A Transform Method of a Force Curve Obtained by Surface Force Apparatus to the Density Distribution of a Liquid on a Surface: An Improved Version

We propose a transform method from a force curve obtained by a surface force apparatus (SFA) to a density distribution of a liquid on a surface of the SFA probe. (We emphasize that the transform method is a theory for the experiment.) In the method, two-body potential between the SFA probe and the solvent sphere is modeled as the soft attractive potential with rigid wall. The model potential is more realistic compared with the rigid potential applied in our earlier work. The introduction of the model potential is the improved point of the present transform method. The transform method is derived based on the statistical mechanics of a simple liquid where the simple liquid is an ensemble of small spheres. To derive the transform method, Kirkwood superposition approximation is used. It is found that the transformation can be done by a sequential computation. It is considered that the solvation structure can be obtained more precisely by using the improved transform method.

💡 Research Summary

The paper presents a theoretical framework that converts force–distance curves measured with a Surface Force Apparatus (SFA) into the spatial density distribution of a liquid adjacent to the SFA probe surface. The authors begin by noting that, while SFA provides highly accurate quantitative force data, there has been no systematic method to translate these forces into microscopic structural information such as the solvent density profile ρ(z). Their earlier work employed a rigid‑wall (hard‑sphere) potential to model the interaction between the probe and solvent molecules, which neglected the attractive part of the real intermolecular forces. The present study improves upon this by introducing a “soft attractive potential with a rigid wall.” In practice, the potential is defined as infinite repulsion for inter‑particle separations r < σ (σ being the effective solvent radius) and a Lennard‑Jones‑type attractive tail for r ≥ σ, V(r) = ε