Coarse-grained depletion potentials for anisotropic colloids: application to lock-and-key systems

TL;DR

This paper introduces a method to derive approximate effective interaction potentials for anisotropic colloids, specifically lock-and-key systems, by integrating out depletants and matching virial coefficients, enabling better understanding of their behavior.

Contribution

It presents a novel coarse-graining approach for anisotropic colloids that accurately captures depletion interactions by matching virial coefficients and can be generalized to various potential forms.

Findings

The method accurately reproduces effective interactions in lock-and-key colloids.

Piecewise-constant potentials can be derived for complex anisotropic particles.

The approach is adaptable to different functional forms of interaction potentials.

Abstract

When a colloid is mixed with a depletant such as a non-adsorbing polymer, one observes attractive effective interactions between the colloidal particles. If these particles are anisotropic, analysis of these effective interactions is challenging in general. We present a method for inference of approximate (coarse-grained) effective interaction potentials between such anisotropic particles. Using the example of indented (lock-and-key) colloids, we show how numerical solutions can be used to integrate out the (hard sphere) depletant, leading to a depletion potential that accurately characterises the effective interactions. The accuracy of the method is based on matching of contributions to the second virial coefficient of the colloids. The simplest version of our method yields a piecewise-constant effective potential; we also show how this scheme can be generalised to other functional forms, where appropriate.