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A Statistical Mechanical Study of Current Spikes Due to Phase Transitions at Electrode-Electrolyte Interfaces

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Abstract

We develop a statistical mechanical description of current spikes experimentally measured during first-order phase transitions on electrode surfaces. We interpret an experimental current spike as an averaged result of the finite-size effects for a large ensemble of crystalline domains (crystals) that are formed on the electrode surface, i.e., as an envelope of mutually shifted single-crystal spikes of various heights and widths. Rather than starting with a particular lattice gas model, we use rigorous results of Borgs and Kotecký on the finite-size effects valid for a large class of models to describe, in a unifying way, a spike corresponding to a first-order phase transition in a single crystal. We apply our results to fit theoretical spikes to experiment with very good precision. Whenever a phase transition is microscopically simulated by a lattice gas model, the data taken from experiment can be used to determine the strength of interactions in the model. As an illustration, we consider two experimental processes, both of which we model with the standard one-component lattice gas.

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References

  1. Kolb, D.M.: Physical and electrochemical properties of metal monolayers on metallic substrates. In: Advances in Electrochemistry and Electrochemical Engineering, vol. 11, pp. 125–271. Wiley, New York (1978)

    Google Scholar 

  2. Huckaby, D.A., Blum, L.: A model for sequential first-order phase transitions occurring in the underpotential deposition of metals. J. Electroanal. Chem. 315, 255–261 (1991)

    Article  Google Scholar 

  3. Blum, L., Huckaby, D.A.: Underpotential deposition of Cu on Au(111): implications of the HB model. J. Electroanal. Chem. 375, 69–77 (1994)

    Article  Google Scholar 

  4. Huckaby, D.A., Blum, L.: Rigorous analysis of low-temperature phases in a model for underpotential deposition of copper on the (111) surface of gold in the presence of bisulfate. Langmuir 11, 4583–4587 (1995)

    Article  Google Scholar 

  5. Huckaby, D.A., Legault, M.D., Blum, L.: Cluster variation study of the underpotential deposition of Cu on Au(111) in the presence of bisulfate. J. Chem. Phys. 109, 3600–3606 (1998)

    Article  ADS  Google Scholar 

  6. Blum, L., Huckaby, D.A.: Phase transitions at liquid-solid interfaces: Padé approximant to adsorption isotherms and voltammograms. J. Chem. Phys. 94, 6887–6894 (1991)

    Article  ADS  Google Scholar 

  7. Brown, G., Rikvold, P.A., Mitchell, S.J., Novotny, M.A.: Monte Carlo methods for equilibrium and nonequilibrium problems in interfacial electrochemistry. In: Interfacial Electrochemistry: Theory, Experiment, and Applications, pp. 47–61. Dekker, New York (1999)

    Google Scholar 

  8. Rikvold, P.A., Brown, G., Mitchell, S.J.: Statistical mechanics of lattice models of electrochemical interfaces. In: Encyclopedia of Surface and Colloid Science, pp. 4814–4824. Dekker, New York (2002)

    Google Scholar 

  9. Zhang, J., Sung, Y.-E., Rikvold, P.A., Wieckowski, A.: Underpotential deposition of Cu on Au(111) in sulfate-containing electrolytes: a theoretical and experimental study. J. Chem. Phys. 104, 5699–5712 (1996)

    Article  ADS  Google Scholar 

  10. Brown, G., Rikvold, P.A., Novotny, M.A., Wieckowski, A.: Simulated dynamics of underpotential deposition of Cu with sulfate on Au(111). J. Electrochem. Soc. 146, 1035–1040 (1999)

    Article  Google Scholar 

  11. Huckaby, D.A., Medved’, I.: Shapes of voltammogram spikes explained as resulting from the effects of finite electrode crystal sizes. J. Chem. Phys. 117, 2914–2922 (2002)

    Article  ADS  Google Scholar 

  12. Medved’, I., Huckaby, D.A.: Voltammogram spikes interpreted as envelopes of spikes resulting from electrode crystals of various sizes: application to the UPD of Cu on Au(111). J. Chem. Phys. 118, 11147–11159 (2003)

    Article  ADS  Google Scholar 

  13. Borgs, C., Kotecký, R.: Surface-induced finite-size effects for the first-order phase transitions. J. Stat. Phys. 79, 43–116 (1995)

    Article  MATH  Google Scholar 

  14. Zahradník, M.: An alternate version of Pirogov–Sinai theory. Commun. Math. Phys. 93, 559–581 (1984)

    Article  ADS  Google Scholar 

  15. Borgs, C., Imbrie, J.Z.: A unified approach to phase diagrams in field theory and statistical mechanics. Commun. Math. Phys. 123, 305–328 (1989)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. van Enter, A.C.D., Ferndández, R., Sokal, A.D.: Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory. J. Stat. Phys. 72, 879–1167 (1993)

    Article  MATH  Google Scholar 

  17. Kotecký, R., Preiss, D.: Cluster expansions for abstract polymer models. Commun. Math. Phys. 103, 491–498 (1986)

    Article  MATH  ADS  Google Scholar 

  18. Bovier, A., Zahradník, M.: A simple inductive approach to the problem of convergence of cluster expansions of polymer models. J. Stat. Phys. 100, 765–778 (2000)

    Article  MATH  Google Scholar 

  19. Miracle-Solé, S.: On the convergence of cluster expansions. Physica A 279, 244–249 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  20. Sokal, A.D.: Chromatic polynomials, Potts models, and all that. Physica A 279, 324–332 (2000)

    Article  ADS  Google Scholar 

  21. Zahradník, M.: A short course on the Pirogov–Sinai theory. Rend. Mat. Ser. VII 18, 411–486 (1998)

    MATH  Google Scholar 

  22. Kotecký, R.: Phase transitions: on a crossroads of probability and analysis. In: Highlights of Mathematical Physics, pp. 191–207. Amer. Math. Soc., Providence (2002)

    Google Scholar 

  23. Borgs, C., Kotecký, R.: A rigorous theory of finite-size scaling at first-order phase transitions. J. Stat. Phys. 61, 79–119 (1990)

    Article  Google Scholar 

  24. van Enter, A.C.D., Medved’, I., Netočný, K.: Chaotic size dependence in the Ising model with random boundary conditions. Markov Proc. Rel. Fields 8, 479–508 (2002)

    MATH  Google Scholar 

  25. Ruelle, D.: Statistical Mechanics: Rigorous Results. Benjamin, Reading (1969)

    MATH  Google Scholar 

  26. White, J.H., Abruña, H.D.: Coadsorption of copper with anions on platinum (111): the role of surface redox chemistry in determining the stability of a metal monolayer. J. Chem. Phys. 94, 894–900 (1990)

    Article  Google Scholar 

  27. Bittner, A.M., Wintterlin, J., Ertl, G.: Strain relief during metal-on-metal electrodeposition: a scanning tunneling microscopy study of copper growth on Pt(100). Surf. Sci. 376, 267–278 (1997)

    Article  Google Scholar 

  28. Kolb, D.M.: The initial stages of metal deposition: an atomistic view. In: Schering Lectures, vol. 2, pp. 5–35. Schering Research Foundation, Berlin (1991)

    Google Scholar 

  29. Yee, H.S., Abruña, H.D.: In-situ X-ray studies of the underpotential deposition of copper on platinum(111). J. Chem. Phys. 97, 6278–6288 (1993)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Constantine the Philosopher University, 949 74, Nitra, Slovakia

    Igor Medved’

  2. Department of Chemistry, Texas Christian University, Fort Worth, TX, 76129, USA

    Dale A. Huckaby

Authors
  1. Igor Medved’
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  2. Dale A. Huckaby
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Correspondence to Dale A. Huckaby.

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Medved’, I., Huckaby, D.A. A Statistical Mechanical Study of Current Spikes Due to Phase Transitions at Electrode-Electrolyte Interfaces. J Stat Phys 129, 335–376 (2007). https://doi.org/10.1007/s10955-007-9359-0

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  • DOI: https://doi.org/10.1007/s10955-007-9359-0

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