# Interdisciplinary Applied Mathematics

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Recently, (Gonnet et al., 2004) have suggested that the contact angle decreases weakly with increasing concentration of impurities like ions in water, and that chemisorption12 of water onto the graphite surface, altering the partial charge distribution on the graphite surface, can influence the contact angle significantly.

FIGURE 11.17.    Side    (top    row)    and top    view (bottom row)    of    the    initial    (t = 0)

and equilibrated (t = 0.2 ns) water droplet. The lateral graphite dimensions in the simulation are 119 A x118 A. (Courtesy of P. Koumoutsakos.)

###### 11.2.4 Dielectric Constant

From the results presented in this section, we can conclude that confinement can change the dipole orientation of water molecules significantly. This could lead to a change in the dielectric constant of water, which, in turn, can influence the dynamic properties and the electrostatic interactions between water molecules and between ion and water molecules. (Senapati and Chandra, 2001) studied the dielectric constant of water inside spherical cavities of various sizes using two different water models, namely, soft sticky dipole (SSD) (Liu and Ichiye, 1996) and SPC/E (Berendsen et al., 1987) models    (see    Section 11.1    for    details).    Figure    11.18    shows    the    dielectric constant    computed    using    the    two    models    as a    function of    the    cavity

size (Senapati and Chandra, 2001). Clearly, the dielectric constant in a nanocavity is significantly different from that in the bulk, and it decreases as the cavity radius decreases. Specifically, a nearly 50% decrease of the dielectric constant is observed in a cavity of about 12 A diameter. Since the cavity surface is not charged, the reduction of the dielectric constant is purely an effect of confinement.

Cavity diameter (Angstrom)

FIGURE 11.18. Dielectric constant of water confined in nanocavities of different cross sections. (Courtesy of A. Chandra.)

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