Mass Transport to Nanoelectrode Arrays and Limitations of the Diffusion Domain Approach: Theory and Experiment

Abstract

RECEIVED DATE (to be automatically inserted after your manuscript is accepted if requiredaccording to the journal that you are submitting your paper to) CORRESPONDING AUTHOR FOOTNOTE. F. Javier del Campo. Tel.: +34-935.947.700; Fax number: +34-935.801.496. 2ABSTRACT. The diffusion domain approach is a general framework for the understanding, interpretation and prediction of the response of microelectrode arrays. This work exposes some of its limitations, particularly when dealing with nanoelectrode arrays of a few microns in size. This article provides an overview of the principles and assumptions underpinning the diffusion domain approach, and then applies it to the study of nanoelectrode arrays. The apparent disagreement between theory and experimental data, due to the importance of radial diffusion to nanoelectrode arrays compared to microelectrode arrays, is explained using simulations and experiments. The principle that an array of micro-or nano-electrodes eventually behaves as if the entire array were a single electrode of the size of the array, with its corresponding properties, applies always. However, while microelectrode arrays tend to behave as macroelectrodes, nanoelectrode arrays on the other hand may behave as microelectrodes.For the case of arrays of small numbers of electrodes, or array sizes of microns or less in size, this compromises one of the key assumptions of the diffusion domain approach, namely that inner electrodes in an array are equivalent, which may lead the unaware to erroneous conclusions.

Electroanalysis at discrete arrays of gold nanowire electrodes

“…Despite this diffusional overlap, at low scan rates (<100 mV s --1 ) sigmoidal voltammograms were observed for all arrays with all achieving steady-state currents see Fig 5(a). This is in agreement with previous reports using nanoscale electrode arrays [8,16,30] and arises from partial and complete diffusional overlap, where the nanowire array it behaves as ultra-microelectrode of the same size of the total array, i.e., the width of a six nanowire array is 6.6 m. Such ultramicroelectrodes also experience enhanced mass transport and exhibit sigmoidal behaviour and steady-state currents.…”

“…However, at the nanoscale, where diffusion profiles have similar dimensions to the diffuse double layer and electrodes typically have non-ideal electrode geometries (such as nanowires) the required inter-electrode spacing may have to be higher to ensure diffusion independence. This has recently been shown to be the case for recessed nanopore electrodes where the spacing should be thirty times the diameter (60r) [16].…”

“…However under the latter conditions the currents yielded would be expected to be reduced in magnitude from those attainable at nanowire arrays that had independent diffusion profiles. [3,16,33] To examine the magnitude of limiting current at each array, ideal arrays would behave These overlapping diffusion profiles resulted in a reduction in the measureable electrochemical response i.e., an analyte molecule can only diffuse to one or other of the neighbouring nanowires and not to both, see Fig 6(b). This would imply that in contrast to the estimation based on equation (2), the electrodes were insufficiently separated to permit diffusional independence to each nanowire in the array.…”

“…in the nanoAmpere range. [8,16,17] To address this challenge, researchers have recently begun to explore high aspect ratio 1-dimensional discrete nanoelectrodes such as nanobands and nanowires. [18][19][20][21][22][23] This newer class of nanoelectrode benefits from radial diffusion due to their nanometre scale critical dimension while achieving relatively large currents (nA) due to the long length of the electrode, typically ≥40 µm.…”

Modification of nanoelectrode ensembles by thiols and disulfides to prevent non specific adsorption of proteins

“…Since the first studies on NEEs [1,30], it was indeed demonstrated that these ensembles of nanodisk electrodes behave as electrodes with partially blocked surface [31], for which the true heterogeneous kinetic constant is substituted by an apparent one, the latter being smaller by a factor which corresponds to the fractional electrode area, that is the ratio between active and geometric area [1,30]. The validity of such a model was confirmed also by more recent theoretical studies [32][33][34][35]. The dashed and dotted lines in Fig.…”