Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements

TL;DR

This study investigates two-dimensional colloidal clusters of six particles, revealing how their ground and excited states are governed by entropy, symmetry, and geometric factors, and introduces a model that predicts their rearrangement dynamics without fitting parameters.

Contribution

It presents a geometric model that accurately predicts rearrangement rates in colloidal clusters based on entropy and soft modes, without requiring potential measurements.

Findings

Rearrangement rates are governed by entropy and soft modes.

The geometric model accurately predicts dynamics without fitting parameters.

Ground states are degenerate and influenced by symmetry.

Abstract

We study experimentally what is arguably the simplest yet non-trivial colloidal system: two-dimensional clusters of 6 spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose equilibrium distribution is determined by entropic factors, principally the symmetry. We observe the equilibrium rearrangements between ground states as well as all of the low-lying excited states. In contrast to the ground states, the excited states have soft modes and low symmetry, and their occupation probabilities depend on the size of the configuration space reached through internal degrees of freedom, as well as a single "sticky parameter" encapsulating the depth and curvature of the potential. Using a geometrical model that accounts for the entropy of the soft modes and the diffusion rates along them, we accurately reproduce the measured rearrangement rates. The success of this model, which requires no fitting parameters or measurements of the potential, shows that the free-energy landscape of colloidal systems and the dynamics it governs can be understood geometrically.