Thermodynamic perturbation theory for association into doubly bonded dimers

Abstract

A theory is proposed for model molecules which may form one or two bonds with other molecules. These molecules may therefore be in one of four states: unbonded, bonded to one other molecule via one bond, bonded to one other molecule via two bonds, and bonded to two other molecules. This model has been extensively studied using a formalism developed by Wertheim but the third state has always been neglected. This neglect is reasonable if the molecule forms bonds in such a way that the two bonded molecules lie on opposite sides of the central molecule. However, if this is not the case, dimers with the molecules bonded together by two bonds can also form. The necessary theory, within Wertheim's formalism, is proposed here. Two specific models are considered: a sphere with two association sites mediating the two bonding interactions, and a chain of spheres with a site on each of the end spheres. According to the model, two approximation schemes are proposed for the additional association graph required to account for the third association state. Both result in analytical expressions for the free energy. Example phase diagrams are calculated for both models, and corresponding plots of the fractions of molecules in each of the bonding states are also shown. The development proposed here is partially motivated by the behaviour of ethanoic acid, which is known to exist as doubly bonded dimers in the gas phase and as chains in the liquid phase. This behaviour cannot be described without the developments proposed here.