Alternating current voltammetry: predicting and visualizing harmonics
Source abstract
Abstract
Abstract Alternating current voltammetry (ACV) is gaining popularity for its ability to improve the yield of electrochemical syntheses, and for its ability to improve the sensitivity of electroanalytical measurements. Chief among the analytical advantages of ACV is its ability to generate an alternating current at integer multiples (harmonics) of the applied frequency, effectively gathering several datasets at once. However, interpretation of ACV data is hindered by the lack of a unified theory to predict higher harmonics for arbitrary reaction schemes, and by the experimental artefacts of uncompensated cell resistance and background current. The present paper outlines a method for predicting an arbitrary number of harmonics for systems with up to two charge transfer events and any number of coupled first-order chemical reactions, accounting also for cell resistance and background current described by a constant phase element. Results for an “ideal" experiment (no cell resistance and no background current) are presented up to the third harmonic for schemes with first-order reactions, and up to the first harmonic for schemes with second-order reactions. After these “ideal" cases, the effects of cell resistance and background current are explored. In general, irreversible charge transfer causes smaller phase angles, and coupled chemical reactions cause the aspect ratios of complex-plane ACV plots to become more circular. Uncompensated cell resistance can also lower the phase angle, imitating the effects of slow charge transfer or fast chemical reactions. At high frequencies, a combination of cell resistance and capacitance can cause the error in the potential to be so great that the current magnitude actually decreases with the onset of charge transfer. An ability to interpret the electrochemical fingerprints of each system in ACV experiments, as a function of the underlying physical parameters, can aid in the design of electrochemical devices that rely on the controlled utilization of electrochemical reactivity.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Electrochemical Analysis and Applications · Electrocatalysts for Energy Conversion · Corrosion Behavior and Inhibition
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (42)
Show source-provided references
1. Y. Hioki, M. Costantini, J. Griffin, K.C. Harper, M.P. Merini, B. Nissl, Y. Kawamata, P.S. Baran, Overcoming the limitations of kolbe coupling with waveform-controlled electrosynthesis. Science 380(6640), 81–87 (2023). https://doi.org/10.1126/science.adf476210.1126/science.adf4762 ↗
2. D. Gunasekera, J.P. Mahajan, Y. Wanzi, S. Rodrigo, W. Liu, T. Tan, L. Luo, Controlling one- or two-electron oxidation for selective amine functionalization by alternating current frequency. J. Am. Chem. Soc. 144(22), 9874–9882 (2022). https://doi.org/10.1021/jacs.2c0260510.1021/jacs.2c02605 ↗
3. S. Rodrigo, A. Hazra, J.P. Mahajan, H.M. Nguyen, L. Luo, Overcoming the potential window-limited functional group compatibility by alternating current electrolysis. J. Am. Chem. Soc. 145(40), 21851–21859 (2023). https://doi.org/10.1021/jacs.3c0580210.1021/jacs.3c05802 ↗
4. N. Behera, S. Rodrigo, A. Hazra, R. Maity, L. Luo, Revisiting alternating current electrolysis for organic synthesis. Curr. Opin. Electrochem. 43(101439), 1–8 (2024). https://doi.org/10.1016/j.coelec.2023.10143910.1016/j.coelec.2023.101439 ↗
5. A.N. Marianov, A.S. Kochubei, S. Gu, Y. Jiang, Charge-transfer mechanism in oxygen reduction over co porphyrins: Single-site molecular electrocatalysts to macromolecular frameworks. ACS Catal. 12(14), 8610–8622 (2022). https://doi.org/10.1021/acscatal.2c0084710.1021/acscatal.2c00847 ↗
6. D. Ji, M. Guo, Y. Wu, W. Liu, S. Luo, X. Wang, H. Kang, Y. Chen, C. Dai, D. Kong, H. Ma, Y. Liu, D. Wei, Electrochemical detection of a few copies of unamplified sars-cov-2 nucleic acids by a self-actuated molecular system. J. Am. Chem. Soc. 144(30), 13526–13537 (2022). https://doi.org/10.1021/jacs.2c0288410.1021/jacs.2c02884 ↗
7. A.M. Bond, Direct current, alternating current, rapid, and inverse polarographic methods for determination of tin(iv). Anal. Chem. 42(11), 1165–1168 (1970). https://doi.org/10.1021/ac60293a02810.1021/ac60293a028 ↗
8. Y. Zhang, L. Chen, F. Li, C.D. Easton, J. Li, A.M. Bond, J. Zhang, Direct detection of electron transfer reactions underpinning the tin-catalyzed electrochemical reduction of co2 using fourier-transformed ac voltammetry. ACS Catal. 7(7), 4846–4853 (2017). https://doi.org/10.1021/acscatal.7b0130510.1021/acscatal.7b01305 ↗
9. B.D. Fleming, J. Zhang, S.G. Bell, L.-L. Wong, A.M. Bond, Separation of electron-transfer and coupled chemical reaction components of biocatalytic processes using fourier transform ac voltammetry. Anal. Chem. 77(11), 3502–3510 (2005). https://doi.org/10.1021/ac048151y10.1021/ac048151y ↗
10. N.G. Baranska, B. Jones, M.R. Dowsett, C. Rhodes, D.M. Elton, J. Zhang, A.M. Bond, D. Gavaghan, H.O. Lloyd-Laney, A. Parkin, Practical guide to large amplitude fourier-transformed alternating current voltammetry - what, how, and why. ACS Measurement Science Au 44(4), 418–431 (2024). https://doi.org/10.1021/acsmeasuresciau.4c0000810.1021/acsmeasuresciau.4c00008 ↗
11. D.E. Smith, in AC Polarography and Related Techniques: Theory and Practice. ed. by A.J. Bard (Marcel Dekker, New York, 1966)
12. C. Bruggeman, Electrochemistry of nicotinamide adenine dinucleotide mimetics. PhD thesis, Michigan State University, East Lansing, MI (2024). https://doi.org/10.25335/ah1z-tt7010.25335/ah1z-tt70 ↗
13. A.M. Bond, R.J. Schwall, D.E. Smith, On-line fft faradaic admittance measurements:Application to a.c. cyclic voltammetry. J. Electroanal. Chem. 85(2), 231–247 (1977). https://doi.org/10.1016/S0022-0728(77)80290-810.1016/S0022-0728(77)80290-8 ↗
14. T.G. McCord, D.E. Smith, Alternating current polarography: An extension of the general theory for systems with coupled first-order homogeneous chemical reactions. Anal. Chem. 40(13), 1959–1966 (1968). https://doi.org/10.1021/ac60269a02110.1021/ac60269a021 ↗
15. T.G. McCord, D.E. Smith, Second harmonic alternating current polarography: A general theory for systems with coupled first-order homogeneous chemical reactions. Anal. Chem. 40(13), 1967–1970 (1968). https://doi.org/10.1021/ac60269a02210.1021/ac60269a022 ↗
16. J.R. Delmaestro, D.E. Smith, Some considerations on the effect of alternating potential amplitude in a.c. polarography. J. Electroanal. Chem. Interfacial Electrochem. 14(3), 261–268 (1967). https://doi.org/10.1016/0022-0728(67)80002-010.1016/0022-0728(67)80002-0 ↗
17. G.F. Kennedy, A.M. Bond, A.N. Simonov, Modelling ac voltammetry with mecsim: facilitating simulation-experiment comparisons. Curr. Opin. Electrochem. 1, 140–147 (2017). https://doi.org/10.1016/j.coelec.2016.12.00110.1016/j.coelec.2016.12.001 ↗
18. T. Tichter, J. Schneider, C. Roth, Convolutive modeling of cyclic voltammetry, ac-voltammetry, sine wave voltammetry and impedance spectroscopy with interfacial cpe behaviour and uncompensated ohmic resistances: A unified theory. Electrochimica Acta 393, 139006 (2021). https://doi.org/10.1016/j.electacta.2021.13900610.1016/j.electacta.2021.139006 ↗
19. R.S. Nicholson, I. Shain, Theory of stationary electrode polarography. Anal. Chem. 36(4), 231–247 (1964). https://doi.org/10.1021/ac60210a00710.1021/ac60210a007 ↗
20. M.E. Orazem, B. Tribollet, Electrochemical Impedance Spectroscopy (John Wiley and Sons, Hoboken, NJ, 2017)10.1002/9781119363682 ↗
21. G.J. Brug, A. van den Eeden, M. Sluyters-Rehbach, J.H. Sluyters, The analysis of electrode impedances complicated by the presence of a constant phase element. J. Electroanal. Chem. Interfacial Electrochem. 176(1–2), 275–295 (1984). https://doi.org/10.1016/S0022-0728(84)80324-110.1016/S0022-0728(84)80324-1 ↗
22. K.B. Oldham, J. Spainer, The replacement of fick’s laws by a formulation involving semidifferentiation. J. Electroanal. Chem. Interfacial Electrochem. 26(2–3), 331–341 (1970). https://doi.org/10.1016/S0022-0728(70)80316-310.1016/S0022-0728(70)80316-3 ↗
23. A.M. Bond, R.J. O’Halloran, I. Ruzic, D.E. Smith, Fundamental and second harmonic alternating current cyclic voltammetric theory and experimental results for simple electrode reactions involving solution-soluble redox couples. Anal. Chem. 48(6), 872–883 (1976). https://doi.org/10.1021/ac60370a03210.1021/ac60370a032 ↗
24. A.M. Bond, D.E. Smith, Direct measurement of er1/2 with reversible and ec electrode processes by second harmonic alternating current polarography and voltammetry. Anal. Chem. 46(13), 1946–1951 (1974). https://doi.org/10.1021/ac60349a02110.1021/ac60349a021 ↗
25. AM. Bond, RJ. O’Halloran, I. Ruzic, DE. Smith, Fundamental and second harmonic alternating current cyclic voltamemmeric theory and experimental results for systems in which a first-order chemical reaction follows the charge-transfer step; the ec mechanism. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 132, 39–57 (1982). https://doi.org/10.1016/0022-0728(82)85004-310.1016/0022-0728(82)85004-3 ↗
26. T.G. McCord, H.L. Hung, D.E. Smith, Alternating current polarography: Theoretical predictions for systems with first-order chemical reactions following the charge transfer step. J. Electroanal. Chem. Interfacial Electrochem. 21(1), 5–33 (1969). https://doi.org/10.1016/S0022-0728(69)80023-910.1016/S0022-0728(69)80023-9 ↗
27. K.R. Bullock, D.E. Smith, Fundamental and second harmonic alternating current polarography of electrode processes with coupled first-order preceding chemical reactions.cadmium-nitrilotriacetate system. Anal. Chem. 46(8), 1069–1074 (1974). https://doi.org/10.1021/ac60344a00810.1021/ac60344a008 ↗
28. T.G. McCord, D.E. Smith, Second harmonic a.c. polarography: Theoretical predictions for systems with first-order chemical reactions preceding the charge transfer step. J. Electroanal. Chem. Interfacial Electrochem. 26(1), 61–89 (1970). https://doi.org/10.1016/S0022-0728(70)80065-110.1016/S0022-0728(70)80065-1 ↗
29. K.R. Bullock, D.E. Smith, Fundamental and second harmonic alternating current polarography of electrode processes with coupled first-order catalytic chemical reactions. theory and experimental results with the iron triethanolamine-chlorite system. Anal. Chem. 46(11), 1567–1575 (1974). https://doi.org/10.1021/ac60347a00610.1021/ac60347a006 ↗
30. B.D. Fleming, J. Zhang, S.G. Bell, L.-L. Wong, A.M. Bond, Separation of electron-transfer and coupled chemical reaction components of biocatalytic processes using fourier transform ac voltammetry. Anal. Chem. 77(11), 3502–3510 (2005). https://doi.org/10.1021/ac048151y10.1021/ac048151y ↗
31. H.L. Hung, D.E. Smith, Alternating current polarography with multi-step charge transfer:I. theory for systems with reversible two-step charge transfer. J. Electroanal. Chem. 11(4), 237–254 (1969). https://doi.org/10.1016/0022-0728(66)80089-X10.1016/0022-0728(66)80089-X ↗
32. I. Ruzic, H.R. Sobel, D.E. Smith, On the theory for d.c. and fundamental harmonic a.c. polarography with the first-order consecutive ece mechanism. J. Electroanal. Chem. Interfacial Electrochem. 65(1), 21–56 (1975). https://doi.org/10.1016/0368-1874(75)85104-510.1016/0368-1874(75)85104-5 ↗
33. I. Ruzic, D.E. Smith, S.W. Feldberg, On the influence of coupled homogeneous redox reactions on electrode processes in d.c. and a.c. polarography: I. theory for two independent electrode reactions coupled with a homogeneous redox reaction. J. Electroanal. Chem. Interfacial Electrochem. 52(2), 157–192 (1974). https://doi.org/10.1016/S0022-0728(74)80360-810.1016/S0022-0728(74)80360-8 ↗
34. I. Ruzic, D.E. Smith, On the influence of coupled homogeneous redox reactions on electrode processes in d.c. and a.c. polarography: Ii. the e.e. mechanism with a coupled homogeneous redox reaction. J. Electroanal. Chem. Interfacial Electrochem. 58(1), 145–175 (1975). https://doi.org/10.1016/S0022-0728(75)80350-010.1016/S0022-0728(75)80350-0 ↗
35. A.R. Dale-Evans, M.J. Robinson, H.O. Lloyd-Laney, D.J. Gavaghan, A.M. Bond, A. Parkin, A voltammetric perspective of multi-electron and proton transfer in protein redox chemistry. Front. Chem. 9, 672831 (2021). https://doi.org/10.3389/fchem.2021.67283110.3389/fchem.2021.672831 ↗
36. L.P. Jenner, J.C. Crack, J.M. Kurth, Z. Soldánová, L. Brandt, K.P. Sokol, E. Reisner, J.M. Bradley, C. Dahl, M.R. Cheesman, J.N. Butt, Reaction of thiosulfate dehydrogenase with a substrate mimic induces dissociation of the cysteine heme ligand giving insights into the mechanism of oxidative catalysis. J. Am. Chem. Soc. 144(40), 18296–18304 (2022). https://doi.org/10.1021/jacs.2c0606210.1021/jacs.2c06062 ↗
37. M.T. Huynh, C.W. Anson, A.C. Cavell, S.S. Stahl, S. Hammes-Schiffer, Quinone 1 e- and 2 e-/2 h+ reduction potentials: Identification and analysis of deviations from systematic scaling relationships. J. Am. Chem. Soc. 138(49), 15903–15910 (2016). https://doi.org/10.1021/jacs.6b0579710.1021/jacs.6b05797 ↗
38. J.W. Hayes, I. Ruzic, D.E. Smith, G.L. Booman, J.R. Delmastro, Fundamental harmonic a.c. polarography with irreversible dimerization following the charge transfer step:Theory and experimental results with the benzaldehyde system. J. Electroanal. Chem. Interfacial Electrochem. 51(2), 269–285 (1974). https://doi.org/10.1016/S0022-0728(74)80244-510.1016/S0022-0728(74)80244-5 ↗
39. J.W. Hayes, I. Ruzic, D.E. Smith, G.L. Booman, J.R. Delmastro, Fundamental harmonic a.c. polarography with disproportionation following the charge transfer step:Theory and experimental results with the u(vi)/u(v) couple. J. Electroanal. Chem. Interfacial Electrochem. 51(2), 245–267 (1974). https://doi.org/10.1016/S0022-0728(74)80243-310.1016/S0022-0728(74)80243-3 ↗
40. L. Pospisil, M. Hromadova, R. Sokolova, C. Lanza, Kinetics of radical dimerization. simple evaluation of rate constant from convolution voltammetry and faradaic phase angle data. Electrochim. Acta 300, 284–289 (2019). https://doi.org/10.1016/j.electacta.2019.01.11910.1016/j.electacta.2019.01.119 ↗
41. R.V. Churchill, Operational Mathematics, 2nd edn. (McGraw-Hill Inc, New York, 1958)
42. E.T. Whittaker, G.N. Watson, Modern Analysis, 4th edn. (Cambridge University Press, New York, 1963)