4.4 Instantaneous Structure of Water and Ice
151
Part (c) in Fig. 4.7 shows the two characteristic polarization spheres formed by
the ionic and molecular species. The small-gray spheres are the hydration shells of
ions, which are formed by the nearest molecular coordination sphere of ionic species.
As discussed in Sect. 4.2.2, the time lag between the displacement of the central ion
and the adaptation of its hydration shell is responsible for the secondary relaxation
of water. This relaxation is not observed in ice, because the lifetime of ionic species
t ± significantly exceeds the relaxation time of the hydration shell. The large-colored
(red or blue) spheres represent the ionic atmospheres, which are formed by the ions
of the opposite sign around the central ion. As one can see, these spheres overlap, and
have a radius equal to the average distance between ionic species L. The polarization
of these large spheres is responsible for the main (Debye) dielectric relaxation of
both ice and water (see Sect. 3.5 for the quantitative analysis).
Finally, part (d) in Fig 4.7 shows the instantaneous proton density. Each hydrogen
atom of a water molecule is shown by the black dot, surrounded by a blue area.
The latter represents the diameter of the proton delocalization. Each overlap of the
proton delocalization area with the nearest molecule is a potential “bridge” for proton transfer, which can be interpreted as a manifold of the complicated concept of
hydrogen bonding (see Sect. 4.1 for details). One can see that the proton density
is higher around the ionic species. The sub-picosecond thermal fluctuations of the
proton density in water are, in principle, observable by neutron scattering.
Thus, the electrodynamic properties of ice and water allow one to reconstruct the
I-structure, whose dynamics gives the slower V- and D-structures. Interestingly, a
single parameter, the height of the potential barrier for proton transfer, is responsible
for the global transformation of the dielectric spectra of ice and water. This barrier
height is 3.5 times larger for ice than that for water (see Fig. 4.6). In other words,
water and ice have an identical I-structure, and their D-structure differs only by the
potential barrier of charge transfer. For water, in particular, the barrier height is 0.2
eV (20 kJ/mol) [48]. Protons randomly walk by hopping over neutral H 2 O molecules
to form short-lived H 3 O
+ OH
− ion pairs.
The separated charges occur in water and ice in high concentrations, n ± , which
accounts for the high value of the static dielectric constant, (0). However, the equilibrium of the separated charges is dynamic. It is maintained by two competitive
mechanisms, the self-dissociation of H 2 O molecules and the recombination of the
H 3 O
+ OH
− ion pairs. A decrease in temperature slows down proton diffusion, thus
shifting the equilibrium to increase the lifetime of the separated charges. This slightly
increases both, n ± and (0), while the general temperature dependence of n ± and
(0) is preserved at the water-ice phase transition. The difference between the activation energies of proton diffusion in water and ice determines the latent heat of the
water-ice phase transition.
151
Part (c) in Fig. 4.7 shows the two characteristic polarization spheres formed by
the ionic and molecular species. The small-gray spheres are the hydration shells of
ions, which are formed by the nearest molecular coordination sphere of ionic species.
As discussed in Sect. 4.2.2, the time lag between the displacement of the central ion
and the adaptation of its hydration shell is responsible for the secondary relaxation
of water. This relaxation is not observed in ice, because the lifetime of ionic species
t ± significantly exceeds the relaxation time of the hydration shell. The large-colored
(red or blue) spheres represent the ionic atmospheres, which are formed by the ions
of the opposite sign around the central ion. As one can see, these spheres overlap, and
have a radius equal to the average distance between ionic species L. The polarization
of these large spheres is responsible for the main (Debye) dielectric relaxation of
both ice and water (see Sect. 3.5 for the quantitative analysis).
Finally, part (d) in Fig 4.7 shows the instantaneous proton density. Each hydrogen
atom of a water molecule is shown by the black dot, surrounded by a blue area.
The latter represents the diameter of the proton delocalization. Each overlap of the
proton delocalization area with the nearest molecule is a potential “bridge” for proton transfer, which can be interpreted as a manifold of the complicated concept of
hydrogen bonding (see Sect. 4.1 for details). One can see that the proton density
is higher around the ionic species. The sub-picosecond thermal fluctuations of the
proton density in water are, in principle, observable by neutron scattering.
Thus, the electrodynamic properties of ice and water allow one to reconstruct the
I-structure, whose dynamics gives the slower V- and D-structures. Interestingly, a
single parameter, the height of the potential barrier for proton transfer, is responsible
for the global transformation of the dielectric spectra of ice and water. This barrier
height is 3.5 times larger for ice than that for water (see Fig. 4.6). In other words,
water and ice have an identical I-structure, and their D-structure differs only by the
potential barrier of charge transfer. For water, in particular, the barrier height is 0.2
eV (20 kJ/mol) [48]. Protons randomly walk by hopping over neutral H 2 O molecules
to form short-lived H 3 O
+ OH
− ion pairs.
The separated charges occur in water and ice in high concentrations, n ± , which
accounts for the high value of the static dielectric constant, (0). However, the equilibrium of the separated charges is dynamic. It is maintained by two competitive
mechanisms, the self-dissociation of H 2 O molecules and the recombination of the
H 3 O
+ OH
− ion pairs. A decrease in temperature slows down proton diffusion, thus
shifting the equilibrium to increase the lifetime of the separated charges. This slightly
increases both, n ± and (0), while the general temperature dependence of n ± and
(0) is preserved at the water-ice phase transition. The difference between the activation energies of proton diffusion in water and ice determines the latent heat of the
water-ice phase transition.