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An eigenvalue problem encountered in the dynamical theory of chain molecules isThis is solved by three methods: use of a Fourier series for , expansion of in associated Legendre polynomials Pm2" alig...

Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss

J. Chem. Phys. 24, 269 (1956); doi:10.1063/1.1742462

Issue Date: February 1956

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Bruno H. Zimm
General Electric Research Laboratory, The Knolls, Schenectady, New York
The problem of the motions of a chain molecule diffusing in a viscous fluid under the influence of external forces or currents is considered for a particular model. This model is a chain of beads connected by ideal springs. Hydrodynamic interaction between the beads is introduced in the approximate form due to Kirkwood and Riseman. It is possible to solve this problem exactly with the use of a transformation to a set of normal coordinates. The viscosity, birefringence of flow, and dielectric and tensile relaxation behavior are calculated explicitly. The intrinsic viscosity in steady flow is somewhat different from the Kirkwood-Riseman result, and there is no change of viscosity with shear rate. The spectrum of relaxation times is similar to that found by Rouse and by F. Bueche, but has its maximum at a lower frequency than those obtained by Kuhn and Kuhn and by Kirkwood and Fuoss in other ways. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
History: Received May 24, 1955
Permalink: http://link.aip.org/link/?JCPSA6/24/269/1
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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (31)
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  1. T. Alfrey, J. Chem. Phys. 12, 374 (1944).
  2. P. E. Rouse, Jr., J. Chem. Phys. 21, 1272 (1953).
  3. F. Bueche, J. Chem. Phys. 22, 603 (1954).
  4. L. Brillouin, Wave Propagation in Periodic Structures (McGraw-Hill Book Company, Inc., New York, 1946) (Dover Publications. Inc., New York, 1953).
  5. W. Kuhn and F. Grün, Kolloid Z. 101, 248 (1942).
  6. W. Kuhn and H. Kuhn, Helv. Chim. Acta 26, 1394 (1943).
  7. W. Kuhn and H. Kuhn, Helv. Chim. Acta 28, 1533 (1945).
  8. W. Kuhn and H. Kuhn, Helv. Chim. Acta 29, 71 (1946).
  9. W. Kuhn and H. Kuhn, Helv. Chim. Acta 29, 609 (1946).
  10. W. Kuhn and H. Kuhn, Helv. Chim. Acta 29, 830 (1946).
  11. W. Kuhn, Helv. Chim. Acta 31, 1092 (1948).
  12. W. Kuhn, Helv. Chim. Acta 31, 1259 (1948);
    13. 33, 2057 (1950).
  13. J. G. Kirkwood and R. M. Fuoss, J. Chem. Phys. 9, 328 (1941).
  14. (a) J. G. Kirkwood, Rec. Trav. Chim. 68, 649 (1949)
    15. (b) J. G. Kirkwood, J. Polymer Sci. 12, 1 (1954).
  15. H. A. Kramers, J. Chem. Phys. 14, 415 (1946).
  16. J. M. Burgers, Second Report on Viscosity and Plasticity of the Amsterdam Academy of Sciences (Nordemann, Publishing Company, New York, 1938).
  17. J. J. Hermans, Rec. Trav. Chim. 63, 219 (1944).
  18. A. Peterlin, Les grosses molécules en solution (Collège de France, Paris, 1948);
    19. “L'interaction hydrodynamique des segments de la grosse molécule,” Dissertation, Academia Scientiarum et Artium Solvenica, Ljubljana, 1950.
  19. J. G. Kirkwood and J. Riseman, J. Chem. Phys. 16, 565 (1948).
  20. M. C. Wang and G. E. Uhlenbeck, Revs. Modern Phys. 17, 323 (1945).
  21. S. Chandrasekhar, Revs. Modern Phys. 15, 1 (1943).
  22. Kirkwood (reference 14) has used a tensor notation for the same quantitites. In his case the use of generalized curvilinear coordinates made desirable explicit recognition of the tensor properties of the operators. In our case the transformation to normal coordinates emphasizes essentially matrix manipulations.
  23. F. Bueche, J. Chem. Phys. 22, 1570 (1954).
  24. P. Debye, J. Chem. Phys. 14, 636 (1946).
  25. M. L. Huggins, J. Phys. Chem. 42, 911 (1938);
    26. 43, 439 (1939).
  26. The inversion of H to obtain Eqs. (92) and (93) is not a trivial matter for the non-free-draining case. I am indebted to Dr. P. L. Auer and Dr. C. S. Gardner for a private communication containing this result. The validity of Eq. (30) with Eq. (92) can be directly established by replacing r with the substitution r = (p−1)/(p+1) and using contour integration along a branch cut on the positive real axis of p and a circle at infinity (see reference 28).
  27. Kirkwood, Zwanzig, and Plock, J. Chem. Phys. 23, 213 (1955).
  28. P. L. Auer and C. S. Gardner [J. Chem. Phys. 23, 1545 (1955)] have obtained a value of 2.90 from a recalculation of the Kirkwood-Riseman result.
  29. Newman, Krigbaum, Laugier, and Flory, J. Polymer Sci. 14, 451 (1954).
  30. J. G. Kirkwood, J. Chem. Phys. 14, 51 (1946).
  31. Courant and Hilbert, Methoden der Mathematischen Physik (Verlag Julius Springer, Berlin, 1924);
    32. Margenau and Murphy, The Mathematics of Physics and Chemistry (D. van Nostrand Company, Inc., New York, 1943).

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