Square-well and square-shoulder fluids: Simulation and equations of state

Abstract

We explore the properties of a simple analytic equation of state, proposed by Heyes and Woodcock [D. M. Heyes and L. V. Woodcock, Mol. Phys. 59, 1369 (1986)] which is a development of the van der Waals equation of state, improved with an analytically simple yet accurate hard-core component for the compressibility factor. We call this the hard-sphere van der Waals (HSvdW) equation of state. We show, for the first time, that the HSvdW equation of state gives analytic values for the critical parameters and that it gives significantly more realistic values for the critical density than the van der Waals and other cubic equations of state. For single-component square wells of arbitrary well width, the HSvdW equation of state also produces a critical temperature and pressure in agreement with those from a recent Gibbs Monte Carlo simulation study. The chief advantage over a similar equation of state with an alternative form for the hard-core compressibility factor, such as Carnahan–Starling, is that it leads to more tractable analytic expressions for thermodynamic properties without loss of accuracy. Extensive Monte Carlo computer simulations of square-well (SW) and square-shoulder (SS) fluids with variable well width have been performed. We have calculated the compressibility factor, internal energy, pair distribution functions, and coordination number (average number of particles within the soft-shell interaction range). We have also determined the gas–liquid coexistence curve using the particle insertion chemical potential method for the square-well case, λ=1.5σ, where λ is the diameter of the soft interaction shell. This agrees well with the Gibbs ensemble simulation coexistence curve. For the purpose of improving the attractive component of the HSvdW equation of state, we have made use of the SW and SS simulation data and that of other workers to develop another new simple equation of state based on the quasichemical local coordination number approximation (QCA) which is a lattice model of a fluid. The QCA is improved to include the local coordination of the hard-sphere fluid. Present adaptations extend the range of earlier QCA models to arbitrary well width and sign of the well (either attractive well or repulsive shoulder). The simulation coordination numbers are reproduced well by the present model, although there is little improvement in the overall equation of state over the simpler HSvdW.

Entropy driven phase transitions in colloid–polymer suspensions: Tests of depletion theories

“…Values are given in Table II for selected values of ⌬. We find this correlation yields ⌸/kT to within 10% of the machine calculations reported by Heyes and Aston 35 and predicts critical temperatures and densities to within 10%. Due to the lack of analytical results for the solid state of square well and AHS solids, we follow Asherie, Lomakin, and Benedek 36 in approximating the chemical potential of the solid phase as…”

Crystal Nucleation Rates for Particles Experiencing Short-Range Attractions: Applications to Proteins

“…Ramakrishnan and Zukoski (10) build on the work of Heyes and Aston (20) to develop an equation of state for square-well fluids,…”

The hierarchical reference theory as applied to square well fluids of variable range

“…21, 27, and 29 for λ → 1+ as opposed to the rigorously constant value in ref. 28. Due to the satisfactory ̺ c -values obtained numerically we will henceforth exclude ̺ c from the discussion; for a demonstration of both ̺ c 's insensitivity to variation of parameters of the numerical procedure and the quantitative agreement with the data of sub-section IV A see figures 1 and 2.…”

“…With just one parameter, viz. λ, to vary, square wells obviously make for a convenient test case of hrt and, indeed, of liquid state theories in general; consequently, a great many simulational and theoretical efforts have been directed at this system, and studies of its phase behavior abound [21][22][23][24][25][26][27][28][29][30][31][32][33] . But square wells are also of interest in their own right, serving as -albeit somewhat crude -models of a wide variety of physical systems including, e. g., 3 He, Ne, Ar, H 2 , CO 2 , CH 4 , C 2 H 6 , n-pentane and n-butane [33][34][35] while current interest in this potential derives mainly from the finding that square wells capture the essential features of the interactions found in colloidal systems [36][37][38][39][40] .…”