### Zhen Cao, William F. M. Daniel, Mohammad Vatankhah-Varnosfaderani, Sergei S. Sheiko, and Andrey V. Dobrynin

The deformation dynamics of bottlebrush networks in a melt state is studied using a combination of theoretical, computational, and experimental techniques. Three main molecular relaxation processes are identified in these systems: (i) relaxation of the side chains, (ii) relaxation of the bottlebrush backbones on length scales shorter than the bottlebrush Kuhn length (*b*_{K}), and (iii) relaxation of the bottlebrush network strands between cross-links. The relaxation of side chains having a degree of polymerization (DP), *n*_{sc}, dominates the network dynamics on the time scales τ_{0} < *t* ≤ τ_{sc}, where τ_{0} and τ_{sc} ≈ τ_{0}(*n*_{sc} + 1)^{2} are the characteristic relaxation times of monomeric units and side chains, respectively. In this time interval, the shear modulus at small deformations decays with time as *G*_{0}^{BB}(*t*) ∼ *t*^{–1/2}. On time scales *t* > τ_{sc}, bottlebrush elastomers behave as networks of filaments with a shear modulus *G*_{0}^{BB}(*t*) ∼ (*n*_{sc} + 1)^{−1/4}*t*^{–1/2}. Finally, the response of the bottlebrush networks becomes time independent at times scales longer than the Rouse time of the bottlebrush network strands, τ_{BB} ≈ τ_{0}*N*^{2}(*n*_{sc} + 1)^{3/2}, where *N* is DP of the bottlebrush backbone between cross-links. In this time interval, the network shear modulus depends on the network molecular parameters as *G*_{0}^{BB}(*t*) ∼ (*n*_{sc} + 1)^{−1}*N*^{–1}. Analysis of the simulation data shows that the stress evolution in the bottlebrush networks during constant strain-rate deformation can be described by a universal function. The developed scaling model is consistent with the dynamic response of a series of poly(dimethylsiloxane) bottlebrush networks (*n*_{sc} = 14 and *N* = 50, 70, 100, 200) measured experimentally.