Variable-Connectivity Monte Carlo Algorithms for the Atomistic Simulation of Long-Chain Polymer Systems

  • Doros N. Theodorou
Part of the Lecture Notes in Physics book series (LNP, volume 605)

Abstract

Recently, our ability to equilibrate atomistic models of synthetic polymers and biopolymers has been significantly enhanced through the development of Monte Carlo schemes employing moves which modify the connectivity of atoms along the chains. In this chapter, the geometric “bridging” construction underlying these moves is explained and the statistical mechanical underpinnings of Monte Carlo algorithms employing these moves to sample various, appropriately designed, ensembles are discussed. Concerted rotation, directed internal bridging, end-bridging, directed end-bridging, scission-fusion, double bridging, intramolecular double rebridging moves, and their combination with parallel tempering are developed in some detail.

Results are presented from applying the connectivity-altering Monte Carlo algorithms to predict volumetric behaviour, packing, chain conformation and entanglement properties in long-chain synthetic polymer melts (polyethylene, polypropylene, polyisoprene); melt elasticity and birefringence under conditions of steadystate flow; sorption equilibria of alkanes in polyethylene melts; and composition profiles at solid/polymer interfaces strengthened with grafted polymer chains. The molecular-level insight gained from these calculations is discussed, as is the role of the new algorithms as tools for the development of hierarchical modelling approaches to structure - processing - property - performance relations in polymer systems.

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References

  1. 1.
    M. Tuckerman, B.J. Berne, G.J. Martyna: J. Chem. Phys. 97, 1990 (1992). G.J. Martyna, M.E. Tuckerman, D.J. Tobias, M.L. Klein: Mol. Phys. 87, 1117 (1996).CrossRefADSGoogle Scholar
  2. 2.
    D.N. Theodorou: SIMU Newsletter 1, 19 (2000) http://simu.ulb.ac.be/newsletters/newsletter.html Google Scholar
  3. 3.
    A. Uhlherr, D.N. Theodorou: Curr. Opin. Solid State and Mat. Sci. 3, 544 (1998)CrossRefGoogle Scholar
  4. 4.
    F.T. Wall, A. Hiller, D.J. Wheeler: J. Chem. Phys. 22, 1036 (1954)CrossRefADSGoogle Scholar
  5. 5.
    F.T. Wall, W.A. Seitz: J. Chem. Phys. 54, 5338 (1971)CrossRefGoogle Scholar
  6. 6.
    K. Binder (ed.): Monte Carlo and Molecular Dynamics Simulations in Polymer Science (Oxford University Press, New York 1995)Google Scholar
  7. 7.
    A.K. Kron: Polymer Sci. USSR 7, 1361 (1965)CrossRefGoogle Scholar
  8. 8.
    M. Vacatello, G. Avitabile, P. Corradini, A. Tuzi: J.Chem.Phys. 73, 543 (1980)CrossRefADSGoogle Scholar
  9. 9.
    R. H. Boyd: Macromolecules 22, 2477 (1989)CrossRefADSGoogle Scholar
  10. 10.
    J.I. Siepmann, D. Frenkel: Mol. Phys. 75, 59 (1992)CrossRefADSGoogle Scholar
  11. 11.
    J.J. de Pablo, M. Laso, U.W. Suter: J. Chem. Phys. 96, 2395 (1992)CrossRefADSGoogle Scholar
  12. 12.
    M.N. Rosenbluth, A.W. Rosenbluth: J. Chem. Phys. 23, 356 (1955)CrossRefGoogle Scholar
  13. 13.
    J.J. de Pablo, F.A. Escobedo: J. Chem. Phys. 105, 4391 (1996)CrossRefADSGoogle Scholar
  14. 14.
    A.P. Lyubartsev, A.A. Martsinovski, S.V. Shevkunov, P.N. Vorontsov-Velyaminov: J. Chem. Phys. 96, 1776 (1991)CrossRefADSGoogle Scholar
  15. 15.
    C.J. Geyer: ‘Markov Chain Monte Carlo Maximum Likelihood’. In: Computing Science and Statistics, Proceedings of23r d Symposium on the Interface (American Statistical Association, New York 1991) pp 156–163. M.C. Tesi, E.J.J. van Rensburg, E. Orlandini, S.G. Whittington: J. Stat. Phys. 82, 155 (1996)Google Scholar
  16. 16.
    M.G. Wu, M.W. Deem: Mol. Phys. 97, 559 (1999)CrossRefADSGoogle Scholar
  17. 17.
    M.G. Wu, M.W. Deem: J. Chem. Phys. 111, 6625 (1999)CrossRefADSGoogle Scholar
  18. 18.
    O.F. Olaj, W. Lantschbauer: Makromol. Chem., Rapid Commun. 3, 847 (1982)CrossRefGoogle Scholar
  19. 19.
    M.L. Mansfield: J. Chem. Phys. 77, 1554 (1982)CrossRefADSGoogle Scholar
  20. 20.
    W.G. Madden: J. Chem. Phys. 87, 1405 (1987); J. Chem. Phys. 88, 3934 (1988)CrossRefADSGoogle Scholar
  21. 21.
    V.G. Mavrantzas, T.D. Boone, E. Zervopoulou, D.N. Theodorou: Macromolecules 32, 5072 (1999)CrossRefADSGoogle Scholar
  22. 22.
    L.R. Dodd, T.D. Boone, D.N. Theodorou: Mol. Phys. 78, 961 (1993)CrossRefADSGoogle Scholar
  23. 23.
    P.J. Flory: Statistical Mechanics of Chain Molecules (Wiley Interscience, New York 1969)Google Scholar
  24. 24.
    N. Gō, H.A. Scheraga: Macromolecules 3, 178 (1970)CrossRefADSGoogle Scholar
  25. 25.
    M.W. Deem, J.S. Bader: Mol. Phys. 87, 1245 (1996)CrossRefADSGoogle Scholar
  26. 26.
    H.-Y. Lee, C.-G. Liang: Mech. Mach. Theory 23, 209 (1988)CrossRefGoogle Scholar
  27. 27.
    H.-Y. Lee, C.-G. Liang: Mech. Mach. Theory 23, 219 (1988)CrossRefGoogle Scholar
  28. 28.
    H.-Y. Lee, C. F. Reinholtz: ASME J. Mech. Design 118, 296 (2000)Google Scholar
  29. 29.
    P.V.K. Pant, D.N. Theodorou: Macromolecules 28, 7224 (1995)CrossRefADSGoogle Scholar
  30. 30.
    L.R. Dodd, D.N. Theodorou: Advan. Polym. Sci. 116, 249 (1994)CrossRefGoogle Scholar
  31. 31.
    T. Spyriouni, I.G. Economou, D.N. Theodorou: Macromolecules 31, 1430 (1998)CrossRefADSGoogle Scholar
  32. 32.
    T. Spyriouni, I.G. Economou, D.N. Theodorou: Phys. Rev. Lett. 80, 4466 (1998)CrossRefADSGoogle Scholar
  33. 33.
    C.T. Samara: Simulation of polypropylene of various tacticities with the Monte Carlo method. Ph.D. Thesis, University of Patras, Patras, Greece (2000)Google Scholar
  34. 34.
    M. Doxastakis, V.G. Mavrantzas, D.N. Theodorou: J. Chem. Phys. 115, 11339 (2001)CrossRefADSGoogle Scholar
  35. 35.
    M. Doxastakis, V.G. Mavrantzas, D.N. Theodorou: J. Chem. Phys. 115, 11352 (2001)CrossRefADSGoogle Scholar
  36. 36.
    E. Nicol, P. Gestoso, M. Doxastakis, D.N. Theodorou, in preparation.Google Scholar
  37. 37.
    A. Uhlherr: Macromolecules 33, 1351 (2000)CrossRefADSGoogle Scholar
  38. 38.
    C.D. Wick, J.I. Siepmann: Macromolecules 33, 7207 (2000)CrossRefADSGoogle Scholar
  39. 39.
    A. Uhlherr, V.G. Mavrantzas, M. Doxastakis, D.N. Theodorou: Macromolecules 34, 8554 (2001)CrossRefADSGoogle Scholar
  40. 40.
    A. Uhlherr, M. Doxastakis, V.G. Mavrantzas, D.N. Theodorou, S.J. Leak, N.E. Adam, P.E. Nyberg: Europhys. Lett. 57, 506 (2002)CrossRefADSGoogle Scholar
  41. 41.
    A.N. Beris, E.J. Edwards: Thermodynamics of flowing systems with internal microstructure (Oxford University Press, Oxford 1994)Google Scholar
  42. 42.
    V.G. Mavrantzas, D.N. Theodorou: Macromolecules 31, 6310 (1998)CrossRefADSGoogle Scholar
  43. 43.
    V.G. Mavrantzas, D.N. Theodorou: Comp.Theor.Polym.Sci. 10, 1 (2000)CrossRefGoogle Scholar
  44. 44.
    V.G. Mavrantzas, D.N. Theodorou: Macromol. Theory Simul. 9, 500 (2000)CrossRefGoogle Scholar
  45. 45.
    V.G. Mavrantzas, H.C. Öttinger: Macromolecules 35, 960 (2002)CrossRefADSGoogle Scholar
  46. 46.
    E. Zervopoulou, V.G. Mavrantzas, D.N. Theodorou: Macromolecules 115, 2860 (2001)Google Scholar
  47. 47.
    J.J. de Pablo, Q. Yan, F.A. Escobedo: Ann. Rev. Phys. Chem. 50, 377 (1999)CrossRefADSGoogle Scholar
  48. 48.
    A.Z. Panagiotopoulos: J. Phys: Condens. Matter 12, R25 (2000)CrossRefADSGoogle Scholar
  49. 49.
    E. Zervopoulou, V.G. Mavrantzas, D.N. Theodorou: J. Chem. Phys. 115, 2860 (2001)CrossRefADSGoogle Scholar
  50. 50.
    T. Spyriouni, I.G. Economou, D.N. Theodorou: Macromolecules 30, 4744 (1997)CrossRefADSGoogle Scholar
  51. 51.
    N.Ch. Karayiannis, V.G. Mavrantzas, D.N. Theodorou: Phys. Rev. Lett. 88, 105503 (2002)CrossRefADSGoogle Scholar
  52. 52.
    J.C. Horton: Macromolecules 22, 681 (1989)CrossRefADSGoogle Scholar
  53. 53.
    L.J. Fetters, W.W. Graessley, R. Krishnamoorti, D.J. Lohse: Macromolecules 30, 4973 (1997)CrossRefADSGoogle Scholar
  54. 54.
    G.T. Dee, T. Ougizawa, D.J. Walsh: Polymer 33, 3462 (1992)CrossRefGoogle Scholar
  55. 55.
    V.A. Harmandaris, M. Doxastakis, V.G. Mavrantzas, D.N. Theodorou: J. Chem. Phys. 116, 436 (2002)CrossRefADSGoogle Scholar
  56. 56.
    K.G. Honnell, J.D. McCoy, J.G. Curro, K.S. Schweizer, A.H. Narten, A. Habenschuss: J. Chem. Phys. 94, 4659 (1991).CrossRefADSGoogle Scholar
  57. 57.
    R. P. Wool: Macromolecules 26, 1564 (1993).CrossRefADSGoogle Scholar
  58. 58.
    J.D. Ferry: Viscoelastic Properties of Polymers (Wiley, New York 1980)Google Scholar
  59. 59.
    U.W. Suter, P. Neuenschwander: Macromolecules 14, 528 (1981)CrossRefADSGoogle Scholar
  60. 60.
    D.G.H. Ballard, P. Cheshire, G.W. Longmann, J. Schelten: Polymer 19, 379 (1978)CrossRefGoogle Scholar
  61. 61.
    U.W. Suter, P.J. Flory: Macromolecules 8, 765 (1975)CrossRefADSGoogle Scholar
  62. 62.
    J.-P. Ryckaert: ‘Simulation of polymers using realistic potentials’. In: Monte Carlo and molecular dynamics of condensed matter systems, Conference Proceedings Vol. 49, ed. by K. Binder, G. Ciccotti (Società Italiana di Fisica, Bologna 1996) Chap. 27, pp 729–746Google Scholar
  63. 63.
    S.J. Antoniadis, C.T. Samara, D.N. Theodorou: Macromolecules 32, 8635 (1999)CrossRefADSGoogle Scholar
  64. 64.
    R.D. Maier, R. Thomann, J. Kressler, R. Mülhaupt: J. Polym. Sci. Polym. Phys. 35, 1135 (1997)CrossRefADSGoogle Scholar
  65. 65.
    S.M. Lippow, X.-H. Qiu, M.D. Ediger: personal communication.Google Scholar
  66. 66.
    N. Nemoto, M. Moriwaki, H. Odani, M. Kurata: Macromolecules 4, 215 (1971)CrossRefADSGoogle Scholar
  67. 67.
    C.D. Han, J. Kim, J.K. Kim: Macromolecules 22, 383 (1989)CrossRefADSGoogle Scholar
  68. 68.
    K. Šolc and W.H. Stockmayer: Macromolecules 54, 2756 (1971)Google Scholar
  69. 69.
    D.N. Theodorou, U.W. Suter: Macromolecules 18, 1206 (1985)CrossRefADSGoogle Scholar
  70. 70.
    V.A. Harmandaris, V.G. Mavrantzas, D.N. Theodorou: Macromolecules 33, 8062 (2000)CrossRefADSGoogle Scholar
  71. 71.
    V.A. Harmandaris, V.G. Mavrantzas, D.N. Theodorou: Macromolecules 31, 7934 (1998)CrossRefADSGoogle Scholar
  72. 72.
    D.C. Bonner, N.F. Brockmeier, Y.I. Cheng: Ind. Eng. Chem. Process Des. Dev. 4, 437 (1974)CrossRefGoogle Scholar
  73. 73.
    K.Ch. Daoulas, A.F. Terzis, V.G. Mavrantzas: J. Chem. Phys., in press (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Doros N. Theodorou
    • 1
    • 2
  1. 1.Department of Materials Science and Engineering, School of Chemical EngineeringNational Technical University of AthensAthensGreece
  2. 2.Molecular Modelling of Materials Laboratory, Institute of Physical ChemistryNational Research Centre for Physical Sciences “Demokritos”Paraskevi AttikisGreece

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