5.1 The Dielectric Response of Electrolyte Solutions
181
More interesting facts related to the frequency-dependent electrodynamic parameters of electrolytes were found by Scherbakov et al. [23]. It has been shown that
the low- (σ dc ) and high-frequency (σ D1 ) conductivity of aqueous electrolytes are
correlated and that the activation energy of DC conductivity coincides with the
activation energy of σ D1 within experimental error. The activation energies of the
high-frequency plateaus were found to have the same value of about 0.15 eV for a
wide range of aqueous electrolytes. In other words, the thermodynamic properties of
the high- and low-frequency conductivity plateaus assume that they are connected
and both represent the same mechanism, but this mechanism is averaged over the
picosecond period for the high-frequency plateau and the microsecond period for the
low-frequency plateau. This fact confirms the results of the analysis within the sum
rule (see above).
Finally, the analysis of the frequency-dependent dielectric function and dynamic
conductivity of aqueous electrolytes in Arrhenius’ approach leads to the paradox of
negative hydration [24, 25]. The problem appears when we calculate the mobility of
ions from their conductivities according to the Stokes–Einstein equation [12]. The
effective radius of an imaginary hydrated ion (for simplicity, let us consider only those
from the first column of the periodic table, namely, Li
+ , Na
+ , K
+ , Rb
+ , Cs
+ , and
Fr
+ , and, thus, having the same electric charge) decreases as the ion size increases.
As follows from the electrochemical mobility measurements, the effective radius of
the hydrated ion changes several times from ion to ion [12]. This result is strange, as
the real (crystallographic) radius of ions does not change much, and similar (by size
and charge) ions should create similar electric fields, which should attract similar
numbers of H 2 O molecules. Moreover, the effective hydration shells of ions of the
large masses, such as Cs
+ and Fr
+ , are smaller than their crystallographic radius.
This is nonsense. This effect also finds some hand-waving interpretations [25], the
paradox obtained from the theory of electrolytic dissociation is evident and suggests
that basic assumptions of the initial model are inaccurate.
Thus, experimental facts that were unavailable when the theory of electrolytic dissociation emerged are beyond Arrhenius’ generalized concept. These results belong
to high-frequency data and assume a dynamic interaction between solvent and solute,
which is missing in the static theories. The new phenomenological approach considered below extends the validity of the ionic model of water (see Chap. 4) from pure
water to the aqueous solutions, providing a new vision of the dynamic structure of
aqueous electrolytes, accounting for picosecond local chemical reactions. Although
this concept needs to be verified and further developed, the general results allow
us to conclude that the basic assumptions are promising and can be used for the
elimination of the anomalies associated with water and aqueous electrolytes.
181
More interesting facts related to the frequency-dependent electrodynamic parameters of electrolytes were found by Scherbakov et al. [23]. It has been shown that
the low- (σ dc ) and high-frequency (σ D1 ) conductivity of aqueous electrolytes are
correlated and that the activation energy of DC conductivity coincides with the
activation energy of σ D1 within experimental error. The activation energies of the
high-frequency plateaus were found to have the same value of about 0.15 eV for a
wide range of aqueous electrolytes. In other words, the thermodynamic properties of
the high- and low-frequency conductivity plateaus assume that they are connected
and both represent the same mechanism, but this mechanism is averaged over the
picosecond period for the high-frequency plateau and the microsecond period for the
low-frequency plateau. This fact confirms the results of the analysis within the sum
rule (see above).
Finally, the analysis of the frequency-dependent dielectric function and dynamic
conductivity of aqueous electrolytes in Arrhenius’ approach leads to the paradox of
negative hydration [24, 25]. The problem appears when we calculate the mobility of
ions from their conductivities according to the Stokes–Einstein equation [12]. The
effective radius of an imaginary hydrated ion (for simplicity, let us consider only those
from the first column of the periodic table, namely, Li
+ , Na
+ , K
+ , Rb
+ , Cs
+ , and
Fr
+ , and, thus, having the same electric charge) decreases as the ion size increases.
As follows from the electrochemical mobility measurements, the effective radius of
the hydrated ion changes several times from ion to ion [12]. This result is strange, as
the real (crystallographic) radius of ions does not change much, and similar (by size
and charge) ions should create similar electric fields, which should attract similar
numbers of H 2 O molecules. Moreover, the effective hydration shells of ions of the
large masses, such as Cs
+ and Fr
+ , are smaller than their crystallographic radius.
This is nonsense. This effect also finds some hand-waving interpretations [25], the
paradox obtained from the theory of electrolytic dissociation is evident and suggests
that basic assumptions of the initial model are inaccurate.
Thus, experimental facts that were unavailable when the theory of electrolytic dissociation emerged are beyond Arrhenius’ generalized concept. These results belong
to high-frequency data and assume a dynamic interaction between solvent and solute,
which is missing in the static theories. The new phenomenological approach considered below extends the validity of the ionic model of water (see Chap. 4) from pure
water to the aqueous solutions, providing a new vision of the dynamic structure of
aqueous electrolytes, accounting for picosecond local chemical reactions. Although
this concept needs to be verified and further developed, the general results allow
us to conclude that the basic assumptions are promising and can be used for the
elimination of the anomalies associated with water and aqueous electrolytes.