A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble

Multivariable extrapolation of grand canonical free energy landscapes

We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.

Predicting structural properties of fluids by thermodynamic extrapolation

We describe a methodology for extrapolating the structural properties of multicomponent fluids from one thermodynamic state to another. These properties generally include features of a system that may be computed from an individual configuration such as radial distribution functions, cluster size distributions, or a polymer's radius of gyration. This approach is based on the principle of using fluctuations in a system's extensive thermodynamic variables, such as energy, to construct an appropriate Taylor series expansion for these structural properties in terms of intensive conjugate variables, such as temperature. Thus, one may extrapolate these properties from one state to another when the series is truncated to some finite order. We demonstrate this extrapolation for simple and coarse-grained fluids in both the canonical and grand canonical ensembles, in terms of both temperatures and the chemical potentials of different components. The results show that this method is able to reasonably approximate structural properties of such fluids over a broad range of conditions. Consequently, this methodology may be employed to increase the computational efficiency of molecular simulations used to measure the structural properties of certain fluid systems, especially those used in high-throughput or data-driven investigations.

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.