Mechanical behaviour of glassy, amorphous polymers

Gibbs and DiMarzio were making comparisons with experimental data, evidently not T2 but rather the kinetic Tg, and they were able to fit their equations to the experimental data. According to their theory, the molar mass dependence of Tg is given by  

To make the story even more complicated, it turns out that the WLF equation may also be derived from both the kinetic and thermodynamic theories. Interesting and confusing  

The creep compliance /(f) = e(f)/ T, where e(f) is the time-dependent strain and a is the constant stress is, at very small strains, less than 1%, approximately independent of stress. The material is said to be linear anelastic or linear visco-elastic. Materials of this category follow the so-called Boltzmann superposition principle which can be expressed as follows  

The lack of a satisfactory molecular theory for the deformation of polymers has led to the development of mechanical analogues and phenomenological models that represent the material. The task is to find combinations of elastic and viscous elements that reproduce the material behaviour. There is more than one combination that will reproduce the same behaviour. Some combinations are more convenient for a given kind of test and less convenient for another. However, a proper combination of elements should in principle be able to represent all the various tests. A condensed summary of the stress-strain behaviour of the various models is given below. 

The ultimate (fracture) properties of a wholly amorphous polymer are strongly dependent on temperature. At low temperatures, in the elastic region, the fracture is predominantly brittle and the fracture toughness is low. A considerable increase in the fracture toughness accompanies the onset of the subglass process when approaching the anelastic region. 

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