Comparison of 2D versus 3D diffusion analysis at Nanowire Electrodes: Finite element analysis and experimental study

Abstract

In electroanalysis, finite element simulations of electrochemical processes occurring at electrodes are used to provide key insight into experimental design in relation to diffusion profiles and expected currents. The diffusion domain approach (DDA) offers a means of reducing a three dimensional design to two dimensions to ease computational demands. However, the DDA approach can be limited when basic assumptions, for example that all electrodes in an array are equivalent, are incorrect. Consequently, to get a more realistic view of molecular diffusion to nanoelectrodes, it is necessary to undertake simulations in 3D. In this work, two and three dimensional models of electrodes comprising of (i) single nanowires, (ii) arrays of nanowires and (iii) interdigitated arrays of nanowires operating in generator-collector mode, are undertaken and compared to experimental results obtained from fabricated devices. The 3D simulations predict a higher extracted current for a single nanowires and diffusionally independent nanowire arrays when compared to 2D simulations since, unlike the 2D model, they take into account molecular diffusion to and from the nanowire termini. This current difference was observed to increase with increasing electrode width and decrease with electrode length. When the nanowire arrays were diffusionally overlapped, they behaved as an electrode of larger width, and the divergence between the two models increased. By contrast, in generator-collector mode, using interdigitated nanowire arrays, the difference between extracted current values obtained using two models was significantly lower. Simulations indicated however that a higher collection efficiency was predicted by the 2D model when compared to the 3D model. Electrochemical experiments were undertaken to confirm the simulation study and demonstrated that the extracted currents from 3D simulations more closely mapped onto experimentally measured currents.