Abstract
Using the Nyquist fluctuation-dissipation theorem, the analysis of thermal fluctuations in a complex electrochemical system is carried out for the case of slow discharge accompanied by surfactant adsorption. It is shown that the dispersion of thermal fluctuations of the total and free charges of a reversible electrode obey an equation general for both Gibbs and Einstein-Landau approaches to the theory of thermal fluctuations of extensive values and also the noise approach based on the Nyquist fluctuation-dissipation theorem. Thus, in contrast to the higher correlations of the fluctuating electrode charge, the Gibbs theory of squared correlations is in complete agreement with the Nyquist fluctuation-dissipation theorem.
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References
Frumkin, A.N., Potentsialy nulevogo zaryada (Zero-Charge Potentials), Moscow: Nauka, 1979.
Tolman, R.T., The Principles of Statistical Mechanics, New York: Dover Publications, 1979.
Landau, L.D. and Lifshitz, E.M., Statisticheskaya fizika (Statistical Physics), Moscow: Nauka, 1964.
Rudoi, Yu.G. and Sukhanov, A.D., Usp. Fiz. Nauk, 2000, vol. 43, p. 1265 [Phys.-Usp. (Engl. Transl.), vol. 43, p.].
Grafov, B.M., Elektrokhimiya, 2005, vol. 41, p. 31 [Russ. J. Electrochem. (Engl. Transl.), vol. 41, p.].
Grafov, B.M., Fluctuation Noise Lett., 2006, vol. 6, p. L367.
Levich, V.G., Vvedenie v statisticheskuyu fiziku (Instroduction to Statistical Physics), Moscow: Gostekhteoretizdat, 1954.
Dubkov, A.A., Hanggi, P., and Goychuk, I., J. Stat. Mechanics, 2009.
Fluktuatsii i shumy v slozhnykh sistemakh zhivoi i nezhivoi prirody (Fluctuations and Noises in Complex Systems and Living and Nonliving Nature), Yul’met’ev, R.M., Mokshin, A.V., Demin, S.A., and Salakhov, M.Kh., Eds., Kazan’: RITs “Shkola”, 2008.
Coffey, W.T., Kalmykov, Yu.P., and Waldron, J.T., The Langevin Equation, New Jersey: World Scientific, 2004.
Gammaitoni, L., Hanggi, P., Jung, P., and Marchesoni, F., Rev. Mod. Phys, 1998, vol. 70, p. 223.
Casado-Pascual, J., Gomez-Ordonez, J., Morillo, M., and Hanggi, P., Fluctuation Noise Lett., 2002, vol. 2, p. L127.
Bixon, M. and Zwanzig, R., J. Stat. Phys., 1971, vol. 3, p. 245.
Nyquist, H., Phys. Rev., 1928, vol. 32, p. 110.
Callen, H.B. and Welton, T.A., Phys. Rev., 1951, vol. 83, p. 34.
Rytov, S.M., Kravtsov, Yu.A., and Tatarskii, V.I., Principles of Statistical Radiophysics 2. Correlation Theory of Random Processes, Berlin: Springer, 1988.
Stratonovich, R.L., Zh. Eksp. Teor. Fiz., 1970, vol. 58, p. 1612.
Kogan, Sh., Electronic Noise and Fluctuations in Solids, Cambridge: Cambridge University, 1996.
Bochkov, G.N. and Kuzovlev, Yu.E., Zh. Eksp. Teor. Fiz., 1977, vol. 72, p. 238.
Bernard, W. and Callen, H.B., Rev. Mod. Phys., 1959, vol. 31, p. 1017.
Grafov, B.M. and Ukshe, E.A., Elektrokhimicheskie tsepi peremennogo toka (Electrochemical Alternating Current Circuits), Moscow: Nauka, 1963.
Grafov, B.M., Elektrokhimiya, 1993, vol. 29, p. 1474 [Russ. J. Electrochem. (Engl. Transl.), vol. 29, p.].
Ginzburg, V.L., Usp. Fiz. Nauk, 1954, vol. 52, p. 494.
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Original Russian Text © B.M. Grafov, 2010, published in Elektrokhimiya, 2010, Vol. 46, No. 2, pp. 249–252.
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Grafov, B.M. Thermal fluctuations of total and free electrode charges. Russ J Electrochem 46, 239–242 (2010). https://doi.org/10.1134/S1023193510020187
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DOI: https://doi.org/10.1134/S1023193510020187