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Origin of attraction between likely charged hydrophobic and hydrophilic walls confining near-critical binary aquaeous mixture with ions

Effect of ionic solute on a near-critical binary aqueous mixture confined between charged walls with different adsorption preferences is considered within a simple density functional theory. For the near-critical system containing small amount of ions a Landau-type functional is derived based on the assumption that the correlation, $ξ$, and the Debye screening length, $κ^{-1}$, are both much larger than the molecular size. The corresponding approximate Euler-Lagrange equations aresolved analytically for ions insoluble in the organic solvent. Nontrivial concentration profile of the solvent is found near the charged hydrophobic wall as a result of the competition between the short-range attraction of the organic solvent and the electrostatic attraction of the hydrated ions. Excess of water may be present near the hydrophobic surface for some range of the surface charge and $ξκ$. As a result, the effective potential between the hydrophilic and the hydrophobic surface can be repulsive far from the critical point, then attractive and again repulsive when the critical temperature is approached, in agreement with the recent experiment [Nellen at.al., Soft Matter {\bf 7}, 5360 (2011)].