Non-additivity of pair interactions in charged colloids

It is general wisdom that the pair potential of charged colloids in a liquid may be closely approximated by a Yukawa interaction, as predicted by the classical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We experimentally determine the effective forces in a binary mixture of like-charged particles, of species 1 and 2, with blinking optical tweezers. The measured forces are consistent with a Yukawa pair potential but the (12) cross-interaction is not equal to the geometric mean of the (11) and (22) like-interactions, as expected from DLVO. The deviation is a function of the electrostatic screening length and the size ratio, with the cross-interaction measured being consistently weaker than DLVO predictions. The corresponding non-additivity parameter is negative and grows in magnitude with increased size asymmetry.