Interdisciplinary Applied Mathematics

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11.3.3 Filling and Emptying Kinetics

In nanopores, confinement of the water can induce the so-called drying transition as a result of the strong hydrogen bonding between water molecules. This state can cause the water molecules to recede from the nonpolar surface to form a vapor layer separating the bulk phase from the surface (Still-inger, 1973; Lum et al., 1999; Lum and Luzar, 1997). This water behavior is important in understanding many biological processes, e.g., ion and water transport in biological channels where the channel dimension is of order a few angstroms and the channel surface is usually hydrophobic (Hummer et al., 2001). Motivated by the design of robust artificial ion and water chan-

0    10    20    30    40    50

Time Lag (ps)


1 0.8



° 0.6


n 0.4


0.2 0.0

0    5    10    15    20

Van der Waals diameter (A)

FIGURE 11.26. Water mobility inside nanotubes at 300 K. (a) Mean-square displacement (MSD) of water traveling along the nanotube axis for various nanotubes. (b) Axial diffusion coefficient of water, normalized to bulk (2.69 x 10~cm2/s is the bulk value with SPC/E water), derived from panel (a).

nels (see Section 13.2 for more details on artificial ion channels), a number of researchers have investigated the filling and emptying of water in carbon nanotubes (Hummer et al., 2001; Waghe et al., 2002; Berezhkovskii and Hummer, 2002; Mann and Halls, 2003) and artificial nanopores (Allen et al., 2002; Beckstein and Sansom, 2003; Allen et al., 2003; Beckstein et al., 2001; Kalko et al., 1995).

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