2.3 Microwave Spectrum: Dielectric Relaxation
63
Fig. 2.5 The temperature
dependencies of: a relaxation
times for first, τ D1 , and
second, τ D2 , relaxation
bands, and b static, σ dc , first
high-frequency, σ D1 , and
second high-frequency, σ D2 ,
conductivities (see Fig. 2.4)
for liquid water. Lines are fit
with parameters given in
Table 2.3. Numbers near
curves are activation
energies in eV
Apart from different interpretations of the microscopic mechanism of polarization,
all three approximations have similar data-fitting accuracy, and can be used for the
analytical description of the microwave spectrum of water in different technological
applications.
Figure 2.5 shows the temperature dependencies of the main parameters of dielectric relaxation. Two relaxation times: the first, τ D1 , and the second, τ D2 , correspond to
the frequencies of the relaxation-peak maxima, ν D1 and ν D2 , respectively (Fig. 2.5a).
In terms of dynamic conductivity, the relaxation time loses its functionality, being
replaced by high-frequency conductivity plateaus, the first, σ D1 , and the second, σ D2 ,
are shown in Fig. 2.5b. The plateaus can be defined by the Debye formula as
σ D1 =
ε 0 D1
τ D1
,
(2.38)
where ε 0 is the permittivity of vacuum.
The parameters of the first relaxation band, shown in Fig. 2.5, have typical Arrhenius behavior with an activation energy E of both high-frequency conductivity, σ D1 ,
and the relaxation frequency, ν D1 , being close to that for the self-diffusion coefficient
(see Table 2.3). Thus, the Debye relaxation in water seems to be a diffusion-controlled
process.
The second relaxation band parameters, on the contrary, do not depend on temperature. Yada et al. suggested [9] that the high-frequency relaxation time corresponds
63
Fig. 2.5 The temperature
dependencies of: a relaxation
times for first, τ D1 , and
second, τ D2 , relaxation
bands, and b static, σ dc , first
high-frequency, σ D1 , and
second high-frequency, σ D2 ,
conductivities (see Fig. 2.4)
for liquid water. Lines are fit
with parameters given in
Table 2.3. Numbers near
curves are activation
energies in eV
Apart from different interpretations of the microscopic mechanism of polarization,
all three approximations have similar data-fitting accuracy, and can be used for the
analytical description of the microwave spectrum of water in different technological
applications.
Figure 2.5 shows the temperature dependencies of the main parameters of dielectric relaxation. Two relaxation times: the first, τ D1 , and the second, τ D2 , correspond to
the frequencies of the relaxation-peak maxima, ν D1 and ν D2 , respectively (Fig. 2.5a).
In terms of dynamic conductivity, the relaxation time loses its functionality, being
replaced by high-frequency conductivity plateaus, the first, σ D1 , and the second, σ D2 ,
are shown in Fig. 2.5b. The plateaus can be defined by the Debye formula as
σ D1 =
ε 0 D1
τ D1
,
(2.38)
where ε 0 is the permittivity of vacuum.
The parameters of the first relaxation band, shown in Fig. 2.5, have typical Arrhenius behavior with an activation energy E of both high-frequency conductivity, σ D1 ,
and the relaxation frequency, ν D1 , being close to that for the self-diffusion coefficient
(see Table 2.3). Thus, the Debye relaxation in water seems to be a diffusion-controlled
process.
The second relaxation band parameters, on the contrary, do not depend on temperature. Yada et al. suggested [9] that the high-frequency relaxation time corresponds