Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Elastic behavior of uniform star polymer chains

Elastic behaviors of uniform star polymer chains with two to seven branches (namely, functionality f = 2-7) are investigated using Monte Carlo simulation and the bond fluctuation model. Here chain dimensions and thermodynamic properties of uniform star polymer chains during the process of tensile elongation are studied, and comparisons with linear chain are also made. Static properties of chains such as chain sizes and asphericities of chains are calculated, and g-value of g = 〈S²〉_star/〈S²〉_linear decreases with elongation ratio increasing for different functionality f. Thermodynamic properties such as average energy 〈U〉, free energy per bond 〈A′〉 and elastic force F are also investigated during the process of tensile elongation. In the meantime, scatting functions P(q) are calculated for star polymer chains with different functionality f. Additionally, we also discuss the influence of elongation ratio on scattering form factor. The impenetrability of the star cores is known to cause a discontinuity in the osmotic pressure showed through a peak in the scattering functions, and some different behaviors in the tensile process for uniform star chain are obtained.     

Monte Carlo simulations and analysis of scattering from neutral and polyelectrolyte polymer and polymer-like systems

Methods for analyzing small-angle scattering data from complex liquids with particles with many internal degrees of freedom have progressed substantially during the past years. This is mainly due to the use of Monte Carlo simulation techniques for obtaining scattering functions and the use of an approach in which the obtained scattering functions are subsequently parameterized, so that they can be used for data fitting. The present paper reviews recent applications of the Monte Carlo technique for obtaining parameterized scattering functions, and the application of these with emphasis on semiflexible polymers and wormlike micelle systems with and without electrostatic interactions.     

Influence of Rigid Side Chain Attraction on Stiffness and Conformations of Comb Copolymer Brushes Strongly Adsorbed on a Flat Surface

The influence of side‐chain attraction on the conformational properties of two‐dimensional polymer brushes with rigid side chains is investigated using Monte Carlo simulations. Using a rigid backbone, a characteristic interaction strength is determined by investigating the critical interaction energy for the collapse of the side chains onto the backbone. For a flexible backbone, the persistence length of the backbone is found to decrease with increasing attraction, irrespective of whether side‐chain flipping is allowed or not. This result is in good agreement with the theoretical modeling presented before. If side‐chain flipping is allowed, the attraction between the side chains leads to aggregation of successive side chains at one side of the backbone resulting in a characteristic local spiraling of the backbone.     

交联聚丙烯酰胺溶液染色研究

采用显微镜研究了预交联聚合物凝胶溶液的染色过程,结果表明由于静电作用,亚甲基蓝溶液中阳离子基团与凝胶颗粒中的阴离子基团相互作用形成一种深蓝色的缔合物;交联聚物线团也可以与亚甲基蓝分子形成深蓝色的缔合物,使交联聚合物线团显色,能够直接观测到交联聚合物线团在溶液中的形态。采用扫描电镜、动态光散射、流变仪和岩心封堵实验研究了染色后交联聚合物的线团形态尺寸和溶液的流变性、封堵特性。结果表明,染色后的交联聚合物线团仍是几百纳米左右的在水中分散的球形体,在形态和尺寸上与未染色的交联聚合物溶液没有发生较大的变化;染色后交联聚合物溶液在一定剪切速率范围内表现为胀流性和负触变性。     

平行板间高分子链构象熵的动力学Monte Carlo模拟

用动力学Monte Carlo方法模拟了受限于两平行板之间的高分子链,并用扫描法计算了链的构象熵S,研究了构象熵相对于自由链的减小量（S0-S）与平行板间距D和高分子链长n的关系.结果证实了de Gennes的自由能标度关系,并给出了标度关系适用的范围.当D非常小时,高分子链受到强烈限制,S0-S与n成正比,表明单链节受到平行板的平均排斥作用力与链长无关.随着D增大,平行板对构象熵的影响越来越弱,单链节受到平行板的平均排斥作用力随链长的增长而增大.当D比较大时,平行板对构象熵的影响近似可以忽略,高分子链构象熵与自由空间中的结果一致.     

A novel approach to the calculation of the free energy due to molecular flexibility

The contribution of the molecular flexibility to the solvation excess free energy is expressed in terms of probabilities of reaching hard limits on intramolecular coordinates in a series of calculations successively relaxing those limits. Numerical tests on the harmonic oscillator are also presented and used to make suggestion about computational issues.     

One‐ and Two‐Component Bottle‐Brush Polymers: Simulations Compared to Theoretical Predictions

Scaling predictions for bottle‐brush polymers with a rigid backbone and flexible side chains under good solvent conditions are discussed and their validity is assessed by a comparison with Monte Carlo simulations of a simple lattice model. It is shown that typically only a rather weak stretching of the side chains is realized, and then the scaling predictions are not applicable. Also two‐component bottle brush polymers are considered, where two types (A,B) of side chains are grafted, assuming that monomers of different kind repel each other. In this case, variable solvent quality is allowed. Theories predict “Janus cylinder”‐type phase separation along the backbone in this case. The Monte Carlo simulations, using the pruned‐enriched Rosenbluth method (PERM) give evidence that the phase separation between an A‐rich part of the cylindrical molecule and a B‐rich part can only occur locally. The correlation length of this microphase separation can be controlled by the solvent quality. This lack of a phase transition is interpreted by an analogy with models for ferromagnets in one space dimension.

     

Free energy and dimensions of macromolecules under confinement in layered assemblies

The changes in the free energy ΔA accompanying penetration of polymer solutions from bulk into slit-like cavities were determined by lattice simulations. In dilute solutions the thermodynamics of penetration is controlled mainly by the parameter ϵ_w specifying interaction between polymer and walls of repulsive or adsorptive cavities. However, the magnitude of |ΔA| is substantially reduced by increasing concentration ∅︁ in bulk solution. Furthermore, compression of chains by concentration in good solvents and adsorptive cavities was found to be larger in the slit then in the bulk. At intermediate confinement, a region of a minimum coil size was observed at all concentrations and attraction strengths, where molecules are squeezed along all three axes.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Computer simulations of ligand–protein binding with ensembles of protein conformations: A Monte Carlo study of HIV‐1 protease binding energy landscapes

We present the results of molecular docking simulations with HIV‐1 protease for the sb203386 and skf107457 inhibitors by Monte Carlo simulated annealing. A simplified piecewise linear energy function, the standard AMBER force field, and the AMBER force field with solvation and a soft‐core smoothing component are employed in simulations with a single‐protein conformation to determine the relationship between docking simulations with a simple energy function and more realistic force fields. The temperature‐dependent binding free energy profiles of the inhibitors interacting with a single protein conformation provide a detailed picture of relative thermodynamic stability and a distribution of ligand binding modes in agreement with experimental crystallographic data. Using the simplified piecewise linear energy function, we also performed Monte Carlo docking simulations with an ensemble of protein conformations employing preferential biased sampling of low‐energy protein conformations, and the results are analyzed in connection with the free energy profiles. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 73–84, 1999     

Monte Carlo simulations of a liquid crystal copolymer in the solid state

The condensed phase of the alternating copolyester of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) is investigated by studying the room temperature packing arrangement of the copolymer chains. A molecular modeling methodology is employed with a Monte Carlo sampling of the configurational phase space. Realistic poly(HBA-alt-HNA) polymer chains are represented by an explicit atom representation of the HBA/HNA dimers. States are sampled from the NVT ensemble using a sampling scheme consisting of (1) valence and torsional variations, (2) rigid body rotations of the chain about the chain axis, and (3) rigid body translations of the chain. The effect of chain packing on the conformation of chains, as well as the relative intra- and intermolecular orientations of aromatic rings, is investigated. Correlation of chain positioning along the chain axis is dominated by aromatic rings maintaining a center-to-center plane of registry. These layers of aromatic units pack with a preference for edge-to-face orientations in a herringbone-type pattern and have an intermolecular ring angle between the pairs of aromatic rings in the unit cell that is ca. 68°. The aromatic rings, on average, are rotated 38° out from the b–c plane. The phenylene rings of these copolyesters are less restricted in their relative orientation in comparison to the naphthalene rings. Intramolecular orientational probability density distributions indicate a preference for staggering the successive aromatic rings along the chain, with a staggering angle of ca. 66°. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 727–741, 1998     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

A new formula for the entropy of mixing in polymer systems and free volume

The famous equations of Flory-Huggins for the entropy of mixing with one highmolecular component are of great importance for polymer physics. But Gujrati stated in 1980 [12] that these equations cannot be exact. This is why we derived a new formula for the dependence of the entropy from the fraction of vacant sites in a quasi-lattice. It differs significantly from that of Huggins and still more from that of Flory in the case of low free volume. The equations of Flory-Huggins are correct with reference to low polymer content only.If our formula for entropy is used instead of that of Huggins an important result of the theory of Gibbs-DiMarzio is called in question. The increase of thermal expansion at the glass transition cannot be explained by an increase of vacant sites. A growth of the number of unoccupied sites according to the thermodynamic equilibrium condition would bring about a far too great thermal expansion coefficient. From estimations of the energy of interaction between polymer molecules, which can be found in literature, it follows that the increase of entropy is far too small to enable the formation of vacant sites above the glass transition. It is unambiguously shown that the free volume, commonly regarded to be the decisive quantity with respect to glass transition, cannot consist of holes as considered in the quasi-lattice model and in many theoretical treatments.     

Monte Carlo simulation of miscibility of polymer blends with repulsive interactions: effect of chain structure

The effects of the chain structure and the intramolecular interaction energy of an A/B copolymer on the miscibility of the binary blends of the copolymer and homopolymer C have been studied by means of a Monte Carlo simulation. In the system, the interactions between segments A, B and C are more repulsive than those between themselves. In order to study the effect of the chain structure of the A/B copolymer on the miscibility, the alternating, random and block copolymers were introduced in the simulations, respectively. The simulation results show that the miscibility of the binary blends strongly depends on the intramolecular interaction energy () between segments A and B within the A/B copolymers. The higher the repulsive interaction energy, the more miscible the A/B copolymer and homopolymer C are. For the diblock copolymer/homopolymer blends, they tend to form micro phase domains. However, the phase domains become so small that the blend can be considered as a homogeneous phase for the alternating copolymer/homopolymer blends. Furthermore, the investigation of the average end-to-end distance () in different systems indicates that the copolymer chains tend to coil with the decrease of whereas the of the homopolymer chains depends on the chain structure of the copolymers. As for the system containing the alternating or the random copolymers, the homopolymer chains also tend to coil with the decrease of . However, for the systems including the block copolymers, there is a slight difference in the of the homopolymer chains with the variation of .     

COMPUTER SIMULATION OF POLYMER SOLUTION THERMODYNAMICS

The statistical counting method for the computer simulation of the ther-modynamic quantities of polymer solution has been reviewed. The calculating results fora single athermal chain confirm the theory of the renormalization group. The results forthe athermal solution are consistent with the scaling law of the osmotic pressure with theexponent 2.25. The results for a single chain with the segmental interaction are in a goodagreement with the exact results obtained by the direct counting method. The results for a single chain with the segmental interaction are in a good agreement with the exact results obtained by the direct counting method.The results for the polymer solution show us that the Flory-Huggins parameter is strongly dependent on both the polymer concentration and the interaction energy between segments.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.