Sample-to-sample torque fluctuations in a system of coaxial randomly charged surfaces

  • Ali Naji
  • Jalal Sarabadani
  • David S. Dean
  • Rudolf Podgornik
Regular Article


Polarizable randomly charged dielectric objects have been recently shown to exhibit long-range lateral and normal interaction forces even when they are effectively net-neutral. These forces stem from an interplay between the quenched statistics of random charges and the induced dielectric image charges. This type of interaction has recently been evoked to interpret measurements of Casimir forces in vacuo, where a precise analysis of such disorder-induced effects appears to be necessary. Here we consider the torque acting on a randomly charged dielectric surface (or a sphere) mounted on a central axle next to another randomly charged surface and show that although the resultant mean torque is zero, its sample-to-sample fluctuation exhibits a long-range behavior with the separation distance between the juxtaposed surfaces and that, in particular, its root-mean-square value scales with the total area of the surfaces. Therefore, the disorder-induced torque between two randomly charged surfaces is expected to be much more pronounced than the disorder-induced lateral force and may provide an effective way to determine possible disorder effects in experiments, in a manner that is independent of the usual normal force measurement.


Soft Matter: Colloids and Nanoparticles 


  1. 1.
    H.T. Baytekin, A.Z. Patashinski, M. Branicki, B. Baytekin, S. Soh, B.A. Grzybowski, Science 333, 308 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    W.J. Kim, M. Brown-Hayes, D.A.R. Dalvit, J.H. Brownell, R. Onofrio, Phys. Rev. A 78, 020101(R) (2008)ADSCrossRefGoogle Scholar
  3. 3.
    W.J. Kim, M. Brown-Hayes, D.A.R. Dalvit, J.H. Brownell, R. Onofrio, Phys. Rev. A 79, 026102 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    W.J. Kim, A.O. Sushkov, D.A.R. Dalvit, S.K. Lamoreaux, Phys. Rev. Lett. 103, 060401 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    R.S. Decca, E. Fischbach, G.L. Klimchitskaya, D.E. Krause, D. López, U. Mohideen, V.M. Mostepanenko, Phys. Rev. A 79, 026101 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    S. de Man, K. Heeck, D. Iannuzzi, Phys. Rev. A 79, 024102 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    W.J. Kim, U.D. Schwarz, J. Vac. Sci. Technol. B 28, C4A1 (2010)CrossRefGoogle Scholar
  8. 8.
    L.F. Zagonel, N. Barrett, O. Renault, A. Bailly, M. Bäurer, M. Hoffmann, S.-J. Shih, D. Cockayne, Surf. Interface Anal. 40, 1709 (2008)CrossRefGoogle Scholar
  9. 9.
    C.C. Speake, C. Trenkel, Phys. Rev. Lett. 90, 160403 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    A. Naji, R. Podgornik, Phys. Rev. E 72, 041402 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    R. Podgornik, A. Naji, Europhys. Lett. 74, 712 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    Y.S. Mamasakhlisov, A. Naji, R. Podgornik, J. Stat. Phys. 133, 659 (2008)MathSciNetADSCrossRefMATHGoogle Scholar
  13. 13.
    E.E. Meyer, Q. Lin, T. Hassenkam, E. Oroudjev, J.N. Israelachvili, Proc. Natl. Acad. Sci. U.S.A. 102, 6839 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    S. Perkin, N. Kampf, J. Klein, Phys. Rev. Lett. 96, 038301 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    S. Perkin, N. Kampf, J. Klein, J. Phys. Chem. B 109, 3832 (2005)CrossRefGoogle Scholar
  16. 16.
    E.E. Meyer, K.J. Rosenberg, J. Israelachvili, Proc. Natl. Acad. Sci. U.S.A. 103, 15739 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    Y. Kantor, H. Li, M. Kardar, Phys. Rev. Lett. 69, 61 (1992)ADSCrossRefGoogle Scholar
  18. 18.
    I. Borukhov, D. Andelman, H. Orland, Eur. Phys. J. B 5, 869 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    A. Naji, D.S. Dean, J. Sarabadani, R.R. Horgan, R. Podgornik, Phys. Rev. Lett. 104, 060601 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    J. Sarabadani, A. Naji, D.S. Dean, R.R. Horgan, R. Podgornik, J. Chem. Phys. 133, 174702 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    D.S. Dean, A. Naji, R. Podgornik, Phys. Rev. E 83, 011102 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    S. Panyukov, Y. Rabin, Phys. Rev E 56, 7055 (1997)ADSCrossRefGoogle Scholar
  23. 23.
    D.B. Lukatsky, K.B. Zeldovich, E.I. Shakhnovich, Phys. Rev. Lett. 97, 178101 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    D.B. Lukatsky, E.I. Shakhnovich, Phys. Rev. E 77, 020901(R) (2008)ADSCrossRefGoogle Scholar
  25. 25.
    K.C. Kao, Dielectric Phenomena in Solids (Elsevier Academic Press, San Diego, 2004)Google Scholar
  26. 26.
    L.P. Pitaevskii, Phys. Rev. Lett. 101, 163202 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    V.A. Parsegian, G.H. Weiss, J. Adhes. 3, 259 (1972)CrossRefGoogle Scholar
  28. 28.
    J.N. Munday, D. Iannuzzi, Y. Barash, F. Capasso, Phys. Rev. A 71, 042102 (2005)ADSCrossRefGoogle Scholar
  29. 29.
    Y. Barash, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 12, 1637 (1978)Google Scholar
  30. 30.
    Xiang Chen, J.C.H. Spence, Phys. Status Solidi B 248, 2064 (2011)Google Scholar
  31. 31.
    A. Lambrecht, V.V. Nesvizhevsky, R. Onofrio, S. Reynaud, Class. Quantum Grav. 22, 5397 (2005)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ali Naji
    • 1
    • 2
  • Jalal Sarabadani
    • 3
  • David S. Dean
    • 4
    • 5
  • Rudolf Podgornik
    • 6
    • 7
    • 4
  1. 1.School of PhysicsInstitute for Research in Fundamental Sciences (IPM)TehranIran
  2. 2.Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK
  3. 3.Department of PhysicsUniversity of IsfahanIsfahanIran
  4. 4.Laboratoire de Physique Théorique (IRSAMC)Université de Toulouse, UPS and CNRSToulouseFrance
  5. 5.Université de Bordeaux and CNRSLaboratoire Ondes et Matière d’Aquitaine (LOMA), UMR 5798TalenceFrance
  6. 6.Department of Theoretical PhysicsJ. Stefan InstituteLjubljanaSlovenia
  7. 7.Department of Physics, Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

Personalised recommendations