For glass formers with very small β-contribution (type A) the dielectric response in the glass appears quite uniform, cf. Fig. IV.27. According to this figure, the amplitude of the dielectric response of type A systems in the glass appears to correlate with the amplitude of the α-peak. This is not the case for type B systems, as discussed next.
For comparison, the temperature dependence of the dielectric loss ε’’(T),
measured at 1 kHz, is present in Fig. IV.28 for systems with strong β-processes, that may obscure the presence of any EW contribution below Tg. The data are obtained as part of this work by applying the high-precision bridge AH 2700. In Fig. IV.28 only single frequency data are presented, while the results obtained within three decades in frequency (covered by the bridge) are analyzed in details in next Chapter.
For type B systems the ε’’(T) curves appear as distinctive. At high temperatures, above Tg, ε’’(T) is dominated by the α-peak, while in the glass by the β-peak. For the high molecular mass PB2000 even two secondary relaxation peaks can be identified in the glass, as discussed in details in Chapter VII. The data for m-TCP are also added here to indicate a β-contribution at low temperatures.
0 50 100 150 200 250 10-5
10-4 10-3 10-2 10-1 100
101 mTCP
mFAN toluene PB2000 PB330 cchex glycerol
T / K
ε ''
1 kHz
(a)
Fig. IV.28 Temperature dependence of ε’’ at 1 kHz for the type B systems and glycerol as obtained with the high precision bridge.
As for these systems the β-contribution appears not to correlate with the α-amplitude (cf. also Fig. IV.8.b), it becomes interesting to present all the data (for type A and type B) scaled by the value of the molecular dipole moment that controls the amplitude of the latter.
Up to our knowledge, such a scaling was not done yet. This maybe due to the fact that one cannot find in literature the values for the molecular dipole moments μmol for many molecular systems. In order to overcome this problem, we estimate μmol using the Curie law at temperatures well above Tg, as discussed next.
The Curie law (introduced in II.1) relates the dielectric strength Δε of any relaxation process with the relaxing dipole moment μ, the number density of the dipoles in the dielectric material and the temperature T:
kT n mol
0 2
3ε ε = μ
Δ (II.6) This law was found to interpolate well the data for the α-process for low viscous liquids, however, it usually fails for high viscous liquids close to Tg
[117]. In order to access the values of μmol, we evaluated for most of the systems the dielectric strength of the α-process Δε = εs - ε∞ at the highest accessible temperature (T ), where the Curie law should hold best. For ref
systems the dielectric strength of the α-process Δε = εs - ε∞ at the highest accessible temperature (Tref), where the Curie law should hold best. For systems with very low dipole moment as, e.g. toluene and PB, Δε could not be evaluated directly from ε’(ν) data. Instead, Δε was obtained as a fitting parameter in the interpolation of the spectra ε’’(ν) cf. analysis in IV.2. The reference temperatures Tref and the corresponding values of the strength Δεref
used in the analysis are posted in Table IV.1.
System Tref (K) Δεref
Glycerol 413 23.8
PC 212 65
2-picoline 202 6.5
Salol 245 3.9
Type A
4TBP 187 10.1
m-TCP 260 4
m-FAN 198 17.8
Toluene 127 0.3 (from[26])
Type B
PB330 200 0.06 (from [26])
Table IV.1. The values of Tref and Δεref used for the evaluation of the molecular dipole moments μmol according to the Curie law.
Taking for granted the Curie law at such high temperatures, the following relation should hold:
n kTref ref
mol
ε μ2 = 3ε0 Δ
(V.4)
Since the number density for the systems under consideration vary within a factor smaller than 4 (cf. discussion in V.2), one just have to divide ε’’ by the product TrefΔεref in order to scale out the contribution of the dipole moment.
The result of this scaling is shown in Fig. IV.29. Here ε’’/ (TrefΔεref) is plotted as a function of the reduced temperature T/Tg for all systems investigated in this work down to cryogenic temperatures, around 4 K. Some interesting features are revealed: the systems that do not exhibit secondary relaxation peaks the dielectric loss ε’’, above and also below Tg exhibit a quite similar behavior.
Among these systems the corresponding amplitudes of the α-process, the NCL, the ADWP peak and the tunneling plateau (the last two are discussed in
the next Chapter) vary within a small factor below 5. For systems with strong β-contribution the scaling works well at the highest and the lowest temperatures, but not in the temperature range dominated by the β-peak, i.e.
the β-process does not scale with the molecular dipole moment. As suggested by the behavior of the systems with fast β-processes (e.g., 4-TBP or m-TCP) close to Tg, one may speculate that the EW is always present in molecular glasses as a relaxation background that may be obscured in cases of strong β-contribution.
0.0 0.2 0.4 0.6 0.8 1.0 1.2
10-8 10-7 10-6 10-5 10-4 10-3 10-2
PC m-FAN 2-PIC m-TCP glycerol toluene 4TBP PB300 salol
T / T
g ε''/(
Δε refT
ref)
1 kHz
Fig. IV.29 The imaginary part of permittivity ε’’ for all molecular glasses investigated in this work down to 4 K, scaled by the molecular dipole moment (see text for details) in the
reduced T/Tg scale.
Another remarkable fact is that by scaling out the dipole moment, independent from the particularities observed above, the data at lowest temperatures collapse to a system independent constant value for most of the systems. As discussed in the next Chapter, this may be taken as an indication that the tunneling regime is reached for molecular systems at such low temperatures, below, say, 10 K.