Viscoelasticity of tightly entangled solutions of semiflexible polymers

David C. Morse

doi:10.1103/PhysRevE.58.R1237

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Viscoelasticity of tightly entangled solutions of semiflexible polymers

David C. Morse

Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue Southeast, Minneapolis, Minnesota 55455

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Phys. Rev. E 58, R1237(R) – Published 1 August, 1998

DOI: https://doi.org/10.1103/PhysRevE.58.R1237

Abstract

A molecular model is introduced to describe the linear viscoelasticity of tightly entangled solutions of semiflexible polymers. An expression for the stress of a solution of wormlike chains is derived, and a tube model is used to describe the effects of entanglement. Consideration of the Brownian dynamics of the polymer within its tube yields a dynamic modulus $G^{*} (ω) \propto (i ω)^{3 / 4}$ at high frequencies, in agreement with the results of recent microrheology experiments on actin solutions.

References (15)

M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, London, 1986).
See, e.g., T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).
D. H. Wachsstock, W. H. Schwarz, and T. D. Pollard, Biophys. J. 65, 205 (1993); ibid.66, 801 (1994).
R. Ruddies, W. H. Goldmann, G. Isenberg, and E. Sackmann, Eur. Biophys. J. 22, 309 (1993).
F. Amblard, A. C. Maggs, B. Yurke, A. N. Pargellis, and S. Leibler, Phys. Rev. Lett. 77, 4470 (1996).
F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt, Phys. Rev. Lett. 79, 3286 (1997); B. Schnurr, F. Gittes, F. C. MacKintosh, and C. F. Schmidt, Macromolecules 30, 7781 (1997).
J. Xu, A. Palmer, and D. Wirtz (unpublished).
T. Odijk, Macromolecules 16, 1340 (1983).
M. Doi, J. Polym. Sci., Polym. Symp. 73, 93 (1985).
A. N. Semenov, J. Chem. Soc., Faraday Trans. 86, 317 (1986).
F. C. MacKintosh, P. A. Janmey, and J. Kas, Phys. Rev. Lett. 75, 4425 (1995).
H. Isambert and A. C. Maggs, Macromolecules 29, 1036 (1996); A. C. Maggs, Phys. Rev. E 55, 7396 (1997).
D. C. Morse (unpublished).
R. Granek, J. Phys. II 7, 1761 (1997).
F. Gittes and F. C. MacKintosh, following paper, Phys. Rev. E 58, 1241 (1998).

[c1] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, London, 1986).

[c2] See, e.g., T. Sato and A. Teramoto, Adv. Polym. Sci. 126, 85 (1996).

[c3] D. H. Wachsstock, W. H. Schwarz, and T. D. Pollard, Biophys. J. 65, 205 (1993); ibid.66, 801 (1994).

[c4] R. Ruddies, W. H. Goldmann, G. Isenberg, and E. Sackmann, Eur. Biophys. J. 22, 309 (1993).

[c5] F. Amblard, A. C. Maggs, B. Yurke, A. N. Pargellis, and S. Leibler, Phys. Rev. Lett. 77, 4470 (1996).

[c6] F. Gittes, B. Schnurr, P. D. Olmsted, F. C. MacKintosh, and C. F. Schmidt, Phys. Rev. Lett. 79, 3286 (1997); B. Schnurr, F. Gittes, F. C. MacKintosh, and C. F. Schmidt, Macromolecules 30, 7781 (1997).

[c7] J. Xu, A. Palmer, and D. Wirtz (unpublished).

[c8] T. Odijk, Macromolecules 16, 1340 (1983).

[c9] M. Doi, J. Polym. Sci., Polym. Symp. 73, 93 (1985).

[c10] A. N. Semenov, J. Chem. Soc., Faraday Trans. 86, 317 (1986).

[c11] F. C. MacKintosh, P. A. Janmey, and J. Kas, Phys. Rev. Lett. 75, 4425 (1995).

[c12] H. Isambert and A. C. Maggs, Macromolecules 29, 1036 (1996); A. C. Maggs, Phys. Rev. E 55, 7396 (1997).

[c13] D. C. Morse (unpublished).

[c14] R. Granek, J. Phys. II 7, 1761 (1997).

[c15] F. Gittes and F. C. MacKintosh, following paper, Phys. Rev. E 58, 1241 (1998).

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