Phase Transitions and Relaxation Processes in Macromolecular Systems: The Case of Bottle-brush Polymers

As an example for the interplay of structure, dynamics, and phase behavior of macromolecular systems, this article focuses on the problem of bottle-brush polymers with either rigid or flexible backbones. On a polymer with chain length $N_b$, side-chains with chain length $N$ are endgrafted with grafting density $\sigma$. Due to the multitude of characteristic length scales and the size of these polymers (typically these cylindrical macromolecules contain of the order of 10000 effective monomeric units) understanding of the structure is a challenge for experiment. But due to excessively large relaxation times (particularly under poor solvent conditions) such macromolecules also are a challenge for simulation studies. Simulation strategies to deal with this challenge, both using Monte Carlo and Molecular Dynamics Methods, will be briefly discussed, and typical results will be used to illustrate the insight that can be gained.