Elastic Properties of Semi-Flexible Chains and Networks

Summary: Elastic properties of noncharged polymers of stiffness ranging from flexible to rigid chains are determined from Monte Carlo simulations. The discrete wormlike chain (WLC) model with self-interacting units is applied to chains of intermediate lengths. Elastic free energy and the force-extension profiles of chains of variable stiffness are computed in an isometric ensemble. Occurrence of a plateau on the force-extension curves at intermediate chain stiffness is noted. Qualitative differences are found between force profiles from simulations and from the standard (ideal) WLC model. The single-chain data on influence of bending stiffness were employed in the three-chain model of networks. Stress-strain relations for networks show a highly nonlinear behavior with the marked strain-stiffening effect.     

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.     

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.

     

The Effect of Chain Architecture on the Dynamics of Copolymers in a Homopolymer Matrix: Lattice Monte Carlo Simulations using the Bond‐Fluctuation Model

Summary: The effects of copolymer sequence distribution on the dynamics of a copolymer in a homopolymer matrix are studied using computer simulations within the framework of the bond‐fluctuation model on blends containing low concentrations (10%) of copolymers dispersed in a homopolymer matrix. The sequence distribution of the two copolymer components was changed while maintaining the overall copolymer composition at 50/50. Our results indicate that copolymers with disordered sequence distributions exhibit dynamics that are faster than that of a homopolymer melt, while those with ordered sequence distributions exhibit a tendency to form aggregates that lead to slower dynamics as well as phase separation. Analysis of the structure suggests that copolymers with an alternating sequence distribution form large aggregates that are short‐lived, while diblocks form permanent micelle‐like structures. Analysis of the local composition around a copolymer molecule indicates that aggregation between copolymer chains has a direct impact on the local composition. This in turn has a significant impact on system dynamics. Our results indicate that the dynamics of random, random‐blocky, and alternating copolymers are nearly identical and are faster than that of a homopolymer melt. However, alternating copolymers form aggregates and hence are not uniformly distributed throughout the matrix phase. Thus, alternating copolymers are at a disadvantage in their ability to be effective compatibilizers. From a dynamic perspective, copolymers with random and random‐blocky copolymers seem to be ideal compatibilizers since they are distributed uniformly throughout the system and move rapidly through the matrix phase.

Snapshots of aggregates of alternating copolymer chains. Dark and bright spheres represent A and B monomers, respectively.     

Monte Carlo Simulations of the Phase Separation of a Copolymer Blend in a Thin Film

Monte Carlo simulations were carried out to study the phase separation of a copolymer blend comprising an alternating copolymer and/or block copolymer in a thin film, and a phase diagram was constructed with a series of composed recipes. The effects of composition and segregation strength on phase separation were discussed in detail. The chain conformation of the block copolymer and alternating copolymer were investigated with changes of the segregation strength. Our simulations revealed that the segment distribution along the copolymer chain and the segregation strength between coarse‐grained beads are two important parameters controlling phase separation and chain conformation in thin films of a copolymer blend. A well‐controlled phase separation in the copolymer blend can be used to fabricate novel nanostructures.     

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.

     

Preference Prediction for the Stable Inclusion Complexes between Cyclodextrins and Monocyclic Insoluble Chemicals Based on Monte Carlo Docking Simulations

Cyclodextrins (CDs) are useful functional excipients, which are being used to camouflage undesirable pharmaceutical characteristics, especially poor aqueous solubility, through the inclusion complexation process with insoluble drugs. The selection of more efficient cyclodextrin is important to improve the bioavailability of drugs. In this study, the complexing and solubilizing abilities toward poorly water-soluble monocyclic molecules of natural CDs (α-CD, β-CD, and γ-CD) were investigated using Monte Carlo (MC) docking simulations studies. These theoretical results closely agree with the experimental observation of the complex stability in water of the various guests–CD complexes. Host preferences, based on the experimentally determined stability constants between host CDs and guest molecules, show excellent correlation with the calculated interaction energies of corresponding complexes. The inclusion complex with the lower MC docking interaction energy shows a higher value of stability constant than that of the other complex, and the prediction accuracy of the preferred complex for 21 host–guest pairs is 100%. This result indicates that the MC docking interaction energy could be employed as a useful parameter to select more efficient cyclodextrin as a host for the bioavailability of insoluble drugs. In this study, β-CD shows greater solubilizing efficacies toward guest molecules than those of α-CD and γ-CD, with the exception of one case due to the structure of a guest molecule containing one lipophilic cyclic moiety. The surface area change of CDs and hydrogen bonding between the host and guest also work as major factors for the formation of the stable complex.     

Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles

Monte Carlo computer simulations were carried out on filled networks of poly(dimethylsiloxane) (PDMS), which were modeled as composites of crosslinked chains and randomly arranged spherical filler particles. The primary concern of the investigation was the effect of the excluded volume of these particles on the elastomeric properties of the polymers. Calculations were carried out for PDMS chains with different molecular masses between crosslinks, and for filler particles with different sizes and at various volume percentages. Distributions of end-to-end vectors for both unfilled and filled networks were obtained using Monte Carlo simulations based on rotational isomeric state (RIS) theory. More extended configurations, with a higher end-to-end distance, were observed for networks filled with smaller particles. The nominal stress f* and the modulus or reduced nominal stress [f*] were calculated from the distributions of end-to-end vectors using the Mark-Curro approach. Relatively small filler particles were found to increase the non-Gaussian behavior and to increase the normalized moduli above the reference value of unity. Temperature effects on the stress were also investigated. © 1996 John Wiley & Sons, Inc.     

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.     

Elastomeric Properties of Polysiloxane Networks. Bimodal Elastomers that are Spatially Inhomogeneous and Others that are Very Broadly Multimodal

End‐linking poly(dimethylsiloxane) was used to prepare bimodal elastomers networks so as to have inhomogeneous nanostructures, and also to prepare others having very broadly multimodal chain‐length distributions. Macroscopic phase separation, probably high crosslink density clusters, was observed to occur in some of the bimodal networks. The mechanical properties in simple extension and in equilibrium swelling were measured. The bimodal elastomers that were not obviously inhomogeneous showed very good mechanical properties, but the macroscopically phase‐separated networks, and the broadly multimodal network were weak. Analysis of the Mooney‐Rivlin profiles suggests that the reinforcing mechanism could have a structural component in addition to that from the limited extensibilities of the short chains. The mechanical properties and the extents of swelling support the cluster conjecture, in accord with previous morphological studies on spatially‐inhomogeneous polysiloxane elastomers.     

Thermo‐responsive gels in the presence of monovalent salt at physiological concentrations: A Monte Carlo simulation study

In this work, slightly charged thermo‐responsive gels in the presence of salt at concentrations close to physiological conditions have been simulated within a coarse‐grained model widely used in the last decade. These simulations allow differentiate charge and salt effects, which are antagonist and coupled in many real systems because the degree of ionization might depend on the electrolyte concentration. An analysis in terms of the different contributions to osmotic pressure is also presented, which highlights the role played by excluded volume effects. In addition, our results also permit us to test some predictions based on the ideal Donnan equilibrium, a common assumption made to justify the swelling behavior of gels and microgels in the presence of salt. More specifically, simulations show that, for the slightly charged gels simulated here, such an assumption overestimates the concentration of salt inside collapsed gels and underestimates the excess of osmotic pressure associated to the additional electrolyte. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1403–1411     

Computer Study of Stimuli-Responsive Polyelectrolyte Micelles in Aqueous Media. Comparison of Monte Carlo and Self-Consistent Field Approaches

The behavior of polyelectrolyte micelles with kinetically frozen hydrophobic cores in aqueous solutions was studied by Monte Carlo (MC) simulations and self-consistent field (SCF) calculations. Some results have already been published. The structure of water-soluble shells formed by weak polyelectrolytes, both pure and containing a low fraction of strongly hydrophobic units arranged either in a short sequence or distributed uniformly in the shell-forming chains was studied in detail. In the case of sequenced system, the analysis of concentration profiles of individual species reveals strong segregation and important self-organization of hydrophobic units in the shell. A comparison and critical analysis of results of MC and SCF methods is presented.     

Influence of charged intramolecular hydrogen bonds in weak polyelectrolytes: A Monte Carlo study of flexible and extendible polymeric chains in solution and near charged spheres

For weak polyelectrolytes, the interplay between pH, solvent properties, and polymer structure affects the amount of charges, their distribution, and hence their conformations via Coloumb repulsion. Attractive interactions can also develop between charged and neutral sites counteracting the expected Coulomb‐induced expansion. To gauge how such competition affects polyelectrolyte structure and ionization, the titration of a single polyelectrolyte chain, isolated or close to a charged sphere, mimicked with a novel many‐body potential model is simulated with Monte Carlo. Apart from showing a 10‐fold higher ionization than isolated monomers at low pH, interacting species contracted forming short‐range clusters of charged and neutral ionizable groups. The presence of a charged sphere synergically boosted both effects due to monomer interactions, forcing the chains to condense onto its surface at much lower pH. Structural properties, however, seem to be controlled only by the ionization degree despite the presence of the topological restraint represented by the spherical surface. Using Monte Carlo titration results, the equilibrium ionization of isolated chains is also estimated; the results evidence that even weak interactions can easily lead to a doubling of the total charge. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 650–663     

A Hundred‐Year‐Old Experiment Re‐evaluated: Accurate Ab Initio Monte Carlo Simulations of the Melting of Radon

State‐of‐the‐art relativistic coupled‐cluster theory is used to construct many‐body potentials for the noble‐gas element radon to determine its bulk properties including the solid‐to‐liquid phase transition from parallel tempering Monte Carlo simulations through either direct sampling of the bulk or from a finite cluster approach. The calculated melting temperature are 200(3) K and 200(6) K from bulk simulations and from extrapolation of finite cluster values, respectively. This is in excellent agreement with the often debated (but widely cited) and only available value of 202 K, dating back to measurements by Gray and Ramsay in 1909.     

A Monte Carlo Simulation of Homogeneous Crystallization in Confined Spaces: Effect of Crystallization Kinetics on the Avrami Exponent

Homogeneous nucleation in polymers and subsequent crystallization in spaces confined relative to spherulitic dimensions in one direction has been simulated for a wide range of nucleation and growth rates. An empirical equation based on simulation results relating an Avrami exponent of crystallization to growth and nucleation rates along with the characteristic dimension of crystallizing volume has been proposed. It was found that for ideal homogeneous crystallization, the Avrami exponent can be significantly lower than the anticipated values for free unconstrained growth; therefore, all crystallization conditions and parameters must be taken into account in order to make a conclusion on the character of the observed crystallization.

     

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.     

Computational Prediction for the Slopes of AL-type Phase Solubility Curves of Organic Compounds Complexed With α-, β-, or γ-cyclodextrins Based on Monte Carlo Docking Simulations

A Monte Carlo (MC) docking method was introduced in order to predict the aqueous solubility of inclusion complexes composed of small organic compounds and various cyclodextrins. The slope (S) of the A_L-type phase solubility curve was accurately predicted by a combination of the interaction energy and nonpolar solvation free energy for each of the docked complexes. The regression equation for S, the slope of the phase solubility curve gives a fine correlation coefficient, r ², of 0.913 and standard error of 0.028 for the 63 organic compounds complexed with cyclodextrins.