2.3 Finite element approach for optimization of electrodes design

For our simulation approach, we used commercially available COMSOL 3.5 software multiphysics software, which solves partial differential equations (PDEs) by finite element technique. In the model we assume that 3D carbon microelectrode arrays were uniformly immobilized with glucose oxidase and laccase on anode and cathode respectively with out the use of any mediators. The proposed implantable membraneless EBFC is assumed to be placed inside a blood artery of the human body thus utilizes the glucose extracted from blood as a fuel. In principle, glucose oxidase reacts with glucose and produces gluconolactone and hydrogen peroxide. This hydrogen peroxide oxidizes on the anode to generate electron and hydrogen ions. The hydrogen ions travel from electrolyte to cathode, while electrons flow through an external load and generate electricity. On cathode, dissolved oxygen is reduced via laccase enzyme and by combining with electrons and hydrogen ions forms water.

We applied Michaelis-Menten theory in our 2D model to analyze phenomenon between enzyme kinetics on the electrode surface and glucose diffusion and thus optimize the electrode microarray design rule according to the enzyme reaction rate In order to determine the output potential in developing biofuel cell, we also incorporated Nernst equation. The numerical simulations have been performed with various electrodes heights and well widths (distance between any two electrodes) to obtain the relation between design rule and EBFCs performance. Various 2D models are investigated for same foot print length (600 pm) of SiO2, with fixed electrode diameter of 30 pm and fixed enzyme layer thickness of 10 pm. The height of electrodes is chosen as 60 pm, 120 pm and 240 pm for different well widths (WW-distance between any two electrodes) of 10pm, 20 pm, 40 pm, 60 pm, 80 pm, 100 pm, 120 pm, 140 pm, 160 pm, 180 pm and 200 pm.

The quantification of reaction rates of enzymes on anode and cathode is showed in Fig. 6.

From the results, we observe that the reaction rate decreased from the top to the bottom along the surface of both electrodes due to the lack of diffusion of the substrate as we go towards the bottom; also the outer surfaces of the electrodes have the larger reaction rate in the enzyme layer. The reaction rate along the surface of both electrodes is plotted in Fig. 6. The reaction rate is increased from the bottom to the top along the electrode surface and reached the maximum at edge of the top due to the edge effect. The maximum reaction rates of GOx enzymes vs. different well widths is shown in Fig. 7. for three different heights of electrodes: 60 pm, 120 pm and 240 pm, with 10 pm, 20 pm, 40 pm, 60 pm, 80 pm, 100 pm and 120 pm well widths, respectively. In the case of 60 pm height of electrodes, the maximum reaction rate is obtained when the well width is about 30 pm. For the height of 120 pm and 240 pm, reaction rate reached the highest at the well width of 60 pm and 120 pm respectively. From all these three sets of models both in anode and cathode, we can conclude that the reaction rates of one pair of electrodes reach the maximum when the well width is half as the height of electrodes.

The open circuit output potential also has been simulated for the same heights and well widths of electrodes by applying the Nernst equation. The current collectors are assumed at the bottom of the electrodes and hence these potentials are calculated from the bottom. Fig. 8. shows the open circuit output potential vs. well width of electrodes at different height of electrodes. From the results of simulation, we could find out an empirical relationship between electrodes height and well width to achieve optimized output potential is when height of electrodes is twice than that of well width which is in agreement to the results we obtain for the diffusion of the substrate.