The nature of the rectilinear diameter singularity

Abstract

The rigorous explanation for the term $| t |^{2\beta}$ in the rectilinear diameter equation is given ($t = (T_c-T)/T_c$, $\beta$ is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric is constructed within the canonical formalism. It is shown that the ratio of the amplitudes $\f{D_{2\beta}}{D_{1-\alpha}}$ before $|t|^{2\beta}$ and $|t|^{1-\alpha}$ where $\alpha$ determines the behavior of the heat capacity, takes the universal character. The analysis of entropy for argon and water leads to $\beta = 0.33$ and $\f{D_{2-\beta}}{{D_{1-\alpha}}}\approx - 3.5$.