Interdisciplinary Applied Mathematics

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moves with little resistance through the nanotube, resulting in a burst of the water flow.

Filling Mechanism

When the diameter of the nanopore is small enough for a single-file chain (in a single-file chain the water molecules move as a single chain), the mechanism of filling the nanopore can be understood as summarized below (Waghe et al., 2002):

1. Filling of water molecules in a nanopore can occur from either side of the nanopore, with hydrogens entering first, dipoles oriented outward.

2. Filling of water molecules progresses as a chain from the end; it is initiated with the orientation remaining the same.

3.    Simultaneous    filling    from    both    sides is    not    favorable,    because    the

dipole orientations at the ends repel each other.

Water count in an 8.1 A Dia CNT

FIGURE 11.27. Water occupancy: number of water molecules inside the nanotube as a function of time.

FIGURE 11.28. Water binding energies. a. Probability density pbind(u) of binding energies u for bulk water and water inside the nanotube. Vertical arrows indicate average binding energies. Tilted arrows indicate crossover region, in which weakly bound states are more populated in bulk water. b. In[pint(u)/pins(u)] for water inside the nanotube and in bulk TIP3P water (open circles), fitted to в(т«Т — u) (lines). The    vertical    distance between    the    two    parallel    lines    of    slope    в    gives

the difference in the excess chemical potentials, в(т«Т — Tnt). (Courtesy of G. Hummer.)

4. Depending on the material (wall)-oxygen van der Waal’s interaction forces, the chain can rupture at the ends, causing conduction in bursts as in carbon nanotubes or stable as in silicon dioxide pores.

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