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

Digital video-microscopy measurements are reported for both elastic bandstructures and overdamped phonon decay times in two-dimensional colloidal crystals. Both quantities together allow the determination of the friction coefficients along various high symmetry directions in q-space. These coefficients contain valuable information about the hydrodynamics 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.