Interdisciplinary Applied Mathematics

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a certain threshold angle OHB. The O—O distance and O—H- — O angle are usually referred to as hydrogen bond length (rHB) and hydrogen bond angle (OHB). Typically, EHB is chosen to be —10 kJ/mol, rHB is chosen to be the radius of the first coordination shell of a water molecule, and OHB is chosen to be 30°. The first coordination shell of a water molecule is defined as the first water shell around that water molecule. The radius of the shell, Ri,    is    usually    chosen to be    the    position    of    the    first    minimum

of the oxygen-oxygen radial distribution function (RDFO-O) (see Figure 11.14).

At the molecular level, the water structure is determined by the hydrogen bonding (HB) network. Since HB plays an important role in determining

the transport properties of water molecules and ions, it is important to understand how the HB network is influenced when the water is confined in nanochannels. The HB of water inside slit pores (Galle and Vortler, 1999; Galle and Vortler, 2001) and cylindrical pores (Allen et al., 1999; Rovere and Gallo, 2003; Walther et al., 2001a; Rovere et al., 1998; Werder et al., 2001; Spohr    et    al.,    1999;    Mashl    et    al.,    2003) has been    studied    extensively

in the past decades.

Figure 11.15 shows the number of hydrogen bonds per water molecule in a cylindrical pore as a function of the pore radius and surface properties (Allen et al., 1999). For a hydrophobic pore, the extent of HB is maximized at moderate radii (r « 3.6 A), and drops notably as the pore size decreases. Similar observations have been reported for other hydrophobic pores, e.g., inside a carbon nanotube (Mashl et al., 2003). For a hydrophilic pore, the number of hydrogen bonds per water molecule is not sensitive to the pore size. However, if we exclude the hydrogen bonds between wall atoms and water molecule (dash-dot-dot curve in Figure 11.15), i.e., by counting only the hydrogen bonds between water molecules inside the pore, we find that the average number of hydrogen bonds per water molecule is significantly lower than that for the corresponding hydrophobic pores. This is because the water molecules inside the pore sacrifice water-water hydrogen bonds for the water-wall hydrogen bonds. Since the wall atoms are fixed, the strong interactions between water molecules and the wall atoms are likely to result in a reduced transport (e.g., diffusion transport) of water molecules in a hydrophilic pore compared to that in a hydrophobic pore.

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