Interdisciplinary Applied Mathematics

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11.3.2 Diffusion Transport

One of the motivations to study water behavior at nanoscale is to understand how its transport is influenced by confinement. Since diffusion is usually the dominant transport mechanism at small scales, the diffusion of water in nanochannels has been explored in detail in the past. Several researchers have investigated the diffusion of water inside artificial cylindrical nanopores (Allen et al., 1999; Lynden-Bell and Rasaiah, 1996; Zhou et al., 2003), inside silica nanopores (Rovere and Gallo, 2003; Spohr et al.,

FIGURE 11.24. Self-diffusion coefficient along the axial direction (г-direction) of water molecules inside atomic hydrophobic (solid curve, filled circles), LJ hydrophobic (dotted curve, filled circles), and hydrophilic (dashed curve, open circles) pores. The horizontal dash-dot line is the bulk reference value. (Courtesy of S.-H. Chung.)

1999; Gallo et al., 1999), inside carbon nanotubes (Leo and Maranon, 2003; Mashl et al., 2003; Paul and Chandra, 2003), and inside slit nanopores (Brovchenko et al., 2001; Zhang et al., 2002).

(Allen et al., 1999) investigated the diffusion coefficient of water molecules inside artificial cylindrical pores of various radii and surface properties. Figure 11.24 shows the variation of the axial diffusion coefficient of water with the radii of the pore for atomic hydrophobic, LJ hydrophobic, and hydrophilic channels (see Section 11.2.1 for details on these channels). The result indicates that the axial (z-direction) self-diffusion of water molecules within hydrophobic pores experiences a dramatic fall for channel sizes with a radius    of    3.6 to    4.1    A.    For a    pore    with a radius    of    4.1    A,    the    axial    diffusion decreases to    about    4%    of    the    bulk    value.    This is mainly    caused    by the

stable hydrogen-bonding network. As the pore size increases, the diffusion coefficient    of    water approaches    its    bulk    value.    It was    also    observed    that

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