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Models Involving Transport Coupled with Homogeneous Reactions

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Modelling Electroanalytical Experiments by the Integral Equation Method

Part of the book series: Monographs in Electrochemistry ((MOEC))

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Abstract

The treatment of homogeneous reactions by the integral equation method is generally difficult. One difficulty is that homogeneous reactions cause couplings between concentrations of various species, so that concentration–production rate relationships cannot be determined individually for every species. They must be considered jointly for all species. The simplest situation occurs when the reaction–transport partial differential equations can be decoupled by applying a certain transformation of the concentrations. If the decoupling is not possible, the derivation of the concentration–production rate relationships becomes complicated, and it has been thus far accomplished only for a few simple examples of electroanalytical models. The second difficulty is associated with homogeneous reactions subject to nonlinear kinetic equations, to which one cannot apply the Laplace transformation. Such reactions have been handled, by the integral equation method, under additional assumptions (equilibrium, steady state, the Gerischer linearisation), or by conversion to integro-differential equations.

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References

  1. Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. Dover Publications, New York

    Google Scholar 

  2. Amatore C, Savéant JM (1977) ECE and disproportionation. Part V. Stationary state general solution application to linear sweep voltammetry. J Electroanal Chem 85:27–46

    CAS  Google Scholar 

  3. Amatore C, Nadjo L, Savéant JM (1978) Convolution and finite difference approach. Application to cyclic voltammetry and spectroelectrochemistry. J Electroanal Chem 90:321–331

    CAS  Google Scholar 

  4. Amatore C, Savéant JM, Thiebault A (1979) Electrochemically induced chemical reactions. Kinetics of competition with electron transfer. J Electroanal Chem 103:303–320

    CAS  Google Scholar 

  5. Amatore C, Gareil M, Savéant JM (1983) Homogeneous vs. heterogeneous electron transfer in electrochemical reactions. Application to the electrohydrogenation of anthracene and related reactions. J Electroanal Chem 147:1–38

    CAS  Google Scholar 

  6. Amatore C, Garreau D, Hammi M, Pinson J, Savéant JM (1985) Kinetic analysis of reversible electrodimerization reactions by the combined use of double potential step chronoamperometry and linear sweep voltammetry. Application to the reduction of 9-cyanoanthracene. J Electroanal Chem 184:1–24

    CAS  Google Scholar 

  7. Amatore C, Savéant JM, Combellas C, Robveille S, Thiébault A (1985) Electrochemically induced reactions: kinetics of the competition with homogeneous electron transfer in non-catalytic systems. Application to the substitution of 4-bromobenzophenone by cyanide ions in liquid ammonia. J Electroanal Chem 184:25–40

    CAS  Google Scholar 

  8. Andrieux CP, Savéant JM (1989) Detection of electroactive transient intermediates of electrochemical reactions by steady state and time-dependent techniques. Competition between heterogeneous electron transfer and homogeneous chemical reactions. J Electroanal Chem 267:15–32

    CAS  Google Scholar 

  9. Andrieux CP, Nadjo L, Savéant JM (1970) Electrodimerization 1. One-electron irreversible dimerization. Diagnostic criteria and rate determination procedures for voltammetric studies. J Electroanal Chem 26:147–186

    CAS  Google Scholar 

  10. Andrieux CP, Nadjo L, Savéant JM (1973) Electrodimerization. VII. Electrode and solution electron transfers in the radical–substrate coupling mechanism. Discriminative criteria from the other mechanisms in voltammetric studies (linear sweep, rotating disc, polarography). J Electroanal Chem 42:223–242

    CAS  Google Scholar 

  11. Andrieux CP, Blocman C, Dumas-Bouchiat JM, M’Halla F, Savéant JM (1980) Homogeneous redox catalysis of electrochemical reactions Part V. Cyclic voltammetry. J Electroanal Chem 113:19–40

    CAS  Google Scholar 

  12. Andrieux CP, Hapiot P, Savéant JM (1987) Mechanism of superoxide ion disproportionation in aprotic solvents. J Am Chem Soc 109:3768–3775

    CAS  Google Scholar 

  13. Andrieux CP, Gallardo I, Savéant JM (1989) Outer-sphere electron-transfer reduction of alkyl halides. A source of alkyl radicals or of carbanions? Reduction of alkyl radicals. J Am Chem Soc 111:1620–1626

    CAS  Google Scholar 

  14. Andrieux CP, Grzeszczuk M, Savéant JM (1991) Electrochemical generation and reduction of organic free radicals. α-hydroxybenzyl radicals from the reduction of benzaldehyde. J Am Chem Soc 113:8811–8817

    CAS  Google Scholar 

  15. Andrieux CP, Delgado G, Savéant JM, Su KB (1993) Improvement and estimation of precision in the cyclic voltammetric determination of rate constants and activation parameters of coupled homogeneous second order reactions. Reaction of n-butyl bromide with anthracene anion radicals. J Electroanal Chem 348:141–154

    CAS  Google Scholar 

  16. Aoki K, Ishida M, Tokuda K (1988) Voltammetry at microcylinder electrodes. Part VI. Second-order catalytic reaction of Fe(edta) with H2O2. J Electroanal Chem 245:39–50

    CAS  Google Scholar 

  17. Arévalo M, Farnia G, Severin G, Vianello E (1987) Kinetic analysis of a slow electron transfer coupled with a father–son reaction. J Electroanal Chem 220:201–211

    Google Scholar 

  18. Balducci G, Costa G (1993) The four-member square scheme in cyclic voltammetry: general solution for Nernstian electron transfers. J Electroanal Chem 348:355–365

    CAS  Google Scholar 

  19. Bender MA, Stone HA (1993) An integral equation approach to the study of the steady state current at surface microelectrodes. J Electroanal Chem 351:29–55

    CAS  Google Scholar 

  20. Bieniasz L (1984) Influence of diffusion coefficient ratio D O∕D R on potential-step chronoamperometric and linear voltammetric current at stationary planar electrodes in the case of a pseudo-first-order EC catalytic reaction scheme. J Electroanal Chem 170:77–87

    CAS  Google Scholar 

  21. Bieniasz LK (1985) Linear voltammetric current functions for a pseudo-first-order EC catalytic reaction scheme with D O ≠ D R: series expansion algorithm. J Electroanal Chem 188:13–20

    CAS  Google Scholar 

  22. Bieniasz LK (2011) Analysis of the applicability of the integral equation method in the theory of transient electroanalytical experiments for homogeneous reaction–diffusion systems: the case of planar electrodes. J Electroanal Chem 657:91–97

    CAS  Google Scholar 

  23. Calvente JJ, Andreu R, Roldán E, Domínguez M (1994) On the simultaneous evaluation of charge transfer kinetics and adsorption: reduction of parabanic acid in low acidity xM HCl + (2 − x)M LiCl mixtures. J Electroanal Chem 366:105–125

    CAS  Google Scholar 

  24. Danckwerts PV (1951) Absorption by simultaneous diffusion and chemical reaction into particles of various shapes and into falling drops. Trans Faraday Soc 47:1014–1023

    CAS  Google Scholar 

  25. Davčeva M, Mirčeski V, Komorsky-Lovrić Š (2011) Evaluation of the antioxidative activity by measuring the rate of the homogeneous oxidation reaction with ferroceniumdimethanol cation. Comparative analysis of glutathione and ascorbic acid. Int J Electrochem Sci 6:2718–2729

    Google Scholar 

  26. Delmastro JR (1969) Theory of polarographic kinetic currents for second-order regeneration reactions at spherical electrodes. II. Numerical solution of the integral equations for steady-state behavior. Anal Chem 41:747–753

    CAS  Google Scholar 

  27. Delmastro JR, Booman GL (1969) Polarographic kinetic currents for first-order preceding and regeneration reactions at spherical electrodes. Anal Chem 41:1409–1420

    CAS  Google Scholar 

  28. Dutt J, Chhabra J, Singh T (1989) Linear sweep voltammetry at tubular electrodes. Part IV. Catalytic reactions. J Electroanal Chem 273:69–78

    CAS  Google Scholar 

  29. Fatouros N, Chemla M, Amatore C, Savéant JM (1984) Slow charge transfer associated with a fast equilibriated follow-up dimerization reaction. J Electroanal Chem 172:67–81

    CAS  Google Scholar 

  30. Garay F, Lovrić M (2002) Square-wave voltammetry of quasi-reversible electrode processes with coupled homogeneous chemical reactions. J Electroanal Chem 518:91–102

    CAS  Google Scholar 

  31. Garay F, Lovrić M (2002) Square-wave voltammetry of quasi-reversible CE reactions at spherical microelectrodes. Electroanalysis 14:1635–1643

    CAS  Google Scholar 

  32. Garay F, Lovrić M (2002) Quasi-reversible EC reactions at spherical microelectrodes analysed by square-wave voltammetry. J Electroanal Chem 527:85–92

    CAS  Google Scholar 

  33. Gerischer H (1951) Wechselstrompolarisation von Elektroden mit einem potentialbestimmenden Schritt beim Gleichgewichtspotential I. Z Phys Chem 198:286–313

    CAS  Google Scholar 

  34. Gonzalez J, Hapiot P, Konovalov V, Savéant JM (1999) Investigating the reduction characteristics of transient free radicals by laser-pulse electron photo-injection—mechanism diagnostic criteria and determination of reactivity parameters from time-resolved experiments. J Electroanal Chem 463:157–189

    CAS  Google Scholar 

  35. Gueshi T, Tokuda K, Matsuda H (1979) Voltammetry at partially covered electrodes. Part II. Linear potential sweep and cyclic voltammetry. J Electroanal Chem 101:29–38

    CAS  Google Scholar 

  36. Hapiot P, Audebert P, Monnier K, Pernaut JM, Garcia P (1994) Electrochemical evidence of β-dimerization with short thiophene oligomers. Chem Mater 6:1549–1555

    CAS  Google Scholar 

  37. Harima Y, Kurihara H, Nishiki Y, Aoyagui S, Tokuda K, Matsuda H (1982) Dissociation kinetics of the solvated electron species in methylamine and methylamine–ammonia mixtures. Can J Chem 60:445–455

    CAS  Google Scholar 

  38. Hayes JW, Ružić I, Smith DE, Booman GL, Delmastro JR (1974) 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 51:245–267

    CAS  Google Scholar 

  39. Hayes JW, Ružić I, Smith DE, Booman GL, Delmastro JR (1974) Fundamental harmonic A.C. polarography with irreversible dimerization following the charge transfer step. Theory and experimental results with the benzaldehyde system. J Electroanal Chem 51:269–285

    CAS  Google Scholar 

  40. Henke KH, Hans W (1955) Reaktionskinetisch bedingte polarographische Stromstärke. 3. Mitteilung: Dem Elektrodenprozeß nachgelagerte chemische Reaktionen unter Rückbildung des Depolarisators. Z Elektrochem 59:676–680

    CAS  Google Scholar 

  41. Holmes MH (1995) Introduction to perturbation methods. Springer, New York

    Google Scholar 

  42. Hung HL, Delmastro JR, Smith DE (1964) Alternating current polarography of electrode processes with coupled homogeneous chemical reactions. III. Theory for systems with multi-step first-order chemical reactions. J Electroanal Chem 7:1–25

    CAS  Google Scholar 

  43. Kant R, Rangarajan SK (1989) Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction. J Electroanal Chem 265:39–65

    CAS  Google Scholar 

  44. Kastening B (1969) Note on the polarographic theory for an ECE mechanism. Anal Chem 41:1142–1144

    CAS  Google Scholar 

  45. Keller HE, Reinmuth WH (1972) Theory of potential scan voltammetry with finite diffusion. Kinetics and other complications. Anal Chem 44:1167–1178

    CAS  Google Scholar 

  46. Komorsky-Lovrić Š, Lovrić M (2012) Theory of square-wave voltammetry of two electron reduction with the intermediate that is stabilized by complexation. Electrochim Acta 69:60–64

    Google Scholar 

  47. Kumar VT, Birke RL (1993) Evaluation of electrochemical parameters for an EC mechanism from a global analysis of current–potential–time data: application to reductive cleavage of methylcobalamin. Anal Chem 65:2428–2436

    CAS  Google Scholar 

  48. Lexa D, Rentien P, Savéant JM, Xu F (1985) Methods for investigating the mechanistic and kinetic role of ligand exchange reactions in coordination electrochemistry. Cyclic voltammetry of chloroiron(III)tetraphenylporphyrin in dimethylformamide. J Electroanal Chem 191:253–279

    CAS  Google Scholar 

  49. Lovrić M, Jadreško D, Komorsky-Lovrić Š (2013) Theory of square-wave voltammetry of electrode reaction followed by the dimerization of product. Electrochim Acta 90:226–231

    Google Scholar 

  50. Lovrić M, Tur’yan YI (2003) A model of CE mechanism on spherical electrodes. Croat Chem Acta 76:189–197

    Google Scholar 

  51. Lucas SK, Sipcic R, Stone HA (1997) An integral equation solution for the steady-state current at a periodic array of surface microelectrodes. SIAM J Appl Math 57:1615–1638

    Google Scholar 

  52. Lundquist JT Jr, Nicholson RS (1968) Theory of the potential step–linear scan electrolysis method with a comparison of rate constants determined electrochemically and by classical methods. J Electroanal Chem 16:445–456

    CAS  Google Scholar 

  53. Maran F, Severin MG, Vianello E, D’Angeli F (1993) Self-protonation of electrogenerated carbanions. Competition between electrode reduction and chemical decay of the conjugate base of the substrate. J Electroanal Chem 352:43–50

    CAS  Google Scholar 

  54. Mastragostino M, Nadjo L, Savéant JM (1968) Disproportionation and ECE mechanisms—I. Theoretical analysis. Relationships for linear sweep voltammetry. Electrochim Acta 13:721–749

    CAS  Google Scholar 

  55. Matsuda H (1974) Contributions to the theory of D.C. polarographic current–potential curves for electrode processes involving a chemical reaction. J Electroanal Chem 56:165–175

    CAS  Google Scholar 

  56. McCord TG, Smith DE (1968) Alternating current polarography: an extension of the general theory for systems with coupled first-order homogeneous chemical reactions. Anal Chem 40:1959–1966

    CAS  Google Scholar 

  57. McCord TG, Smith DE (1968) Second harmonic alternating current polarography: a general theory for systems with coupled first-order homogeneous chemical reactions. Anal Chem 40:1967–1970

    CAS  Google Scholar 

  58. Mirčeski V, Bobrowski A, Zarebski J, Spasovski F (2010) Electrocatalysis of the first and second kind: theoretical and experimental study in conditions of square-wave voltammetry. Electrochim Acta 55:8696–8703

    Google Scholar 

  59. Mirkin MV, Bard AJ (1992) Multidimensional integral equations: a new approach to solving microelectrode diffusion problems. Part 2. Applications to microband electrodes and the scanning electrochemical microscope. J Electroanal Chem 323:29–51

    CAS  Google Scholar 

  60. Murphy MM, O’Dea JJ, Arn D, Osteryoung JG (1990) Theory of cyclic staircase voltammetry for first-order coupled reactions. Anal Chem 62:903–909, with correction in Anal Chem 62:1904

    Google Scholar 

  61. Nadjo L, Savéant JM (1971) Dimerization, disproportionation and E.C.E. mechanisms in the reduction of aromatic carbonyl compounds in alkaline media. J Electroanal Chem 33:419–451

    CAS  Google Scholar 

  62. Nadjo L, Savéant JM (1973) Electrodimerization. VIII. Role of proton transfer reactions in the mechanism of electrohydrodimerization. Formal kinetics for voltammetric studies (linear sweep, rotating disc, polarography). J Electroanal Chem 44:327–366

    CAS  Google Scholar 

  63. Nadjo L, Savéant JM (1973) Linear sweep voltammetry: Kinetic control by charge transfer and/or secondary chemical reactions. I. Formal kinetics. J Electroanal Chem 48:113–145

    CAS  Google Scholar 

  64. Nadjo L, Savéant JM, Su KB (1985) Homogeneous redox catalysis of multielectron electrochemical reactions. Part II. Competition between homogeneous electron transfer and addition on the catalyst. J Electroanal Chem 196:23–34

    CAS  Google Scholar 

  65. Ng SLL, Cheh HY (1985) The application of linear sweep voltammetry to a rotating disk electrode with a catalytic process. J Electrochem Soc 132:93–98

    CAS  Google Scholar 

  66. Ng SLL, Cheh HY (1985) The application of linear sweep voltammetry to a rotating disk electrode with a kinetic process. J Electrochem Soc 132:98–102

    CAS  Google Scholar 

  67. Ng SLL, Cheh HY (1986) The application of linear sweep voltammetry to a rotating disk electrode for electrode reactions preceded by a chemical reaction. J Electrochem Soc 133:1385–1388

    Google Scholar 

  68. Nicholson RS (1965) Some examples of the numerical solution of nonlinear integral equations. Anal Chem 37:667–671

    CAS  Google Scholar 

  69. Nicholson RS, Shain I (1964) Theory of stationary electrode polarography. Single scan and cyclic methods applied to reversible, irreversible, and kinetic systems. Anal Chem 36:706–723.

    CAS  Google Scholar 

  70. Nicholson RS, Shain I (1965) Theory of stationary electrode polarography for a chemical reaction coupled between two charge transfers. Anal Chem 37:178–190

    CAS  Google Scholar 

  71. Nicholson RS, Wilson JM, Olmstead ML (1966) Polarographic theory for an ECE mechanism. Application to reduction of p-nitrosophenol. Anal Chem 38:542–545

    CAS  Google Scholar 

  72. Nishihara C (1982) Note on approximate equations of DC polarographic current–potential curves for a catalytic wave. J Electroanal Chem 134:171–176

    CAS  Google Scholar 

  73. Nishihara C, Matsuda H (1974) Contributions to the theory of kinetic and catalytic currents in polarography. J Electroanal Chem 51:287–293

    CAS  Google Scholar 

  74. Nishihara C, Matsuda H (1977) A contribution to the theory of D.C. polarographic current–voltage curves. Electrode reactions with three parallel charge transfer processes. J Electroanal Chem 85:17–26

    CAS  Google Scholar 

  75. Nishihara C, Matsuda H (1979) Note on approximate equations of DC polarographic current–potential curves for electrode reactions coupled with a preceding chemical reaction. J Electroanal Chem 103:261–265

    CAS  Google Scholar 

  76. Nishihara C, Satô GP, Matsuda H (1975) A.C. polarography of the Nernstian charge transfer followed by an irreversible chemical reaction. J Electroanal Chem 63:131–138

    CAS  Google Scholar 

  77. O’Dea JJ, Osteryoung J, Osteryoung RA (1981) Theory of square wave voltammetry for kinetic systems. Anal Chem 53:695–701

    Google Scholar 

  78. O’Dea JJ, Wikiel K, Osteryoung J (1990) Square-wave voltammetry for ECE mechanism. J Phys Chem 94:3628–3636

    Google Scholar 

  79. Ohsaka T, Sotomura T, Matsuda H, Oyama N (1983) Double potential step chronoamperometry for reversible follow-up chemical reactions. Application to the aquation kinetics of bis(ethylenediaminemonoacetato)cobalt(II). Bull Chem Soc Jpn 56:3065–3072

    CAS  Google Scholar 

  80. Oldham KB (1986) Convolution: a general electrochemical procedure implemented by a universal algorithm. Anal Chem 58:2296–2300

    CAS  Google Scholar 

  81. Olmstead ML, Nicholson RS (1967) Theoretical evaluation of effects of electrode sphericity on stationary electrode polarography. Case of a chemical reaction following reversible electron transfer. J Electroanal Chem 14:133–141

    CAS  Google Scholar 

  82. Olmstead ML, Nicholson RS (1969) Cyclic voltammetry theory for the disproportionation reaction and spherical diffusion. Anal Chem 41:862–864

    CAS  Google Scholar 

  83. Olmstead ML, Hamilton RG, Nicholson RS (1969) Theory of cyclic voltammetry for a dimerization reaction initiated electrochemically. Anal Chem 41:260–267

    CAS  Google Scholar 

  84. O’Malley RE Jr (1974) Introduction to singular perturbations. Academic Press, New York

    Google Scholar 

  85. Polcyn DS, Shain I (1966) Theory of stationary electrode polarography for a multistep charge transfer with catalytic (cyclic) regeneration of the reactant. Anal Chem 38:376–382

    CAS  Google Scholar 

  86. Puy J, Salvador J, Galceran J, Esteban M, Díaz-Cruz JM, Mas F (1993) Voltammetry of labile metal-complex systems with induced reactant adsorption. Theoretical analysis for any ligand-to-metal ratio. J Electroanal Chem 360:1–25

    CAS  Google Scholar 

  87. Quentel F, Mirčeski V, L’Her M, Stankoska K (2012) Assisted ion transfer at organic film-modified electrodes. J Phys Chem C 116:22885–22892

    CAS  Google Scholar 

  88. Renault C, Andrieux CP, Tucker RT, Brett MJ, Balland V, Limoges B (2012) Unraveling the mechanism of catalytic reduction of O2 by microperoxidase-11 adsorbed within a transparent 3D-nanoporous ITO film. J Am Chem Soc 134:6834–6844

    CAS  Google Scholar 

  89. Roizenblat EM, Kosogov AA, Kolmanovich VYu (1989) Voltamperometry under conditions of limited diffusion. Irreversible process with a preceding chemical reaction. Elektrohim 25:201–207 (in Russian)

    CAS  Google Scholar 

  90. Rudolph M (1990) An algorithm of general application for the digital simulation of electrochemical processes. J Electroanal Chem 292:1–7

    CAS  Google Scholar 

  91. Ružić I, Smith DE, Feldberg SW (1974) 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 52:157–192

    Google Scholar 

  92. Sánchez Maestre M, Muñoz E, Avila JL, Camacho L (1992) Application of Matsuda’s pulse polarography theory to electrode processes coupled to very fast chemical reactions: study of the CE mechanism by differential pulse polarography. Electrochim Acta 37:1129–1134

    Google Scholar 

  93. Saveant JM (1967) ECE mechanisms as studied by polarography and linear sweep voltammetry. Electrochim Acta 12:753–766

    CAS  Google Scholar 

  94. Saveant JM (1967) Cyclic voltammetry with asymmetrical potential scan: a simple approach to mechanisms involving moderately fast chemical reactions. Electrochim Acta 12:999–1030

    CAS  Google Scholar 

  95. Savéant JM, Su KB (1984) Homogeneous redox catalysis of electrochemical reaction Part VI. Zone diagram representation of the kinetic regimes. J Electroanal Chem 171:341–349

    Google Scholar 

  96. Savéant JM, Su KB (1985) Homogeneous redox catalysis of multielectron electrochemical reactions. Part I. Competition between heterogeneous and homogeneous electron transfer. J Electroanal Chem 196:1–22

    Google Scholar 

  97. Savéant JM, Vianello E (1960) Recherches sur les courants catalytiques en polarographie–oscillographique á balayage linéaire de tension. Etude théorique. In: Advances in polarography. Pergamon Press, London, pp 367–374

    Google Scholar 

  98. Savéant JM, Vianello E (1963) Étude de la polarisation chimique en régime de variation linéaire du potentiel. Cas d’une désactivation spontanée, rapide et irréversible du produit de la réduction. CR Hebd Séances Acad Sci Paris 256:2597–2600

    Google Scholar 

  99. Savéant JM, Vianello E (1963) Potential-sweep chronoamperometry theory of kinetic currents in the case of a first order chemical reaction preceding the electron-transfer process. Electrochim Acta 8:905–923

    Google Scholar 

  100. Savéant JM, Vianello E (1964) Chronoampérométrie á variation linéaire de potentiel. Étude de la polarisation chimique dans le cas d’une désactivation rapide et spontanée du dépolarisant. CR Hebd Séances Acad Sci Paris 259:4017–4020

    Google Scholar 

  101. Savéant JM, Vianello E (1965) Potential-sweep chronoamperometry: kinetic currents for first-order chemical reaction parallel to electron-transfer process (catalytic currents). Electrochim Acta 10:905–920

    Google Scholar 

  102. Savéant JM, Vianello E (1967) Potential-sweep voltammetry: general theory of chemical polarization. Electrochim Acta 12:629–646

    Google Scholar 

  103. Savéant JM, Vianello E (1967) Potential-sweep voltammetry: theoretical analysis of monomerization and dimerization mechanisms. Electrochim Acta 12:1545–1561

    Google Scholar 

  104. Savéant JM, Xu F (1986) First- and second-order chemical–electrochemical mechanisms. Extraction of standard potential, equilibrium and rate constants from linear sweep voltammetric curves. J Electroanal Chem 208:197–217

    Google Scholar 

  105. Schwarz WM, Shain I (1966) A potential step–linear scan method for investigating chemical reactions initiated by a charge transfer. J Phys Chem 70:845–852

    CAS  Google Scholar 

  106. Shuman MS (1970) Calculation of stationary electrode polarograms for cases of reversible chemical reactions other than first-order reactions following a reversible charge transfer. Anal Chem 42:521–523

    CAS  Google Scholar 

  107. Shuman MS, Shain I (1969) Study of the chemical reaction preceding reduction of cadmium nitrilotriacetic acid complexes using stationary electrode polarography. Anal Chem 41:1818–1825

    CAS  Google Scholar 

  108. Singh RP, Singh T (2011) Effect of electrons involved in charge transfer reactions in ECE processes under linear sweep voltammetry: a theoretical model. Model Assist Stat Appl 6:261–266

    Google Scholar 

  109. Singh RP, Singh T, Dutt J, Atamjyot (2000) Mass transfer to tubular electrodes: ECE process. J Math Chem 27:183–190

    Google Scholar 

  110. Singh T, Dutt J, Kaur S (1991) Cyclic and linear sweep voltammetry at tubular electrodes. Part V. Kinetic processes. J Electroanal Chem 304:17–30

    CAS  Google Scholar 

  111. Singh T, Singh RP, Dutt J (1995) Mass transport to tubular electrodes. J Math Chem 17:335–346

    CAS  Google Scholar 

  112. Singh T, Singh RP, Dutt J (1998) Mass transport to tubular electrodes. Part 2: CE process. J Math Chem 23:297–308

    CAS  Google Scholar 

  113. Singh T, Singh RP, Dutt J (2000) Linear sweep voltammetry of irreversible charge transfer coupled with irreversible catalytic reaction under diffusion–convection control: An integral equation approach. Indian J Pure Appl Math 31:363–374

    Google Scholar 

  114. Smith DE (1963) Alternating current polarography of electrode processes with coupled homogeneous chemical reactions. I. Theory for systems with first-order preceding, following, and catalytic chemical reactions. Anal Chem 35:602–609

    CAS  Google Scholar 

  115. Smith DE (1964) Theory of the Faradaic impedance. Relationship between Faradaic impedances for various small amplitude alternating current techniques. Anal Chem 36:962–970

    CAS  Google Scholar 

  116. Sobel HR, Smith DE (1970) D.C. polarography: on the theory for the current–potential profile with an ECE mechanism. J Electroanal Chem 26:271–284

    CAS  Google Scholar 

  117. Stuart A, Foulkes F (1988) Study of ECE reactions with multiple parallel chemical steps using linear scan voltammetry. Electrochim Acta 33:1411–1424

    CAS  Google Scholar 

  118. Tachi I, Senda M (1960) Polarographic current of stepwise electrode process involving chemical reaction. In: Longmuir IS (ed) Advances in polarography, vol 2. Pergamon Press, Oxford, pp 454–464

    Google Scholar 

  119. Teja HS (2012) Mass transport of visco-elastic electrodes. Res Anal Eval 4:40–42

    Google Scholar 

  120. Tokuda K, Matsuda H (1979) Theory of A.C. voltammetry at a rotating disk electrode. Part III. Redox-electrode reactions coupled with first-order chemical reactions. J Electroanal Chem 95:147–157

    CAS  Google Scholar 

  121. Zakharov MS, Bakanov VI (1975) Voltammetry under conditions of semi-infinite spherical and cylindrical diffusion. Electrode process followed by a first order chemical reaction. Izv Tomsk Politekh Inst 197:30–33 (in Russian)

    Google Scholar 

  122. Zakharov MS, Pnev VV (1975) Voltammetry with an arbitrary current (electrode potential) form, under conditions of semi-infinite spherical and cylindrical diffusion. I. Electrode processes preceded by a first order chemical reaction. Tr Tyumen Ind Inst 32:3–11 (in Russian)

    Google Scholar 

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    Lesław K. Bieniasz

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Bieniasz, L.K. (2015). Models Involving Transport Coupled with Homogeneous Reactions. In: Modelling Electroanalytical Experiments by the Integral Equation Method. Monographs in Electrochemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44882-3_8

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