Reduced Variables Applied to Polymers of High Molecular Weight

Reduced Variables Applied to Polymers of High Molecular Weight 

If interest is restricted to the transition zone, the relevant motions are governed by fo and the reduction coordinates 5 through 12 are applicable in fact, the data of Figs. 11-4 refer to such a polymer of high molecular weight which is examined here in the transition zone only. 

If interest is restricted to the terminal zone, the relevant motions correspond to drag through entanglements or escape of a molecule from the effective tube which follows its contour. The terminal relaxation times are predicted to be proportional to the steady-flow viscosity rjo (equations 53 and 57 of Chapter 10), and the reduction coordinates 14 through 18 are applicable, whether or not thd parameter Me is temperature dependent (but if it is they are applicable in the terminal zone only). Reduction thus on the basis of steady-flow viscosity has been rather successful in many cases, including polyisobutylene, poly(vinyl acetate), and very concentrated solutions of polystyrene, poly(vinyl acetate) and poly( -butyl methacrylate). 2  

The question as to whether the same ot reduction factors can be applicable in both the transition and terminal zones depends on whether parameters such as Qe or Me vary with temperature. On the basis of the entanglement concept or the tube model, such temperature dependence would be expected to be very slight. In a number of cases, the same reduction factors have been found to be applicable in both zones to a close approximation. However, in polyisobutylene anc especially in very precise investigations of polystyrene 2 and poly(vinyl acetate) the absolute values of log aj in the transition zone were found to be somewhat greater than those calculated from equation 13. On the other hand, for certain methacrylate polymers and their concentrated solutions, the absolute values of log ar are found to be smaller in the transition zone than in the terminal zone. This behavior, formally attributable to a temperature-dependent Qe or Me, does not prevent successful use of the method of reduced variables within a single zone of the time scale, but in the plateau zone a complicated transition takes place (Section F below). 

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