Mathematical modeling of subdiffusion impedance in multilayer nanostructures

The model of impedance subdiffusion based on the Cattaneo equation in fractional derivatives in applications to multilayer nanostructures is considered. Nyquist diagrams with changes of the parameter $\tau$ (time for which the flow is delayed with respect to the concentration gradient) and the subdiffusion coefficient $D_{\alpha }$ are calculated.

  1. The Electrochemical Impedance / Z. Stoynov, et al. Moscow, Science, 1991. (in Russian).
  2. Bisquert J., Compte A. Theory of the electrochemical impedance of anomalous diffusion. J. Electroanalytical Chem. 499, 112–120 (2001).
  3. Impedance spectroscopy. Theory, experiment and application / Eds.: E. Barsoukov, J. R. Macdonald. Canada: Wiley interscience, 2005.
  4. Grygorchak I., Ponedilok G. Impedance Spectroscopy. Lviv. Lviv Polytechnic National University, 2011. (in Ukrainian).
  5. Bertoluzzi L., Boix P. P., Mora-Sero I., Bisquert J. Theory of Impedance Spectroscopy of Ambipolar Solar Cells with Trap Mediated Recombination. J. Phys. Chem. C. 118, 16574–16580 (2014).
  6. Bisquert J., Bertoluzzi L., Carcia-Belmonte G., Mora-Sero I. Theory of Impedance and Capacitance Spectroscopy of Solar Cells with Dielectric Relaxation, Drift-Diffusion Transport and Recombination. J. Phys. Chem. C. 118, 18983–18991 (2014).
  7. Bertoluzzi L., Lopez Varo P., Tejada J. A. J., Bisquert J. Charge transfer processes at the semiconductor/electrolyte interface for solar fuels production: insight from impedance spectroscopy. J. Mater. Chem. A. (2015), (in press).
  8. Umeda M., Dokko K., at all. Electrochemical impendance study of Li-ion insertion into mesocarbon microbead single particle electrode (Part 1. Graphitized carbon). Electrochim. 47, 885–890 (2001).
  9. Hjeim A.-K. Lindbergh G. Experimental and theoretical analysis of LiMn2O4 cathodes for use in rechargeable lithium batteries by electrochemical impendance spectroscopy (EIS). Electrochim. Acta. 47, 1747–1759 (2002).
  10. Bishchaniuk T. M., Grygorchak I. I., Ivashchyshyn F. O. Multilayer Semiconductor clathrates-cfvitand complex with a fractal quest system. Phys. Suf. Eng. 12, n.3, 360–371 (2014).
  11. Report on the R and D project “The physical processes and their mathematical modeling in nanohybrided structures of sensory and energy accumulative devices” (R and D project supervised by Kostrobij P.), Lviv Polytechnic National University, Lviv, 2014. (in Ukrainian).
  12. Compter A.,and Metzler R. The generalized Cattaneo equation for the description of anomalous transport processes. J. Phys. A: Math. Gen. 30, 7277–7289 (1997).
  13. Sahimi M. Non-linear and non-local transport procesess in heterogeneous media: from long-range correlated percolation to fracture and materials breakdawn. Phys. Rep. 306, n.4, 213–395 (1998).
  14. Metzler R., and Klafter J. The random walk’s quide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000).
  15. Metzler R., and Klafter J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A: Math. Gen. 37, R161–R208 (2004).
  16. Bisquert J. Fractional Diffusion in the Multiple-Trapping Regime and Revision of the Equivalence with the Continuos-Time Random Walk. Phys. Rev. Lett. 91, n.1, 010602(1–4) (2003).
  17. Bisquert J. Interpretation of a fractional diffusion equation with nonconserved probability density in terms of experimental systems with trapping or recombination. Phys. Rev. E. 72, 011109 (2005).
  18. Kosztoiowicz T., Dworecki K., and Mrowczynski S. How to Measure Subdiffusion Parameters. Phys. Rev. Lett. 94, 170602 (2005).
  19. Kosztoiowicz T., Dworecki K., and Mrowczynski S. Measuring subdiffusion parameters. Phys. Rev. E. 71, 041105 (2005).
  20. Korosak D., Cvikl B., Kramer J, Jecl R., Prapotnik A. Fractional calculus applied to the analysis of spectral electrical conductivity of clay-water system. J. Contain. Hydrol. 92, 1–9 (2007).
  21. Uchaikin V. The Method of Fractional Derivatives. Ulyanovsk, “Artichoke”, 2008. (in Russian).
  22. Shibatov R., Uchaikin V. Fractional Differential Approach to Dispersive Transfer in Semiconductors. Usp. fiz. nauk. 179, n.10, 1079–1109 (2009). (in Russian).
  23. Kosztolowicz T., Lewandowska K. D. Hyperbolic subdiffusion impedanse. J. Phys. A: Math. Theor. 42, 055004 (2009).
  24. Kant R., Kumar R., and Yadav V. K. Theory of Anomalous Diffusion Impedance of Realistic Fractal Electrode. J. Phys. Chem. C. 112, 4019-4023 (2008).
  25. Rekhviashvili S., Mamchuyev M. Model of Drift-Diffusion Transport of Charge Carriers in the Layers of Fractal Structure. Physics of Solid Body. 58, n.4, 763–766 (2016). (in Russian).