Asymmetric fluid criticality. I. Scaling with pressure mixing

2002/12/06 by Young C. Kim, Michael E. Fisher, G. Orkoulas +1 · 6 citations
Engineering · Physics and Astronomy · #Phase Equilibria and Thermodynamics #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.67.061506

published as Phys. Rev. E vol. 67, 061506 (2003) · 21 pages in two-column format including 8 figures

arxiv created 2002/12/06 · openalex publication_date 2003/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The thermodynamic behavior of a fluid near a vapor-liquid and, hence, asymmetric critical point is discussed within a general ``complete'' scaling theory incorporating pressure mixing in the nonlinear scaling fields as well as corrections to scaling. This theory allows for a Yang-Yang anomaly in which \ensuremathμ_\ensuremathσ^\ensuremath''(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when \stackrel\ensuremath→TT_c; it also generates a leading singular term, |t|^2\ensuremathβ, in the coexistence curve diameter, where t\ensuremath≡(T\ensuremath-T_c)/T_c. The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which \ensuremathχ^(k)\ensuremath≡\ensuremathχ(\ensuremathρ,T)/\ensuremathρ^k (with \ensuremathχ=\ensuremathρ²k_BTK_T) and C_V^(k)\ensuremath≡C_V(\ensuremathρ,T)/\ensuremathρ^k are maximal at fixed T, is carefully elucidated. These results are useful for analyzing simulations and experiments, since particular, nonuniversal values of k specify loci that approach the critical density most rapidly and reflect the pressure-mixing coefficient. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte. For comparison, a discussion of the classical (or Landau) theory is presented briefly and various interesting loci are determined explicitly and illustrated quantitatively for a van der Waals fluid.

Citations

• The theory of equilibrium critical phenomena

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