Structure of penetrable-rod fluids:Exact properties and comparison between Monte Carlo simulations and two analytic theories

摘要

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems,such as the dilute solutions of polymer chains in good solvents.The simplest bounded potential is that of penetrable spheres,which takes a positive finite value if the two spheres are overlapped,being 0 otherwise.Even in the one-dimensional case,the penetrable-rod model is far from trivial,since interactions are not restricted to nearest neighbors and so its exact solution is not known.In this paper the structural properties of one-dimensional penetrable rods are studied.We first derive the exact correlation functions of the penetrable-rod fluids to second order in density at any temperature,as well as in the high-temperature and zero-temperature limits at any density.It is seen that,in contrast to what is generally believed,the Percus-Yevick equation does not yield the exact cavity function in the hard-rod limit.Next,two simple analytic theories are constructed:a high-temperature approximation based on the exact asymptotic behavior in the limit T->infinity and a low-temperature approximation inspired by the exact result in the opposite limit T-> 0.Finally,we perform Monte Carlo simulations for a wide range of temperatures and densities to assess the validity of both theories.It is found that they complement each other quite well,exhibiting a good agreement with the simulation data within their respective domains of applicability and becoming practically equivalent on the borderline of those domains.A comparison with numerical solutions of the Percus-Yevick and the hypernetted-chain approximations is also carried out.Finally,a perspective on the extension of our two heuristic theories to the more realistic three-dimensional case is provided.