Resummed thermodynamic perturbation theory for central force associating potential: One-patch model

Abstract

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is proposed. We consider a simple one-patch model for associating fluids. The model is represented by the hard-sphere system with a circular attractive patch on the surface of each hard-sphere. Resummation is carried out to account for the blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the model with a doubly bondable patch at all degrees of the blockage are presented. In the limiting case of total blockage, when the particles become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory for dimerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. Very good agreement between predictions of the theory, corrected for ring formation, and Monte Carlo computer simulation values was found in all cases studied. Less accurate are the original versions of the theory and Wertheim's thermodynamic perturbation theory for dimerization, especially at lower temperatures and larger sizes of the attractive patch.