Empirical Correlations Based on the Elastic Modulus

Wu [15] noted the similarity of a plot of [G ( )/G j vs to to that of the cumulative molecular weight distribution for the same polymer and developed a method for estimating the MWD. Tuminello [16] was able to improve the accuracy of the method by use of (G (6 )/G f in place of the simple ratio of the moduli. His reasoning was as follows. 

The storage modulus at a given frequency is looked upon as the plateau modulus of the molecules that have not yet relaxed, as reduced by the solvent effect of those that have relaxed. The reciprocal of the frequency is then associated with the longest relaxation time of the unrelaxed chains. As shown in Chapter 4, this relaxation time is proportional to Af . 

Ferry [17] has presented an argument leading to the conclusion that the plateau modulus of a concentrated solution should be proportional to the square of the concentration, i.e.. 

Ferry notes that de Gennes [18] had derived a slightly different scaling law based on the overlap of random coils. 

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