Ph.D. thesis (pdf) - dirac

86 Alpha Relaxation
2.5
2.5
2
2
log 10
Im(ε) [arb.units]
1.5
1
0.5
ACC
KWW
log 10
Im(ε) [arb.units]
1.5
1
0.5
GGE
GG
0
CD
0
HN
−0.5
2 3 4 5 6
log 10
ν [Hz]
−0.5
2 3 4 5 6
log 10
ν [Hz]
Figure 5.11: Log-log plot of the dielectric loss of m-toluidine at T=216.4K and
122MPa along with best fits to several common functional forms. Figure a) show
the fitting functions from below and up; CD, KWW, AAC. Figure b) shows from
below and up; HN, Gamma distribution, Generalized gamma distribution. CD,
KWW and AAC have 1 parameter characterizing the shape, HN and Gamma have
2, and Generalized gamma has been fitted using 3 adjustable parameters. The
dashed line shows the Gamma distribution corresponding to the generalized gamma
distribution. The curves are displaced along the y-axis by regular amounts.
5.3.2 Spectral shape DBP
The frequency-dependent dielectric loss for a selected set of different pressures and
temperatures is shown in figure 5.12. The first observation is that cooling and
compressing have a similar effect as both slow down the alpha relaxation and separate
the alpha relaxation from higher-frequency beta processes. The data depicted are
chosen so that different combinations of temperature and pressure give almost the
same relaxation time. However, the correspondence is not perfect. In figure 5.13
we have thus slightly shifted the data, by at most 0.2 decade, in order to make
the peak positions overlap precisely. This allows us to compare the spectral shapes
directly. It can be seen from the figure that the shape of the alpha peak itself is
independent of pressure and temperature for a given value of the alpha-relaxation
time (i.e., of the frequency of the peak maximum), while this is not true for the highfrequency
part of the spectrum, which is strongly influenced by the beta-relaxation
peak (or high-frequency wing). When comparing datasets that have the same alpharelaxation
time one finds that the high-frequency intensity is higher for the pressuretemperature
combination corresponding to high pressure and high temperature.
In figure 5.14 we show all the datasets of figure 5.12 superimposed and we zoom on