# Nanoelectrode Ensembles Consisting of Carbon Nanotubes
## 3 Results and Discussion
### CV Characterization of CNT-NEEs
To compare the charging currents of the GC electrode and the CNT-NEEs, a similar approach was used to convert the current response in a blank solution of 50 mM KCl to current density (Figure S3). The electrodes in the CNT-NEEs displayed a lower charging current than the GC electrode, which is promising in terms of the sensitivity of the CNT-NEEs for electrochemical applications, as demonstrated by the low signal-to-noise ratio for the detection of Pb\({}^{2+}\) (see below). The cyclic voltammogram of each CNT-NEE showed diffusion-controlled reduction and oxidation peaks for Ru(NH\({}_{3}\))\({}_{6}\)\({}^{3+/2+}\) instead of a steady-state response, indicating that the electrodes in the CNT-NEE behaved as a macroelectrode. This macroelectrode response indicates that the CNTs within the CNT-NEE acted as a bulk material rather than as an NEA. It was hypothesized that for NEEs with bundles of CNTs as the sensing area, the CNT bundles would fall within the microelectrode range and thus exhibit a steady-state current response if each bundle experienced a radially convergent flux. The high density of CNTs and random distribution of CNTs with in the CNT-NEE material means the distance between the various sensing areas may not be significantly larger (12 times the radius) than the diffusion layer thickness resulting in the radial diffusion to all the CNTs to overlap, leading to planar diffusion to the electrode. These overlapping diffusion layers were also observed by [PERSON] et al. and [PERSON] et al. [6, 40] for CNT-NEAs with a high density of CNTs; however, the fabrication process for these CNT-NEAs requires encapsulating VA-CNT arrays. The CNT-NEEs in this work used a simpler fabrication process, which also created a large amount of bulk material, allowing for many electrodes to be fabricated. The CNT-NEEs reported here were fabricated using drawable CNTs with an average diameter of 8 nm, and the extremely porous CNT ribbon (Figure 2b) was expected to have large spacings within the constituent CNT bundles. As the CNT-NEEs exhibited macroelectrode CV responses, it was concluded that the spacing between the nanoelectrodes was not much greater than the diffusion layer thickness. The diffusion layer thickness was estimated from the CV response using Equation (3). \[\delta=\sqrt{\frac{\pi DRT}{Fv}} \tag{3}\]  
where \(\delta\) is the diffusion layer thickness, \(D\) is the diffusion coefficient (\(8.2\times 10^{-6}\) cm\({}^{2}\)/s), \(R\) is the gas constant (\(8.31\) J/mol\(\cdot\)K), \(T\) is the temperature (298 K), \(F\) is the Faraday constant, and \(\
u\) is the scan rate (0.01 V/s). The estimated diffusion layer thickness of \(\delta\) = 81.3 \(\upmu\)m was significantly larger than the estimated distance of tens of nanometers between the CNTnanoelectrodes within the CNT-NEE. This finding again indicates that the diffusion layers of the individual sensing areas overlapped, resulting in a planar diffusion response at the electrodes in the CNT-NEE. The peak-to-peak separations (\(\Delta\)E\({}_{\text{p}}\)) calculated for the three CNT-NEE samples (107 mV, 124 mV, and 115 mV) were much greater than the reversible peak separation of 59 mV based on the Nernst equation. A similar quasi-reversible electrochemical reaction on CNT electrodes was reported by [PERSON] et al. [40]. The quasi-reversible nature of the CNT-NEEs was further supported by the observation that the cathodic peak currents were higher than the anodic peak currents at various scan rates (Figure 6a) [40; 41; 43]. Both peak currents were plotted against the square root of the scan rate (\(\
u^{1/2}\)) (Figure 6b) and against the scan rate (Figure S4). Linear relationships were observed for the cathodic and anodic peak currents with \(\
u^{1/2}\), as represented by Equations (4) and (5), respectively, indicating that the electron transfer process was diffusion controlled.