# Interdisciplinary Applied Mathematics

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Density distribution and dipole orientation studies have also been performed on charged nanopores. (Hartnig et al., 1998) studied the density distribution and dipole orientation of water molecules in two cylindrical nanopores with a radius of 10.9 A. In the first pore, there are 72 alternating positive and negative elementary charges on the pore surface, and the second pore has no surface charge. Figure 11.10 shows the oxygen and hydrogen density    distribution    for    the    two pores.    From    the    graph,    we    ob

serve that the water oxygen density has a slightly larger peak when the pore is charged. In addition, the density peak of the oxygen atoms is closer to the pore surface when the nanopore is charged. This can be explained by the attraction of the water molecules toward the nanopore surface. The hydrogen atom density    profile    shows    a peak    at    R = 9.2    A,    which    was    not

observed when the pore was not charged. This is caused by the attraction of the hydrogen atoms by the negative surface charges, which is not balanced by the short-range Lennard-Jones repulsion as in the case of oxygen. Figure 11.11 shows the average dipole moment of a water molecule in the radial direction as a function of its radial position. For both charged and noncharged pores, we observe that the water dipole tends to point toward the pore center in the region 6.7 A< R < 7.2 A (where R is the pore radius). However, in the charged pore, there is an additional region R > 8.2 A, where the dipoles point toward the pore surface, consistent with the hump in the hydrogen density profile at R = 9.2 A. From these results, we can conclude that the presence of a charge on the pore surface can influence the density distribution, dipole orientation, and the average dipole moment.

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