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

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MC(JBW): Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules

Many of the most common molecular simulation methods, including Monte Carlo (MC) and molecular or stochastic dynamics (MD or SD), have significant difficulties in sampling the space of molecular potential energy surfaces characterized by multiple conformational minima and significant energy barriers. In such cases improved sampling can be obtained by special techniques that lower such barriers or somehow direct search steps toward different low energy regions of space. We recently described a hybrid MC/SD algorithm [MC(JBW)/SD] incorporating such a technique that directed MC moves of selected torsion and bond angles toward known low energy regions of conformational space. Exploration of other degrees of freedom was left to the SD part of the hybrid algorithm. In the work described here, we develop a related but simpler simulation algorithm that uses only MC to sample all degrees of freedom (e.g., stretch, bend, and torsion). We term this algorithm MC(JBW). Using simulations on various model potential energy surfaces and on simple molecular systems (n-pentane, n-butane, and cyclohexane), MC(JBW) is shown to generate ensembles of states that are indistinguishable from the canonical ensembles generated by classical Metropolis MC in the limit of very long simulations. We further demonstrate the utility of MC(JBW) by evaluating the room temperature free energy differences between conformers of various substituted cyclohexanes and the larger ring hydrocarbons cycloheptane, cyclooctane, cyclononane, and cyclodecane. The results compare favorably with available experimental data and results from previously reported MC(JBW)/SD conformational free energy calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1736–1745, 1998     

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.     

Size of a polymer chain in an environment of quenched chains

We perform high‐coordination three‐dimensional (3D) lattice simulations of a single chain of N monomers embedded in matrices of quenched chains, at different concentrations ρ, using pruned‐enriched Rosenbluth sampling. The partition function is well‐described by the expression, , where is a universal constant, and is the concentration dependent lattice connectivity constant. For sufficiently long chains, , we find that the radius of gyration R varies nonmonotonically with ρ; R decreases gradually from its unperturbed dimensions R₀ until , after which it increases relatively rapidly due to repulsion between monomers. Motivated by the similarity in the shape of the curves, and results on Gaussian chains, we successfully superpose all the simulation data onto a single master curve. Finally, we test the relationship , suggested by a Flory‐type scaling model, where ρ_c is the critical percolation threshold, and is a universal constant. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1611–1619     

Self‐entanglement of a single polymer chain confined in a cubic box

We study the self‐entanglement of a single linear polymer chain with N monomers confined to a cubic box (L × L × L) using the bond‐fluctuation lattice model and primitive path analysis. We probe chains with N between 30 and 750 and vary the degree of confinement L/R_g0 between 0.4 and 12, where R_g0 is the radius of gyration of an unconfined polymer. We find that the conformational properties R_g/R_g0 and L_p/R_g0, where L_p is the average primitive path length, collapse onto a single master curve as a function of the degree of confinement. In the strongly confined regime, L/R_g0 < 1, we find that R_g/R_g0 ～ (L/R_g0)^0.8 and (L_p/R_g0) ～ (L/R_g0)^?2. We verify that the simulation methodology used is quantitatively consistent with experimental data, and the Colby‐Rubinstein entanglement model for unconfined concentrated polymer solutions. The most significant difference between unconfined and confined systems is the variation of L_p with monomer density ?; L_p ～ ?^5/9, in the former, and L_p ～ ?^2/3, in the latter. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1283–1290     

Elastic behavior of ring polymer chains

In this article, the conformational properties and elastic behaviors of ring polymers in the process of tensile elongation are investigated with the Monte Carlo method and the bond fluctuation model. The ratio of the mean‐square diameter <d²> to the mean‐square radius of gyration <S²> increases with the elongation ratio, λ, and the instantaneous shape of ring polymers is more symmetric than that of linear chains in the process of tensile elongation. Here <d²> for ring polymers rather than the mean‐square end‐to‐end distance <R²> for linear polymers is defined as the average of squared distances between two segments separated by N/2 bonds, where N represents the total number of bonds. Local quantities, that is, the mean‐square bond length <b²> and the mean bond angle <θ> increase with λ, especially for short ring chains. The <d²> and <S²> have the same relationship with the chain length, N, that is, <d²> ～ N^1.130±0.020 and <S²> ～ N^1.160±0.013 for a different λ. Some thermodynamics properties are also addressed here. The average energy per bond <U> decreases with λ and the average Helmholtz free energy and elastic force f increase with λ, especially for short ring chains. Comparisons with linear chains are also made. These investigations may provide insight into the elastic behaviors of ring polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 223–232, 2005     

A scalable parallel Monte Carlo method for free energy simulations of molecular systems

We present a method of parallelizing flat histogram Monte Carlo simulations, which give the free energy of a molecular system as an output. In the serial version, a constant probability distribution, as a function of any system parameter, is calculated by updating an external potential that is added to the system Hamiltonian. This external potential is related to the free energy. In the parallel implementation, the simulation is distributed on to different processors. With regular intervals the modifying potential is summed over all processors and distributed back to every processor, thus spreading the information of which parts of parameter space have been explored. This implementation is shown to decrease the execution time linearly with added number of processors.     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Monte Carlo studies of tethered chains

Monte Carlo computer simulations of end-tethered chains grafted onto a hard wall have been performed. The chains were modeled as self-avoiding chains on a cubic lattice at athermal solvent conditions. The simulations spanned a wide range of chain lengths, N (100–1000, i.e., up to molecular weights of a few hundred thousands), and anchoring densities, σ (2 × 10⁻⁴ to 0.4), to properly chart the relevant parameter space. It is shown that the reduced surface coverage σ* = σπR is the most appropriate variable that quantitatively determines the mushroom, overlapping mushroom and brush regimes, where R_g is the radius of gyration of a free chain in solution. The simulation data are analyzed to determine the conformational characteristics and shape of the anchored chains and to compare them with the predictions of the analytical self consistent field theory. The strong stretching limit of the theoretical predictions is obtained only for σ* > 8. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:2449–2461, 2009     

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.     

Absorption and engulfing transitions in nanoparticle infiltration into a polymer brush: A monte carlo simulation

We study the structure of an infiltrating hard spherical nanoparticle into a polymer brush using extensive off‐lattice Monte Carlo simulations of a basic theoretical model. We show that as long as the spherical particle is coated with a surface layer that interacts attractively with brush monomers, it can penetrate deeply into a dense polymer brush near the grafting surface. The infiltration process contains two stages: diffusing nanoparticle absorbing onto the surface of the polymer brush and engulfing of the nanoparticle by polymer chains. After the nanoparticle fully immerses in the dense polymer brush region, the buoyant forces levels off because of symmetric repulsions that endows increasing nanoparticle mobility and encourages the second transition. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Elastic behavior of comb-like polymer chains

<正>Three-dimensional Monte Carlo simulations of comb-like polymer chains with various backbone lengths N_b,arm lengths N_a and arm densities m are carried out to study the elastic behavior of comb-like polymer chains.The radius of gyration,the shape factors and bond length in different cases during elastic process are calculated,and it is found that the comb-like polymer molecules with longer backbone or shorter arm are more close to linear chains.But the arm density m affects the chain conformation non-monotonously.Some thermodynamic properties are also studied.Average Helmholtz free energy and elastic force f all increase with elongation ratioλfor all chains.     

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.     

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。     

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.