Dynamic mechanical response of polymer networks
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چکیده
The dynamic-mechanical response of flexible polymer networks is studied in the framework of tube model, in the limit of small affine deformations, using the approach based on Rayleighian dissipation function. The dynamic complex modulus G∗(ω) is calculated from the analysis of a network strand relaxation to the new equilibrium conformation around the distorted primitive path. Chain equilibration is achieved via a sliding motion of polymer segments along the tube, eliminating the inhomogeneity of the polymer density caused by the deformation. The characteristic relaxation time of this motion τe separates the low-frequency limit of the complex modulus from the high-frequency one, where the main role is played by chain entanglements, analogous to the rubber plateau in melts. The dependence of storage and loss moduli, G′(ω) and G′′(ω), on crosslink and entanglement densities gives an interpolation between polymer melts and crosslinked networks. We discuss the experimental implications of the rather short relaxation time and the slow square-root variation of the moduli and the loss factor tan δ(ω) at higher frequencies. PACS numbers: 83.80.Dr Elastomeric polymers, 62.40.+i Anelasticity, internal friction, stress relaxation, 83.50.Fc Linear viscoelasticity ∗Permanent address: Department of Physics, Faculty of Science and Technology, Keio University, Yokohama 223, Japan
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تاریخ انتشار 2008