Theoretical models for bridging timescales in polymer dynamics

The dynamics of macromolecules are characterized by the presence of several length scales and related timescales in which relevant phenomena take place. This defines the complex nature of the liquid and renders its theoretical treatment a difficult matter. The necessity of developing theoretical approaches that can describe in a comprehensive manner properties observed at many different length scales is a fundamental challenge in polymer physics. This review paper summarizes some key problems arising from this challenge and different approaches taken so far in attempting to solve them. Theoretical models play a pivotal role in building the infrastructure that allows one to model these multiscale properties. We present methods for coarse-graining the structure of soft-matter systems, which provide effective potentials that are input to multiscale simulations. We also present methods for coarse-graining the dynamics of macromolecules in dilute solutions and in the melt state. Although much progress has already been made, obtaining comprehensive theoretical tools that are efficient and reliable in predicting complex fluid dynamics across many timescales of interest still remains an open challenge.