Long range correlations along an interfacial electric double layer

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Abstract
We analyse the density-density correlations along the planar interface of an ionic fluid. We find that the projection of these correlation functions onto the derivatives of the density profiles exhibit an Ornstein-Zernike behaviour with different amplitudes but with a common correlation length l = (γ/b)1/2, where γ is the surface tension while b is determined by the external fields. When the external electric field is uniform b is determined by the external gravitational field alone but a non-uniform electric field can lead to a negative value for b destabilizing hereby the planar interface. Projecting next the correlation functions onto the space orthogonal to that sustained by the derivatives of the density profiles we find that those correlation functions which involve the charge density do exhibit a different type of long range correlation characterized by an algebraic decay and which can be ascribed to the fact that the presence of an electric double layer inhibits the usual Coulomb screening. These findings generalize previous results to interfacial electric double layers.

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