Network Modulus and Superelasticity

We discuss the elastic modulus G and swelling/deswelling behavior of networks as a function of their concentration ϕ and their preparation state. Simple scaling ideas reproduce the prediction of James and Guth for the modulus of networks swollen in a θ solvent (G ∼ ϕ^1/3) but lead to a new prediction in a good solvent (G ∼ ϕ^7/12). We also suggest that both fully swollen modulus and dry modulus are related to swelling in ways that are independent of the network preparation details. By cross-linking long chains at low concentration and removing the solvent, many temporary entanglements are formed that force each network strand into a double-folded treelike compact configuration. These deswollen networks are capable of stretching by enormous amounts (∼ 100×) without breaking (superelastic) and have a much lower modulus than melt-cross-linked networks. The energy stored in temporary entanglements during deswelling is released upon stretching, leading to a weaker-than-linear dependence of stress σ on elongation λ in tension (σ ∼ λ^1/3).