Interdisciplinary Applied Mathematics

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influenced by the strong confinement inside a carbon nanotube, and the strongly stable hydrogen bonding inside the nanotube can change the wetting characteristic of the nanotube significantly (Hummer et al., 2001).

11.2.3 Contact Angle

The contact angle в is a quantitative measure of the wetting of a solid by a liquid, as we have seen in Section 8.1; see Figure 8.4. At nanoscales, where the surface to volume ratio of the system can be orders of magnitude larger compared to a macroscopic system, the surface-water interactions tend to    dominate the    behavior    of    water    in    the    system.    The    contact    angle

of water on the surface is a very important indicator of the strength of the surface-water interactions. Several authors have investigated the static wetting behavior of water on a graphite sheet (Werder et al., 2003) and on a carbon nanotube surface (Werder et al., 2001) and computed the contact angle of water on these surfaces.

(Werder et al., 2003) presented a study on the contact angle of water on a graphite surface by using molecular dynamics simulations. Figure 11.17

FIGURE 11.16. Number    of    hydrogen    bonds    as    a function    of    the    distance    from

the center    of    the    pore,    calculated    with    the    wall-water    interaction    turned    on

(solid line) and off (dashed line). The horizontal dotted line represents the density-weighted average value of number of hydrogen bonds for confined water with the wall-water interaction turned on. (Courtesy of M. Rovere.)

shows snapshots    of    the    system.    It    shows    that    a    cubic    water    block    will

spontaneously evolve to a hemisphere as it reaches equilibrium. The contact angle    of    the    water    droplet    on the graphite    surface is a    function    of    the

Lennard-Jones potential between the carbon atom and the water molecule. The authors found that using a oco = 3.19 A and eCo = 0.392 kJ/mol, one can reproduce the contact angle (86°) of water on a graphite surface as measured at the macroscopic scale. Such interaction parameters can then be very useful in the study of water behavior in carbon nanotubes.

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