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 TV^γ, 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 TV^γ 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.