3.2 The Temperature Dependence of Spectral Parameters
111
Different activation energies for high- and low-frequency conductivity in ice
forced Bjerrum to conclude [19] that they are caused by different mechanisms.
He suggested that σ dc results from the migration of ionic defects, while the highfrequency conductivity, σ D1 , results from the migration of H–O· · · O–H, and O–
H· · · H–O defects (Bjerrum valence defects, or L-D defects, see Fig. 1.5). The latter
are expected to be negatively or positively charged species. The idea of two types of
defects producing two plateaus of conductivity is still very popular in the literature [2,
20–23].
However, apart the fact that no direct experimental confirmation of the existence
of Bjerrum defects has been found, there are some arguments that hinder their application to the dielectric relaxation phenomena:
• Electrostatic repulsion between the partial positive charges on the H atoms of the
D defect and between partial negative charges of the L defect is bound to alter the
defect structure [23], which prevents them from contributing to dielectric losses
on the timescale of dielectric relaxation.
• The mobility of neutral water molecules is found to be an order of magnitude
higher than that expected for L-D defects [24], assuming different mechanisms
for self-diffusion and defect diffusion, which is not the case as both have the same
activation energy (see Fig. 3.4).
• The concentration of Bjerrum defects in ice is expected to be several orders of
magnitude larger than that for ionic defects [2]. In water, this concentration is
expected to be even higher [20], close to the full concentration of H 2 O molecules.
Apart from the fact that such a high concentration of defects calls into question
the crystalline structure of ice, it also assumes a strong electrostatic interaction
between charge carriers (both ionic and L-D). As ionic species and L-D defects
are expected to have different mobilities, their mutual interaction should lead to
two frequency-separated dielectric relaxations, which are not observed.
• The expected concentration n L D of Bjerrum defects is 10
16 cm
3 [2] for the dielectric constant (0) = ∞ + 4π p
2 n/(3k B T ), where p is the dipole moment of the
effective dipoles, giving a value that is 6–7 orders of magnitude lower than the
experimental one. Thus, the L-D defects alone cannot explain the dielectric relaxation, neither for water nor for ice.
These arguments, among others, do not allow us to rely with confidence on the
concept of defects when explaining dielectric phenomena in either water or ice.
An alternative approach, which satisfies the electrodynamic data and does not
contradict the basic physicochemical properties of ice, is to consider the two plateaus
of frequency-dependent electrical conductivity on the same footing. Such a model
was suggested in [25], and further elaborated in [3, 26]. It has been shown that the
static conductivity σ dc and the high-frequency conductivity σ D1 are both due to the
dynamics of H 3 O
+ and OH
− ions, but averaged over different periods of time. The
model is based on the idea that the mobility of ionic species is time-dependent, and
that the two plateaus of conductivity are limiting cases of diffusion with and without
mutual interaction. Thus, the dielectric dispersion area between the two plateaus
of conductivity (Debye relaxation) corresponds to the transition between these two
regimes.
111
Different activation energies for high- and low-frequency conductivity in ice
forced Bjerrum to conclude [19] that they are caused by different mechanisms.
He suggested that σ dc results from the migration of ionic defects, while the highfrequency conductivity, σ D1 , results from the migration of H–O· · · O–H, and O–
H· · · H–O defects (Bjerrum valence defects, or L-D defects, see Fig. 1.5). The latter
are expected to be negatively or positively charged species. The idea of two types of
defects producing two plateaus of conductivity is still very popular in the literature [2,
20–23].
However, apart the fact that no direct experimental confirmation of the existence
of Bjerrum defects has been found, there are some arguments that hinder their application to the dielectric relaxation phenomena:
• Electrostatic repulsion between the partial positive charges on the H atoms of the
D defect and between partial negative charges of the L defect is bound to alter the
defect structure [23], which prevents them from contributing to dielectric losses
on the timescale of dielectric relaxation.
• The mobility of neutral water molecules is found to be an order of magnitude
higher than that expected for L-D defects [24], assuming different mechanisms
for self-diffusion and defect diffusion, which is not the case as both have the same
activation energy (see Fig. 3.4).
• The concentration of Bjerrum defects in ice is expected to be several orders of
magnitude larger than that for ionic defects [2]. In water, this concentration is
expected to be even higher [20], close to the full concentration of H 2 O molecules.
Apart from the fact that such a high concentration of defects calls into question
the crystalline structure of ice, it also assumes a strong electrostatic interaction
between charge carriers (both ionic and L-D). As ionic species and L-D defects
are expected to have different mobilities, their mutual interaction should lead to
two frequency-separated dielectric relaxations, which are not observed.
• The expected concentration n L D of Bjerrum defects is 10
16 cm
3 [2] for the dielectric constant (0) = ∞ + 4π p
2 n/(3k B T ), where p is the dipole moment of the
effective dipoles, giving a value that is 6–7 orders of magnitude lower than the
experimental one. Thus, the L-D defects alone cannot explain the dielectric relaxation, neither for water nor for ice.
These arguments, among others, do not allow us to rely with confidence on the
concept of defects when explaining dielectric phenomena in either water or ice.
An alternative approach, which satisfies the electrodynamic data and does not
contradict the basic physicochemical properties of ice, is to consider the two plateaus
of frequency-dependent electrical conductivity on the same footing. Such a model
was suggested in [25], and further elaborated in [3, 26]. It has been shown that the
static conductivity σ dc and the high-frequency conductivity σ D1 are both due to the
dynamics of H 3 O
+ and OH
− ions, but averaged over different periods of time. The
model is based on the idea that the mobility of ionic species is time-dependent, and
that the two plateaus of conductivity are limiting cases of diffusion with and without
mutual interaction. Thus, the dielectric dispersion area between the two plateaus
of conductivity (Debye relaxation) corresponds to the transition between these two
regimes.