Description
The attached file is an updated version of a simple cyclic voltammetry (CV) simulator written in Microsoft Excel.^{1} The spreadsheet supports up to four chemical species each undergoing up to four redox processes. Experimental CVs with up to 10,000 data points in text format can be copied/pasted into the spreadsheet for comparison to the simulation. The spreadsheet can be operated in protected mode or unprotected and modified as needed. The spreadsheet is provided with no guarantee and it may not be suitable for all applications. System requirements: Microsoft Windows 8.1 Office software or later. New version (v_14) uploaded to website on 5/18/19.
Important notes
List your formal redox potential (E^{o}') values in decreasing order if reduction(s) occur during the forward sweep.^{2 }Reverse this order if oxidation(s) occur during the forward sweep. You can then coalesce two adjacent peaks by exchanging their E^{o}' values. Set the E^{o}' values of unused peaks beyond the switching potential (E_{2}) in the proper order noted above to exclude them from the model. Set the starting potential (E_{1}) value greater than the switching potential (E_{2}) if reduction(s) occur during the forward sweep. Reverse this order if oxidation(s) occur during the forward sweep.
Software updates
Added intervening and removal rate constants for the first species on 5/18/19. The spreadsheet no longer assumes the first process is a charge transfer. Placed the calculations for diffusion, intervening reactions, and removal reactions into separate grids to simplify the equations. The spreadsheet is now using the Sequential method to calculate homogeneous reactions.^{3}
Incorporated the Saul’yev RL variant to simulate Fick’s Second Law of Diffusion on 1/8/17. This method can calculate thinner reaction layers than the combined Taylor series that was used previously.^{3 }Reducing the variable x_{scale}_{ }reduces the length of the diffusion grids and places the concentration points closer to the working electrode surface. However, using diffusion grids that are too short or long will distort your simulations, so adjust this parameter only as needed.
Separated the equations involving the number of electrons in the rate-determining step from the total number of electrons transferred on 12/22/16. The number of electrons in the rate-determining step (n_{a}) now controls the peak width.^{2} The total number of electrons transferred (n) now controls the total current.
Added first-order intervening rate constants (k_{I1}) between electron transfers on 12/20/16. The smaller you make a k_{I1} value, the slower the corresponding species is populated.^{2} Symbols k_{R1} and k_{R2} are now used to indicate first- and second-order apparent forward homogeneous rate constants that remove a corresponding species from the cycle.
Spreadsheet variables
Several variables from the original spreadsheet were renamed to incorporate new features. The following table describes the variables that are used in the newest version of the spreadsheet.
Variable | Definition | Value and/or unit(s) |
Gain | Amplification factor for experimental background | Unitless multiplier |
Offset | Constant added to the experimental current | A |
E^{o}ˊ | Formal potential for a redox couple | V |
n | Total number of electrons transferred per species (controls total peak area) | Unitless |
n_{a} | Number of electrons transferred in the rate determining step (controls peak width) | Unitless |
D | Common diffusion coefficient | ≈ 1 x 10^{-5} cm^{2}/s |
k^{o} | Standard heterogeneous rate constant for an electron transfer | cm/s |
a | Transfer coefficient for a redox couple | ≈ 0.5 (unitless) |
C_{bulk} | Bulk concentration of the analyte | mol/cm^{3} |
E_{1} | Starting potential of the CV experiment | V |
E_{2} | Switching potential of the CV experiment | V |
v | Scan rate used during the CV experiment | V/s |
A | Surface area of the working electrode | cm^{2} |
T | Temperature of the sample during experiment | K |
x_{scale} | Compress or expand x-axes of diffusion grids | Percentage (%) |
k_{I1} | Rate constant for first-order intervening homogenous reaction between electron transfers | s^{-1} |
k_{R1} | Rate constant for a first-order homogeneous reaction that removes a species from electron transfer cycle | s^{-1} |
k_{R2} | Rate constant for second-order homogeneous reaction that removes a species from electron transfer cycle | cm^{3}/mol•s |
Bug report
Bug in the removal grids was corrected on 5/19/19. Minor bug in the stacked plot corrected on 12/11/18. Bug in the intervening homogeneous reaction calculations was corrected on 1/12/17. Bug in the data selection process was corrected on 4/25/16. Bug in the Import data graphics corrected on 12/31/15. Bug in the concentration calculations of the 4^{th} redox couple oxidized form corrected on 12/8/15. Bug in the time increment calculations was corrected on 11/16/15.
References cited
1. J. H. Brown, J. Chem. Educ., 2016, 93 (7), 1326–1329. DOI: 10.1021/acs.jchemed.6b00052.
2. A. J. Bard, L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, Wiley: New York, 1980, ISBN: 0-471-05542-5.
3. D. Britz, Digital Simulation in Electrochemistry 3^{ed} ed., Springer: Berlin, 2010, ISBN: 978-3-642-06307-7.