Consistency of the Vogel — Fulcher — Tammann (VFT) Equations For The Temperature-, Pressure-, Volume-and Density- Related Evolutions of Dynamic Properties in Supercooled and Superpressed Glass Forming Liquids/Systems

Abstract

A consistent set of temperature- (T), pressure- (P), volume- (V) and density- (ρ) related VFT-type equations for portraying the evolution of the structural relaxation time or viscosity is presented, namely: $$\begin{array}{rcl} \tau \left(P \right) & = & \tau _0 \,\exp \left[ {{{D_P \left({P - P_{SL} } \right)}/{\left({P_0 - P} \right)}}} \tau \left(T \right) & = & \tau _0 \,\exp \left[ {{{D_T \left({T_{SL} - T} \right)\left({{{T_0 }/{T_{SL} }}} \right)}/{\left({T - T_0 } \right)}}} \right], \tau \left(\rho \right) & = & \tau _0 \,\exp \left[ {{{D_\rho \left({\rho - \rho _{SL} } \right)}/{\left({\rho _0 - \rho } \right)}}} \right] \end{array}$$ andτ (V) = τ 0 exp[D T (V SL — V)(V 0 V SL )/(V — V 0)], where T 0,P 0,V 0 and ρ0 are VFT estimates of the ideal glass loci and T SL , P SL , V SL and ρ SL are estimates of the location of the absolute stability limit, partially hidden in the negative pressures domain (P<0). For these equations prefactors are well defined via ρ 0 = ρ (T SL ,P SL , V SL ,ρ SL ), ie. they are linked to the absolute stability limit loci (gas-liquid spinodal). Noteworthy is their smooth transformation into VFT-type equations, used so far, on approaching the glass transition, and into Arrhenius-type equations remote from the glass transition, on approaching the absolute stability limit. The latter may suggest the re-examination of experimental data suggesting the VFT-to-Arrhenius crossover far away from the glass transition. Novel VFT counterparts also lead to the consistent set of fragility strength coefficients (D T ,D P ,D V ,D ρ) and fragilities associated with the slope (steepness index) at appropriate “Angell plot” counterparts.