A Hierarchical Framework for Evaluating Network Homogeneity in Polymer Gels

Polymer gels prepared by radical polymerization are widely believed to exhibit intrinsic network inhomogeneity, yet quantitative criteria to distinguish different levels of homogeneity remain limited. Here we establish a quantitative framework to evaluate network homogeneity in polymer gels by integrating optical, osmotic, and elastic criteria. While reversible addition–fragmentation chain transfer (RAFT) polymerization improves the transparency of gels, optical transparency alone does not guarantee homogeneous polymer distribution. Osmotic pressure analysis provides a physically defined primary criterion for network homogeneity, enabling identification of osmotically homogeneous networks. Using this criterion, we show that increasing the monomer concentration beyond a critical level achieves osmotic homogeneity independent of the polymerization scheme, whereas RAFT-mediated polymerization provides only partial improvement at lower monomer concentrations under high cross-linker content. We further demonstrate that elastic effectiveness constitutes a subset of osmotic homogeneity. Even within the osmotically homogeneous regime, elastic effectiveness depends on the network topology: networks prepared by RAFT polymerization exhibit elasticity closer to the ideal proportionality between elastic modulus and cycle rank than their counterparts prepared by free radical polymerization. Together, these results establish a hierarchical relationship among optical transparency, osmotic homogeneity, and elastic effectiveness in polymer gels, providing a unified framework for evaluating the network homogeneity beyond conventional qualitative indicators.