Electrostatic force curves in finite-size-ion electrolytes.

We obtain analytical expressions for electrostatic forces between an atomic force microscope tip and a sample immersed in an electrolyte. These simple expressions relate force to tip-sample separation explicitly incorporating tip size, solvent ion size, and solvent ion concentration. If the ions are much smaller than the tip-sample gap, the force decays monotonically, a consequence of the corresponding monotonic decays of the correlation function in the Debye-Hückel context. If the ions are of size comparable to the tip-sample gap, then oscillations appear superimposed on the overall decay, a consequence of the geometric mismatch between ion cluster size and the gap size.