24
1 A Historical Review of the Structures of Water and Ice
field. The proton exchange causes additional confounding linewidth broadening of
the NMR signal. One can measure the line width and compares it with the reference
value for the liquid with a known concentration of ions. However, water normally
serves as such a reference liquid, and another liquid with known ionic product is
needed. Thus, the method is not absolute and requires some a priori information.
If one assumes that proton exchange occurs via the Grotthuss mechanism, the line
width reflects the concentration of hydronium ions. This method confirms that the
high rate of proton exchange exists on a picosecond time interval [70]. However,
such a short lifetime assumes a high concentration of hydronium ions, which are in
dynamic equilibrium with neutral water molecules. This contradicts the conclusion
made by Bernal and Fowler that the lifetime of H 2 O is about 10 h [9], which assumes
much higher (microsecond) ion lifetime. This fact shows one more inconsistency
between Bernal–Fowler water and modern experimental data.
Some authors explain this inconsistency by the scrambling of protons between
two neighboring molecules, which broadens the NMR line, but does not produce
ionic species [70]. Quantum-chemical calculations, however, do not allow a high
rate of proton scrambling, because of the high potential barrier and the low probability of the corresponding molecular orientations suitable for synchronized proton
exchange [71]. Other authors [15] introduce the lifetime distribution of hydronium
ions, and show that only those ions whose lifetime is long enough to be detected by
relatively slow methods are pH active. In other words, most ions do not contribute
to DC conductivity, but still are accountable by NMR. The latter model is in line
with the fact that the pH of water shows an anomalously strong temperature dependence. This ionic model of water is described in Chap. 4. For instance, at 0
◦ C and
100
◦ C the pHs of pure water are 7.5 and 6.1, respectively. This complicates the
application of the concept of pH for temperatures other than room temperature and
requires accounting for the temperature dependence of the concentration of active
ionic species in water (see Sect. 4.5.5 for details).
Figure 1.18 shows the temperature dependencies of the autoionization constant,
pK w , the DC electrical conductivity, σ dc , and the molar conductivity, m , which
was defined above. There are two “anomalies” that can be observed on these plots.
First, the autoionization constant has a non-monotonic form and shows a minimum
around 250
◦ C. Second, the difference in the concentrations of pH-active protons
between this point and 0
◦ C exceeds four orders of magnitude, which is too high for
the commonly accepted autoionization potential barrier of about 5.1 eV.
The origin of the strange behavior of the autoionization constant, pK w , is
described in Sect. 4.5.5, and lies in the different temperature dependencies of the
equivalent conductivity,
0
w , and the DC conductivity, σ dc , of water, as one can see
in Fig. 1.18. In order to understand this difference, one can rewrite the autodissociation constant in the following way:
K w = [H 3 O
+
][O H
−
] = [H 3 O
+
]
2
= (α[H 2 O])
2
=
=
w
0
w
[H 2 O]
2 =
σ dc
0
w
2 ,
(1.11)
1 A Historical Review of the Structures of Water and Ice
field. The proton exchange causes additional confounding linewidth broadening of
the NMR signal. One can measure the line width and compares it with the reference
value for the liquid with a known concentration of ions. However, water normally
serves as such a reference liquid, and another liquid with known ionic product is
needed. Thus, the method is not absolute and requires some a priori information.
If one assumes that proton exchange occurs via the Grotthuss mechanism, the line
width reflects the concentration of hydronium ions. This method confirms that the
high rate of proton exchange exists on a picosecond time interval [70]. However,
such a short lifetime assumes a high concentration of hydronium ions, which are in
dynamic equilibrium with neutral water molecules. This contradicts the conclusion
made by Bernal and Fowler that the lifetime of H 2 O is about 10 h [9], which assumes
much higher (microsecond) ion lifetime. This fact shows one more inconsistency
between Bernal–Fowler water and modern experimental data.
Some authors explain this inconsistency by the scrambling of protons between
two neighboring molecules, which broadens the NMR line, but does not produce
ionic species [70]. Quantum-chemical calculations, however, do not allow a high
rate of proton scrambling, because of the high potential barrier and the low probability of the corresponding molecular orientations suitable for synchronized proton
exchange [71]. Other authors [15] introduce the lifetime distribution of hydronium
ions, and show that only those ions whose lifetime is long enough to be detected by
relatively slow methods are pH active. In other words, most ions do not contribute
to DC conductivity, but still are accountable by NMR. The latter model is in line
with the fact that the pH of water shows an anomalously strong temperature dependence. This ionic model of water is described in Chap. 4. For instance, at 0
◦ C and
100
◦ C the pHs of pure water are 7.5 and 6.1, respectively. This complicates the
application of the concept of pH for temperatures other than room temperature and
requires accounting for the temperature dependence of the concentration of active
ionic species in water (see Sect. 4.5.5 for details).
Figure 1.18 shows the temperature dependencies of the autoionization constant,
pK w , the DC electrical conductivity, σ dc , and the molar conductivity, m , which
was defined above. There are two “anomalies” that can be observed on these plots.
First, the autoionization constant has a non-monotonic form and shows a minimum
around 250
◦ C. Second, the difference in the concentrations of pH-active protons
between this point and 0
◦ C exceeds four orders of magnitude, which is too high for
the commonly accepted autoionization potential barrier of about 5.1 eV.
The origin of the strange behavior of the autoionization constant, pK w , is
described in Sect. 4.5.5, and lies in the different temperature dependencies of the
equivalent conductivity,
0
w , and the DC conductivity, σ dc , of water, as one can see
in Fig. 1.18. In order to understand this difference, one can rewrite the autodissociation constant in the following way:
K w = [H 3 O
+
][O H
−
] = [H 3 O
+
]
2
= (α[H 2 O])
2
=
=
w
0
w
[H 2 O]
2 =
σ dc
0
w
2 ,
(1.11)