Abstract
General mathematical stability conditions described in chapter “Basic Principles of Nonlinear Dynamics” are applied to electrochemical systems. The stability analysis of such systems refers to the characteristics of the entire electric circuit, and not only to the working electrode–electrolyte interface. The decisive role of the negative differential resistance (NDR), either N-shaped (N-NDR) or S-shaped (S-NDR), in the current–potential characteristics of the electrochemical process, is shown. The sources of NDR in electrode processes are listed. The linear stability analysis of one-dimensional N-NDR system indicates that under potentiostatic conditions, the electric circuit has to possess an appropriate serial resistance to exhibit bistability, while under galvanostatic conditions bistability is directly recordable without additional external resistance. For the two-dimensional electrochemical system, the criteria are derived for the occurrence of oscillations in N-NDR systems under potentiostatic conditions and it is shown the impossibility of oscillations under galvanostatic control, the latter ones being possible for the systems with hidden N-NDR region (HN-NDR type). It is shown that in the N-NDR systems, the electrode potential is an autocatalytic variable (activator), while for the S-NDR system the electrode potential is a negative feedback variable (inhibitor). For the N-NDR systems, the experimental strategy of determination of the variables essential for the oscillatory behavior is outlined.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For the irreversible cathodic process the elements a 11 and a 22 would have the same signs, while a 21 and a 12 will have opposite signs, since the dc ox/dE and dk f/dE derivates have the signs opposite to those of dc red/dE and dk b/dE derivates in anodic process.
References
Gerischer H (1958) Passivität der Metalle. Angew Chem 10:285–298
Koper MTM, Sluyters JH (1993) On the mathematical unification of a class of electrochemical oscillators and their design procedures. J Electroanal Chem 352:51–64
Frumkin AN (1933) Wasserstoffüberspannung und Struktur der Doppelschicht. Z physik Chem 164A:121–133
Bard AJ, Faulkner L (2001) Electrochemical methods. Fundamentals and applications. Wiley, New York, pp 571–572
Śledziewski R (1978) Electronics for the physics students. PWN, Warsaw (in Polish), p 170
Feldberg SW (1969) Digital simulation: a general method for solving electrochemical diffusion-kinetic problems. In: Bard AJ, Rubinstein I (eds) Electroanalytical chemistry, vol 3. Dekker, New York, pp 199–296
Speiser B (1996) Numerical simulation of electroanalytical experiments: recent advances in methodology. In: Bard AJ, Rubinstein I (eds) Electroanalytical chemistry, vol 19. Dekker, New York, pp 1–108
Britz D (2005) Digital simulation in electrochemistry, 3rd edn. Springer, Berlin
Koper MTM, Sluyters JH (1991) Electrochemical oscillators: their description through a mathematical model. J Electroanal Chem 303:73–94
Krischer K (1999) Principles of temporal and spatial pattern formation in electrochemical systems. In: Conway BE et al (eds) Modern aspects of electrochemistry, vol 32. Kluwer, New York
Koper MTM (1992) The theory of electrochemical instabilities. Electrochim Acta 37:1771–1778
Krischer K (2001) Spontaneous formation of spatiotemporal patterns at the electrode|electrolyte interface. J Electroanal Chem 501:1–21
Krischer K, Mazouz N, Flätgen G (2000) Pattern formation in globally coupled electrochemical systems with an S-shaped current–potential curve. J Phys Chem B 104:7545–7553
Mazouz N, Krischer K (2000) A theoretical study on turing patterns in electrochemical systems. J Phys Chem 104:6081–6090
Epelboin I, Ksouri M, Lejay E, Wiart R (1975) A study of the elementary steps of electron-transfer during the electrocrystallization of zinc. Electrochim Acta 20:603–605
Kiss IZ, Kazsu Z, Gáspár V (2005) Experimental strategy for characterization of essential dynamical variables in oscillatory systems: effect of double-layer capacitance on the stability of electrochemical oscillators. J Phys Chem A 109:9521–9527
Clarke BL (1980) Stability of complex reaction networks. Adv Chem Phys 42:1–213
Stephanopoulos G (1984) Chemical process control: an introduction to theory and practice. Prentice Hall, Englewood Cliffs, NJ
Lee MG, Jorné J (1992) On the kinetic mechanism of zinc electrodeposition in the region of negative polarization resistance. J Electrochem Soc 139:2841–2844
Burger M, Körös E (1980) Conditions for the onset of chemical oscillation. J Phys Chem 84:496–500
Ruoff E (1992) Introducing temperature-compensation in any reaction kinetic oscillator model. J Interdiscip Cycle Res 23:92–99
Ruoff P, Loros JJ, Dunlap JC (2005) The relationship between FRQ-protein stability and temperature compensation in the Neurospora circadian clock. Proc Natl Acad Sci USA 102:17681–17686
Nagao R, Epstein IR, Gonzalez ER, Varela H (2008) Temperature (over)compensation in an oscillatory surface reaction. J Phys Chem A 112:4617–4624
Carbonio EA, Nagao R, Gonzalez ER, Varela H (2009) Temperature effects on the oscillatory electro-oxidation of methanol on platinum. Phys Chem Chem Phys 11:665–670
Zhang JX, Datta R (2002) Sustained potential oscillations in proton exchange membrane fuel cells with PtRu as anode catalyst. J Electrochem Soc 149:A1423–A1431
Kiss IZ, Pelster LN, Wickramasinghe M, Yablonsky GS (2009) Frequency of negative differential resistance electrochemical oscillators: theory and experiments. Phys Chem Chem Phys 11:5720–5728
Strogatz SH (1994) Nonlinear dynamics and chaos. Perseus, Reading, MA
Koper MTM, Gaspard P (1992) The modeling of mixed-mode and chaotic oscillations in electrochemical systems. J Chem Phys 96:7797–7813
Yablonsky GS, Mareels IMY, Lazman M (2003) The principle of critical simplification in chemical kinetics. Chem Eng Sci 58:4833–4842
Kiss IZ, Sitta E, Varela H (2012) On the limit of frequency of electrochemical oscillators and its relationship to kinetic parameters. J Phys Chem C 116:9561–9567
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Orlik, M. (2012). Stability of Electrochemical Systems. In: Self-Organization in Electrochemical Systems I. Monographs in Electrochemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27673-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-27673-6_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27672-9
Online ISBN: 978-3-642-27673-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)