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 ${\mu }_{\sigma }^{″}\mathrm{}\left(T\right),$ the second temperature derivative of the chemical potential along the phase boundary, diverges like the specific heat when $\overrightarrow{T}{T}_{\mathrm{c}};$ it also generates a leading singular term, $|t{|}^{2\beta },$ in the coexistence curve diameter, where $t\equiv (T-T_{\mathrm{c}}{)/T}_{\mathrm{c}}.$ The behavior of various special loci, such as the critical isochore, the critical isotherm, the k-inflection loci, on which ${\chi }^{\mathrm{}\left(k\right)\mathrm{}}\equiv \chi (\rho ,T)/{\rho }^k$ (with $\chi ={\rho }^2{k}_{\mathrm{B}}{\mathrm{TK}}_T)$ and $C_V^{\mathrm{}\left(k\right)\mathrm{}}\equiv C_V(\rho ,T)/{\rho }^k$ 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.