The existence of long-range attractive electrostatic forces between particles of like charge is one of the great current controversies ofcolloid science. The established theory (Derjaguin–Landau–Vervey–Overbeek; DLVO) of colloidal interactions predicts that an isolated pair of like-charged colloidal spheres in an electrolyte should experience a purely repulsive screened electrostatic (coulombic) interaction1,2. Direct measurements of such interactions have shown quantitative agreement with DLVO theory3,4,5. Recent experiments, however, provide evidence that the effective interparticle potential can have a long-range attractive component in more concentrated suspensions6,7 and for particles confined by charged glass walls3,5,8,9,10. It is apparent that the long-range attraction in concentrated systems is due to multi-body interactions and may have a similar explanation to the attraction observed for otherwise confined colloids. Theoretical explanations have been proposed11,12,13 but remain the subject of controversy14,15. Here we present a quantitative theoretical explanation of these attractive forces between confined colloidal particles, based on direct solutions of the nonlinear Poisson–Boltzmann equation for two like-charged spheres confined in a cylindrical charged pore. The calculations show that the attraction may be explained by the redistribution of the electric double layers of ions and counterions in solution around the spheres, owing to the presence of the wall; there is thus no need to revise the established concepts underlying theories of colloidal interactions.
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Derjaguin, B. V. & Landau, L. Theory of the stability of strongly charged lyophobic sols and the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochimica (USSR) 14, 633 (1941).
Verwey, E. J. & Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids (Elsevier, Amsterdam, (1948)).
Crocker, J. C. & Grier, D. G. Microscopic measurements of pair interaction potential of charge-stabilised colloid. Phys. Rev. Lett. 73, 352–355 (1994).
Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Coll. Interface Sci. 179, 298–310 (1996).
Grier, D. G. Optical tweezers in colloid and interface science. Curr. Opin. Coll. Interface Sci. 2, 264–270 (1997).
Larsen, A. E. & Grier, D. G. Like-charge attractions in metastable colloidal crystallites. Nature 385, 230–233 (1997).
Ise, N., Okubo, T., Sugimura, M., Ito, K. & Nolte, H. J. Ordered structure in dilute solutions of highly charge polymers lattices as studied by microscopy. I. Interparticle distance as a function of latex concentration. J. Chem. Phys. 78, 536–540 (1983).
Kepler, G. M. & Fraden, S. Attractive potential between confined colloids at low ionic strength. Phys. Rev. Lett. 73, 356–359 (1994).
Carbajal-Tinoco, M. D., Castro-Roman, F. & Arauz-Lara, J. L. Static properties of confined colloidal suspensions. Phys. Rev. E 53, 3745–3749 (1996).
Crocker, J. C. & Grier, D. G. When like charge particles attract: the effects of geometrical confinement on long-range colloidal interactions. Phys. Rev. Lett. 77, 1897–1900 (1996).
Sogami, I. Effect potential between charged spherical particle in dilute suspension. Phys. Lett. A 96, 199–203 (1983).
Sogami, I. & Ise, N. On the electrostatic interaction in macroionic solutions. J. Chem. Phys. 81, 6320–6332 (1984).
Chu, X. & Wasan, D. Attractive interaction between similarly charged colloidal particles. J. Coll. Interface. Sci. 184, 268–278 (1996).
Jönsson, B., Åkesson, T. & Woodward, C. E. in Ordering and Phase Transitions in Colloidal Systems (eds Arora, A. K. & Tata, B. V. R.) Ch. 11, 295–313 (VCH, New York, (1996)).
Smalley, M. V. in Ordering and Phase Transitions in Colloidal Systems (eds Arora, A. K. & Tata, B. V. R.) Ch. 12, 315–337 (VCH, New York, (1996)).
Bowen, W. R. & Sharif, A. O. Adaptive finite element solution of the non-linear Poisson–Boltzmann equation: a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. J. Coll. Interface Sci. 187, 363–374 (1997).
Russel, W. B., Saville, D. A. & Schowalter, W. R. Colloidal Dispersions (Cambridge Univ. Press, (1989)).
Hastings, R. On the crystallisation of macroionic solutions. J. Chem. Phys. 68, 675–678 (1978).
van Roij, R. & Hansen, J-P. Van der Waals-like instability is suspensions of mutually repelling charged colloids. Phys. Rev. Lett. 79, 3082–3085 (1997).
Tata, B. V. R., Yamahara, E., Rajamani, P. V. & Ise, N. Amorphous clustering in highly charged dilute poly(chlorostyrene-styrene sulfonate) colloids. Phys. Rev. Lett. 78, 2660–2663 (1997).
This work was funded by the UK Biotechnology and Biological Sciences Research Council.
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Bowen, W., Sharif, A. Long-range electrostatic attraction between like-charge spheres in a charged pore. Nature 393, 663–665 (1998). https://doi.org/10.1038/31418
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