Dynamics of Bottlebrush Networks: A Computational Study

We study dynamics of deformation of bottlebrush networks using molecular dynamics simulations and theoretical calculations. Analysis of our simulation results show that the dynamics of bottlebrush network deformation can be described by a Rouse model for polydisperse networks with effective Rouse time of the bottlebrush network strand, $\tau_{R} =\tau_{0} N_{s}^{2} (N_{sc} +1)$ where, N$_{\mathrm{s}}$ is the number-average degree of polymerization of the bottlebrush backbone strands between crosslinks, $N_{\mathrm{sc}}$ is the degree of polymerization of the side chains and $\tau_{0} $is a characteristic monomeric relaxation time. At time scales $t$ smaller than the Rouse time, $t<\tau_{R} $, the time dependent network shear modulus decays with time as $G(t)\propto \rho k_{B} T(\tau_{0} /t)^{1/2}$, where $\rho $is the monomer number density. However, at the time scale $t$ larger than the Rouse time of the bottlebrush strands between crosslinks, the network response is pure elastic with shear modulus $G(t)=G_{0} $, where $G_{\mathrm{0}}$ is the equilibrium shear modulus at small deformation. The stress evolution in the bottlebrush networks can be described by a universal function of $t/\tau_{R} $.