Interdisciplinary Applied Mathematics

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FIGURE 11.31. Normalized dipole of water molecules inside the tube projected onto the tube axis as a function of the position г of the water-oxygen atom along the tube axis. Each point corresponds to one water molecule in a saved configuration. The results are separated for N = 1 to 5 water molecules inside the tube (top to bottom). It was observed that for a single molecule in a tube, the water dipole moments point inward preferentially. With subsequent molecules entering into the tube, this orientational preference is maintained, such that the chain grows with all dipoles pointing inward. As a consequence, the dipolar orientations of water chains    entering    from    the    two    ends    simultaneously    are    not    compatible,


thus disfavoring simultaneous filling from both sides. (Courtesy of G. Hummer.)


analyzing Figure 11.33, where the average number of percolating chains in the channel is plotted as a function of the number of water molecules inside the channel. Clearly, when n is small, there is never a percolating cluster, and when n is large enough, there is almost always one present. (Beckstein et al., 2001) show that the filling can be enhanced by placing dipoles along the walls of the nanotube at diameters at which water cannot enter the tube.


0.5



§ 0



200    300    400    500    600    700    800    900


T (K)


FIGURE 11.32. Snapshot of a “percolating cluster” from a biased simulation run with a pore radius of 0.6 nm and length of 0.8 nm. Only the water molecules near the pore are shown. The positions of the confining walls are indicated. (Courtesy of S. Melchionna.)


FIGURE 11.33. Probability of finding an unbroken chain of water molecules through the    pore    as a    function    of    the    wat er molecules inside    the    pore    shown in

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