×

Multiple branches of ordered states of polymer ensembles with the Onsager excluded volume potential. (English) Zbl 1220.82185

Summary: We study the branches of equilibrium states of rigid polymer rods with the Onsager excluded volume potential in two-dimensional space. Since the probability density and the potential are related by the Boltzmann relation at equilibrium, we represent an equilibrium state using the Fourier coefficients of the Onsager potential. We derive a non-linear system for the Fourier coefficients of the equilibrium state. We describe a procedure for solving the non-linear system. The procedure yields multiple branches of ordered states. This suggests that the phase diagram of rigid polymer rods with the Onsager potential has a more complex structure than that with the Maier-Saupe potential. A study of free energy indicates that the first branch of ordered states is stable while the subsequent branches are unstable. However, the instability of the subsequent branches does not mean they are not interesting. Each of these unstable branches, under certain external potential, can be made metastable, and thus may be observed.

MSC:

82D60 Statistical mechanics of polymers
82B35 Irreversible thermodynamics, including Onsager-Machlup theory
74A15 Thermodynamics in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Onsager, L., Ann. (N.Y.) Acad. Sci., 51, 627 (1949)
[2] Rey, A. D.; Denn, M. M., Annu. Rev. Fluid Mech., 34, 233 (2002)
[3] Doi, M.; Edwards, S. F., The Theory of Polymer Dynamics (1986), Oxford Univ. Press
[4] Hess, S. Z., Z. Naturforsch. A, 31, 1034 (1976)
[5] Forest, M. G.; Zhou, R.; Wang, Q., Phys. Rev. E, 66, 031712 (2002)
[6] Faraoni, V.; Grosso, M.; Crescitelli, S.; Maffetone, P. L., J. Rheol., 43, 829 (1999)
[7] Gopinath, A.; Mahadevan, L.; Armstrong, R. C., Phys. Fluids, 18, 028102 (2006)
[8] Larson, R. G., Macromolecules, 23, 3983 (1990)
[9] Larson, R. G., The Structure and Rheology of Complex Fluids (1999), Oxford Univ. Press
[10] Lasher, G., J. Chem. Phys., 53, 4141 (1970)
[11] Vroege, G. J.; Lekkerkerker, H., Rep. Prog. Phys., 55, 1241 (1992)
[12] Chrzanowska, A., Acta Phys. Pol. B, 36, 3163 (2005)
[13] Forest, M. G.; Zhou, R.; Wang, Q., Phys. Rev. Lett., 93, 8, 088301 (2004)
[14] Liu, H.; Zhang, H.; Zhang, P., Commun. Math. Sci., 3, 201 (2005)
[15] Fatkullin, I.; Slastikov, V., Nonlinearity, 18, 2565 (2005)
[16] Zhou, H.; Wang, H.; Forest, M. G.; Wang, Q., Nonlinearity, 18, 2815 (2005)
[17] Gopinath, A.; Armstrong, R. C.; Brown, R. A., J. Chem. Phys., 121, 6093 (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.