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     

高分子链形状与尺寸关联的Monte Carlo模拟

运用MonteCarlo方法对线型高分子链格点模型的构型进行了模拟,研究了构型的尺寸(采用平方末端距R²,平方回转半径S²来表征)和形状(由非球形因子A表征)之间的关联.对任何长度的高分子链,其关联系数CA,R²和CA,S²均为正值,表明高分子链的形状与尺寸之间存在正关联,即尺寸小的构型其非球形因子A一般也小,反之尺寸大的构型其非球形因子A一般也大.关联系数CA,R²和CA,S²均随链长的增大而减小,近似地与链长的倒数(n^-1)成正比.研究还表明,关联系数的极限值(链长n很大时)与格点的类型无关,与链样本产生的方式也无关,但与链是否考虑排斥体积有关,考虑了排斥体积后,关联系数增大.     

Monte Carlo Simulation of Uniaxial Deformation of Polyethylene‐Like Polymer Glass: Role of Constraints and Deformation Protocol

The deformation of a glassy amorphous polymer has been simulated by Monte Carlo. A molecular model with constrained chemical bonds (rigid‐bond model) and one with chemical bonds represented by Gaussian springs (flexible‐bond model) have been compared. Furthermore, two different deformation protocols have been tested. Comparisons on the basis of stress–strain behavior, contributions of various interactions to stress and energy, evolution of density and distribution of dihedral angles, and of pair correlation functions show that both the introduction of constrained bonds and the deformation protocol influence the results dramatically. The results obtained using the flexible‐bond model, employing a deformation protocol in which all the monomers are displaced affinely with the box size, show the best agreement with experimental facts.

     

Monte Carlo方法在高分子科学中的应用

介绍了Monte Carlo方法的历史及其特点,并描述了它在现代高分子科学研究中的广泛应用情况,并对其前景作了一些展望。     

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.     

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star‐branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star‐branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.     

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 Coil-to-Globule Transition of Compact Polymer Chains: Role of Monomer Interacting

Coil-to-globule transitions are fundamental problems existing in polymer science for several decades; however, some features are still unclear, such as the effect of chain monomer interaction. Herein, we use Monte Carlo simulation to study the coil-to-globule transition of simple compact polymer chains. We first consider the finite-size effects for a given monomer interaction, where the short chain exhibits a one-step collapse while long chains demonstrate a two-step collapse, indicated by the specific heat. More interestingly, with the decrease of chain monomer interaction, the critical temperatures marked by the peaks of heat capacity shift to low values. A closer examination from the energy, mean-squared radius of gyration and shape factor also suggests the lower temperature of coil-to-globule transition.     

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 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.

     

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…     

Adsorption of Semiflexible Chains on Nanostriped Surfaces: Monte Carlo Simulations

Monte Carlo simulations were carried out to investigate the adsorption of semiflexible chains from a semidilute solution to substrates with periodic stripes of width w. The chains are made of fused N = 10 monomers of diameter σ interacting with each other through excluded volume interactions and with the stripes via a square‐well potential of depth ε and width σ. The surface coverage was found to increase upon increasing the chain stiffness and decreases on increasing the width of the stripes. At small w, more flexible chains are adsorbed than stiff chains. Analysis of the radius of gyration for the chains showed that when w < 8σ, the component along the stripe direction is significantly larger than the others. Orientational order parameter reveals that, for small w, chains have preference to align along the stripe direction.

     

高分子链超声裂解新的Monte Carlo算法

设计了一种新的Monte Carlo算法，在计算机上模拟了高分子链的超声裂解过程。首先根据Ovenall模型用遍历法对高分子链进行模拟断裂，随后进行倒接，进而反演了整个裂解过程。在获得大量模拟结果的基础上，分别研究了极限断裂次数的频率分布，最可几极限断裂次数与聚合度之间的关系，极限断片长度的平均分布，以及分子量多分散系数与裂解程度之间的关系。     

O—酰基—α—酮肟光分解反应的Monte Carlo处理

本文首次对光化学反应体系用Monte Carlo方法进行模拟处理。通过5个O-酰基-α-酮肟光分解反应的Monte Carlo模拟,可避免解析解中由于对吸收光强须采用一级近似求解动力学微分方程组,而造成拟合反应在后期产生与实验结果的偏差。     

水溶性高分子弱凝胶体系凝胶化过程的Monte Carlo模拟

为研究弱凝胶的形成过程,并把高分子弱凝胶用于三次采油,采用三维Monte Carlo模拟了高分子溶液凝胶化过程. 模拟预测了凝胶化开始的时间,得到了凝胶化过程中分子量分布的演化规律和胶团生长的三维图像. 发现生成溶胶与凝胶团的歧化过程,初始聚合物的浓度对能否形成凝胶至关重要,低于临界浓度不能形成凝胶. 模拟了凝胶化速度和聚合物浓度以及交联剂浓度的关系,并与粘度随凝胶化时间变化的实验结果进行比较, 结果表明, 聚合物浓度较高时,浓度对交联反应的影响减弱,这一趋势与实验结果相一致.     

Monte Carlo Study on Spontaneous Recoil of Confined DNA Chain

A part of a long DNA chain was driven into a confined environment by an electric field, while the rest remains in the higher-entropy region. Upon removal of the field, the chain recoils to the higher-entropy region spontaneously. This dynamical process was investigated by Monte Carlo simulations. The simulation reproduces the experimentally-observed phenomenon that the recoil of the DNA chain is initially slow and gradually increases in speed due to the presence of the confinement-entropic force. The results show that with increasing the dimension or decreasing the spacing of the nanopillars the recoil velocity of the DNA chain will increase. Further analysis suggests that the characteristic entropy per monomer in the confinement is proportional to the area fraction of the free part in the confinement.     

Elastic Behavior of Polymer Chains

The elastic behavior of the polymer chain was investigated in a three-dimensional off-lattice model. We sample more than 109 conformations of each kind of polymer chain by using a Monte Carlo algorithm, then analyze them with the non-Gaussian theory of rubberlike elasticity, and end with a statistical study. Through observing the effect of the chain flexibility and the stretching ratio on the mean-square end-to-end distance, the average energy, the average Helmholtz free energy, the elastic force, the contribution of energy to the elastic force, and the entropy contribution to elastic force of the polymer chain, we find that a rigid polymer chain is much easier to stretch than a flexible polymer chain. Also, a rigid polymer chain will become difficult to stretch only at a quite high stretching ratio because of the effect of the entropy contribution. These results of our simulation calculation may explain some of the macroscopic phenomena of polymer and biomacromolecular elasticity.     

嵌段高分子尾形链构象性质的Monte Carlo研究

基于简立方格点模型对AB两嵌段高分子尾形链的构象性质及其链节的空间分布进行了MonteCarlo模拟.结果表明,链的尺寸、形状和链节的空间分布等统计性质和B链节与平面壁之间的相互吸引能有关.随着B链节与壁之间的吸引能的增加,链的尺寸和形状均呈现出先下降后升高的变化趋势,而且B链节的比例越大,这种变化越明显.     

Kinetic Monte Carlo Studies on the Importance of the Reaction Scheme in Segmental Exchange of Copolymer Chains

Kinetic Monte Carlo studies (confirmed by integration of the corresponding differential equations) are used to demonstrate the fundamental differences between the two most often accepted schemes of segmental exchange. Modeling of reshuffling systems, originally composed of homopolymers of various , various mass distributions, and different compositions, is carried out until the equilibrium copolymers are obtained. It is shown that one of the schemes leads always to a random microstructure (Bernoulli statistics) whereas modeling of the other one indicates possibility of formation of all achievable distributions of comonomer units (from multiblock to nearly alternate). The concepts of the degrees of randomness and reshuffling are discussed and new definitions are proposed.

     

Monte Carlo模拟研究抗体-抗原复合物生长的标度行为

通过Monte Carlo模拟方法对抗体-抗原复合物在等活性和非等活性条件下生长的标度行为进行了研究. 模拟所用算法的有效性通过在等活性条件下的模拟结果与解析结果之间的一致性得以证明. 在模拟中, 主要考察了抗体-抗原复合物的数量分布函数、重均聚合度以及特征关联长度在临界点附近的标度行为, 给出相应的标度指数, 并以其检验溶胶-凝胶相变的广义标度律. 研究结果表明, 非等活性对抗体-抗原复合物的生长具有显著影响, 可为临床免疫分析提供相应的理论线索.