Empirical Correlations Between Free Volume Fractions from Pals Data and Various Dynamic Quantities in Ortho-Terphenyl

Phenomenologically, the mobility properties of supercooled liquids such as viscosity (M = η), relaxation time (M = τ) and diffusion coefficient (M = 1/D) are usually described by the Vogel -Fulcher (VF) equation or, equivalently, by the Williams - Landel - Ferry (WLF) equation, Williams et al (1955). Both the equations are often interpreted within the free volume concept at a phenomenological level using the empirical Doolittle equation, Doolittle (1951) or/and at a quasi-molecular one by means of a free volume model of Cohen, Turnbull (1959). The WLF Doolittle formula for the shift factor a(T) = M(T)/M(Tg) can be expressed as follows: $$ln{\text{ }}a(T) = B_f [l/f(T) - l/f(T_g )]$$ (1)