Molecular association at the microscopic level

TL;DR

This paper calculates the Helmholtz free-energy for molecular pairs to evaluate association constants and phase transition temperatures, providing a unified approach for dilute solutions and dense fluids.

Contribution

It introduces a method to derive association constants and phase transition temperatures directly from the free-energy function W, linking microscopic interactions to macroscopic phase behavior.

Findings

Derived association constant K for ionic molecules matching Bjerrum's result.

Established a criterion for bound species based on the free-energy W.

Obtained an expression for the freezing temperature in dense ionic fluids.

Abstract

The Helmholtz free-energy W is calculated as a function of separation distance for two molecules in a fluid, A and B, whose mutual interaction is described by a spherically symmetric potential. For the equilibrium A + B = AB occurring in a dilute solution or gas, W is used to evaluate the association constant K, which for ionic A and B is identical to the Bjerrum result. The criterion defining the bound species is not arbitrary; i.e., the cutoff separation distance in the configuration integral used to calculate K arises directly from the definition of W. For a one-component dense fluid, W permits the derivation of the phase-condensation temperature, which for a gas is the critical temperature and for a liquid the freezing temperature. For ionic A and B (e.g., Sodium and Chloride ions in molten NaCl), an expression for the freezing temperature is obtained, which is similar to the expression for the melting temperature derived by Kosterlitz and Thouless for two-dimensional systems.