Extension to Bulk Polymer

Quite disappointing, however, is the comparison of the curves in this figure with those presented in Chapters 2, 4 and 5 that show the observed experimental response of bulk polymers. Experimentally, high-molecular-weight polymers exhibit two major transitions while the bead-and-spring model predicts only one, albeit with a broadened time response relative to a Maxwell model. 

Landel, and Williams10 have suggested a simple but appealing explanation for this apparent shortcoming of the theory and, moreover, have put 

We now ask which of the two friction factors has been used in the expression for zp equation (3-88). The segmental friction factor ps has been eliminated from this expression through its dependence on 77, the steady-state 

Remembering that the viscosity of a generalized Maxwell model is just the sum of the viscosities of the individual Maxwell elements will help shed light on the 2.4 factor in equation (3-92). We have already noted that all of the viscosity of a high-molecular-weight polymer derives from long-range translational motion of the polymer, that is, from motions with zp zc or where the friction factor ps is operative. Thus we may write 

If pc is greater than five, for example, the summation is relatively insensitive to changes in pc and essentially may be considered as a constant. Examination of each variable in equation (3-94) with respect to molecular-weight dependence reveals 

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