Hydrodynamic Effects of Particle Motions in Colloidal Crystal

We analyzed the particle motion in colloidal crystals by digital video microscopy, and obtained the dispersion relation of amplitude and relaxation time for the normal cooperative relaxation mode of particle dynamics. These results were found to be differ from the prediction of simple overdamped bead-spring lattice (OBS) model which predicts relaxation time to be proportional to |q|-2 for small q region. These discrepancies are believed to be the results of hydrodynamic coupling between particles. We found that relaxation mode in which large number of particles move to the same direction, i.e. small q, has much shorter relaxation time compared to the simple theory. So we introduce a simple power law dependence to dispersion relation of the q-dependent viscous drag coefficient and lattice factor. The results of modified OBS model were in good agreement with the experimental results.