Static dynamics approach to relaxation modes and times for deformed polymers

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 2 1, 2003, Pages

  Rzehak, Roland ^a   Zimmermann, Walter ^b  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b SAARLAND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONFORMATIONS; DEFORMATION; EIGENVALUES AND EIGENFUNCTIONS; EQUATIONS OF MOTION; HYDRODYNAMICS; LINEAR EQUATIONS; MATRIX ALGEBRA; MOLECULAR DYNAMICS; MOLECULAR STRUCTURE; THERMODYNAMIC STABILITY;

BROWNIAN DYNAMIC SIMULATION; DEFORMED POLYMERS; POLYMER CHAIN; RELAXATION MODES; STATIC DYNAMICS; TETHERED POLYMER; THERMAL EQUILIBRIUM;

POLYMERS;

EID: 42749108737     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (73)

1. J.D. Ferry, Viscoelastic Properties of Polymers (John Wiley, New York, 1964).
2. R.B. Bird, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, 2nd ed. (Wiley, New York, 1987), Vol. 1. Vol. 1.
3. H. Giesekus, J. Non-Equilib. Thermodyn. 11, 157 (1986).
4. R.G. Larson, Rheol. Acta 31, 213 (1992).
5. R.G. Larson, Rheol. Acta 31, 497 (1992).
6. U.S. Agarval, A. Dutta, and R.A. Mashelkar, Chem. Eng. Sci. 49, 1693 (1994).
7. J.L. Lumley, Annu. Rev. Fluid Mech. 1, 367 (1969).
8. P.S. Virk, AIChE J. 21, 625 (1975).
9. A. Gyr and H.-W. Bewersdorff, Drag Reduction of Turbulent Flows by Additives (Kluwer Academic, Dordrecht, 1995).
10. A. Groisman and V. Steinberg, Nature (London) 405, 53 (2000).
11. P.E. Rouse, Jr., J. Chem. Phys. 21, 1272 (1953).
12. B,H. Zimm, J. Chem. Phys. 24, 269 (1956).
13. B.H. Zimm, G.M. Roe, and L.F. Epstein, J. Chem. Phys. 24, 279 (1965).
14. P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1981).
15. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986)
16. A. Onuki, J. Phys. Soc. Jpn. 54, 3656 (1985).
17. P.-G. de Gennes, J. Chem. Phys. 60, 5030 (1974).
18. E.J. Hinch, Phys. Fluids 20, S22 (1977).
19. P.-G. de Gennes, Physica A 140, 9 (1986).
20. R.B. Bird, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids, Vol. II: Kinetic Theory, 2nd ed. (Wiley, New York, 1987).
21. R.G. Larson, Constitutive Equations for Polymer Melts and Solutions (Butterworth, Stoneham, MA, 1988).
22. L.G. Leal, in Structure of Turbulence and Drag Reduction, edited by A. Gyr (Springer, Heidelberg, 1990).
23. H.C. Öttinger, Stochastic Processes in Polymeric Fluids (Springer, Heidelberg, 1996).
24. T.T. Perkins, S.R. Quake, D.E. Smith, and S. Chu, Science 264, 822 (1994).
25. T.T. Perkins, D.E. Smith, R.G. Larson, and S. Chu, Science 268, 83 (1995).
26. S. Manneville, P. Cluzel, J.L. Viovy, D. Chatenay, and F. Caron, Europhys. Lett. 36, 413 (1996).
27. S.R. Quake, H. Babcock, and S. Chu, Nature (London) 388, 151 (1997).
28. P. Pincus, Macromolecules 9, 386 (1976).
29. P. Pincus, Macromolecules 10, 210 (1977).
30. F. Brochard-Wyart, Europhys. Lett. 23, 105 (1993).
31. F. Brochard-Wyart, H. Hervet, and P. Pincus, Europhys. Lett. 26, 511 (1994).
32. Y. Marciano and F. Brochard-Wyart, Macromolecules 28, 985 (1995).
33. F. Brochard-Wyart, Europhys. Lett. 30, 387 (1995).
34. J.W. Hatfield and S.R. Quake, Phys. Rev. Lett. 82, 3548 (1999).
35. L. Harnau and P. Reineker, New J. Phys. 1, 3.1 (1999).
36. R.G. Larson, T.T. Perkins, D.E. Smith, and S. Chu, Phys. Rev. E 55, 1794 (1997).
37. B.H. Zimm, Macromolecules 31, 6089 (1998).
38. R. Rzehak, D. Kienle, T. Kawakatsu, and W. Zimmermann, Europhys. Lett. 46, 821 (1999).
39. R. Rzehak, W. Kromen, T. Kawakatsu, and W. Zimmermann, Eur. Phys. J. E 2, 3 (2000).
40. C. Pierleoni, G. Arialdi, and J.-P. Ryckaert, Phys. Rev. Lett. 79, 2990 (1997).
41. D. Kienle and W. Zimmermann, Macromolecules 34, 9173 (2001).
42. R. Rzehak and W. Zimmermann, Europhys. Lett. 59, 779 (2002).
43. H.C. Öttinger and W. Zylka, J. Rheol. 36, 885 (1992).
44. Y. Rabin and J.W. Dash, Macromolecules 18, 442 (1985).
45. P. Ahlrichs and B. Dünweg, J. Chem. Phys. 111, 8225 (1999).
46. S.W. Provencher, Comput. Phys. Commun. 27, 213 (1982).
47. C. Elster and J. Honerkamp, J. Rheol. 36, 911 (1992).
48. B. Dünweg, M. Stevens, and K. Kremer, in Monte Carlo and Molecular Dynamics Simulations in Polymer Science, edited by K. Binder (Oxford University Press, Oxford, UK, 1995), Chap. 3.
49. B.H. Zimm, Macromolecules 13, 592 (1980).
50. M. Fixman, J. Chem. Phys. 78, 1588 (1983).
51. H.C. Öttinger, J. Chem. Phys. 86, 3731 (1987).
52. R. Zurmühl and S. Falk, Matrizen und Ihre Anwendungen (Springer, Heidelberg, 1984).
53. R.A. Horn, Matrices (Cambridge University Press, Cambridge UK, 1985).
54. H. Goldstein, C. Poole, and J. Safko, Classical Mechanics, 3rd ed. (Addison-Wesley, Reading, MA, 2002).
55. R. Rzehak, Eur. Phys. J. E. (to be published).
56. H. Fischer and H. Kaul, Mathematik für Physiker (Teubner, Stuttgart, 1988), Vol. I.
57. C.W. Gardiner, Handbook of Stochastic Methods (Springer, Heidelberg, 1983).
58. H. Risken, The Fokker-Planck Equation, 2nd ed. (Springer, Heidelberg, 1989).
59. H. Yamakawa, Modern Theory of Polymer Solutions (Harper & Row, New York, 1971).
60. R. Rzehak, A. Arend, D. Kienle, and W. Zimmermann, in Numerical Solutions of Polymer and Cell Dynamics, edited by W. Alt, M. Chaplain, J. Griebel, and J. Lenz (Birkäuser, Basel, 2003).
61. M.C. Williams, J. Chem. Phys. 42, 2988 (1965).
62. N.W. Tschoegl, J. Chem. Phys. 40, 473 (1964).
63. R. Rzehak, T. Kawakatsu, and W. Zimmermann (unpublished).
64. H. C. Öttinger, J. Chem. Phys. 90, 463 (1988).
65. B,H. Zimm and R.W. Kilb, J. Polym. Sci. 37, 19 (1959).
66. R.L. Sammler and J.L. Schrag, Macromolecules 21, 1132 (1988).
67. K. Kremer and G.S. Grest, J. Chem. Phys. 92, 5057 (1990).
68. R. Zwanzig, Adv. Chem. Phys. 15, 325 (1969).
69. C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, UK, 1992).
70. H.C. Öttinger and Y. Rabin, J. Rheol. 33, 725 (1989).
71. M.R. Spiegel, Calculus of Finite Differences and Difference Equations (McGraw-Hill, New York, 1971).
72. This figure corrects an erroneous normalization in Fig. 2 of Ref. [42].
73. Case (ii) arises for the center-of-mass motion of a free-Rouse chain.