136
4 The Dielectric Properties and Dynamic Structure of Water and Ice
to the second relaxation of water (see Sect. 2.6.3), thus, indirectly confirming the
connection of the excess wing of the Debye relaxation to the orientational dynamics
of H 2 O dipoles in the hydration shell of short-lived ionic species.
While the short-range dynamics are diffusion controlled, the large-amplitude
intermolecular proton dynamics are better described by the Grotthuss mechanism
(see Sect. 1.3.1), in which the excess proton moves from one molecule to another
by minimal displacements of individual H 2 O species,
9 while the charge each time
hops a larger distance, equal to the molecular diameter. Hassanali et al. [20] showed
that rather than undergoing an exclusive step-wise hopping, the excess proton goes
through periods, when it can cover 4–8 Å in distance over several H 2 O molecules on
sub-picosecond timescales, followed by a relatively long resting time τ r , when the
proton does not propagate through the water network, obeying Frenkel’s oscillatory
motion together with the host molecule. The authors showed that the excess proton
resting time equals τ r ≥ 10 ps, and that the correlated back-and-forth vibrations of
protons between the neighboring water molecules exist on femtosecond timescales.
The latter defines the lifetime of the Zundel complex.
Thus, in addition to Frenkel’s idea of the simultaneous oscillatory-diffusional
motion of molecules in a liquid, for water, we add the exchange of atoms by
molecules. In other words, water differs from other liquids by the ability of molecules
to exchange protons, which means that the species of water are short-lived and continuously being reconstructed.
10 The two types of atoms (oxygen and hydrogen)
provide the formation of the following species in water: H 2 O, H 3 O
+ , OH
− , and their
derivatives: H 3 O
+
·3H 2 O (Eigen cation), H 5 O
+
2 (Zundel cation), OH
−
·3H 2 O (Eigen
anion), and H 3 O
−
2 (Zundel anion) [10]. All species are converted into each other by
proton exchange and have different lifetimes. However, all of them contribute to the
IR spectrum, showing high concentrations of short-lived ionic species [10]. Note
that each act of proton exchange is accompanied by a charge transfer, followed by
the adaptation of the surrounding molecules, or local polarization, which can be also
seen in the absorption spectrum.
4.2.2 The Spectral Signature of the Excess Proton
The details discussed above assume the electrodynamic response of the excess proton
in the dielectric spectrum, with a particular contribution to the infrared, terahertz,
and microwave frequency ranges, down to radio waves. Note that the spectroscopic
signature of the excess proton was identified in gas-phase water clusters only [21],
and, its contribution to the spectrum of bulk water has not yet to be unambiguously
identified. Nevertheless, by comparing the characteristic times of proton transport
9 The transfer of the negative charge, represented by a hydroxyle ion is realized by analogy. The
dynamics of the proton hole is realized by the proton transfer in the opposite direction.
10 This property differentiates the modern models of water from those of a hundred years ago.
4 The Dielectric Properties and Dynamic Structure of Water and Ice
to the second relaxation of water (see Sect. 2.6.3), thus, indirectly confirming the
connection of the excess wing of the Debye relaxation to the orientational dynamics
of H 2 O dipoles in the hydration shell of short-lived ionic species.
While the short-range dynamics are diffusion controlled, the large-amplitude
intermolecular proton dynamics are better described by the Grotthuss mechanism
(see Sect. 1.3.1), in which the excess proton moves from one molecule to another
by minimal displacements of individual H 2 O species,
9 while the charge each time
hops a larger distance, equal to the molecular diameter. Hassanali et al. [20] showed
that rather than undergoing an exclusive step-wise hopping, the excess proton goes
through periods, when it can cover 4–8 Å in distance over several H 2 O molecules on
sub-picosecond timescales, followed by a relatively long resting time τ r , when the
proton does not propagate through the water network, obeying Frenkel’s oscillatory
motion together with the host molecule. The authors showed that the excess proton
resting time equals τ r ≥ 10 ps, and that the correlated back-and-forth vibrations of
protons between the neighboring water molecules exist on femtosecond timescales.
The latter defines the lifetime of the Zundel complex.
Thus, in addition to Frenkel’s idea of the simultaneous oscillatory-diffusional
motion of molecules in a liquid, for water, we add the exchange of atoms by
molecules. In other words, water differs from other liquids by the ability of molecules
to exchange protons, which means that the species of water are short-lived and continuously being reconstructed.
10 The two types of atoms (oxygen and hydrogen)
provide the formation of the following species in water: H 2 O, H 3 O
+ , OH
− , and their
derivatives: H 3 O
+
·3H 2 O (Eigen cation), H 5 O
+
2 (Zundel cation), OH
−
·3H 2 O (Eigen
anion), and H 3 O
−
2 (Zundel anion) [10]. All species are converted into each other by
proton exchange and have different lifetimes. However, all of them contribute to the
IR spectrum, showing high concentrations of short-lived ionic species [10]. Note
that each act of proton exchange is accompanied by a charge transfer, followed by
the adaptation of the surrounding molecules, or local polarization, which can be also
seen in the absorption spectrum.
4.2.2 The Spectral Signature of the Excess Proton
The details discussed above assume the electrodynamic response of the excess proton
in the dielectric spectrum, with a particular contribution to the infrared, terahertz,
and microwave frequency ranges, down to radio waves. Note that the spectroscopic
signature of the excess proton was identified in gas-phase water clusters only [21],
and, its contribution to the spectrum of bulk water has not yet to be unambiguously
identified. Nevertheless, by comparing the characteristic times of proton transport
9 The transfer of the negative charge, represented by a hydroxyle ion is realized by analogy. The
dynamics of the proton hole is realized by the proton transfer in the opposite direction.
10 This property differentiates the modern models of water from those of a hundred years ago.