The Behavior of Entanglements in a Polymer Gel under Isotropic Swelling

Cross-links and entanglements are two molecular features in a polymer network that transfer the macroscopic load to individual polymer chains. Existing theories assume that (1) entanglements can slide and lead to distinct elastic responses compared to cross-links in both isotropic and anisotropic deformation, and (2) permanent entanglements form during network synthesis and transient entanglements form when deswelling the polymer network from the synthesis state. Using the constrained swelling test to directly measure the osmotic pressure, we show that (1) entanglements and cross-links behave identically under isotropic swelling, indicating no entanglement sliding, and (2) the osmotic pressure follows the power law of transient entanglement in both swollen and deswollen states, indicating transient entanglements also form during network synthesis.