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.

Multiple occupancy crystals formed by purely repulsive soft particles

“…The PSM has also been extensively studied recently [50][51][52][53][54][55][56][57][58][59][60]. Surprisingly, its phase behavior is markedly different from that of the GCM.…”

A numerical test of a high-penetrability approximation for the one-dimensional penetrable-square-well model

“…Note that a similar matching of the low-and high-penetrability approximation has already been carried out by two of the present authors in the framework of the PS model. 7,8 It turns out that the high-penetrability approximation in the context of bounded potentials coincides with the linearized Debye-Hückel classical approximation originally introduced in the framework of the Coulomb potential. 9 It has been recently shown 10 that two of the three standard routes to thermodynamics (the energy and the virial routes) are automatically consistent within the linearized Debye-Hückel approximation, for any potential and dimensionality.…”

“…From a physical viewpoint this amounts to starting from the ideal gas limit γ r → 0 (one of the common reference systems for simple fluids) and progressively building up interactions by increasing γ r . An additional mathematical advantage stems from the simple observation 7,8,20 that in the (exact) cluster expansion of g(r) only the dominant chain diagrams need to be retained at all orders, thus leading to the possibility of an exact summation of those leading contributions. As we shall see shortly, this is in fact a procedure known as the Debye-Hückel approximation in the context of charged fluids.…”

Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties

“…In the ϵ → 0 limit, the interactions are completely ideal. The PS model has been extensively studied analytically and through simulation [23][24][25][26][27][28][29] as it provides for a simple theoretical model describing the anomalous structural and dynamical behavior observed in soft-matter systems. Systems governed by bounded interactions can give rise to an interesting phase behavior in which completely repulsive pairwise interactions give rise to multiple occupancy lattice geometries in the formation of "cluster crystals."…”