Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories

Abstract

The two-body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials, the simplest of which being that of penetrable spheres (PSs). In this paper we construct two simple analytical theories for the structural properties of PS fluids: a low-temperature (LT) approximation, that can be seen as an extension to PSs of the well-known solution of the Percus-Yevick (PY) equation for hard spheres, and a high-temperature (HT) approximation based on the exact asymptotic behavior in the limit of infinite temperature. Monte Carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories. It is found that, despite their simplicity, the HT and LT approximations exhibit a fair agreement with the simulation data within their respective domains of applicability, so that they complement each other. A comparison with numerical solutions of the PY and the hypernetted-chain approximations is also carried out, the latter showing a very good performance, except inside the core at low temperatures.

14 pages, 8 figures; v2: some figures redone; small changes

References in corpus (19)

• The Phase Diagram of Star Polymer Solutions
• Mean Field Fluid Behavior of the Gaussian Core Model
• Exact Criterion for Determining Clustering vs. Reentrant Melting Behavior for Bounded Interaction Potentials
• Fluid and solid phases of the Gaussian core model
• Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
• Phase diagram of the Gaussian-core model
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• Freezing and clustering transitions for penetrable spheres
• Phase diagram of softly repulsive systems: The Gaussian and inverse-power-law potentials
• Evaluation of phenomenological one-phase criteria for the melting and freezing of softly repulsive particles
• Formation of Polymorphic Cluster Phases for Purely Repulsive Soft Spheres
• Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids
• Thermodynamically self-consistent liquid state theories for systems with bounded potentials
• Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
• The penetrable-sphere fluid in the high-temperature, high-density limit
• Are the energy and virial routes to thermodynamics equivalent for hard spheres?
• Radial distribution function of penetrable sphere fluids to second order in density
• A theorem on the absence of phase transitions in one-dimensional growth models with onsite periodic potentials
• Kinetic Theory of Soft Matter. The Penetrable-Sphere Model

Cited by in corpus (9)

• Structure of hard-hypersphere fluids in odd dimensions
• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Structure of the square-shoulder fluid
• Multicomponent fluids of hard hyperspheres in odd dimensions
• A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
• Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-Hückel theory
• The penetrable square-well model: extensive versus non-extensive phase
• Molecular dynamics simulation study of self-diffusion for penetrable-sphere model fluids
• Kinetic Theory of Soft Matter. The Penetrable-Square-Well Model