2.2 The Broadband Dielectric Spectroscopy of Water
57
The listed modes of non-perturbing (an approximation of a linear response) sensing of water cover the range from intramolecular vibrations in the IR region, with
characteristic times of the order of tens of femtoseconds, to structural relaxations
that take hours, and are combined under the general name of ultra-broadband dielectric spectroscopy. The broadband dielectric spectroscopy method has an advantage
over other methods (for example, inelastic neutron scattering, nuclear magnetic resonance, and isotope substitution (see Chap. 1)), because it allows one to observe a wide
time window of the dielectric polarization effects. All types of structures of water
from instantaneous (I-structure) to diffusion averaged (D-structure) (see Sect. 1.1)
are available for analysis by this technique. The main limitation of this method is
the integrity of measurements and the difficulty of the unambiguous identification
of contributions from various mechanisms, such as molecular reorientations, charge
separation, and the flickering or drift of the charge. This limitation, however, is tempered by analysis of the temperature, phase transition, and isotope effects on the
broadband spectrum.
Figure 2.2 shows the generalized ultra-broadband dielectric response of water,
collated from experimental data, using (2.15)–(2.19). The spectrum covers 14 orders
of the frequency magnitude, and includes the radio wave, microwave, terahertz,
infrared, optical, and ultraviolet regions. In terms of the dielectric function (upper
panel), the spectrum is characterized by the main feature: the Debye relaxation, and by
the static dielectric constant (0). The dynamic conductivity spectrum, σ (ω), consists
of two parts which partially overlap in the visible region: the low-frequency atomic
contribution (blue) and high-frequency electronic (yellow). The low-frequency limit
corresponds to DC conductivity (see Sect. 1.3). Particular details of the spectrum
shown in Fig. 2.2 are discussed in Sects. 2.3–2.8 for water and Sects. 3.2–3.5 for ice.
The microscopic interpretation of the spectrum is given in Chap. 4. More spectral
data on ice and water can be found in appendix.
2.3 Microwave Spectrum: Dielectric Relaxation
2.3.1 Experimental Data
The dielectric (Debye) relaxation band is the main part of the broadband dielectric
spectrum of water shown in Fig. 2.2, and one of the most fundamental properties
that characterize its molecular dynamics. The phenomenon of dielectric relaxation in
water has been extensively studied for several decades, and is based on the individual
properties of the dielectric function and the specific structural properties of water (see
Sect. 4.5.1).
In terms of permittivity
∗
(ω) =
(ω)+i
(ω) (see Fig. 2.2 upper panel), water
shows a wide bell-shaped band (see
(ω)) and the corresponding changes in
(ω).
In other words, water shows frequency variation in the dielectric parameters or dispersion. If the external field frequency is low, water simply reduces the strength of
57
The listed modes of non-perturbing (an approximation of a linear response) sensing of water cover the range from intramolecular vibrations in the IR region, with
characteristic times of the order of tens of femtoseconds, to structural relaxations
that take hours, and are combined under the general name of ultra-broadband dielectric spectroscopy. The broadband dielectric spectroscopy method has an advantage
over other methods (for example, inelastic neutron scattering, nuclear magnetic resonance, and isotope substitution (see Chap. 1)), because it allows one to observe a wide
time window of the dielectric polarization effects. All types of structures of water
from instantaneous (I-structure) to diffusion averaged (D-structure) (see Sect. 1.1)
are available for analysis by this technique. The main limitation of this method is
the integrity of measurements and the difficulty of the unambiguous identification
of contributions from various mechanisms, such as molecular reorientations, charge
separation, and the flickering or drift of the charge. This limitation, however, is tempered by analysis of the temperature, phase transition, and isotope effects on the
broadband spectrum.
Figure 2.2 shows the generalized ultra-broadband dielectric response of water,
collated from experimental data, using (2.15)–(2.19). The spectrum covers 14 orders
of the frequency magnitude, and includes the radio wave, microwave, terahertz,
infrared, optical, and ultraviolet regions. In terms of the dielectric function (upper
panel), the spectrum is characterized by the main feature: the Debye relaxation, and by
the static dielectric constant (0). The dynamic conductivity spectrum, σ (ω), consists
of two parts which partially overlap in the visible region: the low-frequency atomic
contribution (blue) and high-frequency electronic (yellow). The low-frequency limit
corresponds to DC conductivity (see Sect. 1.3). Particular details of the spectrum
shown in Fig. 2.2 are discussed in Sects. 2.3–2.8 for water and Sects. 3.2–3.5 for ice.
The microscopic interpretation of the spectrum is given in Chap. 4. More spectral
data on ice and water can be found in appendix.
2.3 Microwave Spectrum: Dielectric Relaxation
2.3.1 Experimental Data
The dielectric (Debye) relaxation band is the main part of the broadband dielectric
spectrum of water shown in Fig. 2.2, and one of the most fundamental properties
that characterize its molecular dynamics. The phenomenon of dielectric relaxation in
water has been extensively studied for several decades, and is based on the individual
properties of the dielectric function and the specific structural properties of water (see
Sect. 4.5.1).
In terms of permittivity
∗
(ω) =
(ω)+i
(ω) (see Fig. 2.2 upper panel), water
shows a wide bell-shaped band (see
(ω)) and the corresponding changes in
(ω).
In other words, water shows frequency variation in the dielectric parameters or dispersion. If the external field frequency is low, water simply reduces the strength of