Properties of the hard-sphere fluid at a planar wall using virial series and molecular-dynamics simulation

Chemical potential and surface free energy of a hard spherical particle in hard-sphere fluid over the full range of particle diameters

The excess chemical potential $\mu^\mathrm{ex}(\sigma,\eta)$ of a test hard spherical particle of diameter $\sigma$ in a fluid of hard spheres of diameter $\sigma_0$ and packing fraction $\eta$ can be computed with high precision using Widom's particle insertion method [J.~Chem.~Phys.~{\bf 39}, 2808 (1963)] for $\sigma$ between 0 and just larger than 1 and/or small $\eta$. Heyes and Santos [J.~Chem.~Phys.~{\bf 145}, 214504 (2016)] showed analytically that the only polynomial representation of $\mu^\mathrm{ex}$ consistent with the limits of $\sigma$ at zero and infinity has a cubic form. On the other hand, through the solvation free energy relationship between $\mu^\mathrm{ex}$ and the surface free energy $\gamma$ of hard-sphere fluid at a hard spherical wall, we can obtain precise measurements of $\mu^\mathrm{ex}$ for large $\sigma$, extending up to infinity (flat wall) [J.~Chem. Phys.~{\bf 149}, 174706 (2018)]. Within this approach, the cubic polynomial representation is consistent with the assumptions of Morphometric Thermodynamics. In this work, we present measurements of $\mu^\mathrm{ex}$ that combine the two methods to obtain high-precision results for the full range of $\sigma$ values from zero to infinity, which show statistically significant deviations from the cubic polynomial form. We propose an empirical functional form for $\mu^\mathrm{ex}$ dependence on $\sigma$ and $\eta$ which better fits the measurement data while remaining consistent with the analytical limiting behaviour at zero and infinite $\sigma$.

Equation of state for confined fluids

Fluids confined in small volumes behave differently than fluids in bulk systems. For bulk systems, a compact summary of the system’s thermodynamic properties is provided by equations of state. However, there is currently a lack of successful methods to predict the thermodynamic properties of confined fluids by use of equations of state, since their thermodynamic state depends on additional parameters introduced by the enclosing surface. In this work, we present a consistent thermodynamic framework that represents an equation of state for pure, confined fluids. The total system is decomposed into a bulk phase in equilibrium with a surface phase. The equation of state is based on an existing, accurate description of the bulk fluid and uses Gibbs’ framework for surface excess properties to consistently incorporate contributions from the surface. We apply the equation of state to a Lennard-Jones spline fluid confined by a spherical surface with a Weeks–Chandler–Andersen wall-potential. The pressure and internal energy predicted from the equation of state are in good agreement with the properties obtained directly from molecular dynamics simulations. We find that when the location of the dividing surface is chosen appropriately, the properties of highly curved surfaces can be predicted from those of a planar surface. The choice of the dividing surface affects the magnitude of the surface excess properties and its curvature dependence, but the properties of the total system remain unchanged. The framework can predict the properties of confined systems with a wide range of geometries, sizes, interparticle interactions, and wall–particle interactions, and it is independent of ensemble. A targeted area of use is the prediction of thermodynamic properties in porous media, for which a possible application of the framework is elaborated.

On the virial expansion of model adsorptive systems

We investigate the thermodynamic properties of various super-critical model adsorptive systems with different fluid-solid attractive strengths using the confined-density virial expansion, with coefficients calculated using the Mayer-sampling Monte Carlo method up to fifth order. We find that the virial expansion converges for adsorptive systems over a density range corresponding approximately to the film-formation regime. Beyond this regime, higher order effects become increasingly important. The virial expansion of the density profile is also investigated. It is determined that this expansion gives insight into the structure associated with adsorption. We also find that weakly attractive systems have a more negative second virial coefficient than strongly attractive systems. This runs counter to the usual interpretation of bulk fluid virial coefficients. This is due to the infinite-dilution limit being very different for adsorbed fluids compared to bulk fluids.