Real Moduli of Elasticity

The moduli of elasticity determined by stress / strain measurements are generally much lower than the lattice moduli of the same polymers (Table 11-3). The difference is to be found in the effects of entropy elasticity and viscoelasticity. Since the majority of the polymer chains in such polymer samples do not lie in the stress direction, deformation can also occur by conformational changes. In addition, polymer chains may irreversibly slide past each other. Consequently, E moduli obtained from stress/strain measurements do not provide a measure of the energy elasticity. Such E moduli are no more than proportionality constants in the Hooke s law equation. The proportionality limit for polymers is about 0.l%-0.2% of the 

Theoretical and experimental moduli of elasticity of polymers of different degrees of crystallinity a cryst. 

Polymer 10 A in cm Theory E/GPa Lattice Tensile stress Q cryst / % 

Strain produced. Above this so-called proportionality limit, the relationship between stress and strain can be quite different (Section 11.5). For this reason, the modulus of elasticity of polymers is usually measured over a strain of 0.2% and over a time of 100 s. Moduli measured over higher strains or longer times are lower. 

The influence of the degree of crystallinity on the modulus of elasticity can in many cases be described with the aid of the two-phase model in the same way as for blends or fiber-reinforced plastics (see Chapter 35). The partially crystalline polymer is considered as a composite material consisting of the 

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