Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
   
 
 
 
Previous Article
Coil size oscillatory packing in polymer solutions near a surface
The theory developed by Scheutjens and Fleer to describe polymer adsorption and depletion is used to calculate the density profile of nonadsorbing polymers near a surface. The theory predicts damped o...
Next Article
Reactions in microemulsions: Effect of thermal fluctuations on reaction kinetics
In this paper we address the generic effects arising from the interplay of thermal fluctuations and reactions. This is accomplished by considering specifically the kinetics of reactions effected in mi...

Hydrodynamic interactions in long chain polymers: Application of the Chebyshev polynomial approximation in stochastic simulations

J. Chem. Phys. 113, 2894 (2000); doi:10.1063/1.1305884

Issue Date: 15 August 2000

You are not logged in to this journal. Log in

Richard M. Jendrejack, Michael D. Graham, and Juan J. de Pablo
Department of Chemical Engineering and Rheology Research Center, University of Wisconsin–Madison, Madison, Wisconsin 53706-1691
We have simulated Brownian bead-spring chains of up to 125 units with fluctuating hydrodynamic and excluded volume interactions using the Chebyshev polynomial approximation proposed by Fixman [Macromolecules 19, 1204 (1986)] for the square root of the diffusion tensor. We have developed a fast method to continuously determine the validity of the eigenvalue range used in the polynomial approximation, and demonstrated how this range may be quickly updated when necessary. We have also developed a weak first order semiimplicit time integration scheme which offers increased stability in the presence of steep excluded volume potentials. The full algorithm scales roughly as O(N2.25) and offers substantial computational savings over the standard Cholesky decomposition. The above algorithm was used to obtain scaling exponents for various static and zero shear rate dynamical properties, which are found to be consistent with theoretical and/or experimental predictions. ©2000 American Institute of Physics.
History: Received 23 February 2000; accepted 18 May 2000
Permalink: http://link.aip.org/link/?JCPSA6/113/2894/1
BUY THIS ARTICLE   (US$28)
Download HTML Download Sectioned HTML Download PDF (90 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 61.25.Hq
    Structure of solids and liquids; crystallography Studies of specific liquid structures Macromolecular and polymer solutions; polymer melts; swelling
  • 83.70.Gp
    Rheology Material form Homogeneous isotropic liquids; solutions and melts
  • YEAR: 2000

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (73)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. D. Petera and M. Muthukumar, J. Chem. Phys. 111, 7614 (1999).
  2. J. G. Kirkwood and J. Riseman, J. Chem. Phys. 16, 565 (1948).
  3. B. H. Zimm, J. Chem. Phys. 24, 269 (1956).
  4. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Clarendon, Oxford, 1986).
  5. M. Fixman, J. Chem. Phys. 42, 3831 (1965).
  6. C. W. Pyun and M. Fixman, J. Chem. Phys. 42, 3838 (1965).
  7. C. W. Pyun and M. Fixman, J. Chem. Phys. 44, 2107 (1966).
  8. M. Fixman, J. Chem. Phys. 45, 785 (1966).
  9. M. Fixman, J. Chem. Phys. 45, 793 (1966).
  10. H.-C. Öttinger, J. Chem. Phys. 86, 3731 (1987).
  11. H.-C. Öttinger, J. Chem. Phys. 90, 463 (1989).
  12. J. J. Magda, R. G. Larson, and M. E. Mackay, J. Chem. Phys. 89, 2504 (1988).
  13. R. G. Larson and J. J. Magda, Macromolecules 22, 3004 (1989).
  14. W. Zykla and H.-C. Öttinger, J. Chem. Phys. 90, 474 (1989).
  15. H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 26, 207 (1987).
  16. L. E. Wedgewood and H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 27, 245 (1988).
  17. L. E. Wedgewood, D. N. Ostrov, and R. B. Bird, J. Non-Newtonian Fluid Mech. 40, 119 (1991).
  18. Y. Oono, Adv. Chem. Phys. 61, 301 (1985).
  19. Y. Oono and M. Kohmoto, J. Chem. Phys. 78, 520 (1983).
  20. Y. Oono, J. Chem. Phys. 79, 4629 (1983).
  21. B. Schaub, B. A. Friedman, and Y. Oono, Phys. Lett. A 110, 136 (1985).
  22. A. Jagannathan, B. Schaub, and Y. Oono, Phys. Lett. A 113, 341 (1985).
  23. A. Jagannathan, Y. Oono, and B. Schaub, J. Chem. Phys. 86, 2276 (1987).
  24. B. Schaub, D. B. Creamer, and H. Johannesson, J. Phys. A 21, 1431 (1988).
  25. S. Wang, Phys. Rev. A 40, 2137 (1989).
  26. S. Wang, J. Chem. Phys. 92, 7618 (1990).
  27. H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 33, 53 (1989).
  28. H.-C. Öttinger, Phys. Rev. A 40, 2664 (1989).
  29. H.-C. Öttinger, Phys. Rev. A 41, 4413 (1990).
  30. W. Zykla and H.-C. Öttinger, Macromolecules 24, 484 (1991).
  31. P. R. Baldwin and E. Helfand, Phys. Rev. A 41, 6772 (1990).
  32. R. S. Adler, J. Chem. Phys. 69, 2849 (1978).
  33. S. Q. Wang and K. F. Freed, J. Chem. Phys. 88, 3944 (1988).
  34. Y. Rabin, Europhys. Lett. 7, 25 (1988).
  35. Y. Rabin, S. Q. Wang, and K. F. Freed, Macromolecules 22, 2420 (1989).
  36. Y. Rabin, S. Q. Wang, and D. B. Creamer, J. Chem. Phys. 90, 570 (1989).
  37. H. P. Wittmann and G. H. Fredrickson, J. Phys. I 4, 1791 (1994).
  38. B. H. A. A. van den Brule, J. Non-Newtonian Fluid Mech. 47, 357 (1993).
  39. J. J. L. Cascales, F. G. Diaz, and J. G. de la Torre, Polymer 36, 345 (1995).
  40. M. Herrchen and H.-C. Öttinger, J. Non-Newtonian Fluid Mech. 17, 68 (1997).
  41. M. Fixman, J. Chem. Phys. 69, 1527 (1978).
  42. M. Fixman, Macromolecules 14, 1710 (1981).
  43. D. L. Ermak and J. A. McCammon, J. Chem. Phys. 69, 1352 (1978).
  44. S. A. Allison and J. A. McCammon, Biopolymers 23, 167 (1984).
  45. C. Pierleoni and J. P. Ryckaert, Macromolecules 28, 5097 (1995).
  46. Z. Xu, S. Kim, and J. J. de Pablo, J. Chem. Phys. 101, 5293 (1994).
  47. W. S. Stewart and J. P. Sorensen, Trans. Soc. Rheol. 16, 1 (1972).
  48. X. Fan, J. Chem. Phys. 85, 6237 (1985).
  49. X. Fan, J. Non-Newtonian Fluid Mech. 17, 125 (1985).
  50. T. C. B. Kwan and E. S. G. Shaqfeh, J. Non-Newtonian Fluid Mech. 82, 139 (1999).
  51. P. G. de Gennes, Proc. Natl. Acad. Sci. USA 96, 7262 (1999).
  52. B. H. Zimm, Macromolecules 31, 6089 (1998).
  53. B. B. Haab and R. A. Mathies, Anal. Chem. 71, 5137 (1999).
  54. R. G. Larson, T. T. Perkins, D. E. Smith, and S. Chu, Phys. Rev. E 55, 1794 (1997).
  55. R. G. Larson, H. Hua, D. E. Smith, and S. Chu, J. Rheol. 43, 267 (1999).
  56. J. G. H. Cifre and J. G. de la Torre, J. Rheol. 43, 339 (1999).
  57. M. Fixman, Macromolecules 19, 1204 (1986).
  58. J.-C. Öttinger, B. H. A. A. van der Brule, and M. A. Hulsen, J. Non-Newtonian Fluid Mech. 70, 255 (1997).
  59. T. W. Bell, Ph.D. thesis, University of Wisconsin–Madison, 1998.
  60. R. M. Jendrejack, T. W. Bell, J. J. de Pablo, and M. D. Graham, Proceedings of the XIIIth International Congress on Rheology, Cambridge, UK, 2000 (unpublished).
  61. The quantities used for nondimensionalization throughout this article are sqrt(kT/H) for distance, zeta/4H for time, kT for energy, sqrt(kTH) for force, and nkT for the stress tensor. The parameter k is Boltzmann's constant, T is temperature, H is Hooke's spring constant, n is the number density of polymer, and zeta is the bead friction coefficient.
  62. R. B. Bird, C. F. Curtiss, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley, New York, 1987), Vol. 2.
  63. H.-C. Öttinger, Stochastic Processes in Polymeric Fluids (Springer, Berlin, 1996).
  64. J. Rotne and S. Prager, J. Chem. Phys. 50, 4831 (1969).
  65. A. Rey, J. Freire, and J. G. de la Torre, Macromolecules 24, 4666 (1991).
  66. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics (Springer-Verlag, Berlin, 1988).
  67. C. R. Wylie and L. C. Barrett, Advanced Engineering Mathematics, 6th ed. (McGraw-Hill, New York, 1995).
  68. R. B. Lehoucq, D. C. Sorensen, and C. Yang, Arpack Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods, 1997, ftp://ftp.caam.rice.edu/pub/software/ARPACK.
  69. Y. Saad and M. H. Schultz, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856 (1986).
  70. In our nondimensionalization, the Weissenberg number is defined as We = gamma-dot tau1, where tau1 = 2/sin(pi/2N) is the longest Rouse relaxation time, and gamma-dot is the shear rate (nondimensionalized with zeta/4H).
  71. G. R. Strobl, The Physics of Polymers (Springer, Berlin, 1997).
  72. B. Li, N. Madras, and A. Sokal, J. Stat. Phys. 80, 661 (1995).
  73. Y. Oono and M. Kohmoto, J. Chem. Phys. 78, 520 (1983).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics