Interdisciplinary Applied Mathematics

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FIGURE 11.11. Average dipole moment (divided by the molecular dipole of TIP4P water    model)    as    a    function    of    the radial position    (p)    in the pore.    Solid

line: charged pore wall. Dotted line: uncharged pore wall. (Courtesy of E. Spohr.)

Nw=500    Nw=1000

FIGURE 11.12. Snapshots of equilibrium configuration of confined water at different hydration levels. Only the oxygen atoms of water are shown projected on the xy-plane perpendicular to the axis of the confining cylinder. Nw is the number of water molecules in the pore. Nw = 500, 1000, 1500, 2000, and 2600 correspond to approximately 20%, 40%, 60%, 75%, and 100% hydration levels. (Courtesy of M. Rovere.)

to another electronegative atom, and such a bond is usually termed as a hydrogen bond. Water molecules in liquid state can form an extensive hydrogen bonding network. Figure 11.13 shows the scenario of hydrogen bonding between two water molecules. The strength of hydrogen bonds (« 21 kJ/mol) is normally intermediate between that of the weak van der Waals interactions (« 1.25 kJ/mol) and that of the covalent chemical bonds (« 420 kJ/mol).

In atomistic simulations, there are two types of criteria for determining whether two water molecules form a hydrogen bond, namely, an energetic criterion and a geometric criterion. In the energetic criterion, two water

FIGURE 11.13. Schematic of the hydrogen bonding between two water molecules.


FIGURE 11.14. Schematic of bulk water molecules and the definition of the first coordination shell.

molecules are said to form a hydrogen bond if their interaction energy is less than a certain threshold energy EHB. In the geometric criterion, two water molecules are said to form a hydrogen bond if (a) the O—O distance is less than certain distance    rHB    and    (b)    the    O—H-    • • O angle    is    less    than

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