Skip to main content

Electrostatic interaction between charged colloid particles entrapped in a thin electrolyte film: confinement effects


In this paper we consider the electrostatic interaction between charged particles confined in a thin electrolyte film. We calculate the electrostatic interaction energy between two charged particles in electrolyte film for different configurations of the particles at the film surfaces. Simple asymptotic formulae are derived for the interaction between: (i) two charged particles located in the middle of the film, (ii) two charged particles adsorbed on a single film surface and (iii) two charged particles adsorbed on opposite film surfaces. The results obtained have direct application in studies of 2D colloid crystal formation in confined geometries, in thin liquid films and oil-in-water emulsions stabilised by solid particles.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2a–c.
Fig. 3a–c.
Fig. 4a–c.
Fig. 5.
Fig. 6.
Fig. 7.


  1. Derjaguin BV (1989) Theory of stability of colloids and thin liquid films. Plenum, New York

  2. Stillinger FH (1961) J Chem Phys 35:1584

    CAS  Google Scholar 

  3. Hurd A (1985) J Phys A: Math Gen 18:L1055

  4. Pieranski P (1980) Phys Rev Lett 45:569

    Article  CAS  Google Scholar 

  5. Earnshaw JC (1986) J Phys D: Appl Phys 19:1863

    Google Scholar 

  6. Goulding D, Hansen J-P (1998) Mol Phys 95:649

    Article  CAS  Google Scholar 

  7. Aveyard R, Clint JH, Nees D, Paunov VN (2000) Langmuir 16:1969

    Article  CAS  Google Scholar 

  8. Larsen AE, Grier DG (1997) Nature 385:230

    Google Scholar 

  9. Grier DG (1998) Nature 393:621

    Article  CAS  Google Scholar 

  10. Bowen WR, Sharif AO (1998) Nature 393:663

    Article  CAS  Google Scholar 

  11. Medina-Noyola M, Ivlev BI (1995) Phys Rev E 52:6281

    Article  CAS  Google Scholar 

  12. Carbajal-Tinoco MD, Castro-Roman F, Arauz-Lara JL (1996) Phys Rev E 53:3745

    Article  CAS  Google Scholar 

  13. Kepler GM, Fraden S (1994) Phys Rev Lett 73:356

    Article  CAS  PubMed  Google Scholar 

  14. Crocker JC, Grier DG (1996) Phys Rev Lett 77:1897

    Article  CAS  PubMed  Google Scholar 

  15. Trizac E, Raimbault J-L (1999) Phys Rev E 60:6530

    Article  CAS  Google Scholar 

  16. Trizac E (2000) Phys Rev E 62:R1465

    Article  CAS  Google Scholar 

  17. Neu JC (1999) Phys Rev Lett 82:1072

    Google Scholar 

  18. Sader JE, Chan DYC (2000) Langmuir 16:324

    Article  CAS  Google Scholar 

  19. Chen SB (1998) J Colloid Interface Sci 205:354

    Article  CAS  PubMed  Google Scholar 

  20. Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover, New York

  21. Richmond P (1974) J Chem Soc Faraday Trans 70:1066

    CAS  Google Scholar 

  22. Kralchevsky PA, Paunov VN (1992) Colloids Surf 64:245

    Article  Google Scholar 

  23. Hunter RJ (1981) Zeta potential in colloid science. Academic Press, New York

  24. Gradshtein IS, Ryzhik IM (1980) Table of integrals series and products, Academic Press, New York

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Vesselin. N. Paunov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Paunov, V.N. Electrostatic interaction between charged colloid particles entrapped in a thin electrolyte film: confinement effects. Colloid Polym Sci 281, 701–707 (2003).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Electrostatic interaction
  • Image forces
  • Thin liquid films
  • Confined geometry
  • Adsorbed particles