Asymmetry of the vapor-liquid coexistence curve: The asymptotic behavior of the "diameter"

We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent term in the "diameter" of the coexistence curve asymptotically close to the vapor-liquid critical point. For this purpose, we use a simple non-parametric equation of state which we develop by meeting several general requirements. Namely, we require that the desired equation (1) lead to correct asymptotic behavior for a limited number of the fluid's parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop below the critical point, and (3) be consistent with a rigorous definition of the isothermal compressibility in the critical region. For the temperature interval in question, the proposed equation approximates experimental data with an accuracy comparable to those given by Schofield's parametric equation and by other authors' equations. The desired term is obtained by applying the Maxwell rule to the equation and can be represented as D2β|τ|2β, where |τ| = |T − Tc|/Tc and β is the critical exponent for the order parameter. The amplitude D2β is determined explicitly for the volume-temperature and entropy-temperature planes. The results obtained are contrasted with experiment to estimate the values of the amplitude coefficients of the nonanalytic terms in the "diameters" for the volume-temperature and density-temperature planes.