Quasichemical theory and the description of associating fluids relative to a reference: Multiple bonding of a single site solute

TL;DR

This paper develops a new, intuitive formulation for the chemical potential of associating solutes using quasichemical theory, incorporating multi-body effects and relating to SAFT without complex graph theory.

Contribution

It introduces a graph-theory-free, quasichemical approach to model associating fluids, explicitly including multi-body interactions and connecting to SAFT.

Findings

Provides a new expression for the monomer fraction in associating fluids.

Demonstrates the approach with examples including colloids and Janus particles.

Reveals multi-body effects are naturally incorporated into the theory.

Abstract

We derive an expression for the chemical potential of an associating solute in a solvent relative to the value in a reference fluid using the quasichemical organization of the potential distribution theorem. The fraction of times the solute is not associated with the solvent, the monomer fraction, is expressed in terms of (a) the statistics of occupancy of the solvent around the solute in the reference fluid and (b) the Widom factors that arise because of turning on solute-solvent association. Assuming pair-additivity, we expand the Widom factor into a product of Mayer f-functions and the resulting expression is rearranged to reveal a form of the monomer fraction that is analogous to that used within the statistical associating fluid theory (SAFT). The present formulation avoids all graph-theoretic arguments and provides a fresh, more intuitive, perspective on Wertheim's theory and SAFT. Importantly, multi-body effects are transparently incorporated into the very foundations of the theory. We illustrate the generality of the present approach by considering examples of multiple solvent association to a colloid solute with bonding domains that range from a small patch on the sphere, a Janus particle, and a solute whose entire surface is available for association.