SURFACE ROUGHNESS EFFECT IN THE KINETICS OF HETEROGENEOUS PROCESSES
Abstract
The review analyzes and gives generalization of the data on the role of geometric inhomogeneity of solid surfaces in the kinetics of heterogeneous processes. The generalized classi¿ cation of rough surfaces on the type and size of irregularities is given. The basic approaches to the mathematical description of fractal and non-fractal interfaces, as well as methods of modeling the diffusion-controlled processes taking into account the roughness effect are discussed. It is shown that the problem of interface roughness is quite versatile in the physical chemistry of heterogeneous processes. Obviously, this effect is complex, and it is of non-linear manner and should manifest itself in the kinetics of diffusion-controlled processes studied by different transient methods. Therefore, their correct application to establish the diffusion-kinetic parameters of such processes is possible only on the basis of the solution of the corresponding non-stationary problem, taking into account the roughness effect. Of particular note is the question of its role in the mixed kinetics of heterogeneous processes, as well as in the case of diffusion fluxes conjugation at the interface. It is necessary to systematically analyze the role of geometrical irregularities of various fractal and non-fractal type with the same roughness factor in the value of the measured extensive characteristics of a physicochemical process.
Downloads
References
2. Gao X., Hamelin A., Weaver M. W. Phys. Rev. Lett., 1991, vol. 67, no. 5, pp. 618–621. DOI: 10.1103/ PhysRevLett.67.618.
3. Bard A. J., Faulkner L. R. Electrochemical Methods. Fundamentals and Applications. N.-Y. (USA), Wiley, 2000, 856 p.
4. McNaught A. D., Wilkinson A. Compendium of Chemical Terminology. N.-Y. (USA), Blackwell Science, 1997, 464 p.
5. Brunauer S., Emmett P. H., Teller E. J. Am. Chem. Soc., 1938, vol. 60, no. 2, pp. 309-319. DOI: 10.1021/ ja01269a023
6. Trasatti S., Petrii O. A. Pure & Appl. Chem., 1991, vol. 63, no. 5, pp. 711-734. DOI: 10.1351/ pac199163050711
7. Trasatti S., Petrii O. A. J. Electroanal. Chem., 1992, vol. 327, no. 1–2, pp. 353-376. DOI: 10.1016/0022- 0728(92)80162-W
8. Trasatti S., Petrii O. A. Elektrokhimiya, 1993, vol. 29, no. 4, pp. 557–575.
9. Lust E., Jänes A., Lust K., Sammelselg V., Miidla P. Electrochim. Acta, 1997, vol. 42, no. 19, pp. 2861–2879. DOI: 10.1016/S0013-4686(97)00107-2
10. Vallete G. J. Electroanal. Chem., 1987, vol. 224, no. 1–2, pp. 285-294. DOI: 10.1016/0022-0728(87)85100-8
11. Zelinskii A. G., Bek R. Yu. Elektrokhimiya, 1978, vol. 14, no. 12, pp. 1825–1829.
12. Jarzâbek G., Borkowska Z. Electrochim. Acta., 1997, vol. 42, no. 19, pp. 2915–2918. DOI: 10.1016/S0013- 4686(97)00112-6
13. Podobaev A. N., Kruglikov S. S., Bekker P., Mattsson M. Protection of Metals (Zashchita Metallov), 2005, vol. 41, no. 4, pp. 395–401.
14. Popov A. Electrochim. Acta, 1995, vol. 40, no. 5, pp. 551–559. DOI: 10.1016/0013-4686(94)00375-B.
15. Woods R. J. Electroanal. Chem., 1974, vol. 49, ʋ2, pp. 217–226. DOI: 10.1016/S0022- 0728(74)80229-9.
16. Vashkyalis A., Demontaite O. Russian Journal of Electrochemistry (Elektrokhimiya), 1978, vol. 14, no. 8, pp. 1213–1215.
17. Rodriguez J. F., Mebrahtu T., Soriaga M. P. J. Electroanal. Chem., 1987, vol. 233, ʋ 1–2, pp. 283–289. DOI: 10.1016/0022-0728(87)85023-4
18. Motheo A. J., Machado S. A. S., Van Kampen M. H., Santos J. J. Braz. Chem. Soc., 1993, vol. 4, no. 3, pp. 122– 127.
19. Galyus Z. Theoretical Basis of Electrochemical Analysis. Moscow, Mir Publ., 1974, 552 p. (in Russian)
20. McDonald D. D. Transient Techniques in Electrochemistry. New-York (USA), Plenum Press, 1997, 623 p.
21. Arutyunov P. A., Tolstikhina A. L., Demidov V. N. Industrial Laboratory (Zavodskaya Laboratoriya. Diagnostika Materialov), 1999, vol. 65, no. 9, pp. 27–37.
22. Go J-Y., Pyun S-I., Hahn Y-D. J. Electroanal. Chem., 2003, vol. 549, pp. 49–59. DOI: 10.1016/S0022- 0728(03)00244-4
23. Danilov A. I. Russian Chemical Reviews (Uspekhi Khimii), 1995, vol. 64, no. 8, pp. 818–833.
24. Hideki Y. Shueh-Lin Y., Kingo I. Appl. Phys. Lett., 1996, vol. 68, no. 11, pp. 1473–1475. DOI: 10.1063/1.116258
25. Green J.-B. Interface, 1997, vol. 6, no. 1, pp. 60– 61.
26. Huang Q. J. Lanzhon Daxue Xuebao. Ziran Kexue Ban., 1997, vol. 33, pp. 183–184.
27. Czerwinski F., Kondo K., Szpunar J. A. J. Electrochem. Soc., 1997, vol. 144, no. 2, pp. 481–484. DOI: 10.1149/1.1837436
28. Vela M. E., Andreasen G., Aziz S. G., Salvarezza R. C., Arvia A. J. Electrochim. Acta, 1998, vol. 43, no. 1–2, pp. 3–12. DOI: 10.1016/S0013-4686(97)00222-3
29. Kasatkin E. V., Neburchilova E. B. Russian Journal of Electrochemistry (Elektrokhimiya), 1998, vol. 34, no. 10, pp. 1154–1165.
30. Shi C. H., Cai X. W., Chen Y. A., Chen Y. X., Tian Z. Q., Mao B. W. Appl. Surf. Sci., 2000, vol. 158, no. 1–2, pp. 11–15.
31. Kibler L. A., Cuesta A., Kleinert M., Kolb D. M. J. Electroanal. Chem., 2000, vol. 484, no. 1, pp. 73–82. DOI: 10.1016/S0022-0728(00)00065-6
32. Rakochevich Z., Dzhurovich D. R., Popov K. I., Nikolich N. D. Russian Journal of Electrochemistry (Elektrokhimiya), 2006, vol. 42, no. 10, pp. 1245–1251.
33. Zaichenko N. A., Vasil’eva V. I., Grigorchuk O. V., Grechkina M. V., Bogatikov E. V. Proceedings of Voronezh State University. Series: Chemistry. Biology. Pharmacy, 2009, no. 1, pp. 5–14. Available at: http://www.vestnik.vsu. ru/pdf/chembio/2009/01/2009-01-01.pdf
34. Vasil’eva V. I., Kranina N. A., Malykhin M. D., Akberova E. M., Zhil’tsova A. V. Journal of Surface Investigation: X-Ray, Synchrotron and Neutron Techniques (Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya), 2013, no. 2, p. 51.
35. Nayar S. K., Ikeuchi E., Kanade T. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, vol. 13, no. 7, pp. 611–634.
36. Tong W. M., Williams R. S. Ann. Rev. Phys. Chem., 1994, vol. 45, p. 401–438. DOI: 10.1146/annurev. pc.45.100194.002153
37. Collins G. W., Letts S. A., Fearon E. M., McEachern R. L., Bernat T. P. Phys. Rev. Lett., 1994, vol. 73, no. 5, pp. 708–711. DOI: 10.1103/PhysRevLett.73.708
38. Zipin R. B. Appl. Surf. Sci., 1981, vol. 9, no. 1–4, pp. 266-287. DOI: 10.1016/0378-5963(81)90042-8
39. Mandel’brot B. Fractal Geometry of Nature. Moscow, Institute of Computer Science Publ., 2002, 656 p. (in Russian)
40. Sokirko A. V., Oldham K. B J. Electroanal. Chem., 1997, vol. 430, no. 1-2, pp. 15-24. DOI: 10.1016/S0022- 0728(96)04909-1
41. Wein O., Sobolik V. Collect. Czechosl. Chem. Commun., 1997, vol. 62, no. 3, pp. 397-419.
42. Wein O., Sobolik V., Tihon J. Collect. Czechosl. Chem. Commun., 1997, vol. 62, no. 3, pp. 420–441.
43. Cooper J. A., Compton R. G. Electroanalysis, 1998, vol. 10, no. 3, pp. 141–155. DOI: 10.1002/(SICI)1521- 4109(199803)10:33.0.CO;2-F
44. Li Z., Cai J., Zhou S. J. Phys. Chem. B., 1998, vol. 102, no. 9, pp. 1539–1542. DOI: 10.1021/jp972340l
45. Brown A. P., Krumpelt M., Loutfy R. O., Yao N. P. Electrochim. Acta, 1982, vol. 27, no. 5, pp. 557–560. DOI: 10.1016/0013-4686(82)85039-1
46. Ramanauskas R., Jurgaitiene I., Vaškelis A. Electrochim. Acta, 1997, vol. 42, no. 2, pp. 191–195. DOI: 10.1016/0013-4686(96)00143-0
47. Vaškelis A., Norkus E., Stalnionien I., Stalnionis G. Electrochim. Acta, 2004, vol. 49, no. 9-10, pp. 1613–1621. DOI: 10.1016/j.electacta.2003.11.023
48. Ardizzone S., Cappelletti G., Doubova L. M., Mussini P. R., Passeri S. M., Rondinini S. Electrochim. Acta, 2003, vol. 48, no. 25-26, pp. 3789–3796. DOI: 10.1016/ S0013-4686(03)00512-7
49. Manzhos R. A., Maksimov Yu. M., Podlovchenko B. I. Russian Journal of Electrochemistry (Elektrokhimiya), 2004, vol. 40, no. 5, pp. 636–643.
50. Morozov M. V., Gil’mutdinov A. Kh., Salakhov M. Kh. Scientists Notes of the Kazan University. Series: Physics and Mathematics (Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki), 2013, vol. 155, no. 1, pp. 119–126.
51. Sukhorukova I. V., Sheveiko A. N., KiryukhantsevKorneev F. V., Shtanskii D. V. Russian Journal of Non-Ferrous Metals, 2015, no. 3, pp. 53–61. DOI: 10.17073/1997- 308X-2015-3-53-61
52. Rodrigues I. D., Desouza J. P. I., Pastor E., Nart F. C. Langmuir, 1997, vol. 13, no. 25, pp. 6829–6835. DOI: 10.1021/la9704415
53. Lee J., Wang W. B., Zei M. S., Ertl G. Phys. Chem. Chem. Phys., 2002, vol. 4, no. 8, pp. 1393–1397. DOI: 10.1039/B109547A
54. Menshykau D., Streeter I., Compton R. G. J. Phys. Chem. C, 2008, vol. 112, no. 37, pp. 14428-14438. DOI: 10.1021/jp8047423
55. Menshykau D., Compton R. G. J. Phys. Chem. C, 2009, vol. 113, no. 35, pp. 15602–15620. DOI: 10.1021/ jp904187t
56. Hamelin A., Stoicoviciu L. J. Electroanal. Chem., 1994, vol. 365, no. 1–2, pp. 47–57.
57. Simonov V. N., Krasil’nikova O. K., Khozina E. V., Zolotarevskii V. I. Protection of Metals and Physical Chemistry of Surfaces, 2014, vol. 50, no. 3, pp. 316–324. DOI: 10.7868/S004418561403019X
58. Brantseva T. V., Ignatenko V. Ya., Kostyuk A. V., Kharenko A. V., Smirnova N. M., Antonov S. V. Polymer Science, 2014, vol. 56, no. 6, pp. 660–669. DOI: 10.7868/ S2308112014060017
59. Lust E., Jänes A., Sammelselg V., Miidla P., Lust K. Electrochim. Acta, 1998, vol. 44, no. 2–3, pp. 373–383. DOI: 10.1016/S0013-4686(98)00084-X
60. Pajkossy T. J. Electroanal. Chem., 1994, vol. 364, no. 1–2, pp. 111–125. DOI: 10.1016/0022-0728(93)02949-I
61. Kerner Z., Pajkossy T. J. Electroanal. Chem., 1998, vol. 448, no. 1, pp. 139–142. DOI: 10.1016/S0022- 0728(98)00025-4
62. Kerner Z., Pajkossy T. Electrochim. Acta, 2000, vol. 46, no. 2–3, pp. 207–211. DOI: 10.1016/S0013- 4686(00)00574-0
63. Bidóial E. D., Bulhões L. O. S., Rocha-Filho R. C. Electrochim. Acta, 1994, vol. 39, no. 5, pp. 763–769. DOI: 10.1016/0013-4686(94)80021-9
64. Rammelt U., Reinhard G. Electrochim. Acta, 1990, vol. 35, no. 6, pp. 1045–1049. DOI: 10.1016/0013- 4686(90)90040-7
65. Pound B. G. Electrochim. Acta, 1993, vol. 38, no. 14, pp. 2021–2027. DOI: 10.1016/0013-4686(93)80335- W
66. Bandyopadhyay S., Chakravorty D. J. Phys. Soc. Jap., 1996, vol. 65, no. 12, pp. 4081–4083. DOI: 10.1143/ jpsj.65.4081
67. Abdel-Aziz M. H., Nirdosh I., Sedahmed G. H. Int. J. Heat Mass Transfer., 2014, vol. 72, pp. 595–601. DOI: 10.1016/j.ijheatmasstransfer.2014.01.026
68. Mahato B. K., Shemilt L. W. Chem. Engin. Sci., 1968, vol. 23, no. 2, pp. 183–185. DOI: 10.1016/0009- 2509(68)87061-7
69. Wuttig M. Scripta Metallurgica, 1969, vol. 3, no. 3, pp. 175–177. DOI: 10.1016/0036-9748(69)90280-4
70. Fouad M. G., Zatout A. A. Electrochim. Acta, 1969, vol. 14, no. 9, pp. 909–919. DOI: 10.1016/0013- 4686(69)87012-X
71. Dawson D. A., Trass O. Int. J. Heat and Mass Transfer, 1972, vol. 15, no. 7, pp. 1317–1336. DOI: 10.1016/0017-9310(72)90015-4
72. Poulson B. Corrosion Sci., 1990, vol. 30, no. 6–7, pp. 743-746. DOI: 10.1016/0010-938X(90)90037-6
73. Khulbe K. C., Chowdhury G., Kruczek B., Vujosevic R., Matsuura T., Lamarche G. J. Membr. Sci., 1997, vol. 126, no. 1, pp. 115–122. DOI: 10.1016/S0376- 7388(96)00278-5
74. Gronda A. M., Buechel S., Cussler E. L. J. Membr. Sci., 2000, vol. 165, no. 2, pp. 177–187. DOI: 10.1016/ S0376-7388(99)00230-6
75. Yao Y. Y., Guo S. W., Zhang Y. X. J. Appl. Polym. Sci., 2007, vol. 105, no. 3, pp. 1261–1266. DOI: 10.1002/ app.25656
76. Hirose M., Ito H., Kamiyama Y. J. Membr. Sci., 1996, vol. 121, no. 2, pp. 209–215. DOI: 10.1016/S0376- 7388(96)00181-0
77. Isteiwy O. A. Self-supported Palladium-Copper Membranes, Characterization of Vacuum Deposited Membranes and InÀ uence of Air Treatment on Cold-Rolled Membranes. Ph.D. Thesis. Colorado School of Mines (USA), 2005, 114 p.
78. Roa F., Way J. D. Appl. Surf. Sci., 2005, vol. 240, no. 1–4, pp. 85–104. DOI: 10.1016/j.apsusc.2004.06.023
79. Goodyer C. E., Bunge A. L. J. Membr. Sci., 2012, vol. 409–410, pp. 127–136. DOI: 10.1016/j.memsci.2012.03.043
80. Tzanetakis N., Scott K., Taama W. M., Jachuck R. J. J. Appl. Therm. Eng., 2004, vol. 24, no. 13, pp. 1865–1875. DOI: 10.1016/j.applthermaleng.2003.12.007
81. Daikhin L. I., Kornyshev A. A., Urbakh M. Electrochim. Acta, 1997, vol. 42, no. 19, pp. 2853–2860. DOI: 10.1016/S0013-4686(97)00106-0
82. Gamburg Yu. D., Davydov A. D., Kharkats Yu. I. Russian Journal of Electrochemistry (Elektrokhimiya),1994, vol. 30, no. 4, pp. 422–443.
83. Popov K. I., Nikoliü N. D., Živkoviü P. M., BrankoviüG. Electrochim. Acta, 2010, vol. 55, no. 6, pp. 1919–1925. DOI: 10.1016/j.electacta.2009.10.085
84. Urbakh M. I. Double Layer and Adsorption on Solid Electrodes, 1988, no. 8, pp. 379–381. 85. Elias M., Menu M. Optics Commun., 2000, vol. 180, no. 4–6, pp. 191–198. DOI: 10.1016/S0030- 4018(00)00714-8
86. Robbe-Valloire F. Wear, 2001, vol. 249, no. 5–6, pp. 401–408. DOI: 10.1016/S0043-1648(01)00548-8
87. Arvia A. J., Salvarezza R. C., Vara J. M. Electrochim. Acta, 1992, vol. 37, no. 12, pp. 2155–2167. DOI: 10.1016/0013-4686(92)85106-U
88. Gɭmez M. M, Vara J. M., Hernández J. C., Salvarezza R. C., Arvia A. J. Electrochim. Acta, 1998, vol. 44, no. 6–7, pp. 1255–1262. DOI: 10.1016/S0013- 4686(98)00229-1
89. Iskandarova I. M., Knizhnik A. A., Belov I. V., Rykova E. A., Bagatur’yants A. A., Umanskii S. Ya., Potapkin B. V., Stoker M. W. Russian Journal of Physical Chemistry B: Focus on Physics., 2007, vol. 26, no. 3, pp. 79–89.
90. Policastro S. Atomistic Monte-Carlo Simulations of Dissolution. In book: Molecular Modeling of Corrosion Processes: Scienti¿ c Development and Engineering Applications. Hoboken (USA), Wiley, 2015, pp. 99–124.
91. Hernɛndez Creus A., Carro P., Salvarezza R. C., Arvia A. J. Langmuir, 1997, vol. 13, no. 4, pp. 833–841. DOI: 10.1021/la960449z
92. Aramanovich I. G., Levin V. I. Equations of Mathematical Physics. Moscow, Nauka Publ., 1969, 287 p. (in Russian)
93. Ditkin V. A., Prudnikov A. P. Integral Transformation and Operational Calculus. Nauka Publ., 1974, 544 p. (in Russian)
94. Ditkin V. A., Prudnikov A. P. Handbook of Operational Calculus. Moscow, Vysshaya shkola Publ., 1965, 466 p. (in Russian)
95. Naife A. Kh. Introduction to Perturbation Methods. Moscow, Mir Publ., 1984, 535 p. (in Russian)
96. Wagner C. J. Electrochem. Soc., 1956, vol. 103, no. 10, pp. 571–580. DOI: 10.1149/1.2430159
97. Gallager R. The Finite Element Method: Fundamentals. Moscow, Mir Publ., 1984, 428 p. (in Russian)
98. Nolen T. R., Fedkiw P. S. J. Electroanal. Chem., 1989, vol. 258, no. 2, pp. 265–280. DOI: 10.1016/0022- 0728(89)85113-7
99. Louch D. S., Pritzker M. D. J. Electroanal. Chem., 1991, vol. 319, no. 1–2, pp. 33–53. DOI: 10.1016/0022- 0728(91)87066-D
100. Louch D. S., Pritzker M. D. J. Electroanal. Chem., 1993, vol. 346, no. 1–2, pp. 211–237. DOI: 10.1016/0022- 0728(93)85014-8
101. Kant R. Phys. Rev. Lett., 1993, vol. 70, no. 26, pp. 4094–4097. DOI: 10.1103/PhysRevLett.70.4094
102. Kant R., Rangarajan S. K. J. Electroanal. Chem., 1994, vol. 368, no. 1–2, pp. 1–21. DOI: 10.1016/0022- 0728(93)03069-2
103. Kant R. J. Phys. Chem., 1994, vol. 98, no. 6, pp. 1663–1667. DOI: 10.1021/j100057a020
104. Kant R., Rangarajan S. K. J. Electroanal. Chem., 1995, vol. 396, no. 1–2, pp. 285–301. DOI: 10.1016/0022- 0728(95)03971-I
105. Dhillon S., Kant R. Electrochim. Acta, 2014, vol. 129, pp. 245–258. DOI: 10.1016/j.electacta.2014.02.096
106. Fedkiw P. S., Nolen T. R. J. Electrochem. Soc., 1990, vol. 137, no. 1, pp. 158–162. DOI: 10.1149/1.2086351
107. Filoche M., Sapoval B. Electrochim. Acta, 2000, vol. 46, no. 2–3, pp. 213–220. DOI: 10.1016/S0013- 4686(00)00575-2
108. Zuo X., Xu C., Xin H. Electrochim. Acta, 1997, vol. 42, no. 16, pp. 2555–2558. DOI: 10.1016/S0013- 4686(96)00448-3
109. Chaudhari A., Yan S. C.-C., Lee S.-L. Chem. Phys. Lett., 2002, vol. 351, no. 5–6, pp. 341–348. DOI: 10.1016/ S0009-2614(01)01419-1
110. Chaudhari A., Yan S. C.-C., Lee S.-L. Appl. Surf. Sci., 2004, vol. 238, no. 1–4, pp. 513–517. DOI: 10.1016/ j.apsusc.2004.05.247
111. Kant R., Rangarajan S. K. J. Electroanal. Chem., 2003, vol. 552, pp. 141–151. DOI: 10.1016/S0022- 0728(03)00039-1
112. Patrikar R. M. Appl. Surf. Sci., 2004, vol. 228, no. 1–4, pp. 213–220. DOI: 10.1016/j.apsusc.2004.01.010
113. Pajkossy T. J. Electroanal. Chem., 1991, vol. 300, no. 1–2, pp. 1–11. DOI: 10.1016/0022-0728(91)85379-4
114. Pajkossy T. Heterogen. Chem. Rev., 1995, vol. 2, no. 2, pp. 143–147
115. Gimenez-Romero D., Garcia-Jareno J. J., Vicente F. Electrochem. Commun., 2004, vol. 6, no. 2, pp. 148– 152. DOI: 10.1016/j.elecom.2003.11.003
116. Eftekhari A., Kazemzad M., Keyanpour-Rad M. Appl. Surf. Sci., 2005, vol. 239, no. 3–4, pp. 311–319. DOI: 10.1016/j.apsusc.2004.05.279
117. Jha S. K., Sangal A., Kant R. J. Electroanal. Chem., 2008, vol. 615, no. 2, pp. 180–190. DOI: 10.1016/ j.jelechem.2007.12.014
118. Kant R., Islam M. M. J. Electroanal. Chem., 2014, vol. 713, pp. 82–90. DOI: 10.1016/j.jelechem.2013. 12.007
119. Jha S. K., Kant R. J. Electroanal. Chem., 2010, vol. 641, no. 1–2, pp. 78–82. DOI: 10.1016/j.jelechem.2009.12.017
120. Dhillon S., Kant R. Appl. Surf. Sci., 2013, vol. 282, pp. 105–114. DOI: 10.1016/j.apsusc.2013.05.071
121. Kumar R., Kant R. Electrochim. Acta, 2011, vol. 56, no. 20, pp. 7112–7123. DOI: 10.1016/j.electacta.2011.05.092
122. Jha S. K., Kant R. Electrochim. Acta, 2010, vol. 55, no. 24, pp. 7266–7275. DOI: 10.1016/j.electacta.2010.07.010
123. Parveen, Kant R. Electrochim. Acta, 2013, vol. 111, pp. 223–233. DOI: 10.1016/j.electacta.2013.07.163
124. Kant R., Singh M. B. Electrochim. Acta, 2015, vol. 163, pp. 310–322. DOI: 10.1016/j.electacta.2015.02.107
125. Kant R., Sarathbabu M., Srivastav S. Electrochim. Acta, 2013, vol. 95, pp. 237–245. DOI: 10.1016/j.electacta.2013.02.010
126. Kumar R., Kant R. Electrochim. Acta, 2013, vol. 95, pp. 275–287. DOI: 10.1016/j.electacta.2013. 02.021
127. Srivastav S., Kant R. Electrochim. Acta, 2015, vol. 180, pp. 208–217. DOI: 10.1016/j.electacta.2015. 08.035
128. Swamy T., Kumbur E. C., Mench M. M. Electrochim. Acta, 2011, vol. 56, no. 8, pp. 3060–3070. DOI: 10.1016/j.electacta.2010.12.068
129. Kutateladze S. S. Basics of Functional Analysis. Novosibirsk, Institute of Mathematics Publ., 2000, 336 p.
130. Potapov A. A. Fractals in Radiophysics and Radar: Sample Topology. Moscow, University Book Publ., 2005, 848 p.
131. Berry M. V., Lewis Z. V. Proc. R. Soc. Lond. A, 1980, vol. 370, no. 1743, pp. 459–484
132. Lin N., Lee H. P., Lim S. P., Lee K. S. J. Modern Optics, 1995, vol. 42, no. 1, pp. 225–241. DOI: 10.1080/0 9500349514550181
133. Mehaute A., Crepy G. Solid State Ionics, 1983, vol. 9–10, part 1, pp. 17–30. DOI: 10.1016/0167- 2738(83)90207-2
134. Mehaute A. Solid State Ionics, 1987, vol. 25, no. 1, pp. 99–100. DOI: 10.1016/0167-2738(87)90184-6
135. Pajkossy T., Nyikos L. Electrochim. Acta, 1989, vol. 34, no. 2, pp. 171–179. DOI: 10.1016/0013- 4686(89)87082-3
136. Pajkossy T., Nyikos L. Electrochim. Acta, 1989, vol. 34, no. 2, pp. 181–186. DOI: 10.1016/0013- 4686(89)87083 -5
137. Nikosh L., Paikoshi T., Martem’yanov S. A. Russian Journal of Electrochemistry (Elektrokhimiya), 1989, vol. 25, no. 11, pp. 1543–1545.
138. Nyikos L., Pajkossy T. Electrochim. Acta, 1990, vol. 35, no. 10, pp. 1567–1572. DOI: 10.1016/0013- 4686(90)80011-C
139. Borosy A. P., Nyikos L., Pajkossy T. Electrochim. Acta, 1991, vol. 36, no. 1, pp. 163–165. DOI: 10.1016/0013- 4686(91)85196-E
140. Pajkossy T., Nyikos L. Bulg. Chem. Commun., 1994, vol. 27, no. 3–4, pp. 509–514.
141. Schaefer D. W., Martin J. E., Wiltzius P., Cannell D. S. Phys. Rev. Lett., 1984, vol. 18, no. 26, pp. 2371–2374. DOI: 10.1103/PhysRevLett.52.2371
142. Pfeifer P. Appl. Surf. Sci., 1984, vol. 18, no. 1–2, pp. 146–164. DOI: 10.1016/0378-5963(84)90042-4
143. Nyikos L., Pajkossy T. Electrochim. Acta, 1986. vol. 31, no. 10, pp. 1347–1350. DOI: 10.1016/0013- 4686(86)80160-8
144. Wang Y.-B., Yuan R.-K., Willander M. Appl. Phys. A, 1996, vol. 63, no. 5, pp. 481–486. DOI: 10.1007/ BF01571678
145. Keddam M., Takenouti H. Electrochim. Acta, 1988, vol. 33, no. 3, pp. 445–448. DOI: 10.1016/0013- 4686(88)85045-X
146. Bates J. B., Chu Y. T., Stribing W. T. Phys. Rev. Lett., 1988, vol. 60, no. 7, pp. 627–630. DOI: 10.1103/PhysRevLett.60.627