Wertheim and Bjerrum-Tani-Henderson theories for associating fluids: a critical assessment

TL;DR

This paper critically compares Wertheim and Bjerrum-Tani-Henderson theories for associating fluids, highlighting their differences in accounting for phenomena like percolation and condensation, supported by Monte Carlo simulations.

Contribution

It provides a detailed comparison of the two theories, proving solution uniqueness for Bjerrum-Tani-Henderson and demonstrating their applicability through simulations.

Findings

Wertheim theory accounts for percolation and condensation.

Bjerrum-Tani-Henderson theory neglects intercluster correlations.

Simulations show quantitative agreement with Wertheim theory predictions.

Abstract

Two theories for associating fluids recently used to study clustering in models for self-assembling patchy particles, Wertheim's and Bjerrum-Tani-Henderson theories, are carefully compared. We show that, for a fluid allowing only for dimerization, Wertheim theory is equivalent to the Bjerrum-Tani-Henderson theory neglecting intercluster correlations. Nonetheless, while the former theory is able to account for percolation and condensation, the latter is not. For the Bjerrum-Tani-Henderson theory we also rigorously prove the uniqueness of the solution for the cluster's concentrations and the reduction of the system of equations to a single one for a single unknown. We carry out Monte Carlo simulations of two simple models of dimerizing fluids and compare quantitatively the predictions of the two theories with the simulation data.