Test of athermal terms of activity coefficient models by Monte Carlo simulation with hard-core models

The infinite dilution activity coefficients of exactly athermal fluids were calculated by Monte Carlo simulation with hard-core models. The hard-core models used in this work were hard-sphere and hard-spherocylinder models. The Widom test particle method was adopted to calculate the residual chemical potentials of solutes in pure solvent and in pure solute solutions. The infinite dilution activity coefficients of solutes were obtained from the residual chemical potentials of solutes. The infinite dilution activity coefficients calculated by Monte Carlo simulation were compared with those of athermal terms in activity coefficient equations. Staverman–Guggenheim equation overestimates the activity coefficients. The deviations of activity coefficients increase with increasing the hard-core volume of solute. Flory–Huggins equation based on molar volume gives good results for the hard-spherocylinder systems. Elbro-FV equation gives good results for both the hard-sphere and hard-spherocylinder systems.     

Monte Carlo simulations for predicting the precision of results and for optimizing data acquisition schedules

Monte Carlo simulations can be used to determine the precision of an analytical method if the standard deviations of the component unit operations are estimated accurately. Alternative methods for estimating the standard deviation have been compared by evaluating the success of Monte Carlo simulations to predict the precision of a second-order rate constant determined by spectrophotometry and of an equivalent weight and acid dissociation constant determined by potentiometry. Monte Carlo simulation has also been used with simplex optimization to predict a data acquisition schedule which gives high precision in the equivalent weight determination. By comparison with a naive design, a 22-fold improvement was predicted. A 15-fold improvement was observed experimentally.     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.     

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.     

Dynamic Monte Carlo simulations of competition in crystallization of mixed polymers grafted on a substrate

Nowadays, preparation of poly(lactide) (PLA) with high content of stereocomplex crystallites (SCs) is receiving more and more attentions. The stereocomplex formation between enantiomeric poly(l ‐lactide) and poly(d ‐lactide) can efficiently improve the corresponding mechanical properties and thermal stability. In the current work, using dynamic Monte Carlo simulations, the microscopic mechanism of SC formation in grafted polymers was investigated. The increase in grafting density can lead to the enhancement of SC formation. On one hand, the miscibility between the chains of different types can be improved due to the grafting. On the other hand, the increase in grafting density can result in the higher degree of chain extension and the change in crystal nucleation and growth modes. The changes facilitate the stereocomplex formation. These findings not only provide an effective way to prepare PLAs with high content of SCs, but also reveal the underlying mechanisms controlling the SC formation. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 89–97     

Dynamics of polyethylene melts studied by Monte Carlo simulations on a high coordination lattice

A detailed comparison is made between the experiment, prior simulations by other groups, and our simulation based on a newly designed dynamic Monte Carlo algorithm, on the dynamics of polyethylene (PE) melts. The new algorithm, namely, noncross random two-bead move has been developed on a high coordination lattice (the 2nnd lattice) for studying the dynamics of realistic polymers. The chain length (molecular weight) in our simulation ranges from C40 (562 Da) to C324 (4538 Da). The effects of finite chain length have been confirmed and significant non-Gaussian statistics evidently results in nonstandard static and dynamic properties of short PE chains. The diffusion coefficients scale with molecular weight (M) to the −1.7 power for short chains and −2.2 for longer chains, which coincides very well with experimental results. No pure Rouse scaling in diffusion has been observed. The transitional molecular weight to the entanglement regime is around 1500 Da. The detailed mean square displacements of middle bead (g1) are presented for several chain lengths. The reptation-like slowdown can be clearly observed only above M ∼ 2400 Da. The slope 0.25 predicted by the theory for the intermediate regime is missing; instead a slope close to 0.4 appears, indicating that additional relaxation mechanism exists in this transitional region. The relaxation times extracted by fitting the autocorrelation function of end-to-end vectors with reptation model scale with M to 2.5 for long chains, which seemingly conflicts with the scaling of diffusion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2556–2571, 2006     

Melting behaviors of icosahedral metal clusters studied by Monte Carlo simulations

We present an atom‐resolved analysis method that traces physical quantities such as the root‐mean‐square bond length fluctuation and coordination number for individual atoms as functions of temperature or time. This method is applied to explain the temperature‐dependent behaviors of three types of Ni_N (N=12,13,14) clusters. The detailed studies for the three types of clusters reveal characteristics as follows: (a) as the temperature increases, all three types of clusters undergo two‐stage melting, irrespective of the existence of vacancy or adatom on the icosahedral surfaces, (b) the melting of icosahedral clusters with vacancy starts with vacancy hopping, which has not been observed for any type of small clusters (N<34), (c) the melting of the icosahedral clusters with adatom (N=14) is initiated by adatom hopping, followed by the site exchange between the adatom and surface atoms. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 380–387, 2000     

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.     

Monte Carlo study of the coil-to-globule transition of a model polymeric system

Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment–segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20–10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0–0.45k_BT, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and underwent a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties (“volume approximation”) is only valid for extraordinarily long chains [molecular weight of O(10⁹)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3651–3666, 2006     

Monte Carlo simulations of biomolecules: The MC module in CHARMM

We describe the implementation of a general and flexible Monte Carlo (MC) module for the program CHARMM, which is used widely for modeling biomolecular systems with empirical energy functions. Construction and use of an almost arbitrary move set with only a few commands is made possible by providing several predefined types of moves that can be combined. Sampling can be enhanced by noncanonical acceptance criteria, automatic optimization of step sizes, and energy minimization. A systematic procedure for improving MC move sets is introduced and applied to simulations of two peptides. The resulting move sets allow MC to sample the configuration spaces of these systems much more rapidly than Langevin dynamics. The rate of convergence of the difference in free energy between ethane and methanol in explicit solvent is also examined, and comparable performances are observed for MC and the Nosé-Hoover algorithm. Its ease of use combined with its sampling efficiency make the MC module in CHARMM an attractive alternative for exploring the behavior of biomolecular systems.     

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。     

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 a novel X-ray tube anode design

When energetic electrons are incident on high atomic number absorbers, a substantial fraction is back-scattered. This phenomenon is responsible for several undesirable effects in X-ray tubes, in particular a reduction in the X-ray output. The extent of this shortfall has been estimated by using Monte Carlo simulation to start electrons at increasing depth inside the anode, the results indicating that an output enhancement of nearly 50% could be achieved in principle if the electrons wasted in back-scatter events could be trapped inside a tungsten anode. To test this idea a further set of simulations were done for a novel anode geometry. Results showed that X-ray tube efficiencies might be substantially enhanced by this approach.     

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     

Positron backscattering from an Al target: analytical calculation and Monte Carlo simulation

Positron backscattering coefficients are analytically calculated and numerically simulated for an Al target in the positron energy range 0.50–4 keV and for incident angles between 0° and 80° . The differential elastic scattering cross section has been obtained using the Bentabet and Bouarissa approximation (Phys. Lett. 2006; A 355: 390). Both the analytical and simulated results show good agreement with the experiment and previous theoretical work. Copyright © 2007 John Wiley & Sons, Ltd.     

Three-dimensional Molecular Geometry of PEG Hydrogels by an “Expansion-Contraction” Method through Monte Carlo Simulations

Three-dimensional(3-D) coarse-grained Monte Carlo algorithms were used to simulate the conformations of swollen hydrogels formed by copper(I)-catalyzed azide-alkyne cycloaddition(Cu AAC). The simulation consists of three successive steps including diffusion, cross-linking and relaxation. The cross-linking of multifunctional reaction sites is simulated instantly followed by fast crosslinking. In order to explore the validity of this approach pristine poly(ethylene glycol)(PEG) hydrogels with tri- and tetra-functional reaction sites(G3 and G4 respectively) were prepared and characterized. The data from the simulations were found to be in good agreement with experimental results such as PEG lengths between crosslinks, pore volume and pore radius distribution, indicating the validity of the modeling algorithm. The calculated PEG lengths in G3 and G4 networks are close(≈ 4.6 nm). The 3-D visual topological structure of the hydrogel network suggests that the "ideal" hydrogel is far from cubic, diamond or any well defined structures of regular repeating cells.     

Monte Carlo model of the temperature rise at a GaAs surface under an electron beam

Scanning electron microscopy (SEM) has frequently been used to study semiconductor materials. It offers the possibility of obtaining reliable qualitative and quantitative information on relevant local material parameters. The temperature rise due to electron‐beam bombardment can influence some semiconductor parameters, which then will influence the SEM information. In this work we propose a model calculation based on the Monte Carlo (MC) method to calculate the temperature rise due to electron‐beam heating. The results show that the temperature rise increases with increasing numbers of electrons (electron‐beam current), and the inverse behavior is observed with respect to the electron energy (electron‐beam voltage). The decrease in temperature rise with depth is also obtained. Copyright © 2006 John Wiley & Sons, Ltd.     

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.