Modelling the Critical Region

Here Q and are the density fluctuations for the short-range and long-range attraction, respectively, p ax the maximum possible molecular density, and K is defined by 

The density fluctuations are calculated through evaluation of the following integral. 

Vega and co-workers have applied the method of White to the soft-SAFT 

The approach of Kiselev, based on the work of Sengers and co-workers and Kiselev and co-workers, utilizes a renormalized Landau expansion that smoothly transforms the classical Helmholtz energy density into an equation that incorporates the fluctuation-induced singular scaling laws near the critical point, and reduces to the classical expression far from the critical point. The Helmholtz energy density is separated into ideal and residual terms, and the crossover function applied to the critical part of the Helmholtz energy Aa(AT, Av), where Aa(AT, Av) = a(T, v) — a, g(T, v) and the background contribution abg(T, v) is expressed as. 

In eqs 8.39 and 8.40 AT=TITqc— 1 and Av = v/vqc— 1 are dimensionless distances from the calculated classical critical temperature (Toc) and classical critical molar volume (vqc), ao(T) is the dimensionless temperature-dependent ideal-gas term, and Po(T) = P T,vo c)vo,c/RT and a T,v) are the dimensionless pressure and residual Helmholtz energy along the critical isochore, respectively. The AT and Av are then replaced with the renormalized values in 

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