Flexible subchain

As has already been reported the latter type of distribution is obtained by solving a dynamic problem for a model of flexible Gaussian subchains. It is possible to consider also a very general distribution of L(t) of Gavriliak-Negami . ... 

The theory of relaxation spectra in polarized luminescence for various dynamic models of a flexible polymer chain has been developed by several groups of workers. Wahl has proposed a theory for the model of Gaussian subchains. The authors and coworkers used dynamic chain models consisting of rigid or deformable elements with continuous visco-elastic mechanism of mobility and rotational-isomeric lattice chain... 

Figure 5.19c shows that for the hyperbranched homopolymer chains, Rg)/ Rh) decreases as the temperature decreases before the chains start to associate because Rg) decreases faster than (Rh). Note that (Rg) describes how mass is distributed in space, while Rh) contains the hydrodynamic draining. Such a size decrease as the chain shrinks was also observed for linear homopolymer chains before because of a less change in Rh) [45, 46], especially in the low temperature region. However, an opposite trend was observed for the hyperbranched copolymer chains, presumably because the shrinking of each PS block makes the subchain less flexible, which has an opposite effect on (Rg). 

It is important to emphasize that the SOR is not the inevitable consequence of fundamental physical principles rather, it is a very plausible hypothesis, which has extensive experimental support for polymer solutions and melts. In other words, there is no reason to assume that the SOR is valid under all possible flow conditions or for all possible polymer liquids. Some situations under which the SOR is expected to fail are mentioned in the next section. Many constitutive relations for solutions and melts predict that the SOR will hold, but even this apparent generality is somewhat misleading. The derivation of an SOR starts at a measurable molecular property, the optical polarizability of an isolated molecule a, and leads to a macroscopic refractive index tensor n, in a nontrivial way several substantial assumptions are necessary. Most rheological models (for flexible chains) that proceed to an SOR assume the derivation of Kuhn and Gritn (1942) for the polarizability anisotropy of a Gaussian subchain and thus in a sense make the same assumptions for the optical half of the SOR (Larson, 1988). Therefore differences between constitutive relations and their predictions for an SOR usually stem from differences in the calculation of t. 

In dilute solutions in a theta solvent, flexible polymer chains are in an isolated, ideal random coil state. For description of the dynamics in such solutions, Zimm model subdivides the chain into subchains (cf Figure 2), represents the friction and elasticity of the subchain by a bead (friction center of the subchain) and the entropic springs conneaing the beads, respectively, and analyzes the motion of this bead-spring chain in the presence of hydrodynamic and thermal... 

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