Attraction between like-charge surfaces in polar mixtures

We examine the force between two charged surfaces immersed in aqueous mixtures having a coexistence curve. For a homogeneous water-poor phase, as the distance between the surfaces is decreased, a water-rich phase condenses at a distance D_t in the range 1-100 nm. At this distance the osmotic pressure can become negative leading to a long-range attraction between the surfaces. The osmotic pressure vanishes at a distance D_e < D _t, representing a very deep metastable or globally stable energetic state. We give analytical and numerical results for D_t and D _e on the Poisson-Boltzmann level.