Subcritical and supercritical thermodynamic geometry of Mie fluids

•The Thermodynamic Geometry of Mie fluids in the supercritical region is explored.•The R-Widom line is studied varying range and stiffness of Mie potentials.•The R-crossing method is used to reproduce coexistence curves of range dependent Mie fluids. The Thermodynamic Geometry (TG) of Mie fluids in the subcritical and supercritical region is studied using a third order thermodynamic perturbation theory equation of state (EOS). The R-crossing method of TG is applied to reproduce the coexistence curves related to Mie fluids and it is found that the validity of this methodology is range dependent. Besides, defining the R-Widom line, as the curve obtained from the extreme of the isotherms of the scalar curvature in the (P,T) plane, the behavior of this Widom line is analyzed varying the range and stiffness of Mie potentials and it is compared to the locus of the maxima of some response functions. A strong dependence of the R-Widom line is found with respect to stiffness and range potential for the Mie fluids. Besides, a kind of correspondence states principle it is found for the R-Widom line, and a Clausius–Clapeyron-type relation near the critical point in the supercritical region is fulfilled.