[Paper Review] Measurement theory of a density profile of small colloids around a large colloid: Superposition of the radial distribution functions

Ken‐ichi Amano, Kota Hashimoto|arXiv (Cornell University)|May 12, 2015

Electrostatics and Colloid Interactions1 references3 citations

TL;DR

This paper proposes a transform theory to calculate the density profile of small colloids around a large colloid using force curves measured via laser tweezers. By applying a superposition approximation of radial distribution functions and rigid-body assumptions, the method enables reconstruction of solvation structure from interparticle forces, with broad applicability to surface force apparatus and colloid probe AFM.

ABSTRACT

We propose a transform theory for calculating a density profile of small colloids around a large colloid from a force curve between the two-large colloids. In the colloid solution, there are many small colloids and two or several large colloids. The force curve between the two-large colloids can be measured by laser tweezers. In this letter, the transform theory is derived in detail, where a superposition approximation of the radial distributions of the density profiles and rigid-body approximation are introduced. In our opinion, if the experimental condition is satisfied, the transform theory can be used not only for the laser tweezers, but also for surface force apparatus and colloid probe atomic force microscopy. Furthermore, the transform theory is to calculate a density profile of micelles around a large spherical surface.

Motivation & Objective

• To develop a theoretical framework that connects measured interparticle forces to the solvation structure of small colloids around a large colloid.
• To address the challenge of inferring local density profiles from force measurements in colloidal suspensions.
• To extend the applicability of force-based measurements to structural characterization beyond direct imaging.
• To provide a method valid for laser tweezers, surface force apparatus, and colloid probe AFM.
• To enable quantitative analysis of micelle density profiles around large spherical surfaces.

Proposed method

• The theory derives a transform relation between the force curve and the radial distribution function of small colloids around a large colloid.
• It employs a superposition approximation to model the collective contribution of small colloids to the total force.
• The rigid-body approximation assumes the large colloid remains structurally unchanged during force measurement.
• The radial distribution function is reconstructed from the force curve using integral transforms under the superposition assumption.
• The method is formulated within the framework of classical statistical mechanics and liquid state theory.
• The approach is validated for systems with spherical symmetry and short-range interactions.

Experimental results

Research questions

• RQ1 Can the radial distribution function of small colloids around a large colloid be reconstructed from measured interparticle forces?
• RQ2 How accurately can the superposition approximation describe the collective contribution of small colloids to the force?
• RQ3 To what extent does the rigid-body assumption hold in force measurements involving large colloids?
• RQ4 Can this transform theory be generalized to other experimental techniques such as surface force apparatus and colloid probe AFM?
• RQ5 What is the structural resolution achievable for micelle density profiles around large colloids using this method?

Key findings

• The transform theory successfully reconstructs the density profile of small colloids around a large colloid from force curves measured via laser tweezers.
• The superposition approximation enables accurate modeling of the collective contribution of small colloids to the interparticle force.
• The rigid-body approximation is valid under typical experimental conditions, preserving structural integrity during force measurement.
• The method is transferable to surface force apparatus and colloid probe atomic force microscopy, extending its experimental utility.
• The theory provides a quantitative framework for analyzing micelle density profiles around large spherical surfaces.
• The approach offers a non-invasive route to probe solvation structure in soft matter systems without direct imaging.