Dynamics of Bottlebrush Networks

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.