Thermodynamic perturbation theory for association into chains and rings

Abstract

A theory for the formation of rings at equilibrium is proposed. The formalism previously derived by Wertheim [J. Stat. Phys. 35, 19 (1984); 35, 35 (1984); 42, 459 (1986); 42, 477 (1986)] is used together with a way of approximating the ring graphs which are found. The theory is developed to treat two model molecules: spheres with two attraction sites, each mediating an interaction very like a hydrogen bond, and chains of spheres with a similar site on the first and on the last sphere. Unlike previous work these molecules are allowed to form ring structures as well as chains. For both models the free energy is a simple analytical expression in terms of the fraction of attraction sites bonded, very like other work within the Wertheim formalism. The fraction of sites bonded is obtained from mass action equations. Phase diagrams are shown, and we discuss the difference in phase behavior between that predicted by the theory proposed here, and that of work which excludes rings. It is found that if the possibility of forming rings is excluded a very different phase diagram can be produced. In particular, the vapor pressure far from the critical point is severely underestimated. This corresponds to the formation of a high proportion of rings in the gas phase while the liquid phase remains dominated by chains. The case where the model molecules can only form rings is also discussed, and expressions for the free energy derived. In the limit of complete association this case reduces to an earlier result, derived and tested against simulation data by the authors. The motivation of the work on the first model is the formation of rings by both hydrogen fluoride and sulfur. The second model is motivated by the possibility of intramolecular bonding in organic compounds with two functional groups capable of forming hydrogen bonds separated by a flexible carbon backbone.