Generalized Gaussian structures: Models for polymer systems with complex topologies

A fundamental and long-standing problem in polymer physics is to deduce the relationship between the topology of a polymer and its dynamics. Generalized Gaussian structures (GGS), originating from the familiar Rouse model, represent a valuable tool for this purpose. This review summarizes theoretical efforts that have been undertaken in studying the dynamics of polymer systems with complex internal topologies by employing the GGS approach. The dynamic properties of a wide range of polymeric structures (ranging from polymer networks to dendritic and hybrid polymers) are discussed, while emphasizing systems that can be treated analytically (or semi-analytically). These studies provide considerable insight into the problem of relating the structure of a polymer to its dynamics. In many cases the GGS-treatment represents a first step in understanding the dynamics of polymers, and it may serve as a reference point for the development of more realistic models.