Reduced Variables for Concentration Dependence

The corresponding-state plot of Fig. 17-10 implies, insofar as the curves coincide in the transition region, that all relaxation times are proportional to ib and that the magnitudes of contributions to H are all proportional to c as well as to T. This is, of course, exactly what the bead-spring chain theories predict, as in equations 18 and 20 of Chapter 9, for example (recalling that n is proportional to c). On this basis, a scheme of reduced variables can be devised to combine measurements at different concentrations as well as temperatures, without actually calculating fo and without requiring that the detailed shapes of the viscoelastic functions conform to the simple theories. 

Any composition may be chosen as a reference state. If the undiluted polymer is selected, and Uc denotes as above the ratio of relaxation times at concentration 

The effects of a diluent on viscoelastic properties of an,uncross-linked polymer in the plateau zone are dominated by its influence on the entanglement network, and especially the average entanglemept spacing. They are apparent in several characteristic aspects.  

Manifestations of Changes in Entanglement Spacing with Concentration 

The plateau compliance J% or its reciprocal, the modulus G%, can be obtained from stress relaxation, creep, or dynamic data by integrations such as equations 3 to 5 of Chapter 13 in order to determine its concentration dependence without complication of time scale shifts. Examples are shown in Fig. 17-14 for concentrated solutions of poly(methyl methacrylate) and m-polyisoprene. The 

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