Asymptotic Behavior of the Widom Line in Supercritical Fluids: Theory of Complete Scaling and Experimental Verification

The isochoric heat capacity of supercritical fluids is a key thermodynamic property for investigating the asymptotic behavior of the Widom line in the vicinity of the critical point. In this wrk, the experimentally determined loci of the isochoric heat capacity maxima along supercritical isotherms are analyzed for a variety of molecular fluids. The experimental results show that the Widom line originates at the critical point, initially shifts toward lower densities with increasing temperature, subsequently reverses direction, and finally approaches the critical density again. Consequently, the Widom line crosses the critical isochore twice. The observed behavior is compared with the predictions of complete and incomplete scaling theories. It is demonstrated that the experimental data are accurately described by the asymptotic relation derived from complete scaling theory, for which the leading coefficient (\(\propto t^{2\beta}\), complete scaling term) is negative, \(D_{\mathrm{CS}} < 0\). This prediction is in excellent agreement with the experimental observations. In contrast, incomplete scaling predicts a different asymptotic behavior (\(\propto t^{1-\alpha}\)) along supercritical isotherms and therefore fails to reproduce the experimentally observed evolution of the Widom line over a wide temperature range. The predictive capability of widely used multiparameter reference equations of state (NIST/REFPROP) is also examined. Although these equations of state accurately represent thermodynamic properties over broad regions of the fluid phase diagram, they fail to reproduce the correct asymptotic behavior of the Widom line in the immediate vicinity of the critical point. This deficiency arises because conventional non-scaling equations of state do not correctly capture the critical anomalies associated with long-range density fluctuations. The present results provide the first experimental confirmation of the asymptotic behavior of the Widom line predicted by complete scaling theory and demonstrate the necessity of incorporating scaling behavior into equations of state intended for accurate description of critical and supercritical fluids thermodynamic behavior.