1.3 Direct Current Conductivity and pH of Water
17
1.3 Direct Current Conductivity and pH of Water
1.3.1 Electrical Conduction Mechanism
According to the theory of electronic band structure [47], water and ice are dielectrics
with negligibly small macroscopic electronic conductivity. The gap between the
valence band and the conduction band of about 5.1 eV [48] (see Fig. 1.13) prescribes
water to be a good dielectric, such as, e.g., quartz (6.3 eV) or diamond (5.5 eV).
However, when an external electric field is applied, even very pure water shows
anomalously high (for a dielectric) electrical conductivity σ dc = 5.5·10
−8 S/cm,
which was measured by Kohlrausch [8]. This value is several orders of magnitude
higher than those for quartz and diamond. Thus, the analogy between water and
quartz, which was made by Bernal and Fowler on the basis of X-rays diffraction,
is not complete, in particular, for the electrodynamic properties. What structural
features make water so conductive in comparison with other dielectrics (Fig. 1.14)?
von Grotthuss (1806) (Fig.1.15a) suggested [50] that the relay-race transfer of
protons among water molecules (see Fig.1.15b) provides an effective mechanism
for charge transfer through the water sample. The Grotthuss mechanism allows one
to describe quantitatively the anomalously high electrical conduction of water. This
mechanism, the modern understanding of which is shown in Fig.1.15c, was used to
explain the higher mobility of H
+ (H 3 O
+ ) and OH
− ions in water in comparison with
Fig. 1.13 a Energy band
structure (left), and the
energy levels as a function of
the spacing between
molecules (right). b
Snapshots of bulk liquid
water as observed by path
integral molecular-dynamic
simulations with
isoprobability contours of the
lowest unoccupied molecular
orbital. Part (b) adapted
from [49] with permission
from Springer Nature
r
E
Band gap
(a)
(b)
p
s
p
s
Conduction
band
Valence
band
17
1.3 Direct Current Conductivity and pH of Water
1.3.1 Electrical Conduction Mechanism
According to the theory of electronic band structure [47], water and ice are dielectrics
with negligibly small macroscopic electronic conductivity. The gap between the
valence band and the conduction band of about 5.1 eV [48] (see Fig. 1.13) prescribes
water to be a good dielectric, such as, e.g., quartz (6.3 eV) or diamond (5.5 eV).
However, when an external electric field is applied, even very pure water shows
anomalously high (for a dielectric) electrical conductivity σ dc = 5.5·10
−8 S/cm,
which was measured by Kohlrausch [8]. This value is several orders of magnitude
higher than those for quartz and diamond. Thus, the analogy between water and
quartz, which was made by Bernal and Fowler on the basis of X-rays diffraction,
is not complete, in particular, for the electrodynamic properties. What structural
features make water so conductive in comparison with other dielectrics (Fig. 1.14)?
von Grotthuss (1806) (Fig.1.15a) suggested [50] that the relay-race transfer of
protons among water molecules (see Fig.1.15b) provides an effective mechanism
for charge transfer through the water sample. The Grotthuss mechanism allows one
to describe quantitatively the anomalously high electrical conduction of water. This
mechanism, the modern understanding of which is shown in Fig.1.15c, was used to
explain the higher mobility of H
+ (H 3 O
+ ) and OH
− ions in water in comparison with
Fig. 1.13 a Energy band
structure (left), and the
energy levels as a function of
the spacing between
molecules (right). b
Snapshots of bulk liquid
water as observed by path
integral molecular-dynamic
simulations with
isoprobability contours of the
lowest unoccupied molecular
orbital. Part (b) adapted
from [49] with permission
from Springer Nature
r
E
Band gap
(a)
(b)
p
s
p
s
Conduction
band
Valence
band