Harmonic lattice behavior of two-dimensional colloidal crystals

TL;DR

This study uses video-microscopy data and harmonic lattice theory to measure and analyze the wave-vector-dependent normal mode spring constants in a two-dimensional colloidal crystal, confirming theoretical predictions.

Contribution

It introduces a method to experimentally determine the band-structure of colloidal crystals and compares it with harmonic lattice theory predictions.

Findings

Good agreement between measured and predicted band-structure

Measured spring constants match elastic moduli as q approaches zero

Validates harmonic lattice theory for 2D colloidal crystals

Abstract

Using positional data from video-microscopy and applying the equipartition theorem for harmonic Hamiltonians, we determine the wave-vector-dependent normal mode spring constants of a two-dimensional colloidal model crystal and compare the measured band-structure to predictions of the harmonic lattice theory. We find good agreement for both the transversal and the longitudinal mode. For $q\to 0$, the measured spring constants are consistent with the elastic moduli of the crystal.