Structural and thermodynamic properties of freely-jointed hard-sphere rings and chains

In this paper, we employ the product-reactant Ornstein-Zernike approach (PR OZA) developed by the authors to investigate the structural and thermodynam ic properties of freely-jointed hard-sphere ring fluids. Using an Mxm compo nent sticky two-point (S2P) model and specifying an appropriate association rule between various species, the associating monomers will form M rings w ith each ring composed of m beads in the complete-association limit. Applyi ng the PROZA to such a Hamiltonian and considering the limit of complete as sociation, we are able to derive analytical expressions for the average mon omer-monomer radial distribution function (RDF) as well as its intermolecul ar and intramolecular contributions and a closed form of the compressibilit y pressure. To test the theory, we also perform Monte Carlo simulations for the freely-jointed hard-sphere ring model over a wide range of densities a nd ring sizes. Compared to the simulation results, we find that the predict ions of the PROZA for the compressibility factor of flexible ring melts are quantitatively accurate and the average monomer-monomer RDF g(r) is in exc ellent agreement with the simulation data over a wide range of densities th at includes the polymer-melt regime. Based upon such a comparison as well a s theoretical considerations, we conclude that ring-size independence of g( r) is a quantitatively accurate approximation and also that the g(r) of rin gs will be a good approximation for melts of long chains. Finally, we find that we must go beyond our PROZA framework in order to accurately obtain th e separate intramolecular and intermolecular parts of g(r), for which we gi ve a quantitatively satisfactory recipe. (C) 2000 American Institute of Phy sics. [S0021-9606(00)50206-2].