Long-range electrostatic attraction between like-charge spheres in a charged pore

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.