Interdisciplinary Applied Mathematics

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sium ion current because K+ ions are bound electrostatically to the COO~ groups at the mouth, causing an energy barrier, thereby reducing the K+ occupancy in the tube. Thus, this decorated nanotube is an example of one possible nanotube functionalization that can lead to a modulation of the ionic current via ion selectivity.

Symmetric functionalization can be used to selectively transport one species. Figure 13.16 shows the trajectories of ions in a symmetrically functionalized (16,16) tube with COO~ on both ends and in the middle with protonated carbon atoms. The chloride occupancy is much larger than that of potassium.

13.2.6 Anomalous Behavior

An interesting aspect of electrolytic transport through charged carbon nanotubes is the observation of anomalous behavior (Qiao and Aluru, 2003d). Specifically, we have performed molecular dynamics simulations of electroosmotic transport of NaCl solution through a 5.42 nm diameter singlewalled carbon nanotube with different surface charge densities. We observed that if the carbon nanotube surface is negatively charged (charge density of —0.076 C/m2), a significant amount of Na+ ion is contact adsorbed on the nanotube wall and immobilized, resulting in negligible electroosmotic transport. However, if the carbon nanotube surface is positively charged (charge density    of    0.076    C/m2),    the    contact    adsorption    of the    Cl_    ion is

moderate, and the adsorbed Cl_ ions are not immobilized, thus generating a significant electroosmotic transport and a velocity slip on the carbon nanotube surface. The flow is driven by an external electric field Eext, applied along the channel in the z-direction. Because of the extremely high thermal noise, a strong electric field was applied in our simulations so that the fluid

FIGURE 13.14. Functionalized carbon nanotube in a bath of 1.5 M KCl. CH2-NH3+ is    attached    one    per    carbon ring    to    the    top, and    CH2-COO~    is    attached at    the    bottom. The tube    is inserted    in a    slab    (not    shown).    Chloride    ions

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