Theoretical approaches to the structural properties of the square-shoulder fluid

Abstract

A comparison of simulation results with the prediction of the structural properties of squareshoulder fluids is carried out to assess the performance of three theories: Tang-Lu's first-order mean spherical approximation, the simplified exponential approximation of the latter and the rational-function approximation. These three theoretical developments share the characteristic of being analytical in Laplace space and of reducing in the proper limit to the Percus-Yevick result for the hard-sphere fluid. Overall, the best agreement with the simulation data is obtained with the simplified exponential approximation.

Structural and Thermodynamic Properties of Hard-Sphere Fluids

“…144,210,211 . The application of RFA-like approaches to systems of the second class (i.e., those lacking an exact PY solution) includes the penetrablesphere model, 141,212 the penetrable-square-well model, 213 the square-well and square-shoulder potentials, [214][215][216][217][218] , piecewise-constant potentials with several steps, [219][220][221] nonadditive HS mictures, [222][223][224] , and Janus particles with constrained orientations. 225 In those cases, the simplest RFA is already quite accurate, generally improving on the (numerical) solution of the PY approximation.…”

Temperature expansions in the square-shoulder fluid. II. Thermodynamics

“…In the following, we shall combine it with the results of the previously established pressure equation of state, with the same coefficients as in Eq. (29). In that way, we get the most precise equation of state that can be obtained from FIG.…”

Temperature expansions in the square-shoulder fluid. I. The Wiener–Hopf function

“…Moreover, this potential has two natural hardsphere limits: when the shoulder potential is very strong -or equivalently the temperature is very low -the outer-core becomes hard, on the other hand, when it becomes very soft -or equivalently when the temperature is very high -only the hard inner-core plays a significant role. Despite these properties, and a significant effort towards the theoretical understanding of this potential by use of various methods -improved mean-spherical approximation [23], thermodynamic perturbation theories [24][25][26], Rational Fraction Approximation [27,28]), no explicit analytical expression of the associated structure factor has been proposed yet, to the best of our knowledge. The closest result to such a solution has been * Electronic address: oliver.coquand@dlr.de † Electronic address: matthias.sperl@dlr.de gotten by use of the Rational Fraction Approximation (RFA) [27,28], which in the spirit of the first works on the hard-sphere system [5][6][7] is based on truncations of functions in Laplace space.…”

“…Despite these properties, and a significant effort towards the theoretical understanding of this potential by use of various methods -improved mean-spherical approximation [23], thermodynamic perturbation theories [24][25][26], Rational Fraction Approximation [27,28]), no explicit analytical expression of the associated structure factor has been proposed yet, to the best of our knowledge. The closest result to such a solution has been gotten by use of the Rational Fraction Approximation (RFA) [27,28], which in the spirit of the first works on the hard-sphere system [5][6][7] is based on truncations of functions in Laplace space. More precisely, one function related to the Laplace transform of the pair-correlation function g(r) is expressed as a Padé approximant, the coefficients of which are then fixed by physical constraints.…”