180
5 Electrodynamics of Aqueous Media
parameters only, ignoring the frequency dependencies of the dielectric response,
which defines the static dielectric constant according to (2.14) and missing the natural
dynamism of the water-electrolyte molecular system.
Figure 5.4b shows the dielectric relaxation time τ D1 = 1/(2πν D1 ) of a NaCl solution
as a function of concentration. The small effect of the electrolyte on the ν D1 of
water is observed up to the saturation point (about 6.1 mol/l). However, one can
unambiguously identify the blue shift of the relaxation maximum. In Chap. 4, we
associated the relaxation time with the lifetime of molecules of H 2 O. In the context
of this shift, we can assume that the averaged lifetime of H 2 O molecules in water
decreases as the electrolyte concentration increases, which, according to (4.1), leads
to an increase of the effective concentration n ± of intrinsic ions. Thus, according
to the ionic model, the lifetime distribution of the intrinsic ionic species of water is
affected by the species of electrolyte, once again hinting at their interaction.
Further, according to the Debye formula (2.38), high-frequency terahertz conductivity is defined as σ D1 = 0 /τ D1 , where = (0) − T Hz . The latter is about 3
(see Fig. 2.4). Figure 5.4c shows the concentration dependence of the plateau σ D1 ,
calculated by the Debye formula. As one can see, σ D1 decreases as the concentration
increases, while the DC conductivity shows the opposite behavior (compare with
Fig. 5.2a). It is interesting to analyze this fact in the context of the conductivity sum
rule discussed in Sect. 2.8. The rule states that the total integral of the dynamic conductivity function (the area under the curve) is conserved and depends on the number
of charge carriers per unit volume. The decrease of the high-frequency conductivity plateau and the increase of the low-frequency DC conductivity plateau can be
understood as the transfer of the dielectric contribution from high frequencies to low
frequencies. In other words, the particles of the electrolyte affect the dynamic structure of water in such a way that the intrinsic ionic species, which contributed only at
high frequencies due to their mutual interactions, extend their contribution into the
low frequencies, while the total contribution to the integral (2.63) is conserved. This
effect of communicating high- and low-frequency plateaus can explain the observed
synchronous decrease of σ D1 and increase of σ dc with concentration.
Note that the increase of the conductivity of electrolytes at high frequencies of
the external field (see Fig. 5.3) was predicted by Falkenhagen [22] (the Debye–
Falkenhagen effect). He associated the phenomenon with the mutual screening of
ionic species, which have low conductivity at low frequencies as they are locked by
the potential of electrostatic interaction. According to Falkenhagen, as the frequency
of the external field increases, the ionic species interact with the field more effectively, as they can move inside the potential (the rattle effect), and, thus, show higher
conductivity. The conductivity of the electrolyte increases starting from frequencies
of about 10 MHz (see Fig. 5.3c), however, Falkenhagen’s analysis did not show that
the slope repeats exactly those observed for pure water, which would not show the
increase of the conductivity according to his assumptions. In other words, modern
data show that the spectrum looks more like the intrinsic species of water (not an
electrolyte) interacting with the external field. Further, the frequency dispersion of
the conductivity is better considered as a result of the interaction of the solvent and
solute, not as an intrinsic property of the solute itself.
5 Electrodynamics of Aqueous Media
parameters only, ignoring the frequency dependencies of the dielectric response,
which defines the static dielectric constant according to (2.14) and missing the natural
dynamism of the water-electrolyte molecular system.
Figure 5.4b shows the dielectric relaxation time τ D1 = 1/(2πν D1 ) of a NaCl solution
as a function of concentration. The small effect of the electrolyte on the ν D1 of
water is observed up to the saturation point (about 6.1 mol/l). However, one can
unambiguously identify the blue shift of the relaxation maximum. In Chap. 4, we
associated the relaxation time with the lifetime of molecules of H 2 O. In the context
of this shift, we can assume that the averaged lifetime of H 2 O molecules in water
decreases as the electrolyte concentration increases, which, according to (4.1), leads
to an increase of the effective concentration n ± of intrinsic ions. Thus, according
to the ionic model, the lifetime distribution of the intrinsic ionic species of water is
affected by the species of electrolyte, once again hinting at their interaction.
Further, according to the Debye formula (2.38), high-frequency terahertz conductivity is defined as σ D1 = 0 /τ D1 , where = (0) − T Hz . The latter is about 3
(see Fig. 2.4). Figure 5.4c shows the concentration dependence of the plateau σ D1 ,
calculated by the Debye formula. As one can see, σ D1 decreases as the concentration
increases, while the DC conductivity shows the opposite behavior (compare with
Fig. 5.2a). It is interesting to analyze this fact in the context of the conductivity sum
rule discussed in Sect. 2.8. The rule states that the total integral of the dynamic conductivity function (the area under the curve) is conserved and depends on the number
of charge carriers per unit volume. The decrease of the high-frequency conductivity plateau and the increase of the low-frequency DC conductivity plateau can be
understood as the transfer of the dielectric contribution from high frequencies to low
frequencies. In other words, the particles of the electrolyte affect the dynamic structure of water in such a way that the intrinsic ionic species, which contributed only at
high frequencies due to their mutual interactions, extend their contribution into the
low frequencies, while the total contribution to the integral (2.63) is conserved. This
effect of communicating high- and low-frequency plateaus can explain the observed
synchronous decrease of σ D1 and increase of σ dc with concentration.
Note that the increase of the conductivity of electrolytes at high frequencies of
the external field (see Fig. 5.3) was predicted by Falkenhagen [22] (the Debye–
Falkenhagen effect). He associated the phenomenon with the mutual screening of
ionic species, which have low conductivity at low frequencies as they are locked by
the potential of electrostatic interaction. According to Falkenhagen, as the frequency
of the external field increases, the ionic species interact with the field more effectively, as they can move inside the potential (the rattle effect), and, thus, show higher
conductivity. The conductivity of the electrolyte increases starting from frequencies
of about 10 MHz (see Fig. 5.3c), however, Falkenhagen’s analysis did not show that
the slope repeats exactly those observed for pure water, which would not show the
increase of the conductivity according to his assumptions. In other words, modern
data show that the spectrum looks more like the intrinsic species of water (not an
electrolyte) interacting with the external field. Further, the frequency dispersion of
the conductivity is better considered as a result of the interaction of the solvent and
solute, not as an intrinsic property of the solute itself.