# Nanoelectrode Ensembles Consisting of Carbon Nanotubes
## 3 Results and Discussion
### CV Characterization of CNT-NEEs  
Using optical microscope images and ImageJ software, the geometrical surface area of the CNT-NEE was determined. Figure 5a shows the CNT-NEE surface, where the area outlined in red corresponds to the geometrical area of the CNT-NEE (Table 1) and the shiny region outside the red line corresponds to the dielectric epoxy that covered the edges to prevent electrolyte leaching into the metal connection sites. It is important to note that the area exposed to solution (named as the geometrical area) varied between CNT-NEE samples, as shown in Figure S2 and Table 1. The CNT-NEEs were initially tested using CV in the potential window of +0.2 V to \(-\)0.45 V at a scan rate of 0.01 V/s. A solution of 50 mM KCl was used as a blank to ensure the electrical connection was sufficient and that no contamination peaks were present. Using a solution of 2.5 mM Ruhex in 25 mM KCl, the redox activities of the electrodes were investigated. The CV results for three CNT-NEEs (CNT-NEE 1, CNT-NEE 2, and CNT-NEE 3) and a traditional glassy carbon (GC) electrode are shown in Figure 5b. Owing to the differences in electrode areas, comparisons were made using the current densities, as determined by dividing the current response of each electrode by the corresponding active area (Table 1). The active areas of the electrodes were determined by capacitance measurements, as follows. In a solution of 0.1 M acetate buffer (pH 4.5), the CV response was recorded in the potential window of +0.2 V to +0.1 V at a scan rate of 0.2 V/s. From \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Cathodic Peak** & **Anodic Peak** & **Active Area** & **Geometrical** \\  & **Current (μA)** & **Current (μA)** & **(cm\({}^{2}\)) from \(i_{\text{pc}}\)** & **Area (cm\({}^{2}\))** \\ \hline
**CNT-NEE 1** & 1.59 & \(-\)1.42 & 0.0101 & 0.0084 \\
**CNT-NEE 2** & 1.62 & \(-\)1.41 & 0.0051 & 0.0120 \\
**CNT-NEE 3** & 1.70 & \(-\)1.41 & 0.0062 & 0.0082 \\
**Glassy Carbon** & 14.9 & \(-\)12.9 & 0.1493 & 0.0706 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of CNT-NEEs and the glassy carbon electrode. Figure 5: CNT-NEE characterization. (**a**) Optical microscope image of the electrode face at 150\(\times\) magnification. The exposed area of the CNT-NEE is outlined in red. (**b**) Cyclic voltammograms of the GC electrode (black) and CNT-NEE 1 (red), CNT-NEE 2 (blue), and CNT-NEE 3 (pink) in 2.5 mM Ruhex and 25 mM KCl at a scan rate of 0.01 V/s normalized by the active area of each electrode. the CV response, the charging current was determined, which was then used to calculate the active area. First, the double layer capacitance was calculated using Equation (1). \[i_{c}=\
u C_{dl} \tag{1}\]  
where \(i_{c}\) is the charging current (A), \(\
u\) is the scan rate (V/s), and \(C_{dl}\) is the double layer capacitance (F). Subsequently, \(C_{dl}\) was employed to determine the active area of each electrode using Equation (2). \[C_{dl}=\varepsilon_{0}\varepsilon_{r}\frac{A}{d} \tag{2}\]  
where \(\varepsilon_{0}\) is the permittivity of free space (\(8.854\times 10^{-12}\) F/m), \(\varepsilon_{r}\) is the dielectric permittivity of the solution (6.15), \(A\) is the active area of the electrode (m\({}^{2}\)), and \(d\) is the diffusion layer thickness (m). As summarized in Table 1, the active areas of the CNT-NEEs were smaller than the geometrical areas, indicating that only a small percentage of the CNT-NEE geometrical area was occupied by CNTs while the remainder was occupied by HNBR. This finding is consistent with the SEM images and the estimation of the area occupied by CNTs (Figure S1). A comparison of the normalized current responses revealed higher current densities for the CNT-NEEs than for the GC electrode. Thus, although the electrodes in the CNT-NEE were smaller than the traditional GC electrode, they showed larger current densities.