The virial equation of fluid state and non-classical criticality

The analysis of fluid criticality in the framework of the “virial” approach leads, usually, to pure classical results. In the present paper we propose a consistent procedure allowing us to find the non-classical critical parameters of real fluid starting from the representation of the pressure near the critical point as the sum of a regular (a few of the first terms of the virial series) and a singular (non-analytical “remainder” of the series) part. The critical temperature, density, and the singular contribution to the fluid pressure are found self-consistently using not two (by van der Waals) but three (as in the fluctuation theory) conditions on the density partial derivatives of the pressure at the critical point. The calculated critical parameters converge rather rapidly to some limiting values as the number of terms in the regular part of the representation of the pressure is increased. Our calculations (when taking account of the virial terms up to the sixth one, inclusively) are in accordance, on the whole, with the numerical “experiments” data for the Lennard-Jones fluid, although we predict a somewhat greater (approximately 10%) value of the critical density. The refinement of the obtained results can be achieved when using more precise values of the higher (i.e. the seventh onwards) virial coefficients