Abstract
The main problem in electrocapillarity of solid electrodes is the lack of clarity in determining the surface stress and basic equations. Within the framework of the Gibbs concept of geometrical dividing surface, the “surface stress” cannot be defined because methods of continuum mechanics can be applied to a physical surface layer (of finite thickness), but not to a mathematical surface. Gibbs never used the concept of surface stress, introducing only “surface tension” for a liquid electrode and “closely related quantity” for a solid electrode. Revisiting the derivation of the Gibbs adsorption equation, we prove its applicability to solid surfaces without the limiting requirement of constant state of strain, which was undeservedly interpreted by Eriksson as a shortcoming of the Gibbs theory caused to look for other approaches to surface stress problem. A critical analysis shows that the attempts (Shuttleworth, Eriksson, Couchman, Gokhstein, Weissmüller, etc.) to create a thermodynamic definition of the surface stress (as well as the formulation of fundamental thermodynamic equations and Maxwell relations operating with surface stresses) contain mathematical defects. It is shown that confusing interpretations of some Gibbs’ concepts encountered in the literature have led to “modifications” of the Lippmann equation based on the critical error in the Gibbs–Duhem relation due to the occurrence of an extensive variable, which is inadmissible. The famous Lippmann equation should not be modified, and it remains a unique electrocapillary relation applicable to liquid and solid electrodes.
Similar content being viewed by others
References
IUPAC. Compendium of chemical terminology (Last update: 2014-02-24; version: 2.3.3). doi:10.1351/goldbook.E01941]
Trasatti S, Parsons R (1986) Pure Appl Chem 58(3):437
Linford RG (1978) Chem Rev 78:81
Gutman EM (1995) J Phys Condens Matter 7:L663
Gutman EM (2011) Surf Sci 605:644
Gutman EM (2011) Surf Sci 605:1872
Gutman EM (2012) Surf Sci 606:772
Gibbs JW (1961) The scientific papers of J. Willard Gibbs, thermodynamics, vol 1. Dover, New York
Láng GG, Barbero CA (2012) Laser techniques for the study of electrode processes, monographs in electrochemistry. Springer, Berlin Heidelberg
Eriksson JC (1969) Surf Sci 14:221
Couchman PR, Jesser WA (1973) Surf Sci 34:212
Couchman PR, Everett DH, Jesser WA (1975) J Colloid Interface Sci 52(2):410
Couchman PR, Davidson CR (1977) J Electroanal Chem 85:407
Eriksson JC, Rusanov AI (2010) Surf Sci 604:1062
Eriksson JC, Rusanov AI (2011) Surf Sci 605:646
Shuttleworth R (1950) Proc Phys Soc 63:44
IUPAC green book quantities, units and symbols in physical chemistry (3rd edn. 2007), page 6 (page 20 of 250 in PDF file)
Hill R (1968) Int J Mech Phys Solids 16:229
Bower AF (2010) Applied Mechanics of Solids. CRC Press, New York, p 820
Hansen NR (1994) Int J Solids Struct 31(3):359
Callen HB (1961) Thermodynamics. Wiley, New York
Li JCM (1978) Metall Trans 9A:1353
Magnenet V, Rahouadj R, Ganghoffer J-F, Cunat C (2007) Int J Plast 23:87
Bockris JO’M, Reddy AKN (1973) Modern electrochemistry, vol II. Plenum, New York
Müller P, Saúl A (2004) Surf Sci Rep 54:157
Landau LD, Lifshitz EM (1981) Theory of elasticity. Pergamon, Oxford
Lippmann G (1875) Ann Chim Phys 5:494
Parsons R (1955) Trans Faraday Soc 51:1518
Li N, Lipkowski J (2000) J Electroanal Chem 491:95
Craxford SR (1940) Trans Faraday Soc 36:85
Frumkin AN, Petrii OA, Damaskin BB (1970) J Electroanal Chem 27:81
Vetter KJ (1967) Electrochemical kinetics. Academic, New York
Grahame DC, Whitney RB (1942) J Am Chem Soc 64:548
Grahame DC (1947) Chem Rev 41:441
Plieth WJ (1970) J Electroanal Chem 27:466
Gokhstein AY (1976) Poverhnostnoe natyajenie tverdyh tel i adsorbtsiya (Surface tension of solids and adsorption). Nauka, Moscow, in Russian
Gokhstein AY (1975) Russ Chem Rev 44(11):921
Gokhstein AY (2012) J Solid State Electrochem 16:3683
Lipkowski J, Schmickler W, Kolb DM, Parsons R (1998) J Electroanal Chem 452:193
Damaskin BB, Petrii OA, Batrakov VV (1971) Adsorption of organic compounds on electrodes. Plenum, New York
Gutman EM (2011) Surf Sci 605:1923
Gutman EM (2012) J Solid State Electrochem 16:2283
Gutman EM (2014) J Solid State Electrochem 18:2061. doi:10.1007/s10008-014-2433-z
Gokhstein AY (2013) J Solid State Electrochem 17:1743
Fletcher S (2013) J Solid State Electrochem. doi:10.1007/s10008-013-2287-9
Deng O, Smetanin M, Weissmüller J (2014) J Catal 309:351
Weissmüller J, Kramer D (2005) Langmuir 21:4592
Kramer D, Weissmüller J (2007) Surf Sci 601:3042
Smetanin M, Deng O, Weissmüller J (2011) Phys Chem Chem Phys 13:17313
Frumkin AN (1979) Potentials of zero charge. Nauka, Moscow (in Russian)
Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, New Jersey
Guz AN (1998) Int Appl Mech 34(10):965
Donea J, Huerta A, Ponthot Ph and Rodríguez-Ferran A (2004) in: Stein E, Borst R and Hughes T (eds), Encyclopedia of computational mechanics. Vol. 1: Fundamentals, Chapter 14, Wiley
Chung T J (2007) General continuum mechanics. Cambridge University Press
Xiao J (2007) Chen rational mechanics I. Introduction to rational mechanics. Science paper online. Ministry of Education, R.P. China
Frumkin AN, Petrii OA (1975) Electrochim Acta 20:347
Frumkin AN (1923) Z Phys Chem 103:43
Delahay P (1966) Double layer and electrode kinetics. Wiley
Trimarco C (2009) Acta Mech 204:193
Weissmüller J, Viswanath RN, Kibler LA, Kolb DM (2011) Phys Chem Chem Phys 13:2114
Smetanin M (2010) Mechanics of electrified interfaces in diluted electrolytes. Dissertation, Universitat des Saarlandes, urn:nbn:de:bsz:291-scidok-33803
Ziman JM (1964) Principles of the theory of solids. University Press, Cambridge
Gutman EM (1994) Mechanochemistry of solid surfaces. World scientific, New Jersey
Láng G, Heusler KE (1999) J Electroanal Chem 472:168
Zimmels Y (1997) J Chem Soc Faraday Trans 93(3):393
Acknowledgments
The author would like to thank Prof. F. Marken for the invitation to present this contribution.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gutman, E.M. Theoretical problems in solid electrocapillarity. J Solid State Electrochem 18, 3217–3237 (2014). https://doi.org/10.1007/s10008-014-2617-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10008-014-2617-6