Interdisciplinary Applied Mathematics

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(Rovere et al., 1998) also reported on the HB of water molecules inside a 4.0 nm diameter cylindrical SiO2 pore. Figure 11.16 shows the number of hydrogen bonds as a function of distance from the center of the pore computed as the wall-water interactions are turned “on” (solid line) and “off”    (dash    line).    Note    that    the    number    of hydrogen    bonds decreases    al

most monotonically as we approach the pore surface when the wall-water interaction is turned on. However, when the surface atom-water interaction is turned off, the number of hydrogen bonds is essentially constant up to 15 A from the pore center. Comparison of these two results indicates that the pure geometrical confinement can alone be responsible for the reduction in the number of hydrogen bonds at the interface.

Finally, the dynamic properties of HB have also been investigated. (Hummer et al., 2001) investigated HB inside a carbon nanotube of 8.1 A diameter. They found that the HB inside the carbon nanotube is much more stable and highly oriented compared to that in the bulk. For example, the average lifetime of a hydrogen bond inside a carbon nanotube is 5.6 ps, compared to 1.0 ps in the bulk. In addition, less than 15% of the H-O- • • H angles inside the carbon nanotube exceeds 30°, compared to 30% in the bulk. It    was    also    reported    that    the    OH    bonds    involved    in the    hydrogen

bonds are nearly aligned with the nanotube axis, collectively flipping direction every 2 to 3 ns on average. In summary, the HB can be significantly

FIGURE 11.15. The effect    of    pore    radius    on the    number    of    hydrogen    bonds    per

water molecule for atomic hydrophobic (solid curve, filled circles), LJ hydrophobic (dotted curves, filled circles), and hydrophilic channels (dashed curve, open circles). The number of hydrogen bonds in hydrophilic pores when channel wall molecules are excluded are drawn as dash-dot-dot curves (open circles). (Courtesy of S.-H. Chung.)

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