Interdisciplinary Applied Mathematics

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3. Asymmetrically functionalized tube in a pseudo bilayer (opposite charge groups at either ends), and

4. Symmetrically functionalized tube (same charge groups at the ends) in a pseudo bilayer.

The results of the above simulations are summarized below.

Occupancy of K+ ions in CNT

21.696 A dia fixed tube, 13.4 A long; E=0; CNT surface charge=0

Occupancy of Cl- in a fixed CNT (16,16)

21.696 A dia 13.4 A long, E=0 , surface partial charge=0

FIGURE 13.11. Very low ion occupancy in a (16,16) carbon nanotube (13.4 A long, 21.696 A diameter) fixed in the center of the box with a solution of 1.85 M KCl. There is neither an external electric field nor partial charges on the rim.

The ion occupancy (or the number of ions) inside uncapped carbon nanotubes of various diameters ranging from (6, 6) to (16,16) tubes in a solution of 1.85 M KCl was tested. The tubes were fixed in the box center and were of length 13.4 A. For a simulation with a tube of 21.7 A diameter, the box had 925 water molecules and 40 potassium and chloride ions each. Initially, the tube had 7 potassium and 6 chloride ions. Over the course of 3 ns,    the    ion    occupancy    was    observed    to be largely    0 or    1,    as    shown

in Figure 13.11. The ions enter the tube from either end, but they do not travel across the length of the tube.

13.2.4 Transport Through Nanotubes with Charges at the Ends

To increase the occupancy of ions in the tube, partial charges of ±0.38e were placed at atoms on the rim of the tube to create a dip ole, the positive charges being on the top rim and the negative charges on the bottom rim. Nonequilibrium molecular dynamics simulations (NEMD) were performed with the tube fixed in the center of a box of length 33 A and an applied external electric field of 0.015 V/nm, which is of comparable order to that of some ion channel membrane potentials, along the axial direction to mimic the membrane potential. It was observed that the ion occupancy is much higher compared to the ion occupancy in nanotubes with no charges (see Figure 13.12). Figure 13.13 shows how the ion occupancy varies with the diameter of the tube. An interesting observation is that the average occupancy of chloride ions is higher than that of the potassium ions with a ratio of 3:2.    This    could    be due to    the    difference in    water    structure    around    the

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