2
1 A Historical Review of the Structures of Water and Ice
applicable to both forms. The short-order structure is mainly formed by pair interactions of water molecules, which are identical in ice and water. The local molecular
environment is also expected to be nearly the same. Pair interactions, and the corresponding local water structure, can be tested by simulations of molecular dynamics
1
and by the adjustment of the potential of the interaction of water molecule pairs.
Abascal et al. [1] introduced the most popular rigid four-point model of the water
molecule (TIP4P/2005 model), which quantitatively reproduces the phase diagram
and the density of water and ice. Using this model, Ramirez et al. [2] showed that
the temperature (the thermal energy) of a system of water molecules defines the condition of the long-range order formation. Figure 1.1 shows two quasi-equilibrium
configurations of TIP4P/2005 water molecules that represent the quasi-equilibrium
“structure” of water and ice. These two configurations are obtained at two different
thermal energies and both have nearly the same local molecular environment, while
the “structure” looks different. This example shows that, although the pair potential
stays the same, the residence time of molecule near the equilibrium position defines
the condition of long-order formation.
Figure 1.1 shows quasi-equilibrium configurations. In real ice, however, each
molecule has a chance to overcome the potential barrier and change the equilibrium
configuration, which in the frame of ergodicity,
2 means that, when the observation
period is long enough, the structure shown in Fig. 1.1b is equivalent to the structure
shown in Fig. 1.1a (and vice versa). The difference between what we call the “structures” of ice and water is in the corresponding observation times and the period of
the averaging of relative molecular configurations.
As the structure of water and ice depends on the time and spatial scales over
which it is determined, we should define these characteristic timescales. Eisenberg
and Kauzmann [3] suggested several types of water structures, depending on the
time of averaging [3] and the experimental techniques used for their determination.
In particular, they introduced the instantaneous or I-structure, which is used for the
timescale less than 1 ps; the vibrationally averaged, or V-structure, for 1–10 ps;
the diffusion averaged, or D-structure, for the timescale more than 10 ps; and the
potential-energy-minimum static F-structure (t → ∞). According to this classification, Fig. 1.1 represents the F-structure, as they were obtained by potential energy
minimization and do not reflect the real instantaneous I-structure. The latter is an
idealization, because no method can accurately measure it. For example, conventional electrochemical methods deal with D-structure, while infrared spectroscopy
measures V-structure. Even neutron and X-ray scattering techniques, which have
a shortest interaction time of a single photon/neutron with a sample, still have a
1 Experimental methods of the short-order test are considered in Sects. 1.2 and 1.5.
2 Ergodicity expresses the idea that any particle of a moving dynamic system will eventually visit all
parts of the space that the system moves in. This implies that the average behavior of the system can
be deduced from the trajectory of a selected particle. Equivalently, a sufficiently large collection of
random samples from a process can represent the average statistical properties of the entire process.
1 A Historical Review of the Structures of Water and Ice
applicable to both forms. The short-order structure is mainly formed by pair interactions of water molecules, which are identical in ice and water. The local molecular
environment is also expected to be nearly the same. Pair interactions, and the corresponding local water structure, can be tested by simulations of molecular dynamics
1
and by the adjustment of the potential of the interaction of water molecule pairs.
Abascal et al. [1] introduced the most popular rigid four-point model of the water
molecule (TIP4P/2005 model), which quantitatively reproduces the phase diagram
and the density of water and ice. Using this model, Ramirez et al. [2] showed that
the temperature (the thermal energy) of a system of water molecules defines the condition of the long-range order formation. Figure 1.1 shows two quasi-equilibrium
configurations of TIP4P/2005 water molecules that represent the quasi-equilibrium
“structure” of water and ice. These two configurations are obtained at two different
thermal energies and both have nearly the same local molecular environment, while
the “structure” looks different. This example shows that, although the pair potential
stays the same, the residence time of molecule near the equilibrium position defines
the condition of long-order formation.
Figure 1.1 shows quasi-equilibrium configurations. In real ice, however, each
molecule has a chance to overcome the potential barrier and change the equilibrium
configuration, which in the frame of ergodicity,
2 means that, when the observation
period is long enough, the structure shown in Fig. 1.1b is equivalent to the structure
shown in Fig. 1.1a (and vice versa). The difference between what we call the “structures” of ice and water is in the corresponding observation times and the period of
the averaging of relative molecular configurations.
As the structure of water and ice depends on the time and spatial scales over
which it is determined, we should define these characteristic timescales. Eisenberg
and Kauzmann [3] suggested several types of water structures, depending on the
time of averaging [3] and the experimental techniques used for their determination.
In particular, they introduced the instantaneous or I-structure, which is used for the
timescale less than 1 ps; the vibrationally averaged, or V-structure, for 1–10 ps;
the diffusion averaged, or D-structure, for the timescale more than 10 ps; and the
potential-energy-minimum static F-structure (t → ∞). According to this classification, Fig. 1.1 represents the F-structure, as they were obtained by potential energy
minimization and do not reflect the real instantaneous I-structure. The latter is an
idealization, because no method can accurately measure it. For example, conventional electrochemical methods deal with D-structure, while infrared spectroscopy
measures V-structure. Even neutron and X-ray scattering techniques, which have
a shortest interaction time of a single photon/neutron with a sample, still have a
1 Experimental methods of the short-order test are considered in Sects. 1.2 and 1.5.
2 Ergodicity expresses the idea that any particle of a moving dynamic system will eventually visit all
parts of the space that the system moves in. This implies that the average behavior of the system can
be deduced from the trajectory of a selected particle. Equivalently, a sufficiently large collection of
random samples from a process can represent the average statistical properties of the entire process.