Formation of Buckled Equilibrium Shapes in Growing Polymer Gels

We study the effects of boundary constraints and structural patterning on the morphology of growing polymer gels using computer simulations. The 3D simulation model is based on the gel lattice-spring approach, and accounts for the neo-Hookean gel elasticity, polymer-solvent inter-diffusion, and structural changes in the polymer network in the course of growth. These gels exhibit growth by incorporating monomeric units from the surrounding solution into their network. At Stage 0 of growth, a flat parent gel swells in a solution of monomers and cross-linkers until reaching equilibrium. The presence of boundary constraints (hard walls) during swelling of the parent gel causes a spatially non-uniform distribution of monomer solution in the gel sample with the degree of swelling close to the constrained surfaces being less than that far from them. The gel loses its initial flat shape and buckles. With the walls remaining in place, we then model Stage 1 of growth which consists of polymerization and cross-linking of the species, which diffused into the parent gel during swelling, followed by the chain-exchange with the primary network to form a random copolymer network (RCN). After the removal of the sol fraction, the resulting RCN gel is put back into the initial solution and swells until equilibrium under the same boundary constraints. The resulting Stage 1 RCN gel almost replicates the shape of Stage 0 parent network buckled due to the confinement. In effect, the shape of the Stage 0 parent gel templates the morphology of the subsequently grown gel. Moreover, when the grown RCN gel is detached from the walls, it does not relax back to a flat configuration but remains in a buckled state. The growth fixes an energetically unfavorable, deformed shape into a stable configuration. We consider several scenarios of growth of the RCN gels with a stable buckled shape by introducing various combinations of the boundary constraints and structural patterning of the growing gel through varying the crosslink density in a sample. In all cases considered, upon releasing the boundary constraints, the grown RCN gels take an equilibrium buckled shape with a shape pattern governed by the compositional heterogeneity during the growth process. These gels can be used as building blocks for polymeric materials design, and have potential applications as actuators, shape morphing materials, and controlled gradient materials.