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Statistical description of electro-diffusion processes of ions intercalation in "electrolyte – electrode" system

Kostrobij P. P., Markovych B. M., Tokarchuk R. M., Tokarchuk M. V., Chernomorets Yu. I.
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Keywords:

Abstract: 
We propose a statistical theory of classical-quantum description of electro-diffusion processes of intercalation in "electrolyte – electrode" system. Using the nonequilibrium statistical operator method the generalized transport equations of Nernst-Planck type for ions and electrons in the "electrolyte – electrode" system are obtained. These equations take into account time memory effects and spatial heterogeneity. Within a classical description an analytical calculation of spatially inhomogeneous diffusion coefficients for ions is carried out.
References: 
  1. Advances in Lithium-Ion Batteries, edited by W. A. van Schalkwijk, B. Scrosati. Kluwer Academic, Plenum Publ., N.-Y. (2002).
  2. Skundin A. M., Efimov O. N., Yarmolenko O. V. Russian Chemical Rev. 71(4), 378 (2002) (in Russian).
  3. Wagemaker M. Structure and Dynamics of Lithium in Anatase TiO2. Delft Univer. Press, Netherlands (2002).
  4. Korovin N. V., Skundin A. M. Chemical power sources. Moscow (2003), (in Russian).
  5. Manthiram A. Lithium batteries, edited by Gholam-Abbas Nazri. Springer, USA (2009).
  6. Ferguson T. R., Ferguson T. R., Bazant M. Z. Nonequilibrium Thermodynamics of Porous Electrodes. J. Electrochem. Soc. 159, A1967 (2012).
  7. Xie Y., Li J., Yuan C. Mathematical modeling of the electrochemical impedance spectroscopy in lithium ion battery cycling. Electrochimica. Acta. 127, 266 (2014).
  8. Pinson M. B., Bazant M. Z. Theory of SEI Formation in Rechargeable Batteries: Capacity Fade, Accelerated Aging and Lifetime Prediction. J. Electrochem. Soc. 160, A243 (2013).
  9. Bisquert J., Compte A. Theory of the electrochemical impedance of anomalous diffusion. J. Electroanalytical Chem. 499, 112 (2013).
  10. Impedance spectroscopy. Theory, experiment and application, edited by E. Barsoukov, J. R. Macdonald. Wiley interscience, Canada (2005).
  11. Gryhorchak I. I., Ponedilok H. V. Impedance spectroscopy. Lviv Polytechnic National University, Lviv (2011), (in Ukrainian).
  12. 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 (2001).
  13. 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 (2002).
  14. Kern R., Sastrawan R., Ferbar J., Stangl R., Luther J. Modeling and interpretation of electrical impendance spectra of dye solar cells operated under open-circuit conditions. Electrochim. Acta. 47, 4213 (2002).
  15. Churikov A. V., Volgin M. A., Pridatko K. I. On the determination of kinetic characteristics of lithium intercalation into carbon. Electrochim. Acta. 47, 2857 (2002).
  16. Churikov A. V., Ivanischev A. V. Application of pulse methods to the determination of the electrochemical characteristics of lithium intercalates. Electrochim. Acta. 48, 3677 (2003).
  17. Portnyagin D. Modelling of discharge of lithium battery with microporous carbon electrode. Preprint of National Acad. of Sci. of Ukraine; Inst. for Cond. Matter Phys.: ICMP-06-11E, Lviv, (2006).
  18. Biesheuvel P. M., Bazant M. Z. Diffuse charge and Faradaic reactions in porous electrodes. Phys. Rev. E. 83, 061507 (2011).
  19. Rica R., Ziano A. R., Salerno D., Mantegazza F., Bazant M. Z., Brogioli D. Electro-diffusion of ions in porous electrodes for capacitive extraction of renewable energy from salinity differences. Electrochimica Acta. 92, 304 (2013).
  20. Bazant M.Z. Theory of Chemical Kinetics and Charge Transfer based on Nonequilidrium Thermodynamics. arXiv, 1208.1587V2. cond - mat.mtrl-sci, 2013, 17p.
  21. Biesheuvel P. M., Fu Y., Bazant M. Z. Electrochemistry and Capacitive Charging of Porous Electrodes in Asymmetric Multicomponent Electrolytes. Russian Jour. Electrochem. 48, 580 (2012).
  22. McKinnon W. R., Haering R. R. Physical Mechanisms of Intercalation, in: Modern Aspects of Electrochemistry. Academic Press, New York, 15, 235 (1983).
  23. Marcus R. A. Electron Transfer Reactions in Chemistry: Theory and Experiment (Nobel Lecture). Angev. Chem. Int. Ed. Engl. 32/2, 1111 (1993).
  24. Marcus R. A. Interaction Theory and Experiment in Reaction Kinetics. Chapt. 1, Comprehensive Chemical Kinetics (eds. R. G. Compton and G. Hancock). Elsevier, Amsterdam, 37, 1 (1999).
  25. Dugaev V. K. Mechanism of Bipolar Diffusion of Intercalated Ions in Layered Crystals. Phys. Stat. Sol. 219, 31 (2000).
  26. Gao Y. Q., Georgievskii Yu., Marcus R. A. On the theory of electron transfer reactions at semiconductor electrode / liquid interfaces. J. Chem. Phys. 112, 3358 (2000).
  27. Lukiyanets B. A., Matulka D. V., Grygorchak I. I. Quantum mechanic tunneling and efficiency of Faraday current-generating process in porous nanostructures. Condens. Matter Phys. 14, 23705 (2011).
  28. Vakarin E. V., Badiali J. P. Role of host distortion in the intercalation process. Phys. Rev. B. 63, 014304 (2000).
  29. Velychko O. V., Stasyuk I. V. Lattice model for lithium intercalated anatase: phase equilibrium, thermodynamic and dielectric properties. Preprint of National Acad. of Sci. of Ukraine; Inst. for Cond. Matter Phys.: ICMP-08-16U, Lviv, (2008).
  30. Velychko O. V., Stasyuk I. V. Phase separation in lithium intercalated anatase: A Theory. Condens. Matter Phys. 12, 249 (2009).
  31. Stasyuk I. V., Dublenych Yu. I. Phase transitions and phase separations in an S=1 pseudospin-electron model: Application of the model to the intercalated crystals. Phys. Rev. B. 72, 224209 (2005).
  32. Khaldeev G. V., Petrov S. N. Computer simulation of electrochemical processes on interfaces. Russian Chem. Rev. 67(2), 107 (1998).
  33. Wagemaker M., Van Der Ven A., Morgan D., Ceder G., Mulder F. M., Kearley G. J. Thermodynamics of spinel LixTiO2 from first principles. Chem. Phys. 317, 130 (2005).
  34. Moriguchi K., Yutaka Itoh, Munetoh Shinji, Kamei Kazuhito, Abe Masaru, Omaru Atsuo, Nagamine Masayuki. Nano-tube-like surface structure in graphite anodes for lithium-ion secondary batteries. Physica B. 323, 127 (2002).
  35. Korovin N. V. Intercalation into cathode materials. Diffusion coefficient of Lithium. Elektrokhimiya. 33, No.6, 739 (1999) (in Russian).
  36. Xia H., Lu Li, Ceder G. Li diffusion in thin films prepared by pulsed laser deposition. J. Power Sour. 159, 1422 (2006).
  37. Ding N., Xu J., Yao Y. X., Wegner G., Fang X., Chen C. H., Lieberwirth I. Determination of the diffusion coefficient of lithium ions in nano-Si. Solid State Ionics. 180, 222 (2009).
  38. Goncalves W. D., Iost R. M., Crespilho F. N. Diffusion Mechanisms in Nanoelectrodes: Evaluating the Edge Effect. Electroch. Acta. 123, 66 (2014).
  39. Rui X. H., Ding N., Liu J., Li C., Chen C. H. Analysis of the chemical diffusion coefficient of lithium ions in Li3V2(PO4)3 cathode material. Electroch. Acta. 55, 2384 (2010).
  40. Mandzyuk V. I., Nagirna N. I., Lisovskyy R. P. Morphology and Electrochemical Properties of Thermal Modified Nanoporous Carbon as Electrode of Lithium Power Sources. J. of Nano- and Electronic Phys. 6, No.1, 01017 (2014) (in Ukrainian).
  41. Zubarev D. N., Morozov V. G., Röpke G. Statistical Mechanics of Nonequilibrium Processes, vol.1. Akademie Verlag, Berlin (1997).
  42. Kostrobij P. P., Tokarchuk M. V., Markovych B. M., Ignatyuk V. V., Hnativ B. V. Reaction-diffusion processes in systems “metal–gas”. Lviv Polytechnic National University, Lviv (2009), (in Ukrainian).
  43. Kostrobij P. P., Markovych B. M., Vasylenko A. I., Tokarchuk M. V. Viscoelastic description of electron subsystem of a semi-bounded metal within generalized "jellium" model. Condens. Matter Phys. 14, 43001 (2011).
Bibliography: 
Math. Model. Comput. Vol.1, No.2, pp.178-194 (2014)