Variation of crystallinity with temperature for homopolymers and random copolymers

An earlier treatment assumed that crystallization places portions of the polymer molecule between tie‐points under strain, which limits the equilibrium crystallinity at any temperature. If these strained chains can be treated in the Gaussian approximation, (1 – ω)−2 should be a linear function of T−1, where ω is the degree of crystallinity. This prediction is unchanged by inclusion of the crystal surface energy. The degree of crystallinity is primarily governed by the deformation entropy at high supercoolings, while near the apparent melting point the crystal surface energy dominates, hence the Hoffman and Weeks procedure for evaluating thermodynamic melting point remains valid. Random introduction of comonomer lowers the apparent melting point and increases the tie‐point density. The latter limits both the degree of crystallinity and the initial Young's modulus of a random copolymer at high supercoolings. Values obtained for N (the number of statistical links between tie‐points) by fitting crystallinity data near the melting points for isothermally crystallized isotactic polypropylene and linear and branched polyethylene by using the Gaussian approximation, are identical to those previously obtained at high supercoolings by using inverse Langevin statistics. In fact, if the effects of crystal surface energy and the presence of a comonomer are included and the amorphous chains are treated by inverse Langevin statistics, one obtains a satisfactory representation of the variation of crystallinity with temperature over the entire range studied. Finally, the predicted linear variation of ω at high supercoolings with N−½ is verified for polyethylene.