Diffusion-controlled vinyl polymerization. I. The gel effect

It is well known that the reaction rate and molecular weight of vinyl polymers can change markedly during the course of polymerization and that these changes are due to the influence of diffusion on the termination reaction. The chain length dependence of the termination rate constant has been considered in this work and has resulted in a general method of treating the polymerization kinetics and molecular weight distribution. This method is independent of the form of the chain length dependency and is capable of dealing with both disproportionation and recombination modes of termination. A specific model for the termination rate constant with chain length dependence is proposed and is based on free volume theory and entanglement coupling. Master curves for the characteristics of the reaction rate and molecular weight distribution are presented with the application of this model.     

Monte Carlo simulation of chain length distribution in radical polymerization with transfer reaction

In this paper, the basic principle and a Monte Carlo method are described for numerically simulating the chain-length distribution in radical polymerization with transfer reaction to monomer. The agreement between the simulated and analytical results shows that our algorithm is suitable for systems with transfer reaction. With the simulation algorithm, we confirm that transfer reaction has a similar effect as disproportionation on the molecular weight distribution in radical polymerization with continuous initiation. In the pulsed laser (PL) initiated radical polymerization with transfer reaction, the ‘waves’ on the chain-length distribution profile become weaker as the ratio of transfer reaction rate constant, k_tr, to the propagation rate constant, k_p, is increased in the case with either combination-type or disproportionation-type termination. Moreover, it seems that the combination termination has a broadening effect on the waves. Therefore, k_p can also be determined by precisely locating the inflection point L_o on the chain-length distribution profile for radical polymerization with transfer reaction, unless k_tr is large enough to smear out the waves on the chain-length distribution.     

Polymerization and reptation,an analytical treatment

Free-radical polymerization without crosslinking is considered. By taking the chain length as a continuous variable the reaction kinetics is treated in a simple way for the stationary state. Equations for instantaneous average degrees of polymerization and related quantities are generalized to allow for chain-length dependence of the termination rate constant. For the Ito model, which treats reptation-controlled termination, approximate versions of these equations are derived in the limits of low and high conversion. The observed structure in the peak of the gel permeation chromatograms is shown not to be related to the bimodality in the instantaneous molecular weight distribution. None of the results is very sensitive to the precise reptation behavior.     

Emulsion polymerization of styrene. I. Review of experimental data and digital simulation

Isothermal emulsion polymerization at 60°C of styrene in a batch reactor were studied by using sodium lauryl sulfate as surfactant and potassium persulfate as initiator source. The concentrations of surfactant and initiator were varied during the runs. The polymerization evolution was followed as samples were taken at regular intervals. These emulsion samples were analyzed for monomer conversion, rate of polymerization, as well as for the size and the size distribution of the particles. The molecular weight and molecular weight distribution were obtained by gel permeation chromatography. Our study showed that fresh nucleation takes place even at high conversion, causing a continuous shifting toward broadening of particle size distribution. Contrary to the theory of Smith and Ewart, which assumes a constant number of particles during interval II of the polymerization reaction, our digital simulation of the reaction presents better experimental results with a variable number of particles, and indicates that the Hui–Hamielec model for termination constant k_t as function of conversion is not applicable under our working conditions.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007     

含芳酰胺结构的新型甲壳型液晶高分子PMPACS的聚合反应动力学研究

采用称量法和GPC,研究了以二甲基乙酰胺为溶剂,偶氮二异丁腈为引发剂,自由基溶液聚合制备含芳酰胺结构的新型甲壳型液晶高分子聚[乙烯基对苯二甲酸二(4-甲氧基苯胺)](PMPACS)的聚合反应动力学.研究发现,(1)MPACS的聚合反应在60℃时主要为双基偶合终止,所以反应后期聚合物分子量明显增大,分子量分布变窄;(2)该反应的聚合反应速率方程为Rp=kp[M][I]1/2,表观活化能Eα=44 kJ/mol,在60℃时的聚合反应常数kp=1.04 L·mol-1·h-1;(3)相同聚合条件下,单体的转化率和数均分子量随单体初始浓度[M]0的增加而增大,当引发剂浓度[I]0增加时,聚合物的分子量随之降低,分子量分布增大;(4)该研究虽采用普通自由基聚合,所得聚合物的分子量分布却较窄,仅为1.1～1.4.     

Molecular weight distribution in thermal polymerization of styrene

The molecular weight distribution in thermal polymerization, for which the termination rate is comparable with the transfer rate, is analyzed by assuming that (1) the termination rate is independent of chain length; (2) the rate is translational diffusion-controlled; and (3) the rate is influenced by the excluded volume. The theoretical distribution, based on the assumption that the rate is translational diffusion-controlled, is the best fit to the experimental data at high temperature. The dependence of the rate on chain length is stronger at higher temperature (>80°C). The ratio of the termination rate to the transfer rate increases with increasing temperature.     

Diffusion-controlled rate constant of termination reaction in radical polymerization

Smoluchowski's theory has been modified and the improved theory was applied to diffusion-controlled polymerization. This application proved that the rate-controlling process is not transrational diffusion but the segmental diffusion. The segmental diffusion-controlled rate constant was derived by the collision theory. This rate constant explains the experimental fact that the diffusion-controlled rate constant of bimolecular termination in radical polymerization of alkyl methacrylate is inversely proportional to solution viscosity and independent of the molecular weight of the polymeric free radical.     

Synthesis and kinetic analysis of DPE controlled radical polymerization of MMA

The 1,1‐diphenylethene (DPE) controlled radical polymerization of methyl methacrylate was performed at 80 °C by using AIBN as an initiator and DPE as a control agent. It was found that the molecular weight of polymer remained constant with monomer conversion throughout the polymerization regardless of the amounts of DPE and initiator in formulation. To understand the result of constant molecular weight of living polymers in DPE controlled radical polymerization, a living kinetic model was established in this research to evaluate all the rate constants involved in the DPE mechanism. The rate constant k₂, corresponding to the reactivation reaction of the DPE capped dormant chains, was found to be very small at 80 °C (1 × 10^?5 s^?1), that accounted for the result of constant molecular weight of polymers throughout the polymerization, analogous to a traditional free radical polymerization system that polymer chains were terminated by chain transfer. The polydispersity index (PDI) of living polymers was well controlled <1.5. The low PDI of obtained living polymers was due to the fact that the rate of growing chains capped by DPE was comparable with the rate of propagation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

Study of radiation-induced polymerization of vinyl monomers adsorbed on inorganic substances. IX. Preirradiation polymerization of styrene–silica gel system

Preirradiation polymerization of the styrene–silica gel system was studied in detail. Both graft polymers and homopolymers have bimodal GPC spectra. High molecular weight peaks were formed in a radical mechanism and the low molecular weight peaks were formed in a cationic mechanism as same as those in the simultaneous irradiation polymerization. The rate of formation of the low molecular weight peaks was very high compared with that of the high molecular weight peaks. Monomer conversion and percent grafting leveled off at about 1–2 Mrad. Radiation dose dependence of the four peaks were different from each other. Monomer conversion and percent grafting decreased as the preheating temperature of silica gel increased. The amount of the low molecular weight peaks of graft polymers depended on the number of silanol groups, as in the case of the simultaneous irradiation polymerization. A reaction mechanism for the preirradiation polymerization is proposed based on the results obtained.     

Synthesis of PMMA‐b‐PBA block copolymer in homogeneous and miniemulsion systems by DPE controlled radical polymerization

In this research, poly(methyl methacrylate)‐b‐poly(butyl acrylate) (PMMA‐b‐PBA) block copolymers were prepared by 1,1‐diphenylethene (DPE) controlled radical polymerization in homogeneous and miniemulsion systems. First, monomer methyl methacrylate (MMA), initiator 2,2′‐azobisisobutyronitrile (AIBN) and a control agent DPE were bulk polymerized to form the DPE‐containing PMMA macroinitiator. Then the DPE‐containing PMMA was heated in the presence of a second monomer BA, the block copolymer was synthesized successfully. The effects of solvent and polymerization methods (homogeneous polymerization or miniemulsion polymerization) on the reaction rate, controlled living character, molecular weight (M_n) and molecular weight distribution (PDI) of polymers throughout the polymerization were studied and discussed. The results showed that, increasing the amounts of solvent reduced the reaction rate and viscosity of the polymerization system. It allowed more activation–deactivation cycles to occur at a given conversion thus better controlled living character and narrower molecular weight distribution of polymers were demonstrated throughout the polymerization. Furthermore, the polymerization carried out in miniemulsion system exhibited higher reaction rate and better controlled living character than those in homogeneous system. It was attributed to the compartmentalization of growing radicals and the enhanced deactivation reaction of DPE controlled radical polymerization in miniemulsified droplets. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4435–4445, 2009     

Study of radiation-induced polymerization of vinyl monomers adsorbed on inorganic substances. VII. Effect of pretreatment temperature of silica gel on styrene–silica gel system

To investigate the reaction mechanism of radiation-induced polymerization of styrene adsorbed on silica gel, the effect of pretreatment temperature of silica gel was studied. Preheating of silica gel was carried out at 200, 500, and 800°C. The number of silanol groups of silica gel surface decreased as preheating temperature increased. The rate of polymerization on the silica gel preheated at 500°C was faster than that at 200°C, but the polymerization rate on the silica gel preheated at 800°C was the lowest. These results suggest that rate of polymerization on the silica gel is affected by the conditions of silica gel surface such as the number of silanol groups and the pore size. At the same monomer conversion, percent grafting decreased as preheating temperature of silica gel increased. The GPC spectra of both graft polymers and homopolymers have two peaks at all preheating temperatures. The monomer conversion of low molecular weight peaks of graft polymers decreased as preheating temperature of silica gel increased. This result suggests that there is a probability that the grafting sites of low molecular weight peaks of graft polymers somehow interact with silanol groups.     

聚γ-缩水甘油醚氧丙基三甲氧基硅烷的合成与表征

采用双金属氰化络合物催化剂(DMC)催化γ-缩水甘油醚氧丙基三甲氧基硅烷(KH560)开环聚合,合成出结构规整的均聚产物PKH560.通过FTIR2、9Si-NMR1、H-NMR对聚合物的结构进行表征.结果表明,以DMC为催化剂,可以实现KH560的开环聚合,合成出分子量较大的目标产物PKH560.凝胶渗透色谱与多角度激光联用仪(GPC/MALLS)测得该聚合物PKH560的数均分子量大于1×104,分子量分布介于1.10与1.35之间;分析不同聚合时间PKH560的数均分子量与单体转化率之间的关系可知,聚合物的数均分子量Mn与单体转化率呈线性增长关系,聚合物的分子量分布较窄(Mw/Mn=1.10~1.35),表明该聚合反应具有活性聚合的特征.     

Evolution of the termination rate coefficient in styrene polymerization

Styrene bulk polymerization was conducted at 70 °C with a high initiator concentration, and this ensured that the dominant chain‐stopping mechanism was the combination of free radicals. The evolution of the molecular weight distribution (MWD) of the polymer was measured via the periodic removal of samples during the course of the reaction and their analysis with gel permeation chromatography. The overall termination rate coefficient was independent of the conversion in the dilute regime, as observed from cumulative MWDs. In the middle of the conversion range, the observed trend was compatible with a translational‐diffusion‐controlled mechanism for the termination step. A bimodal distribution of the molecular weights was also found at high conversions and could be explained in terms of an increase in the free‐radical concentration and a very low termination rate coefficient. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 178–187, 2005     

Simulation of pseudostationary radical polymerization, 3. Periodic modulation of the termination process for termination by disproportionation

A procedure is developed that allows the calculation of chain-length distributions of polymers prepared by periodic modulation of the termination rate constant, considering termination by disproportionation. Applying some (hypothetical) field which suppresses — or at least diminishes — the termination rate constant periodically, results in step-function-like chain-length distributions. In principle, the same information may be obtained as in the case of periodical variation of the rate of initiation.     

Modeling of molecular weight development in atom transfer radical polymerization

A kinetic model has been developed for atom transfer radical polymerization processes using the method of moments. This model predicts monomer conversion, number‐average molecular weight and polydispersity of molecular weight distribution. It takes into account the effects of side reactions including bimolecular radical termination and chain transfers. The determining parameters include the ratios of the initiator, catalyst and monomer concentrations, as well as the ratios of the rate constants of propagation, termination, transfer and the equilibrium constant between radicals and their dormant species. The effects of these parameters on polymer chain properties are systematically simulated. The results show that an ideal living radical polymerization exhibiting a linear relationship between number‐average molecular weight versus conversion and polydispersity approaching unity is only achievable under the limiting condition of slow monomer propagation and free of radical termination and transfers. Improving polymerization rate usually accompanies a loss of this linearity and small polydispersity. For polymerization systems having a slow initiation, the dormant species exercise a retention effect on chain growing and tend to narrow the molecular weight distribution. Increasing catalyst concentration accelerates the initiation rate and thus decreases the polydispersities. It is also shown that for a slow initiation system, delaying monomer addition helps to reduce the polydispersities. Radical termination and transfers not only slow down the monomer conversion rates but also broaden polymer molecular weight distributions. Under the limiting conditions of fast propagation and termination and slow initiation, the model predicts the conventional free radical polymerization behaviors.     

Kinetic model for a polymerization process where the rate constants of both propagation and termination by monomer depend on chain-length

A kinetic model with non-constant propagation and termination rate constants is given for a sort of anionic polymerization. The expression of molecular weight distribution and other molecular parameters are derived by a non-steady state procedure. The effect of the reaction conditions on the molecular parameters are illustrated by numerical examples. The theoretical curves of molecular weight distribution with two or three peaks are similar to those of polymers generated in the anionic polymerization of polar monomers in nonpolar solvents.     

甲基丙烯酸甲酯聚合动力学和分子量及分布的开放控制

在甲基丙烯酸甲酯聚合过程中 ,凝胶效应会导致转化率在短时间内出现突变 ,这对工业反应器非常危险 ,同时也导致分子量剧增、分子量分布加宽 .为了使聚合反应速度、分子量及分布同时得到控制 ,提出 3个控制目标 ,即热荷分布指数、预定分子量及变化、分子量分布指数 .在甲基丙烯酸甲酯半间歇聚合动力学和分子量模型的基础上 ,通过单体、溶剂和链转移剂 3种物料的流量和加料方式的仿真计算 ,对动力学、分子量及分布进行开放控制 ,并进行优化 ,得到热荷分布指数和分子量分布指数分别小于 2 0和 2 2的控制策略 ,且分子量达到预定要求 .选择两种优化策略进行实验验证 ,结果与开放控制仿真结果一致     

Modeling stable free-radical polymerization

A kinetic model has been developed for stable free-radical polymerization (SFRP) processes by using the method of moments. This model predicts monomer conversion, number-average molecular weight, and polydispersity of molecular weight distribution. The effects of the concentrations of initiator, stable radical, and monomer, as well as the rate constants of initiation, propagation, termination, transfer, and the equilibrium constant between active and dormant species, are systematically investigated by using this model. It is shown that the ideal living-radical polymerization having a linear relationship between number-average molecular weight and conversion and a polydispersity close to unity is the result of fast initiation, slow propagation, absence of radical termination, and a high level of dormant species. Increasing stable radical concentration helps to reduce polydispersity but also decreases polymerization rate. Thermal initiation significantly broadens molecular weight distribution. Without the formation of dormant species, the model predicts a conventional free-radical polymerization. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2692–2704, 1999