) the relative speed at which monomer molecules add to the low-molecular-weight free radicals generated by chain transfer ; (c) the viscosity inside the latex particles (this was probably similar in all the experiments described above).As shown in table 4, the solubilities of styrene and carbon tetrachloride in water are not dramatically different, although the solubility of carbon tetrabromide is smaller. This suggest? that the solubilities of the corresponding atom-abstracted free radicals would not be greatly different.Accordingly, it would appear that the primary factor that controls the exit rate once the low-molecular-weight free radicals are generated by chain transfer may be their rate of reaction with monomer. Addition of styrene molecules to the low-molecular-weight free radicals reduces their solubilities in water so significantly as to render the resulting growing free radicals incapable of undergoing exit from the latex particles. One simple explanation for the data shown in table 4 is that *CBr, is significantly more reactive with styrene than is *CCl,, which in turn is significantly more reactive than the hydrogen abstracted monomeric species, presumably CH,=C-C,H,.The greater reactivity of CBr, and *CCI, could well be analogous to the postulated complex formation between polystyryl free radicals and carbon tetrahalidesll Note that this explanation requires that, for these three free radical species, the following principle be operative: the more easily is a free radical formed, the faster is its rate of reaction with styrene monomer. Whether this principle has more general validity remains to be determined. EFFECTS OF C HA I N-TR A N SFER AGENTS ON CHEMICALLY INITIATED POLYMERIZATIONS As mentioned in the theoretical section of this paper, the interpretation of data in chemically initiated systems is more complex than in the radiolysis studies, because it is now more difficult to go from the experimental observable (i.e.the time dependence of x) to the quantity necessary to extract values of k from the data, i.e. the value of $1) together with some independent information on pA and/or a. We first present a qualitative discussion of the observed behaviour of x(t) with different chain-transfer agents in chemically initiated systems. Some effects due to the presence of the chain-transfer agent carbon tetrabromide on the kinetics of the seeded emulsion polymerization of styrene initiated by potassium peroxydisulphate are displayed in fig. 4. At the higher initiator concentration (5.0 x lo-, mol dm-3), the presence of the carbon tetrabromide led to a relatively small reduction in the rate of polymerization at all concentrations studied [see fig. 4(a)]. ?‘he rate decreases monotonically with increasing concentration of chain-transfer agent. However, the presence of 1 % carbon tetrabromide appears to have a disproportion- ately large effect on the polymerization rate.In the presence of 6% carbon tetrabromide, the rate of polymerization at this higher initiator concentration was never less than one-half of the rate observed in the absence of chain-transfer agent. In contrast, at the lower initiator concentration (5.0 x mol dm-,), the initial rate of polymerization was only one-seventh of that in the absence of additive at the same2140 SEEDED EMULSION POLYMERIZATION OF STYRENE concentration of the chain-transfer agent. At this initiator concentration it was also found that the addition of 3 and 6% carbon tetrabromide produced almost identical reductions in rate at early times, although the rate of polymerization in the presence of 3% carbon tetrabromide was greater than that for 6% carbon tetrabromide at longer times.The addition of 10% carbon tetrabromide reduced the rate of polym- erization but the reduction in rate at early times was only approximately one-half that observed with 3 and 6% carbon tetrabromide. The shape of the fractional conversion against time curve was also different in this case: whereas the 3 and 6% carbon tetrabromide curves displayed a characteristic ‘knee’ point, this was absent from the 10% carbon tetrabromide curve. 0.8 0.6 0 . 4 g 0.2 $ 0 .... ;n a, C - cd 0 0 .d +4 $ 0.4 0.3 0.2 0 . I 0 t (=) 1 / I- / - 0 50 100 150 time/min FIG. 4.-Effects of different concentrations of carbon tetrabromide on the rate of the seeded emulsion polymerization of latex R007/ 15 initiated by potassium peroxydisulphate.Initiator concentration : (a) 5.0 x and (b) 5.0 x mol dm-3; % CBr,: curve 1, 0; 2, 1; 3, 3; 4, 6; 5 , 10. RETARDATION EFFECT OF CARBON TETRABROMIDE Before proceeding further with the discussion of the chain-transfer effects of carbon tetrabromide on the heterogeneous polymerization kinetics, it is first necessary to consider its role as a retarder of the homogeneous polymerization of styrene. It has long been knownl1-l6 that carbon tetrabromide may decrease the rate of polymerization of styrene, the reduction in rate reaching a plateau at a ratio of additive to monomer concentrations of ca. 5 x lod4. Several different explanations for the observed retardation have been proposed: the low reactivity of radicals such as CBr,,14 or theirLICHTI, SANGSTER, WHANG, NAPPER AND GILBERT 2141 adduct with styrene,14~17 towards styrene; the formation of a retarder such as hydrogen bromide;I3 or, most likely, the formation of a complex between the growing polystyryl radicals and carbon tetrabromide.l1 Such complexed radicals are assumed to be less reactive towards propagation than the uncomplexed species. In these heterogeneous experiments, 1 % carbon tetrabromide in the styrene corresponds to a retarder to monomer concentration in the particles ratio of 3 x assuming ideal mixing. This is almost an order of magnitude greater than that required in bulk systems for maximum retardation to be exhibited.Consequently the maximum decrease in the apparent propagation rate constant due to the presence of carbon tetrabromide ought to be manifested by the addition of 1 % additive. As shown in fig. 4(a), the effect of 1% carbon tetrabromide on the rate of polymerization at high initiator concentration was relatively small ( 5 1273, although it was disproportion- ately large compared with the effects of 3 and 6% carbon tetrabromide. Note that not all of the reduction in rate at 1% concentration must necessarily be attributed to a decrease in the apparent propagation rate constant; an increase in exit rate constant may also contribute to a decrease in ti and, hence, to a decrease in rate. We conclude that although a retardation effect was probably operative in these experiments, as witnessed by the disproportionately large effect of the addition of 1 carbon tetrabromide, the overall reduction in rate due to the decrease in the apparent propagation rate constant was relatively small (probably 5 12%).For this reason, the discussion set forth below concerning the larger reductions in rate at the lower initiator concentration will ignore this small perturbation due to an apparent decrease in the propagation rate constant. C HA I N-T R A N S FE R EFFECTS OF CAR B ON TETRA B R 0 MID E It was pointed out in the theoretical section that for chemically initiated systems, the precise determination of fi was difficult. However, in view of the discussion given above, we may make a semi-quantitative data interpretation by assuming that k , C , for these systems is the same in systems containing chain-transfer agent and in those that do not, and (for the latices used in the present study) we take the value of k , C, from earlier work.* We emphasize that, because of this, the following treatment is only semi-quantitative; nevertheless, certain obvious trends will enable mechanistic deductions to be made from the values of ti found by invoking the above assumption.We have two controllable variables in the systems under study: the concentration of chemical initiator and the concentration (and nature) of chain-transfer agent. We now make qualitative mechanistic deductions based on trends in ti,, observed by changing each of these variables. HIGH INITIATOR CONCENTRATION Some understanding of the reasons for the differing effects of carbon tetrabromide on the polymerization kinetics at different initiator concentrations becomes apparent from estimates of ti,,.In the absence of CBr,, tiss values of 0.50 and 0.17 were found for initiator concentrations of 5.0 x mol dm-3, respectively. Now, from eqn (l), we have ti,, = 1 /(2 + k / p ) , irrespective of the fate of exited free radicals. From this, it is clear that ti,, = 0.5 only if p 9 k . To decrease the value of ti,, in this case to below 0.5 would require a dramatic increase in k since ?is, falls below 0.5 only if k 2 p. Carbon tetrabromide, of course, would not be expected to reduce significantly the value of p. Indeed, as shown below, the value of p may well be increased in the presence ofcarbon tetrabromide.Hence, if tiss is close to 0.5, the effects ofchain-transfer agents are muted because the entry rate coefficient is relatively large. This is what was observed at the higher initiator concentration. and 5.0 x2142 SEEDED EMULSION POLYMERIZATION OF STYRENE LOW INITIATOR CONCENTRATION At low initiator concentration, ti,, < 1 so that from eqn (3), ti,, z p / k . Any significant increase in k will be manifested by a significant decrease in ti,, and thus by a significant reduction in the rate of polymerization. Carbon tetrabromide would therefore be expected to be more effective in reducing the rate of polymerization at lower initiator concentrations than at higher concentrations. Fig. 2(b), however, shows that this explanation of the effects of carbon tetrabromide is incomplete.At early times, the addition of 6% carbon tetrabromide at the lower initiator concentration was no more effective in reducing the rate of polymerization than was the addition of half that amount. The addition of 10% carbon tetrabromide was even less effective than the addition of either of the two lower concentrations. Clearly, at least one additional phenomenon must intrude. For this reason, it is convenient to establish first the mechanistic phenomena in the simpler cases of 3 and 6% added CBr,, and then consider the more complex case of 10% CBr,. 3 AND 6% ADDED CARBON TETRABROMIDE The following discussion shows, unexpectedly, that the comparable rates observed at low conversions with 3 and 6% carbon tetrabromide can be attributed, at least in part, to an increase in the rate of entry of free radicals into the latex particles in the presence of carbon tetrabromide. The rate of polymerization is directly proportional to k , C, 5, where k, is the propagation rate constant.As discussed above, the value of k,, may be reduced by the presence of carbon tetrabromide. The swelling of the latex particles by monomer is unlikely to have been significantly increased in the early stages of the reaction for the 3 and 6% carbon tetrabromide runs since the additive was added to the monomer and few, if any, oligomeric species formed by chain transfer would be present. Accordingly, the comparable rates observed in these runs imply that ti was similar in both cases. The relaxation results presented above show that k was significantly greater in the presence of 6% chain-transfer agent and, since ti = 1 /(2 + k/p), this implies that p must also have been increased by the presence of the larger amount of carbon tetrabromide. Perhaps the simplest explanation for the surprising conclusion that p is increased by the presence of the chain-transfer agent resides in the production of hydrophobic free radicals in the aqueous phase.Using the data shown in table 4, together with the value of k,, = 258 dm3 mol-l we calculate that in the aqueous phase the ratio of the probability of transfer to carbon tetrabromide to the probability of propagation (kt,,cB,4 [CBr,]/k,[St]) is ca. 4 for the 6% additive system. This high probability of transfer to carbon tetrabromide could result in the production of CBr, radicals which, because of their hydrophobic character, might more readily enter the latex particles than the growing oligomers, thus increasing p.The foregoing calculation is, however, far from conclusive because the assumption of ideal mixing might not be correct; moreover, the values of the rate constants for transfer and propagation are those for high-molecular-weight species, not oligomers. Further, CBr, free radicals might be less hydrophobic than the oligomeric free radicals. For these reasons, we provide an alternative or additional mechanism for the influence of carbon tetrabromide on p , based upon our studies18 of the nucleation mechanism in emulsion polymerization. These experiments suggest that there is a range of oligomeric species that enter the seed latex particles, including colloidal precursor particles.These particles, which are composed of aggregates of ' insoluble' oligomeric species, are characterized by a very slow growth rate, probably arising from poor swelling of the aggregate by monomer due to their residual hydrophilic character.LICHTI, SANGSTER, WHANG, NAPPER AND GILBERT 2143 Free radicals associated with such precursor particles propagate slowly relative to those in mature latex particles. They also enter seed particles more slowly than surfactant-like oligomeric species. The presence of chain-transfer agents could increase the rate of exit of free radicals from the precursor particles and thus stimulate the rate of entry of surfactant-like oligomeric species. Additional experiments will be required to clarify the details of the mechanism whereby chain-transfer agents influence the entry rate of free radicals into latex particles.One further piece of evidence that supports the conclusion that carbon tetrabromide increases p is the unexpected linearity of the rate curves obtained at low conversions with 3 and 6% additive. It might be expected that as the carbon tetrabromide in the latex particles is consumed at early times, so the exit rate constant for the particies would decrease. Thus ti, and consequently the rate of polymerization, should increase as polymerization proceeded. The fact that no such rate increase was observed at early times is presumably a consequence of the reduction in p due to the depletion in the aqueous phase of the carbon tetrabromide.Under the conditions of these experiments, the two effects on ii, viz. a decrease in both k and p, apparently cancelled approximately at low conversions with 3 and 6% carbon tetrabromide present. The incorporation of chain-transfer agents into an emulsion polymerization can lead, under certain conditions, to enhanced swelling of the latex particles by monomer.19 This effect, however, is readily discounted in the present study. First, in these experiments the supposition that all of the monomer initially present was inside the latex particles would only increase the concentration of monomer in the latex particles from ca. 6 to ca. 7 mol dm-3. Thus enhanced swelling can increase the rate of polymerization by ca. 15 % at most.Secondly, to achieve a significant enhancement effect, the weight of oligomeric species produced by chain-transfer agent must be at least comparable to the weight of polymer present. In these experiments, the ratio of the weight of seed polymer to monomer is approximately one-half. Consequently, at fractional conversions below 0.15, which is primarily what is discussed here, there is insufficient weight of oligomeric species present to induce enhanced swelling. One additional feature of the 3 and 6% curves that requires explanation is their general shape. Both show two essentially linear regions interconnected by a fairly sharp ‘knee’ point that occurs at approximately the same fractional conversion (ca. 0.04). It was previously1 proposed that this knee point represents the point at which the carbon tetrabromide in the latex particles is consumed by rapid incorporation into the polymer chains.Beyond the knee point, carbon tetrabromide diffuses from the monomer droplets into the latex particles and for this reason the rate of polymerization after the knee point is always less than that observed in the absence of chain-transfer agents. This depletion explanation for the knee point is supported by the calculation of the relative rates of consumption of monomer and carbon tetrabromide at 3% additive. The data presented in table 4, together with the value of k , adopted above, imply that the relative rate of consumption of carbon tetrabromide to that of monomer is ca. 0.6 and so the chain-transfer agent should be depleted within the particles at a fractional conversion of 0.05, in fair agreement with the observed value (0.04). Note that the oligomeric species produced by chain transfer in the early stages of the reaction could cause enhanced swelling of the latex particles by the monomer.This might contribute to the more rapid polymerization rate at higher conversion^.^^^ 2o Experimentally, however, it is found that enhanced swelling actually reduces the rate of polymerization owing to an abnormally low value for the entry rate parameter.213 22 One corollary of the foregoing theory is that the conversion at which the knee point occurs should be relatively independent of the amount of chain-transfer agent present. Thus, for example, doubling the initial amount of carbon tetrabromide in the latex2144 SEEDED EMULSION POLYMERIZATION OF STYRENE particles would also double the rate of chain transfer and thus double the rate of consumption of carbon tetrabromide.The data presented in fig. 4(b) for 3 and 6% chain-transfer agent show that this prediction of the independence of the position of the knee point is confirmed experimentally. The alteration in p observed in chemically initiated systems in the presence of chain-transfer agent is probably unimportant in the radiolysis studies because of the very high flux of aqueous-phase free radicals with the latter technique. However, the complications occurring in chemically initiated systems warn against a too simplistic interpretation of the linear dependence of k on the concentration of chain-transfer agent which was observed with the radiolysis studies.While such a linear dependence is not inconsistent with a diffusion/transfer mechanism for exit, a quantitative interpretation of this linearity would require the complexities which appear to be operative in chemically initiated systems to be taken into account. 10% A D D E D C A R B O N TETRABROMIDE The shape of the rate curve obtained with the addition of 10% carbon tetrabromide is different from that for 3 and 6% additive. It displays no knee point and for the first few minutes corresponds to a rate of polymerization marginally in excess of that observed in the absence of chain-transfer agents. The rate of polymerization shows a monotonic decline as polymerization proceeds. It was established above that the addition of carbon tetrabromide increases the rate of entry of free radicals into the latex particles.It is suggested that the observed monotonic decline in rate is a consequence of the progressive reduction in the entry rate concomitant with a decreasing concentration of carbon tetrabromide in the aqueous phase. The latter is occasioned by the consumption of carbon tetrabromide in the latex particles as polymerization proceeds. Note that the Mayo equation23 for the degree of polymerization of the species produced at this high concentration of carbon tetrabromide predicts a value less than one, which is physically impossible and suggests that chemical reactions may well occur prior to the commencement of polymerization. CONCLUSIONS It has been shown that the exit rate coefficient k for the seeded emulsion polymerization of styrene increases linearly with increasing concentration of chain- transfer agent for both CCI, and CBr,.Moreover, CBr, is significantly more effective in increasing k than is CCl,, as would be expected from its much larger value for the chain-transfer rate coefficient. While this is consistent with a diffusion/transfer mechanism for exit, as also suggested by previous studies2 on the size dependence of k , it is important to note that diffusion and transfer alone are insufficient completely to describe the exit process, since the efficiency of exit of free radicals formed by chain transfer follows the inverse of the chain-transfer order: CBr, < CCl, < styrene. This may well be a consequence of the relative rates of reaction with monomer of the free radicals formed by chain transfer.Moreover, the consumption of chain-transfer agent and the effect of exited oligomeric species originating from the chain-transfer agent must also be taken into account in a detailed mechanistic description of the exit process. It was found that for systems initiated by potassium peroxydisulphate, the presence of carbon tetrabromide reduced the rate of polymerization. The reduction in rate was significantly greater for ii < f than for ii = 8, as expected theoretically. At high concentrations of carbon tetrabromide, the rate of entry of free radicals into the latex partides was increased significantly by the presence of the chain-transfer agent.LICHTI, SANGSTER, WHANG, NAPPER AND GILBERT 2145 As a result, the rate of polymerization passed through a minimum owing to the counterbalancing of the increased exit rate by the increased entry rate.Finally, a combination of steady-state and relaxation runs in the presence of carbon tetrabromide allowed the fate of the exited free radicals to be determined. When the seeded emulsion polymerization occurred in the presence of the y-ray source, exited free radicals underwent cross-termination in the aqueous phase. This is in agreement with what was found previously5 for chemically initiated systems. When the system was removed from the pray source, as in the relaxation studies, re-entry of exited free radicals into latex particles occurred. This change in the fate of the free radicals appears to be associated with the relative concentration and rate of production of free radicals in the aqueous phase. When these are relatively high, the exited free radicals undergo cross-termination in the aqueous phase. When low, the exited free radicals undergo re-entry. We gratefully acknowledge the financial support of both the Australian Research Grants Committee (for B. C. Y. W.) and AINSE (for G. L). The Electron Microscope Unit of the University of Sydney is thanked for their provision of facilities. We also thank Professor C . H. Bamford F.R.S. for helpful discussion. B. C. Y. Whang, G. Lichti, R. G. Gilbert, D. H. Napper and D. F. Sangster, J. Polym. Sci., Polym. Lett. Ed., 1980, 18, 711. B. S. Hawkett, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Faraday Trans. I, 1980, 76, 1323. S. W. Lansdowne, R. G. Gilbert, D. H. Napper and D. F. Sangster, J . Chem. Soc., Faraday Trans. I, 1980, 76, 1344. 4 G. Lichti, B. S. Hawkett, R. 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Thomson and I. R. Walters, Trans. Faraday Soc., 1971, 67, 3046. l7 H. N. Friedlander and M. S. Karasch, J. Org. Chem., 1949, 14, 239. lR G. Lichti, R. G. Gilbert and D. H. Napper, to be published. l 9 J. Ugelstad, P. C. Msrk, K. Herder Kaggerud, T. Ellingsen and A. Berge, Adv. Colloid Interface Sci., 2o B. S. Hawkett, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Faraday Trans. 1 , 1981, 77, 2395. '' B. Chamberlain, D. H. Napper and R. G. Gilbert, J. Chem. SOC., Faraday Trans. I, 1982,78, in press. 22 D. Wood, B. C. Y. Whang, G. Lichti, D. H. Napper and R. G. Gilbert, to be published. 23 F. Mayo, J . Am. Chem. SOC., 1943, 65, 2324. D. A. J. Harker, R. A. M. Thomson and I. R. Waters, Trans. Faraday Soc., 1971, 67, 3057. 1980, 13, 101. (PAPER 1/1311)