3.2 The Temperature Dependence of Spectral Parameters
113
Note that the increase of conductivity with the increase of the sounding frequency
(region 1 in Fig. 3.5b) is, in fact, a Debye–Falkenhagen effect [27].
4 From the other
side, the decrease of the dynamic conductivity as the frequency decreases (region 2
in Fig. 3.5b) is an electrophoretic effect [28].
5
Thus, this phenomenological model allows the frequency dispersion of electrical conductivity to be interpreted using only one type of charge carrier, namely
H 3 O
+ and OH
− ions, the mobility of which is time/frequency dependent. The model
is suitable for both ice and water. The phenomenology, described above, qualitatively explains the experimentally observed coincidence of the activation energies of
molecular mobility, and high-frequency conductivity, σ D1 , and allows one to obtain
the experimental dielectric constant of ice and water on the same footing [3]. The
details of the model are discussed in Sect. 3.5, and the quantitative analysis is given
in Chap. 4.
3.3 Ice Among Other Dielectrics
Quartz served as a prototype for the Bernal–Fowler structure of water based on the
similarity of their X-ray patterns (see Chap. 1). Here, we compare ice, as well as
water, with quartz and other dielectrics from the viewpoint of their electrodynamic
properties.
Table 3.3 shows direct-current conductivity σ dc , and the static dielectric constant
(0), of different ionic and molecular dielectrics, including water and ice. Values are
given at room temperature (where possible), or near the melting/transition point. For
simple dielectrics, ice and water exhibit relatively high static proton conductivity,
which is σ dc ≈ 10
−8 S/m for ice, and three orders of magnitude larger for water. No
other dielectrics, except ionic liquids and superionic conductors, show such a high
ionic conductivity. This fact shows the ability of protons to “tunnel” between water
molecules, while the actual mobility of H 3 O
+ and OH
− ions as a whole is relatively
low. Note that the role of these excess protons (and the corresponding proton holes)
is underestimated in the polarization models of water, which seem to combine the
properties of molecular and ionic systems.
From an electrodynamic point of view, ice looks similar to AgI, a superionic
conductor, which shows high mobility of Ag
+ ions in the lattice formed by iodide
(I
− ) ions. As shown in Sect. 2.6.1, AgI has also similar Raman spectrum to water
and is better suited as a model system for the electrodynamics of ice and water than
quartz (SiO 2 ), which as one can see from Table 3.3 has a relatively low dielectric
constant and DC conductivity.
The static dielectric constants of ice and water are also anomalously high, (0)
≈ 90. The value of (0) is commonly associated with the ability of water to dilute
4 The increase of the conductivity when the applied voltage has a very high frequency.
5 The effect in which the mobility of ions moving under the influence of an applied electric field is
affected by the flow of ions of the opposite charge in the opposite direction.
113
Note that the increase of conductivity with the increase of the sounding frequency
(region 1 in Fig. 3.5b) is, in fact, a Debye–Falkenhagen effect [27].
4 From the other
side, the decrease of the dynamic conductivity as the frequency decreases (region 2
in Fig. 3.5b) is an electrophoretic effect [28].
5
Thus, this phenomenological model allows the frequency dispersion of electrical conductivity to be interpreted using only one type of charge carrier, namely
H 3 O
+ and OH
− ions, the mobility of which is time/frequency dependent. The model
is suitable for both ice and water. The phenomenology, described above, qualitatively explains the experimentally observed coincidence of the activation energies of
molecular mobility, and high-frequency conductivity, σ D1 , and allows one to obtain
the experimental dielectric constant of ice and water on the same footing [3]. The
details of the model are discussed in Sect. 3.5, and the quantitative analysis is given
in Chap. 4.
3.3 Ice Among Other Dielectrics
Quartz served as a prototype for the Bernal–Fowler structure of water based on the
similarity of their X-ray patterns (see Chap. 1). Here, we compare ice, as well as
water, with quartz and other dielectrics from the viewpoint of their electrodynamic
properties.
Table 3.3 shows direct-current conductivity σ dc , and the static dielectric constant
(0), of different ionic and molecular dielectrics, including water and ice. Values are
given at room temperature (where possible), or near the melting/transition point. For
simple dielectrics, ice and water exhibit relatively high static proton conductivity,
which is σ dc ≈ 10
−8 S/m for ice, and three orders of magnitude larger for water. No
other dielectrics, except ionic liquids and superionic conductors, show such a high
ionic conductivity. This fact shows the ability of protons to “tunnel” between water
molecules, while the actual mobility of H 3 O
+ and OH
− ions as a whole is relatively
low. Note that the role of these excess protons (and the corresponding proton holes)
is underestimated in the polarization models of water, which seem to combine the
properties of molecular and ionic systems.
From an electrodynamic point of view, ice looks similar to AgI, a superionic
conductor, which shows high mobility of Ag
+ ions in the lattice formed by iodide
(I
− ) ions. As shown in Sect. 2.6.1, AgI has also similar Raman spectrum to water
and is better suited as a model system for the electrodynamics of ice and water than
quartz (SiO 2 ), which as one can see from Table 3.3 has a relatively low dielectric
constant and DC conductivity.
The static dielectric constants of ice and water are also anomalously high, (0)
≈ 90. The value of (0) is commonly associated with the ability of water to dilute
4 The increase of the conductivity when the applied voltage has a very high frequency.
5 The effect in which the mobility of ions moving under the influence of an applied electric field is
affected by the flow of ions of the opposite charge in the opposite direction.