Osmotic Pressure-Based Quantification of Network Inhomogeneity in Gels via Free Radical Polymerization

Polymer gels synthesized via free radical polymerization inherently exhibit pronounced network inhomogeneity due to spatially nonuniform cross-linking distributions. While conventional light scattering techniques have been widely used to characterize these inhomogeneities, they lack quantitative reliability, particularly in turbid samples, where multiple scattering complicates analysis. Here, we present a novel macroscopic approach based on osmotic pressure measurements that enables the direct quantification of network inhomogeneity in polymer gels. By comparing the measured osmotic pressure of gels with that predicted for homogeneous semidilute polymer solutions, we quantify the fraction of insoluble polymer domains that contribute negligibly to the overall osmotic pressure. Using poly(N,N-dimethylacrylamide) (PDMAAm) hydrogels as a model system, we find a scaling law that predicts the fraction of insoluble polymer domains as a function of monomer and cross-linker concentrations. This scaling law provides a practical guideline for controlling network inhomogeneity. Our approach establishes a general framework for quantifying insoluble components in gels, overcoming the limitations of conventional semiquantitative characterization techniques.