Swelling and mechanical properties of polymer gels with cross-linking gradient

We report a novel approach to model the temperature dependence of the volume and elastic modulus of polymer gels with a cross-linking gradient based on the well-known Flory-Rehner (FR) theory. The proposed model consists of dividing the inhomogeneous polymer gel into an arbitrary number of independent and homogeneous layers that are treated independently by the FR approach. Experimental measurements of volume and elastic modulus with atomic force microscopy (AFM) on PNIPAM microgels, unexplained by the classical FR model, are in good agreement with the proposed model.