Excluded Volume Map Sampling Research Articles

Deformation modeling of polyamide 6 and the effect of water content using molecular dynamics simulation

Polyamide 6 (PA6) shows significant water absorbability and hygroscopicity, which affect its mechanical properties such as Young’s modulus and yield strength, as water content enhances deformability. This study aims to investigate the effect of water molecules on the deformation behavior of PA6 and to elucidate the deformation mechanism at a molecular level. By using excluded volume map sampling method, we explored the possible incursion sites for water molecule absorption in the computational material cell. Using molecular dynamic simulations, we created the computational cell of PA6, and we applied mechanical loadings with and without the water molecule to determine the effect of water molecules on the deformation behavior. To investigate the fundamental reasons why water molecules enhance the deformability of PA6, we calculated the non-bonded potential energy of a pair of amide functional groups with and without the water molecule. The results reveal that water molecules decrease the interaction energy of the amide group, leading to macroscopic deformation. This study clarified the effect of water molecules on the deformation behavior of PA6, and it may be useful for predicting the mechanical deformation of PA6.

Sorption and permeation of gases in hyper-cross-linked hybrid poly(POSS-imide) networks: An in silico study

Networked hybrid materials containing various types of organic imides covalently bonded with polyhedral oligomeric silsesquioxanes (POSS) have recently been developed. One of their possible applications is for gas-separation under extreme conditions of pressure and/or temperature. Experimental results indicate that their permeation properties depend on the specific organic dianhydride precursor used in the synthesis. In this work, atomistic models of 6FDA-based and PMDA-based poly(POSS-imide) crosslinked networks have been used to investigate the sorption, desorption, relaxation and permeation properties of such materials at the molecular level and their dependence on the nature of the imide linker. Results have been compared to available experimental data.A highly-efficient parallelised version of the excluded volume map sampling test particle insertion (EVMS-TPI) method was used to obtain the infinite dilution solubilities of a number of small penetrants (N2, O2, CH4 and CO2) in these model networks. Analyses of the Boltzmann-weighted probability densities for the distribution of the insertion energies showed that very reliable estimates of solubilities could be obtained.Extensive molecular dynamics simulations were then performed to obtain the complete model sorption isotherms for CO2 and CH4 at 35 °C up to pressures of over 60 bar using an iterative technique which matches the chemical potential of the penetrant in the poly(POSS-imide) phase to that in the corresponding gas phase. The sorption-induced changes in volume, the significant space available to penetrants, the mean insertion energies and their distributions were characterized. Comparisons were not only made between both types of poly(POSS-imide) to characterize the effect of the linker, but also with (hypothetical) uncrosslinked mixtures of the POSS and dianhydride molecules in order to elucidate the effects of crosslinking. Given the known conditioning properties of CO2, desorption isotherms were also obtained for this penetrant. These showed significant hysteresis. Prolonged exposure to high concentrations of CO2 was also found to lead to slow relaxations that have significant effects on the solubility.Permeabilities were obtained for methane and carbon dioxide at 100 °C, 200 °C and 300 °C at a pressure of ~ 2 bar. Differences in permeabilities were largely diffusion dependent.

Calculation of the chemical potential of chain molecules using the staged particle deletion scheme

A formulation is presented for the calculation of the chemical potential of chain molecules from molecular simulation based on the staged deletion of a test molecule. This formulation is an extension of a formulation presented recently [Boulougouris et al., Mol. Phys. 96, 905 (1999)] for the case of spherical molecules. An analytical method for the calculation of the volume accessible to a hard-sphere chain molecule is used together with the excluded volume map sampling technique. The new method is applied to a fluid of tangent sphere dimers and to ethane under various conditions. NPT, NVT, and Gibbs ensemble Monte Carlo simulation results are presented. Extensive comparison is made against calculations with the Widom test particle insertion method. In all cases, the new method results in considerable savings in CPU time.

Solubilities of small molecules in polyethylene evaluated by a test-particle-insertion method

Free-energy related properties for penetrant sorption (water, methane, argon, oxygen, nitrogen, ethane, propane, and carbon dioxide) in amorphous polyethylene have been evaluated by a test-particle-insertion method with the excluded volume map sampling (EVMS). Two model systems, one a long chain model composed of 4 linear chains each having 1002 carbon atoms and another a short chain model composed of 167 molecules of C24H50, were compared in relation to the penetrant solubility at 298 K. The time-dependent molecular configurations were obtained by a molecular dynamics (MD) simulation under constant particle number, constant pressure, and constant temperature (NPT) conditions. The solubility coefficient obtained by the EVMS method was larger in the order, C3H8>C2H6>CO2>CH4>Ar>O2>N2, similar to the experimental results, and the absolute values were also in agreement with the experimental value. In the long chain host-molecules, reflecting the higher density, the solubility was about 0.85–0.90 times smaller for most penetrants tested, while ethane and propane showed higher solubility in contrast. Analysis of the averaged unoccupied volume fraction and their distribution in both systems revealed that big holes, in which a sphere with a diameter larger than 5.0 Å can be introduced, were formed in the long chain model irrespective of the denser structure. These findings resulted in higher solubility of a larger penetrant such as ethane and propane in the long chain matrix.

A grand canonical simulation technique for dense and confined fluids with application to a Lennard-Jones fluid

Grand canonical simulations, (specified chemical potential), are performed with a fixed number of particles by coupling variations in the system size to the instantaneous chemical potential determined by virtual test particle methods. This is a modified form of the pseudo- grand canonical method of Mehta and Kofke [Mol. Phys. 86, 139 (1995)]. For dense fluids the method has the advantage of allowing the chemical potential to be specified without inserting particles, and is particularly suited to confined fluids, allowing the geometry to be changed at constant chemical potential. For the test particle determination of the chemical potential a preferential cell sampling method is developed that improves the excluded volume map sampling of Dietrick et al. [J. Chem. Phys. 90, 2370 (1989)]. It is several orders of magnitude more efficient than crude Monte Carlo sampling, and 4–40 times more efficient than restricted umbrella sampling. The methods are tested on Lennard-Jones fluids, in the bulk at reduced densities up to 0.95, and confined between two planar walls.

Molecular Simulation of Permeation of Small Penetrants through Membranes. 2. Solubilities

The excess chemical potentials of methane, water, and ethanol in poly(dimethylsiloxane) (PDMS) and polyethylene (PE) were calculated by the Widom method. The excess chemical potentials of water and ethanol in aqueous ethanol solutions (0, 50, 100 wt %) were also calculated by the Shing-Gubbins method. The excluded volume map sampling (EVMS) method and the continuum configurational bias (CCB) method were used to increase the efficiency of sampling. In spite of the polarity and the internal degrees of freedom of the molecules, the excess chemical potentials could be calculated with a small statistical error. The solubilities of methane, water, and ethanol in the polymers were calculated from excess chemical potentials. Permeation rates calculated from diffusion coefficients and solubilities were in reasonable agreement with experimental data. The free volume cluster of each system was analyzed and was related to the permeation of small penetrants in the membranes.

Molecular design of polymer membranes using molecular simulation technique

Diffusion processes of methane, water, and ethanol in poly(dimethylsiloxane) (PDMS) and polyethylene (PE) were investigated by molecular dynamics simulation. Pure liquid water and ethanol were also simulated. Simulations of 5 nanoseconds were performed for PDMS and PE with penetrant species, methane. The diffusion of methane in the polymer matrices exhibits anomalous (non-Einstein) behavior for time scales of 1 nanosecond. The excess chemical potentials of the penetrants in PDMS and the pure liquids were calculated by the Widom method. The excluded volume map sampling (EVMS) method and the continuum configurational bias (CCB) method were used to increase efficiency of sampling. Permeation rates, which were calculated from diffusion coefficients and solubilities, were in reasonable agreement with experiments.

Efficient Test Molecule Sampling in Molecular Simulation

Abstract Excluded volume map sampling (EVMS) is a particularly efficient means of performing test molecule sampling to estimate or impose chemical potential in molecular simulations. This paper discusses the motivation and applications of excluded volume map sampling, presents computer code demonstrating its implementation, and gives an example of its application.

Application of excluded volume map sampling to phase equilibrium calculations in the Gibbs ensemble

An improved method for studying liquid–liquid phase equilibria in the Gibbs ensemble is described. The improvement is based on the excluded volume map sampling (EVMS) technique, recently introduced by Deitrick et al., which has been shown to increase the liquid density range over which the Widom particle insertion method can be applied for the calculation of the chemical potential. Application of EVMS in the Gibbs ensemble greatly improves the efficiency of the particle interchange moves in a Gibbs simulation. We first demonstrate the improved method with Gibbs simulations of liquid-liquid phase equilibria in a two-component Lennard-Jones fluid. The map method results in a significant reduction in the computing time required for these simulations when the number of attempted interchanges is large. A detailed simulation study of fluid–fluid phase equilibria in a model nitrogen-helium mixture was performed using the EVMS Gibbs technique. Typically, a Gibbs simulation of liquid–liquid equilibrium in this fluid, using the map method, requires only 40% of the time used by a conventional Gibbs ensemble simulation. The results demonstrate that it is possible to determine the form of complex phase diagrams using computer simulation. In this work we calculate the pressure-composition sections of the phase diagram close to the temperature minimum of gas–gas immiscibility. The potential model we used was a Lennard-Jones plus quadrupole interaction, with parameters the same as in a recent theoretical study of this fluid mixture. Comparison of our simulation results with the theoretical work shows that the perturbation theory consistently overestimates the mole fraction of nitrogen in the coexisting phases. At the temperatures and pressures studied the simple potential model predicts thermodynamic properties in surprisingly good agreement with experimental data, even though the potential parameters were not adjusted in any way.

Efficient molecular simulation of chemical potentials

This paper evaluates methods of estimating chemical potential—actually fugacity coefficient—from molecular simulations. These methods are based on formulas given by Widom, by Bennett, and by Shing and Gubbins. They are tested with molecular dynamics simulations of Lennard-Jones liquids along the isotherm kT/ε=1.2 for densities from 0.65σ−3 to 0.90σ−3. A new test molecule sampling method, excluded volume map sampling, is found to be as much as 2 orders of magnitude more efficient than uniform test molecule sampling; it is more efficient and reliable than restricted umbrella sampling proposed by Shing and Gubbins. Several difficulties of estimating the variance of the fugacity coefficient estimates are surmounted by novel application of standard statistical methods. The statistical analysis shows that Bennett’s method yields estimates with the least variance and Widom’s method yields estimates with the greatest variance although all methods are consistent to within statistical error. Pressure and fugacity coefficient estimates obey the Gibbs–Duhem equation along the chosen isotherm up to densities of 0.75σ−3 for 108-molecule, 0.8σ−3 for 200-molecule, and 0.9σ−3 for 500-molecule simulations.