End-to-end distribution function for dilute polymers

Journal of Chemical Physics

Volumn 112, Issue 17, 2000, Pages 7693-7710

  Caracciolo, Sergio ^a   Causo, Maria Serena ^b,d   Pelissetto, Andrea ^c  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b FORSCHUNGSZENTRUM JÜLICH   (Germany)

^c SAPIENZA UNIVERSITY OF ROME   (Italy)

^d UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001048402     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.481362     Document Type: Article

References (60)

1. P. J. Flory, Principles of Polymer Chemistry (Cornell University Press, Ithaca, NY, 1953).
2. P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
3. J. des Cloizeaux and G. Jannink, Les Polymères en Solution (Les Editions de Physique, Les Ulis, 1987); English translation: Polymers in Solution: Their Modeling and Structure (Oxford University Press, Oxford, 1990).
4. J. des Cloizeaux and G. Jannink, Les Polymères en Solution (Les Editions de Physique, Les Ulis, 1987); English translation: Polymers in Solution: Their Modeling and Structure (Oxford University Press, Oxford, 1990).
5. K. F. Freed, Renormatization-Group Theory of Macromolecules (Wiley, New York, 1987).
6. P. G. de Gennes, Phys. Lett. A 38, 339 (1972).
7. M. E. Fisher and B. J. Hiley, J. Chem. Phys. 34, 1253 (1961).
8. M. E. Fisher, J. Chem. Phys. 44, 616 (1966).
9. J. Mazur, J. Res. Natl. Bur. Stand., Sect. A 69, 355 (1965); J. Chem. Phys. 43, 4354 (1965).
10. J. Mazur, J. Res. Natl. Bur. Stand., Sect. A 69, 355 (1965); J. Chem. Phys. 43, 4354 (1965).
11. D. S. Mc Kenizie and M. A. Moore, J. Phys. A 4, L82 (1971).
12. D. S. McKenzie, Phys. Rep., Phys. Lett. 27C, 35 (1976).
13. J. des Cloizeaux, Phys. Rev. A 10, 1665 (1974); J. Phys. (France) 41, 223 (1980).
14. J. des Cloizeaux, Phys. Rev. A 10, 1665 (1974); J. Phys. (France) 41, 223 (1980).
15. P. H. Verdier and W. H. Stockmayer, J. Chem. Phys. 36, 227 (1962).
16. F. T. Wall, S. Windwer, and R. J. Gans, J. Chem. Phys. 38, 2220 (1963).
17. A. Baumgärtner, Z. Phys. 42, 265 (1981).
18. M. Bishop and J. H. R. Clarke, J. Chem. Phys. 94, 3936 (1991).
19. M. Bishop, J. H. R. Clarke, A. Rey, and J. J. Freire, J. Chem. Phys. 95, 4589 (1991).
20. J. Dayantis and J.-F. Palierne, J. Chem. Phys. 95, 6088 (1991).
21. N. Eizenberg and J. Klafter, J. Chem. Phys. 99, 3976 (1993).
22. J. S. Pedersen, M. Laso, and P. Schurlenberger, Phys. Rev. E 54, R5917 (1996).
23. J. P. Valleau, J. Chem. Phys. 104, 3071 (1996).
24. The different proposals appearing in the literature and many old numerical results have been reviewed by Bishop and Clarke (see Ref. 15).
25. Y. Oono, T. Ohta, and K. F. Freed, Macromolecules 14, 880 (1981); J. Chem. Phys. 74, 6458 (1981).
26. Y. Oono, T. Ohta, and K. F. Freed, Macromolecules 14, 880 (1981); J. Chem. Phys. 74, 6458 (1981).
27. N(r) can be identified with the number of walks starting at the origin and ending in r.
28. P. Belohorec and B. G. Nickel, University of Guelph report, September 1997 (unpublished).
29. S. Caracciolo, M. S. Causo, and A. Pelissetto, Phys. Rev. E 57, R1215 (1998); cond-mat/9703250.
30. S. F. Edwards, Proc. Phys. Soc. London 85, 613 (1965).
31. Y. Oono, in Advances in Chemical Physics, edited by I. Prigogine and S. A. Rice (Wiley, New York, 1985), Vol. LXI, p. 301.
32. 0 and the three-loop results for the critical exponents (Ret. 29).
33. E. Brézin, J. C. Le Guillou, J. Zinn-Justin, and B. G. Nickel, Phys. Lett. A 44, 227 (1973).
34. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980).
35. J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980).
36. The resummation procedure depends on two free parameters, α and b in the notation of Ref. 30. The reported errors are related to the variation of the estimates with changes of α and b.
37. M. E. Fisher and R. J. Burford, Phys. Rev. 156, 583 (1967).
38. M. E. Fisher and A. Aharony, Phys. Rev. Lett. 31, 1238 (1973); Phys. Rev. B 7, 2818 (1974).
39. M. E. Fisher and A. Aharony, Phys. Rev. Lett. 31, 1238 (1973); Phys. Rev. B 7, 2818 (1974).
40. A. J. Bray, Phys. Rev. B 14, 1248 (1976).
41. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Europhys. Lett. 38, 577 (1997); Phys. Rev. E 57, 184 (1998).
42. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Europhys. Lett. 38, 577 (1997); Phys. Rev. E 57, 184 (1998).
43. The coupling constant g can be expressed in terms of the second virial coefficient for a polydisperse ensemble of polymers, see Ref. 37.
44. M. Muthukumar and B. G. Nickel, J. Chem. Phys. 80, 5839 (1984); 86, 460 (1987).
45. M. Muthukumar and B. G. Nickel, J. Chem. Phys. 80, 5839 (1984); 86, 460 (1987).
46. G. A. Baker, Jr., B. G. Nickel, and D. I. Meiron, Phys. Rev. Lett. 36, 1351 (1977); Phys. Rev. B 17, 1365 (1977).
47. G. A. Baker, Jr., B. G. Nickel, and D. I. Meiron, Phys. Rev. Lett. 36, 1351 (1977); Phys. Rev. B 17, 1365 (1977).
48. D. B. Murray and B. G. Nickel, University of Guelph report, 1991 (unpublished).
49. A. Pelissetto and E. Vicari, Nucl. Phys. B 519 [FS], 626 (1998); the estimates appearing in this work are affected by a small numerical error. Revised estimates appear in cond-mat/9911452 [to appear in Nucl. Phys. B (2000)].
50. A. Pelissetto and E. Vicari, Nucl. Phys. B 519 [FS], 626 (1998); the estimates appearing in this work are affected by a small numerical error. Revised estimates appear in cond-mat/9911452 [to appear in Nucl. Phys. B (2000)].
51. M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 54, 7301 (1996).
52. M. E. Fisher and J. S. Langer, Phys. Rev. Lett. 20, 665 (1968).
53. E. Brezm, D. Amit, and J. Zinn-Justin. Phys. Rev. Lett. 32, 151 (1974).
54. M. Lal, Mol. Phys. 17, 57 (1969).
55. B. MacDonald, N. Jan, D. L. Hunter, and M. O. Steinitz, J. Phys. A 18, 2627 (1985).
56. N. Madras and A. D. Sokal, J. Stat. Phys. 50, 109 (1988).
57. B. Li, N. Madras, and A. D. Sokal, J. Stat. Phys. 80, 661 (1995).
58. The most precise Monte Carlo estimate of Δ is Δ = 0.517±0.007+0.010 (Ref. 24). Perturbative field theory gives a lower estimate (Ref. 49): Δ = 0.478±0.010 (d = 3 expansion) and Δ = 0.486 ±0.016 (∈ expansion).
59. R. Guida and J. Zinn-Justin, J. Phys. A 31, 8103 (1998).
60. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, San Diego, 1980).