Effects of Chain Architecture on the Gel Modulus of Graft Polymer Networks

Polymer networks whose strands are made of graft polymers have been shown to possess mechanical properties similar to biological tissues and the ability to swell to larger volumes than their linear chain counterparts. We use a combination of theoretical analysis and molecular dynamics simulations to elucidate the effect of graft polymer architecture on the swelling ratio, Q, and the modulus of the swollen gel, G_gel(Q), and its relationship with the modulus of the dry network, G_dr. Our analysis indicates that for networks made of comb-like strands with with few grafted side chains the gel modulus scales as G_gel(Q)=G_dr/Q^α, with exponent α≈0.56 in a good solvent and 1/3 in a θ-solvent. For networks with bottlebrush-like strands, however, we find that the additional chain thickness and rigidity introduced by the swelling of the densely grafted side chains require a significant correction, due to the strong concentration dependence of the effective Kuhn length of the bottlebrush strands. The resulting relationship between chain architecture, swelling ratio, and gel modulus is summarized in a universal equation relating the normalized modulus Q^αG_gel(Q)/G_dr as a function of the strand architecture and effective Kuhn length.