Finite Element Simulation of Fast Sweep Voltammetry at Ultramicroelectrode
Authors: Machado Maria Manuela Pereira , Lucas Francisco Willian de Souza , Pereira Ernesto Chaves , Lopes Mauro Chierici 
Published: February 2020

This work presents the simulation of fast cyclic voltammetry (FSCV) by finite elements method for ultramicroelectrodes(UME). Ultramicroeletrodes have been used in the detection of neurotransmitters of in vivo experiments and,in this work, the experimental results are compared to the simulated ones.
FSCV is based on cyclic voltammetry(CV), a variation of the classic electrochemical technique, that offers accurate response in the separation of different coupled electrochemical processes. In this case, low sweep rate experiments have been accelerated by several orders of magnitude to provide temporal resolution in a subsecond time scale. Using FSCV at carbon-fiber microelectrodes, fast changes in the extracellular concentration of electroactive molecules can be monitored as well intermediate species during a redox reaction1.
The purpose of this work is to develop a model to describe the behavior of a redox pair during a FSCV data and compare them with experimental results.

EXPERIMENTAL
:Sodium hexacyanoferrate(II) 1.0×10-3molL-1 and hexacyanoferrate(III) 1.0×10-3molL-1 in 0.1molL-1 KCl aqueous solutions were prepared using reverse osmosis purified water. The voltammetric experiments were performed in a two-electrode electrochemical cell with a volume of 20mL using a potentiostat(Autolab PGSTAT-30). A carbon-fiber UME was used as working electrode(WE) and an Ag/AgCl/Cl-
(sat) as reference(RE) one. The UME area (A=2.1312x10-7cm2) and the capacitance(Cap=7.54x10-12F) values were determined experimentally. The simulation was performed using finite elements methods in the COMSOL-Multiphysics program.

EQUATIONS
:The investigated electrochemical reaction has been
Equation1
. It was considered only the diffusion mass transport, and Fick equation has been used(
Equation2
), where: ions’ concentration, zi
ions’ charge, F Faraday’s constant, φelectric potencial, u ions’ velocity field, Ri
ions’ reaction term. As consequence, we disregard migration and convection. Besides, we simulate an electrochemical reaction without any chemical step. Diffusion coefficients were set to 6.5x10-6cm2s-1 for all species. The flow of consumption/production of the species at the electrode surface was described by the Butler-Volmer equation(
Equation3
),where: i0
exchange current density, η overpotential, α charge transfer coefficient, R gas constant, T temperature.
Equation3
can be rearranged to
Equation4
, where M is the mass flow density expressed as the number of moles crossing the unit surface in the time unit and Kf
and Kb
are given by
Equation5
and
Equation6
.The parameters were setted khet
=1x10-4, α=0.5, n(number of exchanged electrons)=1 and T=298K. At the RE the potential was set as zero. The total current that flow through the WE is the some of the faradaic current and the capacitive current(icap
(
Equation7
)).The simulations have been performed for a single CV cycle between -0.6V and 1.2V with several scan rates, varying from 100Vs-1 to 3000Vs-1. To reduce the problem from 3D to 2D axial symmetry to limit the computation time, we applied the domain wall approximation as shown in
Figure1(A).

RESULTS:

Table1
shows the peak current for the different experiments and the correspondent simulations.As can be observed, the accuracy of the simulated results is high and there is an important superposition of the experimental and theoretical results. At this point, it is important to stress out that the method is validated in such cases. The model built considers also the capacitance current and we have developed a simple method to subtract the icap from the experimental one which is special large for macroelectrodes measured using FSCV technique.

CONCLUSIONS:The theoretical results fit well the experimental data in all the range of sweep rates investigated. The simulated data can be splitted in two different contributions such as the faradaic and capacitive currents and represented separately.Then, a promising use of this approach is to subtract the background current, which occurs during in an electrochemical experiment in a simple and direct form.

1 Donita L. Robinson et al., Clinical Chemistry,2003,49,1763-1773.