Thermodynamics of crystallization of macromolecules of various degrees of coiling

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Abstract
The crystallization of flexible-chain molecules under conditions of molecular extension is considered. The molecular orientation was characterized by a parameter β that is the ratio of end-to-end distance to the contour length of macromolecule. Calculations were performed for two types of crystals: folded-chain crystals and extended-chain crystals. Thermodynamical analysis shows that the decrease of conformational entropy owing to the drawing of the molecule into a crystal makes an essential contribution to the free-energy change. This value is of great importance in the definition of the equilibrium state of a system and so it is the reason why it is impossible to get the degree of crystallinity equal to 1. The values of molecular orientation at which each of two mechanisms of crystallization takes place are evaluated. It is shown that there is a critical value β* as a boundary between two ranges of extensions: at β < β*, the crystallization with the formation of folded-chain crystals is thermodynamically preferable; if β > β* can be obtained in the melt, extended-chain crystals are formed. The dependence of the degree of crystallinity and the melting temperature on β for each type of crystal are calculated. The data obtained agree with experimental results.

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