Electrode ensembles

Arrays are ensembles of microelectrodes that may consist of regularly, or irregularly, spaced assemblies of identical electrodes, ensembles of electrodes with identical... 

Orthogonal collocation in two dimensions has been used to simulate microdisk edge effects. The first paper in a series (5 up till now), by Speiser and Pons (1982) is a formidable tour de force. A two-dimensional set of polynomials is fitted to the grid and it leads, as in one dimension, to an "easily solved" set of ordinary differential equations. In the fifth part of this series of papers, Cassidy et al (1985), applied the method to electrode ensembles. This is obviously not for the occasional simulator, who is advised to use a simple technique and put up with the long computational times or use someone else s program but the method undoubtedly makes two-dimensional simulations efficient and accurate. 

CNT electrode ensembles consisting of a dense array of CNTs (15-80 nm diameter, 30-100 pm long, with a 100-200 nm nanotube separation) were produced from an ion-sputtered Fe catalyst film on an Al-coated Si wafer. As depicted in Figure 7.3d, the CNTs and the conducting substrate act as the electrode and increase the electroactive surface area. Nanoelectrodes were made from carbon nanopipettes (CNPs) (10-15 nm tip diameter, several micrometers long) on Pt substrates" and low-density arrays of vertically aligned CNTs (50-80 nm diameter, 10-12 pm long, with a nanotube separation of more than 5 pm) from electrodeposited Ni nanoparticles on a Cr-coated Si substrate." 5 To limit the electroactive area to the tips of the CNTs or CNFs, these arrays can be coated with an epoxy to insulate the conductive substrate to expose needle-like tips or surface-polished tips so as to expose only the ends of the nanotubes. 

Cheng IF, Martin CR (1988) Ultramicrodisk electrode ensembles prepared by incorporating carbon paste into a microporous host membrane. Anal Chem 60 2163-2165... 

Figure 2.46 Section of a micro channel with electrodes embedded in the channel walls (left). When an electric field is applied along the channel, different flow patterns may be created depending on the potential of the individual electrodes. The right side shows the time evolution of an ensemble of tracer particles initially positioned in the center of the channel for a flow field alternating between the single- and the four-vortex pattern shown on the left [144].

J. Li, A. Cassell, L. Delzeit, J. Han, and M. Meyyappan, Novel three-dimensional electrodes electrochemical properties of carbon nanotube ensembles. J. Phys. Chem. B 106, 9299-9305 (2002). 

Here we want to report a few results of such simulations that, we believe, shed some light on the structure of water and aqueous solutions on metal electrodes, and that do not depend on the details of the model. As mentioned above, one cannot simulate an ensemble of water and ions because one would need too large an ensemble. Therefore most studies have been limited to pure water. While the various water models that have been employed differ in detail, they all predict an extended boundary region at the surface where the water structure differs from that in the bulk. 

We consider an ensemble of reactants in the reduced state situated at the interface. Their concentration is kept constant by an efficient means of transport. We denote the perturbation describing the interaction between one reactant and the electrode by M(r,R). According to time-dependent first-order perturbation theory, the probability per unit time that a reactant will pass from the initial to the final state is ... 

Qiu, J.-D., et al., Controllable deposition of a platinum nanoparticle ensemble on a polyaniline/graphene hybrid as a novel electrode material for electrochemical sensing. Chemistry - A European Journal, 2012.18(25) p. 7950-7959. 

In order to explore the effects of small electrode size, we have used the template method to prepare ensembles of disk-shaped nanoelectrodes with diameters as small as 10 nm. We have shown that these nanoelectrode ensembles (NEEs) demonstrate dramatically lower electroanalytical detection limits compared to analogous macroelectrodes. The experimental methods used to prepare these ensembles and some recent results are reviewed below. 

Because the fractional electrode area at the lONEE is lower than at the 30NEE (Table 1), the transition to quasireversible behavior would be expected to occur at even lower scan rates at the lONEE. Voltammograms for RuCNHs) at a lONEE are shown in Eig. 8B. At the lONEE it is impossible to obtain the reversible case, even at a scan rate as low as 5 mV s . The effect of quasireversible electrochemistry is clearly seen in the larger AEp values and in the diminution of the voltammetric peak currents at the lONEE (relative to the 30NEE Fig. 8). This diminution in peak current is characteristic of the quasireversible case at an ensemble of nanoelectrodes [78,81]. These preliminary studies indicate that the response characteristics of the NEEs are in qualitative agreement with theoretical predictions [78,81]. 

We have demonstrated a new method for preparing electrodes with nano-scopic dimensions. We have used this method to prepare nanoelectrode ensembles with individual electrode element diameters as small as 10 nm. This method is simple, inexpensive, and highly reproducible. The reproducibility of this approach for preparing nanoelectrodes is illustrated by the fact that NEEs given to other groups yielded the same general electrochemical results as obtained in our laboratory [84]. These NEEs display cyclic voltammetric detection limits that are as much as 3 orders of magnitude lower than the detection limits achievable at a conventional macroelectrode. 

Given the importance of particle size to rate capabilities in Li+ batteries, preparation of nanostructures of Li+ insertion material for possible use as electrodes in Li+ batteries seemed like an obvious extension of our work on nanomaterials. The fact that these nanostructures can be prepared as high-density ensembles that protrude from a surface like the bristles of a brush (Fig, 2A) seemed particularly useful for this proposed application because the substrate surface could then act as a current collector for the nanostructured battery electrode material. 

Without doubt, the advent of carbon nanotubes has opened up iimovative perspectives for research and development of carbon electrodes. In this chapter, we have attempted to highlight the electrochemical properties of carbon nanotubes by rooting them mainly on their structural, electronic and chemical properties. If chirality of SWNTs could be controlled, it would be possible to probe electrochemically the unique electronic properties of the tubes with their corresponding unique DOS distribution and establish direct correlations between electronic structure and electrochemistry. However, so far, most of their electrochemical applications are based on ensembles of CNTs (MWNTs or SWNTs) in thin films supported on conductive surfaces or composites. Such ensembles, not so well defined from the structural point of view, contain a mixture of tubes with different diameters and DOS... 

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