Comment on "Density scaling of the diffusion coefficient at various pressures in viscous liquids".

The thermodynamic scaling idea enables an elegant description of relaxation dynamics near the glass transition and provides a linkage between thermodynamics and molecular dynamics of supercooled liquids. A lot of effort has been put into finding functions, f(T(-1)V(-γ)), which can scale dynamical quantities such as relaxation time, viscosity, and diffusion coefficient. Within the trend, Papathanassiou [A. N. Papathanassiou, Phys. Rev. E 79, 032501 (2009)] has recently derived a new scaling function for the reduced diffusion coefficient. In this Comment, we report that this scaling function is not sufficiently grounded, because it is based on some scaled equation of state which predicts significantly different values of the scaling exponent γ from volumetric data in comparison with those found from the scaling of relaxation or viscosity data. Moreover, we would like to point out that any scaling function f cannot be straightforwardly formulated on the basis of any equation of state which yields the scaling exponent γ different from that used to scale the dynamic quantity.