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Chapter 5
Synthesis of Well-Defined Polystyrene with Molar Mass Exceeding 500 kg/mol by RAFT Emulsion Polymerization Jinwei Fang, Kun Yan, and Yingwu Luo* The State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, 38 Zhe Da Road, Hangzhou 310027, People’s Republic of China *E-mail:
[email protected].
We review and highlight some unexpected findings in our continuous effort to synthesize well defined polymer of very high molecular weight with reversible addition-fragmentation transfer (RAFT) emulsion polymerization. In the RAFT emulsion polymerization using extremely low initiator concentrations, it was found that the polymerization rate could remain fast. The reason is the higher particle nucleation efficiency at the lower initiator concentrations, which leads to an unexpected increase in the particle number with decrease of the initiator concentrations. At very low initiator concentrations, a pronounced particle activation/deactivation effect has been observed. When the average number of the particle activation/deactivation cycle per particle is less than 15 in the whole course of Stage II and III, both molecular weight and particle size distributions quickly broaden controlled by the increasing fluctuation in the number of the particle activation/deactivation cycle experienced by each particle. Well-defined polystyrene of over 550 kg/mol has been synthesized with livingness around 90%, molecular weight distribution dispersity (Ð) around 1.2, polymerization time for over 90% conversion about 780 minutes. The very high livingness at such a high molecular weight is ascribed to significantly lower transfer constant to monomer than well-documented values in conventional radical
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polymerization. It is very likely that RAFT reactions could significantly suppress the transfer reactions to monomer.
Since Michael Szwarc (1) established the living polymerization (LP) at 1956, it has been widely pursued for synthesizing polymers with well-defined chain microstructures and low dispersities of molecular weight. Compared with traditional anionic LPs, Reversible Deactivation Radical Polymerizations (RDRPs) own the advantages of a much larger variety of suitable monomers and significantly milder polymerization conditions. Therefore, RDRPs have been arose a broad interest of both academic and industry for the last two decades (2, 3). However, there are still unavoidable chain-breaking reactions such as irreversible termination and chain transfer in RDRPs, which result in a certain proportion of dead chains in final products (4). The target molecular weight (MW) of typical RDRP products was relatively low (< 5 × 104 g/mol) so that the polymerization could finish within reasonable time to obtain well-defined polymer (5–7). It was generally believed that well-defined polymer with molar mass much higher than 100 kg/mol should be difficult to be synthesized by RDRPs due to the presence of transfer reactions to monomer (5). The low MW would lead to poor mechanical properties of the products and thus limit the application of RDRPs. Higher ratio of propagation rate constant (kp) to termination rate constant (kt) is helpful for synthesizing highly living polymers of higher MW in RDRPs (8). In the case of methyl methacrylate, extremely high reaction pressure (over 500 MPa) (9), which significantly increase the ratio of kp/kt, was used to synthesize narrow molecular weight distribution PMMA of 3600 kg/mol. Emulsion polymerization, where the radical nanosegregation effect is able to significantly decrease the apparent termination rate (10), could be a convenient method for producing highly living polymers of relatively high MW even for monomers with low kp/kt. Reversible addition-fragmentation chain transfer (RAFT) emulsion polymerization has been extensively studied in the past two decades. In those earliest experiments using small RAFT agent as a polymerization mediator, the RAFT emulsion polymerization suffered from the problems of colloidal instability and loss of control over molecular weight (11–13). Continuous efforts have been done to solve those problems (14–17). The problems have been solved by using the carefully designed amphiphilic macroRAFT agent as both polymerization mediator and surfactant (18). It has been evidenced that the superswelling of the particles in the early stage of the RAFT emulsion polymerization should be the reasons for those problems (19, 20). Though it has been expected that RAFT emulsion polymerization could be a convenient approach to synthesize highly living polymer of high molecular weight, the majority of the documents on RAFT emulsion polymerization has targeted molecular weight lower than 100 kg/mol due to the presence of unavoidable transfer reactions to monomer. In the past few years, our group launched a new project to answer a basic question that how high molecular weight one can reach via RAFT emulsion polymerization upon the conditions that the polymerization should be finished within reasonable time period (~10 hrs) and 82
the product should remain highly living (~90% livingness) and low Ð (~1.2). Styrene was used as a model monomer, considering that emulsion polymerization of styrene has been well established and kp/kt is very low. It turned out that we could synthesize polystyrene with unexpected high molar mass (over 500 kg/mol). The polymerization exhibited some particular phenomena with regard to polymerization kinetics, particle activation/deactivation effect and transfer reaction to monomer. In the current chapter, we review and highlight those main findings.
Table 1. Ab Initio RAFT Emulsion Polymerization of Styrene Mediated by MacroRAFT Agent with Various Ratios of [KPS]/[RAFT]. SOURCE: Reproduced with permission from ref. (25). Copyright 2016 John Wiley &Sons
Polymerization Kinetics of RAFT Emulsion Polymerization at Various Initiator Concentrations Due to the existence of irreversible bi-radical termination, a portion of dead chains are produced during the RAFT polymerization. The synthesis of highly living polymer of high molecular weight requires to significantly suppress the irreversible termination reactions. Reducing the ratio of [initiator]/[RAFT] is the key to restrict the dead chain fraction (4). Accompanied is the significant decrease 83
in polymerization rate in the case of homogenous RAFT polymerization systems, resulting in the unacceptable long reaction polymerization time (21–24). Though it is expected that RAFT emulsion polymerization should be much faster than its homogenous polymerization counterpart, the RAFT emulsion polymerization at very low initiator concentration remained unexplored. A series of RAFT emulsion polymerizations of styrene using macroRAFT agent (poly(acrylic acid)20-b-poly(styrene)5 trithiocarbonate) as both surfactant and mediator was conducted at 70 °C. The initiator (KPS) concentration varied from 1.45×10-3 mol/Llatex to 1.13×10-5 mol/Llatex while the RAFT concentrations were kept constant (25). The main results were summarized in Table 1. All the experiments reached over 90% conversion within 4h. No coagulum in Exps 1-5 was collected while a small amount of coagulum was observed in Exps 6-8.
Figure 1. Evolutions of monomer conversion with polymerization time in Exps 1-8. (Reproduced with permission from ref. (25).. Copyright 2016 John Wiley &Sons)
Surprisingly, the polymerization time to reach monomer conversion over 90% didn’t change a lot though the initiator concentration was changed by 16 times, as seen in Figure 1. The polymerization rate (RP) during Stage II of the emulsion polymerization was calculated by the slope value of the monomer conversion vs. the polymerization time curves in the conversion range from 25% to 65%. It was surprising that RPs were almost constant at 3.3 × 10-4 s-1 when the concentration of the initiator concentrations reduced from 1.45 × 10−3 mol/Llatex to 9.04 × 10−5 mol/Llatex, as seen in Figure 2. The Rp started to decrease with further reducing the initiator concentration and reached to 1.3 × 10-4 s-1 in Exp 8. In emulsion polymerization, RP is calculated by equation (1):
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where kp is the propagation rate constant of styrene, [M]p is concentration of monomer in the particles, is the average radical number per particle, Np is the particle numbers, [M]0 is the initial molar concentration of monomer, and NA is Avogadro’s number.
Figure 2. The relation between initiator concentrations ([KPS]) and the polymerization rates (Rp) in Exps 1-8. (Reproduced with permission from ref. (25). Copyright 2016 John Wiley &Sons)
Figure 3. The relation between initiator concentrations ([KPS]) and the particle diameters and particle numbers in Exps 1-8. (Reproduced with permission from ref. (25). Copyright 2016 John Wiley &Sons) The particle number (Np) was estimated from the particle diameter measured by TEM. As shown in Figure 3, the Np increases with the decrease of the initiator concentrations from to in Exps 1-5. The data . The correlation is just contrary to the Smithcan be correlated with Ewart equation, which predicts (26). The reason for this phenomenon 85
will be discussed later. As for Exps 6-8, the particle numbers decreased slightly with the decrease of the initiator concentrations, which should be caused by the limited aggregation of the particles in agreement with the formation of coagulum (see Table 1). It should be pointed out the micells of the macro-RAFT are still able to dissociate as indicated by (25). The average radical number per particle during Stage II was calculated by equation (2)
where [M]0 is the initial molar concentration of monomer (around 1.92 in those cases ), kp is the propagation rate constant of styrene (480 at 70 °C), [M]p is concentration of monomer in the particles (5.8 at 70 °C) (10). As shown in Figure 4, the value of quickly reduces from 0.35 to 0.05 with decrease of the initiator concentration from 1.45 × 10-3 mol/Llatex to 1.13 × 10-5 mol/Llatex. The emulsion polymerization of styrene is a typical "zero-one" kinetic system, in which that the entry of a radical into a particle that already contains growing radical results in instantaneous termination (10). In a typical emulsion polymerization of styrene in which the initiator concentration is around 10-3 mol/ Llatex, is close to 0.5 (10). However, at lower initiator concentrations, would fall below 0.5 for the influence of radical exit out of particles (via monomeric radicals from the radical transfer reactions to monomer) became significant (27). Similar observations have been reported in the traditional emulsion polymerization (28). The polymerization rate retardation in RAFT emulsion polymerization has been discussed (29). However, the current trithiocarbonate RAFT agent should have negligible RAFT retardation effect (30).
Figure 4. The relation between initiator concentration ([KPS]) and average number of radical per particle in Exps 1-8. (Reproduced with permission from ref. (25). Copyright 2016 John Wiley &Sons) 86
The correlations of is related to the rapid decrease in . During the nucleation stage, the particles would grow slower with lower so that more micelles could be nucleated rather than disassociated to stabilize the earlier-nucleated particles, resulting in the higher nucleation efficiency at lower initiator concentration. As a consequence, the polymerization rate remains almost constant in the range of the concentration of initiator concentration reduced from 1.45 × 10−3 mol/Llatex to 9.04 × 10−3 mol/Llatex. As further reducing [KPS] to 1.13 × 10−5 mol/Llatex in Exps 6-8, an observable decrease in polymerization rate should be caused by decrease in and slightly decrease in . In sum, RAFT emulsion polymerization can remain very high polymerization rate even with extremely low initiator concentration. The high polymerization rate should be ascribed to the higher nucleation efficiency at the lower initiator concentrations, which led to an unexpected increase in the particle number with decrease of the initiator concentrations.
Particle Activation/Deactivation Effect As the initiator concentration decreases to an extremely low level, molecular weight remains linear growth with monomer conversion in good agreement with the theoretical prediction, as evidenced in Figure 5. However, the Ðs in the end of the polymerization (over 90% monomer conversion) steadily increases with decrease of the initiator concentration from 1.45 × 10−3 mol/Llatex to 1.13 × 10−5 mol/Llatex. Then, Ð quickly increases up to 1.79 with further decrease in the initiator concentration (see Table 1 and Figure 6). These observations are quite surprising in that the dead chain fraction should be decreased with decrease of the initiator concentration.
Figure 5. Evolution of molecular weight and Ð with monomer conversion in Exp 3. The dash line is the theoretical value of molecular weight. (Reproduced with permission from ref. (25). Copyright 2016 John Wiley &Sons) 87
Figure 6. Plots of Ð and PSD at the end of the polymerizations in Exps 1-8. (a) Ð and PSD vs [KPS]. (b) Correlation between Ð and PSD. (Reproduced with permission from ref. (31). Copyright 2017 John Wiley &Sons)
More surprisingly, the molecular weight distribution dispersity (Ð) are well correlated with the particle size distribution dispersity (PSD) (R2=0.96), as seen in Figure 6b. Generally speaking, Ð and PSD in emulsion polymerization should have no apparent correlation since the controlling systems of PSD and Ð are totally different (10).
Table 2. Ab Initio and Seed RAFT Emulsion Polymerization of Styrene with Different KPS Concentrations Post-Added. SOURCE: Reproduced with permission from ref. (31). Copyright 2017 John Wiley &Sons
A series of seeded RAFT emulsion polymerizations was conducted to eliminate the influence of particle nucleation process (see Table 2). It turned out that a stronger linear correlation between the PSD and Ð in the end of the polymerization was observed with R2=0.98 (see Figure 7c). Figure 7a clearly 88
reveals that Ð begins with the same value but decreases slower with decrease of the amount of the post-added initiator. Figure 7d compares the GPC curves of the final samples of Exps 9 and 13. Both of them look symmetric and have the same peak molecular weight. It is clear that the significant influence of the initiator concentrations on Ð and PSD mainly occurs in Stage II and III. Particle population balance method and Monte Carlo method have been used to model the scenarios occurred in Stage II and III (30) (refer to the Appendix). As discussed previously, is much less than 0.5. It is suggested that there are two populations of particles in the systems in terms of the presence of an active radical i.e. particles with a radical and particles without any radical. Those particles with a radical are named as active particles, where the polymerization occurs. The particles without any radical are dormant particles, where the polymerization does not occur. The dormant particles can be activated via radical entry into the activation particles. On the other hand, the active particles can be deactivated back to the dormant particles via another radical entry or monomer radical exit. This activation/deactivation cycle is illustrated in Scheme 1. Particle population balance was used to model the particle size distribution while Monte Carlo method was used to model molecular weight distribution and the number distribution of the activation/deactivation cycle per particle. Modeling simulations revealed that with decrease of the initiator concentrations the average number of the activation/deactivation cycle per particle during Stage II and III would decrease (see Figure 8). When is less than 15, both Ð and PSD start to quickly increase.
Figure 7. (a) Evolutions of Ð with monomer conversion at various additional initiator concentrations. (b) Plots of Ð and PSD at the end of the polymerizations in Exp 9-13 at 70 °C. (c) Correlation between Ð and PSD. (d) GPC curves of the final samples in Exp 9 and Exp 13. (Reproduced with permission from ref. (31). Copyright 2017 John Wiley &Sons) 89
Scheme 1. Particle activating/deactivating process
Figure 8. Effect of average number of activation/deactivation times per particle on final dispersities of molecular weight distribution and particle size distribution (PSD). (a)Ð and PSD from experimental results. (b)Ð and PSD from model predictions. (Reproduced with permission from ref. (30). Copyright 2017 John Wiley &Sons) It is the random nature of the activation/deactivation process that broadens both molecular weight and particle size distribution in those cases of very low initiator concentrations. In those cases, the number activation/deactivation cycle experienced by a particle during the Stage II and III is much fluctuated as suggested by the high coefficient of variation (CV), as referred to Figure 9. It is suggested that each particle should not have the same opportunity to grow via polymerization, broadening the particle size distribution. Assuming that each seed particle should have the same number of the macroRAFT molecules, the molecular weight in a particle would be directly related to the size of the particle in the end of the polymerization via equation (3)
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where dp is the density of polystyrene (~1.05 g/cm3) and nRAFT is the molar number of living chains (capped with RAFT groups) in the particle. It is equation (3) that leads to the correlation between PSD and Ð. This is clearly evidenced by the strong correlation between PSD and Ð and CV, as shown in Figure 10.
Figure 9. Distributions of the number of the activation/deactivation times in Exp 9 and Exp 13. The frequency counts are fitted by Gaussian distribution. (a) Exp 9 where R2=0.98. (b) Exp 13 where R2=0.97. (Reproduced with permission from ref. (30). Copyright 2017 John Wiley &Sons)
Figure 10. Effect of coefficient of CV on dispersities of molecular weight distribution (Ð) and particle size distribution (PSD). (Reproduced with permission from ref. (30). Copyright 2017 John Wiley &Sons) 91
In sum, a pronounced particle activation/deactivation effect has been observed when RAFT emulsion polymerization was carried out at very low initiator concentrations. When is less than 15 in the whole course of Stage II and III, both Ð and PSD quickly increase due to the increasing fluctuation in the number of the particle activation/deactivation cycle experienced by each particle. Based on the understanding in particle activation/deactivation process, we’ve designed a new polymerization process to overcome the above problems and successfully synthesize well-defined polystyrene of very high molecular weight, which will be discussed in the next part.
The Synthesis of Well-Defined Polystyrene of Very High Molecular Weight and Transfer Constant to Monomer It is generally believed that the highest molecular weight should be limited by transfer constant to monomer (CM) to synthesize well defined polymer by RDRPs. At 70°C, CM is around 10−4 in conventional radical polymerization of styrene (10). It is suggested that the highest target degree of polymerization should be around 1000, i.e. Mn=100 kg/mol to suppress the dead chain fraction lower than 0.1. A well-defined polystyrene with target molar mass of over 105 g/mol was synthesized in ab initio RAFT emulsion polymerization with [initiator]/[RAFT] = 1/5 (14). In an effort further to increase the target molar mass, the target molar mass was set to be 350kg/mol and 640kg/mol with the ratios of [KPS]/[RAFT] to be 1/20 and 1/10, respectively. Such low initiator concentrations made sure the influence of the irreversible termination negligible. As shown in Table 3, the polymerization rates in Exps 14 and 15 were so fast that monomer conversion reached 95% and 97% within 540 min respectively. Yet, the molecular weight distributions of the final polystyrene were broad. The Ð in Exps 14 and 15 were 1.39 and 1.64 respectively. As we discussed in the previous part, the high Ð might be related to the low particle activation/deactivation frequency due to the extremely low initiator mol/Llatex). According to Scheme 1, concentration (around the particle activation/deactivation frequency was directly related to the rate coefficients of radical entry . With the same initiator concentration, would be inversely proportional to the value of (10). It is suggested that the particle activation/deactivation frequency could be improved by reducing particle concentration in a system. To decrease the Ð value, a two-stage synthetic strategy was applied in Exps 16 and 17. In the first stage, all macroRAFT agent but only a fraction of monomer, initiator and water were added into emulsion with the target molar mass of 30 kg/mol. The rest of styrene, initiator, water and NaOH were fed into the reactor after polymerization for 100 min in the first stage. Compared with the batch emulsion polymerization, this two-stage strategy reduces the Np (see Table 3). As shown in Table 3, the Ð s are much lower than those of batch RAFT emulsion polymerization. The Ð reduces to 1.18 in 350 kg/mol case (Exp 16) and 1.26 in 640 kg/mol case (Exp 17). The decrease of Np led to the decrease of polymerization rates as shown in Figure 11a. Yet all experiments reached over 90% monomer conversion within 13 h, which is still acceptable. 92
Table 3. The Main Results of RAFT Emulsion Polymerizations with High Targeted Molecular Weight. SOURCE: Reproduced with permission from ref. (32). Copyright 2017 John Wiley &Sons
As listed in Table 3, the molecular weights of the products are very close to those theoretical values. It is suggested that transfer reactions to monomer is still negligible even in the synthesis of polystyrene with molar mass as high as 550 kg/mol. The high livingness of the products was supported by comparing GPC curves from dual detectors of RI and UV. The UV signals at 311 nm show the distribution of trithiocarbonate RAFT groups while RI signals represent the distribution of all polymer chains. As shown in Figure 12a and 12b, the GPC curves are well symmetric and move to high molecular weight as a whole with increase of monomer conversion and the RI and UV signals match each other perfectly, suggesting that the products are highly living. This was further confirmed by the chain extension experiments. The product of Exp 16 was chain-extended. As the molar mass increases from 317 kg/mol to 556 kg/mol, the GPC curves maintain symmetry. During chain extension, the RI and UV signals just overlap. The Ð increases slightly after the chain extension from 1.18 to 1.25. This slight increase in Ð should not be caused by chain extension operation since the similar increase is observed in Exp 17 (see Figure 12c). It is suggested that the chain extension is very successful. Actually, the fraction of dead chains, as defined by equation (4), can be estimated from GPC data,
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in which
where Ddead is the total dead chain concentration, NRAFT is living chain concentration, m is monomer mass concentration, x is monomer conversion, and Mn is number average molecular weight yielded by GPC curves.
Figure 11. Experimental results of two-stage cases in Exp 16-17. Exp 16 targeted at about 350 kg mol-1 and Exp 17 targeted at 640 kg mol-1. (The concentrations of the macro-RAFT agent in Exps 16 and 17 were 1.12 × 10−3 and 5.6 × 10−4 mol/Llatex, respectively) (a) Monomer conversion versus polymerization time plot. (b) Molecular weight versus monomer conversion plot. (c) Ð versus monomer conversion plot. (Reproduced with permission from ref. (32). Copyright 2017 John Wiley &Sons) 94
Figure 12. The Evolutions of GPC curves with monomer conversions of (a) Exp 16 targeted at 350 kg mol-1, (b) Exp 17 targeted at 640 kg mol-1, (c) chain extension using the latex from Exp 16. (d) Evolution of the living chain fraction and total dead chain fraction with monomer conversion derived from GPC analysis in Exp 16 and Exp17. The GPC results was measured by Waters 1525 binary pump, Waters 717 autosampler with Waters 2414 refractive index detector and Waters 2487 dual wave length UV detector. The fluent was tetrahydrofuran with a flow rate 1.0 mL/min. The measurement temperature was 30 °C. Waters Styragel columns (HR 5,4,3) were utilized. The values of Mn and Ð were derived from a calibration curve based on narrow polystyrene standards. (Reproduced with permission from ref. (32). Copyright 2017 John Wiley &Sons)
As shown in Figure 12d, the fraction of the dead chains linearly increase with monomer conversion and the final fraction of dead chains are 7.3% in Exp 16 and 11.6% in Exp 17. In other words, the livingness of the products remains around 90%. As shown in Table 4, over 90% dead chains were generated from chain transfer to monomer reaction. Yet, the theoretical results of dead chain from both the bi-radical termination and chain transfer to monomer were much higher than the experimental results. The high livingness of the product with molar mass higher than 500 kg/mol is very surprising considering that transfer constant to monomer is around 10-4 (5). In the current cases, the dead chains concentration from irreversible radical termination (Dt) and chain transfer to monomer (Dtr) could be calculated, respectively by (32)
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where a = 1 for combination termination in our cases, f is the initiator efficiency (f = 0.33 in our cases from ref. (32)), [KPS]0 is the initiator concentration at beginning of polymerization, kd is the decomposition rate constant of KPS ( at 70 °C), CM is the chain transfer constant for monomer, and is the initial monomer concentration (32). The value of CM of styrene in radical polymerization has been widely reported to be close to 6 × 10−5 (33–37). Note that
We can estimate Dtr from GPC data by equations (5), (6), and (8). Then, according to equation (7), one can estimate the chain transfer constant from the plot of Dtr versus x. In Figure 13, the data in both Exp 16 and Exp 17 are plotted. It is interesting that Dtr is indeed linearly increased with monomer conversion as predicted by equation (7). All data can be well fitted by the linear equation (R2=0.99). CM is estimated to be 1.75 × 10−5, which is significantly lower than the well documented value 6 × 10−5 in traditional radical polymerization of styrene by a factor 0.29.
Table 4. Dead Chain Fractions in the End of Exp 16 and 17. SOURCE: Reproduced with permission from ref. (32). Copyright 2017 John Wiley &Sons
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Figure 13. The evolutions of dead chain concentration caused by radical transfer to monomer reaction with monomer conversion in Exp 16 and Exp 17 considering the initiator efficiency to be 0.33. (Reproduced with permission from ref. (32). Copyright 2017 John Wiley &Sons)
The lower CM value was also supported by the polymerization kinetics. We modeled the polymerization kinetics of the RAFT seeded emulsion polymerization at various initiator concentrations presented in Figure 14 (30). The model exactly predicted the polymerization kinetics using CM value whereas the model would predict lower polymerization especially in the cases of very low initiator concentrations when using the well-documented value of CM values of conventional radical polymerization of styrene (CM = 6 × 10−5 in conventional radical polymerization of styrene (10)). It is much evidenced that CM value in the RAFT emulsion polymerization should be significantly lower than the well-documented value in the conventional radical polymerization. It is likely that the well-documented values have been over-estimated. More likely, RAFT reactions might suppress the transfer reactions to monomer. It has been reported that the branching reactions via transfer to polymer chains are much suppressed in RDRPs of acrylates compared with that in conventional radical polymerization (38, 39). According to the "competitive process" mechanism proposed by Matyjaszewski et al (40), the reactions of chain transfer to RAFT agent and chain transfer to polymer or monomer are competing with each other. As the additional rate of RAFT reactions is much higher than the chain transfer to monomer, the latter would be much suppressed by the former. This agrees well with our experiment results.
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Figure 14. Effect of initiator concentration on monomer conversion and average radical number per particle . Dots are experimental results and lines are model simulation results. Case 1 using the model and parameters described in another work. ) Case 2 using the same model and parameters as in Case 1, but RAFT reaction term was removed. Case 3 using the same model and parameters as in Case 1, but ktr was set as 0.097 L mol-1 s-1. (a) Evolutions of monomer conversion with polymerization time. (b) Evolutions of with monomer conversion. (Reproduced with permission from ref. (30). Copyright 2017 John Wiley &Sons)
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Conclusions In this chapter, the RAFT emulsion polymerization of styrene using amphiphilic macroRAFT agent as both surfactant and mediator has been conducted with extremely low initiator concentration and extremely high target molecular weight. We come to the following main conclusions: (1). RAFT emulsion polymerization could be highly efficient in synthesizing well-defined polymer of very high molecular weight. Even for low kp/ kt monomer like styrene, low Ð polymer with 90% livingness and over 500 kg/mol molar mass could be synthesized while monomer conversion could reach over 90% around 10 hours. (2). At low initiator concentrations, the number of particles was proportional to [I]-0.4, i.e. the higher nucleation efficiency with the lower initiator concentration. This is why the polymerization rate remains high even at extremely low initiator concentration. (3). At low initiator concentrations, the low particle activation/deactivation frequency could significantly broaden on molecular weight and particle size distribution. One has to carefully design the polymerization process to narrow molecular weight and particle size distribution by taking into account particle activation/deactivation effect. (4). Transfer constant to monomer (1.75 × 10−5) should be significantly lower than the well documented value (6 × 10−5).
Acknowledgments The authors would like to thank the financial support from National Natural Science Foundation of China (#21636008, #21474090), National Natural Science Funds for Distinguished Young Scholar (#21125626). The permissionof the The Royal Society of Chemistry for reproducing some materials from ref. (30). is acknowledged.
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Appendix Modeling on polymerization kinetics, particle size distribution, molecular weight distribution and particle activation/deactivation cycles in a seeded RAFT emulsion polymerization has been reported in ref. (30). For convenience, the models are cited here as an appendix. Please refer to ref. (30) for more details. Population Balance Equations (PBEs) PBEs was used to obtain particle size distribution. We assumed that the zero-one kinetics could be applied to the seeded RAFT emulsion polymerization of styrene, where the entry of a radical into a latex particle within a radical lead to instantaneous termination. The evolution processes of particles in seeded RAFT emulsion polymerization are expressed by the partial differential equation and particle diameters . The addition reactions of polymerization time between monomer radicals and macroRAFT agents are ignored since is far less than . The particles are classsified into four types and the corresponding PBEs are as follows: Particle with no free radical :
Particle with a polymer radical
:
Particle with a monomer radical
:
Particle with an intermediate radical
:
The monomer concentration inside the emulsion particles is calculated by:
where the molar mass of unreacted monomer is calculated by:
And the monomer concentration in aqueous phase is calculated by: 100
We assumed that the macroRAFT agents should be distributed equally in all emulsion particles. The calculation of the parameters used in the PBEs is summarized in Table A1. Monte Carlo Simulations Molecular weight distribution and the number distribution of particle activation/deactivation cylces were simulated by a Monte Carlo (MC) method. This MC simulation method is based on the competition technique, where the imaginary times of various events occurring in a latex particle are calculated and the event with the shortest imaginary time is chosen as a real event. Radical desorption should be considered in the current model. The events considered for a particle include: Event 1. Radical entry into a particle The average time interval between radical entry is given by :
where is a function of reaction time. The imaginary time for radical entry is determined by:
Event 2. Radical desorption from a particle The average time for radical desorption to occur is given by:
and
where is a function of time. The imaginary time for radical desorption is determined by:
Event 3. Monomer radical propagation The average time for this event to occur is given by:
The rate coefficient of monomer radical propagation instead of desorption is calculated by: 101
The imaginary time for radical propagation instead of desorption is determined by:
The simulation starts with a dormant particle. Radical entry is the only event that would happen at the beginning. The time interval for radical entry is determined. After the particle is activated, the imaginary times of three events are calculated. The event with the shortest imaginary time is chosen as the real event. (for example, as radical entry is And the reaction time increases by is calculated the real event). Then the number of reacted monomer units and added to randomly selected chains. If radical entry or radical desorption is chosen as the real event, the active latex particle turns into dormant. The activation/deactivation cycle is counted. And the next simulation starts from the beginning. Detailed calculation process can be found in ref. (30). The data are collected from 200 particles. The parameters used in calculation are listed in Table A2. The values of , the initial molecular weight distribution, the initial particle size distribution, and were measured by experiments, while the other parameters were from the literature.
Table A1. Description of the Parameters Used in PBEs
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Table A2. Parameters Used for the Simulation of the Seeded RAFT Emulsion Polymerization of Styrene
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Nomenclature Symbols
[I] [R]
PBE
monomer concentration in the latex particle, mol L-1 monomer concentration in the aqueous phase, mol L-1 RAFT agent concentration in the latex particle, mol L-1 density of monomer, g L-1 number average diameter, nm density of polymer, g L-1 volume average diameter, nm diffusion coefficient for monomer radical, dm2 aqueous phase concentration of monomer radicals, mol L-1 initiator concentration, mol L-1 aqueous phase concentration of oligomeric radicals, mol L-1 RAFT agent concentration, mol L-1 growth rate for latex particles, L s-1 desorption rate coefficient of monomer radicals, s-1 addition rate coefficient, L mol-1 s-1 fragmentation rate coefficient, s-1 entry rate coefficient of oligomeric radicals, L mol-1 s-1 re-entry rate coefficient of monomer radicals, L mol-1 s-1 propagation rate, L mol-1 s-1 monomer radical propagation rate, L mol-1 s-1 partition coefficient of the monomer between the water and polymer phase rate coefficient of radical chain transfer to monomer, L mol-1 s-1 rate coefficient of RAFT reaction, L mol-1 s-1 number of activation/deactivation times per particle average number of activation/deactivation times per particle particle number, average radical number per particle molar mass of the unreacted monomer, mol L-1 population density function of particle with no free radical, mol L-1 dm-1 population density function of particle with no a monomer radical, mol L-1 dm-1 population density function of particle with no a polymer radical, mol L-1 dm-1 population density function of particle with no an intermediate radical, mol L-1 dm-1 Avogadro’s number population balance equation radius of unswollen latex particles, dm length of discretized radius domain, dm radius of swollen latex particles, dm reaction time, s 104
swollen volume of the latex particle, L volume of the aqueous phase, L critical degree of polymerization
z Greek Letters
overall entry rate, s-1 entry rate for initiator-derived radicals, s-1 entry rate for monomer radicals, s-1
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