The nature of the rectilinear diameter singularity

The rigorous explanation for the term |t|2β|t|2β in the rectilinear diameter equation is given (t=(Tc−T)/Tct=(Tc−T)/Tc, ββ 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 for the diameter singularity of the order parameter D1−αD2β before |t|1−α|t|1−α and |t|2β|t|2β, where αα determines the behavior of the heat capacity and ββ is the critical exponent of the order parameter, takes the universal character modulo non-universal factor which depends on the thermodynamic class of the corresponding states. The analysis of entropy for argon and water leads to β=0.33β=0.33 and the corresponding amplitude ratio S1−αS2β≈3.5.