A new approach to calculating diffusivities, both transport as well as equilibrium, is presented. The dual control volume grand canonical molecular dynamics (or DCV-GCMD) method employs two local control volumes for chemical potential control via particle creation/destruction as in grand canonical Monte Carlo (GCMC) simulations. The control volumes are inserted in a standard NVT molecular dynamics simulation yielding a simulation with stochastic chemical potential control that may be thought of as a hybrid GCMC-MD approach. The geometrical control of the chemical potential enables a steady state chemical potential gradient to be established in the system. By measuring the density profile and flux, Fick’s law is used to determine the diffusivity. An example calculation is presented for a simple Lennard-Jones system.

We present adsorption isotherms, phase diagrams, and density profiles for a Lennard-Jones fluid confined to a cylindrical pore. In particular, we concentrate on the gas–liquid transition in the pore (capillary condensation). We compare simulations for a series of radii and different temperatures with mean field density functional theory (MFT). Two forms of MFT are considered, the simple local density approximation (LDA) and Tarazona’s nonlocal or smoothed density approximation (SDA). We find that the SDA provides a quite accurate description of fluid structure in the pore and that it produces phase diagrams in good agreement with the simulation data. For larger radii and temperatures T/Tc≳0.6 the SDA shows steep rises in adsorption close to the transition. This strongly affects the shape of the coexistence curve in the T, ρ̄ plane. Here ρ̄ is defined as the average density inside the pore. This behavior is confirmed by the simulation. In contrast, LDA gives a poor representation of the fluid structure and this underlies the failure to reproduce the phase diagrams and adsorption isotherms found with SDA or simulation. For extremely small radii (R*≈1) the simulation adsorption isotherms are smooth, and for not too low a temperature they are accurately described by an approach which starts from the potential distribution theorem and uses perturbation theory for the true one-dimensional fluid.

We report molecular dynamics calculations of a Lennard-Jones fluid in a cylindrical pore. Following a temperature quench the fluid spontaneously phase-separates into a liquid-like region and a gas-like region. The two regions are separated by a hemispherical meniscus. The capillary condensation is located for two temperatures via a calculation of the chemical potential of the two-phase system. Coexistence disappears when the temperature is raised to kTe = 1.0, indicating the existence of a capillary critical point.

Recent work in the active area of grand canonical molecular dynamics methods is first briefly reviewed followed by an overview of the dual control volume grand canonical molecular dynamics (DCV-GCMD) method, designed to enable the dynamic simulation of a system with a steady-state chemical potential gradient. A short review of the methods and systems used to prototype the DCV-GCMD method and its parallel implementation follows. Finally a new, novel implementation of the DCV-GCMD method that enables the establishment of a steady-state chemical potential gradient in a multicomponent system without having to insert or delete one of the components is presented and discussed.

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