4.5 The Microscopic Origin of the Electrodynamic Properties of Water and Ice
159
Figure 4.11b shows the 1D chain of electrostatically interacting charges located
along the dashed line in Fig. 4.11a. The average distance L between the ions is
roughly determined by their concentration:
L ≈ (n ± )
−1/3
,
(4.17)
and is approximately equal to 1 nm. The alternating external electric field causes the
displacement of the charges by l, whose amplitude value l = 3.4 Å is determined
by the lifetime of the ionic species (see Table 4.2). The restoring force, which acts
on displaced ions, is F = κκl. According to (4.13), κ = γ 1 m/τ D1 , where τ D1 is the
temperature-dependent dielectric relaxation time.
The dielectric constant of ionic plasma can be found in [49] (see also (3.24) and
the text below it):
ε(0) = ε T Hz +
2
p
ω
2
0
,
(4.18)
where
p =
n ± q
2
mε 0
1/2
(4.19)
is the plasma frequency equal to 1.8 THz, and ω
2
0 = κ/m (see Table 3.5). Equation 4.18 gives (0) = 79 for water.
Thus, within the framework of the ionic model, the high dielectric constant of
water, (0) ≈ 80, is determined by the high concentration of its spontaneously formed
intrinsic ionic species, whose relative displacement creates a dipole moment greater
than the dipole moment of an individual molecule. The next section shows that
the relative contribution T Hz of the orientation of molecular dipoles to the static
dielectric constant is only about 5%.
Note that there are other reasonable models for the dielectric constant, including the famous Clausius–Mossotti, Debye–Onsager, and Kirkwood–Fröhlich models. Although these approaches provide the correct values of the dielectric constant
of polar liquids [53], they still lacking clarity on the microscopic level (see, for
instance, the detailed analysis by Hippel [54]). The basic idea of these models is
the concept of the local field (see Sect. 2.4.2). Such an approach leads to the additional polarizability of individual H 2 O molecules represented by the emperical Kirkwood g-factor.
15 However, the experimental facts are against local polarizability (see
Onsager’s papers and the polarizability catastrophe [56]). In addition, classic neutron
diffraction shows no change of the H 2 O molecule dipole moment in comparison with
15 In his classic 1939 paper, Kirkwood linked the macroscopic dielectric constant of polar liquids to
the local orientational order as measured by the g-factor (later named after him) and suggested that
the corresponding dielectric constant at short-range is effectively equal to the macroscopic value
just beyond the distance of molecular magnitude [55].
159
Figure 4.11b shows the 1D chain of electrostatically interacting charges located
along the dashed line in Fig. 4.11a. The average distance L between the ions is
roughly determined by their concentration:
L ≈ (n ± )
−1/3
,
(4.17)
and is approximately equal to 1 nm. The alternating external electric field causes the
displacement of the charges by l, whose amplitude value l = 3.4 Å is determined
by the lifetime of the ionic species (see Table 4.2). The restoring force, which acts
on displaced ions, is F = κκl. According to (4.13), κ = γ 1 m/τ D1 , where τ D1 is the
temperature-dependent dielectric relaxation time.
The dielectric constant of ionic plasma can be found in [49] (see also (3.24) and
the text below it):
ε(0) = ε T Hz +
2
p
ω
2
0
,
(4.18)
where
p =
n ± q
2
mε 0
1/2
(4.19)
is the plasma frequency equal to 1.8 THz, and ω
2
0 = κ/m (see Table 3.5). Equation 4.18 gives (0) = 79 for water.
Thus, within the framework of the ionic model, the high dielectric constant of
water, (0) ≈ 80, is determined by the high concentration of its spontaneously formed
intrinsic ionic species, whose relative displacement creates a dipole moment greater
than the dipole moment of an individual molecule. The next section shows that
the relative contribution T Hz of the orientation of molecular dipoles to the static
dielectric constant is only about 5%.
Note that there are other reasonable models for the dielectric constant, including the famous Clausius–Mossotti, Debye–Onsager, and Kirkwood–Fröhlich models. Although these approaches provide the correct values of the dielectric constant
of polar liquids [53], they still lacking clarity on the microscopic level (see, for
instance, the detailed analysis by Hippel [54]). The basic idea of these models is
the concept of the local field (see Sect. 2.4.2). Such an approach leads to the additional polarizability of individual H 2 O molecules represented by the emperical Kirkwood g-factor.
15 However, the experimental facts are against local polarizability (see
Onsager’s papers and the polarizability catastrophe [56]). In addition, classic neutron
diffraction shows no change of the H 2 O molecule dipole moment in comparison with
15 In his classic 1939 paper, Kirkwood linked the macroscopic dielectric constant of polar liquids to
the local orientational order as measured by the g-factor (later named after him) and suggested that
the corresponding dielectric constant at short-range is effectively equal to the macroscopic value
just beyond the distance of molecular magnitude [55].