KFU. Card publication. New approach in the description of dielectric relaxation phenomenon: Correct deduction and interpretation of the Vogel-Fulcher-Tamman equation

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NEW APPROACH IN THE DES&SHY;CRIPTION OF DIELECTRIC RELAXATION PHENOMENON: CORRECT DEDUCTION AND INTERPRETATION OF THE VOGEL-FULCHER-TAMMAN EQUATION

Form of presentation

Articles in international journals and collections

Year of publication

2003

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Authors, employees of KFU

Nigmatullin Ravil Rashidovich, author

Osokin Sergey Igorevich, author

Other authors

Smith Geoff , author

Bibliographic description in the original language

Nigmatullin R.R, Osokin S.I, Smith G., New approach in the description of dielectric relaxation phenomenon: Correct deduction and interpretation of the Vogel-Fulcher-Tamman equation//Journal of Physics Condensed Matter. - 2003. - Vol.15, Is.20. - P.3481-3503.

Annotation

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.

Keywords

Vogel-Fulcher-Tamman equation, non-exponential relaxation, complex permittivity functions, dielectric relaxation phenomena

The name of the journal

Journal of Physics Condensed Matter

URL

https://iopscience.iop.org/article/10.1088/0953-8984/15/20/309

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=141101&p_lang=2

Resource files

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Full metadata record

Field DC	Value	Language
dc.contributor.author	Nigmatullin Ravil Rashidovich	ru_RU
dc.contributor.author	Osokin Sergey Igorevich	ru_RU
dc.contributor.author	Smith Geoff	ru_RU
dc.date.accessioned	2003-01-01T00:00:00Z	ru_RU
dc.date.available	2003-01-01T00:00:00Z	ru_RU
dc.date.issued	2003	ru_RU
dc.identifier.citation	Nigmatullin R.R, Osokin S.I, Smith G., New approach in the description of dielectric relaxation phenomenon: Correct deduction and interpretation of the Vogel-Fulcher-Tamman equation//Journal of Physics Condensed Matter. - 2003. - Vol.15, Is.20. - P.3481-3503.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=141101&p_lang=2	ru_RU
dc.description.abstract	Journal of Physics Condensed Matter	ru_RU
dc.description.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.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Vogel-Fulcher-Tamman equation	ru_RU
dc.subject	non-exponential relaxation	ru_RU
dc.subject	complex permittivity functions	ru_RU
dc.subject	dielectric relaxation phenomena	ru_RU
dc.title	New approach in the description of dielectric relaxation phenomenon: Correct deduction and interpretation of the Vogel-Fulcher-Tamman equation	ru_RU
dc.type	Articles in international journals and collections	ru_RU