Temperature dependence of viscoelastic

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.

TABLE 603 Temperature Dependence of Viscoelastic Coefficients of the Red Cell Membrane... 

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). 

Free vibration methods suffer from the disadvantage that the frequency of vibration depends on the stiffness of the specimen, which varies with temperature, so that forced vibration methods are to be preferred when the frequency and temperature dependence of viscoelastic behaviour are to be investigated. 

The simplest theories that attempt to deal with the temperature dependence of viscoelastic behaviour are the transition state or barrier theories [9,10]. The site model was originally developed to explain the dielectric behaviour of solids [11,12], but was later applied to mechanical relaxations in polymers [13]. 

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... 

The fractional free volume f, which is the ratio of the free volume to the overall volume, occupies a central position in tr5nng to understand the molecular origins of the temperature dependence of viscoelastic response. The main assumption of the free-volume theory is that the fractional free volume assumes some universal value at the glass transition temperature. The Williams-Landel-Ferry (WLF) equation for the thermal dependence of the viscosity tj of polymer melts is an outgrowth of the kinetic theories based on the free volume and Eyring rate theory (35). It describes the temperature dependence of relaxation times in polymers and other glass-forming liquids above Tg (33-35). The ratio of a mechanical or dielectric relaxation time, Tm or ra, at a temperature T to its value at an arbitrary reference temperature To can be represented by a simple empirical, nearly universal function. 

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