# Nanoelectrode Ensembles Consisting of Carbon Nanotubes
## 1 Introduction  
Nanoelectrodes have many characteristics that are important for analytical and physiological applications, including a low charging current [1, 2], enhanced mass transport [1, 2, 3, 4, 5, 6, 7, 8], and the ability to perform in more resistive media [2, 3, 9, 10]. However, working with an individual nanoelectrode can be difficult because the small size complicates fabrication, and the low current response requires more sensitive instrumentation. To overcome the low current response of an individual nanoelectrode, nanoelectrode arrays (NEAs) or ensembles (NEEs) have been fabricated [2]. Although the literature makes little distinction between these terms, NEAs tend to consist of nanoelectrodes with controlled interspacing, typically equidistant, whereas NEEs have randomly arranged nanoelectrodes [11]. In both cases, the nanoelectrodes work in parallel, which significantly improves the signal-to-noise ratio [3, 5, 8, 9]. NEAs and NEEs can be fabricated from various materials such as gold [10, 12, 13, 14, 15, 16, 17, 18, 19], platinum [16], TiO\({}_{2}\)[20, 21], ZnO [22, 23], CeO\({}_{2}\)[24], nickel [25], boron-doped diamond [26], carbon fibers [27, 28], SiO\({}_{2}\) with a Ti/Pt coating [29], and carbon nanotubes (CNTs). NEAs and NEEs are typically fabricated using one of two methods. The first method is a template synthesis approach, which involves either electroless or electrical deposition of a metal into a porous template [10, 30]. Common template membranes include anodic aluminum oxide [16, 20] and porous polycarbonate [10, 12, 13, 17, 18, 19, 21, 25]. The second method uses self-assembled monolayers to fabricate NEAs and NEEs [30]. NEAs and NEEs have been applied as biosensors [16, 22, 24, 27], dopamine sensors [14, 15, 23, 26], immunoensors [12, 13, 19], and glucose sensors [17, 31], as well as for intercellular electrophysiological imaging [29, 32]. A crucial factor in the increased sensitivity of NEAs and NEEs as sensors is analyte diffusion to the electrode surface. Becausethe sensing areas of NEAs and NEEs are on the nanoscale, the diffusion layer thickness is comparable to that of the electric double layer, which leads to an increase in the mass transport of molecules to the electrode surface [33]. In cyclic voltammetry (CV) tests with NEAs or NEEs, a redox-active analyte either rapidly establishes a steady-state diffusion profile or exhibits a time-dependent diffusion-limited response. When the spacing between the nanoelectrodes within an array is 12.5 times greater than the nanoelectrode radius, the diffusion profiles of the nanoelectrodes do not overlap. The resulting convergent flux of dissolved redox species leads to a sigmoidal voltammogram, indicating a steady-state response [33]. When the spacing between the nanoelectrodes is less than 10 times the nanoelectrode radius, the radial diffusion to neighboring nanoelectrodes overlaps, leading to a diffusion-controlled CV response for reversible redox analytes. Even with such overlap, NEAs and NEEs can provide greater sensitivity than macroelectrodes [33]. Because an NEE has a smaller electroactive area than a planar electrode, the charging current is lower, which is an important factor for achieving enhanced faradaic signals [3,4,8]. As cylindrical macromolecules with nanoscale diameters, CNTs are an ideal material for fabricating NEAs and NEEs, where dimensions of 1-100 nm are required [2]. NEAs and NEEs typically employ vertically aligned CNTs (VA-CNTs) that are grown through chemical vapor deposition (CVD). CNTs have been reported to exhibit excellent performance as electrodes due to their wide working potential range [5,6,34], chemical inertness [5,9,35], good electrical conductivity [3,5,9,35,36,37,35,37], high surface area [9], functionalization ability [5], electrocatalytic properties [8,9,38], and biocompatibility [6,9,34,37]. CNTs also show fast electron transfer characteristics [6,8,9].