Structure and dynamics of vibrated granular chains: Comparison to equilibrium polymers

We show that the statistical properties of a vibrated granular bead chain are similar to standard models of polymers in equilibrium. Granular chains of length up to N=1024 beads were confined within a circular vibrating bed, and their configurations were imaged. To differentiate the effects of persistence and confinement on the chain, we compared with simulations of both persistent random-walk (RW) and self-avoiding walk (SAW) models. Static properties, such as the radius of gyration and structure factor, are governed for short chains (N≤128) by persistence and can be matched by those of RWs. Self-avoidance and confinement effects are both important for longer chains and the results are well described by equilibrated SAWs. We also find that the collective dynamics of the granular chain is similar to the Rouse model of polymers. In particular, as long as confinement is negligible, the center of mass of the chain diffuses with a diffusion coefficient that scales as 1/N, and the dynamic structure factor decays exponentially in time.