Gibbs-Ensemble Molecular Dynamics: Liquid-Gas Equilibria for Lennard-Jones Spheres and n-Hexane

Optimized expanded ensembles for simulations involving molecular insertions and deletions. II. Open systems

In the Grand Canonical, osmotic, and Gibbs ensembles, chemical potential equilibrium is attained via transfers of molecules between the system and either a reservoir or another subsystem. In this work, the expanded ensemble (EXE) methods described in part I [F. A. Escobedo and F. J. Martinez-Veracoechea, J. Chem. Phys. 127, 174103 (2007)] of this series are extended to these ensembles to overcome the difficulties associated with implementing such whole-molecule transfers. In EXE, such moves occur via a target molecule that undergoes transitions through a number of intermediate coupling states. To minimize the tunneling time between the fully coupled and fully decoupled states, the intermediate states could be either: (i) sampled with an optimal frequency distribution (the sampling problem) or (ii) selected with an optimal spacing distribution (staging problem). The sampling issue is addressed by determining the biasing weights that would allow generating an optimal ensemble; discretized versions of this algorithm (well suited for small number of coupling stages) are also presented. The staging problem is addressed by selecting the intermediate stages in such a way that a flat histogram is the optimized ensemble. The validity of the advocated methods is demonstrated by their application to two model problems, the solvation of large hard spheres into a fluid of small and large spheres, and the vapor-liquid equilibrium of a chain system.

Molecular-dynamics evaluation of fluid-phase equilibrium properties by a novel free-energy perturbation approach: Application to gas solubility and vapor pressure of liquid hexane

A novel free-energy perturbation method is developed for the computation of the free energy of transferring a molecule between fluid phases. The methodology consists in drawing a free-energy profile of the target molecule moving across a binary-phase structure built in the computer. The novelty of the method lies in the difference of the definition of the free-energy profile from the common definition. As an important element of the method, the process of making a correction to the transfer free energy with respect to the cutoff of intermolecular forces is elucidated. In order to examine the performance of the method in the application to fluid-phase equilibrium properties, molecular-dynamics computations are carried out for the evaluation of gas solubility and vapor pressure of liquid n-hexane at 298.15 K. The gas species treated are methane, ethane, propane, and n-butane, with the gas solubility expressed as Henry's constant. It is shown that the method works fine and calculated results are generally in good agreement with experiments. It is found that the cutoff correction is strikingly large, constituting a dominant part of the calculated transfer free energy at the cutoff of 8 A.

A molecular-dynamics simulation study on the dependence of Lennard-Jones gas-liquid phase diagram on the long-range part of the interactions

The particle-transfer molecular-dynamics technique is adopted to construct the Lennard-Jones fluid gas-liquid phase diagram. Detailed study of the dependence of the simulation results on the system size and the cutoff distance is performed to test the validity of the simulation technique. Both the traditional cutoff plus long-range correction (CPC) and Ewald summation methods are used in the simulations to calculate the interactions. In the intermediate range of temperatures, the results with the Ewald summation method are almost the same as those with the CPC method. However, in the range close to the critical point, the results with the CPC method deviate from those with the Ewald summation. Compared with the results obtained via the Ewald summation in a smaller system, simply increasing the system size in the CPC scheme may not give better results.

Swelling of model polymer networks with different cross-link densities: a computer simulation study

The swelling of model polymer networks with different cross-link densities is studied via molecular dynamics simulation. During the simulation, the solvent particles, consisting of one interaction center or six interaction centers, respectively, are transferred between two coupled simulation boxes. The gel box includes both network and solvent particles, whereas the solvent box contains solvent only. The particle transfer is controlled by the solvent chemical potential difference in the two boxes, which is calculated via the Widom test particle method for the one-site solvent and via Rosenbluth sampling for the chainlike solvent. The equilibrium swelling ratio of the network as well as the solvent diffusion coefficient under subcritical and supercritical conditions are computed as functions of the network cross-link density for a wide range of temperatures and pressures. In addition, the simulated swelling behavior is compared to a Flory-Huggins-type theory, which yields qualitative agreement for the systems studied here.

Computer simulation study on the swelling of a model polymer network by a chainlike solvent

A molecular-dynamics-particle-transfer method was used to study the swelling of a model polymer network by a short chain solvent. The solvent chains were transferred depending on the difference between the solvent chemical potentials in the coupled simulation boxes, containing pure solvent and gel, respectively. The chemical potentials were computed via the Rosenbluth sampling method. The simulated swelling ratio of the network under subcritical and supercritical conditions is compared with the prediction of a modified Flory-Huggins theory. In addition, the chains exhibit markedly different structural and dynamic properties in the corresponding phases due to the constraint imposed by the network, which are discussed in detail.

Swelling of a model polymer network by a one-site solvent: computer simulation and Flory-Huggins-like theory

A molecular-dynamics-Widom test particle-simulation was used to investigate the swelling of a model polymer network in contact with a one-site solvent under subcritical and supercritical conditions. Particle motion is computed via molecular dynamics. Simultaneously, the solvent particle concentration is controlled by direct comparison of the chemical potentials in two reference systems (pure solvent and network including solvent), which are calculated using Widom's test particle method. The simulated swelling isotherms exhibit complex behavior: at the subcritical conditions considered here, the swelling ratio decreases with increasing pressure. At the intermediate supercritical temperatures the isotherms exhibit a peak, which disappears with the elevation of temperature. At high temperatures, the swelling ratio of the network increases monotonically with increasing pressure. The corresponding isobars also exhibit a maximum, which broadens and shifts to higher temperatures with increasing supercritical pressure. These results are in qualitative agreement with the prediction of a modified Flory-Huggins theory and with the results of known experiments. Furthermore, the self-diffusion coefficients of the solvent in the network and in its pure state are simulated. The solvent mobility in the network is significantly decreased because of the hindrance of network beads, but exhibits different behavior at subcritical in comparison to supercritical temperatures.