Effect of curvature on the diffusion of colloidal bananas

Editors' Suggestion
Letter

Effect of curvature on the diffusion of colloidal bananas

Justin-Aurel Ulbrich, Carla Fernández-Rico, Brian Rost, Jacopo Vialetto, Lucio Isa, Jeffrey S. Urbach, and Roel P. A. Dullens

Phys. Rev. E 107, L042602 – Published 21 April 2023

Abstract

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods—also known as colloidal bananas—as a function of their opening angle $α$ . We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from $0^{\circ}$ (straight rods) to nearly $360^{\circ}$ (closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when $α > 180^{\circ}$ . We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Received 8 November 2022
Accepted 22 February 2023

DOI:https://doi.org/10.1103/PhysRevE.107.L042602

Physics Subject Headings (PhySH)

Brownian motion Diffusion

Colloids

Optical microscopy

Polymers & Soft Matter

Authors & Affiliations

Justin-Aurel Ulbrich ^1,2, Carla Fernández-Rico ^1,2,*, Brian Rost³, Jacopo Vialetto ², Lucio Isa ², Jeffrey S. Urbach ^3,†, and Roel P. A. Dullens ^1,4,‡

¹Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
²Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
³Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057, USA
⁴Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

^*carla.fernandezrico@mat.ethz.ch
^†urbachj@georgetown.edu
^‡roel.dullens@ru.nl

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 107, Iss. 4 — April 2023

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Diffusion of colloidal SU-8 banana-shaped particles in two dimensions. (a) Typical scanning electron microscopy image of SU-8 colloidal bananas with an average length $L$ , opening angle $α$ , and radius of curvature $R$ (see inset). (b) Optical microscopy images of colloidal bananas with increasing opening angle $α$ . (c) Optical microscopy image of a colloidal banana undergoing Brownian motion in the $x y$ plane in two different time points. The laboratory frame axes ( $x$ and $y$ , white) are fixed, while the body frame axes ( $x_{n}$ and $y_{n}$ , yellow) evolve with the particle's motion, where $n$ is the frame number. We track the displacement of the center of mass (CoM) along $x_{n + 1}$ and $y_{n + 1}$ , and also their orientation $θ_{n}$ , defined as the angle between the $x$ axis and the $x_{n}$ axis. The red arrow and white dotted lines are the orientation vector of the particles and their symmetry axis, respectively. (d) Typical trajectory and orientation field of a diffusive colloidal banana over time. All scale bars are 5 $µ m$ .
Reuse & Permissions
Figure 2
Translational diffusion coefficients as a function of the opening angle $α$ of the particles. (a) Typical mean-squared displacement of a colloidal banana with $α = 100^{\circ}$ (note that the error bars are smaller than the symbols). The inset shows the angular MSD (MSAD). All curves show diffusive behavior ( $\propto t$ ) for lag times below 10 s. The lines show the best linear fit for short times where the fitting error is $< 2 %$ . (b) Translation diffusion coefficients as a function of $α$ , along the short axis, $D_{x x}$ , and the long axis, $D_{y y}$ , of the particles. Each bin of $60^{\circ}$ is averaged over $\sim 15$ particles with a mean length of $10 \pm 2 µ m$ . The error bars represent the standard deviation. (c) Ratio of $D_{x x} / D_{y y}$ as a function of $α$ . The solid line shows the analytical result from slender body theory (SBT) and the inset a sketch of a colloidal banana with a large opening angle.
Reuse & Permissions
Figure 3
(a) Rotational diffusion and coupling coefficients for colloidal bananas as a function of their opening angle. (a) Rotational diffusion $D_{θ}$ as a function of $α$ . Each bin of $60^{\circ}$ is averaged over approximately 15 particles with a mean length of $10 \pm 2 µ m$ . (b) $D_{θ}$ times $L^{3}$ for each particle, normalized by the average value of $D_{θ} L^{3}$ measured for rods ( $N = 20$ ). Solid line: Analytical result from slender body theory. (c) Translational-rotational coupling diffusion coefficients as a function of the opening angle. While no coupling is observed between rotations and the short axis of the particles, a nonzero coupling is observed for intermediate opening angles. The error bars represent the standard deviation of the average value.
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics