Effects of non-Gaussian Brownian motion on direct force optical tweezers measurements of the electrostatic forces between pairs of colloidal particles

  • Allan Raudsepp
  • Martin A.K. Williams
  • Simon B. Hall
Regular Article


Measurements of the electrostatic force with separation between a fixed and an optically trapped colloidal particle are examined with experiment, simulation and analytical calculation. Non-Gaussian Brownian motion is observed in the position of the optically trapped particle when particles are close and traps weak. As a consequence of this motion, a simple least squares parameterization of direct force measurements, in which force is inferred from the displacement of an optically trapped particle as separation is gradually decreased, contains forces generated by the rectification of thermal fluctuations in addition to those originating directly from the electrostatic interaction between the particles. Thus, when particles are close and traps weak, simply fitting the measured direct force measurement to DLVO theory extracts parameters with modified meanings when compared to the original formulation. In such cases, however, physically meaningful DLVO parameters can be recovered by comparing the measured non-Gaussian statistics to those predicted by solutions to Smoluchowski's equation for diffusion in a potential.

Graphical abstract


Soft Matter: Colloids and Nanoparticles 


  1. 1.
    B. Deraguin, L. Landau, Acta Physiochim. URSS 14, 633 (1941)Google Scholar
  2. 2.
    E.J.W. Verwey, J.T.G. Overbeek, Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, 1941)Google Scholar
  3. 3.
    J.N. Israelachvili, Intermolecular and Surface Forces (Academic Press, London, 2011)Google Scholar
  4. 4.
    A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm, S. Chu, Opt. Lett. 11, 4853 (1986)CrossRefGoogle Scholar
  5. 5.
    A. Askin, Proc. Natl. Acad. Sci. U.S.A. 94, 288 (1996)Google Scholar
  6. 6.
    T.P. Koehler, C.M. Brotherton, A.M. Grillet, Colloids Surf. A: Physicochem. Eng. Aspects 384, 282 (2011)CrossRefGoogle Scholar
  7. 7.
    C. Gutsche, U.F. Keyser, F. Kremer, Phys. Rev. E 76, 031403 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    M.M. Elmahdy, A. Synytska, A. Drechsler, C. Gutsche, P. Uhlmann, M. Stamm, F. Kremer, Macromolecules 42, 9096 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    M.M. Elmahdy, C. Gutsche, F. Kremer, Langmuir 25, 12894 (2009)CrossRefGoogle Scholar
  10. 10.
    M.M. Elmahdy, C. Gutsche, F. Kremer, J. Phys. Chem. C 114, 19452 (2010)CrossRefGoogle Scholar
  11. 11.
    C. Wagner, D. Singer, O. Ueberschär, T. Stangner, C. Gutsche, R. Hoffmann, F. Kremer, Soft Matter 7, 4370 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    O. Ueberschär, C. Wagner, T. Stangner, C. Gutsche, F. Kremer, Opt. Laser Eng. 50, 423 (2012)CrossRefGoogle Scholar
  13. 13.
    A. Raudsepp, M.R. Griffiths, A.J. Sutherland-Smith, M.A.K. Williams, Appl. Opt. 54, 9518 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    M.R. Griffiths, A. Raudsepp, K.M. McGrath, M.A.K. Williams, RSC Adv. 18, 14538 (2016)CrossRefGoogle Scholar
  15. 15.
    J.C. Crocker, D.G. Grier, Phys. Rev. Lett. 73, 02352 (1994)CrossRefGoogle Scholar
  16. 16.
    J.C. Crocker, J. Chem. Phys. 106, 072837 (1997)ADSCrossRefGoogle Scholar
  17. 17.
    S.K. Sainis, V. Germain, E.R. Dufresne, Phys. Rev. Lett. 99, 018303 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    S.K. Sainis, V. Germain, C.O. Mejean, E.R. Dufresne, Langmuir 24, 241160 (2008)Google Scholar
  19. 19.
    J.C. Crocker, J.A. Matteo, A.D. Dinsmore, A.G. Yodh, Phys. Rev. Lett. 82, 214352 (1999)ADSCrossRefGoogle Scholar
  20. 20.
    R.J. Owen, J.C. Crocker, R. Verma, A.G. Yodh, Phys. Rev. E 64, 011401 (2001)ADSCrossRefGoogle Scholar
  21. 21.
    J.K. Dreyer, K. Berg-Sørensen, L. Oddershede, Phys. Rev. E 73, 051110 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    A. Levy, D. Andelman, H. Orland, Phys. Rev. Lett. 108, 227801 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    P.S. Grassia, E.J. Hinch, L.C. Nitsche, J. Fluid Mech. 282, 373 (1995)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    W.P. Wong, K. Halvorsen, Opt. Express 14, 12517 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    A. Morita, J. Mol. Liq. 65, 75 (1995)CrossRefGoogle Scholar
  26. 26.
    P.A. Jansson, Deconvolution of Images and Spectra (Academic Press, Inc., San Diego, 1997)Google Scholar
  27. 27.
    A. Raudsepp, M.A.K. Williams, S.B. Hall, J. Mod. Opt. (2016) DOI:10.1080/09500340.2016.1199819
  28. 28.
    P.M. Hansen, J.K. Dreyer, J. Ferkinghoff-Berg, L. Oddershede, J. Colloid Interface Sci. 287, 561 (2005)CrossRefGoogle Scholar
  29. 29.
    F. Gittes, C.F. Schmidt, Opt. Lett. 23, 7 (1998)ADSCrossRefGoogle Scholar
  30. 30.
    D.R. Burnham, I. De Vlaminck, T. Henighan, C. Dekker, PLoS ONE 9, 108271 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    J.F. Marko, E.D. Siggia, Macromolecules 28, 8759 (1995)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Allan Raudsepp
    • 1
  • Martin A.K. Williams
    • 1
    • 2
  • Simon B. Hall
    • 1
    • 2
  1. 1.Institute of Fundamental SciencesMassey UniversityPalmerston NorthNew Zealand
  2. 2.MacDiarmid Institute for Advanced Material and NanotechnologyVictoria University of WellingtonWellingtonNew Zealand

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