Analysis of excess wings in broadband dielectric spectroscopy data of glass forming materials provides evidence for anomalous time evolutions and fractional semigroups. Solutions of fractional evolution equations in frequency space are used to fit dielectric spectroscopy data of glass forming materials with a range between 4 and 10 decades in frequency. It is shown that with only three parameters (two relaxation times plus one exponent) excellent fits can be obtained for 5-methyl-2-hexanol and for methyl-m-toluate over up to 7 decades. The traditional Havriliak-Negami fit with three parameters (two exponents and one relaxation time) fits only 4–5 decades. Using a second exponent, as in Havriliak-Negami fits, the α-peak and the excess wing can be modeled perfectly with our theory for up to 10 decades for all materials at all temperatures considered here. Traditionally this can only be accomplished by combining two Havriliak-Negami functions with 7 parameters. The temperature dependent relaxation times are fitted with the Vogel-Tammann-Fulcher relation which provides the corresponding Vogel-Fulcher temperatures. The relaxation times turn out to obey almost perfectly the Vogel-Tammann-Fulcher law. Computable expressions of time dependent relaxation functions are also reported.


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    Titel :

    Excess wings in broadband dielectric spectroscopy


    Beteiligte:
    Candelaresi, S. (Autor:in) / Hilfer, R. (Autor:in) / Sivasundaram, Seenith (Herausgeber:in)

    Kongress:

    10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 ; 2014 ; Narvik, Norway


    Erschienen in:

    AIP Conference Proceedings ; 1637 , 1 ; 1283-1290


    Erscheinungsdatum :

    10.12.2014


    Format / Umfang :

    8 pages





    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch



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