Thermodynamically self-consistent theories of fluids interacting through short-range forces

Abstract

The self-consistent Ornstein-Zernike approximation (SCOZA), the generalized mean spherical approximation (GMSA), the modified hypernetted chain (MHNC) approximation, and the hierarchical reference theory (HRT) are applied to the determination of thermodynamic and structural properties, and the phase diagram of the hard-core Yukawa fluid (HCYF). We investigate different Yukawa-tail screening lengths lambda, ranging from lambda=1.8 (a value appropriate to approximate the shape of the Lennard-Jones potential) to lambda=9 (suitable for a simple one-body modelization of complex fluids like colloidal suspensions and globular protein solutions). The comparison of the results obtained with computer simulation data shows that at relatively low lambda's all the theories are fairly accurate in the prediction of thermodynamic and structural properties; as far as the phase diagram is concerned, the SCOZA and HRT are able to predict the binodal line and the critical parameters in a quantitative manner. At lambda=4 some discrepancies begin to emerge in the performances of the different theoretical approaches: the MHNC remains, on the whole, reasonably accurate in predicting the energy and the contact value of the radial distribution function; the SCOZA predicts well the equation of state up to the highest lambda values investigated. The GMSA and the MHNC underestimate and overestimate, respectively, the liquid coexisting density, while the SCOZA and HRT yield liquid branches that fall between the two former theoretical predictions, although both appear to overestimate the critical temperature somewhat. At higher lambda's the GMSA and MHNC binodals further worsen, while the SCOZA appears to remain usefully predictive. In general, the predictions of all the theories tend to slightly worsen at low temperatures and high density. The determination of the freezing line, performed by means of a one-phase "freezing criterion" (due to other authors) is not particularly satisfactory within either the SCOZA or the MHNC; the GMSA prediction for the freezing line at lambda=7 and 9 is instead able to follow in a qualitative manner the pattern of the solid-vapor coexistence line as determined through computer simulation studies. The necessity of further assessments of the freezing predictions is also discussed. Finally, versions of the GMSA, SCOZA, and HRT that can be expected to be more accurate for interactions with extremely short-ranged attractions are identified.

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions: Application to protein crystallization

“…The method uses a reasonable choice of functional relationship between c(r) and v(r) on the basis of numerous calculations obtained over a number of years. Furthermore, it has been shown [22] that the results obtained are in excellent agreement with computer simulations, at least for not too narrow ranges of the potential. In this sense it may be viewed as the best semi-analytical method to study the Yukawa potential.…”

“…The application of SCOZA to a hard-core Yukawa fluid provides a semi-analytic calculation of the thermodynamic properties of the fluid, liquid and gas states of the system [21,22]. SCOZA has been applied to Yukawa systems with relatively large values of the range of the potential, with a satisfactory reproduction of the liquidvapour binodal curves and a good description of the critical point region.…”

“…These have proved to be quite accurate theories of the liquid and fluid states. The SCOZA method in particular has been compared to Monte Carlo simulations for a range of screening parameters ("wellwidths") of the Yukawa potential, and it has been shown [21,22] that the agreement for the phase diagrams is quantitative, at least for modest values of screening parameter.…”

Thermodynamically self-consistent liquid state theories for systems with bounded potentials

“…This approach is based on replacing the differential equation for K(̺, β) by one for the excess energy density u = U ex /V . To this end, we consider the following thermodynamic relation (see, e.g., 21 )…”

Vapor–liquid surface tension of strong short-range Yukawa fluid

“…The short-range hard-core attractive Yukawa (HCAY) fluid has been widely used as a simple model for testing a variety of theories [1][2][3][4][5][6] and as a reference system for modeling the behavior of real fluids, such as colloidal suspensions 7,8 and protein solutions [9][10][11] . Its high popularity is due to the fact that it captures the most important features of these systems, such as coexistence and interfacial properties which rule many industrial processes and biological phenomena.…”