# Interdisciplinary Applied Mathematics

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No of K+ inside the CNT    No of Cl- ions in the CNT

21.696 A dia 13.4 A long, E_y=0.015 V/nm, partial charges on the rim    13.4 A Long, 21.696 A Dia, E_y= 0.015, partial charges on the rim

Time (ps)    Time (ps)

FIGURE 13.12. Ion occupancy in a (16,16) carbon nanotube (13.4 A long, 21.696 A diameter)    fixed    in a solution    of    1.85 M    KCl    with    external    electric    field    of

E = 0.015 V/nm and partial charges of ±0.38e on the rim atoms.

Diameter (Angstroms)

FIGURE 13.13. Variation of average ion occupancy with diameter in CNT (13.4 A long) fixed in 1.85 M KCl with an external applied electric field of 0.015 V/nm.

two ions as well as the van der Waals interaction between the ions and the nanotube.

###### 13.2.5 Transport Through Functionalized Nanotubes

Even though an electric field alone would drive ions into the tube, the partial charge on the rim increases the sensitivity and could be used to control the type    and rate    of    ionic flow    into    the tube.    This principle    is    the    basis

of tube end functionalization. Once partial charges were shown to increase

occupancy, the next step was to replace them with functional groups. NH+ and COO~ were used as the functional groups. Both outer wall and end wall chemical functionalization attachments of nanotubes have been successfully realized in experiments (Chen et al., 2001; Chen et al., 1998; Halicioglu and Jaffe, 2002). Functional group attachment can increase solubility and alter nanotube properties, among other things (Sinnott, 2002). In our simulations, an asymmetric functionalization of carboxylate and amino residues was used in place of the partial charges to mimic a real ion channel at either end. Even though functionalizing the inner wall would mimic some ion channels more closely, end wall functionalization is more feasible than inner wall functionalization for tubes of small diameter (Chen et al., 1998). The functionalized carbon nanotube was then placed in a membrane-mimic with properties similar of those of a lipid bilayer with a surrounding bath of 1.5 M KCL solution (see Figure 13.14). An electric field of 0.15 V/nm was used to drive the ions through the tubes, and the trajectories of K+ and Cl_ ions are shown in Figure 13.15. Over the course of 2 ns of simulation time, the    chloride    current    was    found to be    much    higher    than    the    potas

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