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.