ABSTRACT

In the first part of the talk, we present a very simple but general method to calculate cluster integrals that appear in diagrammatic methods of statistical mechanics. The approach is suitable for integrals of any order, and can be applied to potentials of any complexity. The method has the character of a molecular simulation performed on the molecules represented in the integral, and there are two key ideas in its application to cluster integrals. First, we generate the molecule configurations using Metropolis Monte Carlo with importance sampling of configurations based on the magnitude of the interactions represented in the cluster integral. Second, we aim to evaluate the ratio of the desired cluster integral to a known reference integral, and do not attempt to evaluate the cluster integral directly. We propose Mayer sampling as the name given to this technique of computing cluster integrals using importance sampling and free-energy perturbation methods. There are many variations and applications that can be pursued from this basic approach. In the present work we demonstrate the Mayer-sampling method by evaluating the cluster integrals needed to calculate virial coefficients from a molecular model. We present results for the sixth virial coefficient for the LJ model, and the fourth, fifth and sixth virial coefficients for the SPCE model of water, none of which have been reported previously. In the second part of the talk, we present a study of the influence of molecular association on liquid-vapor interfacial properties, and surface tension in particular. Fluids with molecular association such as hydrogen bonding often exhibit a variety of anomalous properties. An extreme example is hydrogen fluoride (HF), in which properties are dominated by the formation of clusters in the fluid and vapor phases. Interfacial properties can be strongly impacted by association phenomena. HF has an anomalously low surface tension, and consequently it has a tendency to form an aerosol that can be very dangerous in an accidental release. Understanding the interfacial properties of these fluids can guide the design of additives that might influence surface properties. We examine a square-well based associating model that is selected to exhibit the basic features of molecular association while being easily characterized. Molecular simulation is applied to evaluate the interfacial behavior. Grand-canonical transition-matrix Monte Carlo with Binder's finite-size scaling formalism is used to measure the surface tension and coexistence conditions. NVT Monte Carlo simulations of a simple liquid-vapor slab at coexistence are studied to understand the structure of the interface. We examine the impact of size, strength and number of association sites on the behavior, and we also consider the influence of solutes on the properties of interest.