146
4 The Dielectric Properties and Dynamic Structure of Water and Ice
Table 4.3 Comparison of the ionic (protonic) and Bernal–Fowler water models from the viewpoint
of structure and electrodynamic parameters
Bernal–Fowler model
Ionic (protonic) model
Interaction of intrinsic ions
No interaction
Ions electrostatically interact
Concentration of intrinsic ions 10 −7 mol/l
1 mol/l (short-lived) and 10 −7
mol/l (long-lived)
Dielectric constant
Described using polarizable
molecular dipoles with fitting
parameters, different for water
and ice
Described by the relative
displacement of positive and
negative ions
DC conductivity
Described by the dynamics of
independent H 3 O + and OH −
ions
Both the DC conductivity and
the dielectric relaxation are the
result of the dynamics of
interacting H 3 O + and OH −
ions, whose mobility is
frequency dependent
Microwave absorption and
dielectric relaxation
Assumes rotational
polarization mechanism
Basic structural element
Molecule of H 2 O
Molecules of H 2 O and
short-lived ionic species
The definition of pH
Autoionization
Thermal activation from the
interaction potential
The main parameters, which
are used for the description of
the electrodynamic properties
The lifetime of bonds, the
concentration of ionic defects,
the concentration of bond
defects, the percentage of
unbound molecules, the
molecular dipole moment, the
molecular polarizability factor,
bond energy. Total: 7
The lifetime of ions, the
concentration of ions, the
high-frequency mobility of
ionic species, the
low-frequency mobility of the
species, the long-order
interaction potential, the
short-order interaction
potential. Total: 6
Lifetime of the water molecule 11 h [37]
50 ps
Lifetime of ionic species
0.1 ms
2.9 ps
tic times assume the time heterogeneity of the dynamic water structure. Although the
authors provide an explanation of the observed effect by the introduction of bounded
and unbounded molecules, it is unclear why single-, double-, and triple-bounded
molecules do not appear. The ionic model suggests an explanation in terms of two
types of species, ionic and molecular, which appear in significantly different environments (see Fig. 4.5), and thus show two discreet characteristic relaxation times.
3. Fast mass and charge transfer in water confined in nanocapillaries (evidence for
long-range order in water)
Bernal–Fowler water does not assume any deviation from the continual behavior
of water down to a single-molecule dimension (0.3 nm). However, Holt et al. [41]
found that already in the 2 nm pores (more than 6 molecular diameters), the water
4 The Dielectric Properties and Dynamic Structure of Water and Ice
Table 4.3 Comparison of the ionic (protonic) and Bernal–Fowler water models from the viewpoint
of structure and electrodynamic parameters
Bernal–Fowler model
Ionic (protonic) model
Interaction of intrinsic ions
No interaction
Ions electrostatically interact
Concentration of intrinsic ions 10 −7 mol/l
1 mol/l (short-lived) and 10 −7
mol/l (long-lived)
Dielectric constant
Described using polarizable
molecular dipoles with fitting
parameters, different for water
and ice
Described by the relative
displacement of positive and
negative ions
DC conductivity
Described by the dynamics of
independent H 3 O + and OH −
ions
Both the DC conductivity and
the dielectric relaxation are the
result of the dynamics of
interacting H 3 O + and OH −
ions, whose mobility is
frequency dependent
Microwave absorption and
dielectric relaxation
Assumes rotational
polarization mechanism
Basic structural element
Molecule of H 2 O
Molecules of H 2 O and
short-lived ionic species
The definition of pH
Autoionization
Thermal activation from the
interaction potential
The main parameters, which
are used for the description of
the electrodynamic properties
The lifetime of bonds, the
concentration of ionic defects,
the concentration of bond
defects, the percentage of
unbound molecules, the
molecular dipole moment, the
molecular polarizability factor,
bond energy. Total: 7
The lifetime of ions, the
concentration of ions, the
high-frequency mobility of
ionic species, the
low-frequency mobility of the
species, the long-order
interaction potential, the
short-order interaction
potential. Total: 6
Lifetime of the water molecule 11 h [37]
50 ps
Lifetime of ionic species
0.1 ms
2.9 ps
tic times assume the time heterogeneity of the dynamic water structure. Although the
authors provide an explanation of the observed effect by the introduction of bounded
and unbounded molecules, it is unclear why single-, double-, and triple-bounded
molecules do not appear. The ionic model suggests an explanation in terms of two
types of species, ionic and molecular, which appear in significantly different environments (see Fig. 4.5), and thus show two discreet characteristic relaxation times.
3. Fast mass and charge transfer in water confined in nanocapillaries (evidence for
long-range order in water)
Bernal–Fowler water does not assume any deviation from the continual behavior
of water down to a single-molecule dimension (0.3 nm). However, Holt et al. [41]
found that already in the 2 nm pores (more than 6 molecular diameters), the water