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The present work deals with the injection and packing of a flexible polymericrod of length $L$ into a simply connected rectangular domain of area $XY$. Asthe injection proceeds, the rod bends over itself and it stores elastic energyin closed loops. In a typical experiment $N$ of these loops can be identifiedinside the cavity in the jammed state. We have performed an extensiveexperimental analysis of the total length $L(N, X, Y)$ in the tight packinglimit, and have obtained robust power laws relating these variables.Additionally, we have examined a version of this packing problem when thesimply connected domain is partially occupied with free discs of fixed size.The experimental results were obtained with 27 types of cavities and obey asingle equation of state valid for the tight packing of rods in domains ofdifferent topologies. Besides its intrinsic theoretical interest andgenerality, the problem examined here could be of interest in a number ofstudies including packing models of DNA and polymers in several complexenvironments.

Tight packing of a flexible rod in two-dimensional cavities