Multiscale modeling of soft matter: scaling of dynamics.

Many physical phenomena and properties of soft matter systems are characterized by an interplay of interactions and processes that span a wide range of length- and time scales. Computer simulation approaches require models, which cover these scales. These are typically multiscale models that combine and link different levels of resolution. In order to reach mesoscopic time- and length scales, necessary to access material properties, coarse-grained models are developed. They are based on microscopic, atomistic descriptions of systems and represent these systems on a coarser, mesoscopic level. While the connection between length scales can be established immediately, the link between the different time scales that takes into account the faster dynamics of the coarser system cannot be obtained directly. In this perspective paper we discuss methods that link the time scales in structure based multiscale models. Concepts which try to rigorously map dynamics of related models are limited to simple model systems, while the challenge in soft matter systems is the multitude of fluctuating energy barriers of comparable height. More pragmatic methods to match time scales are applied successfully to quantitatively understand and predict dynamics of one-component soft matter systems. However, there are still open questions. We point out that the link between the dynamics on different resolution levels can be affected by slight changes of the system, as for different tacticities. Furthermore, in two-component systems the dynamics of the host polymer and of additives are accelerated very differently.