Monte Carlo simulation of microemulsion polymerization

Monte Carlo simulation of chemically reacting systems based on the master equation was used to describe the stochastic time evolution of the microemulsion polymerization system. A model was developed to demonstrate its applicability for hexyl methacrylate and styrene microemulsion polymerization. The properties of final latex, such as the particle size and molecular weight distributions were obtained simultaneously. The polymerization behavior and properties of final latexes were well reproduced. The model is valuable in confirming or elucidating the various mechanisms in the polymerization. The entry and desorption mechanism was well established to account for the polymerization kinetics. The general polymerization behavior of hydrophobic monomer in microemulsions was properly simulated by the model proposed.     

自由基聚合动力学模型及其计算

本文建立了自由基聚合的动力学模型，并利用Ｒｕｎｇｅ－Ｋｕｔｔａ数值解法对组成模型的非线性常数微分方程进行了求解。利用该模型对苯乙烯的本体聚合，溶液聚合进行了模拟计算，与文献报导的实验数据比较表明：此模型能较好的模拟自由基聚合动力学。     

PA6水解聚合反应数学模型及其实验验证

建立了PA6熔体在VK管中边流动边聚合的聚合反应数学模型,采用流态显示技术和文献报道的测定数据验证了数学模型的可靠性,还研究了熔体在具有优化科挡板内部结构的VK管中流过10块交替排列的挡板过程中停留时间分布、单体的转化率、产物的聚合度的变化规律,并从聚合指标反证了挡板结构的合理性。     

Poly(dimethylsiloxane‐b‐styrene) diblock copolymers prepared by reversible addition‐fragmentation chain transfer polymerization: Kinetic model

Well‐defined polydimethylsiloxane‐block‐polystyrene (PDMS‐b‐PS) diblock copolymers were prepared by reversible addition‐fragmentation chain transfer (RAFT) polymerization using a functional PDMS‐macro RAFT agent. The RAFT polymerization kinetics was simulated by a mathematical model for the RAFT polymerization in a batch reactor based on the method of moments. The model described molecular weight, monomer conversion, and polydispersity index as a function of polymerization time. Good agreements in the polymerization kinetics were achieved for fitting the kinetic profiles with the developed model. In addition, the model was used to predict the effects of initiator concentration, chain transfer agent concentration, and monomer concentration on the RAFT polymerization kinetics. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

醋酸乙烯酯乳液聚合数学模型(Ⅱ) 阶段Ⅱ与阶段Ⅲ模型

研究了较大亲水性单体醋酸乙烯酯(VAc)乳液聚合动力学,着重剖析了自由基解吸的影响及水相中的聚合反应对总聚合反应速率的贡献,提出了阶段Ⅱ和阶段ⅢVAc乳液聚合数学模型,成功地预计了聚合反应速率、自由基在乳胶粒中的分布及乳胶粒中平均自由基数随转化率的变化规律.并将模型预计结果和实验数据进行了比较和讨论.     

Development of a comprehensive mathematical model for free radical suspension polymerization of methyl methacrylate

In this work a detailed mathematical model for free radical suspension polymerization of methyl methacrylate (MMA) in water is developed. This model is based on sound principles such as the free volume theory to account for the diffusion limited reactions in suspension polymerization. Additionally, the complex polymerization kinetics process of the aqueous suspension polymerization of MMA is studied as a one‐dimensional numerical experiment. For this purpose, the polymerization process is modeled as a moving boundary mass transfer problem coupled with polymerization reactions. The Galerkin finite element method is used to simultaneously solve the nonlinear governing equations. The model predictions for conversion and average molecular weights vs. time were found to be in close agreement with laboratory data. It is believed that this work, as it provides fundamental understanding of the process, it might contribute to a more rational design of polymerization reactors. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

A Mathematical Approach to the Analysis of Swollen Emulsion Polymerization of Styrene

A mathematical model for swollen emulsion polymerization of styrene was derived in this study. The experimental data were obtained using two different swelling agents: cetyl alcohol and lauryl alcohol. In the studied system, potassium persulfate and sodium dodecyl sulfate were used as initiator and emulsifier, respectively. The variation of total monomer conversion with the polymerization time obtained with different swelling agent-emulsifier combinations and data from SEM photographs of the final latexes were evaluated for estimation of the model parameters. In the mathematical model, it was assumed that the polymerization takes place according to first-order kinetics, within the forming latex particles in the presence of monomer diffusion from the monomer droplets to the forming latex particles. The kinetic rate constants and the variation of effective diffusion coefficient of monomer with the polymerization time were estimated using model expressions. Relative rate factor-Thiele modulus diagrams were derived for swollen emulsion polymerization system.     

氯乙烯悬浮聚合过程引发体系优化

在氯乙烯悬浮聚合过程机理模型的基础上,建立了复合引发体系的优化模型,并进行了二元引发体系的优化研究,得到了不同引发剂配比下的最大聚合速率等高线和临界转化率时的聚合时间等高线。结果可以用来指导复合引发剂的配方设计,有助于聚合热的均匀释放、聚合釜冷却能力的充分利用和聚合釜生产率的提高。     

Modeling of the bulk free radical polymerization up to high conversion—three stage polymerization model I. Model examination and apparent reaction rate constants

In this paper, a simple and useful model, the three stage polymerization model (TSPM) is proposed on the basis of recent experimental evidence and our preliminary treatment of the experimental kinetic results found in the literature. The model accounts for gel effect and glass effect in bulk free-radical polymerization. Equations for calculating the conversion of the polymerization reaction are derived based on TSPM. Using experimental kinetic data available in the literature, general expressions for apparent reaction rate constants in three stages for methylmethacrylate (MMA) and styrene (St) are obtained. In general, the experimental kinetic data can be treated very well with the TSPM from the low conversion stage to high conversion, except for some experimental data near the transition points. However, the deviation for this data may be reasonably explained by the non-isothermal effects that occur in this regime of experiments. This deviation is smaller for a smaller ampoule reactor used in polymerization experiments because of its better heat transfer ability. In order to establish that there is no glass effect stage when the reaction temperature is greater than the glass transition temperature for a polymerization process, some experimental data for ethylmethacrylate (EMA) bulk polymerization at a reaction temperature higher than its glass transition temperature were checked with TSPM. The plots show that the model is also suitable for EMA bulk polymerization.     

A Novel Method to Model Emulsion Polymerization Kinetics: The Explicit Radical-Particle Size Distribution Approach

Abstract:

An alternative approach to model emulsion polymerization is presented that is capable of rigorously solving both particle and radical kinetics for emulsion polymerization: the explicit radical-particle size distribution approach. The method is based on a direct solution of all population balances and fully covers the strong influence of compartmentalization on rates of reactions between macroradicals and, consequently, on chain length averages. An essential and new feature is the compartmentalization factor (D_f), which accounts for compartmentalization in a transparent manner. The generic approach allows for studying the complete emulsion polymerization conversion range, including gel-effect, and the effect of various parameters on both chain length and particle size distribution. Well-known kinetic regimes for emulsion polymerization naturally arise as limiting cases from our model. The dynamic behavior of the model was studied by simulating several realistic seeded emulsion polymerization reactions for styrene. The model dealt with compartmentalization accurately and was able to correctly reproduce the dynamic behavior known to be typical for emulsion polymerization.     

己内酰胺水解聚合过程的计算机模拟

用文献实验数据验证了己内酰胺水解聚合过程动力学模型,并对不同反应温度下聚合产物组成（己内酰胺单体浓度与转化率、环状二聚体及水的浓度、数均聚合度和多分散性指数）进行了模拟,得到己内酰胺水解聚合过程用先高温后低温的程序控温方法,与其工业生产实际控温方法完全一致。     

POLYMERIZATION KINETICS AND MODELING OF SLURRY ETHYLENE POLYMERIZATION PROCESS WITH METALLOCENE/MAO CATALYSTS

Polymerization methods of ethylene include the slurry, solution, and gas-phase processes. This study investigates polymerization conditions and kinetics under slurry process. Typical metallocene catalyst/cocatalyst Cp₂ZrCl₂/MAO system was used for ethylene polymerization. Two kinds of polymerization kinetics were compared in this study, multiple active-site model and transfer-effect model. The kinetic studies used metallocene-type polymerization kinetics, including catalyst activation, initiation, chain propagation, chain transfer, and termination steps. In addition, kinetic constants of polymerization reaction model were calculated. Calculation results of catalyst activity and molecular weight were compared with experimental results, indicating their good correlation. Moreover, the conventional polymerization was modified to accurately predict the molecular weight behaviors under various reaction conditions with the proposed transfer-effect model. Exactly, how reaction time, pressure, catalyst concentration, and cocatalyst ratio affect catalyst activity and molecular weight of the polymer were also discussed.     

Mathematical Modeling of the Poly(lactic acid) Ring-Opening Polymerization using Stannous Octoate as a Catalyst

A novel and simple mathematical model to get the polymerization rate constants for the ring-opening polymerization of poly(lactic acid) is described. The model permits evaluation of the degree of polymerization versus monomer-to-initiator ratio curves. The predicted results are compared with the reported experimental data. The value of rate constants for initiation, propagation, and different modes of termination, are also obtained.     

阴离子聚合反应挤出过程的化学热效应

为定量分析聚合反应倾向、优化反应加工条件,在建立紧密啮合同向旋转双螺杆挤出机的反应器模型及物料的化学反应动力学模型、化学流变模型的基础上,分析了阴离子聚合反应挤出过程的化学热效应,推导出反应热的释放量与反应热强度的数值计算式,并通过算例展示了其变化特点。     

Kinetics of heterogeneous polymerization of vinylidene chloride. I. Mechanism and modeling

The similarities and differences between the heterogeneous polymerization of vinylidene chloride (VDC) and vinyl chloride (VC) were compared and analyzed. The effect of the poly(vinylidene chloride)(PVDC) crystal morphology on the kinetics of VDC polymerization was discussed. Based on the assumption that polymerization occurs in the monomer phase and on the edges of the PVDC lamellar crystals, a mechanism of VDC polymerization is proposed and then a kinetic model for VDC bulk/suspension polymerization is developed according to the elementary reactions. The model can be used to predict polymerization rate and conversion. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 2576‐2581, 2004     

Modeling and simulation of semibatch emulsion polymerization

By taking advantage of recent theoretical developments in emulsion polymerization and radical polymerization kinetics at high conversion, a model is developed for simulating seeded semibatch emulsion polymerization. The model is used to calculate the time evolution of the polymerization rate, the monomer conversion, the instantaneous degree of polymerization, the monomer concentration in particles, the average radical number per particle, and the propagation rate coefficient and termination rate coefficient over the whole course of the polymerization. Experimental observations by previous workers, including the existence of steady-state phenomenon and the broad distributions of molecular weight, are reproduced in the results of the simulation. The gel effect on emulsion polymerization and the open-loop stability of the semibatch process are discussed. © 1993 John Wiley & Sons, Inc.     

Kinetics of bulk styrene polymerization catalyzed by symmetrical bifunctional initiators

The kinetics of bulk styrene polymerization catalyzed by symmetrical bifunctional initiators [2,5-dimethyl-2,5-bis(benzoyl peroxy) hexane] is studied. Being characterized by the presence of two peroxide groups of equal thermal stabilities, this bifunctional initiator system shows complex initiation, propagation, and termination reaction pathways. The kinetic model for bulk styrene polymerization with the bifunctional initiator is presented and compared with experimental data. The experimental data indicate that the model is quite satisfactory in describing the polymerization rate and polymer molecular weights for bulk styrene polymerization catalyzed by the symmetrical bifunctional initiator.     

A model for glow discharge electrolysis

Two models (a cylinder model and a cone model) are proposed to represent the inhomogeneous distribution of radicals in the liquid phase in glow discharge electrolysis. The models have been applied to polymerization by glow discharge electrolysis and the cone model has some success in accounting for the dependence of the rate of polymerization and the degree of polymerization on the monomer concentration and the pressure in the discharge.     

界面聚合制备复合膜过程的数学模型

基于高分子物理化学、质量传递和相分离成膜理论,研究在复合膜制备过程中采用界面聚合反应成膜的机理,建立了非稳态条件下反应．扩散联合控制的数学模型;通过有针对性地简化,该模型可适用于反应控制和扩散控制。模型中无量纲参数有明确的物理意义,较好地反映了界面聚合反应成膜过程的机理。无量纲化处理使模型解析解形式更为简单、实用,模型与实验数据吻合良好,且优于现有模型。通过模拟计算,可得出单体(A组分)浓度、膜的厚度、膜厚增长率随时间的变化关系,并可考察聚合反应速率常数、单体(A组分)在复合层中的扩散系数、单体初始浓度等参数对成膜过程的影响．理论结果可用于指导界面聚合反应成膜实践。     

悬浮聚合反应的数学模型

以苯乙烯悬浮聚合反应为例,从机理分析出发,建立了聚合过程的动态模型,其中通过引入若干个动态校正系数,较充分地考虑了凝胶效应的影响,根据实验结果,对部分参数进行了辨识,提高了模型的精度,并适用整个反应过程,为先进控制规律的研究提供了必要基础.