Abstract
The description of the concentration kinetics in the lattice fluid model used the local equilibrium representation of the distribution function of nonequilibrium states. A set of nonlinear differential-difference equations was formulated to describe the evolution of the concentration field in the system. The calculation of the correlation functions and chemical potentials applied the quasichemical approximation for nonequilibrium states. In the linear approximation, the differential equations were derived for the density region and order parameter, where the former naturally includes the kinetic diffusion coefficient and the latter includes the time of relaxation to the equilibrium state. The initial set of nonlinear difference equations was used to study the processes with high concentration gradients. The examples of these processes include a discharge of intercalation power source and phase stratification, provided that the average density in the system corresponds to unstable state in the field of the condensed-rarefied phase transition.
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References
McKinnon, W.R. and Haering, R.R., Modern Aspects in Electrochemistry, New York: Plenum, 1983, p. 235.
Vorotyntsev, M.A. and Badiali, J.P., Electrochim. Acta, 1994, vol. 39, p. 289.
Levi, M.D. and Aurbach, D., Electrochim. Acta, 1999, vol. 45, p. 167.
Nauman, E.B. and He, D.Q., Chem. Eng. Sci., 2001, vol. 56, p. 1999.
Montella, C., J. Electroanal. Chem., 2002, vol. 518, p. 61.
Han, B.C., Van der Ven, A., Morgan, D., and Ceder, G., Electrochim. Acta, 2004, vol. 49, p. 4691.
Lee, J.-W. and Pyun, S.-I., Electrochim. Acta, 2005, vol. 50, no. 9, p. 1777.
Levi, M.D. and Aurbach, D., J. Solid State Electrochem., 2008, vol. 12, p. 409.
Guo, Y.-G., Hu, Y.-S., Lee, J.-S., and Maier, J., Electrochem. Commun., 2006, vol. 8, p. 1179.
Lauri, A.., Zapadinsky, E., Vehkamaki, H., and Kulmala, M., J. Chem. Phys., 2006, vol. 125, p. 164712.
Rojas, M.J., Gimenez. M.C., Leiva E.P.M, Surf. Sci., 2005, vol. 581, p. L109.
Bisquert, J., Phys. Chem. Chem. Phys., 2008, vol. 10, p. 49.
Bullejos, P.L., Tejada, J.A.J., Deen, M.J., Marinov, O., and Patars, W.R., J. Appl. Phys., 2008, vol. 103, p. 064504.
Hogenberg, P.C. and Halperin, B.J., Rev. Mod. Phys., 1977, vol. 49, p. 435.
Bray, A.J., Adv. Phys., 1994, vol. 43, p. 357.
Gunton, J.D., J. Stat. Phys., 1999, vol. 95, p. 903.
Toxvaerd, S., J. Chem. Phys., 2001, vol. 115, p. 8913.
Rukenstein, E. and Djikaev, Y.S., Adv. Colloid Interf. Sci, 2005, vol. 118, p. 51.
Wang, X. and Aoki, K., J. Electroanal. Chem., 2007, vol. 604, p. 101.
Huot, J., New Trends in Intercalation Compounds for Energy Storage, Julien, C., Pereira-Ramos, J.P., and Momchilov, A, Eds., Dorderecht: Kluver, 2002, p. 109.
Lototsky, M.V., Yartys, V.A., Marinin, V.S., and Lototsky, N.M., J. Alloys Comp., 2003, vol. 356–357, p. 27.
Stromme, M., Solid State Ionics, 2000, vol. 131, p. 261.
Yao, T., Ozawa, N., Aikawa, T., and Yoshinaga, S., Solid State Ionics, 2004, vol. 175, p. 199.
Ukshe, E.A. and Bukun, N.G., Tverdye elektrolity (Solid Electrolytes), Moscow: Nauka, 1977.
Ivanov-Shits, A.K. and Murin, I.V., Ionika tverdogo tela (Solid State Ionics), St. Petersburg, 2000.
Plapp, M. and Gouyet, J.-F., Phys. Rev. E:, 1997, vol. 65, no. 1, p. 45.
Nassif, R., Boughaleb, Y., Hekkuori, A., Gouyet, J.-F., and Colb, M., Eur. Phys. Journ. B, 1998, vol. 1, p. 453.
Gouyet, J.-F., Plapp, M., Dietrich, W., and Maass, P., Adv. Phys., 2003, vol. 52, p. 523.
Bogolyubov, N.N., Problemy dinamicheskoi teorii v statisticheskoi fizike (Problems of Dynamic Theory in Statistical Physics), Moscow: Gostekhizdat, 1946.
Bokun, G.S., Gapanjuk, D.V., Groda, Y.G., and Vikhrenko, V.S., Electrochim. Acta, 2005, vol. 50, p. 1725.
Vikhrenko, V.S., Groda, Ya.G., and Bokun, G.S., Ravnovesnye i diffuzionnye kharakteristiki interkalyatsionnykh sistem na osnove reshetochnykh modelei (Equilibrium and Diffusion Characteristics of Intercalation Systems Based on Lattice Models), Minsk: Izd. BGTU, 2008.
Bokun, G.S., Groda, Y.G., Uebing, C., and Vikhrenko, V.S., Phys. A (Amsterdam), 2001, vol. 296, p. 83.
Eyring, H., Lin, S.H., and Lin, S.M., Basic Chemical Kinetics, New York: Wiley, 1980.
P. Hänggi, P., Talkner, P., and Borkovec, M., Rev. Mod. Phys., 1990, vol. 62, p. 251.
Tovbin, Yu.K., Teoriya fiziko-khimicheskikh protsessov na granitse gaz-tverdoe telo (Theory of Physicochemical Processes on the Gas-Solid Interface), Moscow: Nauka, 1990.
Chumak, A.A. and Tarasenko A.A., Surf. Sci., 1980, vol. 91, p. 694.
Zhdanov, V.P., Surf. Sci., 1985, vol. 149, p. L13.
Tringides, M. and Gomer, R., Surf. Sci., 1986, vol. 166, p. 419.
Uebing, C. and Gomer, R., J. Chem. Phys., 1991, vol. 95, p. 7626.
Chumak, A.A. and Argyrakis, P., Phys. Rev. B, 2002, vol. 66.
Groda, Ya.G., Argyrakis, P., Bokun, G.S., and Vikhrenko, V.S., Euro. Phys. J. B, 2003, vol. 32, p. 527.
Allnatt, A.R. and Lidiard, A.B., Atomic Transport in Solids, Cambridge: Univ. Press, 2004.
Flangen, T.B and Oates, W.A, in Hydrogen in Intermetalic Compounds, Schlapbach, L., Ed., Berlin: Springer, 1988, p. 49.
Manchester, F.D., J. Less-Common Met., 1976, vol. 49, p. 1.
Yao, T., Ozawa, N., Aikawa, T., and Yoshinaga, S., Solid State Ionics, 2004, vol. 175, p. 199.
Kitel, Ch., Vvedenie v fiziku tverdogo tela (Introduction to Solid State Physics), Moscow: Mir, 1978.
Lifshitz, E.M. and Pitaevskii, L.P., Fizicheskaya kinetika (Physical Kinetics), Moscow: Nauka, 1979.
Cahn, J.W. and Hillard, J.E., J. Chem. Phys., 1958, vol. 28, p. 258.
Nastar, M. and Clouet, E., Phys. Chem. Chem. Phys., 2004, vol. 6, p. 3611.
Khuang, K., Statisticheskaya mekhanika (Statistical Mechanics), Moscow: Mir, 1966.
Smirnova, N.A., Kolloidn. Zh., 1979, vol. 41, p. 1152.
Elenin, G.G. and Krylov, V.V., Differents. Uravn, 1983, vol. 18, p. 1223.
Rott, L.A., Statisticheskaya teoriya molekulyarnykh sistem (Statistical Theory of Molecular Systems), Moscow: Nauka, 1979.
Vikhrenko, V.S., Groda, Y.G., and Bokun, G.S., Phys. Lett. A, 2001, vol. 286, p. 127.
Kutner, R., Binder, K., and Kehr, K.W., Phys. Rev. B, 1983, vol. 28, p. 1847.
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Original Russian Text © R.N. Lasovsky, G.S. Bokun, V.S. Vikhrenko, 2010, published in Elektrokhimiya, 2010, Vol. 46, No. 4, pp. 411–422.
Published by report at IX Conference on Fundamental Problems of Solid State Ionics, Chernogolovka, 2008.
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Lasovsky, R.N., Bokun, G.S. & Vikhrenko, V.S. Concentration kinetics of intercalation systems. Russ J Electrochem 46, 389–400 (2010). https://doi.org/10.1134/S102319351004004X
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DOI: https://doi.org/10.1134/S102319351004004X