Temperature dependence of viscoelastic property

Figure 5. Temperature dependence of viscoelastic property of ozonized lignin/epoxy resins cured with hexamethylenediamine. Ozonized lignin content in DGEBA (1) 0 PHR (2) 20 PHR (3) 40 PHR (4) 80 PHR.

Higuchi, H., Yu, Z., Jamieson, A. M., Simha, R., and McGervey, J. D., Thermal history and temperature dependence of viscoelastic properties of polymer glasses relation to free volume quantities, J. Polym. Sci. B, 33, 2295-2305 (1995). 

As is well known, molecular motions such as local mode relaxation of the main chain and rotational mode relaxation of the side chain are not frozra-in at T. The typical temperature dependence of viscoelastic properties is shown schranatkally in Fig. 3 for both crystalline and amoridious polymers. Sub ass transitions (Tp, T, Tg, etc.) corresponding to the freezing of these local motions appear as peaks in a tan temperature curve. 

In the theories for dilute solutions of flexible molecules based on the bead-spring model, the contribution of the solute to the storage shear modulus, loss modulus, or relaxation modulus is given by a series of terms the magnitude of each of which is proportional to nkT, i.e., to cRTjM, as in equation 18 of Chapter 9 alternatively, the definition of [C ]y as the zero-concentration limit of G M/cRT (equations 1 and 6 of Chapter 9) implies that all contributions are proportional to nkT. Each contribution is associated with a relaxation time which is proportional to [ri Ti)sM/RT-, the proportionality constant (= for r i) depends on which theory applies (Rouse, Zimm, etc.) but is independent of temperature, as is evident, for example, in equation 27 of Chapter 9. Thus the temperature dependence of viscoelastic properties enters in four variables [r ], t/j, T explicitly, and c (which decreases slightly with increasing temperature because of thermal expansion). 

Graessley, W. W. Effect of long branches on the temperature dependence of viscoelastic properties of polymer melts. Macromolecules (1982) 15, pp. 1164-1167... 

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