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Advances in Mathematical Physics
Volume 2016, Article ID 9720181, 15 pages
http://dx.doi.org/10.1155/2016/9720181
Research Article

Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel

1CONACYT-Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Colonia Palmira, 62490 Cuernavaca, MOR, Mexico
2Facultad de Ingeniería Mecánica y Eléctrica, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, Mexico
3Facultad de Ingeniería Electrónica y Comunicaciones, Universidad Veracruzana, Avenida Venustiano Carranza S/N, Colonia Revolución, 93390 Poza Rica, VER, Mexico

Received 2 February 2016; Accepted 26 April 2016

Academic Editor: Alexander Iomin

Copyright © 2016 J. F. Gómez-Aguilar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. E. Barsoukov and J. R. Macdonald, Impedance Spectroscopy, Theory, Experiment, and Applications, John Wiley & Sons, New York, NY, USA, 2005.
  2. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974. View at MathSciNet
  3. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  4. I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.
  5. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus: Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, River Edge, NJ, USA, 2012.
  6. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. F. Gómez Aguilar and D. Baleanu, “Solutions of the telegraph equations using a fractional calculus approach,” Proceedings of the Romanian Academy—Series A, vol. 15, no. 1, pp. 27–34, 2014. View at Google Scholar · View at MathSciNet
  8. R. L. Magin, Fractional Calculus in Bioengineering, Begell House, Danbury, Conn, USA, 2006.
  9. J. F. Gómez-Aguilar, H. Yépez-Martínez, R. F. Escobar-Jiménez, C. M. Astorga-Zaragoza, L. J. Morales-Mendoza, and M. González-Lee, “Universal character of the fractional space-time electromagnetic waves in dielectric media,” Journal of Electromagnetic Waves and Applications, vol. 29, no. 6, pp. 727–740, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. D. A. Benson, M. M. Meerschaert, and J. Revielle, “Fractional calculus in hydrologic modeling: a numerical perspective,” Advances in Water Resources, vol. 51, pp. 479–497, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. J. F. Gómez-Aguilar and D. Baleanu, “Fractional transmission line with losses,” Zeitschrift für Naturforschung A, vol. 69, no. 10-11, pp. 539–546, 2014. View at Publisher · View at Google Scholar · View at Scopus
  12. J. F. Gómez-Aguilar, M. Miranda-Hernández, M. G. López-López, V. M. Alvarado-Martínez, and D. Baleanu, “Modeling and simulation of the fractional space-time diffusion equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 30, no. 1–3, pp. 115–127, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. V. Uchaikin, Fractional Derivatives for Physicists and Engineers, Springer, New York, NY, USA, 2012.
  14. K. Diethelm, N. J. Ford, A. D. Freed, and Y. Luchko, “Algorithms for the fractional calculus: a selection of numerical methods,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 6–8, pp. 743–773, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Caputo and M. Fabrizio, “A new definition of fractional derivative without singular kernel,” Progress in Fractional Differentiation and Applications, vol. 1, no. 2, pp. 73–85, 2015. View at Google Scholar
  16. J. Lozada and J. J. Nieto, “Properties of a new fractional derivative without singular kernel,” Progress in Fractional Differentiation and Applications, vol. 1, no. 2, pp. 87–92, 2015. View at Google Scholar
  17. M. E. Orazem and B. Tribollet, Electrochemical Impedance Spectroscopy, vol. 48, John Wiley & Sons, New York, NY, USA, 2011.
  18. I. S. Jesus, J. A. Tenreiro MacHado, and J. Boaventure Cunha, “Fractional electrical impedances in botanical elements,” Journal of Vibration and Control, vol. 14, no. 9-10, pp. 1389–1402, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. A. S. Elwakil and B. Maundy, “Extracting the Cole-Cole impedance model parameters without direct impedance measurement,” Electronics Letters, vol. 46, no. 20, article 1367, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. K. B. Oldham, “Fractional differential equations in electrochemistry,” Advances in Engineering Software, vol. 41, no. 1, pp. 9–12, 2010. View at Publisher · View at Google Scholar · View at Scopus
  21. R. Martín, J. J. Quintana, A. Ramos, and I. de la Nuez, “Modeling of electrochemical double layer capacitors by means of fractional impedance,” Journal of Computational and Nonlinear Dynamics, vol. 3, no. 2, Article ID 021303, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. I. S. Jesus and J. A. T. Machado, “Comparing integer and fractional models in some electrical systems,” in Proceedings of the 4th IFAC Workshop on Fractional Differentiation and its Applications (FDA '10), Badajoz, Spain, October 2010.
  23. I. S. Jesus and J. A. Tenreiro Machado, “Application of integer and fractional models in electrochemical systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 248175, 17 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  24. J.-B. Jorcin, M. E. Orazem, N. Pébère, and B. Tribollet, “CPE analysis by local electrochemical impedance spectroscopy,” Electrochimica Acta, vol. 51, no. 8-9, pp. 1473–1479, 2006. View at Publisher · View at Google Scholar · View at Scopus
  25. H. Sheng, Y. Chen, and T. Qiu, “Analysis of biocorrosion electrochemical noise using fractional order signal processing techniques,” in Fractional Processes and Fractional-Order Signal Processing, pp. 189–202, Springer, London, UK, 2012. View at Google Scholar
  26. I. S. Jesus and J. A. T. MacHado, “Development of fractional order capacitors based on electrolyte processes,” Nonlinear Dynamics, vol. 56, no. 1-2, pp. 45–55, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. K. S. Cole, “Permeability and impermeability of cell membranes for ions,” Cold Spring Harbor Symposia on Quantitative Biology, vol. 8, no. 0, pp. 110–122, 1940. View at Publisher · View at Google Scholar
  28. P. Debye, Polar Molecules, Dover, New York, NY, USA, 1945.
  29. B.-Y. Chang and S.-M. Park, “Electrochemical impedance spectroscopy,” Annual Review of Analytical Chemistry, vol. 3, no. 1, pp. 207–229, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. I. Podlubny, “Geometric and physical interpretation of fractional integration and fractional differentiation,” Fractional Calculus &; Applied Analysis, vol. 5, no. 4, pp. 367–386, 2002. View at Google Scholar · View at MathSciNet
  31. M. Moshrefi-Torbati and J. K. Hammond, “Physical and geometrical interpretation of fractional operators,” Journal of the Franklin Institute, vol. 335, no. 6, pp. 1077–1086, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  32. J. F. Gómez-Aguilara, R. Razo-Hernández, and D. Granados-Lieberman, “A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response,” Revista Mexicana de Fisica, vol. 60, no. 1, pp. 32–38, 2014. View at Google Scholar · View at Scopus
  33. R. Hirayama and S. Hanuyama, “Electrochemical impedance for degraded coated steel having pores,” Corrosion, vol. 47, no. 12, pp. 952–958, 1991. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Amirudin and D. Thieny, “Application of electrochemical impedance spectroscopy to study the degradation of polymer-coated metals,” Progress in Organic Coatings, vol. 26, no. 1, pp. 1–28, 1995. View at Publisher · View at Google Scholar · View at Scopus
  35. P. L. Bonora, F. Deflorian, and L. Fedrizzi, “Electrochemical impedance spectroscopy as a tool for investigating underpaint corrosion,” Electrochimica Acta, vol. 41, no. 7-8, pp. 1073–1082, 1996. View at Publisher · View at Google Scholar · View at Scopus
  36. F. Deflorian, L. Fedrizzi, S. Rossi, and P. L. Bonora, “Organic coating capacitance measurement by EIS: ideal and actual trends,” Electrochimica Acta, vol. 44, no. 24, pp. 4243–4249, 1999. View at Publisher · View at Google Scholar · View at Scopus
  37. M. Criado, I. Sobrados, J. M. Bastidas, and J. Sanz, “Steel corrosion in simulated carbonated concrete pore solution its protection using sol-gel coatings,” Progress in Organic Coatings, vol. 88, pp. 228–236, 2015. View at Publisher · View at Google Scholar · View at Scopus
  38. L. Kong and W. Chen, “Carbon nanotube and graphene-based bioinspired electrochemical actuators,” Advanced Materials, vol. 26, no. 7, pp. 1025–1043, 2014. View at Publisher · View at Google Scholar · View at Scopus
  39. K. R. Ansari, M. A. Quraishi, and A. Singh, “Schiff's base of pyridyl substituted triazoles as new and effective corrosion inhibitors for mild steel in hydrochloric acid solution,” Corrosion Science, vol. 79, pp. 5–15, 2014. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Shreepathi, A. K. Guin, S. M. Naik, and M. R. Vattipalli, “Service life prediction of organic coatings: electrochemical impedance spectroscopy vs actual service life,” Journal of Coatings Technology Research, vol. 8, no. 2, pp. 191–200, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. F. Cadena, L. Irusta, and M. J. Fernandez-Berridi, “Performance evaluation of alkyd coatings for corrosion protection in urban and industrial environments,” Progress in Organic Coatings, vol. 76, no. 9, pp. 1273–1278, 2013. View at Publisher · View at Google Scholar · View at Scopus
  42. J. A. Calderón-Gutierrez and F. E. Bedoya-Lora, “Barrier property determination and lifetime prediction by electrochemical impedance spectroscopy of a high performance organic coating,” Dyna, vol. 81, no. 183, pp. 97–106, 2014. View at Publisher · View at Google Scholar
  43. L. Gómez, A. Quintero, D. Peña, and H. Estupiñan, “Obtención, caracterización y evaluación in vitro de recubrimientos de policaprolactona-quitosano sobre la aleación Ti6Al4V tratada químicamente,” Revista de Metalurgia, vol. 50, no. 3, article e21, 2014. View at Publisher · View at Google Scholar
  44. A. I. Muñoz, J. G. Antón, J. L. Guiñón, and V. P. Herranz, “The effect of chromate in the corrosion behavior of duplex stainless steel in LiBr solutions,” Corrosion Science, vol. 48, no. 12, pp. 4127–4151, 2006. View at Publisher · View at Google Scholar · View at Scopus
  45. G. Herting, I. O. Wallinder, and C. Leygraf, “Factors that influence the release of metals from stainless steels exposed to physiological media,” Corrosion Science, vol. 48, no. 8, pp. 2120–2132, 2006. View at Publisher · View at Google Scholar · View at Scopus
  46. A. Norlin, J. Pan, and C. Leygraf, “Investigation of interfacial capacitance of Pt, Ti and TiN coated electrodes by electrochemical impedance spectroscopy,” Biomolecular Engineering, vol. 19, no. 2-6, pp. 67–71, 2002. View at Publisher · View at Google Scholar · View at Scopus
  47. A. Miszczyk and K. Darowicki, “Multispectral impedance quality testing of coil-coating system using principal component analysis,” Progress in Organic Coatings, vol. 69, no. 4, pp. 330–334, 2010. View at Publisher · View at Google Scholar · View at Scopus
  48. C. Y. Wang, A. Q. Zhao, and X. M. Kong, “Entropy and its quantum thermody-namical implication for anomalous spectral systems,” Modern Physics Letters B, vol. 26, no. 07, 2012. View at Publisher · View at Google Scholar
  49. H.-G. Kim, S.-H. Ahn, J.-G. Kim, S. J. Park, and K.-R. Lee, “Electrochemical behavior of diamond-like carbon films for biomedical applications,” Thin Solid Films, vol. 475, no. 1-2, pp. 291–297, 2005. View at Publisher · View at Google Scholar · View at Scopus
  50. X. M. Liu, S. L. Wu, P. K. Chu et al., “Effects of water plasma immersion ion implantation on surface electrochemical behavior of NiTi shape memory alloys in simulated body fluids,” Applied Surface Science, vol. 253, no. 6, pp. 3154–3159, 2007. View at Publisher · View at Google Scholar · View at Scopus
  51. G. J. Wan, N. Huang, Y. X. Leng et al., “TiN and Ti-O/TiN films fabricated by PIII-D for enhancement of corrosion and wear resistance of Ti-6Al-4V,” Surface and Coatings Technology, vol. 186, no. 1-2, pp. 136–140, 2004. View at Publisher · View at Google Scholar · View at Scopus
  52. E. Katz and I. Willner, “Probing biomolecular interactions at conductive and semiconductive surfaces by impedance spectroscopy: routes to impedimetric immunosensors, DNA-sensors, and enzyme biosensors,” Electroanalysis, vol. 15, no. 11, pp. 913–947, 2003. View at Publisher · View at Google Scholar · View at Scopus
  53. S. Erakovic, A. Jankovic, G. C. P. Tsui, C.-Y. Tang, V. Miskovic-Stankovic, and T. Stevanovic, “Novel bioactive antimicrobial lignin containing coatings on titanium obtained by electrophoretic deposition,” International Journal of Molecular Sciences, vol. 15, no. 7, pp. 12294–12322, 2014. View at Publisher · View at Google Scholar · View at Scopus