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Fractal Approach to Rough Surfaces and Interfaces in Electrochemistry

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Modern Aspects of Electrochemistry

Part of the book series: Modern Aspects of Electrochemistry ((MAOE,volume 39))

Abstract

The real objects found in nature have complex structures which Euclidean geometry can not characterize.

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References

  1. B. B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman and Company, New York, 1983.

    Google Scholar 

  2. H. -O. Peitgen and D. Saupe, Ed., The Science of Fractal Images, Springer Verlag, New York, 1988.

    Google Scholar 

  3. C. A. Pickover, Computers, Pattern, Chaos and Beauty, St. Martin's Press, New York, 1990.

    Google Scholar 

  4. H.-O. Peitgen, H. Jürgens, and D. Saupe, Fractals for the Classroom: Introduction to Fractals and Chaos, Springer Verlag, New York, 1992.

    Google Scholar 

  5. R. N. Mantegna and H. E. Stanley, Nature 376 (1995) 46.

    Article  CAS  Google Scholar 

  6. M. H. R. Stanley, L. A. N. Amaral, S. V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, and H. E. Stanley, Nature 379 (1996) 804.

    Article  CAS  Google Scholar 

  7. H. Takayasu and K. Okuyama, Fractals 6 (1998) 67.

    Article  Google Scholar 

  8. H. Takayasu, M. Takayasu, M. P. Okazaki, K. Marumo, and T. Shimizu, in Paradigms of Complexity, Ed. by M.M. Novak, World Scientific, 2000, p. 243.

    Google Scholar 

  9. P. Pfeifer and M. Obert, in The Fractal Approach to Heterogeneous Chemistry, Ed. by D. Avnir, Wiley, New York, 1989, p. 11.

    Google Scholar 

  10. J. C. Russ, Fractal Surfaces, Plenum Press, New York, 1994.

    Google Scholar 

  11. J. -F. Gouyet, M. Rosso, and B. Sapoval, in Fractals and Disordered Systems, Ed. by A. Bunde and S. Havlin, Springer-Verlag, New York, 1996, p. 263.

    Google Scholar 

  12. R. Brady and R. C. Ball, Nature 309 (1984) 225.

    Article  CAS  Google Scholar 

  13. M. Matsushita, M. Sano, Y. Hayakawa, H. Honjo, and Y. Sawada, Phys. Rev. Lett. 53 (1984) 286.

    Article  CAS  Google Scholar 

  14. D. Grier, E. Ben-Jacob, R. Clarke, and L. M. Sander, Phys. Rev. Lett. 56 (1986) 1264.

    Article  Google Scholar 

  15. P. Meakin, Crit. Rev. Solid State Mater. Sci. 13 (1987) 147.

    Google Scholar 

  16. R. de Levie, J. Electroanal. Chem. 281 (1990) 1.

    Article  Google Scholar 

  17. F. Sagues, F. Mass, M. Villarrasa, and J. Costa, J. Electroanal. Chem. 278 (1990) 351.

    Article  CAS  Google Scholar 

  18. J.M. Gómez-Rodriguez, A.M. Baró, and R.C. Salvarezza, J. Vac. Sci. Technol. B 9(1991) 495.

    Article  Google Scholar 

  19. P. Ocon, P. Herrasti, L. Vázquez, R. C. Salvarezza, J. M. Vara, and A. J. Arvia, J. Electroanal. Chem. 319 (1991) 101.

    Article  CAS  Google Scholar 

  20. J. M. Gómez-Rodriguez, A. M. Baró, L. Vázquez, R. C. Salvarezza, J. M. Vara, and A. J. Arvia, J. Phys. Chem. 96 (1992) 347.

    Article  Google Scholar 

  21. P. Herrasti, P. Ocón, R. C. Salvarezza, J. M. Vara, L. Viázquez, and A. J. Arvia, Electrochim. Acta 37 (1992) 2209.

    Article  CAS  Google Scholar 

  22. L. Vázquez, R. C. Salvarezza, P. Ocón, P. Herrasti, J. M. Vara, and A. J. Arvia, Phys. Rev. E 49 (1994) 1507.

    Article  Google Scholar 

  23. P.L. Antonucci, R. Barberi, A.S. Aricò, A. Amoddeo, and V Antonucci, Mater. Sci. Eng. B 38 (1996) 9.

    Article  Google Scholar 

  24. W. Huang and D. B. Hibbert, Physica A 233 (1996) 888.

    Article  CAS  Google Scholar 

  25. T. Kessler, A. Visintin, A. E. Bolzan, G. Andreasen, R. C. Salvarezza, W E. Triaca, and A. J. Arvia, Langmuir 12 (1996) 6587.

    Article  CAS  Google Scholar 

  26. F. Gobal, K. Malek, M. G. Mahjani, M. Jafarian, and V. Safarnavadeh, Synth. Met. 108 (2000) 15.

    Article  CAS  Google Scholar 

  27. B. B. Mandelbrot, D. E. Passoja, and A. J. Paullay, Nature 308 (1984) 721.

    Article  CAS  Google Scholar 

  28. E. E. Underwood and K. Banerji, Mat. Sci. Eng. 80 (1986) 1.

    Article  Google Scholar 

  29. C.S. Pande, L.E. Richards, N. Louat, B.D. Dempsey, and A.J. Schwoeble, Acta Metall. 35 (1987) 1633.

    Article  CAS  Google Scholar 

  30. Z. G. Wang, D. L. Chen, X. X. Jiang, S. H. Ai, and C. H. Shih, Scr. Metall. 22 (1988) 827.

    Article  CAS  Google Scholar 

  31. C. W. Lung and S. Z. Zhang, Physica D 38 (1989) 242.

    Article  Google Scholar 

  32. A. Imre, T. Pajkossy, and L. Nyikos, Acta Metall. Mater. 40 (1992) 1819.

    Article  CAS  Google Scholar 

  33. R. F. Voss, R. B. Laibowitz, and E. I. Allessandrini, Phys. Rev. Lett. 49 (1982) 1441.

    Article  CAS  Google Scholar 

  34. J. M. Gómez-Rodriguez, A. Asenjo, R. C. Salvarezza, and A. M. Baró, Ultramicroscopy 42–44 (1992) 1321.

    Article  Google Scholar 

  35. M. V. H. Rao, B. K. Mathur, and K. L. Chopra, Appl. Phys. Lett. 65 (1994) 124.

    Article  CAS  Google Scholar 

  36. L. Spanos and E. A. Irene, J. Vac. Sci. Technol. A 12 (1994) 2646.

    Article  CAS  Google Scholar 

  37. C. Douketis, Z. Wang, T. L. Haslett, and M. Moskovits, Phys. Rev. B 51 (1995) 11022.

    Article  CAS  Google Scholar 

  38. G. W. Mbise, G. A. Niklasson, and C. G. Granqvist, Solid State Comm. 97 (1996) 965.

    Article  CAS  Google Scholar 

  39. M. C. Salvadori, M. G. Silveira, and M. Cattani, Phys. Rev. E 58 (1998) 6814.

    Article  CAS  Google Scholar 

  40. M. U. Kleinke, J. Davalos, C. Polo da Fonseca, and A. Gorenstein, Appl. Phys. Lett. 74 (1999) 1683.

    Article  CAS  Google Scholar 

  41. G. A. Niklasson, D. Rönnow, M. Stromme Mattsson, L. Kullman, H. Nilsson, and A. Roos, Thin Solid Films 359 (2000) 203.

    Article  CAS  Google Scholar 

  42. L. L. G. Silva, N. G. Ferreira, M. E. R. Dotto, and M. U. Kleinke, Appl. Surf. Sci. 181 (2001) 327.

    Article  CAS  Google Scholar 

  43. H. -C. Shin, S. -I. Pyun, and J. -Y. Go, J. Electroanal. Chem. 531 (2002) 101.

    Article  CAS  Google Scholar 

  44. X. Sun, Z. Fu, and Z. Wu, Mater. Charact. 48 (2002) 169.

    Article  CAS  Google Scholar 

  45. J. -Y. Go, S. -I. Pyun, and Y. -D. Hahn, J. Electroanal. Chem. 549 (2003) 49.

    Article  CAS  Google Scholar 

  46. J. -Y. Go and S. -I. Pyun, Electrochim. Acta 49 (2004) 2551.

    Article  CAS  Google Scholar 

  47. J. M. Costa, F. Sagués, and M. Vilarrasa, Corros. Sci. 32 (1991) 665.

    Article  CAS  Google Scholar 

  48. T. Jøssang and J. Feder, Phys. Scr. T44 (1992) 9.

    Article  Google Scholar 

  49. T. Holten, T. Jøssang, P. Meakin, and J. Feder, Phys. Rev. E 50 (1994) 754.

    Article  CAS  Google Scholar 

  50. L. Balázs and J. -F. Gouyet, Physica A 217 (1995) 319.

    Article  Google Scholar 

  51. J. -J. Park and S. -I. Pyun, Corros. Sci. 45 (2003) 995.

    Article  CAS  Google Scholar 

  52. J. -J. Park and S. -I. Pyun, J. Solid State Electrochem. 7 (2003) 380.

    CAS  Google Scholar 

  53. J. -J. Park and S. -I. Pyun, Corros. Sci. 46 (2004) 285.

    Article  CAS  Google Scholar 

  54. S. -I. Pyun and J. -J. Park, J. Solid State Electrochem. 8 (2004) 296.

    Article  CAS  Google Scholar 

  55. N. Almqvist, M. Rubel, and E. Franconi, Mater. Sci. Eng. A 201 (1995) 277.

    Article  Google Scholar 

  56. N. Almqvist, M. Rubel, P. Wienhold, and S. Fredriksson, Thin Solid Films 270 (1995) 426.

    Article  CAS  Google Scholar 

  57. N. Almqvist, Surf. Sci. 355 (1996) 221.

    Article  CAS  Google Scholar 

  58. J. C. Arnault, A. Knoll, E. Smigiel, and A. Cornet, Appl. Surf. Sci. 171 (2001) 189.

    Article  CAS  Google Scholar 

  59. A. Kirbs, R. Lange, B. Nebe, J. Rychly, P. Müller, and U. Beck, Mater. Sci. Eng. C 23 (2003) 413.

    Article  Google Scholar 

  60. A. Kirbs, R. Lange, B. Nebe, R. Rychly, A. Baumann, H. -G. Neumann, and U. Beck, Mater. Sci. Eng. C 23 (2003) 425.

    Article  Google Scholar 

  61. J. Feder, Fractals, Plenum Press, New York, 1988.

    Google Scholar 

  62. R. F. Voss, in Dynamics of Fractal Surfaces, Ed. by F. Family and T. Vicsek, World Scientific, New Jersey, 1991, p. 39.

    Google Scholar 

  63. A. -L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995.

    Google Scholar 

  64. H. E. Stanley, in Fractals and Disordered Systems, Ed. by A. Bunde and S. Havlin, Springer-Verlag, New York, 1996, p. 1.

    Google Scholar 

  65. J.F. Gouyet, Physics and Fractal Structures, Springer, New York, 1995.

    Google Scholar 

  66. B. B. Mandelbrot, in Fractals in Physics, Ed. by L. Pietronero and E. Tosatti, North-Holland, Amsterdam, 1986, pp. 3, 17, 21.

    Google Scholar 

  67. T. Vicsek, Fractal Growth Phenomena, 2nd Ed., World Scientific, Singapore, 1991.

    Google Scholar 

  68. A. Majumdar and B. Bhushan, J. Tribal. 112 (1990) 205.

    Google Scholar 

  69. A. Majumdar and C. L. Tien, Wear, 136 (1990) 313.

    Article  Google Scholar 

  70. A. Majumdar and B. Bhushan, in Handbook of Micro/Nano Tribology, Ed. by B. Bhushan, CRC Press, New York, 1995, p. 109.

    Google Scholar 

  71. T. Silk, Q. Hong, J. Tamm, and R. G. Compton, Syn. Met. 93 (1998) 65.

    Article  CAS  Google Scholar 

  72. K. C. Clark, Comput. Geosci. 12 (1986) 713.

    Article  Google Scholar 

  73. J. Liu and T. Furuno, Wood Fiber Sci. 33 (2001) 213.

    CAS  Google Scholar 

  74. J. Liu and T. Furuno, Wood Sci. Technol. 36 (2002) 385.

    Article  CAS  Google Scholar 

  75. C. -H. Kim and S. -I. Pyun, Electrochim. Acta 48 (2003) 3455.

    Article  CAS  Google Scholar 

  76. B. B. Mandelbrot, Phys. Scr. 32 (1985) 257.

    Article  Google Scholar 

  77. R. C. Salavarezza and A. J. Arvia, in Modern Aspects of Electrochemistry, No. 28, Ed. by B.E. Conway, J. O'M. Bockris, and R.E. White, Plenum Press, New York, 1995, p. 289.

    Google Scholar 

  78. V. Lakshminarayanan, R. Srinivasan, D. Chu, and S. Oilman, Surf. Sci. 392 (1997) 44.

    Article  CAS  Google Scholar 

  79. A. Majumdar, B. Bhushan, and C. L. Tien, Adv. Inf. Storage Syst. 1 (1991) 231.

    Google Scholar 

  80. P. I. Oden, A. Majumdar, B. Bhushan, A. Padmanabhan, and J. J. Graham, J. Tribal. 114 (1992) 666.

    CAS  Google Scholar 

  81. P. So, E. Barreto, and B. R. Hunt, Phys. Rev. E 60 (1999) 378.

    Article  CAS  Google Scholar 

  82. A. K. Bisoi and J. Mishra, Patt. Recog. Lett. 22 (2001) 631.

    Article  Google Scholar 

  83. D. Avnir and D. Farin, J. Chem. Phys. 79 (1983) 3566.

    Article  CAS  Google Scholar 

  84. P. Pfeifer and D. Avnir, J. Chem. Phys. 79 (1983) 3558.

    Article  CAS  Google Scholar 

  85. P. Pfeifer, D. Avnir, and D. Farin, Surf. Sci. 126 (1983) 569.

    Article  CAS  Google Scholar 

  86. D. Avnir, D. Farin, and P. Pfeifer, Nature 308 (1984) 261.

    Article  CAS  Google Scholar 

  87. D. Avnir, D. Farin, and P. Pfeifer, J. Colloid Interface Sci. 103 (1985) 112.

    Article  CAS  Google Scholar 

  88. D. Farin, S. Pelog, D. Yavin, and D. Avnir, Langmuir 1 (1985) 399.

    Article  CAS  Google Scholar 

  89. A. Y. Myer, D. Farin, and D. Avnir, J. Am. Chem. Soc. 108 (1986) 7897.

    Article  Google Scholar 

  90. D. Avnir, J. Am. Chem. Soc. 109 (1987) 2931.

    Article  CAS  Google Scholar 

  91. D. Farin and D. Avnir, J. Phys. Chem. 91 (1987) 5517.

    Article  CAS  Google Scholar 

  92. D. Farin and D. Avnir, J. Am. Chem. Soc. 110 (1988) 2039.

    Article  CAS  Google Scholar 

  93. D. Avnir and M. Jaroniec, Langmuir 5 (1989) 1431.

    Article  CAS  Google Scholar 

  94. A. V. Neimark, Adsorpt. Sci. Technol. 7 (1990) 210.

    CAS  Google Scholar 

  95. D. K. Ludlow and T.P. Moberg, Anal. Instrum. 19 (1990) 113.

    Article  CAS  Google Scholar 

  96. K. Kaneko, Langmuir 7 (1991) 109.

    Article  CAS  Google Scholar 

  97. M. Sato, T. Sukegawa, T. Suzuki, S. Hagiwara, and K. Kaneko, Chem. Phys. Lett. 181 (1991) 526.

    Article  CAS  Google Scholar 

  98. D. Avnir, D. Farin, and P. Pfeifer, New J. Chem. 16 (1992) 439.

    CAS  Google Scholar 

  99. Y. Lefebvre, S. Lacelle, and C. Jolicoeur, J. Mater. Res. 7 (1992) 1888.

    Article  CAS  Google Scholar 

  100. W. C. Conner and C. O. Bennett, J. Chem. Soc., Faraday Trans. 89 (1993) 4109.

    Article  CAS  Google Scholar 

  101. K. S. W. Sing, D. H. Evert, R. A. W. Haul, L. Mosocou, R. A. Pierotti, J. Rouquerol, and T. Siemieniewska, Pure Appl. Chem. 57 (1985) 603.

    CAS  Google Scholar 

  102. R. F. Cracknell, P. Gordon, and K. E. Gubbins, J. Phys. Chem. 97 (1993) 494.

    Article  CAS  Google Scholar 

  103. K. Kaneko, R. F. Cracknell, and D. Nichlson, Langmuir 10 (1994) 4606.

    Article  CAS  Google Scholar 

  104. T. Suzuki, K. Kaneko, N. Setoyama, M. Maddox, and K.E. Gubbins, Carbon 34 (1996) 909.

    Article  CAS  Google Scholar 

  105. K. Kaneko, T. Suzuki, and K. Kakei, Langmuir 5 (1989) 879.

    Article  CAS  Google Scholar 

  106. K. Kaneko and C. Ishii, Colloids Surf. 67 (1992) 203.

    Article  CAS  Google Scholar 

  107. M. Sato, T. Sukegawa, T. Suzuki, and K. Kaneko, J. Phys. Chem. B 101 (1997) 1845.

    Article  CAS  Google Scholar 

  108. P. Pfeifer, Y. J. Wu, M. W. Cole, and J. Krim, Phys. Rev. Lett. 62 (1989) 1997.

    Article  CAS  Google Scholar 

  109. P. Pfeifer and M.W. Cole, New J. Chem. 14 (1990) 221.

    CAS  Google Scholar 

  110. P. Pfeifer, J. Kenntner, and M.W. Cole, in Fundamentals of Adsorption, Ed. by A.B. Mersmann and S.E. Scholl, American Institute of Chemical Engineers, New York, 1991, p. 689.

    Google Scholar 

  111. I. M. K. Ismail and P. Pfeifer, Langmuir 10 (1994) 1532.

    Article  CAS  Google Scholar 

  112. P. Pfeifer and K. -Y Liu, in Equilibria and Dynamics of Gas Adsorption on Heterogeneous Solid Surfaces, Ed. by W. Rudziński, W.A. Steele, and G. Zgrablich, Elsevier, New York, 1997, p. 625.

    Chapter  Google Scholar 

  113. J. Frenkel, Kinetic Theory of Liquids, Clarendon, Oxford, 1946.

    Google Scholar 

  114. G. D. Halsey, J. Chem. Phys. 16 (1948) 931.

    Article  CAS  Google Scholar 

  115. T. L. Hill, Adv. Catal. 4 (1952) 211.

    Article  CAS  Google Scholar 

  116. M. K. Wu, Aerosol Sci. Technol. 25 (1996) 392.

    Article  CAS  Google Scholar 

  117. P. Tang, N. Y. K. Chew, H. K. Chan, and J. A. Raper, Langmuir 19 (2003) 2632.

    Article  CAS  Google Scholar 

  118. R. Larraz, Chem. Eng. J. 86 (2002) 309.

    Article  CAS  Google Scholar 

  119. A. J. Bard and L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, John Wiley and Sons, New York, 1980.

    Google Scholar 

  120. L. Nyikos and T. Pajkossy, Electrochim. Acta 31 (1986) 1347.

    Article  CAS  Google Scholar 

  121. T. Pajkossy and L. Nyikos, Electrochim. Acta 34 (1989) 171.

    Article  CAS  Google Scholar 

  122. T. Pajkossy, J. Electroanal. Chem. 300 (1991) 1.

    Article  CAS  Google Scholar 

  123. Y. Dassas and P. Duby, J. Electrochem. Soc. 142 (1995) 4175.

    Article  CAS  Google Scholar 

  124. T. Pajkossy and L. Nyikos, Electrochim. Acta 34 (1989) 181.

    Article  CAS  Google Scholar 

  125. M. Strømme, G. A. Niklasson, and C. G. Granqvist, Phys. Rev. B 52 (1995) 14192.

    Article  Google Scholar 

  126. M. Strømme, G. A. Niklasson, and C. G. Granqvist, Solid State Commun. 96 (1995) 151.

    Article  Google Scholar 

  127. M. Strømme, G. A. Niklasson, and C. G. Granqvist, Phys. Rev. B 54 (1996) 2968.

    Article  Google Scholar 

  128. M. Sttømme, G. A. Niklasson, and C. G. Granqvist, Phys. Rev. B 54 (1996) 17884.

    Article  Google Scholar 

  129. R. de Levie, Electrochim. Acta 9 (1964) 1231.

    Article  Google Scholar 

  130. R. de Levie, Electrochim. Acta 10 (1965) 113.

    Article  Google Scholar 

  131. A. Le Mehaute and G. Crepy, Solid State Ionics 9&10 (1983) 17.

    Google Scholar 

  132. A. Le Mehaute, J. Stat. Phys. 36 (1984) 665.

    Article  Google Scholar 

  133. S. H. Liu, Phys. Rev. Lett. 55 (1985) 529.

    Article  CAS  Google Scholar 

  134. L. Nyikos and T. Pajkossy, Electrochim. Acta 30 (1985) 1533.

    Article  CAS  Google Scholar 

  135. T. C. Halsey, Phys. Rev. A 35 (1987) 3512.

    Article  CAS  Google Scholar 

  136. T. Kaplan, L.J. Gray, and S. H. Liu, Phys. Rev. B 35 (1987) 5379.

    Article  Google Scholar 

  137. B. Sapoval, Solid State Ionics 23 (1987) 253.

    Article  Google Scholar 

  138. Y.T. Chu, Solid State Ionics 26 (1988) 299.

    Article  Google Scholar 

  139. R.M. Hill and L.A. Dissado, Solid State Ionics 26 (1988) 295.

    Article  Google Scholar 

  140. W.H. Mulder and J.H. Sluyters, Electrochim. Acta 33 (1988) 303.

    Article  CAS  Google Scholar 

  141. J. C. Wang, Electrochim. Acta 33 (1988) 707.

    Article  CAS  Google Scholar 

  142. M. Blunt, J. Phys. A: Math. Gen. 22 (1989) 1179.

    Article  Google Scholar 

  143. A. Maritan and F. Toigo, Electrochim. Acta 35 (1990) 141.

    Article  CAS  Google Scholar 

  144. T. Pajkossy and L. Nyikos, Phys. Rev. B 42 (1990) 709.

    Article  Google Scholar 

  145. T. Pajkossy, J. Electroanal. Chem. 364 (1994) 111.

    Article  CAS  Google Scholar 

  146. Z. Kerner and T. Pajkossy, Electrochim. Acta 46 (2000) 207.

    Article  CAS  Google Scholar 

  147. C. -H. Kim, S. -I. Pyun, and J. -H. Kim, Electrochim. Acta 48 (2003) 3455.

    Article  CAS  Google Scholar 

  148. A. P. Borosy, L. Nyikos, and T. Pajkossy, Electrochim. Acta 36 (1991) 163.

    Article  CAS  Google Scholar 

  149. R. Kant, Phys. Rev. E 53 (1996) 5749.

    Article  CAS  Google Scholar 

  150. R. Kant, J. Phys. Chem. B 101 (1997) 3781.

    Article  CAS  Google Scholar 

  151. K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, New York, 1990.

    Google Scholar 

  152. B. R. Hunt, Proc. Am. Math. Soc. 126 (1998) 791.

    Article  Google Scholar 

  153. P. P. Trigueros, F. Mars, J. Claret, F. Sagués, J. Galceran, and J. Puy, J. Electroanal. Chem. 348 (1993) 221.

    Article  CAS  Google Scholar 

  154. A. Maritan, A. L. Stella, and F. Toigo, Phys. Rev. B 40 (1989) 9269.

    Article  Google Scholar 

  155. T. Pajkossy, A. P. Borosy, A. Imre, S. A. Martemyanov, G. Nagy, R. Schiller, and L. Nyikos, J. Electroanal. Chem. 366 (1994) 69.

    Article  CAS  Google Scholar 

  156. F. Normant and A.V. De Walle, Cartographica 33 (1996) 1.

    Google Scholar 

  157. H. Schwarz and H. E. Exner, Powder Technol. 27 (1980) 207.

    Article  Google Scholar 

  158. B. H. Kaye, Powder Technol. 46 (1986) 245.

    Article  CAS  Google Scholar 

  159. B. Sapoval, M. Rosso, and J. -F. Gouyet, in The Fractal Approach to Heterogeneous Chemistry, Ed. by D. Avnir, Wiley, New York, 1989, p. 227.

    Google Scholar 

  160. S. Ye, A. K. Vijh, and L. H. Dao, J. Electrochem. Soc. 144 (1997) 1734.

    Article  CAS  Google Scholar 

  161. S.-B. Lee and S.-I. Pyun, J. Electroanal. Chem. 556 (2003) 75.

    Article  CAS  Google Scholar 

  162. G.-J. Lee and S.-I. Pyun, submitted to Carbon.

    Google Scholar 

  163. K. Oshida, M. Endo, S. L. di Vittorio, and M. S. Dresselhaus, J. Mater. Res. 8 (1993) 512.

    Article  CAS  Google Scholar 

  164. M. Endo, K. Takeuchi, Y. Sasuda, K. Matsubayashi, K. Oshida, and M. S. Dresselhaus, Electron. Commun. Jpn., Part 2, Electron. 77 (1994) 98.

    Article  Google Scholar 

  165. K. Oshida, K. Kogiso, K. Matsubayashi, K. Takeuchi, S. Kobayashi, M. Endo, M. S. Dresselhaus, and G. Dresselhaus, J. Mater. Res. 10 (1995) 2507.

    Article  CAS  Google Scholar 

  166. M. Endo, T. Furuta, F. Minoura, C. Kim, K. Oshida, G. Dresselhaus, and M. S. Dresselhaus, Supramol. Chem. 5 (1998) 261.

    Article  CAS  Google Scholar 

  167. S. -I. Pyun and C. -K. Rhee, Electrochim. Acta in press.

    Google Scholar 

  168. H. -C. Shin and S. -I. Pyun, in Modern Aspects of Electrochemistry, No. 36, Ed. by C. G. Vayenas, B. E. Conway, and R. E. White, Kluwer Academic / Plenum Publishers, New York, 2003, p. 255.

    Google Scholar 

  169. J. -W. Lee, S. -I. Pyun, and S. Filipek, Electrochim. Acta 48 (2003) 1603.

    Article  CAS  Google Scholar 

  170. J. -W. Lee and S. -I. Pyun, submitted to Electrochim. Acta.

    Google Scholar 

  171. S. -J. Lee, S. -I. Pyun, and J. -W. Lee, submitted to Electrochim. Acta.

    Google Scholar 

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Go, JY., Pyun, SI. (2006). Fractal Approach to Rough Surfaces and Interfaces in Electrochemistry. In: Vayenas, C., White, R.E., Gamboa-Adelco, M.E. (eds) Modern Aspects of Electrochemistry. Modern Aspects of Electrochemistry, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31701-4_4

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