A solution for an inverse problem in liquid AFM: calculation of three-dimensional solvation structure on a sample surface

Abstract

Recent frequency-modulated atomic force microscopy (FM-AFM) can measure three-dimensional force distribution between a probe and a sample surface in liquid. The force distribution is, in the present circumstances, assumed to be solvation structure on the sample surface, because the force distribution and solvation structure have somewhat similar shape. However, the force distribution is exactly not the solvation structure. If we would like to obtain the solvation structure by using the liquid AFM, a method for transforming the force distribution into the solvation structure is necessary. Therefore, in this letter, we present the transforming method in a brief style. We call this method as a solution for an inverse problem, because the solvation structure is obtained at first and the force distribution is obtained next in general calculation processes. The method is formulated (mainly) by statistical mechanics of liquid.