Carboxyl Terminated Polymer Chain Extension Using a Bisoxazoline Coupling Agent: Monte Carlo Simulation

Summary: The kinetics of the chain extension reaction of a carboxyl‐terminated polymer using a bisoxazoline coupling agent was simulated by the Monte Carlo method based on the master equation. The effects of temperature and stepwise addition of the chain extender was examined. A comparison between simulated results and those calculated by an amended kinetic model was made. The results show that the highest coupling efficiency and the highest can be obtained when the initial concentrations of carboxyl and oxazoline groups are equal, which is in good agreement with the experiments. It is found that a higher reaction temperature could lead to a bigger coupling efficiency, a higher and narrower MWDs. The stepwise addition of the chain extender can only postpone the chain extension reaction, but cannot affect the final coupling efficiency and the MWDs when the concentration of the oxazoline group is lower than that of the carboxyl group. However, stepwise addition of the chain extender favors bigger coupling efficiency and narrower MWDs when the concentration of the oxazoline group exceeds that of the carboxyl group.

The relationship among three group of polymers, r and ratios of k₂ to k₁. The dots are the data simulated by MC and solid lines are relative data calculated by the kinetic model.     

Kinetic analysis of the cross reaction between dithioester and alkoxyamine by a Monte Carlo simulation

A model reaction of dithioester and alkoxyamine is proposed to probe the reversible addition–fragmentation chain transfer (RAFT) process. The kinetics of the model reaction is analyzed and compared with that of pure alkoxyamine homolysis with a Monte Carlo simulation. Although the pure alkoxyamine obeys the law of persistent radical effect, the model reaction results in higher concentration of the persistent radical during the main period of the reaction. However, for a very fast RAFT process or a very low addition rate constant, the time dependence of the persistent radical concentration is quite close to that of pure alkoxyamine. Furthermore, the cross termination between the intermediate and alkyl radicals causes a retardation effect for the model reaction when the intermediate is relatively long‐lived. The Monte Carlo simulation indicates that it is feasible to measure the individual rate constants of the RAFT process, such as the rate constant of addition, with a large excess of alkoxyamine. In addition, the special feature of the system with different leaving groups in the alkoxyamine and dithioester is also discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 374–387, 2007     

A Parallelised High Performance Monte Carlo Simulation Approach for Complex Polymerisation Kinetics

A novel, parallelised approach to Monte Carlo simulations for the computation of full molecular weight distributions (MWDs) arising from complex polymerisation reactions is presented. The parallel Monte Carlo method constitutes perhaps the most comprehensive route to the simulation of full MWDs of multiple chain length polymer entities and can also provide detailed microstructural information. New fundamental insights have been developed with regard to the Monte Carlo process in at least three key areas: (i) an insufficient system size is demonstrated to create inaccuracies via poor representation of the most improbable events and least numerous species; (ii) advanced algorithmic principles and compiler technology known to computer science have been used to provide speed improvements and (iii) the parallelisability of the algorithm has been explored and excellent scalability demonstrated. At present, the parallel Monte Carlo method presented herein compares very favourably in speed with the latest developments in the h‐p Galerkin method‐based PREDICI software package while providing significantly more detailed microstructural information. It seems viable to fuse parallel Monte Carlo methods with those based on the h‐p Galerkin methods to achieve an optimum of information depths for the modelling of complex macromolecular kinetics and the resulting microstructural information.

     

Monte Carlo Simulation of Ethylene Copolymers: A Look into the Monomer Sequence Distribution

A comprehensive mathematical model was developed using Monte Carlo simulation to describe the mechanism of ethylene and α-olefin copolymerization. The model studies the polymerization mechanism using coordination catalysts and is able to predict molecular weight and detailed chemical composition distributions. This work is considered to be a useful tool that enables us to understand and described the monomer sequence distribution as a function of chain length in semi-batch polymerization reactors.     

Monte Carlo simulation of diepoxides and monoepoxides cured with amines

The diepoxide–monoepoxide–diamine curing systems are investigated with a Monte Carlo simulation. The dependence of the molecular weight distribution (MWD), gel fraction, and cycle rank of the polymers on the differences in the epoxy reactivities and the contents of the monoepoxide as a reactive diluent are discussed. Before gelation, the MWD of the curing systems with a lower content of the monoepoxide is broader than the MWD of the curing systems with a higher content, and it leads to a lower critical conversion. The gel fraction and cycle rank of the polymers decrease with an increasing amount of the diluent. Even fully cured, the system with a 0.6 epoxy molar fraction of the monoepoxide still has a large fraction of sol, about 49%. Although the various reactivities of the monoepoxide result in different ways of forming gels during curing, the final gel fractions are always near 100% as long as the epoxy molar fraction of the diluent is no more than 0.2. The profiles of the molecular weights of the polymers calculated by the model are in agreement with the experimental data. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1857–1868, 2002     

A Monte Carlo Simulation of Homogeneous Crystallization in Confined Spaces: Effect of Crystallization Kinetics on the Avrami Exponent

Homogeneous nucleation in polymers and subsequent crystallization in spaces confined relative to spherulitic dimensions in one direction has been simulated for a wide range of nucleation and growth rates. An empirical equation based on simulation results relating an Avrami exponent of crystallization to growth and nucleation rates along with the characteristic dimension of crystallizing volume has been proposed. It was found that for ideal homogeneous crystallization, the Avrami exponent can be significantly lower than the anticipated values for free unconstrained growth; therefore, all crystallization conditions and parameters must be taken into account in order to make a conclusion on the character of the observed crystallization.

     

Bayesian Modeling and Markov Chain Monte Carlo Simulations for a Kinetic Study of Homo‐ and Co‐ Polymerization Systems

A Bayesian modeling and Markov Chain Monte Carlo simulation was developed for a kinetic study of homopolymerization and copolymerization systems at the molecular scale. Two copolymerization models – the terminal unit model and the penultimate unit model – were considered. Prior estimates of the kinetic parameters were obtained by L₁‐norm robust statistics. Using the structure of experimental data through a likelihood function, Bayesian modeling was employed to update the prior estimates. The joint posterior probability regions and shimmer bands were calculated for updated reactivity ratios. A method for assessing the power of experimental data in discrimination between copolymerization models is presented. This method was validated for free radical polymerization in binary systems. The evolution of species and radical populations during the course of polymerization were determined. The computational time was considerably decreased by calculating the propagation step from lifetime of the polymer chain and local monomer concentration. To avoid inaccuracies in the results caused by poor choice or false computation of the time step, the time step between successive Monte Carlo events was adapted to the time scale of the fastest reaction. The simulation algorithm is exact, in the sense that it takes full account of the fluctuations and correlations.

     

Constitutional isomerism in polyamides derived from isophthaloyl chloride and 1,3‐diamine‐4‐chlorobenzene

Polyamides from isophthaloyl chloride and 1,3‐diamino‐4‐chlorobenzene with diverse constitutional order were obtained in a one‐stage synthesis varying the polymerization temperature and the monomer mixing modes. The constitutional order was calculated by ¹H and ¹³C NMR spectroscopies. A model to determine the constitutional isomerism in these polycondensates was applied with the relevant kinetic reaction parameters obtained from the model reactions. The Monte Carlo technique was used to model the constitution along the polycondensation reaction as a function of the average polymerization degree. Constitution was determined by kinetic factors and not by thermodynamic ones. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1202–1215, 2003     

Monte Carlo Simulation of Controlled/Living Radical Polymerization in Emulsified Systems

A new MC simulation method is proposed for the controlled/living radical polymerization in a dispersed medium, assuming an ideal miniemulsion system. This tool is used to consider the effects of particle size on the polymerization rates and the molecular weight distributions. For NMP, the polymerization kinetics are basically governed by two conflicting factors, (i) the confined space effect that promotes the coupling reaction between a radical and a trapping agent and (ii) the isolation effect of radicals into different particles that suppresses the overall frequency of bimolecular termination. For RAFT polymerization, a significant rate enhancement by reducing the particle size could be observed only for the systems with fast fragmentation of adduct radicals.

     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

Ｔｈｅｐｈａｓｅｂｅｈａｖｉｏｒｉｎｍｕｌｔｉｐｌｅｃｏｍｐｏｎｅｎｔｐｏｌｙｍｅｒｓｃｏｎｓｔｉｔｕｔｅｓａｌｏｎｇｓｔａｎｄｉｎｇａｃｔｉｖｅａｃａｄｅｍｉｃｓｕｂｊｅｃｔｂｏｔｈｉｎｐｏｌｙｍｅｒｓｃｉｅｎｃｅａｎｄｃｏｎｄｅｎｓｅｄｓｔａｔｅｐｈｙｓｉｃｓ.Ｉｔｉｓｅｓｐｅｃｉａｌｌｙｓｉｇｎｉｆｉｃａｎｔｉｎｇｕｉｄｉｎｇｔｈｅｆａｂｒｉｃａｔｉｏｎｏｆｐｏｌｙｍｅｒａｌｌｏｙｓ[1].Ｄｕｒｉｎｇｔｈｅｌａｓｔｄｅｃａｄｅｓｍｕｃｈａｔｔｅｎｔｉｏｎｈａｓｂｅｅｎｐａｉｄｔｏｔｈｅｃｏｍ…     

表面活性剂与高分子链混合体系的模拟

计算机模拟了高分子链对表面活性剂胶束形成过程的影响，以及高分子链构象性质随胶束化过程的变化.结果表明,当高分子链与表面活性剂之间的相互作用强度超过临界值后，高分子链的存在有利于表面活性剂胶束的形成.临界聚集浓度（CAC）与临界胶束浓度（CMC）的比值CAC/CMC随高分子链长的增大和相互吸引作用的增强而减小.在CAC之前，高分子链与表面活性剂分子只有动态的聚集；但在CAC之后，表面活性剂胶束随表面活性剂浓度X的增加而增大，并静态地吸附在高分子链上，形成表面活性剂/高分子聚集体.随着表面活性剂分子的加入，高分子链的均方末端距和平均非球形因子先保持恒定；从X略小于CAC开始， 和快速减小，至极小值后又逐渐增大.模拟结果支持高分子链包裹在胶束表面的实验模型.     

The Kinetic Modeling of Strong Diffusion‐Limited Reaction with Cyclization for Three Isomers – Diallyl Ortho‐, Iso‐ and Tere‐Phthalate in a Bulk

Free radical polymerization kinetic in a bulk for three diallyl phthalate isomers – diallyl orthophthalate, diallyl isophthalate and diallyl terephthalate was investigated in a temperature range from 50 to 70 °C initiated with dicyclohexan peroxydicarbonate as initiator at three different initiator concentrations. Conversion points were measured using Fourier Transform Raman measurements. A new kinetic model for polymerization of three diallyl phthalate isomers was developed. It demands the inclusion of only two new kinetic parameters k_DegC and k_pc which were obtained as a ratio k_DegC/k_pc from an additional set of experiments conducted. Computed conversions from the proposed kinetic model show good agreement with the conversion and molecular weight measured data for all three investigated diallyl phthalate isomers.

     

Monte Carlo模拟表面上吸附态物种的迁移对反应行为的影响

用MonteCarlo方法研究了非均相催化剂表面吸附态氢原子的迁移对催化反应活性的影响,模拟结果表明,吸附态氢原子扩散很慢时,表面活性位很快被氢原子饱和,转换频率TOF增大到一定程度时很快下降;而当表面吸附态氢原子的扩散速率达到足够大的程度时,TOF将不再受氢原子扩散的影响.     

Monte Carlo simulation on layered polymeric films

Thin films of polymer blends composed of alternating copolymer, diblock copolymer and/or homopolymer are studied using Monte Carlo simulation. A multilayer morphology is observed in the film, that is, the blended polymers assemble into individual domains arranged from interior to the surfaces of the film. The coexisting components residing throughout the neighboring domains in the film make no distinguishable interface between any neighboring domains. By this means, it forms a vertical composition gradient in the polymeric film. Being different from layer-by-layer deposition of polyelectrolyte or hydrogen bonding approach etc., the layered structure in this study is formed by polymer blending in one step. Alternating copolymers are found to be essential components to form vertical composition gradient （layered structure） in thin films.     

端点附壁的高分子链形状的Monte Carlo模拟

分别基于简立方格点和四面体格点模型对一端吸附在无限大平面的高分子链（平面接枝高分子链）的形状进行了Ｍｏｎｔｅ Ｃａｒｌｏ模拟,结果表明,接枝高分子链的形状更偏离球形,〈Ｌ＾２１〉：〈Ｌ＾２２〉：〈Ｌ＾２３〉的极限值约为１：２．７５：１２．５,其中〈Ｌ＾２１〉,〈Ｌ＾２２〉和〈Ｌ＾２３〉分别为回转半径张量的本征值Ｌ＾２１,Ｌ＾２２和Ｌ＾２３（Ｌ＾２１〈Ｌ＾２２〈Ｌ＾２３）的统计平均;链长相同时,接枝     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008