Bottlebrushes and Combs With Bimodal Distribution of the Side Chains: Diagram of States

Scaling analysis and coarse-grained molecular dynamics (CGMD) simulations are used to elucidate properties of graft polymers with a bimodal distribution of side chains in a melt. In the scaling analysis, a two-step approach is used to classify graft polymers with grafting density of side chains 1/n_g, fraction of short side chains f, and degree of polymerization (DP) of the short (n_sc,1) and long (n_sc,2) side chains into combs and bottlebrushes. First, a diagram of states of the monodisperse graft polymers with short side chains at grafting density 1/n_g is constructed. Second, these graft polymers are considered as backbones with an effective Kuhn length b₁, to which the longer side chains are attached at grafting density (1-f)/n_g. This approach allows the reduction of four-dimensional architectural parameter space (n_g, n_sc,1, n_sc,2, f) into two two-dimensional projections. Using this representation, we extend the concept of the crowding parameter Φ, describing the degree of mutual interpenetration of the side chains belonging to neighboring macromolecules, and apply it to derive b₁ as a function of Φ. The predictions of the scaling model for b₁ and diagram of states are confirmed by CGMD simulations.