Off-lattice Monte Carlo simulation of the discrete Edwards model

Journal of Polymer Science, Part B: Polymer Physics

Volumn 38, Issue 8, 2000, Pages 1053-1068

  Besold, Gerhard ^a   Guo, Hong ^b   Zuckermann, Martin J ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONFORMATIONS; CRYSTAL LATTICES; MATHEMATICAL MODELS; MONTE CARLO METHODS; SOLVENTS;

CORRECTIONS-TO-SCALING; DISCRETE EDWARDS MODEL;

BLOCK COPOLYMERS;

EID: 0033878830     PISSN: 08876266     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0488(20000415)38:8<1053::AID-POLB6>3.0.CO;2-J     Document Type: Article

References (79)

1. Edwards, S. F. Proc Phys Soc London 1966, 88, 265.
2. Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: Oxford, 1986; p 24-27.
3. Des Cloizeaux, J.; Jannink, G. Polymers in Solution - Their Modelling and Structure; Oxford University Press: Oxford, 1990.
4. Edwards, S. F. J Phys A: Gen Phys 1968, 1(Ser. 2), 15.
5. Doi, M.; Edwards, S. F. J Chem Soc Faraday Trans 2 1978, 74, 1789.
6. De Gennes, P.-G. J Chem Phys 1971, 55, 572.
7. De Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca & London, 1979.
8. The Monte Carlo Method in Condensed Matter Physics, 2nd ed.; Binder, K., Ed.; Springer-Verlag: Berlin, 1995; and references therein.
9. Monte Carlo and Molecular Dynamics Simulations in Polymer Science; Binder, K., Ed.; Oxford University Press: New York, 1995.
10. Kremer, K. In Monte Carlo and Molecular Dynamics of Condensed Matter Systems; Binder, K.; Ciccotti, G., Eds.; Società Italiana di Fisica: Bologna, 1996; p 669-723.
11. Domb, C.; Joyce, G. S. J Phys C 1972, 5, 956.
12. Domb, C. J Stat Phys 1983, 30, 425.
13. Barrett, A. J. J Stat Phys 1990, 58, 617.
14. Madras, N.; Slade, G. The Self-Avoiding Walk; Birkhäuser: Boston, 1993.
15. Grassberger, P.; Sutter, P.; Schäfer, L. J Phys A: Math Gen 1997, 30, 7039.
16. Sutter, P.; Schäfer, L.; Grassberger, P. Int J Mod Phys B 1998, 12, 1397.
17. Laradji, M.; Guo, H.; Zuckermann, M. J. Phys Rev E 1994, 49, 3199.
18. Soga, K. G.; Guo, H.; Zuckermann, M. J. Europhys Lett 1995, 29, 531.
19. Soga, K. G.; Zuckermann, M. J.; Guo, H. Macromolecules 1996, 29, 1998.
20. Miao, L.; Guo, H.; Zuckermann, M. J. Macromolecules 1996, 29, 2289.
21. Besold, G.; Hassager, O.; Mouritsen, O. G. Comput Phys Commun 1999, 121/122, 542.
22. Besold, G., to be published.
23. Li, B.; Madras, N.; Sokal, A. D. J Stat Phys 1995, 80, 661.
24. This expectation is supported by the fact that a mean-field estimate for the scaling exponent v (cf. Scaling Relations and Distribution Functions subsection) can analytically be obtained for our discrete Edwards model, which coincides with the well-known, mean-field estimate v = 3/5 (Flory value) for the 3D SAW.
25. Debye, P. J Chem Phys 1946, 14, 636.
26. Mattice, W. L.; Suter, U. W. Conformational Theory of Large Molecules; Wiley: New York, 1994.
27. Doi, M. Introduction to Polymer Physics; Oxford University Press: Oxford, 1996; p 10-12.
28. Zimm, B. H. J Chem Phys 1956, 24, 269.
29. Sokal, A. D. In Monte Carlo and Molecular Dynamics Simulations in Polymer Science; Binder, K., Ed.; Oxford University Press: New York, 1995; p 47-124.
30. Sokal, A. D. Nucl Phys B Proc Suppl 1996, 47, 172.
31. Lal, M. Mol Phys 1996, 17, 57.
32. MacDonald, B.; Jan, N.; Hunter, D. L.; Steinitz, M. O. J Phys A: Math Gen 1985, 18, 2627.
33. Madras, N.; Sokal, A. D. J Stat Phys 1988, 50, 109.
34. 3.
35. Carmesin, I.; Kremer, K. Macromolecules 1988, 21, 2819.
36. Carmesin, I.; Kremer, K. J Phys Paris 1990, 51, 1567.
37. 6 MCS.
38. Nickel, B. G. Macromolecules 1991, 24, 1358.
39. Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, 1953.
40. Baker, Jr., G. A.; Nickel, B. G.; Meiron, D. L. Phys Rev B 1978, 17, 1365.
41. LeGuillou, J. C.; Zinn-Justin, J. Phys Rev B 1980, 21, 3976.
42. Albert, D. Z. Phys Rev B 1982, 25, 4810.
43. LeGuillou, J. C.; Zinn-Justin, J. J Physique Lett 1985, 46, L137.
44. LeGuillou, J. C.; Zinn-Justin, J. J Physique 1989, 50, 1365.
45. Murray, D. B.; Nickel, B. G. Revised estimates for critical exponents for the continuum n-vector model in 3 dimensions; preprint, 1991.
46. Guida, R.; Zinn-Justin, J. J Phys A: Math Gen 1998, 31, 8103.
47. Des Cloizeaux, J.; Conte, R.; Jannink, G. J Physique Lett 1985, 46, L595.
48. Muthukumar, M.; Nickel, B. G. J Chem Phys 1987, 86, 460.
49. N( · ) it should always be evident which probability density is meant.
50. Fisher, M. E. J Chem Phys 1966, 44, 616.
51. Des Cloizeaux, J. Phys Rev A 1974, 10, 1665.
52. McKenzie, D. S.; Moore, M. A. J Phys A: Gen Phys 1971, 4, L82.
53. The precise value of this RG estimate for γ depends on the value of a renormalized coupling constant, which is not known exactly, compare the discussion in ref. 54.
54. Caracciolo, S.; Causo, M. S.; Pelissetto, A. Phys Rev E 1998, 57, 1215.
55. Des Cloizeaux, J. Phys Rev A 1974, 10, 1665.
56. Redner, S. J Phys A: Math Gen 1980, 13, 3525.
57. From the RG estimates θ = 0.275 and t = 2.427 (refs. 43, 44) one finds C = 0.2996 and K = 1.2714, and from the estimates θ = 0.268 and t = 2.425 derived from MC estimates for v (ref. 29) and γ (ref. 54) via eqs 19 and 21, we obtain C = 0.2987 and K = 1.2700. The corresponding two graphs of the RdC form of f(x) are almost indistinguishable.
58. Domb, C.; Gillis, J.; Wilmer, G. Proc Phys Soc 1965, 85, 625.
59. Chay, T. R. J Chem Phys 1972, 57, 910.
60. Grisham, R. J Chem Phys 1973, 58, 5309.
61. Dayantis, J.; Palierne, J.-F. J Chem Phys 1991, 95, 6088.
62. Bishop, M.; Clarke, J. H. R. J Chem Phys 1991, 94, 3936.
63. Rubio, A. M.; Freire, J. J.; Horta, A. H.; Ferández de Piérola, I. Macromolecules 1991, 24, 5167.
64. Rey, A.; Freire, J. J.; Garcia de la Torre, J. Polymer 1992, 33, 3477.
65. Eizenberg, N.; Klafter, J. J Chem Phys 1993, 99, 3976.
66. Everaers, R.; Graham, I. S.; Zuckermann, M. J. J Phys A: Math Gen 1995, 28, 1271.
67. Wittkop, M.; Kreitmeier, S.; Göritz, D. J Chem Phys 1996, 104, 351.
68. Jorge, S.; Freire, J. J.; Rey, A. Macromol Theory Simul 1997, 6, 271.
69. 2, and cov(u, v) = 〈uv〉 - 〈u〉〈v〉 are the sample variances and covariance, respectively. With increasing N the correlation diminishes slightly, from ρ(N = 10) ≈ 85 to p(N = 237) ≈ 0.79, with p(N = 100) ≈ 0.80.
70. N(u) shifts with decreasing N to smaller u values.
71. Sokal, A. D. Europhys Lett 1994, 27, 661; erratum Europhys Lett 1995, 30, 123.
72. This result remains correct even if slightly different parameter values t and θ are used in the asymptotic RdC ansatz in eqs 22 and 23a,b.
73. Djordjevic, Z. V.; Majid, I.; Stanley, H. E.; dos Santos, R. J. J Phys A: Math Gen 1982, 18, 2627.
74. Lyklema, J. W.; Kremer, K. Phys Rev B 1985, 31, 3182.
75. Here the superscript "t" indicates the transpose.
76. We used the routine "amebsa," as published in Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd ed.; Cambridge University Press: Cambridge, 1992; Chapter 10.9.
77. 2 divided by the number of the degrees of freedom (here 16), at the position of the global minimum is 1.51.
78. Kelly, K.; Hunter, D. L.; Jan, N. J Phys A: Math Gen 1987, 20, 5029.
79. Eizenberg, N.; Klafter, J. Phys Rev B 1996, 53, 5078.