190
5 Electrodynamics of Aqueous Media
and proton holes (short-lived H 3 O
+ and OH
− ions) [41], rather than the rotation of
molecular dipoles, which provide less than a 5% contribution to the static dielectric constant. Thus, the suppression of the dielectric constant of water in the pores,
whose dimensions are less than L, can be associated with the spatial heterogeneity
of water. The dielectric properties of water on a scale of less than the radius L of the
ionic atmosphere of the intrinsic short-lived ions are different in comparison with
the large-scale properties. In other words, the walls of the confining matrix prevent
the formation of the atmosphere of counterions around the central ion, thus, eliminating the polarization unit, which is responsible for the polarization in the bulk.
Note, however, that experiments with water in strong confinement show a different
value of the dielectric constant than for bulk water against the wall of a container. In
the latter case, as, for example, in the Leiden jar (see Sect. 5.6), the charges (H 3 O
+
and OH
− ) form the electric double layer, in which polarizability is very high. The
dielectric constant of a double layer of water is many orders of magnitude larger than
that for the bulk water.
Another important parameter of interfacial water is electric conductivity, which
was studied in [42]. The model system was made of granular particles of nanodiamond of different diameters in such a way that it was possible to change the pore
sizes from 1 to 100 nm. Figure 5.8 shows the dependence of the electrical conductivity of confined water on the pore size. The electrical conductivity increases in inverse
proportion to the pore size and reaches maximum in the pores of about 2 nm, i.e., the
same pore radius as was found for the minimal dielectric constant. The conductivity
σ i of the interfacial water layer was 0.02 S/cm, five orders of magnitude larger than
that of bulk water. The optimal water layer for the maximal protonic conductivity
was h ≈ 1 ± 0.25 nm, which is in agreement with the thickness h i found above. Note
that for the pore size less than h i the conductivity goes down (see Fig. 5.8), which is
presumably connected with the loss of percolation among water volumes between
the grains.
The two experiments described above reveal the presence of an interfacial layer
near aqueous interfaces with a vanishingly small polarization, but very high protonic
conductivity. This layer is found to be a few molecules thick and has an electrical
conductivity five orders of magnitude large than that of bulk water. Note also that σ i
exceeds the ionic conductivity of different superionic conductors in the temperatures
range 0–100
◦ C (see Fig.5.21). These results require interpretation, which satisfy
both the low polarizability and the high protonic conductivity of the interfacial water
layer.
Figure 5.9 shows the difference between bulk and interfacial water from the viewpoint of the ionic model of water (see Chap. 4). In bulk water, the mutual screening
of short-lived spontaneously formed ionic species causes its high dielectric constant
≈ 80 (see Sect. 4.5.3) and low DC conductivity σ dc = 5.5×10
−8 S/cm. The first
parameter results from the dipole moment μ (red arrows), induced by the relative
displacement of ions, and the second is a result of the counteraction of the driving
force, F 1 , and the friction force, F 2 . The latter is due to the electrostatic attraction
of the ion by the center of its ionic atmosphere (the blue “cloud”). Interfacial water
is characterized by the reduced ionic atmosphere, which is incomplete on one side,
5 Electrodynamics of Aqueous Media
and proton holes (short-lived H 3 O
+ and OH
− ions) [41], rather than the rotation of
molecular dipoles, which provide less than a 5% contribution to the static dielectric constant. Thus, the suppression of the dielectric constant of water in the pores,
whose dimensions are less than L, can be associated with the spatial heterogeneity
of water. The dielectric properties of water on a scale of less than the radius L of the
ionic atmosphere of the intrinsic short-lived ions are different in comparison with
the large-scale properties. In other words, the walls of the confining matrix prevent
the formation of the atmosphere of counterions around the central ion, thus, eliminating the polarization unit, which is responsible for the polarization in the bulk.
Note, however, that experiments with water in strong confinement show a different
value of the dielectric constant than for bulk water against the wall of a container. In
the latter case, as, for example, in the Leiden jar (see Sect. 5.6), the charges (H 3 O
+
and OH
− ) form the electric double layer, in which polarizability is very high. The
dielectric constant of a double layer of water is many orders of magnitude larger than
that for the bulk water.
Another important parameter of interfacial water is electric conductivity, which
was studied in [42]. The model system was made of granular particles of nanodiamond of different diameters in such a way that it was possible to change the pore
sizes from 1 to 100 nm. Figure 5.8 shows the dependence of the electrical conductivity of confined water on the pore size. The electrical conductivity increases in inverse
proportion to the pore size and reaches maximum in the pores of about 2 nm, i.e., the
same pore radius as was found for the minimal dielectric constant. The conductivity
σ i of the interfacial water layer was 0.02 S/cm, five orders of magnitude larger than
that of bulk water. The optimal water layer for the maximal protonic conductivity
was h ≈ 1 ± 0.25 nm, which is in agreement with the thickness h i found above. Note
that for the pore size less than h i the conductivity goes down (see Fig. 5.8), which is
presumably connected with the loss of percolation among water volumes between
the grains.
The two experiments described above reveal the presence of an interfacial layer
near aqueous interfaces with a vanishingly small polarization, but very high protonic
conductivity. This layer is found to be a few molecules thick and has an electrical
conductivity five orders of magnitude large than that of bulk water. Note also that σ i
exceeds the ionic conductivity of different superionic conductors in the temperatures
range 0–100
◦ C (see Fig.5.21). These results require interpretation, which satisfy
both the low polarizability and the high protonic conductivity of the interfacial water
layer.
Figure 5.9 shows the difference between bulk and interfacial water from the viewpoint of the ionic model of water (see Chap. 4). In bulk water, the mutual screening
of short-lived spontaneously formed ionic species causes its high dielectric constant
≈ 80 (see Sect. 4.5.3) and low DC conductivity σ dc = 5.5×10
−8 S/cm. The first
parameter results from the dipole moment μ (red arrows), induced by the relative
displacement of ions, and the second is a result of the counteraction of the driving
force, F 1 , and the friction force, F 2 . The latter is due to the electrostatic attraction
of the ion by the center of its ionic atmosphere (the blue “cloud”). Interfacial water
is characterized by the reduced ionic atmosphere, which is incomplete on one side,