Ring formation in a statistical associating fluid theory framework

Hydrogen bonds (HB) form, most commonly, between independent molecules (intermolecular HB), leading to the formation of linear or branched chain-like networks, which can extend in open form and can include ring-like networks (closed loops). In addition, hydrogen bonds may involve atoms in different parts of the same molecule (intramolecular HB), on occasion leading to bent X-H.X conformations in smaller molecules (e.g., Schiff bases) where strong steric conditions apply, or from within large macromolecules (polymers [1,2,3,4,5] and proteins [6,7,8]) with little constraint from the covalent bonds otherwise binding the atoms. The formation of HB leads to long-lived molecular aggregates and the macroscopic manifestation of these two types of HB bond can be rather different and striking [9, 10, 11, 12, 13]. The direct result of the formation of hydrogen bonds is the decrease in the availability of the donor/acceptor sites of the chemical groups involved to associate. In the development of equations of state (EOSs) based on Wertheim’s thermodynamic perturbation theory (TPT), including the statistical associating fluid theory (SAFT), the formation of any ring clusters, that are formed by inter- or intramolecular hydrogen bonding, is typically neglected. As a consequence, the applicability of SAFT-like EOSs is limited to systems where the anomalies arising from ring formation are insignificant. Previous attempts to extend the TPT formalism to account for rings have not provided all the answers. The issue is addressed here whereby the TPT treatment is extended to account for ring formation, under the approximation that the appropriate many-body distribution function of the ring aggregate can be expressed as a power of a (pair) radial distribution function in a homogeneous fluid. The theory developed in this thesis constitutes an improvement to the existing theories of association in that it can be used to account for the competition between free monomers, linear-chain, branched-chain, inter- and intramolecular ring ...