Scattering from Melts of Combs and Bottlebrushes: Molecular Dynamics Simulations and Theoretical Study

We use coarse-grained molecular dynamics simulations to establish correlations between peak position in the static structure factor S(q) of combs and bottlebrushes in a melt and their architectural parameters such as degree of polymerization of the side chains n_sc and number of backbone bonds n_g between side chain grafting points. Analysis of the scattering function derived in the framework of the Random Phase Approximation and one obtained in simulations shows that in the comb regime with dilute side chains, n_g > n_sc, the wave number q* corresponding to the peak position in function S(q) scales with macromolecular parameters as q* ∝ (n_scn_g)^-1/4. A new scaling law q* ∝ n_sc^-3/8 emerges in the bottlebrush regime, where interactions between side chains stiffen the backbone at short length scales causing the effective backbone Kuhn length to increase with the degree of polymerization of the side chains as b_K ∝ n_sc^1/2. The established correlation between the peak position q* and bottlebrush Kuhn length provides foundation for a new method of obtaining the Kuhn length from scattering data. This approach does not require labeling of bottlebrush backbone and relays on natural contrast between side chains and backbones in the bottlebrush melts.