Equilibrium swelling of core–shell composite microgels

A model is developed in finite elasticity of microgels subjected to swelling. Constitutive equations are derived by means of the free energy imbalance relation for an arbitrary three-dimensional deformation with finite strains. The governing equations are applied to the analysis of equilibrium swelling of a core–shell microgel particle with a rigid core and a soft shell. The stress–strain relations involve six material constants whose effect on polymer density profile and distribution of stresses is analyzed numerically. In accord with observations, the model predicts that volume fraction of the polymer network decreases sharply near the core–shell interface, becomes practically constant in the central part of the shell, and decays to zero near the outer surface of a spherical particle.