Conversion of a force curve between chemically the same surfaces into the number density distribution of the particles on the surface using a structure factor

TL;DR

This paper introduces a new transform theory that uses the Ornstein-Zernike equation and structure factor measurements to more accurately determine the particle density distribution on colloidal surfaces from force curves.

Contribution

The authors propose a novel method employing the Ornstein-Zernike equation with a closure relation, improving accuracy over previous Kirkwood superposition-based approaches.

Findings

The new method is theoretically more accurate when structure factor data is reliable.

It utilizes the Nelder-Mead optimization technique for solution finding.

The approach enhances the analysis of force curves in colloidal systems.

Abstract

Line optical tweezer and colloidal-probe atomic force microscopy can measure force curves between two large colloidal particles of chemically the same surfaces in a suspension of small colloidal particles. Recently, the authors proposed a transform theory to obtain the number density distribution of the small colloidal particles on the large colloidal particle from the force curve. In this short letter, we propose another method which utilizes Ornstein-Zernike equation coupled with a closure equation instead of Kirkwood superposition approximation. The new transform theory uses a structure factor measured by x-ray or neutron scattering, and applies Nelder-Mead method to find the solution. Since it is known that Ornstein-Zernike equation coupled with the closure equation is accurate compared with Kirkwood superposition approximation, the new transform theory is theoretically better than the previous methods when the structure factor and the closure equation are reliable.