Electrophoresis, the motion of charged species through liquids and pores under the influence of an external electric field, has been the principle source of chemical pumping for numerous micro- and nanofluidic device platforms. Recent measurements of ion currents through single or few carbon nanotube channels have yielded values of ion mobility that range from close to the bulk mobility to values that are two to seven orders of magnitude higher than the bulk mobility. However, these experiments cannot directly measure ion flux. Experiments on membranes that contain a large number of nanotube pores allow the ion current and ion flux to be measured independently. Here, we report that the mobilities of ions within such membranes are approximately three times higher than the bulk mobility. Moreover, the induced electro-osmotic velocities are four orders of magnitude faster than those measured in conventional porous materials. We also show that a nanotube membrane can function as a rectifying diode due to ionic steric effects within the nanotubes.
Figures at a glance
Figure 1: Characterization of single-walled carbon nanotubes. 
a, TEM images of single-walled nanotubes. Scale bar, 10 nm. b, Raman spectrum of a powder sample of single-walled nanotubes showing the diameters as calculated from the location of the peaks in the spectrum. c, SEM image showing a cross-sectional view of a membrane containing nanotubes uniformly dispersed in an epoxy resin matrix. Scale bar, 5 µm. d, Histogram of inner diameters of the nanotubes (SWNT).
Figure 2: Highly efficient electro-osmotic flow in single-walled carbon nanotubes and the effect of pH. 
a, Ionic currents measured at –0.6 V (circles, left axis) and K+ electrophoretic mobilities (EM, right axis) versus KCl concentration. Mobilities were calculated using equation (1), with Ap = 5.0 × 10−12 m2 and K(λ) = 1 (stars) or K(λ) = 0.48 (triangles). Bulk mobility is also shown (dashed line). b, Ionic current measured at –0.6 V versus pH in 10 mM KCl. HCl was used to change the pH values, and the electrodes were Ag/AgCl.
Figure 3: Effects of ionic concentrations and species, and operation as a rectifying diode. 
a, Current through a nanotube membrane functionalized with carboxyl groups versus bias voltage for KCl (black) and Ru(bpy)3Cl2 (red). There is no apparent threshold voltage for pumping K+ through the membrane. The electrophoretic mobility of Ru(bpy)3Cl2 is dramatically reduced at high ionic strengths. b, Ionic current through a nanotube membrane versus bias voltage for three different experiments. Experiment 1 (blue) is a control experiment in which both sides of the membrane are filled with KCl. In experiment 2 (black), the side containing the working electrode (WE) is filled with 25 mM K3(Fe(CN)6) and the side containing the reference electrode (RE) is filled with 50 mM Ru(bpy)3Cl2. In experiment 3 (red) one positions of the working and reference electrodes are exchanged compared to experiment 2. Rectification can be seen in both experiments 2 and 3. c, Data for experiments 2 and 3 plotted with current on a log scale. d, Schematic showing the effect of reversing the bias voltage on ionic transport through a (10,10) single-walled nanotube: K+ ions, dark green; Cl− ions, light green; Ru2+ ions, dark brown; Fe3+ ions, light brown; C atoms, grey; N atoms, blue; H atoms, white.
Figure 4: Operation as a rectifying diode with other ionic species. 
