Abstract

That likes repel and opposites attract is a statement that does not seem to hold only for electrostatics but has found its way from physics into broader aspects of life as well. In the past several years it has become clear though, that in the case of strongly charged bodies likes can attract as well. This constitutes a major shift in paradigm in the theory of charged soft matter in general and has allowed us to get a deeper understanding of complicated phenomena like DNA collapse. We now show that there can be long-range attractive (or repulsive) forces even between net-neutral dielectric objects if they carry small amounts of positive and negative charges, randomly frozen within their body or on their surface. This long-range interaction arises from the interplay between randomness and image charge effects and stands at odds with the commonly accepted view that neutral objects interact only via multipolar or van der Waals (vdW) forces. It is shown that a long-range disorder-induced attraction between neutral bodies in vacuum may even swamp the ubiquitous Casimir-vdW force under certain circumstances. Indeed, such an additional attractive force has recently been inferred from experiments. We shall also discuss interactions of randomly charged surfaces across an electrolyte solution and in the limit of strong electrostatic correlations in the presence of multivalent counterions.