Phonon dispersion curves of two-dimensional colloidal crystals: on the wavelength dependence of friction

TL;DR

This study measures phonon dispersion and decay times in 2D colloidal crystals to understand how friction varies with wavelength, revealing Stokes-like behavior at short wavelengths and negligible friction at long wavelengths.

Contribution

It provides the first detailed experimental analysis of wavelength-dependent friction coefficients in colloidal crystals using phonon measurements.

Findings

Friction coefficients are Stokes-like near the Brillouin zone edge.

Friction coefficients vanish for long wavelength phonons.

Wavelength dependence affects real-space particle dynamics.

Abstract

Digital video-microscopy measurements are reported of both elastic bandstructures and overdamped phonon decay times in two-dimensional colloidal crystals. Both quantities together allow to determine the friction coefficients along various high symmetry directions in q-space. These coefficients contain valuable information on the hydrodynamic forces acting between the colloidal particles. We find Stokes-like friction for phonons near the edge of the first Brillouin zone and vanishing friction coefficients for long wavelength phonons. The effect of this wavelength dependence in real-space is further investigated by simulating a crystal with constant friction (Langevin simulation) and comparing experimentally measured and simulated particle auto-correlation functions.