24.3 DPS of Water and Solutions
481
relaxation offsets boundaries of structural phases and raises the melting point and
meanwhile lowers the freezing temperature of water ice—known as supercooling and
superheating. The softened O:H elasticity and adaptivity and the high repulsivity of
the polarized supersolid skin takes the responsibility for slipperiness of ice and the
tough skin of liquid water [33]. The high thermal diffusivity of the supersolid skin
ensures the Mpemba paradox—warm water cooling faster [26].
24.4 Fraction of Bond Transition and Solute-Solute
Interactions
Integrating the ω H DPS peaks for the HX, YHO, and YX yields the fraction coefficients f x (C) for the O:H–O bonds transition from its mode of ordinary water to
the hydrating. The division of the fraction coefficient, f x (C)/C, is proportional to the
number of bonds per solute in the hydration shells, which characterizes the hydration shell size and its local electric field. A hydration shell may have one, two or
more subshells, depending on the nature and size of the solute. The size and charge
quantity determine its local electric field intensity that is subject to the screening by
the local H 2 O dipoles and the solute–solute interactions [41].
The f x (C) concentration trends show the following, see Fig. 24.7 and Fig. 24.8:
(1) The f H (C) ≡ 0 means that the H
+ (H 3 O
+ ) is incapable of polarizing its
neighboring HBs but only breaking and slightly repulsing its neighbors [7].
(2) The f Y (C) ∝ C means the constant shell size of the small Y
+ cation (radius
<1.0 Å) without being interfered with by other solutes. The constant slope
indicates that the number of bonds per solute conserves in the hydration shell.
The electric field of a small Y
+ cation is fully screened by the H 2 O dipoles in
its hydration shells; thus, no cation–solute interaction is involved in the YX or
YHO solutions.
(3) The f OH (C) ∝ C (<3100, 3610 cm
−1 ) means that the numbers of the O:⇔:O compression–elongated solvent H–O bonds and the bond–order–deficiency shortened solute H–O bonds are proportional to the solute concentration. Bond order
deficiency shortens and stiffens the bonds between undercoordinated atoms [4].
(4) The f X (C) ∝ 1–exp(–C/C 0 ) toward saturation means the number of H 2 O
molecules in the hydration shells is insufficient to fully screen the X
− (radius
~2.0 Å) solute local electric field because of the geometric limitation to
molecules packed in the crystal–like water. This number inadequacy further
evidences for the well–ordered crystal–like solvent. The solute can thus interact
with their alike—only anion–anion repulsion exists in the X
− —based solutions
to weaken the local electric field of X
− . Therefore, the f X (C) increases approaching saturation, the hydration shells size turns to be smaller, which limits the
solute capability of O:H–O bond relaxation and polarization.
481
relaxation offsets boundaries of structural phases and raises the melting point and
meanwhile lowers the freezing temperature of water ice—known as supercooling and
superheating. The softened O:H elasticity and adaptivity and the high repulsivity of
the polarized supersolid skin takes the responsibility for slipperiness of ice and the
tough skin of liquid water [33]. The high thermal diffusivity of the supersolid skin
ensures the Mpemba paradox—warm water cooling faster [26].
24.4 Fraction of Bond Transition and Solute-Solute
Interactions
Integrating the ω H DPS peaks for the HX, YHO, and YX yields the fraction coefficients f x (C) for the O:H–O bonds transition from its mode of ordinary water to
the hydrating. The division of the fraction coefficient, f x (C)/C, is proportional to the
number of bonds per solute in the hydration shells, which characterizes the hydration shell size and its local electric field. A hydration shell may have one, two or
more subshells, depending on the nature and size of the solute. The size and charge
quantity determine its local electric field intensity that is subject to the screening by
the local H 2 O dipoles and the solute–solute interactions [41].
The f x (C) concentration trends show the following, see Fig. 24.7 and Fig. 24.8:
(1) The f H (C) ≡ 0 means that the H
+ (H 3 O
+ ) is incapable of polarizing its
neighboring HBs but only breaking and slightly repulsing its neighbors [7].
(2) The f Y (C) ∝ C means the constant shell size of the small Y
+ cation (radius
<1.0 Å) without being interfered with by other solutes. The constant slope
indicates that the number of bonds per solute conserves in the hydration shell.
The electric field of a small Y
+ cation is fully screened by the H 2 O dipoles in
its hydration shells; thus, no cation–solute interaction is involved in the YX or
YHO solutions.
(3) The f OH (C) ∝ C (<3100, 3610 cm
−1 ) means that the numbers of the O:⇔:O compression–elongated solvent H–O bonds and the bond–order–deficiency shortened solute H–O bonds are proportional to the solute concentration. Bond order
deficiency shortens and stiffens the bonds between undercoordinated atoms [4].
(4) The f X (C) ∝ 1–exp(–C/C 0 ) toward saturation means the number of H 2 O
molecules in the hydration shells is insufficient to fully screen the X
− (radius
~2.0 Å) solute local electric field because of the geometric limitation to
molecules packed in the crystal–like water. This number inadequacy further
evidences for the well–ordered crystal–like solvent. The solute can thus interact
with their alike—only anion–anion repulsion exists in the X
− —based solutions
to weaken the local electric field of X
− . Therefore, the f X (C) increases approaching saturation, the hydration shells size turns to be smaller, which limits the
solute capability of O:H–O bond relaxation and polarization.