Long range corrections to thermodynamic properties of inhomogeneous systems with planar interfaces

Expressions for the long range corrections to configurational energy, normal pressure, surface tension, and chemical potential of an inhomogeneous system with two planar interfaces are developed. Applying the Euler forward difference scheme to correlate the density at any height to that of a central spatial element separates the corrections into two parts: one relates directly to the central local density, and another is due to the density differences between the central local value and those around the central spatial element. An analytical expression is obtained for the first part when the Lennard-Jones potential function is adopted in the evaluation. Variations of these properties along the normal direction are illustrated in terms of the equilibrium density profiles obtained from Monte Carlo simulations performed at T*=0.90 and T*=1.15.