Swelling of a hemi-ellipsoidal ionic hydrogel for determination of material properties of deposited thin polymer films: an inverse finite element approach

Selective deposition of polymers at the surface of an ionic hydrogel is conventionally used to tailor properties of the composite material for application in for instance drug release and cell encapsulation. Here we describe a method for determination of the mechanical properties of a thin polymer film deposited on an ionic hydrogel core. The ionic strength-dependent hydrogel swelling is affected by the cross-link density and thickness of the deposited polymer layer. A hemi-ellipsoidal geometry of the hydrogel, corresponding to that employed in proof-of-concept experiments, is used to enforce biaxial deformation of the deposited layer when the ionic hydrogel core is equilibrated at various ionic strengths. The ionic strength dependent equilibrium swelling ratio of the hydrogel with the deposited polymer film is modeled using a finite element approach. The free energy of the hydrogel core includes contributions accounting for polymer mixing, elastic deformation of the network and the Donnan equilibrium. The latter type of contribution is not included in the neutral thin layer in the present study. Adding the polymer multilayer/shell at the surface reveals that the ionic strength-dependent swelling constraint is more pronounced the thicker and stiffer the film is. Combining thickness measurements of the polymer film with high resolution interferometric determination of reduction in swelling capacity of ionic hydrogels, an equivalent elastic property of the polymer layer is obtained using inverse finite element analysis. In the proof-of-concept experiments, analysis of data obtained for chitosan-alginate multilayers composed of four and eight polymer bilayers deposited on an anionic acrylamide-based hydrogel core suggests that these bilayers show an elastic stiffness one order of magnitude larger than that of the hydrogel core.