Change of Free Energy during Adsorption of a Molecule

Abstract

A change of the Helmholtz free energy ΔA takes place when a molecule becomes adsorbed out of a bulk solution. The purpose of the paper is to explore routes for the calculation of ΔA from molecular simulations. According to a derivation from the partition function, ΔA is equal to the change of the potential of mean force (PMF) which can be calculated via two different routes. First, the PMF can be obtained as a path integral over the mean force on the solute molecule which can be calculated via a simulation in which the solute molecule is fixed at a given position. Second, the PMF is related to the logarithm of the local density of the solute which can in principle be obtained via a simulation in which the solute molecule moves freely. Simulations are performed for a pure Lennard-Jones fluid and several dilute Lennard-Jones mixtures in contact with a plane Lennard-Jones wall. For the pure Lennard-Jones fluid, both simulation routes yield practically the same result for ΔA. In the case of the dilute solutions, however, simulations do not yield directly reliable local densities of the solute in those cases, in which there is not one very pronounced minimum in ΔA. On the other hand, the path integral over the mean force could be calculated always with reasonable accuracy to yield ΔA. Moreover, via the latter route also the local density of the dilute component can be obtained.