On the swelling induced microstructural evolution of polymer networks in gels

A gel is formed when a polymer network is submerged in a solvent. The solvent molecules penetrate the network and cause the network to swell. In this paper we propose a microscopically-motivated energy-based framework that captures the equilibrium response of gels. The free energy of a gel comprises four contributions - the entropy of a polymer network, the energy of mixing, a total pressure term stemming from the pressure of the liquid molecules and the network in the gel, and the hydrostatic work of the external pressure exerted by the solvent. To compute the entropy of a polymer network, we employ a Langevin-based microscopically motivated model for a polymer chain that captures its finite extensibility. The integration from the chain to the network level is carried out via the numerical micro-sphere technique. The energetic contribution of the mixing process is described by well established models. The proposed framework allows us to study the micro-structural evolution of the polymer chains as the gel swells. To illustrate the macroscopic response and the evolution of the polymer chains as swelling occurs, we study three cases: (1) swelling under a constant force, (2) swelling under displacement boundary conditions, and (3) swelling of a polymeric tube with a fixed inner radius. In the first two examples, swelling leads to a homogeneous deformation and a non-uniform extension of the chains in the network. In the third case, the deformation and the extension of the chains are heterogeneous. We illustrate the spatial chain-distribution. Interestingly, we find that a fixed internal radius leads to a boundary effect that spatially fades. This work provides a better understanding of the microscopic mechanisms that govern the swelling process and suggests that the response can be controlled by micro-structural design.