New approach in the description of dielectric relaxation phenomenon: correct deduction and interpretation of the Vogel-Fulcher-Tamman equation

Based on the relationship between the power-law exponent and relaxation time nu(tau) recently established in Ryabov et al (2002 J. Chem. Phys. 116 8610) for non-exponential relaxation in disordered systems and conventional Arrhenius temperature dependence for relaxation time, it becomes possible to derive the empirical Vogel-Fulcher-Tamman (VFT) equation omega(p)(T) = omega(0) exp[-DTVF/(T - T-VF)], connecting the maximum of the loss peak with temperature. The fitting parameters D and TVF of this equation are related accordingly with parameters (nu(0), tau(s)tau(0)), entering to nu(tau) = nu(0)[ln(tau/tau(s))/ln(tau/tau(0))] and (tau(A), E) figuring in the Arrhenius formula tau(T) = tau(A) exp(E/T). It has been shown that, in order to establish the loss peak VFT dependence, a complex permittivity function should contain at least two relaxation times obeying the Arrhenius formula with two different set of parameters tau(A1,) (A2) and E-1,E-2. It has been shown that (1) at a certain combination of initial parameters the parameter T-VF can be negative or even accept complex valued (2). The temperature dependence of the minimum frequency formed by the two nearest peaks also obeys the VFT equation with another set of fitting parameters. The available experimental data obtained for different substances confirm the validity and specific 'universality' of the VFT equation. It has been shown that the empirical VFT equation is approximate and possible corrections to this equation are found. As a main consequence, which follows from the correct 'reading' of the VFT equation and interpretation of complex permittivity functions with two or more characteristic relaxation times, we suggest a new type of kinetic equation containing non-integer (fractional) integrals and derivatives. We suppose that this kinetic equation describes a wide class of dielectric relaxation phenomena taking place in heterogeneous substances.