Mathematical modeling of interdigitated electrode arrays in finite electrochemical cells

Abstract

Accurate theoretical results for interdigitated array of electrodes (IDAE) in semi-infinite cells can be found in the literature. However, these results are not always applicable when using finite cells. In this study, theoretical expressions for IDAE in a finite geometry cell are presented. At known current density, transient and steady state concentration profiles were obtained as well as the response time to a current step. Concerning the diffusion limited current, a lower bound was derived from the concentration profile and an upper bound was obtained from the limiting current of the semi-infinite case. The lower bound, which is valid when Kirchhoff's current law applies to the unit cell, can be useful to ensure a minimum current level during the design of the electrochemical cell. Finally, a criterion was developed defining when the behaviors of finite and semi-infinite cells are comparable. This allows to obtain higher current levels in finite cells, approaching that of the semiinfinite case. Examples with simulations were performed in order to illustrate and validate the theoretical results.required. Many authors have used numerical simulations to understand this working principle [4][5][6][7]. Also theoretical results are available [7][8][9]. The most significant of these results was obtained by Aoki [8,9], where exact expressions for the current-potential curves and limiting current in steady state were obtained for reversible and irreversible electrode reactions. Later, Morf and colleagues [7] did a theoretical revision of Aoki's results for the case of reversible electrode reactions with internal/external counter electrode.All of the results previously mentioned consider that the IDAE is subject to semi-infinite geometry, which means that the ratio between the 'height of the cell' and the center-to-center 'separation of the electrodes' is very large. This is not always true, as one can see in the case of some microfluidic devices where 'channel height' and 'electrodes separation' are of comparable size [10][11][12][13], especially when using low cost fabrication techniques or materials. Soft lithography and the use of transparency sheet masks are examples of simple and inexpensive techniques commonly used for fabricating microfluidic devices [14,15]. When using soft lithography, the channel height of microfluidic devices is determined by the thickness of the photoresist mold, which can vary in between 1 µm-200 µm [14]. When using photolithography and transparency sheet masks, the electrodes are constrained by the resolution of the transparency sheet mask, which can generate features between 20 µm-50 µm when using a printer operating at 3380 dpi-5080 dpi [14,15]. Therefore, the ratio between the 'height of the cell' and the center-to-center 'separation of the electrodes' obtained using these techniques is clearly finite and may vary between ∼ 0.01 − 10.Electrochemical applications [12,13,[16][17][18][19][20][21] and research through simulations [22][23][24][25] have been reported for IDAE in continuous ...

Exploring Interdigitated Electrode Arrays Screen-Printed on Paper Substrates for Steady-State Electrochemical Measurements

“…The 3D simulation domain of the electrochemical cell was reduced to 2D since the portion of each electrode band in contact with the electrochemical solution was much longer (4 mm) than its width (200 μm-300 μm). [24][25][26][27] Furthermore, it was possible to further reduce the 2D simulation domain to the rectangle delimited by the centers of consecutive bands. This is due to the periodic arrangement of the IDE and the large number of electrode bands (21 × 2 and 14 × 2 in accordance with the previous sections).…”

“…This is due to the periodic arrangement of the IDE and the large number of electrode bands (21 × 2 and 14 × 2 in accordance with the previous sections). [24][25][26][27] Inside this reduced 2D domain, the concentration profile of the electrochemical species can be modeled by the following time-dependent diffusion equation…”

“…where c σ is the concentration of electrochemical species σ (either oxidized or reduced), D is the diffusion coefficient, H is the thickness of the wet paper, and W is the separation between the centers of consecutive bands. 25,27 Independent concentrations were assumed for the electrode bands…”

Comparing the effects of Cu-Ti/RuO2-IrO2 electrode configuration on the electro-reduction of nitrate

“…The electrodes' edges are exposed to both vertical and horizontal diffusion, whereas the centers of the electrodes are only exposed to vertical diffusion. This enables ionic species to escape/reach the edges easier than the rest of the electrode surface (Guajardo et al 2013). The difference between the experimental and theoretical values of the electrolytic cell geometric factor is an indication of the edge effect (Hasson et al 2008).…”

Simulation of the impact of reversible adsorption on the response time of interdigitated electrode arrays

“…Without adsorption, the current follows a step function, due to full redox cycling starting within the order of the diffusion time in between the electrodes [44][45][46]. For the device used here, a response time of approximately 10 ms is predicted [47]. Within this time, a concentration gradient of the molecules with different oxidation states is established due to the diffusive mass transport.…”