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Experimental and Model Spatiotemporal and Spatial Patterns in Electrochemical Systems

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Self-Organization in Electrochemical Systems II

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Abstract

Simple examples of pattern formation in electrochemistry, including progress of active zone along the passivated iron wire, mimicking the conduction of the impulse along the neuron, and spiral waves of codeposited Ag–Sb alloy are invoked as the introduction. Following theory of dissipative spatiotemporal and spatial patterns in the reaction–migration electrochemical systems, outlined in Sect. 1.2 and briefly reminded here, representative experimental examples of such phenomena are collected. These examples illustrate the effects of interaction of the N-NDR and S-NDR characteristics with the migration (nonlocal) and global couplings, leading to, e.g., accelerated fronts of electrode potential, rotating waves, stationary Turing patterns, and more complex regimes. Described systems include electroreduction of peroxodisulfate ions on Ag electrodes; anodic dissolution of Co and Ni electrodes; anodic oxidation of H2, CO, HCOOH on Pt electrodes; and electroreduction of IO 4 ions on Au in the presence of an adsorbed inhibitor. Turing patterns emerge for CO electrooxidation and IO 4 reduction. Furthermore, dendritic (and similar) patterns during electrodeposition of metals on both solid electrodes and at liquid/liquid interfaces are described, including the effect of magnetic field on the morphology of such patterns. In addition to traditional understanding of dendrite formation, based on diffusion schemes (the diffusion-limited aggregation approach), their occurrence in correlation with oscillatory phenomena is described. Also, the formation of dendrite patterns during the anodization of single crystal Si electrodes in fluoride media is mentioned. Experimental studies, involving both classical electrochemical methods and modern techniques of surface analysis, are compared with theoretical modelings of respective phenomena.

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Notes

  1. 1.

    An extension of the Turing model for the case when the system’s size affects the pattern formation, was described by Murray [9].

References

  1. Flätgen G, Krischer K, Pettinger P, Doblhofer K, Junkes H, Ertl G (1995) Two-dimensional imaging of potential waves in electrochemical systems by surface plasmon microscopy. Science 269:668–671

    Article  Google Scholar 

  2. Bonhoeffer KF (1948) Activation of passive iron as a model for the excitation of nerve. J Gen Physiol 32:69–91

    Article  CAS  Google Scholar 

  3. Heatcote HL (1902) Z physik Chem 37:368

    Google Scholar 

  4. Heatcote HL (1907) J Chem Soc Ind 26:899

    Article  Google Scholar 

  5. Lillie RS (1918) Science 48:51

    Article  CAS  Google Scholar 

  6. Lillie RS (1930) J Gen Physiol 14:344

    Google Scholar 

  7. Lillie RS (1936) Biol Rev Camb Philos Soc 16:216

    Google Scholar 

  8. Murray JD (2002) Mathematical biology. I. An introduction, 3rd edn. Springer, New York, NY

    Google Scholar 

  9. Murray JD (2003) Mathematical biology. II. Spatial models and biomedical applications, 3rd edn. Springer, New York, NY

    Google Scholar 

  10. Franck UF (1989) Periodische Strukturen und Vorgänge in gleichgewichtsfernen physikalisch-chemischen Systemen. Nova Acta Leopoldina NF 60:109–131

    CAS  Google Scholar 

  11. Nakabayashi S, Baba R (1998) Spatiotemporal propagation of a non-linear electrochemical reaction over an iron electrode. Chem Phys Lett 287:632–638

    Article  CAS  Google Scholar 

  12. Baba R, Shiomi Y, Nakabayashi S (2000) Spatiotemporal reaction propagation of electrochemically controlled non-linear iron current oscillator. Chem Eng Sci 55:217–222

    Article  CAS  Google Scholar 

  13. Agladze K, Steinbock O (2000) Waves and vortices of rust on the surface of corroding steel. J Phys Chem A 104:9816–9819

    Article  CAS  Google Scholar 

  14. Agladze K, Thouvenel-Romans S, Steinbock O (2001) Electrochemical waves on patterned surfaces: propagation through narrow gaps and channels. J Phys Chem A 105:7356–7363

    Article  CAS  Google Scholar 

  15. Hudson JL, Tabora J, Krischer K, Kevrekidis IG (1993) Spatiotemporal period doubling during the electrodissolution of iron. Phys Lett A 179:355–363

    Article  CAS  Google Scholar 

  16. Koper MTM, Sluyters JH (1993) A simplified approach to the modeling of wave propagation at electrode/electrolyte interfaces. Electrochim Acta 38:1535–1544

    Article  CAS  Google Scholar 

  17. Kristev I, Nikolova M, Nakada I (1989) Spiral structures in electrodeposited silver-antimony alloys. Electrochim Acta 34:1219–1223

    Article  Google Scholar 

  18. Gladyshev VP, Kovaleva SV (1997) Autooscillatory processes and surface periodic patterns, emerging at anodic oxidation of amalgams of alkaline metals. Zh Obshch Khim 67:1743, in Rusian

    Google Scholar 

  19. Krischer K (2001) Spontaneous formation of spatiotemporal patterns at the electrode– electrolyte interface. J Electroanal Chem 501:1–21

    Article  CAS  Google Scholar 

  20. Krischer K (1999) Principles of temporal and spatial pattern formation in electrochemical systems. In: Conway BE, Bockris JO’M, White R (eds) Modern aspects of electrochemistry. Plenum, New York, NY

    Google Scholar 

  21. Krischer K (2003) Nonlinear dynamics in electrochemical systems. In: Alkire RC, Kolb DM (eds) Advances in electrochemical science and engineering. Wiley-VCH, Weinheim

    Google Scholar 

  22. Flätgen G, Krischer K (1995) Accelerating fronts in an electrochemical system due to global coupling. Phys Rev E 51:3997–4004

    Article  Google Scholar 

  23. Flätgen G, Krischer K, Ertl G (1996) Spatio-temporal pattern formation during the reduction of peroxodisulfate in the bistable and oscillatory regime: a surface plasmon microscopy study. J Electroanal Chem 409:183–194

    Article  Google Scholar 

  24. Grauel P, Christoph J, Flätgen G, Krischer K (1998) Stationary potential patterns during the reduction of peroxodisulfate at Ag ring electrodes. J Phys Chem B 102:10264–10271

    Article  CAS  Google Scholar 

  25. Otterstedt R, Plath PJ, Jaeger NI, Sayer JC, Hudson JL (1996) Accelerating fronts during the electrodissolution of cobalt. Chem Eng Sci 51:1747–1756

    Article  CAS  Google Scholar 

  26. Otterstedt R, Plath PJ, Jaeger NI, Hudson JL (1996) Modulated electrochemical waves. Phys Rev E 54:3744–3751

    Article  CAS  Google Scholar 

  27. Otterstedt RD, Plath PJ, Jaeger NI, Hudson JL (1996) Rotating waves on disk and ring electrodes. J Chem Soc Faraday Trans 92:2933–2939

    Article  CAS  Google Scholar 

  28. Lev O, Sheintuch M, Pismen LM, Yarnitzky Ch (1988) Standing and propagating wave oscillations in the anodic dissolution of nickel. Nature 336:458–459

    Article  CAS  Google Scholar 

  29. Lev O, Sheintuch M, Yarnitsky H, Pismen LM (1990) Spatial current distribution during nickel anodic dissolution in sulfuric acid. Chem Eng Sci 45:839–847

    Article  CAS  Google Scholar 

  30. Haim D, Lev O, Pismen LM, Sheintuch M (1992) Modelling spatiotemporal patterns in anodic nickel dissolution. Chem Eng Sci 47:3907–3913

    Article  CAS  Google Scholar 

  31. Bîrzu A, Green BJ, Otterstedt RD, Jaeger NI, Hudson JL (2000) Modeling of spatiotemporal patterns during metal electrodissolution in a cell with a point reference electrode. Phys Chem Chem Phys 2:2715–2724

    Article  Google Scholar 

  32. Bîrzu A, Green BJ, Jaeger NI, Hudson JL (2001) Spatiotemporal patterns during electrodissolution of a metal ring: three-dimensional simulations. J Electroanal Chem 504:126–136

    Article  Google Scholar 

  33. Jaeger NI, Otterstedt RD, Bîrzu A, Green BJ, Hudson JL (2002) Evolution of spatiotemporal patterns during the electrodissolution of metals: experiments and simulations. Chaos 12:231–239

    Article  CAS  Google Scholar 

  34. Bîrzu A, Plenge F, Jaeger NI, Hudson JL, Krischer K (2003) Excitable dynamics during electrodissolution of a metal disk electrode: model calculations. Phys Chem Chem Phys 5:3724–3731

    Article  CAS  Google Scholar 

  35. Bîrzu A, Krischer K (2006) Two-dimensional electrochemical turbulence during the electrodissolution of metal disk electrodes: model calculations. Phys Chem Chem Phys 8:3659–3668

    Article  CAS  Google Scholar 

  36. Holmes P, Lumley J, Berkooz G (1996) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, Cambridge, MA

    Book  Google Scholar 

  37. Grauel P, Krischer K (2001) Fronts and stationary domains during electrochemical H2 oxidation on Pt: the impact of the position of the reference electrode on the spatiotemporal behavior. Phys Chem Chem Phys 3:2497–2502

    Article  CAS  Google Scholar 

  38. Grauel P, Varela H, Krischer K (2001) Spatial bifurcations of fixed points and limit cycles during the electrochemical oxidation of H2 on Pt ring-electrodes. Faraday Discuss 120:165–178

    Article  CAS  Google Scholar 

  39. Varela H, Beta C, Bonnefont A, Krischer K (2005) A hierarchy of global coupling induced cluster patterns during the oscillatory H2-electrooxidation reaction on a Pt ring-electrode. Phys Chem Chem Phys 7:2429–2439

    Article  CAS  Google Scholar 

  40. Plenge F, Varela H, Krischer K (2005) Asymmetric target patterns in one-dimensional oscillatory media with genuine nonlocal coupling. Phys Rev Lett 94:198301-1–198301-4

    Article  CAS  Google Scholar 

  41. Varela H, Beta C, Bonnefont A, Krischer K (2005) Transitions to electrochemical turbulence. Phys Rev Lett 94:174104-1–174104-4

    Article  CAS  Google Scholar 

  42. Mikhailov AS (1994) Foundation of synergetics I. Springer, Berlin

    Book  Google Scholar 

  43. Benjamin TB, Feir J (1967) The disintegration of wave trains on deep water. Part 1. Theory. J Fluid Mech 27:417–430

    Article  Google Scholar 

  44. Shraiman BI, Pumir A, van Saarloos W, Hohenberg PC, Chaté H, Holen M (1992) Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation. Physica D 57:241–248

    Article  Google Scholar 

  45. Krischer K, Varela H, Bîrzu A, Plenge F, Bonnefont A (2003) Stability of uniform electrode states in the presence of ohmic drop compensation. Electrochim Acta 49:103–115

    Article  CAS  Google Scholar 

  46. Plenge F, Li YJ, Krischer K (2004) Spatial bifurcations in the generic N-NDR electrochemical oscillator with negative global coupling: theory and surface plasmon experiment. J Phys Chem B 108:14255–14264

    Article  CAS  Google Scholar 

  47. Baba N, Krischer K (2008) Mixed-mode oscillations and cluster patterns in an electrochemical relaxation oscillator under galvanostatic control. Chaos 18:015103-1–015103-9

    Article  CAS  Google Scholar 

  48. Bonnefont A, Morschl R, Bauer P, Krischer K (2009) Electrochemical impedance spectroscopy of patterned steady-states on electrode surfaces. Electrochim Acta 55:410–415

    Article  CAS  Google Scholar 

  49. Koper MTM, Schmidt TJ, Marković RPN (2001) Potential oscillations and S-shaped polarization curve in the continuous electro-oxidation of CO on platinum single-crystal electrodes. J Phys Chem B 105:8381–8386

    Article  CAS  Google Scholar 

  50. Morschl R, Bolten J, Bonnefont A, Krischer K (2008) Pattern formation during CO electroxidation on thin Pt films studied with spatially resolved infrared absorption spectroscopy. J Phys Chem C 112:9548–9551

    Article  CAS  Google Scholar 

  51. Christoph J, Strasser P, Eiswirth M, Ertl G (1999) Remote triggering of waves in an electrochemical system. Science 284:291–293 doi:10.1126/science.284.5412.291

    Article  CAS  Google Scholar 

  52. Christoph J, Otterstedt R, Eiswirth M, Jaeger NI, Hudson JL (1999) Negative coupling during oscillatory pattern formation on a ring electrode. J Chem Phys 110:8614–8621

    Article  CAS  Google Scholar 

  53. Strasser P, Christoph J, Lin WF, Eiswirth M, Hudson JL (2000) Standing wave oscillations in an electrocatalytic reaction. J Phys Chem A 104:1854–1860

    Article  CAS  Google Scholar 

  54. Christoph J, Eiswirth M (2002) Theory of electrochemical pattern formation. Chaos 12:215–230

    Article  CAS  Google Scholar 

  55. Turing AM (1952) The chemical basis for morphogenesis. Phil Trans R Soc London B 327:37–72

    Article  Google Scholar 

  56. Krömker S (1998) Wave bifurcation in models for heterogeneous catalysis. Acta Math Univ Comenianae 67:83–100

    Google Scholar 

  57. Zhabotinsky AM, Dolnik M, Epstein IR (1995) Pattern formation arising from wave instability in a simple reaction–diffusion system. J Chem Phys 103:10306–10314

    Article  CAS  Google Scholar 

  58. Dolnik M, Zhabotinsky AM, Epstein IR (1996) Modulated standing waves in a short reaction–diffusion system. J Phys Chem 100:6604–6607

    Article  CAS  Google Scholar 

  59. Lee J, Strasser P, Eiswirth M, Ertl G (2001) On the origin of oscillations in the electrocatalytic oxidation of HCOOH on a Pt electrode modified by Bi deposition. Electrochim Acta 47:501–508

    Article  CAS  Google Scholar 

  60. Christoph J, Noh T-G, Lee J, Strasser P, Eiswirth M (2009) Spatiotemporal self-organization in the oscillatory HCOOH oxidation on a Pt ribbon electrode—theory and experiments. Surf Sci 603:1652–1661

    Article  CAS  Google Scholar 

  61. Zhao Y, Wang S, Varela H, Gao Q, Hu X, Yang J, Epstein IR (2011) Spatiotemporal pattern formation in the oscillatory electro-oxidation of sulfide on a platinum disk. J Phys Chem C 115:12965–12971

    Article  CAS  Google Scholar 

  62. Mazouz N, Krischer K (2000) A theoretical study on Turing patterns in electrochemical systems. J Phys Chem B 104:6081–6090

    Article  CAS  Google Scholar 

  63. Li YJ, Oslonovitch J, Mazouz N, Plenge F, Krischer K, Ertl G (2001) Turing-type patterns on electrode surfaces. Science 291:2395–2398 doi:10.1126/science.1057830

    Article  CAS  Google Scholar 

  64. Bonnefont A, Varela H, Krischer K (2003) Stationary small and large amplitude patterns during bulk CO electrooxidation on Pt. Chem Phys Chem 4:1260–1263

    Article  CAS  Google Scholar 

  65. Bonnefont A, Varela H, Krischer K (2005) Stationary spatial patterns during bulk CO electrooxidation on Pt. J Phys Chem B 109:3408–3415

    Article  CAS  Google Scholar 

  66. Strasser P, Eiswirth M, Ertl G (1997) Oscillatory instabilities during formic acid oxidation on Pt(100), Pt(110) and Pt(111) under potentiostatic control. II. Model calculations. J Chem Phys 107:991–1003

    Article  CAS  Google Scholar 

  67. Ihle T, Müller-Krumbhaar H (1994) Fractal and compact growth morphologies in phase transitions with diffusion transport. Phys Rev E 49:2972–2991

    Article  CAS  Google Scholar 

  68. Arneodo A, Argoul F, Couder Y, Rabaud M (1991) Anisotropic Laplacian growths: from diffusion-limited aggregates to dendritic fractals. Phys Rev Lett 66:2332–2335

    Article  Google Scholar 

  69. Matsuyama T, Matsushita M (1993) Fractal morphogenesis by a bacterial cell population. Crit Rev Microbiol 19:117–135

    Article  CAS  Google Scholar 

  70. Ben-Jacob E, Cohen I, Gutnick DL (1998) Cooperative organization of bacterial colonies: from genotype to morphotype. Annu Rev Microbiol 52:779–806

    Article  CAS  Google Scholar 

  71. Sawada Y, Dougherty A, Gollub JP (1986) Dendritic and fractal patterns in electrolytic metal deposits. Phys Rev Lett 56:1260–1263

    Article  CAS  Google Scholar 

  72. Grier DG, Ben-Jacob E, Clarke R, Sander LM (1986) Morphology and microstructure in electrochemical deposition of zinc. Phys Rev Lett 56:1264–1267

    Article  CAS  Google Scholar 

  73. Kuhn A, Argoul F (1995) Diffusion-limited kinetics in thin-gap electroless deposition. J Electroanal Chem 397:93–104

    Article  Google Scholar 

  74. Trigueros PP, Claret J, Mas F, Sagués F (1991) Pattern morphologies in zinc electrodeposition. J Electroanal Chem 312:219–235

    Article  CAS  Google Scholar 

  75. Garik P, Barkey D, Ben-Jacob E, Bochner E, Broxholm N, Miller B, Orn B, Zamir R (1989) Laplace- and diffusion-field-controlled growth in electrochemical deposition. Phys Rev Lett 62:2703–2706

    Article  CAS  Google Scholar 

  76. Matsushita M, Sano M, Hayakawa Y, Honjo H, Sawada Y (1984) Fractal structures of zinc metal leaves grown by electrodeposition. Phys Rev Lett 53:286–289

    Article  Google Scholar 

  77. Hurd AJ, Schaefer DW (1985) Diffusion-limited aggregation in two dimensions. Phys Rev Lett 54:1043–1046

    Article  CAS  Google Scholar 

  78. Nakanishi S, Fukami K, Sakai SI, Nakato Y (2002) New autocatalytic mechanism for metal electrodeposition leading to oscillations and fern-leaf-shaped deposits. Chem Lett (Japan) 31:636–637

    Article  Google Scholar 

  79. Fukami K, Nakanishi S, Sakai SI, Nakato Y (2003) Mechanism of oscillatory electrodeposition of zinc, revealed by microscopic inspection of dendritic deposits during the oscillation. Chem Lett 32:532–533

    Article  CAS  Google Scholar 

  80. Fukami K, Nakanishi S, Tada T, Yamasaki H, Fukushima S, Sakai SI, Nakato Y (2005) Self-organized periodic growth of stacked hexagonal wafers in synchronization with a potential oscillation in zinc electrodeposition. J Electrochem Soc 152:C493–C497

    Article  CAS  Google Scholar 

  81. Nakanishi S, Fukami K, Tada T, Nakato Y (2004) Metal latticeworks formed by self-organization in oscillatory electrodeposition. J Am Chem Soc 126:9556–9557

    Article  CAS  Google Scholar 

  82. Tada T, Fukami K, Nakanishi S, Yamasaki H, Fukushima S, Nagai T, Sakai SI, Nakato Y (2005) Tuning of the spacing and thickness of metal latticeworks by modulation of self-organized potential oscillations in tin (Sn) electrodeposition. Electrochim Acta 50:5050–5055

    Article  CAS  Google Scholar 

  83. Fukami K, Nakanishi S, Yamasaki H, Tada T, Sonoda K, Kamikawa N, Tsuji N, Sakaguchi H, Nakato Y (2007) General mechanism for the synchronization of electrochemical oscillations and self-organized dendrite electrodeposition of metals with ordered 2D and 3D microstructures. J Phys Chem C 111:1150–1160

    Article  CAS  Google Scholar 

  84. Kuroda T, Irisawa T, Ookawa A (1977) Growth of a polyhedral crystal from solution and its morphological stability. J Cryst Growth 42:41–46

    Article  CAS  Google Scholar 

  85. Oaki Y, Imai H (2003) Experimental demonstration for the morphological evolution of crystals grown in gel media. Cryst Growth Des 3:711–716

    Article  CAS  Google Scholar 

  86. Nakanishi S, Sakai S, Nishimura K, Nakato Y (2005) Layer-by-layer electrodeposition of copper in the presence of o-phenanthroline, caused by a new type of hidden NDR oscillation with the effective electrode surface area as the key variable. J Phys Chem B 109:18846–18851

    Article  CAS  Google Scholar 

  87. Rosso M, Gobron T, Brissot C, Chazalviel JN, Lascaud S (2001) Onset of dendritic growth in lithium/polymer cells. J Power Sources 97–98:804–806

    Article  Google Scholar 

  88. González G, Rosso M, Chassaing E, Chazalviel JN (2007) Experimental and theoretical study of the onset of the growth of an irregular metal electrodeposit. Electrochim Acta 53:141–144

    Article  CAS  Google Scholar 

  89. Chazalviel JN (1990) Electrochemical aspects of the generation of ramified metallic electrodeposits. Phys Rev A 42:7355–7367

    Article  CAS  Google Scholar 

  90. Nakanishi S, Sakai S, Nagai T, Nakato Y (2005) Macroscopically uniform nanoperiod alloy multilayers formed by coupling of electrodeposition with current oscillations. J Phys Chem B 109:1750–1755

    Article  CAS  Google Scholar 

  91. Sakai S, Nakanishi S, Nakato Y (2006) Mechanisms of oscillations and formation of nano-scale layered structures in induced co-deposition of some iron-group alloys (Ni–P, Ni–W, and Co–W), studied by an in situ electrochemical quartz crystal microbalance technique. J Phys Chem B 110:11944–11949

    Article  CAS  Google Scholar 

  92. Ihara D, Nagai T, Yamada R, Nakanishi S (2009) Interfacial energy gradient at a front of an electrochemical wave appearing in CuSn-alloy oscillatory electrodeposition. Electrochim Acta 55:358–362

    Article  CAS  Google Scholar 

  93. Zeiri L, Efrima S, Deutsch M (1996) Interfacial electrodeposition of silver: the role of wetting. Langmuir 12:5180–5187

    Article  CAS  Google Scholar 

  94. Zeiri L, Efrima S (1997) Ac driven interfacial electrodeposition of silver. Langmuir 13:4722–4728

    Article  CAS  Google Scholar 

  95. Zeiri L, Efrima S, Deutsch M (1997) Electroaggregation of silver interfacial colloids. J Phys Chem B 101:9757–9766

    Article  CAS  Google Scholar 

  96. Zeiri L, Younes O, Efrima S, Deutsch M (1997) Interfacial electrodeposition of silver. J Phys Chem B 101:9299–9308

    Article  CAS  Google Scholar 

  97. Wagner C (1954) Contribution to the theory of electropolishing. J Electrochem Soc 101:225–228

    Article  CAS  Google Scholar 

  98. Efrima S (1997) Morphology of quasi-two dimensional electrodeposits—a generalized Wagner number. Langmuir 13:3550–3556

    Article  CAS  Google Scholar 

  99. Nakabayashi S, Aogaki R, Karantonis A, Iguchi U, Ushida K, Nawa M (1999) Two-dimensional metal deposition at the liquid–liquid interface; potential and magnetohydrodynamic pattern transition. J Electroanal Chem 473:54–58

    Article  CAS  Google Scholar 

  100. Nakanishi S, Nagai T, Fukami K, Sonoda K, Oka N, Ihara D, Nakato Y (2008) Oscillatory electrodeposition of metal films at liquid/liquid interfaces induced by the large surface energy of growing deposits. Langmuir 24:2564–2568

    Article  CAS  Google Scholar 

  101. Tada E, Oishi Y, Kaneko H (2007) Electrochemical oscillation during electrodeposition of zinc at the interface between two immiscible liquids. Electrochemistry (Japan) 75:731–733

    Article  CAS  Google Scholar 

  102. Saliba R, Mingotaud C, Argoul F, Ravaine S (2002) Spontaneous oscillations in gold electrodeposition. Electrochem Commun 4:629–632

    Article  CAS  Google Scholar 

  103. Fukami K, Nakanishi S, Sawai Y, Sonoda K, Murakoshi K, Nakato Y (2007) In situ probing of dynamic nanostructural change of electrodeposits in the course of oscillatory growth using SERS. J Phys Chem C 111:3216–3219

    Article  CAS  Google Scholar 

  104. Lublow M, Lewerenz HJ (2009) Scaling effects upon fractal etch pattern formation on silicon photoelectrodes. Electrochim Acta 55:340–349

    Article  CAS  Google Scholar 

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Orlik, M. (2012). Experimental and Model Spatiotemporal and Spatial Patterns in Electrochemical Systems. In: Self-Organization in Electrochemical Systems II. Monographs in Electrochemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27627-9_2

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