A method of comparison between a force curve measured on a solvated surface and the solvation structure

Recent atomic force microscopy (AFM) can measure force curves between a probe and a sample surface in solvent. 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 the sample surface. A theoretical relation between the mean force and the solvation structure is not clearly known. Therefore, the relation must be elucidated theoretically to deepen understanding of the mean force measured by the AFM. In this letter, we briefly explain the relation and a method for comparing the measured mean force and the solvation structure (that obtained by a simulation, a liquid theory, or a x-ray reflectivity) by using basic statistical mechanics of liquid.

💡 Research Summary

The paper addresses a fundamental misconception in the interpretation of force–distance curves obtained by atomic force microscopy (AFM) when the probe and the sample are immersed in a liquid. While the oscillatory shape of these curves often mirrors the size of the solvent molecules, researchers have sometimes taken the curve itself as a direct image of the solvation structure. The authors argue that the measured quantity is not the instantaneous solvent density profile but rather the mean force (or potential of mean force, PMF) acting between the probe and the surface, which is a thermodynamic average over many solvent configurations.

Using elementary statistical‑mechanical arguments, the authors derive the exact relationship between the PMF, (W(z)), and the local solvent density, (\rho(z)), along the surface‑normal coordinate (z). Starting from the definition of the PMF as the reversible work required to bring the probe from infinity to a distance (z), they show that \