Simulation of Molecular Bottlebrush Relaxation Dynamics by DPD with Proper Orthogonal Decomposition

Molecular bottlebrushes (BBs) form from a dense grafting of side chains to a macromolecular backbone and can be synthesized in several ways -- including by atom-transfer radical polymerization (ATRP) or ring-opening metathesis polymerization (ROMP). BBs have received considerable attention in recent years due to unique physical properties that result from their architecture. For example, BBs possess very large entanglement molecular weights compared to traditional linear polymers and are typically unentangled. The conformation of BBs, along with their relaxation dynamics, play major roles in determining the physical properties of materials they comprise. Here, we discuss recent results from dissipative particle dynamics (DPD) simulations of BBs as a function of their backbone length, grafting density, and interactions with their local environment. Analyzing the relaxation dynamics is more challenging for BBs than for linear polymers because the eigenbasis used for Rouse mode analysis of linear chains does not produce the normal coordinates of the BB monomers. Using proper orthogonal decomposition (POD), we numerically calculate the eigenbasis for BBs, compare it to linear chains, and offer some interpretation of the first few modes. Finally, we discuss how the relaxation times of the BBs scale with backbone length, grafting density, and other relevant parameters. The results of our simulations are compared with experimental investigations in the literature.