Scaling Theory of Swelling and Deswelling of Polymer Networks

We have developed a scaling theory of the elasticity of swollen and deswollen polymer networks. The elasticity of unentangled networks is primarily due to cross-links, and the elasticity of entangled networks is due to trapped entanglements. In preparation conditions, the number of monomers Nx in strands of the unentangled network is less than the number of monomers Ne0 in an entanglement strand while Nx > Ne0 for the entangled network. A network weakly entangled at preparation conditions is predicted to behave as unentangled network upon swelling. This “disentanglement” occurs due to the separation of neighboring strands upon swelling, which reduces the restrictions on the fluctuations of strands due to their topological interactions with neighboring strands. A network unentangled at preparation conditions is predicted to behave as an entangled network upon deswelling if the number of overlapping network strands exceeds the Kavassalis–Noolandi number. The entanglements produced by network deswelling are transient, and their number increases with deswelling, while the number of trapped entanglements is fixed by cross-linking. The “entanglement” upon deswelling and “disentanglement” upon swelling can be identified by measuring the concentration dependences of the elastic modulus.