Abstract
The molecular relaxation mechanisms of polymers withmulti-scale units of motion in glassy, rubbery and melt states areproposed based upon a fuzzy constraint method and non-equilibriumstatistical thermodynamics. The entanglement effects due to cohesiveforce and steric hindrance are expressed quantitatively in terms of amembership function. The micro-Brownian motion of a polymer chain isgoverned by the Langevin equation, which accounts for viscous force,nonuniform tension, entanglement constraint force and random force.Perturbation solutions have been established for different time and sizescales. The solutions account for the effects of both intramolecular andintermolecular interactions in the relaxation process. The unifiedrelaxation spectrum over many orders of time scale is a naturalconsequence of macromolecular structure, which satisfies thetime-temperature equivalence in the form of the Arrhenius equation atlow and high temperatures and in the form of the WLF equation near theglass transition temperature. The barrier model, the normal mode theory,the retraction and reptation theories can be taken as special casescorresponding to different scales.
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References
Bird, R.B., Hassager, O., Armstrong, R.C. and Curtiss, C.F., Dynamics of Polymeric Liquids, Vol. II, Kinetic Theory, Wiley, New York, 1977.
Chen, X., ‘Statistical mechanics of fuzzy random polymer networks’ Science in China, Series A 38, English edition, 1995, 1095–1104.
Chen, X., Tong, P. and Wang, R., ‘Nonequilibrium statistical thermodynamic theory for viscoelasticity of polymers’ J. Mech. Phys. Solids 46, 1998, 139–152.
Curtiss, C.F. and Bird, R.B., ‘A kinetic theory for polymer melts’ J. Chem. Phys. 74, 1981, 2016–2025.
De Gennes, P.G., ‘Reptation of a polymer chain in the presence of fixed obstacles’ J. Chem. Phys. 55, 1971, 572–279.
Doi, M. and Edwards, S.F., The Theory of Polymer Dynamics, Oxford University Press, New York, 1986.
Ferry, J.D., Viscoelastic Properties of Polymers, 3rd edn., John Wiley & Sons, New York, 1980.
Hoffmann, J.D., Williams, G. and Passaglia, E., ‘Analysis of the α, βand γrelaxations in polychlorotrifluoroethylene and polyethylene: Dielectric and mechanical properties’ J. Polymer Sci. C14, 1966, 173–235.
Mead, D.W., Herbolzhiemer, E.A. and Leal, L., ‘The effect of segmental stretch on theoretical predictions of the Doi–Edwards model’ in Theoretical and Applied Rheology, Proceedings XIth International Congress on Rheology, Brussels, Belgium, August 17–21, 1992, P. Moldenaers and R. Keunings (eds.), Elsevier, Amsterdam, 1992, 100–102.
Qian, R. and Shen, J., ‘On the origin of stress peak in uniaxial stretching of amorphous polymers’ Preprint, 1996.
Qian, R., Wu, L., Shen, D., Napper, D.H., Mann, R.A. and Sangster, D.F., ‘Single-chain polystyrene glasses’ Macromolecules 26, 1993, 2950–2953.
Risken, H., The Fokker–Planck Equations, Spinger-Verlag, Berlin, 1984.
Rouse, P.E., ‘A theory of the linear viscoelastic properties of dilute solutions of coiling polymers’ J. Chem. Phys. 21, 1953, 1272–1280.
Sanchez-Palencia, E., ‘Boundary layers and edge effects in composites’ in Homogenization Techniques for Composite Media, Proceedings, Udine, Italy, July 1–5, 1985, E. Sanchez-Palencia and A. Zaoui (eds.), Spinger-Verlag, Berlin, 1987, 122–192.
Terano, T., Asai, K. and Sugeno, M., Fuzzy Systems Theory and Its Applications, Academic Press, Boston, 1992.
Tong, P. and Mei, C.C., ‘Mechanics of composites of multiple scales’ Comput. Mech. 9, 1992, 195–210.
Wang, R. and Chen, X., ‘Developments on visco-elastic-plastic constitutive relation of polymeric materials’ Adv. Mech. 25, 1995, 289–299.
Ward, I.M., Mechanical Properties of Solid Polymers, 2nd edn., John Wiley & Sons, Chichester, 1983.
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Chen, X., Tong, P. & Wang, R. Unified Relaxation Spectrum for Polymers of Multiple Scales Based upon a Fuzzy Constraint Method and Non-Equilibrium Statistical Thermodynamics. Mechanics of Time-Dependent Materials 3, 263–278 (1999). https://doi.org/10.1023/A:1009895812870
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DOI: https://doi.org/10.1023/A:1009895812870