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Determination of the Thermodynamic Scaling Exponent from Static, Ambient-Pressure Quantities

An equation is derived that expresses the thermodynamic scaling exponent, g, which superposes relaxation times 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 g are equivalent to the scaling exponents obtained directly by superpositioning. The assumptions of the analysis are that the glass transition is isochronal and that the first Ehrenfest relation is valid; the first assumption is true by definition, while the second has been corroborated for many glass-forming materials at ambient pressure. However, we find that the Ehrenfest relation breaks down at elevated pressure, although this limitation is of no consequence herein, since the appeal of the new equation is its applicability to ambient pressure data.