Interdisciplinary Applied Mathematics

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• &CC = 3.36 A, ecc = 0.0969 kcal/mol,

• &oC = 3.23 A, eoC = 0.129 kcal/mol,

and were based on a cutoff of 15 A. Bulk SPC/E water, having atomic charges of —0.8476e and 0.4238e on oxygen and hydrogen, respectively, was equilibrated (300 K) and used to fill the nanotube interior. Electrostatic interactions used the particle-mesh Ewald method with a 10-A real-space cutoff, a 1.5-a reciprocal space gridding, and splines of order 4 with a 10~tolerance (see Section 16.1 for more details on MD simulations). Depending on the box size, 1033 to 2970 water molecules were used to yield a constant density of 1 g/cm3. Concentrations of KCl varied from 1 M to 1.85 M. The slab consisted of pseudoatoms with the same Lennard-Jones parameters as those of a lipid bilayer. The partial charges for NH+ and COO~ were taken from the side groups of lysine and glutamic acid respectively in the GROMACS amino acid database. The simulation time varied between 2 ns and 7 ns, and a time step of 2 fs was used in a leapfrog scheme.

Even though both water and molten ions seem to enter the tube spontaneously, when both ions and water molecules are involved, the situation could be more complex because of the possible interplay between hydrophilic interactions involving the ions and water and the hydrophobic interactions involving the water and the carbon nanotube. Four sets of simulations were performed, comprising:

1.    Carbon    nanotubes    fixed    in    the    center of a    box    in a solution    of    KCl,

2. Tubes fixed in water with artificial charges at the ends,

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