Effect of Electrode Shape and Flow Conditions on the Electrochemical Detection with Band Microelectrodes

Abstract

In this work, we report the analysis of the electrochemical detection of electroactive species with band microelectrodes that operate under controlled convection. The study focuses on the determination of the collection efficiency of the analyte as a function of inlet flow velocity and microband geometry (inlaid, bumped and recessed), also providing a straightforward method for the theoretical determination of the lower detection limit. The analysis has been carried out by simulating the dimensionless mass transport with the finite element method, delivering the stationary limiting current density. Simulations have been performed on systems consisting of single and double band electrodes to investigate the trail effect on the electrochemical detection. We show that the obtained dimensionless results can be easily turned into dimensional data, providing a tool for the design of devices. The proposed method is general and can easily be extended to systems with different geometry.

Keywords: diffusion convection; electrochemical sensors; mass transport; microelectrodes.

Figure 1

Cross sections of the channel geometries with one bumped (a), inlaid (b), or recessed (c) electrode and two bumped electrodes (d). Schemes of the devices containing single (e) and two-microbands electrode (f) (Working electrode not shown).

Figure 2

Geometry meshing for the bumped (a), inlaid (b), recessed (c), and two bumped electrodes (d) configurations. The channel length is represented by the L parameter, while the channel height is represented by the parameter A. The size of the square meshing elements is described in term of the mesh edge size d.

Figure 3

Mesh convergence criterion. Relative difference in electrodic dimensionless current compared with the most accurate d = 0.01 du taken as reference. Five channel heights were considered, namely A = 1, 2, 3, 4, and 5 du. The mesh size d = 0.02 du significantly reduced the discrepancy in current values with the reference mesh size d = 0.01 du, if compared with the less accurate mesh size d = 0.1 du.

Figure 4

Dimensionless currents calculated for five different channel heights A = 1, 2, 3, 4, and 5 du for: (a) bumped (b) inlaid, and (c) recessed electrode geometries. For each of the three geometries considered, the dimensionless current values decreased as the Péclet number and the channel height increased. Mesh size d = 0.02 du. Channel length L = 10 du.

Figure 5

Collection percentage for five different channel heights, A = 1, 2, 3, 4, and 5 du, in the case of (a) bumped, (b) inlaid, and (c) recessed electrodes. Like the dimensionless electrodic currents in Figure 4, the collection percentages decreased as the Péclet number and the channel height were increased. Mesh size d = 0.02 du. Channel length L = 10 du.

Figure 6

Difference between the values for the dimensionless currents (a) and collection percentages (b) obtained for A = 1 and A = 5 du at different values of the Péclet number. The data obtained for the three electrodic geometries were fitted using the power law decay $y=m\bullet x^n+c$ (Table 2).

Figure 7

Collection percentages for Pe (a) 10, (b) 50 and (c) 100 calculated at the second electrode of the multielectrodic configuration. Five channel heights A were considered. The reported values were obtained setting the channel length to the fixed value of L = 20 du. Filled markers instead, represent control points from different simulations at A = 1, 3, 5 du which were performed to evaluate the presence of relevant border effects. This was achieved increasing the distances between the electrodes and the left and right borders of the channel, from 1 and 2 du to 4 and 9 du respectively (channel length L set to L = 30 du); no significant changes in collection percentages were detected. The mesh size d = 0.02 du was set according to the mesh convergence criterion of Figure 3.

Figure 8

Contour plots of the dimensionless concentration for the bumped electrodic geometry with dimensionless channel height A = 5 du, dimensionless channel length L = 30 and variable electrode-electrode interdistance f for: (a) Pe = 10, f = 1; (b) Pe = 10, f = 15; (c) Pe = 100, f = 1; (d) Pe = 100, f = 15. Mesh size d = 0.02 du.

Figure 9

Dimensional currents for five different channel heights in the case of (a) bumped, (b) inlaid, and (c) recessed electrodes. The current values increased with increasing Péclet number value, and decreased as greater A values were considered.

Figure 10

Trail effect. Dimensional model for the collection percentage at the second electrode, bumped configuration: (a) Pe = 10, (b) Pe = 50, (c) Pe = 100. Channel heights A = 1, 2, 3, 4, and 5, du were considered for the modeling and conversion to dimensional units. As for the monoelectrodic case, greater A values brought a reduction in the collection percentage of electroactive species at the second electrode.