5.1 The Dielectric Response of Electrolyte Solutions
179
It has been found [17] that the dielectric decrement becomes saturated (takes
the value of about half that for pure water) at the same concentration point where
the DC conductivity reaches its maximum (see Fig. 5.2a). Interestingly, the level of
maximal static electric conductivity σ
e
dc of all strong electrolytes is always higher
than the σ dc of pure water, and below, but close to, the high-frequency conductivity
plateau σ D1 ≈ 1 S/cm of pure water (see the dashed black line in Fig. 5.3c). This
looks as if the high-frequency dynamic structure of water would establish the limit
for the maximal conductivity of electrolytes.
7 As in the ionic model of water (see
Chap. 4), we associated the plateau, σ D1 , with the conductivity of spontaneously
formed short-lived ionic species (H 3 O
+ and OH
− ) of water, the fact that the maximal
conductivity of the electrolyte is observed when the solute concentration is close to
the concentration of intrinsic ions, indicates that the species of solute and solvent
interact with each other, as was highlighted by Mendeleev [8]. Further details are
explained in Sect. 5.1.3.
Note that the dielectric decrement was not considered in Arrhenius’ model, as it
was not observed until later. For the past decades, several ideas on how to incorporate this effect into the concept of electrolytic dissociation have been suggested by
Haggis, Hasted, and others. Haggis et al. [19] modeled the observed linear dielectric
decrement by assuming that the water molecules, adjusting to the electric field of the
ion of the electrolyte, create a small spherical region (hydration shell) with a smaller
dielectric constant than the rest of the water. The effective medium, in which some
of the H 2 O molecules are trapped in the hydration shell and, thus, cannot effectively
respond to the external electric field, was shown qualitatively to explain the static
dielectric constant. However, such theoretical deductions suffer from the introduction of arbitrary assumptions such as the saturation level of the hydration shell, with
no chance to give a quantitative description, although the right order of magnitude
of the dielectric constant of solutions can be obtained.
In fact, the electric field of a charge with the size of a monovalent ion, placed in a
polarizable environment, is a way that the first shell is far from saturated. Glueckauf
suggested [20] improving the Haggis’s model by introducing variation in the local
dielectric constant near the ion. As this approach gave better but still not perfect
results, a further improvement was suggested by Liszi et al. [21] to account for
the exclusion volume by ions and the corresponding finite-size effects. Although the
correct values of the dielectric constants were finally obtained, the model still contains
poorly defined coefficients, whose microscopic physical meaning lack clarity. The
main problem is that the theory of Arrhenius works well for the static dielectric
7 Note that apart the very specific cases of superacids and superbases, the pH values of aqueous
electrolytes lie in the interval between pH = 0 and pH = 14, with the middle point of pH = 7 for
the pure water. By definition, the concentration of [H 3 O + ] = 10 − pH , the maximal difference in
the concentration of hydronium or hydroxide ions with those in neutral water is seven orders of
magnitude (7 is exactly in the middle of the 0 and 14). The difference between the low-frequency
DC plateau of pure water and its high-frequency plateau is also seven orders of magnitude. Thus,
the difference in between σ dc and σ D1 of pure water (see Fig. 5.2c) sets the dynamic range of the
pH of all aqueous solutions of electrolytes.
179
It has been found [17] that the dielectric decrement becomes saturated (takes
the value of about half that for pure water) at the same concentration point where
the DC conductivity reaches its maximum (see Fig. 5.2a). Interestingly, the level of
maximal static electric conductivity σ
e
dc of all strong electrolytes is always higher
than the σ dc of pure water, and below, but close to, the high-frequency conductivity
plateau σ D1 ≈ 1 S/cm of pure water (see the dashed black line in Fig. 5.3c). This
looks as if the high-frequency dynamic structure of water would establish the limit
for the maximal conductivity of electrolytes.
7 As in the ionic model of water (see
Chap. 4), we associated the plateau, σ D1 , with the conductivity of spontaneously
formed short-lived ionic species (H 3 O
+ and OH
− ) of water, the fact that the maximal
conductivity of the electrolyte is observed when the solute concentration is close to
the concentration of intrinsic ions, indicates that the species of solute and solvent
interact with each other, as was highlighted by Mendeleev [8]. Further details are
explained in Sect. 5.1.3.
Note that the dielectric decrement was not considered in Arrhenius’ model, as it
was not observed until later. For the past decades, several ideas on how to incorporate this effect into the concept of electrolytic dissociation have been suggested by
Haggis, Hasted, and others. Haggis et al. [19] modeled the observed linear dielectric
decrement by assuming that the water molecules, adjusting to the electric field of the
ion of the electrolyte, create a small spherical region (hydration shell) with a smaller
dielectric constant than the rest of the water. The effective medium, in which some
of the H 2 O molecules are trapped in the hydration shell and, thus, cannot effectively
respond to the external electric field, was shown qualitatively to explain the static
dielectric constant. However, such theoretical deductions suffer from the introduction of arbitrary assumptions such as the saturation level of the hydration shell, with
no chance to give a quantitative description, although the right order of magnitude
of the dielectric constant of solutions can be obtained.
In fact, the electric field of a charge with the size of a monovalent ion, placed in a
polarizable environment, is a way that the first shell is far from saturated. Glueckauf
suggested [20] improving the Haggis’s model by introducing variation in the local
dielectric constant near the ion. As this approach gave better but still not perfect
results, a further improvement was suggested by Liszi et al. [21] to account for
the exclusion volume by ions and the corresponding finite-size effects. Although the
correct values of the dielectric constants were finally obtained, the model still contains
poorly defined coefficients, whose microscopic physical meaning lack clarity. The
main problem is that the theory of Arrhenius works well for the static dielectric
7 Note that apart the very specific cases of superacids and superbases, the pH values of aqueous
electrolytes lie in the interval between pH = 0 and pH = 14, with the middle point of pH = 7 for
the pure water. By definition, the concentration of [H 3 O + ] = 10 − pH , the maximal difference in
the concentration of hydronium or hydroxide ions with those in neutral water is seven orders of
magnitude (7 is exactly in the middle of the 0 and 14). The difference between the low-frequency
DC plateau of pure water and its high-frequency plateau is also seven orders of magnitude. Thus,
the difference in between σ dc and σ D1 of pure water (see Fig. 5.2c) sets the dynamic range of the
pH of all aqueous solutions of electrolytes.