Excess wing

Usually, spin-lattice relaxation experiments are performed at one or a few magnetic fields. The spectral density can thus be determined at only a few Larmor frequencies, so that a detailed analysis of its temperature variation is not possible. Here, an analysis of the spin-spin relaxation times, T, can provide further information about the spectral density, since T2 1 S2(to = 0). Often, the Cole-Davidson distribution Gco(lnT2) [34] is chosen to interpolate the relaxation around the maximum. However, one has to keep in mind that the spectral density close to Tg contains additional contributions from secondary relaxations, such as the excess wing and/or the (i-process discussed in the following sections. In Section IV.C we give an example of a quantitative description of 7) (T) at T > 7 obtained by approximating the spectral density S2(co) using dielectric data. 

Given the good interpolation of the susceptibility spectra by the GGE distribution we can focus on the temperature dependence of the parameters. We compiled the results from analyzing DS spectra of several type A glass formers [6,136,137,142,230,273,275], Note that the glass formers trimethyl phosphate (TMP, [230,275]), 3-fluoro aniline (FAN, [142]) and methyl tetrahydrofuran (MTHF, [331]) show both the excess wing and a p-process (cf. Fig. 35). In this... 

Figure 28. The excess wing exponent y for ten different glass formers (cf. Fig. 27) rescaled by " g = y(Tg) so that all the datasets coincide on a master curve. The solid line represents Eq. (40). For more details see Ref. [275],...

Figure 29. Dielectric spectra of several type A glass formers shifted by a temperature independent factor k to provide coincidence at highest frequencies, i.e., in the region of the excess wing (compiled from [137,142,230]) note that although the spectra exhibit virtually the same excess wing the a-peak itself is different along different a values of the GGE distribution, cf. Eq. 36.

Nagel scaling approach and also to that obtained by decomposition into separate relaxation processes [9,258]. Though different in detail, all the mentioned approaches agree that the high-frequency exponents of the a-peak and the excess wing both vary with temperature and thus that the FTS principle does not apply close to Tg. 

A further complication arises, because many glass formers exist exhibiting an excess wing in addition to a p-process, and it is by no means clear whether in those cases two intrinsic relaxation processes are present [6,142,152,230, 331,137,321]. In particular, for a relatively weak and well-separated p-process, it appears that the excess wing as well as a-peak still manifest themselves distinctly (i.e., the type A characteristics ), and a simple superposition model may apply for both processes [6,284], On the other hand, a strong p-process leads to a pronounced change of the a-peak, and then it is quite impossible to tell whether or not an additional excess wing is present. Furthermore, one may even have to face the fact that different JG processes may be probed in a different manner by the various methods. This, if true, would allow for a further distinction. 

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