True Widom line for a square-well system

In the present paper we propose a van der Waals–like model that allows a purely analytical study of fluid properties including the equation of state, phase behavior, and supercritical fluctuations. We take a square-well system as an example and calculate its liquid-gas transition line and supercritical fluctuations. Employing this model allows us to calculate not only the thermodynamic response functions (isothermal compressibility ${\beta }_T$, isobaric heat capacity $C_P$, density fluctuations ${\zeta }_T$, and thermal expansion coefficient ${\alpha }_T$), but also the correlation length in the fluid $\xi$. It is shown that the bunch of extrema widens rapidly upon departure from the critical point. It seems that the Widom line defined in this way cannot be considered as a real boundary that divides the supercritical region into gaslike and liquidlike regions. As it has been shown recently, a dynamic line on the phase diagram in the supercritical region, namely, the Frenkel line, can be used for this purpose.

Figure 1

Three isotherms for the SW system: below the critical temperature $T_c$, at $T=T_c$, and above $T_c$.

Figure 2

(a) Density fluctuations ${\zeta }_T$, (b) isothermal compressibility ${\beta }_T$, (c) heat capacity $c_P$, and (d) isobaric thermal expansion coefficient ${\alpha }_P$ along several isotherms.

Figure 3

Correlation length $\xi$ along several isotherms.

Figure 4

Location of maxima of different thermodynamic quantities close to the LG curve in the (a) $\eta \text{−}T$ and (b) $P\text{−}T$ planes.