88
2 The Interaction of Electromagnetic Waves with Water
2.6.3 Second Dielectric Relaxation (“Excess Wing”)
The frequency gap between IR oscillations and the dielectric relaxation is the most
poorly studied part of the dielectric response of water. The corresponding frequency
range from 50 GHz to about 10 THz is hard to reach by dielectric spectroscopy
techniques from the left side and IR spectroscopy from the right side. That is why, the
right-hand side of Debye relaxation has been long unstudied, and even today a large
uncertainty of the data point exists, as shown in Fig. 2.18b, in this part of the spectrum.
Recently, terahertz time-domain spectroscopy revealed two sub-picosecond spectral
features, which have been treated as fast relaxation processes, ν D2 , near 60 cm
−1 (2
THz), and ν D3 , near 5 cm
−1 (0.2 THz) [91], which constitute the so-called “excess
wing” of the dielectric relaxation, because the dielectric losses here exceed the level
expected from the Debye formula 2.24. This deviation from Debye’s prediction has
been called a “fast relaxation” process [9].
The relaxation process ν D2 was initially assigned to the reorientation of an individual water molecule [91], as predicted by computer simulations [92, 93]. This interpretation assumes a two-component structural model of water, which has been revealed
by Raman spectroscopy [94] and neutron scattering [95]. However, a different interpretation has been proposed based on the results of ultrafast spectroscopy [96]. It has
been shown that both the main and the fast relaxation processes are due to collective
dynamics, in which the main relaxation is caused by the collective reorganization
of water molecules [97], and the fast relaxation is the inertial motion of individual
water molecules [98].
Yada et al. [7], using terahertz time-domain spectroscopy, showed that the temperature dependence and the isotope shift of fast relaxation are in good agreement
with the individual relaxation mode, thus confirming the existence of free molecules
in the sub-picosecond timescale. The fast relaxation ν D2 is assigned to the collision
process, which means that the heterogeneity of the water is dynamic, and the ambient
water is regarded as two-component mixtures in a sub-picosecond time interval.
The mode ν D3 , which has been shown to be Raman active and similar to those
observed in superionic conductors (see Sect. 2.6.1) and by neutron scattering [99], is
assigned to the hindered translations [100, 101]. Arbe et al. [99] compared the dielectric relaxation data and the neutron scattering data and found that on sub-picosecond
timescales, the hydrogen atom moves in a “cage” with a size of 0.5 Å. Such a size corresponds to the amplitude of the vibration of hydrogen atoms (presumably together
with the host molecule) and is much smaller than the intermolecular distance, which
is 2.8 Å. These results confirm that the mode ν D3 is related to the local translational
movements of molecules, presumably in the excess-proton state, as discussed in [73].
Several phenomenological models have recently been suggested to describe the
main dielectric relaxation near 20 GHz and the high-frequency processes shown in
Fig. 2.4) on the same footing. Figure 2.23 compares these models with the experimental data in terms of dielectric permittivity. The classic Debye model (magenta)
2 The Interaction of Electromagnetic Waves with Water
2.6.3 Second Dielectric Relaxation (“Excess Wing”)
The frequency gap between IR oscillations and the dielectric relaxation is the most
poorly studied part of the dielectric response of water. The corresponding frequency
range from 50 GHz to about 10 THz is hard to reach by dielectric spectroscopy
techniques from the left side and IR spectroscopy from the right side. That is why, the
right-hand side of Debye relaxation has been long unstudied, and even today a large
uncertainty of the data point exists, as shown in Fig. 2.18b, in this part of the spectrum.
Recently, terahertz time-domain spectroscopy revealed two sub-picosecond spectral
features, which have been treated as fast relaxation processes, ν D2 , near 60 cm
−1 (2
THz), and ν D3 , near 5 cm
−1 (0.2 THz) [91], which constitute the so-called “excess
wing” of the dielectric relaxation, because the dielectric losses here exceed the level
expected from the Debye formula 2.24. This deviation from Debye’s prediction has
been called a “fast relaxation” process [9].
The relaxation process ν D2 was initially assigned to the reorientation of an individual water molecule [91], as predicted by computer simulations [92, 93]. This interpretation assumes a two-component structural model of water, which has been revealed
by Raman spectroscopy [94] and neutron scattering [95]. However, a different interpretation has been proposed based on the results of ultrafast spectroscopy [96]. It has
been shown that both the main and the fast relaxation processes are due to collective
dynamics, in which the main relaxation is caused by the collective reorganization
of water molecules [97], and the fast relaxation is the inertial motion of individual
water molecules [98].
Yada et al. [7], using terahertz time-domain spectroscopy, showed that the temperature dependence and the isotope shift of fast relaxation are in good agreement
with the individual relaxation mode, thus confirming the existence of free molecules
in the sub-picosecond timescale. The fast relaxation ν D2 is assigned to the collision
process, which means that the heterogeneity of the water is dynamic, and the ambient
water is regarded as two-component mixtures in a sub-picosecond time interval.
The mode ν D3 , which has been shown to be Raman active and similar to those
observed in superionic conductors (see Sect. 2.6.1) and by neutron scattering [99], is
assigned to the hindered translations [100, 101]. Arbe et al. [99] compared the dielectric relaxation data and the neutron scattering data and found that on sub-picosecond
timescales, the hydrogen atom moves in a “cage” with a size of 0.5 Å. Such a size corresponds to the amplitude of the vibration of hydrogen atoms (presumably together
with the host molecule) and is much smaller than the intermolecular distance, which
is 2.8 Å. These results confirm that the mode ν D3 is related to the local translational
movements of molecules, presumably in the excess-proton state, as discussed in [73].
Several phenomenological models have recently been suggested to describe the
main dielectric relaxation near 20 GHz and the high-frequency processes shown in
Fig. 2.4) on the same footing. Figure 2.23 compares these models with the experimental data in terms of dielectric permittivity. The classic Debye model (magenta)