# Interdisciplinary Applied Mathematics

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Gallo et al., 2000; Lynden-Bell and Rasaiah, 1996; Leo and Maranon, 2003; Gallo et al., 2002a; Gallo et al., 2002b; Green and Lu, 1997) (2-D confinement) and inside a cavity (Levinger, 2002; Brovchenko et al., 2001; Egorov and Brodskaya, 2003) (3-D confinement). Here we focus on how the density and the dipole orientation of the water molecules are influenced by the degree of confinement (e.g., size of nanopore), by the properties of surface (e.g., hydrophobic vs. hydrophilic surface), and by the presence of surface charge.

(Allen et al., 1999) studied the water density and the dipole orientation in a cylindrical pore systematically by varying the pore size and the surface properties. Three types of pores were considered. The first is a hydrophobic wall consisting of a regular array of Lennard-Jones (LJ) 12-6 centers on a cylindrical shell; the second is a structureless one-dimensional potential function that approximates the atomic hydrophobic wall; and the third is a hydrophilic surface containing an array of bound water molecules. Figure 11.7 shows the water oxygen atom density profiles against distance from the effective wall radius for each surface type and for an effective radius R = 2.1 A to 5.6 A. The pore is solvated by a band of water molecules centered at 1.2 to 1.4 A from the effective channel radius. The hydrophobic and hydrophilic channels result in very different water density profiles. Inside hydrophobic channels, for R < 3.6 A, there is only one layer of water, while there are two layers for larger cross-sections. In a hydrophilic channel, the water molecules are able to approach closer to the channel wall, resulting in a more sharply defined density peak compared to that in a hydrophobic channel. The location of the first water density peak near the channel wall is also shifted toward the channel wall for the hydrophilic surface case. In addition, in large pores, a third peak of water density appears when the channel surface is hydrophilic.

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