Scaling Theory of Hairy Polymer Gels with Semiflexible Strands

We present a theory of hairy gel with variable thermodynamic rigidities of the bottlebrush strand backbone and side chains. Scaling arguments allow for the renormalization of the bottlebrush strand with a long backbone in the linear chain of impermeable subunits-superblobs. Application of de Genne's c* theorem allows for power law dependences of the swelling coefficient Q and osmotic modulus G of hairy gels in a hollow mesh regime. A filled mesh regime predicted for hairy gels with short backbones is described as a semidilute solution of side chains. We construct scaling-type diagrams of states to delineate the different regimes of hairy gel behavior and demonstrate how scaling dependences for Q and G change upon the (i) increasing stiffness of the backbone and/or side chains and (ii) inferior solvent strength from the athermal to theta solvent. The predictions of the scaling model are contrasted against computer simulations and experiments.