11.2 O:H–O Bond Oscillator Pair
221
as molecular undercoordination [5, 6, 57–59], mechanical compression [27, 47, 54,
60], thermal excitation [2, 61], solvation [62] and determines the molecular behavior
such as solute and water molecular thermal fluctuation, solute drift motion dynamics,
or phonon relaxation.
11.2.3 Specific Heat and Phase Transition
Figure 11.1d shows the superposition of the specific heat η x (T/ Dx ) of Debye approximation for the O:H and the H–O segments [2]. The segmental specific heat meets
two conditions. One is the Einstein relation, Dx ∝ ω x , which directly correlates the
shape of the specific heat curve to the measured phonon frequency ω x . The specific
heat curves vary with external perturbation through Einstein’s relation. The other is
the thermal integration that is proportional to the bond energy E x . The (ω x , E x ) are
(200 cm
−1 , ~0.1–0.2 eV) for the O:H nonbond and they are (3200 cm
−1 , ~4.0 eV)
for the H–O bond. The superposition of the segmental specific heats η x defines the
phases from high temperature downward of Vapor (not shown), Liquid, Quasisolid
(QS), I h+c ice, XI, and the QS boundaries of extreme densities that are closing to the
T m and the T N [2, 4].
The thermodynamics of water ice is subject to its segmental specific heat difference in terms of the η L /η H ratio. The segment having a lower specific heat follows the
regular rule of thermal expansion, but the other segment responds to thermal excitation contrastingly. The thermodynamics and density oscillation of the bulk water ice
under the ambient pressure proceed in the following phases [2, 4]:
(1) In the Vapor phase (≥373 K), η L ∼ = 0, the O:H interaction is negligibly weak
though the H 2 O motifs still hold.
(2) In the Liquid phase (277, 373 K), η L /η H < 1, O:H cooling contraction and H–O
elongation take place, but the O:H contracts more than H–O contracts, cooling
contraction of water take place, reaching to the value of d OO = d H + d L =
1.0004 + 2.6946 Å.
(3) In the QS phase (258, 277 K), η L /η H > 1, H–O cooling contracts less that the
O:H expands; O:H–O expands, which triggers ice floating.
(4) At the QS boundaries (258, 277 K), η L /η H = 1, the density drops from its
maximum 1.0 to its minimum of 0.92 g cm
−3 . No apparent singularity presents
to the specific heat or to the density profile, so the 277 K is recommended be
the temperature for phase transition from Liquid to the QS phase. The 258 K
corresponds to the T N for the homogeneous ice nucleation.
(5) The I c+h ice (258, 100 K), η L /η H < 1, repeats the thermodynamics of the Liquid
phase at a lower transition rate, transiting the density from 0.92 to 0.94 g cm
−3 .
(6) In the XI phase, η L ∼ = η H ∼ = 0, neither O:H nor H–O responds sensitively to
thermal excitation, so the density remains almost constant except for the slight
∠O:H–O angle expansion at cooling.
221
as molecular undercoordination [5, 6, 57–59], mechanical compression [27, 47, 54,
60], thermal excitation [2, 61], solvation [62] and determines the molecular behavior
such as solute and water molecular thermal fluctuation, solute drift motion dynamics,
or phonon relaxation.
11.2.3 Specific Heat and Phase Transition
Figure 11.1d shows the superposition of the specific heat η x (T/ Dx ) of Debye approximation for the O:H and the H–O segments [2]. The segmental specific heat meets
two conditions. One is the Einstein relation, Dx ∝ ω x , which directly correlates the
shape of the specific heat curve to the measured phonon frequency ω x . The specific
heat curves vary with external perturbation through Einstein’s relation. The other is
the thermal integration that is proportional to the bond energy E x . The (ω x , E x ) are
(200 cm
−1 , ~0.1–0.2 eV) for the O:H nonbond and they are (3200 cm
−1 , ~4.0 eV)
for the H–O bond. The superposition of the segmental specific heats η x defines the
phases from high temperature downward of Vapor (not shown), Liquid, Quasisolid
(QS), I h+c ice, XI, and the QS boundaries of extreme densities that are closing to the
T m and the T N [2, 4].
The thermodynamics of water ice is subject to its segmental specific heat difference in terms of the η L /η H ratio. The segment having a lower specific heat follows the
regular rule of thermal expansion, but the other segment responds to thermal excitation contrastingly. The thermodynamics and density oscillation of the bulk water ice
under the ambient pressure proceed in the following phases [2, 4]:
(1) In the Vapor phase (≥373 K), η L ∼ = 0, the O:H interaction is negligibly weak
though the H 2 O motifs still hold.
(2) In the Liquid phase (277, 373 K), η L /η H < 1, O:H cooling contraction and H–O
elongation take place, but the O:H contracts more than H–O contracts, cooling
contraction of water take place, reaching to the value of d OO = d H + d L =
1.0004 + 2.6946 Å.
(3) In the QS phase (258, 277 K), η L /η H > 1, H–O cooling contracts less that the
O:H expands; O:H–O expands, which triggers ice floating.
(4) At the QS boundaries (258, 277 K), η L /η H = 1, the density drops from its
maximum 1.0 to its minimum of 0.92 g cm
−3 . No apparent singularity presents
to the specific heat or to the density profile, so the 277 K is recommended be
the temperature for phase transition from Liquid to the QS phase. The 258 K
corresponds to the T N for the homogeneous ice nucleation.
(5) The I c+h ice (258, 100 K), η L /η H < 1, repeats the thermodynamics of the Liquid
phase at a lower transition rate, transiting the density from 0.92 to 0.94 g cm
−3 .
(6) In the XI phase, η L ∼ = η H ∼ = 0, neither O:H nor H–O responds sensitively to
thermal excitation, so the density remains almost constant except for the slight
∠O:H–O angle expansion at cooling.