fuzzy constraint method
non-equilibrium statistical thermodynamics
unified relaxation spectrum
Springer Online Journal Archives 1860-2000
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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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