Interdisciplinary Applied Mathematics

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FIGURE 12.4.    Cl    ion    and water    concentration    profile    across    the    channel    for

case 2 (W = 3.49 nm, aa = +0.320 C/m2).

compared to case 1; hence, the second concentration peak is more distinct in this case.

The water concentration profile in Figure 12.4 shows two interesting features. First, compared to the previous case (see Figure 12.3 (a)), the first concentration peak of water is about 33% higher. Second, there is an additional water concentration peak located at about 0.44 nm away from the channel wall, and the second concentration peak is very close to the second peak of the Cl_ concentration. This result indicates that under high surface charge density, the high concentration of ions near the channel wall can change the concentration of water significantly. Such a change can be partly explained by the hydration of the ions. Typically there will be several water molecules bound to each ion due to the strong charge-dipole interaction between the ion and water (Israelachvili, 1992a). Therefore, a region with very high ion concentration tends to have a high water concentration region near it.

Figure 12.5 shows the Na+ ion concentration profile across the channel for case 3, where the channel width is 3.49 nm and the charge density on the channel wall is —0.120 C/m2. The only difference from the first case is that the wall is oppositely charged and the Cl_ ions are replaced by Na+ ions. We    observe    that    (1)    the    first    Na+    concentration    peak near    the wall

is about 37% lower compared to the Cl_ concentration peak in the first case, (2) the position of the first peak is located about 0.42 nm away from the channel wall, i.e., about 0.07 nm farther away from the channel wall compared to the    first    case,    where    the    first    Cl_    ion    peak is located    at    0.35

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