Determination of the Thermodynamic Scaling Exponent for Relaxation in Liquids from Static AmbientPressure Quantities
Abstract
An equation is derived that expresses the thermodynamic scaling exponent, γ, which superposes relaxation times τ and other measures of molecular mobility determined over a range of temperatures and densities, in terms of static physical quantities. The latter are available in the literature or can be measured at ambient pressure. We show for 13 materials, both molecular liquids and polymers, that the calculated γ are equivalent to the scaling exponents obtained directly by superpositioning. The assumptions of the analysis are that the glass transition T_{g} is isochronal (i.e., τ_{α} is constant at T_{g}, which is true by definition) and that the pressure derivative of the glass temperature is given by the first Ehrenfest relation. The latter, derived assuming continuity of the entropy at the glass transition, has been corroborated for many glassforming materials at ambient pressure. However, we find that the Ehrenfest relation breaks down at elevated pressure; this limitation is of no consequence herein, since the appeal of the new equation is its applicability to ambientpressure data. The ability to determine, from ambientpressure measurements, the scaling exponent describing the highpressure dynamics extends the applicability of this approach to a broader range of materials. Since γ is linked to the intermolecular potential, the new equation thus provides ready access to information about the forces between molecules.
 Publication:

Physical Review Letters
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevLett.113.085701
 arXiv:
 arXiv:1403.4551
 Bibcode:
 2014PhRvL.113h5701C
 Keywords:

 64.70.kj;
 78.35.+c;
 Glasses;
 Brillouin and Rayleigh scattering;
 other light scattering;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 9 pages, 3 figures, 1 table