Swelling of Hydrogels With Imperfect Polymer Networks

Abstract A hydrogel consists of a cross-linked polymer network and water. There are various types of molecule chains in the polymer network, including long chains, short chains, and dangling chains. Under tensile loading, the long chains are stretched entropically, the short chains break progressively, and the dangling chains remain unchanged. The breaking of short chains results in progressive damage to the network. Meanwhile, water can easily diffuse within the network and mix with polymer chains, leading to the swelling of hydrogels. Therefore, the network damage and water diffusion are coupled for the swelling of hydrogels with imperfect polymer networks. In this work, we analyze the swelling of hydrogels with imperfect polymer networks, in which the coupling of network damage and water diffusion is addressed. We argue that the network imperfection influences not only the free energy of mixing but also the free energy of stretching. Considering three examples, free swelling of hydrogel, re-swelling of hydrogel after fast loading, and stress-relaxation of a cylindrical hydrogel bar due to water diffusion, we find that the damage of polymer network has a significant impact on the swelling of hydrogel. Particularly, the present work can capture the re-swelling behavior of hydrogel reported experimentally, and can reproduce the previous analysis for perfect hydrogel without polymer network damage.