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 configurational degrees of freedom of both chains and network, yet a quantitative understanding remains elusive. Using model hydrogels with precisely defined network structures, we experimentally reveal a universal law governing linear polymer partitioning into flexible polymer networks. We establish a novel label-free, contactless method to measure partition ratio, based on the increase in osmotic pressure induced by external polymer chains partitioning into the network. Moreover, we find a universal law in which the partition constant is solely determined by the squared ratio $(R_g\mathrm{/}{l}_{\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e}}{)}^2$, where $R_g$ is the gyration radius of the polymer chain and $l_{\mathrm{c}\mathrm{y}\mathrm{c}\mathrm{l}\mathrm{e}}$ is the characteristic mesh size of the network, as defined by the cycle length.