Interdisciplinary Applied Mathematics

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Water confined in silica pores has also been investigated. Silica and other porous materials are of great interest for a number of nanotechnology applications including catalytic and separation processes. (Gallo et al., 2000) have examined the density profiles of water confined in a cylindrical Vy-cor glass pore at various hydration levels (the smaller the number of water molecules in the pore, the smaller the hydration level). Figure 11.12 shows the snapshot of equilibrium configuration of confined water at various hydration levels (the pore diameter is 4.0 nm). The hydrophilic nature of the Vycor glass is    evident,    since    all    the    water    molecules    are    attracted    to

ward the pore surface. Low amounts of water (e.g., the number of water molecules is 500) are almost completely adsorbed on the pore surface. With increasing water concentration, water molecules occupy an increasing fraction of the free volume of the pore. For about 2600 water molecules, the hydration level is found to be close to 100%.

FIGURE 11.9. Water dipole orientation distributions for channels of effective radius 2.6 A (A), 4.1 A (B), and 5.6 A (C). The left panels show the average projection of    dipole    orientation    onto    the    г-axis    (cos(^))    for    atomic    hydrophobic

(solid curve), LJ hydrophobic (dotted curve), and hydrophilic (dashed curve) channels. The right    panels show    the    projections    of    the    dipole    onto    the    radial

vector r (cos^)). (Courtesy of S.-H. Chung.)

11.2.2 Hydrogen Bonding

A hydrogen atom covalently bound to an electronegative atom (e.g., nitrogen, oxygen) has a significant positive charge and can form a weak bond

FIGURE 11.10. Oxygen and hydrogen density distribution in a cylindrical pore of radius 10.9 A (p denotes the radius of the pore in A) when the pore wall has alternating positive and negative elementary charges (solid line) and when the pore wall has no charges (dotted line). (Courtesy of E. Sphor.)

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