Interdisciplinary Applied Mathematics

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the axial diffusion coefficient of water molecules inside a hydrophilic pore increases monotonically with the increase in the pore radius. The results also show that inside a small (R < 3.0 A) or a large (R > 5.0 A) pore, the water diffusion in a hydrophilic pore is slower than that in a hydrophobic pore. This can be explained by the preferred dipole orientation of the water molecules with the stationary wall molecules.

(Mashl et al., 2003) studied the diffusion of water inside carbon nanotubes with different diameters. Figure 11.25 shows snapshots of the system studied, and Figure 11.26 shows the mean-square displacement and axial diffusion coefficient of water molecules obtained inside different-sized nanotubes. Similar to the studies in (Allen et al., 1999), the water molecules

FIGURE 11.25. Snapshots from molecular dynamics simulations at 300 K with a composite image of three typical systems with nanotube size increasing from left to right. In narrow nanotubes (left), the water adopts a single-file arrangement with a 1-D hydrogen bonding but becomes more disordered in a fashion similar to that of bulk water in wider nanotubes (right). Confined within a nanotube of a “critical” diameter (center), the water spontaneously orders itself into a regular array with a 2-D hydrogen bonding.

are “immobilized” in a nanotube of 8.6 A diameter. Panel (b) of Figure 11.25 shows the cross-sectional view of water structure inside the critically sized 8.6-A-diameter nanotube. A stable hydrogen-bonding network is observed as expected. This is consistent with the diffusion coefficient results. Since the simulations were performed at 300 K, these results indicate that when the water is confined in a critical-diameter pore, it can behave in an ice-like manner even at room temperature. Such an effect can be very useful for a number of applications, such as proton conduction in synthetic ion channels.

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