Skip to main content
SpringerLink
Log in
Book cover

Modelling Electroanalytical Experiments by the Integral Equation Method pp 9–47Cite as

Basic Assumptions and Equations of Electroanalytical Models

  • Chapter
  • First Online:

  • 857 Accesses

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

Abstract

Electrochemical systems are generally multiphase and multicomponent systems. The various chemical species can be distributed in spatially extended phases, or localised at interfaces (for example adsorbed). The distributed species are subject to transport phenomena and homogeneous reactions. The transport is most often described by diffusion partial differential equations, but convection-diffusion equations are also in frequent use, in particular in models of dropping mercury electrodes, rotating disk electrodes, or channel and tubular electrodes. The kinetics of homogeneous reactions affect the transport equations. Anomalous diffusion transport is also known. All species may participate in heterogeneous reactions at interfaces, in particular in charge transfer reactions. The kinetics of heterogeneous reactions determine boundary conditions at the interface studied. All reactions influence the initial conditions. The dimensionality of spatial domains depends on the symmetry and coordinate systems most suitable for mathematical description. Spatial domains can be infinite, semi-infinite, or finite. Additional effects considered in electroanalytical models are the uncompensated Ohmic potential drop and double layer charging.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Albery J (1975) Electrode kinetics. Clarendon Press, Oxford

    Google Scholar 

  2. Alexiadis A, Cornell A, Dudukovic MP (2012) Comparison between CFD calculations of the flow in a rotating disk cell and the Cochran/Levich equations. J Electroanal Chem 669:55–66

    CAS  Google Scholar 

  3. Alkire RC (1985) Transport processes in electrochemical systems. Chem Eng Commun 38:401–413

    CAS  Google Scholar 

  4. Alpatova NM, Krishtalik LI, Pleskov YuV (1987) Electrochemistry of solvated electrons. Top Curr Chem 138:149–219

    CAS  Google Scholar 

  5. Amatore C (1995) Electrochemistry at ultramicroelectrodes. In: Rubinstein I (ed) Physical electrochemistry, principles, methods, and applications. Dekker, New York, pp 131–208

    Google Scholar 

  6. Andrieux CP (1994) Terminology and notations for multistep electrochemical reaction mechanisms (IUPAC Recommendations 1994). Pure Appl Chem 66:2445–2450

    CAS  Google Scholar 

  7. Aoki K (1993) Theory of ultramicroelectrodes. Electroanalysis 5:627–639

    CAS  Google Scholar 

  8. Aris R (1965) Prolegomena to the rational analysis of systems of chemical reactions. Arch Ration Mech Anal 19:81–99

    Google Scholar 

  9. Bagotsky VS (2006) Fundamentals of electrochemistry. Wiley-Interscience, Hoboken

    Google Scholar 

  10. Bard AJ, Faulkner LR (2001) Electrochemical methods, fundamentals and applications. Wiley, New York

    Google Scholar 

  11. Baronas R, Ivanauskas F, Kulys J (2010) Mathematical modeling of biosensors. An introduction for chemists and mathematicians. Springer, Dordrecht

    Google Scholar 

  12. Bieniasz LK (1996) Automatic derivation of the governing equations that describe a transient electrochemical experiment, given a reaction mechanism of arbitrary complexity. Part 1. Problem parameters and initial conditions. J Electroanal Chem 406:33–43

    Google Scholar 

  13. Bieniasz LK (1996) Automatic derivation of the governing equations that describe a transient electrochemical experiment, given a reaction mechanism of arbitrary complexity. Part 2. Governing equations in one-dimensional geometry. J Electroanal Chem 406:45–52

    Google Scholar 

  14. Bieniasz LK (1996) A reaction compiler for electrochemical kinetics. Comput Chem 20:403–418

    CAS  Google Scholar 

  15. Bieniasz LK (2012) A procedure for rapid and highly accurate computation of Marcus–Hush–Chidsey rate constants. J Electroanal Chem 683:112–118

    CAS  Google Scholar 

  16. Blum EH, Luus R (1964) Thermodynamic consistency of reaction rate expressions. Chem Eng Sci 19:322–323

    CAS  Google Scholar 

  17. Bond AM (1994) Past, present and future contributions of microelectrodes to analytical studies employing voltammetric detection. A review. Analyst 119:R1–R21

    CAS  Google Scholar 

  18. Boudart M (1968) Kinetics of chemical processes. Prentice–Hall, Englewood Cliffs

    Google Scholar 

  19. Britz D (1978) iR elimination in electrochemical cells. J Electroanal Chem 88:309–352

    CAS  Google Scholar 

  20. Britz D, Kastening B (1974) On the electrochemical observation of a second-order decay of radicals generated by flash photolysis or pulse radiolysis. J Electroanal Chem 56:73–90

    CAS  Google Scholar 

  21. Britz D, Strutwolf J (2014) Digital simulation of electrochemistry at microelectrodes. In: Lei KF (ed) Microelectrodes: techniques, structures for biosensing and potential applications. Nova Science Publishers, Hauppauge, pp 1–85

    Google Scholar 

  22. Cattey H, Audebert P, Sanchez C, Hapiot P (1997) Electrochemical investigations on the sol–gel polymerization of transition-metal alkoxides. J Mater Chem 7:1461–1466

    CAS  Google Scholar 

  23. Cattey H, Audebert P, Sanchez C, Hapiot P (1998) Electrochemical investigations on liquid-state polymerizing systems: case of sol–gel polymerization of transition-metal alkoxides. J Phys Chem B 102:1193–1202

    CAS  Google Scholar 

  24. Chidsey CED (1991) Free energy and temperature dependence of electron transfer at the metal–electrolyte interface. Science 251:919–922

    CAS  Google Scholar 

  25. Cochran WG (1934) The flow due to a rotating disc. Proc Camb Philos Soc 30:365–375

    Google Scholar 

  26. Compton RG, Unwin PR (1986) Channel and tubular electrodes. J Electroanal Chem 205:1–20

    CAS  Google Scholar 

  27. Cooper JA, Compton RG (1998) Channel electrodes—A review. Electroanalysis 10:141–155

    CAS  Google Scholar 

  28. Cooper JA, Alden JA, Oyama M, Compton RG, Okazaki S (1998) Channel electrode voltammetry: the kinetics of the complexation of the chloranil radical anion with M2+ ions by waveshape analysis. J Electroanal Chem 442:201–206

    CAS  Google Scholar 

  29. Corio PL (1989) Theory of reaction mechanisms. Top Curr Chem 150:249–283

    CAS  Google Scholar 

  30. Cottrell FG (1903) Der Reststrom bei galvanischer Polarisation, betrachtet als ein Diffusionsproblem. Z Phys Chem 42:385–431

    Google Scholar 

  31. Damaskin BB, Petrii OA, Batrakov W (1975) Adsorption organischer Verbindungen an Elektroden. Akademie, Berlin

    Google Scholar 

  32. Delahay P (1954) New instrumental methods in electrochemistry. Theory, instrumentation, and applications to analytical and physical chemistry. Interscience, New York

    Google Scholar 

  33. Delahay P (1965) Double layer and electrode kinetics. Interscience, New York

    Google Scholar 

  34. Eklund JC, Bond AM, Alden JA, Compton RG (1999) Perspectives in modern voltammetry: basic concepts and mechanistic analysis. Adv Phys Org Chem 32:1–120

    CAS  Google Scholar 

  35. Everett DH (1959) An introduction to the study of chemical thermodynamics. Longmans, London

    Google Scholar 

  36. Fleischmann M, Pons S, Rolison DR, Schmidt PP (1987) Ultramicroelectrodes. Datatech Systems, Morganton

    Google Scholar 

  37. Forster RJ (1994) Microelectrodes: new dimensions in electrochemistry. Chem Soc Rev 23:289–297

    CAS  Google Scholar 

  38. Fujihira M, Rubinstein I, Rusling JF (eds) (2007) Modified electrodes. In: Bard AJ, Stratmann M (eds) Encyclopedia of electrochemistry, vol 10. Wiley-VCH, Weinheim.

    Google Scholar 

  39. Galus Z (1994) Fundamentals of electrochemical analysis. Ellis Horwood, Chichester

    Google Scholar 

  40. Gileadi E (1993) Electrode kinetics for chemists, chemical engineers and materials’ scientists. Wiley-VCH, New York

    Google Scholar 

  41. Gileadi E, Conway BAE (1964) The behaviour of intermediates in electrochemical catalysis. Mod Asp Electrochem 3:347–443

    Google Scholar 

  42. Girault HH (1993) Charge transfer across liquid–liquid interfaces. Mod Asp Electrochem 25:1–62

    CAS  Google Scholar 

  43. Girault HH (2010) Electrochemistry at liquid–liquid interfaces. Electroanal Chem 23:1–104

    CAS  Google Scholar 

  44. Gmucová K (2012) A review of non-Cottrellian diffusion towards micro- and nano-structured electrodes. In: Shao Y (ed) Electrochemical cells—new advances in fundamental researches and applications. http://www.intechopen.com. Accessed 10 June 2014

  45. Go JY, Pyun SI (2007) A review of anomalous diffusion phenomena at fractal interface for diffusion-controlled and non-diffusion-controlled transfer processes. J Solid State Electrochem 11:323–334

    CAS  Google Scholar 

  46. Gosser DK Jr (1993) Cyclic voltammetry. Simulation and analysis of reaction mechanisms. Wiley-VCH, New York

    Google Scholar 

  47. Gregory DP, Riddiford AC (1956) Transport to the surface of a rotating disc. J Chem Soc Lond 3:3756–3764

    Google Scholar 

  48. Gründler P, Kirbs A, Dunsch L (2009) Modern thermoelectrochemistry. Chem Phys Chem 10:1722–1746

    Google Scholar 

  49. Hammerich O (2000) Methods for studies of electrochemical reactions. In: Lund H, Hammerich O (eds) Organic electrochemistry. Marcel Dekker, New York, pp 95–182

    Google Scholar 

  50. Hampson NA, McNeil AJS (1984) The electrochemistry of porous electrodes: flow-through and three-phase electrodes. In: Pletcher D (ed) Specialist periodical reports. Electrochemistry, vol. 9. RSC, London, pp 1–65

    Google Scholar 

  51. Heinze J (1993) Ultramicroelectrodes in electrochemistry. Angew Chem Int Ed Engl 22:1268–1288

    Google Scholar 

  52. Henstridge MC, Laborda E, Rees NV, Compton RG (2012) Marcus–Hush–Chidsey theory of electron transfer applied to voltammetry: A review. Electrochim Acta 84:12–20

    CAS  Google Scholar 

  53. Hernández-Labrado GR, Collazos-Castro JE, Polo JL (2008) Digital simulations to solve electrochemical processes involving a diffusion coefficient varying linearly with the concentration. J Electroanal Chem 615:62–68

    Google Scholar 

  54. Hubbard AT (1969) Study of the kinetics of electrochemical reactions by thin-layer voltammetry. J Electroanal Chem 22:165–174

    CAS  Google Scholar 

  55. Hubbard AT, Anson FC (1970) The theory and practice of electrochemistry with thin layer cells. Electroanal Chem 4:129–214

    CAS  Google Scholar 

  56. Hush NS (1968) Homogeneous and heterogeneous optical and thermal electron transfer. Electrochim Acta 13:1005–1023

    CAS  Google Scholar 

  57. Ibl N (1983) Fundamentals of transport phenomena in electrolytic systems. In: Yeager E, Bockris J O’M, Conway BAE, Sarangapani S (eds) Comprehensive Treatise of Electrochemistry, vol. 6, Electrodics: Transport. Plenum Press, New York, pp 1–63

    Google Scholar 

  58. Ilkovič D (1938) Sur la valeur des courants de diffusion observés dans l’électrolyse a l’aide de l’électrode a gouttes de mercure. Étude polarographique. J Chim Phys 35:129–135

    Google Scholar 

  59. International Union of Pure and Applied Chemistry, Analytical Chemistry Division, Commission on Electroanalytical Chemistry (1976) Classification and nomenclature of electroanalytical techniques. Pure Appl Chem 45:81–97

    Google Scholar 

  60. International Union of Pure and Applied Chemistry, Analytical Chemistry Division, Commission on Electroanalytical Chemistry (1976) Recommendations for sign conventions and plotting of electrochemical data. Pure Appl Chem 45:131–134

    Google Scholar 

  61. Jain RK, Gaur HC, Welch BJ (1977) Chronopotentiometry: a review of theoretical principles. J Electroanal Chem 79:211–236

    CAS  Google Scholar 

  62. Johnson KA, Goody RS (2011) The original Michaelis constant: translation of the 1913 Michaelis–Menten paper. Biochem 50:8264–8269

    CAS  Google Scholar 

  63. Koper MTM, Lebedeva NP, Hermse CGM (2002) Dynamics of CO at the solid/liquid interface studied by modeling and simulation of CO electro-oxidation on Pt and PtRu electrodes. Faraday Discuss 121:301–311

    CAS  Google Scholar 

  64. Kortüm G (1965) Treatise on electrochemistry. Elsevier, Amsterdam

    Google Scholar 

  65. Laviron E (1978) Theory of regeneration mechanims in thin layer potential sweep voltammetry. J Organomet Chem 87:31–37

    CAS  Google Scholar 

  66. Leskovac V (2003) Comprehensive enzyme kinetics. Kluwer/Plenum, New York

    Google Scholar 

  67. Lévêque MA (1928) Les lois de la transmission de chaleur par convection, Chapitre V. Résolution théorique de quelques problèmes simples. Ann Mines Mem Ser 12, 13: 237–304

    Google Scholar 

  68. Levich VG (1962) Physicochemical Hydrodynamics. Prentice–Hall, Englewood Cliffs

    Google Scholar 

  69. Ludwig K, Speiser B (2004) EChem++—An object-oriented problem solving environment for electrochemistry. 2. The kinetic facilities of Ecco—a compiler for (electro-)chemistry. J Chem Inf Comput Sci 44:2051–2060

    CAS  Google Scholar 

  70. Luo W, Feldberg SW, Rudolph M (1994) Ensuring self-consistent assignment of thermodynamic parameters in simulations of electrochemical-chemical systems. J Electroanal Chem 368:109–113

    CAS  Google Scholar 

  71. Macdonald DD (1977) Transient techniques in electrochemistry. Plenum, New York

    Google Scholar 

  72. Macpherson JV, Simjee N, Unwin PR (2001) Hydrodynamic ultramicroelectrodes: kinetic and analytical applications. Electrochim Acta 47:29–45

    CAS  Google Scholar 

  73. Marangoni AG (2003) Enzyme kinetics. A modern approach. Wiley, Hoboken

    Google Scholar 

  74. Marcus RA (1964) Chemical and electrochemical electron-transfer theory. Ann Rev Phys Chem 15:155–196

    CAS  Google Scholar 

  75. Marcus RA (1993) Electron transfer reactions in chemistry: theory and experiment (Nobel lecture). Angew Chem Int Ed Engl 32:1111–1121

    Google Scholar 

  76. Migliore A, Nitzan A (2012) On the evaluation of the Marcus–Hush–Chidsey integral. J Electroanal Chem 671:99–101

    CAS  Google Scholar 

  77. Mikkelsen Ø, Schrøder KH (2003) Amalgam electrodes for electroanalysis. Electroanalysis 15:679–687

    CAS  Google Scholar 

  78. Mirčeski V, Komorsky-Lovrić Š, Lovrić M (2007) Square-wave voltammetry, theory and application. Springer, Berlin

    Google Scholar 

  79. Mount AR (2003) Hydrodynamic electrodes. In: Bard AJ, Stratmann M (eds) Encyclopedia of electrochemistry, vol. 3, Instrumentation and electroanalytical chemistry. Wiley-VCH, Weinheim, pp 134–159

    Google Scholar 

  80. Nernst W (1888) Zur Kinetik der in Lösung befindlichen Körper. I. Theorie der Diffusion. Z Phys Chem 2:613–637

    Google Scholar 

  81. Nernst W (1889) Die elektromotorische Wirksamkeit der Jonen. Z Phys Chem 4:129–181

    Google Scholar 

  82. Newman JS (1973) Electrochemical systems. Prentice–Hall, Englewood Cliffs

    Google Scholar 

  83. Nyikos L, Pajkossy T (1986) Diffusion to fractal surfaces. Electrochim Acta 31:1347–1350

    CAS  Google Scholar 

  84. Nyikos L, Pajkossy T, Borosy AP, Martemyanov SA (1990) Diffusion to fractal surfaces—IV. The case of the rotating disc electrode of fractal surface. Electrochim Acta 35:1423–1424

    CAS  Google Scholar 

  85. Oldham KB, Myland JC (2011) On the evaluation and analysis of the Marcus–Hush–Chidsey integral. J Electroanal Chem 655:65–72

    CAS  Google Scholar 

  86. Opekar F, Beran P (1976) Rotating disk electrodes. J Electroanal Chem 69:1–105

    CAS  Google Scholar 

  87. Pajkossy T (1991) Electrochemistry at fractal surfaces. J Electroanal Chem 300:1–11

    CAS  Google Scholar 

  88. Pajkossy T, Nyikos L (1989) Diffusion to fractal surfaces—II. Verification of theory. Electrochim Acta 34:171–179

    CAS  Google Scholar 

  89. Pajkossy T, Nyikos L (1989) Diffusion to fractal surfaces—III. Linear sweep and cyclic voltammograms. Electrochim Acta 34:181–186

    CAS  Google Scholar 

  90. Pajkossy T, Borosy AP, Imre A, Martemyanov SA, Nagy G, Schiller R, Nyikos L (1994) Diffusion kinetics at fractal electrodes. J Electroanal Chem 366:69–73

    CAS  Google Scholar 

  91. Parsons R (1964) The description of adsorption at electrodes. J Electroanal Chem 7:136–152

    CAS  Google Scholar 

  92. Parsons R (1974) Manual of symbols and terminology for physicochemical quantities and units. Appendix III Electrochemical nomenclature. Pure Appl Chem 37:499–516

    CAS  Google Scholar 

  93. Parsons R (1979) Electrode reaction orders, transfer coefficients and rate constants. Amplification of definitions and recommendations for publication of parameters. Pure Appl Chem 52:233–240

    Google Scholar 

  94. Parsons R (1990) Electrical double layer: recent experimental and theoretical developments. Chem Rev 90:813–826

    CAS  Google Scholar 

  95. Planck M (1890) Ueber die Erregung von Electricität und Wärme in Electrolyten. Ann Phys Chem NF 39:161–186

    Google Scholar 

  96. Planck M (1890) Ueber die Potentialdifferenz zwischen zwei verdünnten Lösungen binärer Electrolyte. Ann Phys Chem NF 40:561–576

    Google Scholar 

  97. Pound BC (1993) Electrochemical techniques to study hydrogen ingress in metals. Mod Asp Electrochem, 25:63–133

    CAS  Google Scholar 

  98. Puy J, Mas F, Díaz-Cruz JM, Esteban M, Casassas E (1992) Induced reactant adsorption in normal pulse polarography of labile metal+polyelectrolyte systems. Part 2. Study of the current–potential relationship assuming potential-dependent adsorption parameters. J Electroanal Chem 328:271–285

    CAS  Google Scholar 

  99. Rajendran L (2013) Mathematical modeling in microelectrodes. In: Brennan CR (ed) Mathematical modelling. Nova Science Publishers, Hauppauge, pp 1–110

    Google Scholar 

  100. Reder C (1988) Metabolic control theory: a structural approach. J Theor Biol 135:175–201

    CAS  Google Scholar 

  101. Rees NV, Compton RG (2008) Hydrodynamic microelectrode voltammetry. Russ J Electrochem 44:368–389

    CAS  Google Scholar 

  102. Reinert KE, Berg H (1962) Theorie der polarographischen Verfolgung schneller chemischer Reaktionen in Lösung mittels reaktionsbedingter Diffusionsstrom–Zeit–Kurven

    Google Scholar 

  103. Reymond F, Fermin D, Lee HJ, Girault HH (2000) Electrochemistry at liquid | liquid interfaces: methodology and potential applications. Electrochim Acta 45:2647–2662

    CAS  Google Scholar 

  104. Ritchie M (1966) Chemical kinetics in homogeneous systems. Oliver & Boyd, Edinburgh

    Google Scholar 

  105. Samec Z (2004) Electrochemistry at the interface between two immiscible electrolyte solutions (IUPAC technical report). Pure Appl Chem 76:2147–2180

    CAS  Google Scholar 

  106. Samec Z, Langmaier J, Trojánek A (1996) Evaluation of parasitic elements contributing to experimental cell impedance: Impedance measurements at interfaces between two immiscible electrolyte solutions. J Chem Soc Faraday Trans 92:3843–3849

    CAS  Google Scholar 

  107. Sanecki PT, Skitał PM (2012) Mathematical modeling of electrode processes—potential dependent transfer coefficient in electrochemical kinetics. http://www.intechopen.com. Accessed 10 June 2014

  108. Sauro HM, Ingalls B (2004) Conservation analysis in biochemical networks: computational issues for software writers. Biophys Chem 109:1–15

    CAS  Google Scholar 

  109. Schmickler W (1996) Electronic effects in the electric double layer. Chem Rev 96:3177–3200

    CAS  Google Scholar 

  110. Scott K, Sun YP (1995) Simulation and reaction engineering of electrochemical gas/liquid reactions. Electrochim Acta 40:423–431

    CAS  Google Scholar 

  111. Sequeira CAC, Santos DMF (2010) Mass transfer to microelectrodes and arrays. Z Phys Chem 224:1297–1336

    CAS  Google Scholar 

  112. Shi Y, Cai N, Li C (2007) Numerical modeling of an anode-supported SOFC button cell considering anodic surface diffusion. J Power Sources 164:639–648

    CAS  Google Scholar 

  113. Speiser B (1999) From cyclic voltammetry to scanning electrochemical microscopy: modern electroanalytical methods to study organic compounds, materials, and reactions. Curr Org Chem 3:171–191

    CAS  Google Scholar 

  114. Strathmann H (2011) Introduction to membrane science and technology. Wiley-VCH, Weinheim

    Google Scholar 

  115. Strathmann H, Giorno L, Drioli E (2006) An introduction to membrane science and technology. Institute on Membrane Technology, Rende

    Google Scholar 

  116. Stutter E (1974) Zur photopolarographischen Untersuchung schneller, der Durchtrittsreaktion parallelgelagerter Reaktionen zweiter Ordnung. J Electroanal Chem 50:315–321

    CAS  Google Scholar 

  117. Su L, Wu BL (2004) Investigation of surface diffusion and recombination reaction kinetics of H-adatoms in the process of the hydrogen evolution reaction (her) at Au electrodes. J Electroanal Chem 565:1–6

    CAS  Google Scholar 

  118. Tansel T, Magnussen OM (2006) Video STM studies of adsorbate diffusion at electrochemical interfaces. Phys Rev Lett 96:026101:1–4

    Google Scholar 

  119. Tokuda K, Matsuda H (1977) Theory of A.C. voltammetry at a rotating disk electrode. Part I. A Reversible electrode process. J Electroanal Chem 82:157–171

    CAS  Google Scholar 

  120. Volgin VM, Davydov AD (2012) Mass-transfer problems in the electrochemical systems. Russ J Electrochem 48:565–569

    CAS  Google Scholar 

  121. Vydra F, Štulik K, Juláková (1976) Electrochemical stripping analysis. Ellis Horwood, Coll House

    Google Scholar 

  122. Walcarius A (2010) Template-directed porous electrodes in electroanalysis. Anal Bioanal Chem 396:261–272

    CAS  Google Scholar 

  123. Wang J (1985) Stripping analysis, principles, instrumentation, and applications. Wiley-VCH, Deerfield Beach

    Google Scholar 

  124. Wildgoose GG, Giovanelli D, Lawrence NS, Compton RG (2004) High-temperature electrochemistry: A review. Electroanalysis 16:421–433

    CAS  Google Scholar 

  125. Wopschall RH, Shain I (1967) Effects of adsorption of electroactive species in stationary electrode polarography. Anal Chem 39:1514–1527

    CAS  Google Scholar 

  126. Zutshi K (2006) Introduction to polarography and allied techniques. New Age International Publishers, New Delhi

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Cracow University of Technology, Cracow, Poland

    Lesław K. Bieniasz

Authors
  1. Lesław K. Bieniasz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bieniasz, L.K. (2015). Basic Assumptions and Equations of Electroanalytical Models. 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_2

Download citation

Publish with us

Policies and ethics

Search

Navigation