182
5 Electrodynamics of Aqueous Media
5.1.3 The Mechanism of Dynamic Conductivity
in Electrolytes
In Chap. 4, we modeled the spectrum of the dynamic conductivity of water using
the notion of short-lived excess protons, which spontaneously appear and disappear
on the picosecond timescale, while some of them can live longer, contributing to
the static DC conductivity. Although most ions are short-lived, their concentration
up to 1 mol/l (see Fig. 4.5 for the approximate proportions between ions and water)
is high enough to induce an electrostatic field, which significantly determines the
properties of water at high frequencies (above 1 MHz) and, as it shown in Sect. 5.2,
at nanoscales. Such a consideration makes water a strong intrinsic electrolyte with
electrophoretic effects (among others) of ion–ion and ion–molecule interactions,
which are usually missing in the models of aqueous electrolytes. Here we avoid the
analysis of the standard models, which can be found in a variety of textbooks [12,
26–30] and consider the model which accounts for the full dielectric spectrum of
aqueous electrolytes from the DC plateau to the far-IR region.
The implementation of intrinsic short-lived ionic species to the water model
assumes interactions between them and the particles of solute both electrostatically
and via exchange reactions. For simplicity, we consider the aqueous solutions of
HCl (acid), NaOH (base), and NaCl (salt) in order to embrace the full spectrum of
possible interactions of the solute with water particles. However, the model can be
easily extended to a wide range of aqueous electrolytes. The initial particles of the
solute are short-lived HCl, NaOH, and NaCl. In the ionic model, these molecular
species can interact with molecules of H 2 O, forming ions, such as Na
+ and Cl
− (note
that Arrhenius’ model postulated the complete dissociation of electrolyte molecules),
but in addition can also interact with the intrinsic ions of water, H 3 O
+ and OH
− ,
forming molecules of HCl and NaOH. A further development of the model assumes
the identification of corresponding reaction rates between all these species.
For clarity, we distinguish the intrinsic water ions, H 3 O
+ and OH
− , and the H 3 O
∗
and OH
∗ ions which have just been born due to the electrolyte-water reaction [17].
The ions of these two types differ by their lifetimes and by their contribution to the
dielectric spectrum. While the first pair respond to the high-frequency conductivity
plateau σ D1 (see Fig. 5.3c) the second pair are born initially free of the electrophoretic
effect. In fact, the HCl and NaOH molecules, being neutral, do not feel the interionic
potential. Since they generate the H 3 O
∗ and OH
∗ ions in a random way, the averaged
potential for these ions is flat in comparison with that for the intrinsic ions. Their
conductivity spectrum can be considered as a frequency-independent horizontal line
(see Fig. 4.8), whose altitude (the level of conductivity) depends on their concentration and reaches the maximal values of the dashed black line in Fig. 5.3c. Thus, the
conductivity produced by the ions born due to the chemical reaction with the solute
(H 3 O
∗ and OH
∗ ) varies in the limits from the σ dc of the pure water to the σ D1 . In other
words, we consider the activation of ionic species from electrophoretic suppression
by the electrolyte and their manifestation in DC conductivity.
5 Electrodynamics of Aqueous Media
5.1.3 The Mechanism of Dynamic Conductivity
in Electrolytes
In Chap. 4, we modeled the spectrum of the dynamic conductivity of water using
the notion of short-lived excess protons, which spontaneously appear and disappear
on the picosecond timescale, while some of them can live longer, contributing to
the static DC conductivity. Although most ions are short-lived, their concentration
up to 1 mol/l (see Fig. 4.5 for the approximate proportions between ions and water)
is high enough to induce an electrostatic field, which significantly determines the
properties of water at high frequencies (above 1 MHz) and, as it shown in Sect. 5.2,
at nanoscales. Such a consideration makes water a strong intrinsic electrolyte with
electrophoretic effects (among others) of ion–ion and ion–molecule interactions,
which are usually missing in the models of aqueous electrolytes. Here we avoid the
analysis of the standard models, which can be found in a variety of textbooks [12,
26–30] and consider the model which accounts for the full dielectric spectrum of
aqueous electrolytes from the DC plateau to the far-IR region.
The implementation of intrinsic short-lived ionic species to the water model
assumes interactions between them and the particles of solute both electrostatically
and via exchange reactions. For simplicity, we consider the aqueous solutions of
HCl (acid), NaOH (base), and NaCl (salt) in order to embrace the full spectrum of
possible interactions of the solute with water particles. However, the model can be
easily extended to a wide range of aqueous electrolytes. The initial particles of the
solute are short-lived HCl, NaOH, and NaCl. In the ionic model, these molecular
species can interact with molecules of H 2 O, forming ions, such as Na
+ and Cl
− (note
that Arrhenius’ model postulated the complete dissociation of electrolyte molecules),
but in addition can also interact with the intrinsic ions of water, H 3 O
+ and OH
− ,
forming molecules of HCl and NaOH. A further development of the model assumes
the identification of corresponding reaction rates between all these species.
For clarity, we distinguish the intrinsic water ions, H 3 O
+ and OH
− , and the H 3 O
∗
and OH
∗ ions which have just been born due to the electrolyte-water reaction [17].
The ions of these two types differ by their lifetimes and by their contribution to the
dielectric spectrum. While the first pair respond to the high-frequency conductivity
plateau σ D1 (see Fig. 5.3c) the second pair are born initially free of the electrophoretic
effect. In fact, the HCl and NaOH molecules, being neutral, do not feel the interionic
potential. Since they generate the H 3 O
∗ and OH
∗ ions in a random way, the averaged
potential for these ions is flat in comparison with that for the intrinsic ions. Their
conductivity spectrum can be considered as a frequency-independent horizontal line
(see Fig. 4.8), whose altitude (the level of conductivity) depends on their concentration and reaches the maximal values of the dashed black line in Fig. 5.3c. Thus, the
conductivity produced by the ions born due to the chemical reaction with the solute
(H 3 O
∗ and OH
∗ ) varies in the limits from the σ dc of the pure water to the σ D1 . In other
words, we consider the activation of ionic species from electrophoretic suppression
by the electrolyte and their manifestation in DC conductivity.