Computer Simulations of Bottle Brushes: From Melts to Soft Networks

Using a combination of molecular dynamics simulations and analytical calculations, we study dense bottle-brush systems in a melt and network state. Analysis of our simulation results shows that bottle-brush macromolecules in melt behave as ideal chains with effective Kuhn length b_K. Simulations show that the bottle-brush-induced bending rigidity is due to an entropy decrease caused by redistribution of the side chains upon backbone bending. The Kuhn length of the bottle brushes increases with increasing the side-chain degree of polymerization n_sc as b_K ∝ n_sc^0.46. This model of bottle-brush macromolecules is extended to describe mechanical properties of bottle-brush networks in linear and nonlinear deformation regimes. In the linear deformation regime, the network shear modulus scales with the degree of polymerization of the side chains as G₀ ∝ (n_sc + 1)^-1 as long as the ratio of the Kuhn length, b_K, to the size of the fully extended bottle-brush backbone between cross-links, R_max, is smaller than unity, b_K/R_max 蠐 1. Bottle-brush networks with b_K/R_max ∝ 1 demonstrate behavior similar to that of networks of semiflexible chains with G₀ ∝ n_sc^-0.5. In the nonlinear network deformation regime, the deformation-dependent shear modulus is a universal function of the first strain invariant I₁ and bottle-brush backbone deformation ratio β describing stretching ability of the bottle-brush backbone between cross-links. (Graph Presented).