ISSN 0021-3640, JETP Letters, 2015, Vol. 102, No. 1, pp. 41–45. © Pleiades Publishing, Inc., 2015.
Original Russian Text © V.G. Artemov, I.A. Ryzhkin, V.V. Sinitsyn, 2015, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2015, Vol. 102, No. 1, pp. 45–49.
41
Currently, a huge body of experimental data on
transport characteristics of water and ice is accumu-
lated. With a generally formulated query, the Google
search engine gives millions of related references.
However, it is quite surprising that systematization and
comparative analysis involving the whole set of these
data have not yet been performed. Such a situation is
due first of all to the difference in the theoretical mod-
els and approaches used for the description of the
transport and relaxation characteristics of water and
ice, which makes such analysis rather difficult. In the
case of water, the phenomenological Debye model is
widely used to describe its dielectric characteristics.
This model is based on the concept of rotating dipoles
(water molecules) in a viscous medium. On the other
hand, Jaccard [1] (see also [2]) formulated the theory
of electrical relaxation for ice taking into account the
characteristic features of its atomic structure and the
ice rules. It is important that this theory agrees well
with many experimental data obtained for ice [3].
At the same time, the idea of the similarity of elec-
trical characteristics of ice and water was first pro-
posed in [4]. This idea is based on the comparison of
the dispersion curves for the generalized permittivity
and conductivity at the temperature of thermody-
namic equilibrium of these phases (T = 273 K). In this
regard, questions are raised: To what extent does such
similarity hold true for other transport characteristics,
what is the microscopic mechanism of this phenome-
non, and does such similarity occur in a wider temper-
ature range? To answer these questions, we perform a
comparative analysis of all available experimental data
with the aim to check the conjecture concerning the
possibility of describing the electrical and diffusion
characteristics of water with the use of the Jaccard the-
ory initially formulated and still used only for the
description of ice.
Since this work is based primarily on the Jaccard
theory of the electrical relaxation, we start with the
description of its essence and the main results. As was
mentioned above, dipoles in ice exhibit a strong inter-
action obeying the ice rules [5, 6]. According to these
rules, two protons are located near each oxygen ion
and each hydrogen bond involves one proton (Fig. 1).
Such a distribution is frozen; i.e., any displacement of
an individual proton is forbidden by the ice rule. This
implies the absence of any electrical relaxation. The
electrical relaxation becomes possible at nonzero tem-
peratures, at which ice contains two types of defects
(violations of the ice rules): ionic defects H
3
O
+
and
OH
–
(Fig 1a) and hydrogen bond defects such as
bonds with two or zero protons referred to as D and L
defects, respectively (Fig. 1b). In the range of intrinsic
conductivity of ice, the partial conductivity related to
the D and L defects is higher than that related to the
ionic defects. Therefore, the applied electric field first
gives rise to the current of the former type of defects,
which polarizes the proton lattice. At the same time,
ionic defects exhibiting five orders of magnitude lower
partial conductivity can also move through the lattice,
depolarizing it. As a result, the ionic defects are
responsible for the low-frequency (dc) conductivity
σ(0), whereas the bond defects are responsible for the
high-frequency σ(∞) conductivity of the ice. In the
framework of the Jaccard model, the partial conduc-
tivities related to the majority charge carriers (bond
Similarity of the Dielectric Relaxation Processes
and Transport Characteristics in Water and Ice
V. G. Artemov
a
, I. A. Ryzhkin
b
, and V. V. Sinitsyn
a, b
a
Prokhorov General Physics Institute, Russian Academy of Sciences,
ul. Vavilova 38, Moscow, 119991 Russia
b
Institute of Solid State Physics, Russian Academy of Sciences,
ul. Akademika Osipyana 2, Chernogolovka, Moscow region, 142432 Russia
e-mail: sinitsyn@issp.ac.ru
Received April 7, 2015; in final form, May 29, 2015
The electrical characteristics of ice and water in wide temperature and frequency ranges are analyzed and
compared. It is found that the experimental data agree well with the conjecture that the mechanisms of elec-
trical relaxation in ice and water are similar to each other. In particular, it is shown that the theory of electrical
relaxation developed for ice gives a quantitative description of the same data for water under the assumption
that the activation energy of defects (violations of the ice rule) is lower in water. The reasons for the similarity
of electrical relaxation mechanisms and possible applications of such similarity are discussed.
DOI: 10.1134/S0021364015130020