The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power-law potential, most notably the superpositioning of relaxation data as a function of the variable ${\mathrm{TV}}^{\gamma }$, where $T$ is temperature, $V$ the specific volume, and γ a material constant. A related scaling law $T_m{V}_m^{\Gamma }$, with the same exponent Γ$=$γ, links the melting temperature $T_m$ and volume $V_m$ of the model IPL liquid; liquid dynamics is then invariant at the melting point. Motivated by a similar invariance of dynamics experimentally observed at transitions of liquid crystals, we determine dynamic and melting-point scaling exponents γ and Γ for a large number of nonassociating liquids. Rigid, spherical molecules containing no polar bonds have Γ$=$γ; consequently, the reduced relaxation time, viscosity, and diffusion coefficient are each constant along the melting line. For other liquids γ > Γ always; that is, the dynamics is more sensitive to volume than is the melting point, and for these liquids the dynamics at the melting point slows down with increasing $T_{\mathrm{m}}$ (that is, increasing pressure).

• Received 26 October 2010

DOI:https://doi.org/10.1103/PhysRevE.83.031504