Freezing transition and correlated motion in a quasi-two-dimensional colloid suspension

Recent experiments have demonstrated that the deviation of the single-particle displacement distribution from Gaussian form in a dense quasi-two-dimensional colloid suspension is a result of heterogenous dynamics that involves cooperative motions of neighboring colloid particles [J. Chem. Phys. 47, 9142 (2001)]. In this paper, we report the results of molecular dynamics (MD) simulations of a quasi-two-dimensional assembly of nearly hard-sphere colloid particles. The colloid-colloid interaction we use is short ranged and everywhere repulsive; it is related to the Marcus-Rice (MR) and modified MR interactions used in a previous study [Phys. Rev. E 58, 7529 (1998)]. As is the case for those systems, the one we study supports liquid, hexatic, and solid phases. Our calculations show that the deviation of the single-particle displacement distribution from Gaussian form is present in the liquid phase, and that a sharp increase in its magnitude occurs at the liquidus density and extends into the crystalline phase. For densities greater than the liquidus density we find three dynamical relaxation processes that include, at intermediate times, a slowing down in the rate of growth of the diffusive displacement of a particle due to the cage effect. As the density increases toward the solidus density, the dependence of the mean squared displacement on time, at intermediate times, changes from sublinear to zero. The onset of the long-time relaxation mode corresponds to the time at which the deviation of the particle displacement distribution from Gaussian form is a maximum. At this time, which increases exponentially with the density, the self-part of the van Hove function exhibits multiple maxima with respect to r while the distinct part of the van Hove function is a maximum at the origin, thereby signaling jump dynamics. At long times the particle mean square displacement has diffusive character at all densities including solid phase densities. A remarkable feature of our findings is the continuity of character of the particle displacement from the liquid phase through the hexatic phase and into the solid phase. Cooperative jumps that lead to diffusive process in crystals can be explained by a mechanism that involves many such correlated hops in random locations and random directions (but along the crystallographic axes) thereby generating effective random walk behavior. We argue that the collective motion we have found is generated by superpositions of instantaneous normal mode vibrations along diffusive paths. The diffusive paths are along the directions with strong bond orientation correlation, and start to grow in amplitude rapidly on entry into the hexatic phase.