Statistics of Ties and Loops in Amorphous Regions of Polymer Crystals

Polymer crystals grown from melt consist of alternating lamellar crystalline regions and amorphous regions. We study the statistics of ties and loops in the amorphous region. Mechanical properties of crystalline polymers are highly dependent on the relative populations of ties and loops in the amorphous regions. We develop a statistical mechanical formulation to calculate the conformational entropy of ties and loops with consideration of finite chain length and possible association of a chain with multiple lamellae. Results of our numerical calculations show that, the fraction of the tie population relative to loops increases with increasing chain length, and it decreases with increasing the interlamellar separation and the lamellar thickness. The average number of lamellae connected by a chain is also calculated. It is also found to increase with increasing the chain length and to decrease with increasing the amorphous thickness.