Bond-Counting Approach for Representing Association Effects in the Interfacial Region of Multicomponent Systems

Abstract

Explicit expressions for the excess Helmholtz free energy due to hydrogen bonding in multicomponent systems, containing either a solid−liquid or a vapor−liquid interface, have been derived. The approach followed in the present article is based on the works of Levine and Perram (1968), who proposed that the focus should be on the correct counting of H-bonds in the system. This approach is distinctly simpler than the reaction equilibrium theory (RET) or the thermodynamic perturbation theory (TPT), proposed earlier by Suresh and Naik (1996), which focuses on the distribution of chain length of H-bonded oligomers/clusters. In this letter, we demonstrate that, despite the striking difference in the conceptual physical picture of fluids as visualized by RET/TPT and the bond-counting approach, the expressions for the excess free energy of the system in the interfacial region due to H-bonding, derived using either approaches, turn out to be entirely identical. While the mathematical and physical origins of this coincidence need to be investigated, this finding opens up an opportunity to rigorously and quantitatively incorporate association effects into rigorous, but mathematically complex, multilayer theories for interfacial phenomena in a straightforward and simple manner.