Collapse kinetics of vibrated granular chains

The kinetics of the collapse of the coil state into condensed states is studied with vibrated granular chain composed of N metal beads partially immersed in water. The radius of gyration of the chain, R(g) is measured. For short chains (N < 140), disk-like condensed state is formed and R(g) decreases with time such that the function ΔR(g)(2) (≡ R(g)(2) - R(g)(2)(∞)) = A e(-t/τ), where the relaxation time τ follows a power-law dependence on the chain length N with an exponent γ = 1.9 ± 0.2. For the chains with length N ≥ 300, rod-like clusters are observed during the initial stage of collapse and R(g)(2) = R(g)(2)(0) - Bt(β), with β = 0.6 ± 0.1. In the coarsening stage, the exponential dependence of ΔR(g)(2) on time still holds, however, the relaxation time τ fluctuates and has no simple dependence on N. Furthermore, the time dependence of the averaged radius of gyration of the individual clusters, R(g,cl) can be described by the theory of Lifshitz and Slyozov. A peak in the structure function of long chains is observed in the initial stage of the collapse transition. The collapse transition in the bead chains is a first order phase transition. However, features of the spinodal decomposition are also observed.