Equations of state for hard-sphere chain fluids

Abstract

A method of modeling thermodynamic properties of hard-sphere chain fluids is considered. The method is based on the Baxter’s results for the Percus–Yevick theory. We discuss the recent reformulation of Baxter’s results given by Chiew for athermal linear chain molecules and show that it fails as soon as one considers more complicated molecules, in particular, the proper transition to the thermodynamic limit is not always possible. An improved formulation is given which enables us to obtain previous results and not yield divergencies. Examples of the equations of state are given. It is shown that the equation of state for branched chains is the same as for linear chains. For cyclic chain molecules, the equation of state is found to be independent of chain length and polydispersity. Experimental data obtained by S. J. Clarson in 1985 confirms this surprising result. Limitations of the method are discussed; it is shown that it fails in the low-density limit as soon as the molecules with cyclic fragments are considered.