Monte Carlo Simulation of Polymers: Coarse-Grained Models

A coarse-grained simulation model eliminates microscopic degrees of freedom and represents a polymer by a simplified structure. A priori, two classes of coarse-grained models may be distinguished: those which are designed for a specific polymer and reflect the underlying atomistic details to some extent, and those which retain only the most basic features of a polymer chain (chain connectivity, short-range excluded-volume interactions, etc.). In this article we mainly focus on the second class of generic polymer models, while the first class of specific coarse-grained models is only touched upon briefly. Generic models are suited to explore general and universal properties of polymer systems, which occur particularly in the limit of long chains. The simulation of long chains represents a challenging problem due to the large relaxation times involved. We present some of the Monte Carlo approaches contrived to cope with this problem. More specifically, our review contains two main parts. One part (Sec. 5) deals with local and non-local updates of a polymer. While local moves allow to extract information on the physical polymer dynamics from Monte Carlo simulations, the chief aim of non-local moves is to accelerate the relaxation of the polymers. We discuss some examples for such non-local moves: the slithering-snake algorithm, the pivot algorithm, and its recently suggested variant, the double-pivot algorithm, which is particularly suited for the simulations of concentrated polymer solutions or melts. The second part (Sec. 6) focuses on modern Monte Carlo methods that were inspired by the Rosenbluth-Rosenbluth algorithm proposed in the 1950s to simulate self-avoiding walks. The modern variants discussed comprise the configuration-bias Monte Carlo method, its recent extension, the recoil-growth algorithm, and the pruned-enriched Rosenbluth method, an algorithm particularly adapted to the simulation of attractively interacting polymers.