Connection between dynamics and thermodynamics of liquids on the melting line

The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power law (IPL) potential, most notably the superpositioning of relaxation data as a function of the variable TV{\gamma}, where T is temperature, V the specific volume, and {\gamma} a material constant. A related scaling law, TmVm{\Gamma}, with the same exponent {\Gamma}={\gamma}, links the melting temperature Tm and volume Vm 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 {\gamma} and {\Gamma} for a large number of non-associating liquids. Rigid, spherical molecules containing no polar bonds have {\Gamma}={\gamma}; consequently, the reduced relaxation time, viscosity and diffusion coefficient are each constant along the melting line. For other liquids {\gamma}>{\Gamma} always; i.e., 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 Tm (that is, increasing pressure).