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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 1-100nm. 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.