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 mu(")(sigma)(T), the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when T-->T(c); it also generates a leading singular term, /t/(2beta), in the coexistence curve diameter, where t[triple bond](T-T(c))/T(c). The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which chi((k))[triple bond]chi(rho,T)/rho(k) (with chi=rho(2)k(B)TK(T)) and C((k))(V)[triple bond]C(V)(rho,T)/rho(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.