Measurement theory of a density profile of small colloids around a large colloid: Conversion of force between two-large spheres into pressure on the surface element

TL;DR

This paper introduces a new transform theory to accurately derive the density profile of small colloids around a large colloid from force measurements, improving upon existing approximations.

Contribution

It presents a novel transform method that converts force curves into surface pressure and then into density profiles, differing from the Derjaguin approximation.

Findings

Numerical matrix calculation enhances conversion accuracy.

Prototype results demonstrate the method's feasibility.

The approach offers a more precise analysis of colloidal interactions.

Abstract

We suggest a transform theory for calculating a density distribution of small colloids around a large colloid from a force curve between the two-large colloids. The main idea (calculation process) is that the force curve between the two-large colloids is converted into the pressure on the surface element of the large colloid. This conversion is different from the celebrated Derjaguin approximation. A numerical matrix calculation is performed in the conversion to calculate it more precisely. Subsequently, the pressure on the surface element is transformed into the density distribution of the small colloids around the large colloid by using a transform theory for surface force apparatus proposed by Amano. In this letter, the process of the transformation is explained and a prototype result of the transformation is shown.