Using a laser tweezers method, we have determined the long-range repulsive force as a function of separation between two charged, spherical polystyrene particles ( $2.7\mu \mathrm{m}$ diameter) present at a nonpolar oil-water interface. At large separations (6 to $12\mu \mathrm{m}$ between particle centers) the force is found to decay with distance to the power $-4\mathrm{}$ and is insensitive to the ionic strength of the aqueous phase. The results are consistent with a model in which the repulsion arises primarily from the presence of a very small residual electric charge at the particle-oil interface. This charge corresponds to a fractional dissociation of the total ionizable (sulfate) groups present at the particle-oil surface of approximately $3\times {10}^{-4\mathrm{}}$.

• Received 11 October 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.246102