Theoretical Description of Extension in Molten Polydisperse Polymers

3 Theoretical Description of Extension in Molten Polydisperse Polymers 

Numerous works aimed at theoretical description of the extension experiments (see, e.g. 42 ) failed to produce satisfactory results. It should be noted that description of shear experiments was adequate in many works (see, e.g. 43-4S)). 

Finally, in Ref.461 a satisfactory description of extension experiments and model calculations 47) was provided. 

The basis for the above-mentioned model47) was provided by Maxwell s nonlinear model obtained in general form in Ref. 48). Flere the total strain was divided into irreversible strain and elastic strain X, Stress a and velocity of irreversible strain ep were determined from the elastic strain. In Ref. 48) a number of functions a (a.) and ep(X) were defined more specifically. Beside that, Maxwell s nonlinear models were connected in parallel. Note that in case of one Maxwell s element X = a23), but in case of several elements connected in parallel this is not true and a is determined from the solution of the respective problem. In case of the uniaxial extension the model of Ref.47) takes the following form  

Note that the model given in Ref. 47) takes into account the distortion of potential barriers in activation flow under the action of stress. Relaxation time is 0k = 0k exp (—mWk) (here mk = yk/RT where yk is constant, R is gas constant, T is temperature). Normally, two Maxwell s elements (N = 2) and one viscous element with vis- 

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