24.2 O:H–O Bond Segmental Cooperativity
475
length and bond angle relaxation changes system energy, but structural fluctuation
contributes little to the system energy on an average.
With the known H–O and O:H segmental length relaxation derived from ρ(P)
(1/V(P)) profile measured from compressed ice [18, 19] and the framework of
tetrahedral-coordination for a water molecule [20], one can correlate the size d H ,
separation d OO , bond geometry, and mass density ρ of molecules packed in water
and ice in the following manner (Fig. 24.3) [21],
d O O = 2.6950ρ
−1/3
(Molecular separation)
d L
d L0
=
2
1+ex p[(d H −d H 0 )/0.2428]
; (d H 0 = 1.0004 and d L0 = 1.6946 at 4
◦ C)
(24.2)
The O:H nonbond and the H–O bond segmental disparity and the O–O coupling
dislocate the O
2− along the segmented O:H–O bond in the same direction but by
different amounts under an external stimulus [16, 18, 22, 23]. The softer O:H nonbond always relaxes more than the stiffer H–O bond with respect to the H
+ as the
coordination origin. The ∠O:H–O angle θ relaxation contributes to the geometry and
mass density. The H–O relaxation absorbs or emits energy and the O:H relaxation
dissipates energy caped with the 0.1 eV. The O:H–O bond segmental energy and specific heat disparity dictate the extraordinary adaptivity, cooperativity recoverability,
sensitivity, properties of water and ice under external stimulus such as mechanical
compression and thermal excitation.
Heating lengthens the O:H nonbond from 1.695 to 1.750 Å, but the H–O bond
responds to heating contrastingly from 1.000 to 0.985 Å when heating from 273 to
377 K. The segmental disparity defines the manner of O:H–O thermal relaxation.
The O:H having a lower specific heat follows the regular thermal expansion, which
shortens the H–O bond by the O–O coupling [16]. Compression always shortens the
O:H and lengthens the H–O regardless of the phase structures. The O:H nonbond
contracts from 1.78 to 1.10 Å under compression up to 60 GPa when transits from the
VII/VIII phase into phase X of identical O:H and H–O lengths. The segmental energy
E x varies with a certain power of its inverse length d x . The phonon spectroscopy
probes the length and energy as the phonon frequency shift, or segmental stiffness, in
the form of (ω x )
2
∝ (E/d
2 ) x . A Lagrangian-Laplacian resolution to the oscillation
dynamics of the O:H–O oscillator pair has transformed the measured segmental
length and vibration frequency (d x , ω x ) int to the respective force constant and binding
energy (k x , E x ) and hence produces the potential paths of the O:H–O under continued
perturbation [24, 25].
Table 24.1 summarizes the thermodynamics of O:H –O bond length and stiffness,
mass density under the ambient pressure, and the molecular CN, polarization and
pressure effect [16]. External perturbation changes the phase boundaries through
Einstein relation Dx ∝ ω x (P, T, z, E,…), referring discussions on the specific
heat η x disparity and the derives density anomalies in Chap. 11.
Numerical reproduction of the Mpemba effect—hot water cools faster [26], evidences directly the essentiality of the 0.75 gcm
−3 mass density of the supersolid skin
that promotes heat conduction outward the water of heat source. Exothermic reaction
475
length and bond angle relaxation changes system energy, but structural fluctuation
contributes little to the system energy on an average.
With the known H–O and O:H segmental length relaxation derived from ρ(P)
(1/V(P)) profile measured from compressed ice [18, 19] and the framework of
tetrahedral-coordination for a water molecule [20], one can correlate the size d H ,
separation d OO , bond geometry, and mass density ρ of molecules packed in water
and ice in the following manner (Fig. 24.3) [21],
d O O = 2.6950ρ
−1/3
(Molecular separation)
d L
d L0
=
2
1+ex p[(d H −d H 0 )/0.2428]
; (d H 0 = 1.0004 and d L0 = 1.6946 at 4
◦ C)
(24.2)
The O:H nonbond and the H–O bond segmental disparity and the O–O coupling
dislocate the O
2− along the segmented O:H–O bond in the same direction but by
different amounts under an external stimulus [16, 18, 22, 23]. The softer O:H nonbond always relaxes more than the stiffer H–O bond with respect to the H
+ as the
coordination origin. The ∠O:H–O angle θ relaxation contributes to the geometry and
mass density. The H–O relaxation absorbs or emits energy and the O:H relaxation
dissipates energy caped with the 0.1 eV. The O:H–O bond segmental energy and specific heat disparity dictate the extraordinary adaptivity, cooperativity recoverability,
sensitivity, properties of water and ice under external stimulus such as mechanical
compression and thermal excitation.
Heating lengthens the O:H nonbond from 1.695 to 1.750 Å, but the H–O bond
responds to heating contrastingly from 1.000 to 0.985 Å when heating from 273 to
377 K. The segmental disparity defines the manner of O:H–O thermal relaxation.
The O:H having a lower specific heat follows the regular thermal expansion, which
shortens the H–O bond by the O–O coupling [16]. Compression always shortens the
O:H and lengthens the H–O regardless of the phase structures. The O:H nonbond
contracts from 1.78 to 1.10 Å under compression up to 60 GPa when transits from the
VII/VIII phase into phase X of identical O:H and H–O lengths. The segmental energy
E x varies with a certain power of its inverse length d x . The phonon spectroscopy
probes the length and energy as the phonon frequency shift, or segmental stiffness, in
the form of (ω x )
2
∝ (E/d
2 ) x . A Lagrangian-Laplacian resolution to the oscillation
dynamics of the O:H–O oscillator pair has transformed the measured segmental
length and vibration frequency (d x , ω x ) int to the respective force constant and binding
energy (k x , E x ) and hence produces the potential paths of the O:H–O under continued
perturbation [24, 25].
Table 24.1 summarizes the thermodynamics of O:H –O bond length and stiffness,
mass density under the ambient pressure, and the molecular CN, polarization and
pressure effect [16]. External perturbation changes the phase boundaries through
Einstein relation Dx ∝ ω x (P, T, z, E,…), referring discussions on the specific
heat η x disparity and the derives density anomalies in Chap. 11.
Numerical reproduction of the Mpemba effect—hot water cools faster [26], evidences directly the essentiality of the 0.75 gcm
−3 mass density of the supersolid skin
that promotes heat conduction outward the water of heat source. Exothermic reaction