Electronic friction and liquid-flow-induced voltage in nanotubes

A recent exciting experiment by Ghosh et al. [Science 299, 1042 (2003)] reported that the flow of an ion-containing liquid such as water through bundles of single-walled carbon nanotubes induces a voltage in the nanotubes that grows logarithmically with the flow velocity $v_0$. We propose an explanation for this observation. Assuming that the liquid molecules nearest the nanotube form a two-dimensional solidlike monolayer pinned through the adsorbed ions to the nanotubes, the monolayer sliding will occur by elastic loading followed by the local yield (stick-slip motion). The drifting adsorbed ions produce a voltage in the nanotube through electronic friction against free electrons inside the nanotube. Thermally excited jumps over force-biased barriers, well known in the stick-slip model, can explain the logarithmic voltage growth with flow velocity. We estimate the short-circuit current and the internal resistance of the nanotube voltage generator.

Figure 1

The voltage $U$ as a function of the logarithm of the (average) fluid velocity $v_0$. The solid line is a fit of the form $U=U_c\ln (v_0∕v_c)$. Adapted from Ref. 1.

Figure 2

Carbon nanotube immersed in a flowing liquid. We assume that the liquid molecules nearest the nanotube form a two-dimensional (2D) solidlike monolayer, pinned to the nanotube by the adsorbed ions. As the liquid flows, the solid sliding motion along the nanotube is of a stick-slip nature: time intervals of elastic deformation (loading phase) are followed by rapid local yield events. This will result in a force on the ions which increases logarithmically with the fluid flow velocity. The drifting adsorbed ions will produce a voltage in the nanotube through electronic friction against free electrons inside the nanotube. In the stationary state there is a net flow of ions adsorbing on the nanotube upstream and a net flow of ion desorption downstream.

Figure 3

Mechanical model representing the stick-slip process (loading by elastic deformation followed by abrupt yield) of the 2D solid in the vicinity of an ion [see Fig. 2a]. The spring represents the elastic deformation of the 2D solid. When the spring force reaches a critical value (the static friction force) the block starts to slip, reverting back to the pinned state when the spring force approximately vanishes.