Monte carlo study of a simple model for micelle structure

A simple lattice model for a micelle is formulated and studied by Monte Carlo numerical methods. Results are presented for aggregates of 20, 30, and 50 chain molecules. The density profiles are much broader than is usually assumed in conventional pictures of micelle structure and the average shape found to be distinctly aspherical.     

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.     

多嵌段高分子的溶解性和分子形状的蒙特卡罗研究

利用 Ｍｏｎｔｅ Ｃａｒｌｏ 方法模拟了两组分多嵌段高分子链在稀溶液中的行为,着重探讨了不同的嵌段长度对高分子性质的影响．研究中以自避的分子链为研究对象,分别考察了稀溶液中该分子链的溶解性、分子线团形状和嵌段单元的空间分布,与嵌段长度的关系．结果表明,在相同溶剂条件下,嵌段序列的长度对共聚高分子溶解性有较大影响,嵌段序列长度与溶解性能具有非单调的变化规律．该分子链在溶剂中的形状同样受到嵌段序列长度的影响．嵌段间的相互作用能的差别越大,则高分子的溶解性和形状对嵌段长度的依赖性就越显著     

Perturbed-chain equation of state for the solid phase

A perturbed chain equation of state for the solid phase has been derived. Although the equation is general with respect to intermolecular potential, we incorporate the Lennard-Jones potential in this work in order to compare results from the model with available Monte Carlo simulation data. Two forms of the radial distribution function for the hard-sphere solid chain reference state are used in the model. First, a theoretically rigorous approach is taken by using a correlation of actual solid-phase Monte Carlo hard-sphere chain data for the radial distribution function. This results in good agreement with the Monte Carlo data only at high density. Second, a simple extended-density approximation was used for the radial distribution function. This second approach was found to work well across the entire density range including the vicinity of the solid-fluid equilibrium.     

Monte Carlo-studium der reversiblen copolymerisation. I. Theorie,memøry-6 programm,anwendungen

The binary reversible copolymerization, taking into account the length of the terminal sequence, are studied by the Monte Carlo method. We discuss the theoretical model, the algorithm, and a FR?RAN program. Finally, the α-methylstyrene-methyl methacrylate copolymerization is studied by means of the proposed Monte Carlo model, and the results obtained are compared with those obtained using the Markov chain model and Wittmer's equations.     

Comparative molecular dynamics and Monte Carlo study of statistical properties for coarse-grained heteropolymers

Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nosé-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nosé-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nosé-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.     

A coarse-grained model and associated lattice Monte Carlo simulation of the coil-helix transition of a homopolypeptide

A new coarse-grained lattice model neglecting atomic details is proposed for the coil-helix transition and a new physical parameter is suggested to characterize a helical structure. In our model, each residue is represented by eight lattice sites, and side groups are not considered explicitly. Chirality and hydrogen bonding are taken into consideration in addition to chain connectivity and the excluded volume effect. Through a dynamic Monte Carlo simulation, the physical properties of the coil-helix transition of a single homopolypeptide have been produced successfully within a short computing time on the PC. We also examined the effects of the variation of chain configurations including chain size and chain shape, etc. A spatial correlation function has been introduced in order to characterize periodicity of a helical chain in a simple way. A propagation parameter and a nucleation parameter have also been calculated, which compares favorably with the results of the Zimm-Bragg theory for the coil-helix transition.     

Atomistic molecular-dynamics simulations of the size and shape of polyethylene in hexane at infinite dilution

Parameters characteristic of size and shape of single polyethylene chains consisting of 15-60 monomer units dissolved in hexane are calculated by use of molecular-dynamics simulations based on a fully atomistic representation of the system. Results are compared with corresponding calculations in vacuum as well as Monte Carlo simulations of coarse-grained chains. The major concern of the study is a careful check of actual limits and possibilities of atomistic simulations of global properties of polymers. As expected such simulations are still restricted to rather small chain lengths but are already large enough to obey the characteristics of polymer coils.     

Monte Carlo simulation and molecular theory of tethered polyelectrolytes

We investigate the structure of end-tethered polyelectrolytes using Monte Carlo simulations and molecular theory. In the Monte Carlo calculations we explicitly take into account counterions and polymer configurations and calculate electrostatic interaction using Ewald summation. Rosenbluth biasing, distance biasing, and the use of a lattice are all used to speed up Monte Carlo calculation, enabling the efficient simulation of the polyelectrolyte layer. The molecular theory explicitly incorporates the chain conformations and the possibility of counterion condensation. Using both Monte Carlo simulation and theory, we examine the effect of grafting density, surface charge density, charge strength, and polymer chain length on the distribution of the polyelectrolyte monomers and counterions. For all grafting densities examined, a sharp decrease in brush height is observed in the strongly charged regime using both Monte Carlo simulation and theory. The decrease in layer thickness is due to counterion condensation within the layer. The height of the polymer layer increases slightly upon charging the grafting surface. The molecular theory describes the structure of the polyelectrolyte layer well in all the different regimes that we have studied.     

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.     

Shielding effects in polymer-polymer reactions. II. Reactions between linear and star-branched chains with up to six arms

The shielding effect of surrounding arms and chains on the encounter probability of reactive sites located both at the end of a linear chain and at several positions along the arms of star-branched chains with up to six arms is calculated by means of exact enumeration of samples prepared by Monte Carlo simulation. The changes of parameters that characterize the size and the shape of chain configurations during the approach of reactive centers located at the end of the linear chain and at the center of the star are evaluated. In addition to this specific case, which represents the central reaction step in reversible addition-fragmentation chain transfer star polymerization following the Z-group approach, a general discussion is given on the chain-length dependence of shielding factors associated with distinct segment positions.     

Polymer-particle mixtures: depletion and packing effects

The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.     

Order parameters and molecular shapes of phosphonic acid dialkyl esters in a uniaxial hydrophobic environment. A theoretical study

The conformational behaviour of phosphonic acid dialkyl ester (PAE) molecules in a uniaxial hydrophobic environment was studied using the Monte Carlo method with the well-known Metropolis algorithm. The influence of the surrounding molecules on ordering processes of the intrinsic PAE molecules was taken into account by a molecular field. The intramolecular energy was calculated using 6–12 atom-atom and torsion potential functions. Conformations were analysed using torsion angle distributions, segment and bond order parameters. The order parameters of the C-H bonds are compared with experimental results of²H NMR. Further a general method of determining the effective shape of a molecule is presented. The shape is defined by probability distribution for finding atomic coordinates within volume elements during a Monte Carlo run. Thus the asymmetry of a molecule can be visualized. PAE molecules studied show a positive asymmetry in all cases.     

Monte Carlo Simulation of the Topology and Conformational Behavior of Hyperbranched Molecules: Pd–Diimine‐Catalyzed Polyethylene

A kinetic Monte Carlo model was developed to simulate the polymerization of ethylene with palladium–α‐diimine catalyst wherein hyperbranched molecules are formed through a chain‐walking mechanism. The total degree of branching and the distribution of short branches obtained with the model agree well with reported ¹³C NMR experimental results. Different chain topologies were generated by varying the probability of chain walking, P_w , which controls the competition between chain‐walking and monomer insertion. Molecular Monte Carlo simulations were subsequently conducted to study the conformations of isolated molecules (created by the kinetic Monte Carlo scheme) to relate molecular shape and topology. Our results provide evidence that the topology varies from predominantly linear with many short branches at low P_w to a densely branched, globular structure at high P_w . In contrast to experimental observations, our results for the molecular weight (N) dependence of the radius of gyration (R_g ∝ N^v) indicate that the branching topology has an effect on this relation, i. e., high‐P_w molecules have a smaller scaling exponent v. The simulated N‐dependence of the second virial coefficient exhibits a similar behavior. We also discuss the unusual conformational behavior of highly branched polymers obtained when P_w → 1.     

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.     

磁性高分子链的磁性质和构象性质的Monte Carlo模拟

采用退火 (Annealing)MonteCarlo方法 ,从高温到低温顺序模拟了简立方格点上考虑最近邻Ising相互作用的磁性高分子链在不同温度的磁性质和构象性质 .磁性高分子链在低温下存在自发磁矩 ,无限长链的临界温度Tc=1 77± 0 0 5J kB.在临界温度附近 ,高分子链经历了从伸展的无规线团到紧缩球体的塌缩相变 .对链的尺寸、形状、近邻数及能量的分析表明 ,高分子链的构象性质从温度Tc=1 77开始发生较明显的变化 ,这表明高分子Ising链的相变是Ising相互作用和链节运动协同作用的结果 .     

Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials

A coarse-grained residue-residue interaction potential derived from a statistical analysis of the Protein Data Bank is used to investigate the coil-to-helix transition for polyalanine. The interaction potentials depend on the radial distance between interaction sites, as well as the relative orientation of the sites. Two types of interaction sites are present in the model: a site representing the amino acid side chain, and a site representing a "virtual backbone," i.e., a site located in the peptide bond which accounts for backbone hydrogen bonding. Two chain lengths are studied and the results for the thermodynamics of the coil-to-helix transition are analyzed in terms of the Zimm-Bragg model. Results agree qualitatively and quantitatively with all-atom Monte Carlo simulations and other reduced-model Monte Carlo simulations.     

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。     

端基附壁高分子模型链的塌缩转变

借MonteCarlo和模拟退火方法研究了端基附壁高分子尾形链在不同温度下的形态变化 ,链的模型采用有最近邻相互吸引作用的自避行走 .计算机实验结果表明 ,对于端基附壁的高分子尾形链 ,与自由链一样 ,当温度逐渐降低时高分子链会发生从松散的无规线团到紧密球体的塌缩转变 .计算机模拟得到了端基附壁链的均方末端距及其分量 ,均方回转半径及分布随温度的变化 .由于刚性壁的影响 ,使得有限链长的高分子尾形链与自由链相比 ,其表示链尺寸 温度关系的曲线要稍低 .模拟还发现 ,在高温时壁对链形状的影响比较大 ,壁垂直方向上尺寸明显大于平行方向的尺寸 ,后者接近于自由链的尺寸分量 .然而 ,低于θ温度时 ,尤其是完全塌缩之后 ,壁对链形状的影响已经很小 .     

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.