Gaussian structures

Equation (22) has been confirmed by a variety of techniques including neutron scattering, dynamic light scattering, and osmotic pressured measurements [23]. As concentration increases the concentration blob decreases in size until the Kuhn length is reached and the coil displays concentrated or melt Gaussian structure. The coil accommodates concentrations between the overlap and concentrated through adjustment of the concentration blob size. 

Gurtovenko, A. A. and Blumen, A. Generalized Gaussian Structures Models for Polymer Systems with Complex Topologies. Vol. 182, pp. 171-282. 

It is interesting that the normalized memory function for , which has non-Gaussian structure, lies very dose to the normalized correlation function /< I > for the angular momentum vector, while the memory function for the angular momentum is very neariy Gaussian. The former correspondence is not surprising, since the motion of a linear molecule is equival it to that of a particle on a sphere, so that the Kubo-Shimizu consideration of a plane rotation may apply with only the numerical change which makes the relevant correlation function in the exponent of Kubo s formula. 

The characteristic Gaussian structure of the Kelvin wave was illustrated in Fig. 12. In other respects, the Kelvin wave resembles the gravity waves discussed in Section rV.B. 1 in particular, its dispersion relation is... 

Keywords Polymers Dynamics Theory Gaussian Structures Networks Dendrimers... 

The extension of Rouse s approach from linear chains to other polymer systems is quite straightforward and leads eventually to the concept of generalized Gaussian structures (GGS), which are the subject of this review. In the framework of the GGS approach, a polymer system is modeled as a collection of beads (subject to viscous friction), coimected to each other by means of elastic springs in a system-spedfic way. Initially, the GGS concept was inspired by the study of cross-linked polymer networks however, its applications have turned out to cover large classes of substances, such as dendritic polymers, hybrid polymers, and hierarchically-built structmes. 

In this article we review theoretical works which have employed the GGS model. We start - evidently - with the classical Rouse chain [1], but we will emphasize the developments that have occurred over the last decade. We want to stress from the beginning that our paper is essentially devoted to the dynamics of polymeric systems a detailed analysis of the statistical equi-hbrium properties of Gaussian structures is beyond the scope of this paper. Also, we do not aim to provide an exhaustive exposition of the GGS literature. Our choice of topics reflects in large part our research interests and is, in this sense, biased. We would also like to point out that our choice covers only limited classes of complex polymeric systems, and that we focus on such particular systems in which one can attain, to a large degree, an (almost) analytical solution of the dynamical problem. 

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