Flow-induced voltage and current generation in carbon nanotubes

New experimental results, and a plausible theoretical understanding thereof, are presented for the flow-induced currents and voltages observed in single-walled carbon nanotube samples. In our experiments, the electrical response was found to be sublinear—nearly logarithmic—in the flow speed over a wide range, and its direction could be controlled by an electrochemical biasing of the nanotubes. These experimental findings are inconsistent with the conventional idea of a streaming potential as the efficient cause. Here we present Langevin-equation based treatment of the nanotube charge carriers, assumed to be moving in the fluctuating field of ions in the flowing liquid. The resulting “Doppler-shifted” force-force correlation, as seen by the charge carriers drifting in the nanotube, is shown to give a sublinear response, broadly in agreement with experiments.

Figure 1

Schematic sketch of the nanotube flow sensor placed along the flow direction $\left(u_L\right)$. SWNT bundles are packed between two metal electrodes. The insulating substrate keeps the SWNT in place. The electrical leads are taken out from the metal electrodes.

Figure 2

Voltage (full circles) and current (open circles) as functions of flow speed $u_L$. The solid line is a fit to the logarithmic function as explained in the text. Inset shows the theoretical plot of current $(I=ne{u}_{D}A)$ versus flow speed based on Eqs. (1, 4) for typical choice of parameters: $T=300\mathrm{K}$; $ϵ=80$ (CGS units); $D\kappa ={10}^{-4}\mathrm{cm}∕\mathrm{s}$; ${\tau }_D={10}^{-16}\mathrm{s}$; ${\rho }_0={10}^{13}{\mathrm{cm}}^{-3}$; charge carrier density in nanotubes $(n={10}^{18}{\mathrm{cm}}^{-3})$; cross-sectional-area $\left(A\right)={10}^{-3}{\mathrm{cm}}^2$. The strong sublinearity is clearly seen.

Figure 3

Flow-induced voltage as a function of bias $V_B$. Inset, schematic of electrochemical biasing of the nanotubes; CE is the counterelectrode. The solid line is a guide to the eye.