Partitioning law of polymer chains into flexible polymer networks

The equilibrium partitioning of linear polymer chains into flexible polymer networks is governed by intricate entropic constraints arising from the configurational degrees of freedom of both chains and networks; however, a quantitative understanding remains elusive. Using model hydrogels with precisely defined network structures, we experimentally demonstrate a universal law governing the partitioning of linear polymers into flexible polymer networks. We establish a label-free contactless method to measure the partition ratio, based on the increase in the osmotic pressure induced by the partitioning of the external polymer chains. Moreover, we reveal a universal law in which the partition ratio is determined solely by R_{g}/l_{cycle}, where R_{g} is the gyration radius of the polymer chain and l_{cycle}≡ξ^{-1/3} is the characteristic mesh size of the network, defined by the cycle rank ξ, i.e., the number density of elastically effective cycles.