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

Abstract

Based on the relationship between the power-law exponent and relaxation time ν(τ) 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 ωp (T) = ω0 exp [−DTVF /(T − TVF)], connecting the maximum of the loss peak with temperature. The fitting parameters D and TVF of this equation are related accordingly with parameters (ν0, τs τ0), entering to ν(τ) = ν0 [ln (τ/τs)/ ln (τ/τ0)] and (τA, E) figuring in the Arrhenius formula τ(T) = τA 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 τA1,A2 and E1,2. It has been shown that (1) at a certain combination of initial parameters the parameter TVF 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.

New method and treatment technique applied to interband transition in GaAs1−x Px ternary alloys

“…The basic principles of the ECs method are outlined in [8,9]. The application in detection of impedances and dielectric spectroscopy can be found in references [10][11][12][13][14][15][16][17][18][19][20][21][22]. The reader can find some information about the application in recognition of different statistical distributions in [23][24][25] and to dynamical chaos in [26].…”

Evidences of the fractional kinetics in temperature region: Evolution of extreme points in ibuprofen

“…The limiting value R 0 determines the mean cutoff size of a spherically-symmetric cluster in the 3D-space associated with a rotational/translational movement of electric dipoles over the given self-similar structure. We suppose [14][15][16] also that a possible connection between mean relaxation time s and temperature T is given by the Arrhenius relationship. It is convenient to express the mean reorientation energy (E) in temperature units (K)…”

“…For further consideration it is important to consider the general expression for the complex permittivity. It can be derived in papers [5,[14][15][16] and the last term in Eq. (5) is obtained in the result of the stationary solution of kinetic equation containing non-integer operators of differentiation and integration…”

“…The first two terms in (5) take into account a possible contribution of conductive $ 1=ðjxÞ and the low-frequency dispersion (LFD) $ 1=ðjxs d Þ j terms, correspondingly [5,[14][15][16]. Expression (5) reflects correctly the linear structure of the fractional kinetic equation written in the time-domain.…”

“…So, the generalized VFT-equation can be considered as a specific label in the certain temperature region separating two neighboring reduced motions. The generalized VFT equation for the x m ðTÞ has been derived in papers [16,17] and in this paper it is written as…”