Title: Structure and dynamics of a vibrated granular bead-chain

Author (Poster): Kevin Safford, Clark University

Abstract:

We investigate the dynamics of a vibrated granular bead-chain with experiments and numerical simulations of random-walk models of polymers. Experiments are conducted with a chain composed of hollow 3~mm steel beads connected by flexible links confined to move on a 300mm diameter rough circular bed and observations made with digital imaging. We analyze the radius of gyration Rg, the structure factor of the chain configurations, and the diffusion of the center of mass. We find that the radius of gyration and the structure factor scale with the exponent nu ~ 3/4, consistent with the two dimensional self avoiding random walk model. Further, we observe confinement effects in the scaling of Rg as the chain length increases relative to the size of the container. We perform simulations of non-self avoiding walks confined to the same sized domain and find good agreement with experiment. The simulations show confinement effects dominates over self-avoided crossings in the experiments even when the length of chain is smaller than system size. We then examine the chain dynamics in the experiments and find that the diffusion of its center of mass scales inversely as the length of the chain, consistent with the Rouse model of polymers. We observe an exponential decay in the the dynamical structure factor and compare this exponent with the measurement of the diffusion constant from the center of mass.