Skip to main content
Log in

Current state and problems in surface tension of solids, logical and experimental analysis of basic equations

  • Modern Problems of Physical Chemistry of Surfaces, Materials Science and Protection
  • Published:
Protection of Metals and Physical Chemistry of Surfaces Aims and scope Submit manuscript

Abstract

Of the four basic thermodynamic equations for the surface tension of solids: the generalized and classical Lippmann equations, and the Shuttleworth and Gokhshtein equations, only the Gokhshtein equation has been confirmed experimentally. The generalized Lippmann equation is generally considered to be more universal, since three other equations could be derived from it. This fact has been widely accepted, but recently it was reevaluated in two opposite ways. In the first approach, the experimental verification of the Gokhshtein equation should support the correctness of the generalized Lippmann and Shuttleworth equations. In the second approach, the incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics raises doubts upon all its corollaries, including the generalized Lippmann and Gokhshtein equations. Both these logical approaches are shown to be erroneous, since the Gokhshtein equation cannot be correctly derived from any of the above-mentioned equations, and the opposite is also true: neither the generalized Lippmann nor Shuttleworth equations could be derived from the Gokhshtein equation. The high sensitivity of the contact electric resistance method to negative adsorbate charge allows detail investigation of the kinetics of the charge transfer during anion adsorption. For the fist time, this permits a tentative approach to quantify the potential dependence of the partial charge transfer during halide ions adsorption on IB metals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lippmann, F., Ann. Chem. Phys., 1875, vol. 5, p. 494.

    Google Scholar 

  2. Gibbs, J.W., The Scientific Papers of J. Willard Gibbs, N.Y.: Longmans and Green, 1931, vol. 1, p. 315.

    Google Scholar 

  3. Shuttleworth, R., Proc. Phys. Soc., 1959, vol. A 63, p. 444.

    ADS  Google Scholar 

  4. Udin, H., Shaler, A.J., and Wulff, J., Metall. Trans. AIME, 1949, vol. 185, p. 186.

    Google Scholar 

  5. Eriksson, J.C., Surface Sci., 1969, vol. 14, p. 221.

    Article  CAS  ADS  Google Scholar 

  6. Couchman, P.R. and Jesser, W.A., Surface Sci., 1973, vol. 34, p. 212.

    Article  CAS  ADS  Google Scholar 

  7. Couchman, P.R. and Davidson, C.R., Electroanal. J. Chem., 1977, vol. 85, p. 407.

    Article  CAS  Google Scholar 

  8. Trasatti, S. and Parsons, R., Pure Appl. Chem., 1986, vol. 59, p. 437.

    Article  Google Scholar 

  9. Gokhshtein, A.Ya., Russian Chem. Rev., 1975, vol. 44, p. 921.

    Article  ADS  Google Scholar 

  10. Gokhshtein, A.Ya., Surface Tension of Solids and Adsorption, Moscow: Nauka, 1976.

    Google Scholar 

  11. Guidelli, R., J. Electroanal. Chem., 1998, vol. 453, p. 69.

    Article  CAS  Google Scholar 

  12. Haiss, W., Nichols, R.J., Sass, J.K., and Charle, K.P., J. Electroanal. Chem., 1998, vol. 452, p. 199.

    Article  CAS  Google Scholar 

  13. Haiss, W., Rep. Prog. Phys., 2001, vol. 64, p. 591.

    Article  CAS  ADS  Google Scholar 

  14. Valincius, G., J. Electroanal. Chem., 1999, vol. 478, p. 40.

    Article  CAS  Google Scholar 

  15. Proost, J., J. Solid State Electrochem., 2005, vol. 9, p. 660.

    Article  CAS  Google Scholar 

  16. Garcia-Araez, N., Climent, V., Herrero, E., et al., J. Electroanal. Chem., 2005, vol. 576, p. 33, vol. 582, p. 76

    Article  CAS  Google Scholar 

  17. Lipkowski, J., Shi, Z., Chen, A., et al., Electrochim. Acta, 1998, vol. 43, p. 2875.

    Article  CAS  Google Scholar 

  18. Grafov, B.M. and Paasch, G., J. Solid State Electrochem., 2006, vol. 10, p. 636, Russian J. Electrochem., 2009, vol. 45, p. 78

    Article  Google Scholar 

  19. Eriksson, J.C. and Rusanov, A.I., Surface Sci., 2009, vol. 603, p. 2348.

    Article  CAS  ADS  Google Scholar 

  20. Frumkin, A.N., Potentials of Zero Charge, Moscow: Nauka, 1979.

    Google Scholar 

  21. Làng, G. and Heusler, K.E., J. Electroanal. Chem., 1994, vol. 377, p. 1.

    Article  Google Scholar 

  22. Làng, G. and Heusler, K.E., J. Electroanal. Chem., 1999, vol. 472, p. 168.

    Article  Google Scholar 

  23. Guidelli, R., J. Electroanal. Chem., 1999, vol. 472, p. 174.

    Article  CAS  Google Scholar 

  24. Marichev, V.A., Surface Sci. Rep., 2001, vol. 44, p. 51

    Article  CAS  ADS  Google Scholar 

  25. Marichev, V.A., Surface Sci. Rep., 2005, vol. 56, p. 277.

    Article  CAS  ADS  Google Scholar 

  26. Marichev, V.A., Surface Sci., 2006, vol. 600, p. 4527, 2008, vol. 602, p. 1131.

    Article  CAS  ADS  Google Scholar 

  27. Marichev, V.A., Chem. Phys. Lett., 2007, vol. 434, p. 218.

    Article  CAS  ADS  Google Scholar 

  28. Marichev, V.A., Protection of Metals, 2008, vol. 44, no. 1, p. 99.

    CAS  Google Scholar 

  29. Marichev, V.A., Protection of Metals, 2008, vol. 44, no. 2, p. 105.

    CAS  Google Scholar 

  30. Marichev, V.A., Protection of Metals and Physical Chemistry of Surfaces, 2009, vol. 45, no. 1, p. 1.

    CAS  Google Scholar 

  31. Marichev, V.A., Protection of Metals and Physical Chemistry of Surfaces, 2009, vol. 45, no. 3, p. 241.

    CAS  Google Scholar 

  32. Bottomley, D.J., Makkonen, L., and Kolari, K., Surface Sci., 2009, vol. 603, p. 97.

    Article  CAS  ADS  Google Scholar 

  33. Hermann, R., Geometry, Physics and Systems, N.Y.: Marcel Dekker Inc., 1973, Ch. 6, p. 259.

    MATH  Google Scholar 

  34. Marichev, V.A., Surface Sci., 2009, vol. 603, p. 2345.

    Article  CAS  ADS  Google Scholar 

  35. Eriksson, J.C. and Rusanov, A.I., Surface Sci., 2009, vol. 603, p. 2348.

    Article  CAS  ADS  Google Scholar 

  36. Ibach, H., Surface Sci., 2009, vol. 603, p. 2352.

    Article  CAS  ADS  Google Scholar 

  37. Bottomley, D.J., Makkonen, L., and Kolari, K., Surface Sci., 2009, vol. 603, (a) p. 2347; (b) p. 2350; (c) p. 2356.

    Article  CAS  ADS  Google Scholar 

  38. Marichev, V.A., Electrochem. Commun., 2008, vol. 10, p. 643.

    Article  CAS  Google Scholar 

  39. Marichev, V.A., Electrochim. Acta, 2008, vol. 53, p. 7953.

    Google Scholar 

  40. El-Aziz, A.M. and Kibler, L., Electrochem. Commun., 2002, vol. 4, p. 866.

    Article  CAS  Google Scholar 

  41. Spendelow, J.S., Goodpaster, J.D., Kenis, P.J.A., and Wieckowski, A., J. Chem. Phys. B, 2006, vol. 110, p. 9545.

    Article  CAS  Google Scholar 

  42. Lorenz, W. and Salie, G., Z. Phys. Chem., 1961, vol. 218, p. 259.

    CAS  Google Scholar 

  43. Lorenz, W., Z. Phys. Chem., 1961, vol. 218, p. 272.

    CAS  Google Scholar 

  44. Vetter, K.J., Schultze, J.W., and Bunsenges, Ber., Phys. Chem., 1972, vol. 76, pp. 920, 927.

    CAS  Google Scholar 

  45. Schultze, J.W. and Rolle, R., J. Electroanal. Chem., 2003, vol. 552, p. 163.

    Article  CAS  Google Scholar 

  46. Frumkin, A.N, Damaskin, B.B., and Petrii, O.A., J. Electroanal. Chem., 1974, vol. 53, p. 57.

    Article  CAS  Google Scholar 

  47. Frumkin, A.N. and Petrii, O.A., Electrochim. Acta, 1975, vol. 20, p. 347.

    Article  CAS  Google Scholar 

  48. Horanyi, G., Thermodynamic and Electrified Interfaces, Encyclopedia of Electrochemistry, Gileadi, E. and Urbakh, M., Eds., Weinheim: Wiley-VCH, 2002, p. 349.

    Google Scholar 

  49. de Levie, R., J. Electroanal. Chem., 2004, vol. 562, p. 273.

    Article  Google Scholar 

  50. Guidelli, R. and Schmickler, W., Modern Aspects of Electrochemistry, 2005, no. 38, p. 303.

  51. Bangle, B., Parsons, R., Sass, J.K., and Straehler, B., J. Electroanal. Chem., 1987, vol. 229, p. 87; Parsons, R., Chem. Rev., 1990, vol. 90, p. 813.

    Article  Google Scholar 

  52. Ueno, K. and Seo, M., J. Electrochem. Soc., 1999, vol. 146, p. 1496.

    Article  CAS  Google Scholar 

  53. Mrozek, M.F. and Weaver, M.J., J. Am. Chem. Soc., 2000, vol. 122, p. 150; Gao, P. and Weaver, M.J., J. Electroanal. Chem., 1987, vol. 233, p. 337.

    Article  CAS  Google Scholar 

  54. Kazarinov, V.E., Foontikov, A.M., and Tsirlina, G.A., J. Electroanal. Chem., 1990, vol. 282, p. 253.

    Article  CAS  Google Scholar 

  55. Hanewinkel, C., Otto, A., and Wandlowski, Th., Surface Sci., 1999, vol. 429, p. 255; Rikvold, R.A., Wandlowski, Th., Abou Hamad, I., et al., Electrochim. Acta, 2007, vol. 52, p. 1932.

    Article  CAS  ADS  Google Scholar 

  56. Wandlowski, Th., Wang, J.X., and Ocko, B.M., J. Electroanal. Chem., 2001, vol. 500, p. 418.

    Article  CAS  Google Scholar 

  57. Marichev, V.A., Chem. Phys. Lett., 2005, vol. 411, p. 434.

    Article  CAS  ADS  Google Scholar 

  58. Pearson, R.G., Inorganica Chimica Acta, 1995, vol. 240, p. 93.

    Article  CAS  Google Scholar 

  59. Sass, J.K. and Gimzewski, J.K., J. Electroanal. Chem., 1988, vol. 251, p. 241.

    Article  CAS  Google Scholar 

  60. Hasegawa, S. and Grey, F., Surface Sci., 2002, vol. 500, p. 84.

    Article  CAS  ADS  Google Scholar 

  61. Schmickler, W., Chem. Phys., 2003, vol. 289, p. 349.

    Article  CAS  ADS  Google Scholar 

  62. Yoon, J.-S., Bae, S.-E., Yoon, J.-H., et al., Electrochim. Acta, 2005, vol. 50, p. 4230.

    Article  CAS  Google Scholar 

  63. Crowe, M.J., Duhem and History and Philosophy of Mathematics, Syntheses, 1990, vol. 83, p. 431.

    MathSciNet  Google Scholar 

  64. Marichev, V.A., Phil. Mag., 2009, vol. 89, no. 33, p. 3037.

    Article  CAS  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Marichev.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marichev, V.A. Current state and problems in surface tension of solids, logical and experimental analysis of basic equations. Prot Met Phys Chem Surf 46, 383–402 (2010). https://doi.org/10.1134/S2070205110040015

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070205110040015

Keywords

Navigation