Analysis of the G t Line Shape

In practice, two approaches have been found to take the molecular-weight distribution into account in comparing Eq. (9.19) with the measured G t) line shapes of nearly monodisperse polymers  

One is to convolute Eq. (9.19) with a distribution consisting of multiple discrete components whose molecular weights and weight fractions are adjustable parameters under the constraint that the weight-average molecular weight is kept equal to the value determined from the sample characterization. That is 

The other approach is to assume that the molecular-weight distribution is described by the Schulz distribution given by 

Equation (10.4) indicates that the polydispersity of the Schulz distribution is characterized by the single parameter, Z. In this approach for a certain polymer sample, a series of G t) curves are first calculated by convoluting Eq. (9.19) with Eq. (10.3) at different Z values. Then, the optimum Z value is determined by the best superposition of the measured on the calculated G t) curve. In calculating the Git) curve at a certain Z value, the value used in Eq. (10.3) is first calculated from Eq. (10.4) with the known value of the sample. 

For polystyrene polymers with a molecular weight smaller than lOMe, the modulus plateau region is not that fiat and declines more quickly with decreasing molecular weight. As explained in Chapter 9 and will further be seen from the analysis of the G t) line shapes shown below, the main reason for this observed phenomenon is that the four relaxation processes, jjtxit), ft sit) and are getting closer to one another in time. In the 

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