Isomolar semigrand ensemble molecular dynamics: development and application to liquid-liquid equilibria

An extended system molecular dynamics method for the isomolar semigrand ensemble (fixed number of particles, pressure, temperature, and fugacity fraction) is developed and applied to the calculation of liquid-liquid equilibria (LLE) for two Lennard-Jones mixtures. The method utilizes an extended system variable to dynamically control the fugacity fraction xi of the mixture by gradually transforming the identity of particles in the system. Two approaches are used to compute coexistence points. The first approach uses multiple-histogram reweighting techniques to determine the coexistence xi and compositions of each phase at temperatures near the upper critical solution temperature. The second approach, useful for cases in which there is no critical solution temperature, is based on principles of small system thermodynamics. In this case a coexistence point is found by running N-P-T-xi simulations at a common temperature and pressure and varying the fugacity fraction to map out the difference in chemical potential between the two species A and B (mu(A)-mu(B)) as a function of composition. Once this curve is known the equal-distance/equal-area criterion is used to determine the coexistence point. Both approaches give results that are comparable to those of previous Monte Carlo (MC) simulations. By formulating this approach in a molecular dynamics framework, it should be easier to compute the LLE of complex molecules whose intramolecular degrees of freedom are often difficult to properly sample with MC techniques.     

Rapid shear viscosity calculation by momentum impulse relaxation molecular dynamics

Recently, Arya et al. [J. Chem. Phys. 113, 2079 (2000)] introduced a new molecular dynamics method to rapidly compute the viscosity of fluids. The technique, termed momentum impulse relaxation (MIR), involves the imposition of a Gaussian velocity profile on an equilibrated system, after which the decay in the profile is monitored as a function of time. The shear viscosity is computed by matching the rate of decay of the velocity profile to the corresponding solution of the Navier-Stokes equation. The method was originally applied to simple systems (argon and n-butane) and found to give a comparable accuracy to conventional equilibrium and nonequilibrium methods with more than an order of magnitude reduction in computing time. In this work, we extend and generalize the method to examine larger molecules with higher viscosities than have been examined previously. A detailed analysis of the method is given, including the effect the velocity boundary conditions have on the viscosity, the sensitivity of the results to the velocity profile fitting procedure, the effect of preequilibration of the Gaussian profile, and the effect the system size and box shape have on the accuracy and speed of the method. It is shown that the MIR method can be extended to treat multiatom systems without loss of accuracy or computational efficiency.     

Monte Carlo simulations of gas solubility in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate

The Henry's constants of water, carbon dioxide, ethane, ethene, methane, oxygen, and nitrogen are computed in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF(6)]) using test particle insertion and expanded ensemble Monte Carlo methods. The partial molar enthalpy and partial molar entropy of solvation are also computed for water, carbon dioxide, and oxygen. The results from the simulations are compared against experimental data from the literature. In addition, the accuracy and precision of the two methods in determining the Henry's constant are examined. Local organization of the ionic liquid around a solute molecule is analyzed, and the interactions responsible for the experimentally observed solubility trends are identified.     

Knudsen diffusivity of a hard sphere in a rough slit pore

An analytic theory for the Knudsen self-diffusivity D(s) of hard spheres in an atomically rough slit-shaped pore is presented which quantitatively matches simulation results. The theory assumes that, due to chaotic molecular trajectories caused by surface morphology, collisions of gas molecules with the wall are partly diffuse and partly specular, the relative magnitude of each depending upon the magnitude of the tangential momentum accommodation coefficient f. The theory thus represents a universal Knudsen fluctuation-dissipation correlation between longitudinal momentum loss and diffusivity that can simplify efforts to estimate D(s). It is also found that D(s) computed using Maxwell's theory of slip, in which collisions with the walls are assumed to be purely diffuse or specular, overpredicts the simulated D(s) by a large margin.     

A method for computing the solubility limit of solids: application to sodium chloride in water and alcohols

We present an adaptable method to compute the solubility limit of solids by molecular simulation, which avoids the difficulty of reference state calculations. In this way, the method is highly adaptable to molecules of complex topology. Results are shown for solubility calculations of sodium chloride in water and light alcohols at atmospheric conditions. The pseudosupercritical path integration method is used to calculate the free energy of the solid and gives results that are in good agreement with previous studies that reference the Einstein crystal. For the solution phase calculations, the self-adaptive Wang-Landau transition-matrix Monte Carlo method is used within the context of an expanded isothermal-isobaric ensemble. The method shows rapid convergence properties and the uncertainty in the calculated chemical potential was 1% or less for all cases. The present study underpredicts the solubility limit of sodium chloride in water, suggesting a shortcoming of the molecular models. Importantly, the proper trend for the chemical potential in various solvents was captured, suggesting that relative solubilities can be computed by the method.     

Molecular modeling and experimental studies of the thermodynamic and transport properties of pyridinium-based ionic liquids

A combined experimental and molecular dynamics study has been performed on the following pyridinium-based ionic liquids: 1-n-hexyl-3-methylpyridinium bis(trifluoromethanesulfonyl)imide ([hmpy][Tf(2)N]), 1-n-octyl-3-methylpyridinium bis(trifluoromethanesulfonyl)imide ([ompy][Tf(2)N]), and 1-n-hexyl-3,5-dimethylpyridinium bis(trifluoromethanesulfonyl)imide ([hdmpy][Tf(2)N]). Pulsed field gradient nuclear magnetic resonance spectroscopy was used to determine the self-diffusivities of the individual cations and anions as a function of temperature. Experimental self-diffusivities range from 10(-11) to 10(-10) m(2)/s. Activation energies for diffusion are 44-49 kJ/mol. A classical force field was developed for these compounds, and molecular dynamics simulations were performed to compute dynamic as well as thermodynamic properties. Evidence of glassy dynamics was found, preventing accurate determination of self-diffusivities over molecular dynamics time scales. Volumetric properties such as density, isothermal compressibility, and volumetric expansivity agree well with experiment. Simulated heat capacities are within 2% of experimental values.