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

Abstract

Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as 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 we first derive the exact correlation functions of 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. Next, two simple analytic theories are constructed: a high-temperature approximation based on the exact asymptotic behavior in the limit $T\to \infty$ and a low-temperature approximation inspired by the exact result in the opposite limit $T\to 0$. 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 perspective on the extension of both approaches to the more realistic three-dimensional case is provided.

19 pages, 11 figures, 4 tables: v2: minor changes; published final version

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Cited by in corpus (14)

• Penetrable Square-Well fluids: Exact results in one dimension
• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Virial series for fluids of hard hyperspheres in odd dimensions
• Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids
• Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories
• Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
• Phase diagram of the penetrable square well-model
• Thermodynamic and structural anomalies of the Gaussian-core model in one dimension
• A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
• Radial distribution function of penetrable sphere fluids to second order in density
• Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids
• The penetrable square-well model: extensive versus non-extensive phase
• Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement
• Thermodynamic consistency between the energy and virial routes in the mean spherical approximation for soft potentials