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 potential, most notably the superpositioning of relaxation data as a function of the variable TV^{γ}, where T is temperature, V the specific volume, and γ a material constant. A related scaling law T{m}V{m}{Γ}, 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{m} (that is, increasing pressure).