66
2 The Interaction of Electromagnetic Waves with Water
time, because the orientation lags with increasing frequency due to viscous friction.
Although this simple idea is still popular, it has been shown (see, for example, [11])
that the orientation of H 2 O dipoles gives incorrect values of the static dielectric
constant of water and fails to reproduce its temperature dependence. Nowadays,
it is obvious that the process of dielectric relaxation has more complex collective
dynamics [13, 14], which are only partially associated with molecular reorientations
(see Sect. 4.5).
Jaccard [16] assumed that dielectric relaxation in ice, which has been shown to
be very similar to that in water [17], can be explained by two types of charged
defects. First are conventional H 3 O
+ and OH
− ions responsible for DC conduction,
and second are Bjerrum valence defects, which have either two protons (D defect) or
no protons (L defect) between two neighboring molecules, which manifest at high
frequencies. This model allows one to qualitatively describe the dielectric spectrum
of ice [18], although Bjerrum defects have never been observed experimentally.
Recently, Jaccard’s theory has been applied to water, and the main dielectric
relaxation has been explained by the dynamics of Bjerrum defects [19]. Although
the dielectric spectrum of water has been qualitatively described, the relatively high
value of the high-frequency conductivity of water, σ D1 , assumes that the defect concentration is as high as a few percent of all water molecules. This means that the
strong interaction between all charge carriers, which is missing in the proposed
model, should be accounted for. However, the authors do not imply any interaction between different types of defects. The interaction should, first, affect the DC
conductivity that the authors assumed is due to the free motion of H 3 O
+ and OH
−
ions, which is not the case, and second, give additional relaxation time, which is
not observed. Moreover, the lifetime of Bjerrum defects is expected to be about a
few picoseconds, as it is determined by molecular reorientations, while the Debye
relaxation time is dozens of picoseconds, thus significantly exceeding the expected
lifetime of the charge carriers. In other words, the model of two types of charged
defects does not fully satisfy the experimental results.
An alternative mechanism for the dielectric relaxation of water was first suggested
in [17]. The authors explained static conductivity and Debye relaxation by the Brownian dynamics of interacting H 3 O
+ and OH
− ions, thus considering only one type of
charge carrier. The high-frequency dielectric response, which includes Debye relaxation, is shown to be the result of the polarization of interacting counterions, while
low-frequency DC conductivity is produced by the same ionic species, which are
long-lived enough to overcome mutual screening and contribute to static conductivity. Although the concentration of all H 3 O
+ and OH
− ions was shown to be high, the
effective concentration of those ions participating in DC conductivity is exactly the
same as assumed by pH. It was also shown that this model (the ionic model of water
presented in Sect. 4.2.3) describes the experimental conductivity spectrum of water
and ice from DC current to THz [8]. For a detailed analysis of the ionic model, see
Chap. 4.
Thus, the microscopic description of dielectric relaxation in water is still debated.
We can say for sure that it does not reduce to the orientations of H 2 O dipoles. The rotational mechanism of polarization is fully confirmed for the gas phase (water vapor)
2 The Interaction of Electromagnetic Waves with Water
time, because the orientation lags with increasing frequency due to viscous friction.
Although this simple idea is still popular, it has been shown (see, for example, [11])
that the orientation of H 2 O dipoles gives incorrect values of the static dielectric
constant of water and fails to reproduce its temperature dependence. Nowadays,
it is obvious that the process of dielectric relaxation has more complex collective
dynamics [13, 14], which are only partially associated with molecular reorientations
(see Sect. 4.5).
Jaccard [16] assumed that dielectric relaxation in ice, which has been shown to
be very similar to that in water [17], can be explained by two types of charged
defects. First are conventional H 3 O
+ and OH
− ions responsible for DC conduction,
and second are Bjerrum valence defects, which have either two protons (D defect) or
no protons (L defect) between two neighboring molecules, which manifest at high
frequencies. This model allows one to qualitatively describe the dielectric spectrum
of ice [18], although Bjerrum defects have never been observed experimentally.
Recently, Jaccard’s theory has been applied to water, and the main dielectric
relaxation has been explained by the dynamics of Bjerrum defects [19]. Although
the dielectric spectrum of water has been qualitatively described, the relatively high
value of the high-frequency conductivity of water, σ D1 , assumes that the defect concentration is as high as a few percent of all water molecules. This means that the
strong interaction between all charge carriers, which is missing in the proposed
model, should be accounted for. However, the authors do not imply any interaction between different types of defects. The interaction should, first, affect the DC
conductivity that the authors assumed is due to the free motion of H 3 O
+ and OH
−
ions, which is not the case, and second, give additional relaxation time, which is
not observed. Moreover, the lifetime of Bjerrum defects is expected to be about a
few picoseconds, as it is determined by molecular reorientations, while the Debye
relaxation time is dozens of picoseconds, thus significantly exceeding the expected
lifetime of the charge carriers. In other words, the model of two types of charged
defects does not fully satisfy the experimental results.
An alternative mechanism for the dielectric relaxation of water was first suggested
in [17]. The authors explained static conductivity and Debye relaxation by the Brownian dynamics of interacting H 3 O
+ and OH
− ions, thus considering only one type of
charge carrier. The high-frequency dielectric response, which includes Debye relaxation, is shown to be the result of the polarization of interacting counterions, while
low-frequency DC conductivity is produced by the same ionic species, which are
long-lived enough to overcome mutual screening and contribute to static conductivity. Although the concentration of all H 3 O
+ and OH
− ions was shown to be high, the
effective concentration of those ions participating in DC conductivity is exactly the
same as assumed by pH. It was also shown that this model (the ionic model of water
presented in Sect. 4.2.3) describes the experimental conductivity spectrum of water
and ice from DC current to THz [8]. For a detailed analysis of the ionic model, see
Chap. 4.
Thus, the microscopic description of dielectric relaxation in water is still debated.
We can say for sure that it does not reduce to the orientations of H 2 O dipoles. The rotational mechanism of polarization is fully confirmed for the gas phase (water vapor)