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     

Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

大分子固液界面吸附行为的数字模拟研究方法

介绍了随机数字模拟方法在研究链状大分子吸附行为的一般原理,以立方格子模型的自避行走为例,分析了模型的建立、初始位形的产生以及分子链运动的处理方法.回顾了随机数字模拟方法在研究大分子界面吸附行为方面的发展状况.预测了随机数字模拟方法在大分子吸附行为研究方面的应用前景.     

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.     

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.     

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.

     

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.     

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…     

高分子链构造、构型与构象的比对教学

高分子链的结构包括构造、构型、构象三个方面,涉及较多知识和内容.在"高分子物理"课程的教学中,将此三个概念放在一起进行比对,从不同角度考察彼此间的联系和差别,则更有利于深入理解这些概念的内涵,从而更好地掌握高分子链结构.本文选取四个视角来陈述相关内容,为编写"高分子物理"教材和进行课堂教学时参考.     

Properties of Star-Branched Polymer Chains Near a Surface

We considered two model systems of star-branched polymers near an impenetrable surface. The model chains were constructed on a simple cubic lattice. Each star polymer consisted of f = 3 arms of equal length and the total number of segments was up to 799. The excluded volume effect was included into these models only and therefore the system was studied at good solvent conditions. In the first model system polymer chain was terminally attached with one arm to the surface. The grafted arm could slide along the surface. In the second system the star-branched chain was adsorbed on the surface and the strength of adsorption was were varied. The simulations were performed using the dynamic Monte Carlo method with local changes of chain conformations. The internal and local structures of a polymer layer were determined. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. The lateral diffusion and internal mobility of star-branched chains were studied as a function of strength of adsorption and the chain length. It was shown that the behavior of grafted and weakly adsorbed chains was similar to that of a free three-dimensional polymer, while the strongly adsorbed chains behave as a two-dimensional system.     

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.     

Studies on the Adsorption of Asymmetrical Triblock Copolymers by Scheutjens-Fleer Theory and Monte Carlo Simulation

The adsorption of asymmetrical triblock copolymers from a non-selective solvent on solid surface has been studied by using Scheutjens-Fleer mean-field theory and Monte Carlo simulation method on lattice model. The main aim of this paper is to provide detailed computer simulation data, taking A8-kB20Ak as a key example, to study the influence of the structure of copolymer on adsorption behavior and make a comparison between MC and SF results. The simulated results show that the size distribution of various configurations and density-profile are dependent on molecular structure and adsorption energy. The molecular structure will lead to diversity of adsorption behavior. This discrepancy between different structures would be enlarged for the surface coverage and adsorption amount with increasing of the adsorption energy. The surface coverage and the adsorption amount as well as the bound fraction will become larger as symmetry of the molecular structure becomes gradually worse. The adsorption layer becomes thicker with increasing of symmetry of the molecule when adsorption energy is smaller but it becomes thinner when adsorption energy is higher. It is shown that SF theory can reproduce the adsorption behavior of asymmetrical triblock copolymers. However, systematic discrepancy between the theory and simulation still exists.The approximations inherited in the mean-filed theory such as random mixing and the allowance of direct back folding may be responsible for those deviations.     

Entropic Sampling of Free and Ring Polymer Chains

Summary: We extend Monte Carlo (MC) methods developed in our previous paper (J. Phys. A, Math. Gen. 2004 , 37, 1573) and based on entropic sampling within Wang‐Landau (WL) algorithm to the simulation of lattice and continuous models of ring polymers. For a continuous freely joined ring chain (an equilateral polygon) with hard sphere monomer units, the excess entropy of rings relative to the corresponding reference system, a phantom ring chain, is obtained. The excess specific entropy is calculated for a set of various diameters of monomer units d and chain lengths N. Its limiting values for ( ) are estimated for each d and coincidence with those for corresponding free chains is demonstrated. We also develop a WL approach to calculate thermal properties of free and ring continuous chains with an Lennard‐Jones attraction between nonbonded beads being added to hard core repulsion at fixed d. The obtained energy distributions provide calculation of canonical properties such as conformational energy, heat capacity, entropy, and mean square radius of inertia. Thermal results for free and ring chains are being finally compared. Analogous calculations are performed for lattice‐free chains and rings.

     

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.     

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。     

聚合物纳米复合体系中聚合物结构及动力学研究进展

从计算模拟及实验角度系统总结了聚合物结构、聚合物构象、聚合物扩散及聚合物多尺度动力学的研究进展,阐述了各影响因素及其变化规律,并对聚合物动力学的未来研究进行了展望.     

Monte Carlo Computer Simulation of a Single Semi-Flexible Macromolecule at a Plane Surface

Summary: The properties of a single semiflexible mushroom chain at a plane surface with a long-ranged attracting potential are studied by means of lattice Monte Carlo computer simulation using the bond fluctuation model, configurational bias algorithm for chain re-growing and the Wang-Landau sampling technique. We present the diagram of states in variables temperature T vs. strength of the adsorption potential, ε_w, for a quite short semiflexible chain consisting of N = 64 monomer units. The diagram of states consists of the regions of a coil, liquid globule, solid isotropic globule, adsorbed coil and cylinder-like liquid-crystalline globule. At low values of the adsorption strength ε_w the coil–globule and the subsequent liquid–solid globule transitions are observed upon decreasing temperature below the adsorption transition point. At high values of ε_w these two transitions change into a single transition from an adsorbed coil to a cylinder-like liquid-crystalline solid globule. We conclude that for a semiflexible chain the presence of a plane attracting surface favors the formation of a globule with internal liquid-crystalline ordering of bonds.     

氮气和氧气在膜表面和狭缝孔内平衡吸附的分子模拟

采用巨正则系综的MonteCarlo方法(GCMC)模拟常温(T=303K)下,氮气和氧气在具有狭缝状膜孔的碳膜内的吸附.气体分子之间、气体分子与膜原子之间的相互作用均采用Shifted-Lennard-Jones势能模型.研究了303K和10MPa下,不同膜厚度和膜孔宽度时氧气在膜面和膜孔内的密度分布以及303K和压力从1MPa到10MPa变化时,氮气和氧气在狭缝膜孔内超额吸附等温线.实验结果表明,膜孔端口效应显著,膜厚和膜孔宽度对孔内吸附影响较大,而膜构型对膜面吸附影响显著.     

Monte Carlo Studies on the Deformation Behavior of Entangled Polymer Chains

In this work we present a continuous three‐dimensional bond‐fluctuation model (CBFM) in combination with the method of confined self‐avoiding walks (CSAW). This method enables us to analyse both the compression and the stretching regime of the deformation process of two entangled polymer chains. We studied the deformation behavior in respect to the number of entanglements, the distance of the end monomers on the confining surfaces and the orientation of the entanglements to the deformation axis. Our analysis of the behavior of the force and the structural properties of the systems during the deformation process leads us to the assumption that the entanglements act as one topological crosslink with variable strength.