Segmental relaxation

The mathematical treatment that arises from the dynamic dilution hypothesis is remarkably simple - and very effective in the cases of star polymers and of path length fluctuation contributions to constraint release in Hnear polymers. The physics is equally appealing all relaxed segments on a timescale rare treated in just the same way they do not contribute to the entanglement network as far as the unrelaxed material is concerned. If the volume fraction of unrelaxed chain material is 0, then on this timescale the entanglement molecular weight is renormalised to Mg/0 or, equivalently, the tube diameter to However, such a... 

A more informative representation of the reversible transition is obtained by plotting the intensity of absorption bands which are characteristic of the stressed and relaxed segments, respectively, as a function of strain. For this prupose the absorbance variations of the 1459 cm and 916cm (a-form) and 1485 an and 960 cm" (P-form) absorption bands were selected in Fig. 25. The absorbances have been corrected for changes in sample thickness wiUi the aid of the aromatic v(C—C) absorption at 1505 cm" as reference band. 

A single calculation of the discrete path integral with a fixed length of time t can be employed to compute the state conditional probability at many other times. It is possible to use segments of the path of time length At, 2At,..., NAt sampled in trajectories of total length of NAt and to compute the corresponding state conditional probabilities. The result of the calculations will make it possible to explore the exponential relaxation of P Ao B,t) for times between 0 and t. 

Suppose we divide the flow segments into classes according to relaxation times and index the various states by the subscript i. Thus the relaxation time and the component of shear stress borne by the segments in class i are and Fj, respectively. The applied shear force is related to the Fj s through... 

The isothermal curves of mechanical properties in Chap. 3 are actually master curves constructed on the basis of the principles described here. Note that the manipulations are formally similar to the superpositioning of isotherms for crystallization in Fig. 4.8b, except that the objective here is to connect rather than superimpose the segments. Figure 4.17 shows a set of stress relaxation moduli measured on polystyrene of molecular weight 1.83 X 10 . These moduli were measured over a relatively narrow range of readily accessible times and over the range of temperatures shown in Fig. 4.17. We shall leave as an assignment the construction of a master curve from these data (Problem 10). 

Studies have considered the effect of crystallinity on the performance of CR adhesives (97), on segmental mobiUty as determined by nqr studies (101), on strain induced property changes (102), and on relaxation processes (103). 

The randomization stage refers to the equilibration of the nonequilibrium conformations of the chains near the surfaces and in the case of crack healing and processing, the restoration of the molecular weight distribution and random orientation of chain segments near the interface. The conformational relaxation is of particular importance in the strength development at incompatible interfaces and affects molecular connectivity at polymer-solid interfaces. 

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

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