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4 Results

[1286.4.1] Model A fits for 5-methyl-2-hexanol are shown in Fig. 1 and for methyl-m-toluate Fig. 2. [1286.4.2] Note that in our notation \varepsilon=\varepsilon^{{\prime}}-i\varepsilon^{{\prime\prime}}. [1286.4.3] Model A fits the data remarkably well for five, respectively seven orders of magnitude, where both the \alpha-peak and the excess wing can be fitted simultaneously with only three parameters. [1286.4.4] Model A is better suited than the Havriliak-Negami model which only fits reasonably well for up to four orders of magnitudes for these materials. [1286.4.5] This improvement is due to the positive curvature of the function in (11) at frequencies above the \alpha-peak. [1286.4.6] Sometimes this curvature poses also the main difficulty when fitting with model A. [1286.4.7] An example is glycerol as seen in the left part of Fig. 3. [1286.4.8] While it is easy to fit closely the the \alpha-peak it is more difficult to simultaneously fit the excess wing.

[1286.5.1] Model B can fit the data much better than model A, because it contains one more parameter. [1286.5.2] Nevertheless, it is remarkable that it can fit a range of up to 10 orders of magnitude with little deviation from the data points. [1286.5.3] We believe that this model can be used to fit over some more orders of magnitude, but at this time there is no experimental data available which covers a broader range.

Figure 3: Simultaneous fits of real and imaginary part with model A (left figure) and model B (right figure) for glycerol at 185\,{\rm K}. While model A is not able to fit the data well, model B still gives an excellent fit over 10 decades. The data are from [8].