Molecular Weight Distribution (Soluble and Insoluble Fraction) in

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5934

Ind. Eng. Chem. Res. 2008, 47, 5934–5947

Molecular Weight Distribution (Soluble and Insoluble Fraction) in Emulsion Polymerization of Acrylate Monomers by Monte Carlo Simulations Gurutze Arzamendi† and Jose Ramon Leiza*,‡ Departamento de Quıı´mica Aplicada, UniVersidad Pu´blica de NaVarra, Campus de Arrosadia, 31006 Irun˜a-Pamplona, Spain, and Institute for Polymer Materials (Polymat)/Department of Applied Chemistry, UniVersity of the Basque Country, Joxe Mari Korta Zentroa, Tolosa Etorbidea 72, 20018 Donostia-San Sebastian, Spain

A Monte Carlo simulation model for the semibatch emulsion polymerization of acrylate monomers was developed. The model accounts for the complex kinetics of acrylate monomers (presence of chain-end and midchain radicals), the compartmentalization of emulsion polymerization systems and the development of the entire molecular weight distribution (MWD) as well as the branching density. It was found that the MWD produced in the semibatch process was bimodal (a sharp and extremely high Mw peak and a broad and lower Mw mode), the midchain radicals were predominant during the polymerization, and most of the branches were short and produced by the backbiting mechanism. Interestingly, the bimodality of the MWD could be avoided under certain experimental conditions (those who led to a decrease of particles with more than two radicals), but this did not prevent the formation of polymer chains of molecular weights above 107 g/mol (which are typically insoluble). The model also shows the importance of the presence of midchain radicals in the microstructure of the polymer formed. Thus, the fraction of termination by combination and disproportionation of the midchain radicals had a significant influence on the location of the high molecular weight peak. The predictions of the Monte Carlo model were in good agreement with experimental data and a previously developed deterministic mean-field theory model for the seeded semibatch emulsion polymerization of n-butyl acrylate. Introduction Acrylate monomers (methyl acrylate, MA, n-butyl acrylate, BA, 2 ethyl-hexyl acrylate, 2EHA, etc.) are commonly used in latex formulations to produce adhesives, coatings, calks, sealants, and impact modifiers among others. Acrylate monomers usually reduced the Tg of the copolymers (specially when tackiness (adhesives) and soft cores (impact modifiers) are required) and also impart durability due to their resistance to UV light. These latexes are typically prepared by seeded semibatch processes, and the polymerization proceeds under rather starved conditions. The microstructure of the polymer (composition, molecular weight distribution, branching, and cross-linking density and morphology) has a great impact on the end-used properties of the material. Therefore, understanding the effect of operation conditions on the microstructure of acrylate polymers prepared by semibatch emulsion polymerization is important. Plessis et al.1–5 studied the seeded semibatch emulsion polymerization of n-BA and 2EHA at 75 °C. For n-BA,1–4 the effects of initiator concentration, monomer feeding time, amount of CTA, and the properties of the seed on the kinetics and microstructure were extensively investigated. Gonzalez et al.6 extended this work by studying the effect of the polymerization temperature and very long feeding times on the microstructure and adhesive performance of the latexes. Plessis et al.7 also developed a deterministic mean-field theory mathematical model of the seeded semibatch emulsion polymerization and were able to reasonable predict the evolution of the instantaneous conversion, sol molecular weight distribution, insoluble polymer fraction (so-called microgel) content, and branching density. The * To whom correspondence should be addressed. Phone: +34 943 015329. Fax: +34 943 017065. E-mail: [email protected]. † Universidad Pu´blica de Navarra. ‡ University of the Basque Country.

most relevant results that were published for the first time from this extensive work on the emulsion polymerization of BA can be summarized as follows: (i) The polymerization of BA, and in general the acrylate monomer family, proceeds with the presence of two radicals. A chain-end (secondary) radical and a midchain (tertiary and significantly less reactive) radical that were predominantly formed by a backbiting process (that produced short chain branches). The midchain radicals could also be formed by intermolecular chain transfer to polymer (leading to long chain branches), but its contribution was small. The presence of the two radicals had tremendous implications on the kinetics (propagation rate) as well as on the microstructure of the polyBA produced. Due to the presence of midchain radicals, the effective propagation rate of butyl acrylate was an order of magnitude lower and this feature was adopted years later by the IUPAC Working Party Modeling of kinetic and processes of polymerization.8 The presence of the two radicals was also demonstrated experimentally by the group of Yamada9,10 for cyclohexyl acrylate and phenyl acrylate and more recently by Willemse et al.11 for BA by means of electron spin resonance (ESR) spectroscopy. (ii) The seeded semibatch emulsion polymerization of BA produced a significant amount of insoluble polymer (50-60%). The amount of microgel and the total branching density were not correlated, indicating that most of the branches were short chain branches formed by the backbiting mechanism that did not lead to polymer network formation. The mean-field theory model developed by Plessis et al.7 needed of kinetic parameters that were unknown, especially those related with the midchain radical. Thus, the backbiting rate coefficient, kbb, the propagation rate of the midchain radical with BA monomer, kpb, the chain transfer to monomer, and the termination rate constants of the midchain radicals were unknown, and even today, there is still an important uncertainty associated to these parameters (others still remain unknown).

10.1021/ie701752f CCC: $40.75  2008 American Chemical Society Published on Web 07/22/2008

Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5935 7

b

Plessis et al. estimated kbb and kp and used the same chain transfer to monomer for both radicals. Besides, the termination rate coefficient, which was assumed that occurred only by combination, was considered to be equal for all the radicals, but it was estimated in order to fit the experimental data. More recent work made by our group,12 Hutchinson and Nikitin,13,14 and others15 has allowed to improve the knowledge about some of these parameters. However, there is still a lack of accurate and reliable temperature dependence (Arrhenius type) of most of these parameters. In addition, for the termination reactions we do not know what fraction of the midchain radicals terminate by combination or disproportionation. In the model developed by Plessis et al.,7 the molecular weight distribution was computed using a numerical fractionation technique,16,17 which means that the method of moments was used in the generations and then Schulz-Flory distributions were applied to compute the sol molecular weight distribution (MWD). The microgel content was calculated by subtracting the total amount of monomer polymerized to the polymer present in the generations. The molecular weights and the kinetics were calculated using the pseudokinetic rate constant approach.18 In order to correctly fit the experimentally measured sol molecular weights and microgel content by the mean-field model it was necessary to assume that polymer in the soluble generations with a molecular weight higher than 7 × 106 g/mol (the maximum molecular weight on the gel permeation chromatography (GPC) traces) was also insoluble. Furthermore, the compartmentalization of emulsion polymerization processes is not fully attained by mean-field theory models as explained by Tobita19,20 in the pioneering Monte Carlo simulation models for emulsion polymerization systems with nonlinear or long chain branching kinetics. In this work, we propose a Monte Carlo algorithm to model the semibatch emulsion polymerization of acrylate monomers accounting for the complex reaction mechanisms found operative in the polymerization of these monomers. Our goal with the Monte Carlo model was to obtain the entire molecular weight distribution produced during the semibatch polymerization of acrylates, without any a priori assumption. At the same time, we aimed at gaining further information on the kinetic rate coefficients, which are still unknown for these systems, and also to understand the effects of these parameters on the microstructure of the polymer. For this reason, the seeded semibatch emulsion polymerization of BA was chosen because it is probably the only acrylate monomer for which extensive experimental data on kinetics and microstructure have been gathered in the literature. This work upgrades Tobita’s Monte Carlo models for emulsion polymerization with long chain branching in the sense that for the first time the emulsion polymerization of acrylate monomers (with the complex kinetics resulting from the interand intramolecular reactions and the presence of the two radicals) is considered and because a typical semibatch industrial process is fully simulated. The article has been organized as follows: In the first part, the complex kinetic scheme of acrylate monomers and the kinetic parameters associated to these reactions are presented and discussed for BA. Second, the Monte Carlo algorithm employed is described. The algorithm, which is based on our previous modeling of PLP/SEC experiments by Monte Carlo simulations,21 considers all the specific features of an emulsion polymerization process addressed by other authors.19,20,22,23 In addition for the first time in Monte Carlo simulations of emulsion polymerization systems, the presence of the two types

Scheme 1. Kinetic Scheme of the Free-Radical Polymerization of n-Butyl Acrylate

of radicals (chain-end and midchain) and the detailed kinetics and development of chain-length distribution during a semibatch emulsion polymerization of acrylate monomers is presented. Third, the simulation of the seeded semibatch emulsion polymerization of BA is addressed. The computation of the entire MWD, including sol and insoluble fractions (microgel), the effect of the termination mode of both type radicals on the MWD, and the effects of the operation conditions on the simulated kinetics and microstructure of the polymer are discussed. Finally a comparison of the simulated kinetics and microstructure with experimental data gathered by Plessis et al.1 for a standard formulation is also presented. Kinetic Scheme and Kinetic Parameters The polymerization of n-butyl acrylate will be considered as representative of the alkyl acrylate monomer family. Scheme 1 is currently accepted for the polymerization of BA at moderate temperatures.7,8,12–14,21 In emulsion polymerization, all but the initiator decomposition reaction occur within the polymer particles. In the aqueous phase, the number of reactions is limited because of the low solubility of the BA monomer in water. In Scheme 1, I is initiator, M is monomer, R0 is the radical generated from the initiator decomposition, Ri is the chain-end radical of length i (which is a secondary radical), Rib is a midchain radical of length i (tertiary radical) generated by either backbiting (intramolecular transfer to polymer) or intermolecular

5936 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 Table 1. Frequency Factors and Activation Energies of the Kinetic Rate Constants for BA frequency factor (L/(mol s) or 1/s)

activation energy (kJ/mol)

value at 75 °C (L/(mol s) or 1/s)

ref

chain-end radical (secondary) propagation, kp chain transfer to monomer, ktr,M chain transfer to polymer, kfp backbiting, kbb termination, kt

2.21 × 107 2.88 × 105 2.48 × 103 1.81 × 107 5.1 × 108

17.9 32.6 27.7 27.7 4.0

45321 3.68 0.172 (cfp ) 3.8 × 10-6) 1252 1.27 × 108

8 37 7 this work 27

148 2.4 × 10-2 b 0.172 (cfp ) 1.16 × 10-3) 3.12 × 106

this work 37 7 this work

midchain radical (tertiary) b

propagation, kp b chain transfer to monomer, ktr,M b chain transfer to polymer, kfp termination, ktb

4.12 × 10 2.0 × 105 2.48 × 103 1.29 × 107 6

chain transfer to polymer, and Mi is the polymer dead chain of length i. kI is the initiator decomposition rate (1/s), kp is the monomer propagation rate constant (L/(mol s)), kbb is the backbiting rate coefficient (1/s), kpb is the propagation rate coefficient of the tertiary or midchain radical with a monomer unit (L/(mol s)), ktr,M and kbtr,M are the chain transfer to monomer of secondary and tertiary radicals (L/(mol s)), respectively, kfp b and kfp are the intermolecular chain transfer to polymer of sb bb secondary and tertiary radicals (L/(mol s)), ktd, ktc, ktd , ksb tc , ktd , bb and ktc are the bimolecular termination rate constants (L/(mol s)) of two secondary radicals (no superscript), a secondary and tertiary radical (sb superscript), and two tertiary radicals (bb superscript). The presence of the midchain radicals makes the kinetic scheme of the polymerization of the BA complex because the kinetic parameters related to the midchain radical are uncertain or difficult to obtain by the typical methods used in the literature for chain-end radical monomers (such as styrene, MMA, etc.). Table 1 presents the rate constants for the reactions of Scheme 1. As mentioned above there is an important uncertainty with several kinetic rate constants for the butyl acrylate system. Therefore, in order to get Arrhenius type temperature dependencies, some of them were recalculated using data from different sources. Thus, the backbiting rate coefficient, kbb, was reestimated by combining data from different sources.7,12,14 Chain transfer to polymer for BA as reported by the Polymer Handbook24 (cfp ) kfp/kp) is 5 × 10-4. Plessis et al.7 considered the chain transfer to polymer rate constant, kfp, to be the same for secondary (chain-end) and tertiary (midchain) radicals that imply two different cfp ratios, as it is displayed in Table 1. In the absence of further data in the literature, these rate constants were used. For the propagation of the midchain radicals with BA monomer, there is some data available in the literature. However, all of them were estimated by fitting model predictions and experimental data in different polymerization systems and conditions. Thus, Plessis et al.7 at 75 °C estimated a value of 100 L/(mol s), Hutchinson and Nikitin14 at 50 °C obtained recently 67 L/(mol s), and Peck and Hutchinson25 reported a value of 139 L/(mol s) at 138 °C. In this work, kbp was calculated from the value of ref 14 and the activation energy of the methyl acrylate dimmer monomer, calculated from PLP measurements.15 Very recently Nikitin et al.26 have published a new method to determine the backbiting rate coefficient, kbb, and the propagation rate coefficient, kpb, of the midchain radical by pulsed laser polymerization. They reported Arrhenius type dependencies for these rate coefficients, and at 75 °C, the values are kbb ) 839 1/s and kpb )70 L/(mol s), which are in good agreement with the values used in this work. Furthermore, the activation energies determined by the PLP method26 for these two reactions do not significantly differ with those used in this work and listed in Table 1 (EA(kbb) ) 31.7 kJ/mol and EA(kpb)

29.6 46.1 27.7 4.1

) 28.9 kJ/mol). The chain transfer rate constant of the midchain radical was considered equal to that of the MMA monomer. The termination rate constant of the midchain radicals was calculated using the data obtained by Hutchinson and Nikitin14 at 50 °C and considering the activation energy of methacrylate type of monomers as reported by Beuermann and Buback.27 The cross-termination rate constants were calculated by geometric average of the termination coefficients for the secondary and tertiary radicals; namely ktsb ) (ktktbb)1/2. This assumption is well supported by the data estimated by Hutchinson and Nikitin at 50 °C. All the remaining rate coefficients of Table 1 were taken from the corresponding references shown in the table. Monte Carlo Algorithm for the Simulation of the Seeded Semibatch Emulsion Polymerization of BA The flow diagram of the algorithm employed to carry out the simulations of the seeded semibatch emulsion polymerization of BA is shown in Figure 1. Since a seeded emulsion polymerization was simulated, the polymer particles considered contained at the beginning of the simulation a certain amount of polymer of a given molecular weight. In order to mimic the properties of the seed polymer used by Plessis et al.,1,7 the simulated seed particles were assumed to have an average diameter of 97 nm, sol weight average molecular weight of 2 × 106 g/mol, and 10% insoluble polymer. For the sake of simplicity, in the simulations it was assumed that the sol polymer chains (90% of the monomer units) had all the same chain length or molar mass; in this case, 2 × 106 g/mol. For the remaining 10%, the insoluble fraction, the same assumption was adopted, that is, all the insoluble polymer chains had the same molecular weight (polydispersity equal to 1). On the basis of the experimental data gathered by Plessis et al.1–4 for polyBA, the critical molecular weight that separates both populations (soluble and insoluble) should be of the order of 7 × 106 g/mol. Therefore, a higher value (107 g/mol) was considered for the insoluble polymer chains of the seed. Thus, the seed polymer was initialized in each particle considered in the Monte Carlo simulation as follows: 136 polymer molecules of 2 × 106 g/mol and 3 microgel molecules of 107 g/mol per particle. In order to obtain statistically valid results, a minimum number of polymer molecules must be simulated. Tobita19 proposed 104 polymer molecules to be simulated. In the algorithm employed in this work, the simulated number of polymer molecules depends on the number of polymer particles considered in the simulation. It was found that for the type of process simulated 10 particles provided representative data of the process. This meant that the number of simulated polymer molecules per particle was between 2500 and 9000 (from the initial 139 chains of the seed) depending on the kinetic chain length (see the Supporting Information and Table 3 for further details).

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Figure 1. Flow diagram of the Monte Carlo algorithm employed to simulate the seeded semibatch emulsion polymerization of BA. Table 2. Formulation of the Simulated Seeded Semibatch Emulsion Polymerization Experiment as Taken from the Work of Plessis et al.1 initial charge seed latex (g)a water (g) surfactant (g) BA(g) K2S2O8(g)

100 17.5 1.25 0.34

stream 1b 20

stream 2b 255 2.5 225.4

0.34

Solids content: 20 wt %; dp ) 97 nm; sol Mw ) 2 × 106 g/mol; gel content ) 10% (gel Mw ) 107 g/mol). b Feeding time ) 3 h; T ) 75 °C. a

The simulation algorithm of the semibatch process can be viewed as a hybrid model where the overall concentrations of monomer, initiator, and water in the reactor are computed from the material balances in the semibatch reactor di ) Fi - Ri dt

(1)

Where, i is the amount of monomer (mol), initiator (mol), or water (L), Fi is the flow rate (mol/s or L/s), and Ri is the rate of consumption of each of them, except for water, that is not consumed (mol/s). The rate of polymerization, monomer consumption, is computed in detail from the Monte Carlo approach that is applied to the polymerization in the polymer particles. The polymerization in the aqueous phase is not considered in the simulations. The concentration of radicals in the aqueous phase is computed by solving for the material balance of the radicals in the aqueous phase under pseudosteady-state conditions Np Np d[Rw] ) 0 ) 2fkI[I2] + kdjn - ka[Rw] - ktw[Rw]2 dt NAVw NAVw (2) Where kI is the initiator decomposition rate (1/s), f the initiator efficiency, [I2] the initiator concentration in the aqueous phase (mol/L), kd the desorption coefficient rate coefficient (1/s), ka the entry rate coefficient (L/(mol s)), ktw the rate coefficient for bimolecular termination of radicals in the aqueous phase (L/ (mol s)), nj the average number of radicals per particle, [Rw]

the concentration of radicals in the aqueous phase (mol/L), Np the total number of polymer particles, and Vw the volume of aqueous phase (L). The number of particles for the computation of [Rw] was assumed that varied according to the experimental data gathered in the real experiments carried out by Plessis et al.1 Monomer partitioning was calculated by means of an iterative algorithm using the partition equilibrium and the material balance as described elsewhere.28,29 At this point, the reactions that the radicals present in each particle can undergo are analyzed by means of a Monte Carlo approach similar to that described in ref 21 (in the Integration box in Figure 1). The radicals (chain-end and midchain) could undergo any of the reactions shown in the kinetic scheme above. The specific reaction, k, that a radical underwent in a time interval was determined by a unit-interval uniformly distributed random number, rj, according to the following relation k-1

k

∑P 107). For the 0.0375 wt %, the low molecular weight mode is rather broad too, but the high molecular weight cluster is present at lower Mw. However, the final microgel content was very close for all the cases except for the lowest initiator concentration (0.0188 wt %), likely because of the lower instantaneous conversions obtained in the first part of the process. This result indicated that the insoluble polymer fraction might have a completely different structure (molecular weight and branching density) even though the total amount of insoluble polymer, the actual experimental measurement, was roughly the same. Table 3 displays details on the simulated structure of the gel polymer for these simulations and the available experimental data. As discussed above, the final microgel content is rather similar for all the initiator concentrations, but the molecular weights of the sol polymer decreased whereas that of the gel content increased for increasing concentration of initiator. Note that the model and experimental results are in good agreement. Furthermore, the number of polymer chains in the microgel increased as the initiator concentration was reduced, and for the highest initiator concentration, the number of polymer chains approached one, which explained the sharp molecular weight distribution of the high Mw cluster. This information cannot be obtained using the mean-field theory models, and as far as we know, no one has reported the analysis of the microstructural characteristics of the microgel (insoluble fraction). We believe that the

Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008 5943

Figure 7. Simulated evolution of the number of particles with i radicals and of the MWD for the seeded semibatch emulsion polymerization of BA carried out with different initiator concentrations: (a) 0.018 and (b) 0.075 wt % based on monomer.

microstructure of the gel polymer might have implications on the end-use properties of the latexes. We have found, especially in adhesive formulations made out of latexes containing BA or 2EHA as the main component, that shear and peel resistances dramatically changed for relatively small increases in the insoluble polymer content; namely, up to a critical amount of microgel content, the adhesive performance of the latexes was superior.6,35,36 We could not found a clear explanation for such behavior. Let us now explain the differences in the shape of the MWD for the initiator concentration. The differences can be explained by analyzing the evolution of the number of particles with i radicals together with the conversion evolution of the MWD for two levels of initiator concentration (Figure 7). For the lowest initiator concentration, a unimodal MWD was obtained and this was mainly due to the lack of particles with two or more radicals during the process. This prevented termination by combination to occur, and hence, a cluster of high molecular weight was not formed. Nevertheless, the molecular weights were still high because of the low initiator concentration used (high kinetic chain length) and the chain transfer to polymer reactions. For the lowest initiator concentration that shows a clear bimodal MWD (0.075 wt %), the particles with 2 and 3 radicals were present from the beginning of the process, and as shown in the evolution of the MWD, coupling took place at early conversions and eventually led to the formation of the high molecular weight cluster that grew as polymerization proceeded.

Effect of Temperature. Three reaction temperatures were simulated 50, 75, and 90 °C. The remaining operation conditions were those of the standard recipe of Table 2; namely, 0.3 wt % initiator concentration and monomer feeding time 3 h. The kinetic parameters of Table 1 were used to calculate the rate coefficients at each temperature. The instantaneous conversion increased with the increase of the reaction temperature (not shown). The evolution of the MWD for the experiments with 50, 75, and 90 °C is shown in Figure 8. It can be seen that except for the lowest temperature, the previously discussed bimodal MWD (sharp and high molecular peak and broader and lower molecular weight mode) was obtained from the very beginning of the process. At 50 °C, the bimodal MWD was almost formed but there are peaks at lower Mw that were not incorporated to the high Mw cluster. Again the lower number of particles with more than two radicals produced during the polymerization (see Figure 8) at 50 °C explained this behavior. In this case, fewer radicals were generated at 50 °C because a thermal initiator was simulated. Note that if a redox initiator, with the same radical generation rate than a thermal initiator at higher temperatures was employed, the same bimodal distributions would have been obtained. Figure 8 also shows that the low molecular weight mode shifted to lower molecular weights as the reaction temperature increased due to the lower kinetic chain lengths produced at higher temperatures.

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Figure 8. Simulated evolution of the number of particles with i radicals and the MWD for the seeded semibatch emulsion polymerization of BA carried out at different temperatures: (a) 50; (b) 75; and (c) 90 °C.

In Figure 9, model predictions and experimental data are compared for the experiment carried out with the formulation of Table 2 at 75 °C and 3 h feeding time. The kinetic parameters used in the simulation were those estimated for the mean-field model by Plessis et al.7 Predictions of the instantaneous conversion, microgel content, weight average molecular weight of the soluble fraction, and the branching level were in reasonable agreement with the experimental data. Interestingly, the MWD of the sol predicted by the Monte Carlo model

compares well with the experimental data that is broader and shifted to lower molecular weights. The advantage of the Monte Carlo model however is that additional details on the microstructure can be obtained and this information can be used to better understand end-use properties of the latexes; in other words, it might help to developing microstructure-property relationships for latex formulations. Finally, Figure 10 compared the sol MWD prediction of the previously developed mean-field model with the Monte Carlo

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Figure 9. Model predictions and experimental data for the seeded semibatch emulsion polymerization of n-BA carried out with the recipe of Table 2 at 75 °C and 3 h of feeding time.

model (full MWD) presented in this work for three different initiator concentrations. It can be seen that both models predicted similar sol MWD. Conclusions A Monte Carlo algorithm was used to model the kinetics and microstructure of the semibatch emulsion polymerization of acrylate monomers. The complex kinetics of the polymerization of acrylate monomers (two radicals and one monomer present

in the reaction loci), the compartmentalized nature of the emulsion polymerization, and the nonlinearities of the polymer architecture (short-chain branches formed by backbiting, long chain branching formed by chain transfer to polymer, and the eventual formation of extremely high molecular weight polymer by termination by combination) were accounted for the model. It was found that the MWD produced in a seeded semibatch polymerization was bimodal with a cluster of narrow and extremely high molecular weight (∼109 g/mol) and a broader

5946 Ind. Eng. Chem. Res., Vol. 47, No. 16, 2008

(CTQ2006-03412/PPQ), and the Universidad Pu´blica de Navarra is greatly appreciated. This work was presented at the IUPAC meeting Macro 2006 held in July 2006 in Rio de Janeiro (Brasil). Supporting Information Available: Table S1 and Figures S1-S4. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited

Figure 10. Comparison of the MWD calculated by the Monte Carlo (MC) model (this work) and the mean-field (MF) theory model7 for the seeded semibatch emulsion polymerization of n-BA carried out with three concentrations of initiator.

molecular weight mode at lower molecular weights. Interestingly, it was found that the presence of the cluster at high molecular weight could be avoided under certain experimental conditions (i.e., low initiator concentration or low temperature) but this did not prevent gel polymer formation. However, the nature of gel polymer chains was different and this might have implications on the end-use properties of these polymers. As far as we know, no one has published results about the characteristic of the gel polymer (so far only the insoluble fraction is reported), but in view of these results and of unexpected results obtained in adhesive performance of several latexes synthesized in our laboratory, we believe that understanding the role of the microstructure of the gel polymer in the end-use properties should be addressed. In this vane, Monte Carlo models are an excellent tool to the development of microstructure-property relationships. The model also confirmed that midchain radicals are predominant in the polymerization of acrylate monomers and that therefore the mode of termination of these radicals influences on the bimodal structure of the MWD. It is therefore necessary to address these mechanistic features in the polymerization of acrylate monomers if models with predictive capabilities are to be developed. Theoretical studies to elucidate the fate of midchain and chain-end radicals during termination reactions determined by ab-initio and molecular dynamic simulations might help understanding the development of the MWD. One of the drawbacks for the Monte Carlo models has always been the enormous computation time required to obtain meaningful results. This is less true nowadays because of the increase of computation power of modern computers and the expected increase for the future. For instance, the simulation of an entire semibatch emulsion polymerization of BA required less than 1 h on a personal computer. This is probably too large as to be applied for online optimization and advanced control strategies of emulsion polymerization reactors, but we think that in the near future this will not be the case. Besides, the additional information that one can extract from the detailed Monte Carlo models would made these models to be more and more employed in the polymer reaction engineering field. Acknowledgment The financial support of the University of the Basque Country (UPV 221.215-13594/2001), Ministerio de educación y Ciencia

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ReceiVed for reView December 22, 2007 ReVised manuscript receiVed May 30, 2008 Accepted June 3, 2008 IE701752F