The small-strain properties of isotropic polymers

This section is concerned only with the short-term, essentially instantaneous, response of polymeric solids to applied stresses that give rise to very small strains. The response at longer times is considered in the next chapter. The emphasis in this section is on the comparison of various types of polymer with each other and with non-polymeric solids. 

There are basically four categories of polymer to consider amorphous polymers above and below their glass-transition temperatures, Tg, and semicrystalline polymers in which the amorphous regions are above or below Jg. 

Amorphous polymers well above Jg behave either as liquids or, if they are cross-linked, as rubbers the properties of rubbers are discussed in the next section. In the region close to Jg the viscoelastic properties dominate even at small strains and relatively short times and these are considered in the next chapter. This means that the static small-strain properties of amorphous polymers can be discussed meaningfully only when the polymers are well below Tg. Semicrystalline polymers are really composite materials. At temperatures well below the Tg of the amorphous regions the material has small-strain elastic properties that depend on the proper- 

The problem of calculating the moduli of semicrystalline polymers is even more difficult. It involves in principle four steps (i) the calculation of the modulus of the amorphous material, (ii) the calculation of the elastic constants of the anisotropic crystalline material, (iii) the averaging of the elastic constants of the crystalline material to give an effective isotropic modulus and (iv) the averaging of the isotropic amorphous and crystalline moduli to give the overall modulus. The second of these steps can now be done fairly accurately, but the other three present serious difficulties. 

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