A Simplified Method for the Estimation of Hole Free Volume Fraction from the Specific Volume

A brief introduction in the equation of state of the Simha-Somcynsky hole theory is presented. This theory allows to calculate the volume fraction h of free volume holes from pressure-volume-temperature experiments. These holes are detected by ortho-positronium and from the value of h and the mean ortho-positronium hole size the hole density may be calculated. We discuss a simplified method to estimate h which makes use of the relation V* = 1.52 $V_W$ between the scaling volume V* of the Simha-Somcynsky hole theory equation of state and the van der Waals volume $V_W$. Moreover, we present a new simplified method for the estimation of h which starts with the Schottky (Arrhenius) equation for the concentration of thermal vacancies and makes use of a linear relation between the scaling temperature T* and the hole formation enthalpy $H_h$, $H_h$(kJ/mol)=6.54×$10^{-4}$T*(K).