Scaling of the local dynamics and the intermolecular potential

The experimental fact that relaxation times, τ, of supercooled liquids and polymers are uniquely defined by the quantity TVγ, where T is temperature, V specific volume, and γ a material constant, leads to a number of interpretations and predictions concerning the dynamics of vitrification. Herein we examine means to determine the scaling exponent γ apart from the usual superpositioning of relaxation data. If the intermolecular potential can be approximated by an inverse power law, as implied by the TVγ scaling, various equations are derived relating γ to the Grüneisen parameter and to a common expression for the pressure derivative of the glass temperature. In addition, without assumptions, γ can be obtained directly from pressure-volume-temperature data. These methods for determining γ from molecular or thermodynamic properties are useful because they enable the P- and V-dependences of τ to be obtained, and thereby various analyses of the dynamics to be explored, without the need to carry out relaxation measurements beyond ambient pressure.