Crossover between short- and long-time behavior of stress fluctuations and viscoelasticity of liquids

Siegfried Hess; Martin Kröger; Denis Evans

doi:10.1103/PhysRevE.67.042201

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Crossover between short- and long-time behavior of stress fluctuations and viscoelasticity of liquids

Siegfried Hess¹, Martin Kröger^1,2, and Denis Evans³

¹Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
²Polymer Physics, Materials Science, ETH Zürich, CH-8092 Zürich, Switzerland
³Research School of Chemistry, The Australian National University, Canberra ACT 0200, Australia

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Phys. Rev. E 67, 042201 – Published 28 April, 2003

DOI: https://doi.org/10.1103/PhysRevE.67.042201

Abstract

An effective viscosity coefficient is introduced based on definite time averages of equilibrium stress fluctuations rather than stress correlations. Analysis of this quantity via molecular dynamics of a simple model liquid reveals a crossover between the expected short-time elastic and the long-time viscous behavior with increasing averaging time. The procedure allows us to extract the zero-rate shear viscosity when the averaging time becomes one order of magnitude larger than the relevant relaxation time. A relationship between this effective viscosity and the dynamic viscosities is established.

References (21)

E. Helfand, Phys. Rev. 119, 1 (1960).
S. Hess and D.J. Evans, Phys. Rev. E 64, 011207 (2001).
M.S. Green, J. Chem. Phys. 22, 398 (1954); R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).
H. Müller-Krumbhaar and K. Binder, J. Stat. Phys. 8, 1 (1973); M. Kikuchi, N. Ito, and Y. Okabe, Int. J. Mod. Phys. C 7, 379 (1996).
S. Sengupta, P. Nielaba, M. Rao, and K. Binder, Phys. Rev. E 61, 1072 (2000).
J.W. Dufty, Mol. Phys. 100, 2331 (2002).
J.G. Powles and D.M. Heyes, Mol. Phys. 98, 917 (2000); ibid.D.M. Heyes and J.G. Powles, 99, 1077 (2001).
D.M. Heyes, J.G. Powles, and G. Rickayzen, Proc. R. Soc. London, Ser. A 455, 3725 (1999); Mol. Phys. 100, 595 (2002).
I.M. de Schepper, Phys. Rev. A 24, 2789 (1981).
M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
D.J. Evans and G.P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic Press, London, 1990).
R. Zwanzig and N.K. Ailawadi, Phys. Rev. 182, 280 (1969).
D. Searles and D.J. Evans, J. Chem. Phys. 112, 9727 (2000).
S. Hess, M. Kröger, and W.G. Hoover, Physica A 239, 449 (1997).
S. Hess and M. Kröger, Phys. Rev. E 64, 011201 (2001).
B.D. Butler, G. Ayton, O.G. Jepps, and D.J. Evans, J. Chem. Phys. 109, 6519 (1998).
D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986); Z. Naburforscn., A: Phys. Sci. 43, 662 (1988); L. Bennett and S. Hess, Phys. Rev. E 60, 5561 (1999).
S. Sarman and D.J. Evans, J. Chem. Phys. 99, 9021 (1993); S. Sarman, Physica A 240, 160 (1997); J. Chem. Phys. 103, 393 (1995); ibid.107, 3144 (1997).
M. Kröger and S. Hess, Phys. Rev. Lett. 85, 1128 (2000).
M. Schoen, S. Hess, and D.J. Diestler, Phys. Rev. E 52, 2587 (1995).
T. Gruhn and M. Schoen, Phys. Rev. E 55, 2861 (1997); Mol. Phys. 93, 681 (1998); J. Chem. Phys. 108, 9124 (1998).

[c1] E. Helfand, Phys. Rev. 119, 1 (1960).

[c2] S. Hess and D.J. Evans, Phys. Rev. E 64, 011207 (2001).

[c3] M.S. Green, J. Chem. Phys. 22, 398 (1954); R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).

[c4] H. Müller-Krumbhaar and K. Binder, J. Stat. Phys. 8, 1 (1973); M. Kikuchi, N. Ito, and Y. Okabe, Int. J. Mod. Phys. C 7, 379 (1996).

[c5] S. Sengupta, P. Nielaba, M. Rao, and K. Binder, Phys. Rev. E 61, 1072 (2000).

[c6] J.W. Dufty, Mol. Phys. 100, 2331 (2002).

[c7] J.G. Powles and D.M. Heyes, Mol. Phys. 98, 917 (2000); ibid.D.M. Heyes and J.G. Powles, 99, 1077 (2001).

[c8] D.M. Heyes, J.G. Powles, and G. Rickayzen, Proc. R. Soc. London, Ser. A 455, 3725 (1999); Mol. Phys. 100, 595 (2002).

[c9] I.M. de Schepper, Phys. Rev. A 24, 2789 (1981).

[c10] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).

[c11] D.J. Evans and G.P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic Press, London, 1990).

[c12] R. Zwanzig and N.K. Ailawadi, Phys. Rev. 182, 280 (1969).

[c13] D. Searles and D.J. Evans, J. Chem. Phys. 112, 9727 (2000).

[c14] S. Hess, M. Kröger, and W.G. Hoover, Physica A 239, 449 (1997).

[c15] S. Hess and M. Kröger, Phys. Rev. E 64, 011201 (2001).

[c16] B.D. Butler, G. Ayton, O.G. Jepps, and D.J. Evans, J. Chem. Phys. 109, 6519 (1998).

[c17] D. Baalss and S. Hess, Phys. Rev. Lett. 57, 86 (1986); Z. Naburforscn., A: Phys. Sci. 43, 662 (1988); L. Bennett and S. Hess, Phys. Rev. E 60, 5561 (1999).

[c18] S. Sarman and D.J. Evans, J. Chem. Phys. 99, 9021 (1993); S. Sarman, Physica A 240, 160 (1997); J. Chem. Phys. 103, 393 (1995); ibid.107, 3144 (1997).

[c19] M. Kröger and S. Hess, Phys. Rev. Lett. 85, 1128 (2000).

[c20] M. Schoen, S. Hess, and D.J. Diestler, Phys. Rev. E 52, 2587 (1995).

[c21] T. Gruhn and M. Schoen, Phys. Rev. E 55, 2861 (1997); Mol. Phys. 93, 681 (1998); J. Chem. Phys. 108, 9124 (1998).

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Crossover between short- and long-time behavior of stress fluctuations and viscoelasticity of liquids

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