1 Introduction

[page 1283, §1]   
[1283.1.1] Many physical properties of glass forming liquids (e.g. their viscosity) vary dramatically (often over 15 or more decades) within a narrow temperature interval around the glass transition [1]. [1283.1.2] The change of physical properties during the glass transition has not yet been fully understood and remains a subject of intense investigations [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].

[1283.2.1] In this work we study the glass transition by investigating the dielectric susceptibility. [1283.2.2] The dielectric susceptibility quantifies the response of permanent and induced dipoles to an applied frequency dependent electric field. [1283.2.3] The dielectric loss (resp. imaginary part of the complex dielectric susceptibility) typically shows a temperature dependent maximum, the α-peak, at low frequencies. [1283.2.4] It is followed at higher frequencies by a so-called excess wing [13]. [1283.2.5] This excess wing has not yet been understood nor has it been described by any model with less than 4 fit parameters [13]. [1283.2.6] Existing theories, such as the mode coupling theory (see [14, 15] and references therein), do not allow to fit the excess wing. [1283.2.7] Traditional phenomenological fits of the excess wing employ a superposition of two Havriliak-Negami functions [16, 5, 13], and they need 7 fit parameters to fit a range of 10 decades.

[1283.3.1] The aim of this work is to provide analytical expressions for excess wings with only three and four parameters. [1283.3.2] The formulae are obtained from the previously introduced method of fractional time evolution [17, 18, 19], and applied to experimental data exhibiting a clear excess wing over a frequency range as broad as possible. [1283.3.3] The fit functions need only three parameters (one exponent and two relaxation times in model A) or four parameters (two exponents and two relaxation times for model B). [1283.3.4] This is a significant improvement compared to six parameters for the superposition of the Havriliak-Negami and Cole-Cole expression presently used [19, 20]. [1283.3.5] We study the glass forming materials 5-methyl-2-hexanol [6], glycerol [8] and methyl-m-toluate [12].