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Relation between a force curve measured on a solvated surface and the solvation structure: Relational expressions for a binary solvent and a molecular liquid

Recent atomic force microscopy (AFM) can measure force curves between a probe and a sample surface in several solvents. The force curve is thought as the solvation structure in some cases, because its shape is generally oscilltive and pitch of the oscillation is about the same as diameter of the solvent. However, it is not the solvation structure. It is just only a mean force between the probe and sample surface. Since theoretical relation between the mean force and the solvation structure had not been clearly known, we have recently derived a relational expression within a simple liquid. Although we have derived the relational expression within the simple liquid, the relational expressions for a binary solvent and a molecular liquid have still not known clearly. Hence, we try to obtain the relational expressions in the two types of the solvents. In this letter, we briefly derive the relations and explain a method for comparing the mean force measured by liquid AFM and the solvation structure (obtained by a simulation, a liquid theory, or a x-ray reflectivity). The derivations of the relational expressions are performed in the basis of classical statistical mechanics of liquid.