Interdisciplinary Applied Mathematics

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Water Entry in Hydrophobic Nanopores


Simulations of water conduction through carbon nanotubes (Hummer et al., 2001) indicate that even though nanotubes are hydrophobic, the channel has a steady occupancy of water molecules during the course of the simulation (Figure 11.27). Even for a 60-ns simulation (Hummer et al., 2001), the occupancies are not different. As mentioned in Section 11.2.2, the high occupancy of water inside the hydrophobic nanotube is mainly caused by the stable hydrogen bond inside the nanotube. (Hummer et al., 2001) explained this quantitatively by computing the local excess chemical potential, Ant, defined as the negative free energy of removing a water molecule from the channel. Such a free energy is not dominated by how strongly bound a water molecule is on average, but by how populated weakly bound states are. Even though the binding energy of water molecules inside the nanotube is unfavorable compared to bulk water, the binding energy inside the nanotube is more sharply distributed (see Figure 11.28), and high-energy states dominating the free energy are less frequently occupied. As a result, though the water molecules inside the nanotube lose about 2 kcal/mol in energy, they have a lower excess chemical potential of Ant ~ — 6.87± 0.07 kcal/mol, compared to bulk water of Ant ~ — 6.05± 0.02 kcal/mol. Water molecules not only penetrate the nanotube, but they also transport across the nanotube, and on average, about 17 water molecules pass through the nanotube per nanosecond (see Figure 11.29). The conduction occurs in a burst-like manner because of the tight hydrogen-bonding network inside the nanotube; rupturing the water chain is energetically costly, and so rare. However,    once the    rupture    of    the    hydrogen    bond    occurs,    the    water chain

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