端基被平面壁吸附的高分子链的Monte Carlo研究

运用Monte Carlo方法研究了端基被无限大平面壁吸附的线型无规飞行链的末端距矢量R的分布P(R)和链的形状,计算了末端距矢量R与z轴（垂直于平板）的夹角θ,链的最大主轴L3与z轴的夹角α,以及R与L3的夹角β的平均值 <θ>、<α>、<β>和各自的分布.得到如下结论： 　　1.端基吸附的高分子链的均方末端距≈(4/3)n,末端距矢量的径向分布为非高斯型,P(R)dR=2A4exp(－A2R2)R3dR,其中n为链长,A2=3/(2n).表明链受到限制后,较小的末端距R的分布概率减小,而较大的R的分布概率增大,导致链变得较为伸展. 　　2.角θ的平均值 <θ>≈45°,分布为P(θ)dθ =sin2θdθ ,表明吸附高分子链的末端极少处于平面附近,即平面对高分子链具有排斥作用 .但角α的平均值 <α>≈55.5°,分布近似为P(α )dα =sinαdα,均与自由链的情况相近,表面平面对最大主轴L3的方向的影响不大. 　　3.端基吸附的高分子链的末端距矢量R与最大主轴L3之间有较强的关联,它们的夹角β的平均值 <β>≈27°,其分布的峰值所对应的β值约为 10°. 　　4.吸附高分子链的形状更偏离球形,形状因子:: 约等于1:2.73:12.5.     

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     

高分子链构象性质和溶解性的Monte Carlo模拟

运用Monte Carlo方法对线型高分子链格点模型的构象进行了模拟,研究了单链体系的构象的尺寸（采用均方末端距,均方回转半径来表征）、形状（采用平均非球形因子来表征）和溶解性随溶剂与链段间相互作用能的变化情况.结果表明,、和随着εPS的增大而减小,具有相同的变化规律;随着Δε增大,溶剂变得越来越不利于溶解,高分子链的形状蜷曲为椭球形,高分子线团相互穿插交叠.     

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.     

高分子动态Monte Carlo模拟的协同运动算法

在高分子动力学的研究中 ,动态 Monte Carlo模拟发挥了重要的作用 [1] .动态 Monte Carlo模拟的关键是选择具有物理真实性的高分子运动算法 .目前广为采用的算法是经 Hilhorst和 Deutch[2 ] 修正的 Verdier- Stockmayer算法 [3] 以及 Carmesin和 Kremer等的键长涨落算法 [4 ] ,陆建明和杨玉良曾提出一种高分子动态算法 [5] ,在他们的算法中很长一段链节可能作蛇行运动 ,但是冯捷等 [6 ] 指出这种运动模式不满足微观可逆性条件 .本文对该运动模式进行修正 ,得到一种协同运动算法 ,并对其动力学行为进行检验 .1　算　法在平面正方形格子…     

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.     

Monte Carlo模拟研究高分子单链在基体中扩散的拓扑效应

高分子流体的性质同高分子的链结构及其动力学行为密切相关. 在高分子共混物中,共混组分的性质不仅依赖于自身的拓扑结构,还受到其它组分分子拓扑的影响. 本文中采用基于格子模型的Monte Carlo模拟方法研究了在高分子基体中扩散的4种不同拓扑组合（环形或线形高分子链）体系中目标单链的静态和动态性质. 结果发现,环形目标单链的性质受基体分子拓扑结构的影响要大于线形目标单链;其中环/线这一拓扑组合中目标单链的扩散机理相比其本体已经发生了较大改变,链末端在其中起了重要作用. 此外,我们对引起这一现象出现的可能原因做了分析.     

Adsorption Transition of a Polymer Chain at a Weakly Attractive Surface: Monte Carlo Simulation of Off‐Lattice Models

A bead‐spring model of a polymer chain with one end attached to a wall is studied by Monte Carlo simulations for chain lengths 16 ≤ N ≤ 256. Two types of adsorption potentials, 9‐3 and 10‐4 Lennard‐Jones (LJ) potentials, between the effective monomers and the wall are assumed. For both cases the adsorption transition where the chain changes its asymptotic statistical properties from a three‐dimensional to a two‐dimensional configuration is located using a scaling analysis. It is shown that the crossover exponent φ = 0.50 ± 0.02 is the same for both LJ potentials. This value is compatible with recent theoretical predictions and simulation results for lattice models with short‐range wall potentials. The results of our study support the expectation that the exponents describing the adsorption transition are universal, i.e., they are not influenced by the precise form and the long‐range character of the adsorption potentials used. The technical aspects of the simulations (which use configurational bias methods as well as histogram re‐weighting) are also carefully discussed.

Snapshot pictures of a bead‐spring model of a polymer chain with N = 256 beads with one end anchored on the surface: (a)“mushroom configuration”, (b) ε_a ≈ ε_w at the adsorption transition, and (c)“pancake configuration” of a strongly adsorbed chain.     

Monte Carlo Simulation of Polymer Reactions at Interfaces

Adhesion of immiscible polymers during two‐component injection moulding may be improved by transreactions of properly functionalised components. We performed MC simulations based on the three‐dimensional coarse‐grained bond fluctuation model (BFM) including a thermal interaction potential in with energy to characterise the behaviour of several selected types of chemical reactions, which are governed by activation energies of E_A = 0, 1, 3 and 5 k_BT. The consumption of reactive monomers for all the reactions in the time interval below the Rouse time τ_R exhibits a typical crossover from a kinetic‐controlled to a diffusion‐controlled behaviour and can be described by a bimolecular kinetic ansatz.

     

Monte Carlo Simulation of Thin Film Polymer Melts

We present Monte Carlo simulation data on conformations and dynamics of polymer melts confined in narrow slits of different widths and compare with data of bulk systems. We find that in confined geometries the chains swell laterally; they retain and even expand their spatially long-range correlations compared to bulk polymers and in contrast to the assumption of a complete screening of excluded volume. Long chains in bulk melts show entangled dynamics with a clear signature of a t^1/4-power law for the mean square displacements of innermost monomers at intermediate time scales. This behavior is gradually lost by confining the melts in slits with decreasing width. For ultra-thin films, the dynamics appears to follow a Rouse-like behavior over the entire subdiffusive regime. However, the terminal relaxation time is significantly increased compared to Rouse relaxation. This interesting observation was not reported previously and is the focus of our ongoing research.     

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.

     

二维三角格子上高分子动态 Monte Carlo模拟的协同运动算法

在动态Monte Carlo模拟的协同运动算法中,几个相邻的链节可以同时运动,这可以理解为高分子链中张力的作用引起的协同运动。将这一算法用于二维三角格子模型上RW链和SAW链的模拟。结果表明RW链的动力学行为符合Rouse理论,说明说明该算法可以用于高分子动力学研究,其优点是不需要使用键长涨落模型。     

Monte Carlo Simulation of Phase Behavior of Polymer Blends with Special Interactions

The phase behavior of A–B-random copolymer/C-homopolymer blends with special interaction was studied by a Monte Carlo simulation in two dimensions. The interaction between segment A and segment C was repulsive, whereas it was attractive between segment B and segment C. The simulation results showed that the blend became two large co-continuous phase domains at lower segment-B component compositions, indicating that the blend showed spinodal decomposition. With an increase of the segment-B component, the miscibility between the copolymer and the polymer was gradually improved up to being miscible. In addition, it was found that segment B tended to move to the surface of the copolymer phase in the case of a lower component of segment B. On the other hand, it was observed that the average end-to-end distances (h) for both copolymer and polymer changed slowly with increasing segment-B component of the copolymer up to 40%, thereafter they increased considerably with increasing segment B component. Moreover, it was found that the h of the copolymer was obviously shorter than that of the homopolymer for the segment-B composition region from 0% to 80%. Finally, a phase diagram showing I phase and II phase regions under the condition of constant temperature is presented.     

分形表面上CO氧化反应的蒙特卡罗模拟

众所周知,人们在理想完好的单晶表面上的动力学研究已取得了很大的成功[1],然而对许多实际催化剂来说,传统催化理论和实验之间不符的情况仍然俯拾皆是．现在人们对造成这种情况的原因已经有了更加深入的认识：大量的实验事实表明,在表面催化反应体系中,不但催化剂表面具有复杂的分形结构,而且催化剂表面上的活性中心分布也具有复杂的分形特性[2]．“分形”是指那些具有分数维数的几何对象．这些对象往往是不规则的,不能用通常的欧氏几何来描述[3]．将分形引入催化科学中最早的是Pfeifer和Avnir等[4]人,至今已有近二十年的历史,现…     

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. k_p /k _tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.     

Preparation of End Grafted Polyacrylonitrile Brushes through Surface Confined Radical Chain Transfer Reaction

End grafted polyacrylonitrile (PAN) brush was prepared through surface initiated polymerization via the chain transfer process.The thiol-terminated monolayer and PAN brushes were characterized by FTIR,X-ray photoelectron spectroscopy(XPS),atomic force microscopy (AFM),ellipsometry and contact angle measurements etc.It is demonstrated that radical chain transfer reaction and surface initiated precipitate polymerization can used to prepare end-grafted polymer brushes.     

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.     

Understanding the Formation of Linear Olefin Block Copolymers with Dynamic Monte Carlo Simulation

Chain‐shuttling polymerization with dual catalysts has introduced a new class of polyolefins called olefin block copolymers (OBCs). A dynamic Monte Carlo model to describe the kinetics of chain‐shuttling copolymerization in a semi‐batch reactor is developed, and used it to study how the microstructure of OBCs with different numbers of blocks per chain evolves during polymerization. The model also describes how chain‐shuttling rate constants and concentration of chain‐shuttling agent affect populations of OBCs with different numbers of blocks per chain. These model predictions are useful to make OBCs with precisely designed microstructures.