Scaling probability distribution of granular chains in two dimensions

•Scaling probability distribution of granular chains in 2-D packing is studied.•The chain length in the experiment ranges from N=64N=64 to 2048.•The distributions of chains show a scaling behavior, agreeing with polymer models.•Contact exponents are compared with self-avoiding walk and compacted polymer.•Macroscopic chains are able to capture some essential aspects of real polymers.

We experimentally investigate the scaling probability distributions of various intrachain distances of granular chains in two-dimensional static packing, the chain length of which ranges from N=64N=64 to 2048. With the scaling method proposed in the polymer theory, the scaled data from granular chains tend to cluster together so as to form a single experimental fitting curve. We find that the statistical distributions for all chains show a striking scaling behavior which can be described by Redner–des Cloizeaux formula in polymer theory. Finally, a crucial contact exponent is estimated from the fitting curve and compared with that from self-avoiding walk and compacted polymer models.