Abstract
The equilibrium state of polymer single crystals is considered by explicitly taking into account the amorphous fraction formed by loops and tails of the chains using a statistical model introduced by Muthukumar (Philos. Trans. R. Soc. London, Ser. A 361, 539 (2003)). We show that under realistic conditions below the equilibrium melting temperature, tight loops and close re-entries are favored, and that the amorphous fraction can be mapped into an excess surface free energy. The model is extended to many-chain crystals where it is shown that the lamellar thickness increases with the number of chains in the crystal and extended-chain conformations are thermodynamically favored if the number of chains in the crystal is sufficiently large. The number of chains necessary to form an extended-chain crystal in thermodynamic equilibrium scales with the square of the degree of polymerization of the chains. We discuss the temperature behavior of the equilibrium crystal thickness in the under-cooled state.
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