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Crystallization in melts of short, semiflexible hard polymer chains: An interplay of entropies and dimensions

T. Shakirov and W. Paul*

  • Institute of Physics, Martin-Luther-University, 06099 Halle, Germany

  • *wolfgang.paul@physik.uni-halle.de
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Phys. Rev. E 97, 042501 – Published 5 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.042501

Abstract

What is the thermodynamic driving force for the crystallization of melts of semiflexible polymers? We try to answer this question by employing stochastic approximation Monte Carlo simulations to obtain the complete thermodynamic equilibrium information for a melt of short, semiflexible polymer chains with purely repulsive nonbonded interactions. The thermodynamics is obtained based on the density of states of our coarse-grained model, which varies by up to 5600 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density. This crystallization can be understood by the interplay of the maximization of different entropy contributions in different spatial dimensions. At sufficient stiffness and density, the three-dimensional orientational interactions drive the orientational ordering transition, which is accompanied by a two-dimensional translational ordering transition in the plane perpendicular to the chains resulting in a hexagonal crystal structure. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition can be understood in terms of the liquid-hexatic transition of hard disks. Due to the domination of lateral two-dimensional translational entropy over the one-dimensional translational entropy connected with columnar displacements, the chains form a lamellar phase. Based on this physical understanding, orientational ordering and translational ordering should be separable for polymer melts. A phenomenological theory based on this understanding predicts a qualitative phase diagram as a function of volume fraction and stiffness in good agreement with results from the literature.

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References (45)

  1. T. Palberg, Crystallization kinetics of colloidal model suspensions: Recent achievements and new perspective, J. Phys.: Condens. Matter 26, 333101 (2014).
  2. P. Tarazona, J. A. Cuesta, and Y. Martinez-Raton, in Theory and Simulation of Hard-Sphere Fluids and Related Systems, edited by A. Mulero, Lecture Notes in Physics, Vol. 753 (Springer, Berlin, Heidelberg, 2008), p. 247.
  3. G. Strobl, The Physics of Polymers (Springer, Berlin, 2007).
  4. Progress in Understanding of Polymer Crystallization, edited by G. Reiter and G. Strobl, Lecture Notes in Physics, Vol. 714 (Springer, Berlin, 2007).
  5. S. Stepanow, Kinetic mechanism of chain folding in polymer crystallization, Phys. Rev. E 90, 032601 (2014).
  6. C. Luo and J. U. Sommer, Frozen Topology: Entanglements Control Nucleation and Crystallization in Polymers, Phys. Rev. Lett. 112, 195702 (2014); Role of thermal history and entanglement related thickness selection in polymer crystallization, ACS Macro Lett. 5, 30 (2016).
  7. E. B. Sirota, H. E. King, D. M. Singer, and H. H. Shao, Rotator phases of the normal alkanes: An x-ray scattering study, J. Chem. Phys. 98, 5809 (1993); E. B. Shirota and D. M. Singer, Phase transitions among the rotator phases of the normal alkanes, ibid. 101, 10873 (1994); E. B. Sirota, Polymer crystallization: metastable mesophases and morphology, Macromolecules 40, 1043 (2007).
  8. J. P. Ryckaert, M. L. Klein, and I. R. McDonald, Disorder at the Bilayer Interface in the Pseudohexagonal Rotator Phase of Solid n-Alkanes, Phys. Rev. Lett. 58, 698 (1987); Disorder in the pseudohexagonal rotator phase of n-alkanes: Molecular-dynamics calculations for tricosane, Mol. Phys. 67, 957 (1989); Computer simulations and the interpretation of incoherent neutron scattering experiments on the solid rotator phases of long-chain alkanes, 83, 439 (1994).
  9. J. Naghizadeh, in Advances in Chemical Physics, Vol. 65, edited by I. Prigogine and S. Rice (Wiley, New York, 1986), p. 45.
  10. N. Wentzel and S. T. Milner, Crystal and rotator phases of n-alkanes: A molecular dynamics study, J. Chem. Phys. 132, 044901 (2010); Simulation of multiple ordered phases in C23 n-alkane, 134, 224504 (2011).
  11. P. K. Mukherjee, Phase transitions among the rotator phases of the normal alkanes: A review, Phys. Rep. 588, 1 (2015).
  12. W. Paul, Do Y. Yoon, and G. D. Smith, An optimized united atom model for simulations of polymethylene melts, J. Chem. Phys. 103, 1702 (1995).
  13. P. Yi and G. C. Rutledge, Molecular simulation of crystal nucleation in n-octane melts, J. Chem. Phys. 131, 134902 (2009); Molecular simulation of bundle-like crystal nucleation from n-eicosane melts, 135, 024903 (2011); P. Yi, C. R. Locker, and G. C. Rutledge, Molecular dynamics simulation of homogeneous crystal nucleation in polyethylene, Macromolecules 46, 4723 (2013).
  14. M. Anwar, F. Turci, and T. Schilling, Crystallization mechanism in melts of short n-alkane chains, J. Chem. Phys. 139, 214904 (2013); M. Anwar, J. T. Berryman, and T. Schilling, Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow, 141, 124910 (2014); M. Anwar and T. Schilling, Crystallization of polyethylene: A molecular dynamics simulation study of the nucleation and growth mechanisms, Polymer 76, 307 (2015).
  15. A. Jabbarzadeh and R. I. Tanner, Crystallization of alkanes under quiescent and shearing conditions, J. Non-Newtonian Fluid Mech. 160, 11 (2009); A. Jabbarzadeh and X. Chen, Surface induced crystallization of polymeric nano-particles: Effect of surface roughness, Faraday Discuss. 204, 307 (2017).
  16. J. M. Poulson and D. Frenkel, Calculation of solid-liquid phase equilibria for systems of chain molecules, J. Chem. Phys. 109, 318 (1998).
  17. N. Ch. Karayiannis and M. Laso, Dense and Nearly Jammed Random Packings of Freely Jointed Chains of Tangent Hard Spheres, Phys. Rev. Lett. 100, 050602 (2008); N. Ch. Karayiannis, K. Foteinopoulou, and M. Laso, Entropy-Driven Crystallization in Dense Systems of Athermal Chain Molecules, ibid. 103, 045703 (2009).
  18. N. Sushko, P. van der Schoot, and M. A. J. Michels, Density-functional theory of the crystallization of hard polymeric chains, J. Chem. Phys. 115, 7744 (2001); Erratum: Density-functional theory of the crystallization of hard polymeric chains [J. Chem. Phys. 115, 7744 (2001)], 116, 5325 (2002); On the role of connectivity in the relative stability of crystal types for model polymeric solids, 118, 6098 (2003).
  19. F. Wang and D. P. Landau, Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States, Phys. Rev. Lett. 86, 2050 (2001).
  20. W. Janke and W. Paul, Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations, Soft Matter 12, 642 (2016).
  21. F. Rampf, W. Paul, and K. Binder, On the first-order collapse transition of a three-dimensional, flexible homopolymer chain model, Europhys. Lett. 70, 628 (2005); W. Paul, T. Strauch, F. Rampf, and K. Binder, The unexpectedly normal phase behavior of single homopolymer chains, Phys. Rev. E 75, 060801(R) (2007).
  22. M. P. Taylor, W. Paul, and K. Binder, All-or-none proteinlike folding transition of a flexible homopolymer chain, Phys. Rev. E 79, 050801(R) (2009); Phase transitions of a single polymer chain: A Wang-Landau simulation study, J. Chem. Phys. 131, 114907 (2009).
  23. T. Wüst and D. P. Landau, Versatile Approach to Access the Low Temperature Thermodynamics of Lattice Polymers and Proteins, Phys. Rev. Lett. 102, 178101 (2009); D. T. Seaton, S. Schnabel, D. P. Landau, and M. Bachmann, From Flexible to Stiff: Systematic Analysis of Structural Phases for Single Semiflexible Polymers, ibid. 110, 028103 (2013).
  24. B. Werlich, T. Shakirov, M. P. Taylor, and W. Paul, Stochastic approximation Monte Carlo and Wang-Landau Monte Carlo applied to a continuum polymer model, Comput. Phys. Commun. 186, 65 (2015).
  25. F. Liang, C. Liu, and R. J. Carroll, Stochastic approximation in Monte Carlo computation, J. Am. Stat. Assoc. 102, 305 (2007).
  26. M. Bachmann and W. Janke, Multicanonical Chain-Growth Algorithm, Phys. Rev. Lett. 91, 208105 (2003); S. Schnabel, W. Janke, and M. Bachmann, Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers, J. Comput. Phys. 230, 4454 (2011).
  27. W. Paul, F. Rampf, T. Strauch, and K. Binder, Phase transitions in a single polymer chain: A microcanonical analysis of Wang-Landau simulations, Comput. Phys. Commun. 179, 17 (2008).
  28. M. P. Taylor, P. P. Aung, and W. Paul, Partition function zeros and phase transitions for a square-well polymer chain, Phys. Rev. E 88, 012604 (2013).
  29. K. Binder, Theory of the evaporation/condensation transition of equilibrium droplets in finite volumes, Physica A (Amsterdam) 319, 99 (2003); A. Tröster and K. Binder, Microcanonical determination of the interface tension of flat and curved interfaces from Monte Carlo simulations, J. Phys.: Condens. Matter 24, 284107 (2012).
  30. J. Zierenberg, P. Schierz, and W. Janke, Canonical free-energy barrier of particle and polymer cluster formation, Nat. Commun. 8, 14546 (2017).
  31. A. R. Khokhlov and A. N. Semenov, On the theory of liquid-crystalline ordering of polymer chains with limited flexibility, J. Stat. Phys. 38, 161 (1985).
  32. A. Yethiraj and H. Fynewever, Isotropic to nematic transition in semiflexible polymer melts, Mol. Phys. 93, 693 (1997).
  33. F. A. Escobedo and J. de Pablo, Monte Carlo simulation of athermal mesogenic chains: Pure systems, mixtures, and constrained environments, J. Chem. Phys. 106, 9858 (1997).
  34. K. M. Jaffer, S. B. Opps, D. E. Sullivan, B. G. Nickel, and L. Mederos, The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids, J. Chem. Phys. 114, 3314 (2001).
  35. M. Engel, J. A. Anderson, S. C. Glotzer, M. Isobe, E. P. Bernard, and W. Krauth, Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods, Phys. Rev. E 87, 042134 (2013).
  36. C. Avendaño and F. A. Escobedo, Phase behavior of rounded hard-squares, Soft Matter 8, 4675 (2012).
  37. P. Panine, V. Urban, P. Boesecke, and T. Narayanan, Combined small- and wide-angle x-ray scattering study of early stages of polymer crystallization, J. Appl. Crystallogr. 36, 991 (2003).
  38. V. Padmanabhan, S. Kumar, and A. Yethiraj, Phase behavior of semiflexible polymer chains, J. Chem. Phys. 128, 124908 (2008).
  39. P. Bolhuis and D. Frenkel, Tracing the phase boundaries of hard spherocylinders, J. Chem. Phys. 106, 666 (1997).
  40. R. C. Hidalgo, D. E. Sullivan, and J. Z. Y. Chen, Smectic ordering of homogeneous semiflexible polymers, Phys. Rev. E 71, 041804 (2005).
  41. A. Abe, J. Furuya, Z. Zhou, T. Hiejima, and Y. Kobayashi, Stepwise phase transitions of chain molecules: Crystallization/melting via a nematic liquid-crystalline phase, Adv. Polym. Sci. 181, 121 (2005).
  42. V. Ho, B. W. Boudouris, and R. A. Segalman, Tuning Polythiophene Crystallization through systematic side chain functionalization, Macromolecules 43, 7895 (2010).
  43. W. Zhang, E. D. Gomez, and S. T. Milner, Predicting nematic phases of semiflexible polymers, Macromolecules 48, 1454 (2015).
  44. A. Gil-Vellegas, F. del Rio, and C. Vega, Thermodynamics of fluids obtained by mapping the collision properties, Phys. Rev. E 53, 2326 (1996).
  45. T. Shakirov and W. Paul (unpublished).

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Phys. Rev. E 97, 042501– Published 5 April, 2018
  • Received 9 August 2017
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