The relationship between local liquid density and force applied on a tip of atomic force microscope: a theoretical analysis for simple liquids.

The density of a liquid is not uniform when placed on a solid. The structured liquid pushes or pulls a probe employed in atomic force microscopy, as demonstrated in a number of experimental studies. In the present study, the relation between the force on a probe and the local density of a liquid is derived based on the statistical mechanics of simple liquids. When the probe is identical to a solvent molecule, the strength of the force is shown to be proportional to the vertical gradient of ln(ρDS) with the local liquid's density on a solid surface being ρDS. The intrinsic liquid's density on a solid is numerically calculated and compared with the density reconstructed from the force on a probe that is identical or not identical to the solvent molecule.