(331d) A Thermodynamic Perturbation Theory for Sterically Hindered Hydrogen Bonding Fluids

The hydrogen bonding contribution to the statistical associating fluid theory (SAFT) class of equations of state is derived in Wertheim’s first order perturbation theory (TPT1). A major assumption in TPT1 is that hydrogen bonding at a given site on the molecule, is independent of the hydrogen bonding state of the remaining sites on that molecule. This assumption allows for a general and elegant solution to the theory, but it cannot capture second order effects such as steric hindrance between association sites. Within the SAFT literature there is often a debate on whether alcohols should be treated with a 2 site (1 hydrogen donor and 1 oxygen acceptor) or 3 site (1 hydrogen donor and 2 oxygen acceptors). An argument is often made that the 2 site case should be chosen, due to the fact that once one oxygen site is hydrogen bonded, the other will be partially blocked. In this work we seek to encode this steric hindrance in the hydrogen bonding theory, such that these higher order interactions are emergent from the theory, instead of artificially invoking otherwise unphysical association schemes. To accomplish this, we develop a general second order solution to thermodynamic perturbation theory (TPT2) which allows for the steric coupling between a pair of hydrogen bonding sites. The accuracy of the new approach is demonstrated by application to pure methanol and ethanol and binary ethanol/water mixtures. It is demonstrated that the new approach gives a substantial improvement in the prediction of the hydrogen bonding structure of both pure alcohol and alcohol/water mixtures, as compared to conventional approaches which do not include steric effects between the alcohol association sites.