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

摘要

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: τ(P)= τ_0 exp[D_P(P - P_(SL))/ (P_0 - P)] τ(T)= τ_0 exp[D_T (T_(SL) -T)(T_0/T_(SL))/(T - T_0)], τ(ρ)=τ_0 exp[Dρ(ρ-ρ_(SL))/ρ_0-ρ)] and τ(V)= τ_0 exp[D_T (V_(SL)-V)(V_0/V_(SL))/(V - V_0)]A, where T_0, P_0, V_0 and ρ_0 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 τ_0 = τ(T_(SL), P_(SL), V_(SL), ρ_(SL)), i.e. 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.