Viscoelastic Properties of Entangled Polymers. I. The Elastically Coupled Entanglement Model.

摘要

The bead-and-spring model of Rouse, Bueche and Zimm is extended to describe the viscoelastic behavior of polymers with chain entanglements. Motion of the macromolecules is retarded by the presence of entanglements with neighboring chains. This effect is in part represented by selected beads along the chain having enhanced friction coefficients. These selected beads may have values of friction coefficients that are uniformly higher than the unentangled beads, or are progressively higher as a function of the position along the chain. Major improvements in the model result when these entangled points are also assumed to be elastically coupled to the surrounding medium. This coupling is modelled by interconnecting the entangled beads with springs having low spring constants. The resulting equations of motion of the model contain a modified Zimm matrix that is nonsymmetrical. The eigenvalues were obtained numerically on the computer to yield the relaxation spectra, permitting calculation of dynamic moduli, relaxation moduli, equilibrium shear compliance and zero-shear viscosity for a series of molecular weights. Agreement with experimental data on monodisperse polystyrene was found to be excellent for all these properties. Of particular interest is the ability of the model to predict the equilibrium shear compliance as a function of molecular weight, which was not achievable by earlier theories. The sensitivity of J suber to the fitting parameters renders it a useful discriminator in selecting the best model for describing chain entanglement effects in polymer viscoelasticity.