Monte Carlo Simulation of the Microstructure of Linear Olefin Block Copolymers

Summary: Linear olefin block copolymers (OBCs) are novel polyolefins with unique properties developed using the chain shuttling polymerization technology. Typically, OBCs are made in a single reactor with two catalysts having different 1-olefin reactivity ratios and a chain shuttling agent (CSA), producing linear polymer chains with complex, multi-block structures, although a dual reactor approach is also possible In this study, OBC chain microstructures were examined using Monte Carlo simulation. Effects of polymerization parameters (chain shuttling probability, propagation probability, and catalyst ratio) on the distribution of number of blocks per chain were investigated and reported for the first time. These results provide useful insights on how to control and describe the microstructures of these important polymers and can be used to establish quantitative relationships between the microstructure and properties of OBCs.     

Understanding the Microstructure of Living Ethylene/1‐Octene Block Copolymers with Dynamic Monte Carlo Simulation

Living ethylene/1‐olefin copolymerization with multiple comonomer feeding stages allows the production of living block copolymers (LBCs) with well‐controlled microstructures. A dynamic Monte Carlo model is developed to simulate the production of LBCs in a semibatch reactor, and it is used to study how the polymer microstructure evolves during the polymerization. The model also describes how chain transfer reactions affect the microstructure of LBC blocks. These model predictions provide useful guidelines for producing LBCs with precisely designed microstructures.

     

Simulation of Crystallization Analysis Fractionation (Crystaf) of Linear Olefin Block Copolymers

Summary: Linear olefin block copolymers (OBCs) have microstructures that are unique among polyolefins and exhibit properties that are different from those of other polyolefin elastomers. Characterizing their chain microstructures is a challenging task, as conventional characterization techniques cannot probe directly block length distribution or composition. In this work, we used a Monte Carlo model to predict the microstructure details of OBCs and a modified version of the Crystaf model previously developed in our groups to describe theoretical Crystaf profiles for model OBCs. This model can be used as a tool to interpret Crystaf results of these interesting new polyolefins and to relate them to OBC microstructures. Effects of polymerization parameters on OBC microstructure and Crystaf profiles were also discussed.     

Gradient Copolymers by ATRP in Semibatch Reactors: Dynamic Monte Carlo Simulation

We developed a dynamic Monte Carlo model for ATRP in semibatch reactors. Semibatch reactors can be used to produce gradient copolymers even if the difference between the reactivity ratios of the comonomers is not significant by using different comonomer feed policies. The model was used to predict average molecular weights, polydispersity index, copolymer composition and complete distributions of molecular weight, chemical composition, and comonomer sequence length at any polymerization time. Two case studies, poly[styrene‐co‐(methyl methacrylate)] and poly[acrylonitrile‐co‐(methyl methacrylate)], were chosen to demonstrate the effect of comonomer feed compositions on the final chemical composition distribution of the copolymer.

     

Dynamic Monte Carlo Simulation of Graft Copolymers Made with ATRP and Metallocene Catalysts

The synthesis of polyolefin graft copolymers made with coordination polymerization was studied by dynamic Monte Carlo simulation. Narrow molecular weight distribution macromonomers, containing terminal vinyl groups made with atom-transfer radical polymerization (ATRP), were incorporated randomly into the polyolefin backbone. In addition to average molecular weights and polydispersity index, the model predicts the complete molecular weight distribution (MWD) and branching density of the graft copolymer. The effect of the concentration of macromonomers on the grafting efficiency was also studied.     

Dynamic Monte Carlo Simulation of ATRP with Bifunctional Initiators

A dynamic Monte Carlo model was developed to simulate ATRP with bifunctional initiators in a batch reactor. Model probabilities were calculated from polymerization kinetic parameters and reactor conditions. The model was used to predict monomer conversion, average molecular weight, polydispersity and the complete CLD as a function of polymerization time. The Monte Carlo model was compared with simulation results from a mathematical model that uses population balances and the method of moments. We also compared polymerizations with monofunctional and bifunctional initiators to illustrate some of the advantages of using bifunctional initiators in ATRP. In addition, we used the model to investigate the effect of the control volume and several polymerization conditions on simulation time, monomer conversion, molecular weight averages and CLD. Our results indicate that computational times can be reduced without sacrificing the quality of the results if we run several simulations with small control volumes rather than one single simulation with a large control volume.

     

Dynamic Monte Carlo Simulation of ATRP in a Batch Reactor

A dynamic MC model was developed to simulate the polymerization kinetics and the detailed microstructure of copolymers made with ATRP in a batch reactor. The model was used to predict monomer conversion, average molecular weight, polydispersity index, and copolymer composition as a function of polymerization time. The model can also predict the distribution of molecular weight, chemical composition, and comonomer sequence length at any polymerization time or comonomer conversion. The simulation was used to explore the effects of rate constants and reactant stoichiometry on the microstructure of chains. Two copolymerization systems were chosen to demonstrate the effect of reactivity ratios and comonomer feed compositions on the final chemical composition distribution.

     

基于格子链的缩聚反应的动态Monte Carlo模拟

采用描述自回避格子链的键长涨落模型, 以动态Monte Carlo方法对AB型单体的线型缩聚反应动力学过程进行了模拟. 通过该方法可以得到反应过程中链的瞬时构象, 还可以得到反应程度、聚合度、分子量分布及其随时间的演化. 模拟得到了合理的结果, 同时验证了无规线团尺寸与平均链长的标度关系, 表明该方法用于研究逐步聚合反应过程是可行的, 并且与一般的研究聚合反应的Monte Carlo方法相比, 还能够同时得到构象等空间信息. 还比较了不同大小的模拟体系所得到的分子量和多分散系数的异同, 讨论了有限元胞效应.     

嵌段序列对聚合物囊泡形成过程影响的Monte Carlo模拟

采用Monte Carlo模拟方法研究了具有相同链长和组分比的不同嵌段序列的AB两嵌段共聚物与ABA三嵌段共聚物在选择性溶剂中形成囊泡的动力学过程. 模拟结果表明, AB两嵌段共聚物囊泡的形成与ABA三嵌段共聚物囊泡的形成的动力学过程不同. 在慢速退火条件下, ABA三嵌段共聚物囊泡是通过亲水链段向胶束的表面和中心扩散而形成的, 而AB两嵌段共聚物囊泡则由片层弯曲闭合而形成. 相对而言, 退火速度对AB两嵌段共聚物囊泡形成的动力学过程没有显著影响, 其改变仅影响亲水链段与疏水链段发生相分离的难易程度. 当退火速度较快时, 亲水链段和疏水链段发生相分离的速度较快且相分离发生在囊泡形成之前; 而当退火速度较慢时亲水链段和疏水链段之间的相分离在囊泡形成之后仍在进行.     

Monte Carlo Study of Heteroarm Star Copolymers in Good and Selective Solvents

Lattice Monte Carlo simulations of conformations of hereroarm star copolymers A_nB_n in selective solvents were performed using a special variant of the Siepman and Frenkel algorithm. The effects of solvent quality, the number and lengths of blocks on the collapse of the insoluble block A, segregation of the two types of blocks and the behavior of the soluble blocks B were studied mainly for “hairy” stars containing high numbers of long arms. The simulation shows that insoluble blocks collapse in strongly selective solvents and the gravity centers of soluble and insoluble blocks separate which suggests the possibility of the formation of non‐spherical structures.

Snapshots of star a in a very bad solvent (T = 3.00) for blocks A. There are two different views of the star with a total number of arms f = 16 and number of segments N = 300.     

Stereocomplex Crystallization in Asymmetric Diblock Copolymers Studied by Dynamic Monte Carlo Simulations

Stereocomplex crystallization in asymmetric diblock copolymers was studied using dynamic Monte Carlo simulations, and the key factor dominating the formation of stereocomplex crystallites(SCs) was uncovered. The asymmetric diblock copolymers with higher degree of asymmetry exhibit larger difference between volume fractions of beads of different blocks, and local miscibility between different kinds of beads is lower, leading to lower SC content. To minimize the interference from volume fraction of beads, the SC formation in blends of asymmetric diblock copolymers was also studied. For the cases where the volume fractions of beads of different blocks are the same, similar local miscibility between beads of different blocks and similar SC content was observed. These findings indicate that the volume fraction of beads of different blocks is a key factor controlling the SC formation in the asymmetric diblock copolymers. The SC content can be regulated by adjusting the difference between the contents of beads of different blocks in asymmetric diblock copolymers.     

Adsorption Behavior of Asymmetrical Triblock Copolymers at the Solid‐Liquid Interface by Monte Carlo Simulation

Summary: Monte Carlo simulation on a simple lattice model has been used to study the adsorption of asymmetrical triblock copolymers from a non‐selective solvent at the solid‐liquid interface. The size distributions of train, loop and tail configurations for those copolymers are obtained as well as other details of the adsorption layer microstructure. Also the influence of adsorption energy and the role of molecular symmetry are investigated. A segment‐density profile, the adsorption amount, the surface coverage, and the adsorption layer thickness have been determined. Finally, it is shown that the adsorption behavior of an asymmetrical copolymer can be predicted from the symmetrical copolymer.

Size distributions of the tail configuration for A_8−kB₂₀A_k.     

环形嵌段共聚物的胶束化行为模拟简

利用Monte Carlo模拟,对比了相同组成下环形二嵌段共聚物AB和线形三嵌段共聚物ABA在选择性溶剂中的胶束化行为. 结果发现,相同链组成的环形和线形嵌段共聚物的临界胶束浓度(cmc)的差别与A嵌段的比例(fA)及B嵌段间的吸引强度(ε)密切相关. 在fA较小、ε较大的情况下,相应环形嵌段共聚物的cmc值更小;而在fA较大、ε较小的情况下,线形嵌段共聚物的cmc值更小. 为了进一步理解胶束化行为同fA及ε的关系,计算了胶束化过程中熵和势能部分对自由能的贡献. 结果表明,在所研究的fA和ε范围内,环形嵌段共聚物形成胶束时的熵损失更小,因而从熵贡献角度来看,环形嵌段共聚物更易发生胶束化. 而从势能贡献角度来看,当fA较小、ε较大时,环形嵌段共聚物形成胶束时势能有较大程度的降低,对自由能的贡献更大,因而此时环形嵌段共聚物更易发生胶束化. 而当fA较大、ε较小时,线形嵌段共聚物形成胶束时势能有较大程度的降低,对自由能的贡献更大,因而此时线形嵌段共聚物更易发生胶束化. 由此可见,对体系的胶束化自由能进行系统分析,有助于更好地理解环形和线形嵌段共聚物的胶束化行为.     

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.     

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.     

自由基聚合反应的Monte Carlo模拟方法

本文将化学反应动力学的MonteCarlo模拟方法运用到引发剂引发的自由基聚合反应的非稳态动力学,针对自由基聚合反应动力学数值模拟所特有的"无伸缩问题",采用"偏倚抽样法"解决了MonteCarlo模拟中的"无伸缩问题",模拟结果与非稳态动力学解的结果完全一致,此算法易推广到研究更复杂的自由基聚合反应体系。