Probability density of macrostates and density of states for multi-component mixtures from semi-empirical equations of state

Abstract

We demonstrate how the density of states (Ω) and the probability density of macrostates (H) for multi-component systems can be extracted from empirical and semi-empirical equations of state (EoS), thus allowing a useful connection between molecular models and widely used classical thermodynamic models. The approach is based on the fact that the configurational Ω is related to residual thermodynamic properties that could be found from an EoS. The key relation is Boltzmann's entropy equation, which is used to relate Ω to the entropy of the mixture (evaluated from an EoS). Using the Massieu's formalism, generalized expressions are presented that show how the method can be used to obtain Ω and H relevant to simulations with different ensembles. Applications are presented for hard-sphere mixtures and Lennard–Jones mixtures as model multi-component fluids, and the Mansoori–Carnahan–Starling–Leland EoS and a cubic EoS as thermodynamic models, respectively.