Nonlinear Elasticity and Swelling of Comb and Bottlebrush Networks*

We use a combination of analytical calculations, coarse-grained molecular dynamics simulations and experiments to elucidate the effect of branched architecture on swelling of comb-like and bottlebrush networks. The equilibrium swelling ratio of such networks is shown to be larger than that of conventional linear chain networks as a result of two effects: architectural disentanglement of network strands and amplification of polymer-solvent interactions by side chains. For networks of brush-like strands with poly(dimethyl siloxane) side chains in toluene, we achieve a swelling ratio of Q = 30, which is larger than that of linear chain networks with the same strand length. All of the studied systems, including linear chain, comb, and bottlebrush networks, follow a universal scaling relation, G(Q) ∝ Q^-δ, between the shear modulus G(Q) and swelling ratio Q with scaling exponents δ = 2.6±0.08 (simulations) and δ = 2.6±0.12 (experiments). These values agree with the theoretically predicted exponent δ = 8/3, confirming dominant contribution of three body interactions to the osmotic pressure which drives network swelling.