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Excess Wings in Broadband Dielectric Spectroscopy

S. Candelaresi{}^{{1,2}} and R. Hilfer{}^{{3}}
{}^{1}Division of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom
{}^{2}NORDITA, AlbaNova University Center, Roslagstullsbacken 23, 10691 Stockholm, Sweden
{}^{3}Institut für Computer Physik, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany

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 \alpha-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.

Key words and phrases:
time evolution, anomalous dynamics, fractional derivatives, glass transition, excess wing, dielectric spectroscopy
PACS: 77.22.Gm,64.70.Q-,77.22.Ch,67.70.pj,77.84.Jd,02.60.Nm