Incorporating multi-body effects in SAFT by improving the description of the reference system. I. Mean activity correction for cluster integrals in the reference system

TL;DR

This paper improves the statistical association fluid theory for patchy colloids by incorporating multi-body correlations and bulk solvent effects through a mean activity correction, leading to more accurate thermodynamic predictions.

Contribution

The authors introduce a mean activity correction to account for multi-body effects and bulk solvent influence in the reference system of SAFT, enhancing its predictive accuracy.

Findings

Better agreement with simulation data for solvent distribution.

Improved predictions of bonding states and chemical potentials.

Enhanced applicability at higher system densities.

Abstract

A system of patchy colloidal particles interacting with a solute that can associate multiple times in any direction is a useful model for patchy colloidal mixtures. Despite the simplicity of the interaction, because of the presence of multi-body correlations predicting the thermodynamics of such systems remains a challenge. Earlier Marshall and Chapman developed a multi-body formulation for such systems wherein the cluster partition function for the hard-sphere solvent molecules in a defined inner-shell (or coordination volume) of the hard-sphere solute is used as the reference within the statistical association fluid theory formalism. The multi-body contribution to these partition functions are obtained by ignoring the bulk solvent, thus limiting the applicability of the theory to low system densities. Deriving inspiration from the quasichemical theory of solutions where these partition functions occur in the guise of equilibrium constants for cluster formation, we develop a way to account for the multi-body correlations including the effect of the bulk solvent. We obtain the free energy to evacuate the inner-shell, the chemistry contribution within quasichemical theory, from simulations of the hard-sphere reference. This chemistry contribution reflects association in the reference in the presence of the bulk medium. The gas-phase partition functions are then augmented by a mean activity factor that is adjusted to reproduce the chemistry contribution. We show that the updated partition function provides a revised reference that better captures the distribution of solvent around the solute up to high system densities. Using this updated reference, we find that theory better describes both the bonding state and the excess chemical potential of the colloid in the physical system.