A theory for calculating the number density distribution of small particles on a flat wall from pressure between the two walls

TL;DR

This paper introduces a new theoretical method to determine the number density distribution of small particles on a flat wall from force measurements, eliminating the need for pair potential and approximation by using structure factors from scattering data.

Contribution

The paper presents a novel theory that derives particle distribution without pair potential or Kirkwood approximation, utilizing structure factors from scattering experiments.

Findings

The new theory successfully relates force curves to particle distributions.

It removes the reliance on pair potential and Kirkwood approximation.

The approach uses experimentally obtainable structure factors.

Abstract

Surface force apparatus (SFA) and atomic force microscopy (AFM) can measure a force curve between a substrate and a probe in liquid. However, the force curve had not been transformed to the number density distribution of solvent molecules (colloidal particles) on the substance due to the absence of such a transform theory. Recently, we proposed and developed the transform theories for SFA and AFM. In these theories, the force curve is transformed to the pressure between two flat walls. Next, the pressure is transformed to number density distribution of solvent molecules (colloidal particles). However, pair potential between the solvent molecule (colloidal particle) and the wall is needed as the input of the calculation and Kirkwood superposition approximation is used in the previous theories. In this letter, we propose a new theory that does not use both the pair potential and the approximation. Instead, it makes use of a structure factor between solvent molecules (colloidal particles) which can be obtained by X-ray or neutron scattering.