(209b) Selective Ion Transport through Carbon Nanotubes

Carbon nanotubes are promising
materials with a vast range of potential applications, such as nanoscale
electronic devices, nanoscale sensors, selective molecular filters, gas storage
devices, nanofluidic devices, and targeted drug delivery devices, among many
others. Water has unique properties and an understanding of the interaction
between water and carbon nanotubes is key to the development of many of these
devices. The confinement of water in carbon nanotubes as compared to bulk water
has been shown to produce some remarkable features, which include but are not
limited to a lower number of hydrogen bonds, the increased lifetime of hydrogen
bonds, the layered structure of water under confinement, its reduced density
and viscosity, and an increased proton mobility in 1-D water chains. One of the
more exciting results of water under confinement is the high slip lengths that
result at high flow rates, which is conducive to ultrafiltration and
nanofiltration. High water flow rates along with selective ion transport is an
important feature of ion channels in living organisms; however experimental
analysis to study ion channels is a real challenge as ion channels can degrade
under experimental conditions, have dimensions of the order of few nanometers,
possess non-uniform surfaces, and uneven charge distributions that make them a
complex system to study. Carbon nanotubes can be easily embedded into lipid
membranes, and hence can be used as biomimetic devices to study water and ion
transport at nanoscopic levels.

Flow of water and ions in nanotubes can
be achieved by application of an electric field, pressure difference,
concentration gradient, uneven charge distribution, and osmotic pressure. The
rate and selectivity of ion transport can be controlled by various means such
as varying the pore size, the ion concentration, the charge distribution, the
density of charge and through chemical functionalization. Because of the large
surface to volume ratio as compared with macro and microscopic length scales,
surface charge has a pronounced effect on the fluid volume in the hydrophobic
cavity at the nanoscopic length scale, leading to a rejection of the co-ions.
This phenomenon can thus help improve the selectivity of the ions beyond steric
hindrance to include the use of larger diameter nanotubes enabling greater
water eflux, which can be exploited to model nano-level filters. Since
continuum Navier-Stokes equations for fluid transport break down at nanometer
level, molecular dynamics (MD) simulations, which explicitly calculate the
motion of all particles in the system described by Newton's equations of
motion, is the favored method of study.

Water and ion transport through
uncharged and charged carbon nanotube membranes (d = 0.8nm -3.25nm) were
studied using long-time MD simulations. The OPLS force field parameters of
benzene are employed for carbon atoms. The carbon atoms were held fixed during
the course of the simulation. The TIP4P water potential was used to model the
water intermolecular interactions. All simulations were carried out in GROMACS
4.6.1. in the NVT ensemble. Various cases were simulated by varying pore size
at different electrolyte (NaCl) concentrations and application of electric
field for both charged and uncharged CNT membranes at these different pore
sizes and concentrations. For uncharged CNTs in the absence of electric field,
steric hindrance is the only factor controlling transport of ions. For small
pore diameters (<0.8nm) the ion occupancy and passage of ions through the
tube is negligible as  the hydration radius of the ions is comparable to the 
pore size. In this case, water diffuses to the chamber containing electrolyte
through osmosis. At larger pore sizes the concentration gradient drives ion
transport with ion occupancy in the CNT and ion passage progressively
increasing. In the case of uncharged CNTs in the presence of electric field,
electro-osmosis dominates with increasing field strength. In charged CNTs at
low electrolyte concentrations, the thickness of the electric double layer is of
the same order as the diameter of the pore and this results in selectivity
governed by the Donnan equilibrium. As the concentration strength increases the
Debye length becomes smaller, the charges are screened and both ions can pass
through. Electrokinetic flow is observed in the case of charged CNT under an
electric field, which can be described by the Poisson-Boltzmann equation along
with the Nernst-Planck equation. Modulating the strength of the surface charges
can be used to tune both ion transport and water flow through the nanotubes.

The structural characteristics of water
and ions confined in CNT for the various cases simulated are compared.
Measurements of ion occupancy in the nanotube, water flux, ion flux, rejection
rates, and other transport properties are obtained using MD simulations. A
complete account of ion and water transport under the influence of charge is
obtained in this study spanning a large number of CNT diameters. Fast water
flow can thus be integrated with ion selectivity through modulation of surface
charges and pore size, which not only helps to understand biological processes,
but can also help design advanced nanofluidic devices in the future.