Dynamics and Thermodynamics Along the Melting Line

For more than 100 liquids and polymers, dynamic properties such as the viscosity, relaxation time, and diffusion constant superpose as a function of the variable r^γ/T, where r is density, T is temperature, and γ a material constant. A related scaling law, r_m^Γ/T_m = constant, is known for liquid crystals, where the subscript refers to the (pressure-dependent) phase transition. We have found that these two exponents are equal, i.e., Γ=γ, for most liquid crystals. This means that their viscosity and rotational relaxation times must be invariant along the transition line, evincing a connection between dynamics and thermodynamics.

We carried out the same analysis on crystal melting point data for more than 40 materials, and similarly found that r_m^Γ/T_m = constant. However, the dynamic, γ, and melting point, Γ, scaling exponents are equal only for rigid, spherical molecules containing no polar bonds. For this small number of materials, the viscosity and other dynamic properties are constant along the melting line. For the vast majority of substances, γ>Γ, which means that the viscosity at the melting point increases with increasing melting temperature (that is, increasing pressure).

From the scaling relations, the Lindemann-Gilvarry, relating the change in volume along the melting curve to the Grüneisen parameter, and the Andrade equation for the viscosity at the melting point, can be derived. These are useful for estimating melting points and flow behavior at experimentally inaccessible temperatures and pressures.