(614e) A ‘2D Route’ to the Effective Tangential Pressure in Adsorbed Films: High-Density Equation of State for a Two-Dimensional Lennard-Jones Solid

The estimation of the tangential pressure in adsorbed films on planar surfaces and in slit-shaped pores remains a challenge in both experiment and theory. While the normal pressure is uniquely defined for a planar surface, the tangential pressure, P_T, at a point r is not uniquely defined at the nanoscale. In the commonly used ‘virial-route’ the statistical mechanical equation for P_T(r) requires an integration of the intermolecular forces over a contour connecting the interacting particles, so that the numerical value of the tangential pressure depends on the choice of this integration path. Therefore, it is useful to have an alternative route to estimate the effective tangential pressure.

In this work we propose a new route, the ‘2D-route’, to P_T based on the observation that adsorbed films on a planar solid surface consist of quasi-two-dimensional (2D) layers near the surface. We present a new equation of state for a 2D Lennard-Jones solid (2D LJ-EOS) that is valid at high densities. The new 2D LJ-EOS is of analytic form, consisting of a zero-temperature contribution and vibrational contributions up to and including the second anharmonic term. Comparisons between the 2D LJ-EOS and Monte Carlo simulation results show that the 2D LJ-EOS is very accurate over a wide range of temperature in the high-density region. A criterion to find the temperature range over which the 2D LJ-EOS is applicable is derived. We calculate an effective tangential pressure for the adsorbed contact layer near the wall in a slit-pore system, and show that the tangential pressures predicted by this ‘2D-route’ are in qualitative agreement with those found by the more traditional virial route of Irving and Kirkwood.