Ginzburg criterion for the crossover behavior of model fluids

Abstract

The Ginzburg criterion, which is based on the three coefficients in the Landau–Ginzburg (LG) expansion of the Helmholtz free energy density of a nonuniform system, is believed to give a reasonable estimate for the temperature scale on which crossover occurs. To compute the contribution of the square-gradient term in the LG expansion, we extend the van der Waals theory of surface tension and, in contrast to our earlier treatment, account for the dependence of the pair distribution function on the spatially varying density. Via this approach we calculate and compare the Ginzburg temperatures of ionic, dipolar, and simple model fluids, namely the restricted primitive model (RPM), the Onsager model, and the square-well fluid (the second and third virial coefficients, for which we also present exact results). To compute the properties of the RPM, we employ the Fisher–Levin theory and its recent extension for Debye-shielded dipole–dipole interactions and a state-dependent dielectric constant that was developed by us. In contrast to the results of our earlier work and in accordance with the calculations of Fisher and Lee, we now find that the RPM has no exceptionally small region in which mean-field theory fails.