Theory for staircase voltammetry and linear scan voltammetry onfractal electrodes: Emergence of anomalous Randles-Sev̌cik behavior

Electrochimica Acta

Volumn 111, Issue , 2013, Pages 223-233

  Rama Kant, Parveen ^a  

^a UNIVERSITY OF DELHI   (India)

Author keywords

Diffusion limited charge transfer; Finite fractal electrodes; LSV; Staircase voltammetrya

Indexed keywords

CHARGE TRANSFER; ELECTRODES; FRACTAL DIMENSION; FRACTALS; VOLTAMMETRY;

CHARACTERISTIC PEAKS; CURRENT TRANSIENTS; DIFFUSION LIMITED; FRACTAL ELECTRODES; GENERAL EXPRESSION; LINEAR-SCAN VOLTAMMETRY; STAIRCASE VOLTAMMETRY; STAIRCASE VOLTAMMETRYA;

STAIRS;

EID: 84884524827     PISSN: 00134686     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.electacta.2013.07.163     Document Type: Article

References (65)

1. N. Markovic, H. Gasteiger, P.N. Ross, Kinetics of oxygen reduction on Pt(hkl)electrodes: implications for the crystallite size effect with supported Pt electrocatalysts, Journal of the Electrochemical Society 144 (1997) 1591.
2. V. Climent, R. Gomez, J.M. Orts, J.M. Feliu, Thermodynamic analysis of the tem-perature dependence of OH adsorption on Pt(1 1 1) and Pt(1 0 0) electrodes inacidic media in the absence of specific anion adsorption, Journal of PhysicalChemistry B 110 (2006) 11344.
3. G. Bontempelli, R. Toniolo, in: P.J. Worsfold, A. Townshend, C. Poole (Eds.), Ency-clopedia of Analytical Science, Second edition, Elsevier, Oxford, U.K, 2005, p.188.
4. A.J. Bard, L.R. Faulkner, Electrochemical Methods: Fundamentals and Application, Wiley, New York, 1980.
5. X.J. Huang, L. Aldous, A.M. O'Mahony, F.J. Campo, R.G. Compton, Towardmembrane-free amperometric gas sensors: a microelectrode array approach, Analytical Chemistry 82 (2010) 5238.
6. J.E.B. Randles, A cathode ray polarograph. Part II - The current-voltage curves, Transactions of the Faraday Society 44 (1948) 327.
7. A. Sevcik, Oscillographic polarography with periodical triangular voltage, Collection of Czechoslovak Chemical Communications 13 (1948) 349.
8. P. Delahay, Theory of irreversible waves in oscillographic polarography, Journalof the American Chemical Society 75 (1953) 1190.
9. H. Matsuda, Y. Ayabe, Zur theorie der Randles-Sevikschen kathodenstrahl-polarographie, Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaftfür physikalische Chemie 59 (1955) 494.
10. R.S. Nicholson, I. Shain, Theory of stationary electrode polarography, AnalyticalChemistry 36 (1964) 706.
11. R. Compton, C. Banks, Understanding Voltammetry, Imperial College Press, London, 2011.
12. O.A. Kozaderov, A.V. Vvedenskii, Diffusion problem in chronopotentio- andchronoamperometry for electrode with rough surface, Russian Journal of Elec-trochemistry 37 (2001) 798.
13. T.R. Nolen, P.S. Fedkiw, The transient diffusion-limited current to a sinusoidalwall: extension of the Cottrell equation, Journal of Electroanalytical Chemistry 258 (1989) 265.
14. R. Kant, S.K. Rangarajan, Effect of surface roughness on diffusion-limited chargetransfer, Journal of Electroanalytical Chemistry 368 (1994) 1.
15. D. Menshykau, I. Streeter, R.G. Compton, Influence of electrode roughness oncyclic voltammetry, Journal of Physical Chemistry C 112 (2008) 14428.
16. B.B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, CA, 1977.
17. J. Feder, Fractals, Plenum, New York, 1988.
18. S. Zalis, L. Pospisil, Diffusion-limited processes on fractal surfaces generatedas a set of scaled Walsh functions, Journal of Electroanalytical Chemistry 349(1993) 443.
19. X. Zuo, C. Xu, H. Xin, Simulation of voltammogram on rough electrode, Elec-trochimica Acta 42 (1997) 2555.
20. L.H.L. Miaw, P.A. Boudreau, S.P. Perone, Theoretical and experimental evalua-tion of cyclic staircase voltammetry, Analytical Chemistry 50 (1978) 1988.
21. U. Kalapathy, D.E. Tallman, Equivalence of staircase and linear sweep voltam-metries for reversible systems including conditions of convergent diffusion, Analytical Chemistry 64 (1992) 2693.
22. T. Pajkossy, L. Nyikos, Diffusion to fractal surfaces - III. Linear sweep and cyclicvoltammograms, Electrochimica Acta 34 (1989) 181.
23. T. Pajkossy, Electrochemistry at fractal surfaces, Journal of Electroanalytical Chemistry 300 (1991) 1.
24. A. Imre, T. Pajkossy, L. Nyikos, Electrochemical determination of the fractaldimension of fractured surfaces, Acta Metallurgicaet Materialia 40 (1992) 1819.
25. M. Stromme, G.A. Niklasson, C.G. Granqvist, Determination of fractal dimen-sion by cyclic I-V studies: the Laplace-transform method, Physical Review B 52(1995) 14192.
26. Y. Dassas, P. Duby, Diffusion toward fractal interfaces, Journal of the Electro-chemical Society 142 (12) (1995) 4175.
27. J.Y. Go, S.I. Pyun, A review of anomalous diffusion phenomena at fractal inter-face for diffusion-controlled and non-diffusion-controlled transfer processes, Journal of Solid State Electrochemistry 11 (2007) 323.
28. V. Mirceski, Z. Tomovski, Voltammetry based on fractional diffusion, Journal of Physical Chemistry B 113 (9) (2009) 2794.
29. J. Bisquert, A. Compte, Theory of the electrochemical impedance of anomalousdiffusion, Journal of Electroanalytical Chemistry 499 (2001) 112.
30. E.K. Lenzi, L.R. Evangelista, G. Barbero, Fractional diffusion equation andimpedance spectroscopy of electrolytic cells, Journal of Physical Chemistry B:Letters 113 (33) (2009) 11371.
31. H. Randriamahazaka, V.N.C. Chevrot, Anomalous diffusion on the active zoneof p-doped poly(3, 4-ethylenedioxythiophene) modified electrodes, Journal of Electroanalytical Chemistry 556 (2003) 35.
32. R. Kant, S.K. Jha, Theory of anomalous diffusive reaction rates on realistic self-affine fractals, Journal of Physical Chemistry C 111 (2007) 14040.
33. S. Srivastav, R. Kant, Theory of generalized Cottrellian current at rough electrodewith solution resistance effects, Journal of Physical Chemistry C 114 (2010)10066.
34. M.M. Islam, R. Kant, Generalization of the Anson equation for fractal and non-fractal rough electrodes, Electrochimica Acta 56 (2011) 4467.
35. S.K. Jha, A. Sangal, R. Kant, Diffusion-controlled potentiostatic current transi-ents on realistic fractal electrodes, Journal of Electroanalytical Chemistry 615(2008) 180.
36. R. Kant, S.K. Rangarajan, Effect of surface roughness on interfacial reaction-diffusion admittance, Journal of Electroanalytical Chemistry 552 (2003) 141.
37. R. Kant, M. Sarathbabu, S. Srivastav, Effect of uncompensated solution resistance on quasireversible charge transfer at rough and finite fractal electrode, Electrochimica Acta 95 (2013) 237.
38. R. Kant, M.M. Islam, Theory of absorbance transients of an optically transparentrough electrode, Journal of Physical Chemistry C 114 (2010) 19357.
39. R. Kumar, R. Kant, Diffusional impedance on realistic self-affine fractals: com-parative study of statistically corrugated and isotropic fractals, Journal ofChemical Sciences 121 (2009) 579.
40. S. Srivastav, R. Kant, Anomalous Warburg impedance: influence of uncom-pensated solution resistance, Journal of Physical Chemistry C 115 (2011)12232.
41. R. Kumar, R. Kant, Theory of generalized Gerischer admittance of realistic fractal electrode, Journal of Physical Chemistry C 113 (2009) 19558.
42. R. Kumar, R. Kant, Admittance of diffusion limited adsorption coupled toreversible charge transfer on rough and finite fractal electrodes, Electrochimica Acta 95 (2013) 275.
43. S. Srivastav, S. Dhillon, R. Kumar, R. Kant, Experimental validation of rough-ness power spectrum based theory of anomalous Cottrell response, Journal of Physical Chemistry C 117 (2013) 8594.
44. R. Kant, General theory of arbitrary potential sweep methods on an arbitrarytopography electrode and its application to random surface roughness, Journal of Physical Chemistry C 114 (2010) 10894.
45. G.C. Barker, I.S. Longmuir (Eds.), Advances in Polarography, Pergamon Press, New York, 1960.
46. C.K. Mann, Stationary electrode polarography with a staircase voltage sweep, Analytical Chemistry 33 (1961) 1484.
47. C.K. Mann, An instrument for cyclic voltammetry, Analytical Chemistry 37(1965) 326.
48. R.S. Nigmatullin, M.R. Vyaselev, Oscillographic polarography with a staircasevoltage sweep, Zhurnal analiticheskoi khimii 19 (1964) 545.
49. J.H. Christie, P.J. Lingane, Theory of staircase voltammetry, Journal of Electro-analytical Chemistry 10 (1965) 176.
50. D.R. Ferrier, R.R. Schroeder, Staircase voltammetry with varied current samp-ling times. Theory for diffusion controlled, rate controlled, and mixed rateand diffusion controlled electrode reactions, Electroanalytical Chemistry and Interfacial Electrochemistry 45 (3) (1973) 343.
51. A. Molina, J. Gonzalez, M.C. Henstridge, R.G. Compton, Voltammetry of electro-chemically reversible systems at electrodes of any geometry: a general, explicitanalytical characterization, Journal of Physical Chemistry C 115 (2011) 4054.
52. M. Abramowitz, A. Stegan, Handbook of Mathematical Functions, Dover Publi-cations Inc., New York, 1972.
53. A.R. Osborne, A. Pastorello, Simultaneous occurrence of low-dimensional chaosand colored random noise in nonlinear physical systems, Physics Letters A 181(2) (1993) 159.
54. P. Ocon, P. Herrasti, L. Vazquez, R.C. Salvarezza, J.M. Vara, A.J. Arvia, Fractal characterisation of electrodispersed gold electrodes, Journal of Electroanalytical Chemistry 319 (1991) 101.
55. P. Pfeifer, D. Avnir, Chemistry in noninteger dimensions between two and three.I. Fractal theory of heterogeneous surfaces, Journal of Chemical Physics 79 (7)(1983) 3558.
56. D. Farin, P. Pfeifer, Chemistry in noninteger dimensions between two and three.II. Fractal surfaces of adsorbents, Journal of Chemical Physics 79 (7) (1983) 3566.
57. R. Kant, Statistics of approximately self-affine fractals: random corrugated surface and time series, Physical Review E 53 (1996) 5749.
58. J.M. William, T.P. Beebe Jr., Analysis of fractal surfaces using scanning probemicroscopy and multiple-image variography. 1. Some general considerations, Journal of Physical Chemistry 97 (1993) 6249.
59. O.I. Yordanov, N.I. Nickolaev, Self-affinity of time series with finite domainpower-law power spectrum, Physical Review E 49 (1994) R2517.
60. R. Kant, Can current transients be affected by the morphology of the nonfractalelectrode? Physical Review Letters 70 (1993) 4094.
61. S.K. Rangarajan, K.S.G. Doss, Faradaic admittance: sign conventions, Electrochimica Acta 7 (1962) 201.
62. A. Molina, J. Gonzalez, M.C. Henstridge, R.G. Compton, Analytical expressions for transient diffusion layer thicknesses at non-uniformly accessible electrodes, Electrochimica Acta 56 (2011) 4589.
63. C. Montella, B.L. Gorrec, J.P. Diard, Diffusion layer approximation under transient conditions, Journal of Electroanalytical Chemistry 584 (2005) 182.
64. O. Wein, V.T. Valentin, V. Sobolik, Transient convective diffusion to a circularsink at finite Peclet number, International Journal of Heat and Mass Transfer 49 (2006) 4596.
65. S.K. Kim, I.J. Park, D.Y. Lee, Influence of surface roughness on the electrochemical behavior of carbon steel, Journal of Applied Electrochemistry 43 (5) (2013)507.