Asymmetric fluid criticality. I. Scaling with pressure mixing

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 μ_σ^''(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when →TTc; it also generates a leading singular term, |t|^2β, in the coexistence curve diameter, where t≡(T-Tc)/Tc. The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which χ⁽ᵏ⁾≡χ(ρ,T)/ρᵏ (with χ=ρ²kBTKT) and CV⁽ᵏ⁾≡CV(ρ,T)/ρᵏ 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.