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 ideal chain statistics, a general expression for the free energy excess of the amorphous part is derived. I show that tight loops and close reentries are favored under experimental conditions for under-cooling of polymer single crystals. For many chain crystals, I show that the lamellar thickness increases with the number of chains in the crystal, and that extended chain conformations are thermodynamically favored when the number of chains in the crystal is sufficiently large. The role of finite bending rigidity of chains is discussed for folded chain crystals, as well as tilt effects in extended chain crystals.
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References
A. Keller. A note on single crystals in polymers – evidence for a folded chain configuration. Phil. Mag., 2(21):1171, 1957.
E. W. Fischer. Stufenförmiges und spiralförmiges wachstum bei hochpolymeren. Z. Naturf. A, 12(9):753–754, 1957.
P. H. Till. The growth of single crystals of linear polyethylene. J. Polym. Sci., 24(106):301–306, 1957.
J. D. Hoffmann, G. T. Davis, and J. I. Lauritzen. The Rate of Crystallization of Linear Polymers with Chain Folding, volume 3, pp. 497–614. Plenum Press, treatise in solid state chemistry edition, 1976.
D. M. Sadler. New explanation fro chain folding in polymers. Nature, 326:174–177, March 1987.
M. Hikosaka, K. Amano, S. Rastogi, and A. Keller. Lamellar thickening growth of an extended chain single crystal of polyethylene. 1. pointers to a new crystallization mechanism of polymers. Macromolecules, 30(7):2067–2074, March 1997.
M. Al-Hussein and G. Strobl. The melting line, the crystallization line, and the equilibrium melting temperature of isotactic polystyrene. Macromolecules, 35(5):1672–1676, February 2002.
G. Reiter, G. Castelein, and J.-U. Sommer. Liquidlike morphological transformations in monolamellar polymer crystals. Phys. Rev. Lett., 86(26):1918–5921, June 2001.
J.-U. Sommer and G. Reiter. Morphogegesis of lamellar polymer crystals. Europhys. Lett., 56(5):755–761, December 2001.
G. Ungar, J. Stejny, A. Keller, and M. C. Whiting. The crystallization of ultralong normal paraffines – the onset of chain folding. Science, 229(4711):386–389, 1985.
S. Rastogi, M. Hikosaka, H. Kawabata, and A. Keller. Role of mobile phase in the crystallization of polyetylene. 1. matastability and lateral growth. Macromolecules, 24:6384–6391, 1991.
J. A. Subirana. Elucidation of chain folding in polymer crystals: Comparison with proteins. Trends in Pol. Sci., 5(10):321–326, October 1997.
K. Armistead and G. Goldbeck-Wood. Polymer crystallization theories. Adv. Polym. Sci., 100:219–312, 1992.
G. Strobl. The Physics of Polymers. Springer, Berlin, Heidelberg, N.Y., 2 edition, 1997.
H. Zachmann. Der Eeinfluss der Konfigurationsentropie auf das Kristallisationsund Schmelzverhalten von hochpolymeren Stoffen. Kolloid Z. Z. Polym., 216–217:180–191, 1967.
E. W. Fischer. Das grenzflächenschmelzen der kristallite in teilkristallisierten hochpolymeren. teil i: Theoretische grundlagen. Kolloid Z. Z. Polym., 218(2): 97–114, June 1967.
W. Hu, T. Albrecht, and G. Strobl. Reversible surface melting of pe and peo crystallites indicated by tmdsc. Macromolecules, 32(22):7548–7554, 1999.
M. Muthukumar. Molecular modelling of nucleation in polymers. Phil. Trans. R. Soc. Lond. A, 361:539–556, 2003.
P. Welch and M. Muthukumar. Molecular mechanisms of polymer crystallization from solution. Phys. Rev. Lett., 87(21):218302, November 2001.
L. Larini, A. Barbieri, P. A. Rolla, and D. Leporini. Equilibrated polyethylene single-molecule crystals: molecular-dynamics simulations and analytic model of the global minimum of the free-energy landscape. J. Phys: Condens. Matter, 17(19):L199–L208, 2005.
J. D. Hoffman. Thermodynamic driving force in nucleation and growth processes. J. Chem. Phys., 29(5):1192–1193, November 1958.
G. Wulff. On the question of speed of growth and dissolution of crystal surfaces. Zeitschrift für Kristallographie und Mineralogie, 34:449, 1901.
J.-U. Sommer and G. Reiter. Crystallization in ultra-thin polymer films morphogenesis and thermodynamical aspects. Thermochimica Acta, 432(2):135–147, June 2005.
P. de Gennes. Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca and London, 1979.
J.-U. Sommer. The role of the amorphous fraction for the equilibrium shape of polymer single crystals. Eur. Phys. J. E, 19, 413–422, 2006.
M. Doi and S. Edwards. The Theory of Polymer Dynamics. Clarendon Press, Oxford, 1986.
D. S. M. de Silva, X. B. Zeng, G. Ungar, and S. J. Spells. Chain tilt and surface disorder in lamellar crystals. a ftir and saxs study of labeled long alkanes. Macromolecules, 35(20):7730–7741, September 2002.
D. S. M. de Silva, X. B. Zeng, G. Ungar, and S. J. Spells. On perpendicular and tilted chains in lamellar crystals. J. Macromol. Sci., B42(3,4):915–927, May 2003.
J.-P. Gorce and S. J. Spells. Ftir studies of conformational disorder: crystal perfecting in long chain n-alkanes. Polymer, 45(10):3297–3303, May 2004.
A. Silberberg. Distribution of conformations and chain ends near the surface of a melt of linear flexible macromolecules. J. Coll. Interface Sci., 90(1):86–91, November 1981.
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Sommer, JU. (2007). Theoretical Aspects of the Equilibrium State of Chain Crystals. In: Reiter, G., Strobl, G.R. (eds) Progress in Understanding of Polymer Crystallization. Lecture Notes in Physics, vol 714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47307-6_2
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DOI: https://doi.org/10.1007/3-540-47307-6_2
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