Derivative-based analysis for temperature and pressure evolution of dielectric relaxation times in vitrifying liquids

Aleksandra Drozd-Rzoska and Sylwester J. Rzoska

Phys. Rev. E 73, 041502 – Published 4 April 2006

Abstract

The derivative-based analysis for detecting regions of the validity of the Vogel-Fulcher-Tammann (VFT) dependence for superpressed and supercooled liquids is discussed. For the temperature $(T)$ path the analysis introduced by Stickel et al. [J. Chem. Phys. 104, 2043 (1996); J. Chem. Phys. 107, 1086 (1997)] is recalled. For the pressure $(P)$ path the derivation based on the counterpart of the VFT dependence proposed in Paluch et al. [J. Phys.: Condens. Mater 10, 4131 (1998)] is presented. The appearance of two ideal glass temperatures $(T_{0})$ or pressures $(P_{0})$ , fragility strength coefficients $(D_{T}, D_{P})$ , and prefactors $(τ_{0}^{T}, τ_{0}^{P})$ for VFT equations in following dynamical domains, i.e., high-temperature $(Δ T_{h i g h})$ and low-temperature $(Δ T_{l o w})$ or low-pressure $(Δ P_{l o w})$ and high-pressure $(Δ P_{h i g h})$ , is stressed. It is noteworthy that the values of $T_{0} (Δ T_{h i g h}) > T_{0} (Δ T_{l o w}), D_{T} (Δ T_{h i g h}) ⪡ D_{T} (Δ T_{l o w})$ , and $τ_{0}^{T} (Δ T_{h i g h}) ⪢ τ_{0}^{T} (Δ T_{l o w})$ . Analogous behavior was noted for isothermal $Δ P_{L}$ and $Δ P_{H}$ dynamic domains. A similar derivative-based approach is also applied to test the validity of the mode coupling theory (MCT) critical-like equation $τ (T) \propto (T - T_{X})^{- g}$ . It yields the temperature $T_{X}$ and the MCT power (“critical”) exponent $g$ exclusively from the simple linear regression. The extension of such an analysis for the pressure path is also given. The hardly discussed question of the error of estimations of $g$ and $T_{X}$ is emphasized. The relation between the derivative based behavior mentioned above and the apparent activation enthalpy (temperature path) or the apparent activation volume (pressure path) is indicated. The presented analysis was applied to discuss the dynamic crossovers in supercooled and superpressed diethyl phthalate, based on experimental data supplemented by those given in Pawlus et al. [Phys. Rev. E 68, 021503 (2003)].