Thermodynamic analysis of Lennard-Jones binary mixtures using Kirkwood-Buff theory

The ability to extract thermodynamic properties of mixtures from molecular geometry and interactions is one of the major advantages of atomistic simulations, but, at the same time, can be a great challenge, especially for statistical properties such as the Gibbs energy of mixing (ΔmixG). This challenge becomes even greater in the case of mixtures of complicated molecules or macromolecules. Kirkwood-Buff theory offers a promising avenue for estimating ΔmixG from atomistic simulation of binary mixtures. In this work we perform molecular dynamics simulations of both ideal and real binary Lennard-Jones mixtures at various mole fractions. We estimate the Kirkwood-Buff integrals by two different methods and identify the most efficient one. Then we validate our methodology by comparing several thermodynamic properties of the ideal mixtures against the theoretical expressions of thermodynamics. Finally, we calculate the mixing thermodynamic properties for the real mixtures, namely the enthalpy, Gibbs energy, volume, and entropy of mixing, as well as their excess parts relative to an ideal solution. We compare our results against the predictions of the well-known modified Benedict-Webb-Rubin equation of state for Lennard-Jones systems and find good agreement.