Entanglement, conformational analysis

It is instructive to compare the system of equations (3.46) and (3.47) with the system (3.37). One can see that both the radius of the tube and the positions of the particles in the Doi-Edwards model are, in fact, mean quantities from the point of view of a model of underlying stochastic motion described by equations (3.37). The intermediate length emerges at analysis of system (3.37) and can be expressed through the other parameters of the theory (see details in Chapter 5). The mean value of position of the particles can be also calculated to get a complete justification of the above model. The direct introduction of the mean quantities to describe dynamics of macromolecule led to an oversimplified, mechanistic model, which, nevertheless, allows one to make correct estimates of conformational relaxation times and coefficient of diffusion of a macromolecule in strongly entangled systems (see Sections 4.2.2 and 5.1.2). However, attempts to use this model to formulate the theory of viscoelasticity of entangled systems encounted some difficulties (for details, see Section 6.4, especially the footnote on p. 133) and were unsuccessful. 

One of the simplest ways to access chiral macrocydes involves the use of achiral building blocks and takes advantage of molecular entanglements to bias the cyclic core such that a helical conformation is preferred. An early example of a carbon-rich macrocycle possessing helical chirality is racemic compound 1, prepared by Staab and coworkers in 1972 (Fig. 6.2) [6]. The synthesis of 1 was inspired by an interest in the intramolecular interactions of transatmular triple bonds. Crystallographic analysis later confirmed the hdical structure of 1 (Fig. 6.2) and the distance between the centers of the triple bonds was measured to be 2.851 A [7]. 

The efficiency of diluent removal was found to decrease with the increase in Md and with the decrease in Me, as expected. High molecular weight diluents are extremely hard to remove at values of Me of interest in the preparation of model networks, a circumstance complicating the analysis of soluble polymer fractions in terms of degrees of perfection of the network structure. The diluents added after the end linking were the more easily removed, possibly because they were less entangled with the network structure, and this could correspond to differences in chain conformations of the diluent. 

The theoretical equations presented above can be used to interpret stress-strain measurements in uniaxial extension and thus to fully characterize elastomeric networks. In this regard, equations (124) and (125) are of particular interest since they relate the parameter k, quantifying the entanglement constraints in the Flory and Erman model, to the polymer microstructure and conformational properties and to the network topology. An illustrative analysis of stress-strain data due to Queslel, Thirion and Monnerie is reported below. 

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