Effect of Cooperative Hydrogen Bonding and Ring Formation for a Fluid with Associating Sites: Application to Hydrogen Fluoride

Predicting the thermodynamic properties and self-assembly of patchy colloids and of hydrogen bonding molecules (e.g., hydrogen fluoride and water) continues to be a challenge of statistical mechanics based theories. The most commonly applied approach is Wertheim’s perturbation theory and its extensions for associating particles. The first order limit of this theory treats associating sites independently and assumes all bonds between the sites has similar energy. This approach allows for the development of a very general equation of state for associating molecules in homogeneous (SAFT) and inhomogeneous systems (iSAFT) with any number of association sites. However, in case of fluid with the potential of cooperative hydrogen bonding (e.g., hydrogen fluoride and water), the assumption of identical bonding energy for every bond may not be accurate anymore. Therefore, a higher order theory is needed to take such effect into account. Here we apply Wertheim’s thermodynamic perturbation theory beyond first order for a fluid with two associating sites where the energy of association may change with respect to the state of the bonding of associating species. The effect of steric hindrance between two associating sites on a species is included, and the equation of state derived for this system is dependent on the size of the angle between two sites of a molecule. The theory has been applied to predict thermodynamic properties of hydrogen fluoride and the results are in a good agreement with experimental measurements.