A route to the thermodynamics of colloid-polymer mixtures from structural information

Abstract

Liquid-state theory provides a fundamental connection between microscopic structure and macroscopic thermodynamic behaviour. Here, we develop a framework for predicting thermodynamics and phase behaviour directly from structural correlations, using either radial distribution functions or static structure factors as input. The approach constructs a free-energy functional from structural information obtained at a single thermodynamic state point, without requiring explicit knowledge of the underlying interaction potentials. This circumvents a central difficulty in modelling complex fluids, for which effective interactions are often unknown or rely on approximations. We demonstrate the framework for a range of model fluids, including colloidal and colloid--polymer systems, with predictions in good agreement with molecular simulation data. The results show that structural information at a single state point can provide sufficient information to predict the broader thermodynamic response of a system. This establishes a route toward inferring phase behaviour directly from experimentally measured structure, even when the microscopic interactions are not known a priori.