On the Ginzburg temperature of ionic and dipolar fluids

Abstract

Critical fluctuations in fluids are investigated within the framework of the generalized van der Waals theory. The square-gradient term—added to the Landau expansion of the Helmholtz free energy density—is obtained following a procedure similar to that originally proposed by van der Waals in the theory of surface tension, however replacing the Heaviside step function originally used by an approximative pair distribution function. Representative for ionic fluids we choose the restricted primitive model (RPM) and treat it within the Debye–Hückel theory, thus neglecting effects of ion pairing. The other approximative extreme—complete ion pairing resulting in a fluid of hard dipolar dumbbells—is mimicked by a fluid composed of dipolar hard spheres (DHS). For this case we use the Onsager reaction field and the second pressure virial coefficient. We calculate the amplitudes of the correlation length and the Ginzburg temperatures, and find (in reduced quantities) ξ0*=3.50 and ΔTGi*=0.0087 for the ionic system, and ξ0*=0.82 and ΔTGi*=1.63 for the dipolar fluid. For calibration we compute the same quantities for simple neutral fluids and obtain ξ0*=0.50 and ΔTGi*=2.89 for a Sutherland fluid (hard core term plus attractive r−6-potential) and ξ0*=0.43 and ΔTGi*=8.50 for a square-well fluid. The result of a smaller Ginzburg temperature for the ionic fluid than for nonionic fluids in a treatment that neglects ion pairing is clearly at variance with the results of other groups. The correlation length in the low-density limit obtained from our approach has the same functional dependencies as the Lee–Fisher expression, but differs by a numerical factor of 5.7.