Effects of Translation-Rotation Coupling on the Displacement Probability Distribution Functions of Boomerang Colloidal Particles

TL;DR

This study investigates how translation-rotation coupling affects the displacement probability distribution functions of boomerang-shaped colloidal particles, revealing shape changes in PDFs due to tracking point location and confirming Gaussian behavior at long times.

Contribution

It demonstrates the impact of translation-rotation coupling on PDFs of boomerang colloids and highlights the importance of tracking point selection in analyzing their Brownian motion.

Findings

Short-time PDFs change shape with tracking point distance from CoH.

2D PDFs evolve from elliptical to crescent shape due to coupling.

Long-time PDFs revert to Gaussian distribution.

Abstract

Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with the center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arms. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical to crescent shape and the angle averaged PDFs from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. This crescent shape of 2D PDF provides a clear physical picture of the non-zero mean displacements observed in boomerangs particles.