Disordered entanglements

Since the first theoretical attempts in the 1970s (Hall and DeWames 1975 Hansen and Shen 1975a, 1975b Stockmayer and Kennedy 1975 Wang and DiMarzio 1975) to describe the chain dynamics of disordered block copolymers, little progress has been made. The molecular theory for the linear viscoelasticity of disordered block copolymers is still in its infancy. In this section, we present first the currently held linear viscoelasticity theory for unentangled disordered block copolymer and then an extended version for disordered, entangled block copolymer. 

Molecular Theory for Linear Viscoelasticity of Disordered Entangled Block Copolymers... 

At present, there is no comprehensive theory for the chain dynamics of disordered, entangled block copolymers. Using the concept of the tube model, Kim and Han (1992) modified on an ad hoc basis the Stockmayer-Kennedy theory to interpret their experimental results for the linear viscoelastic behavior of disordered, entangled PS-block-PaMS copolymers. They used the expression... 

Now, using Eq. (8.20), let us calculate the % biock of a series of disordered, entangled PS- tock-PotMS copolymers, the linear viscoelastic properties of which are presented in Figures 8.40-8.43. Since information on is not available, let us... 

At present there is no comprehensive theory predicting the linear viscoelasticity of disordered entangled block copolymers. As shown in Chapter 7, which discusses the dynamics of miscible polymer blends, the inclusion of the intermolecular interactions (perhaps via segmental interaction parameter) between the constituent blocks in a block copolymer would be very important to the development of a comprehensive molecular theory predicting the linear viscoelasticity of disordered block copolymers. 

The amorphous state, which is a disordered entanglement of polymer chains... 

For the entanglement study, FCCs were isothermally crystallized at atmospheric pressure and ECSCs with different l were isothermally crystallized from the melt to the hexagonal (disordered mobile) phase at... 

Even if completely homogeneous and disordered in the relaxed state, a real network differs from the ideal network, defined in Chapter I. Three types of network defects are commonly considered to be present in polymer networks unreacted functionalities, closed loops, and permanent chain entanglements. Within each group there are several possibilities dependent on the arrangement of chains the effect of defects on the elastic properties of the network is thus by no means simple, as has been stressed e.g. by Case (28). Several possible arrangements are shown in Fig. 1, where only nearest neighbour defect structures have been drawn. 

Fig.3 Computer simulation of a disordered densely packed amorphous polymer (BPAPC, M= 19800) the density of the simulated structure (1.2 x 103kg/m3) agrees with experimental data. Note that the shown cube of 3 nm edge length contains segments of about 30 different chains thus giving rise to a large number of topological interactions or entanglements (Courtesy U. Suter [7])...

The flow properties of disordered micellar phases are now reasonably well understood. For spherical micelles the viscosity can be estimated from modified hard-sphere-suspension theories, while for disordered semidilute cylindrical micelles the Cates theory of entangled living polymers provides at least a good starting point, and in some cases nearly quantitative prediction of rheological properties. 

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