Crystal, defect, point extended-chain

In the equilibrium states of polymer crystals, the chain ends can be regarded as the crystalline defects in the infinitely large crystals formed by extended chains, which will apparently result in a depression of melting points with the increase of concentrations of chain ends, or in other words, with the decrease of chain lengths. 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

The lower limit of segregation is set by the hypothetical equilibrium of crystallization. It is assumed that dynamic equilibrium is achieved between fully extended-chain crystals and the surrounding melt. At equilibrium, the molecular length of the crystallizable species corresponds closely to the lamellar thickness, and molecules too short or too long introduce defects and increase the free energy and are thus rejected from the crystal. The equilibrium melting point of a given molecular species is dependent not only on its molar mass but also on the molar masses of the other difFerent species present in the blended melt ... 

It is important to keep in mind that the theoretical development outlined above, and its implications, are for equilibrium conditions at, and below, the melting temperature. It requires the participation of all sequences above a critical value, particularly the very long ones. All must be in extended form. Very practical and important matters such as the kinetic barriers to the crystallization, possible folding of the chains, defects within the crystallites, as well as other nonequilibrium phenomena are not taken into account at this point. However, the ideal equilibrium requirements serve as reference base from which nonideal contributions as well as nonequilibrium behavior can be treated. 

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