Macroscopic and Microscopic Elasticity of Heterogeneous Polymer Gels

Polymer-network gels often exhibit local defects and spatial heterogeneity of their cross-linking density, which may differently affect their elasticity on microscopic and macroscopic scales. To appraise this effect, we prepare polymeric gels with defined extents of nanostructural heterogeneity and use atomic force microscopy to probe their local microscopic Young's moduli in comparison to their macroscopic elastic moduli measured by shear rheology. In this comparison, the moduli of the heterogeneous gels are found to be progressively smaller if the length scale of the probed gel region exceeds the size of the purposely imparted polymer-network heterogeneities. This finding can be explained with a conceptual picture of nonaffine deformation of the densely cross-linked polymer network domains in the heterogeneous gels.