Study on the Rheological Behaviors of Polymer Melts and Concentrated Solutions A New multiple Reptation Mechanism to Predict the Dependence of Linear Viscoelasticity on the Primary Molecular Weight and Its Distribution

Based on a new mutiple reptation mechanism, a set of new relations of linear viscoelastic functions (the aero shear and extensional rate viscosities \eta_\mathrmc and \eta_e x t, the first normal stress coeficient \psi_15^2, and the terminal relaxation time \tau_t ) to the primary molecular weight and its distribution were formulated. It is first to propose a new conception of the average constrained dimentional number of entanglements in the long and short entanglement spacings (\tildev). Then a quantitative characteristics for \tildev was formulated with the dimensional number of each constituent chains and the sequence distribution function of entanglement sites \widetildeN_1 j, a relation of ( \tildev.to the primary molecular weight ( M ) and the molecular weight ( M_,) between entanglements is obtained, and a new method for determination of (\tildev) was proposed. When the primary polymer chains are modeled by Lansing-Kraemer molecular distribution function \barW (M) .the dependence of \eta_2, \psi_1^0, \eta_2 x t^0 and \tau_i on the weight average molecular weight ( M_u ) and its distribution \left(M_w, M_n\right) was calculated from the molecular theory of viscoelasticity and the average constrained dimensional number of entanglements by the statstical method. The relations were verified by a great mount of experimental data, it shows an agreement between the relations with experimental results. And it is also shown that the value of \barv slightly varies with the primary molecular weight and the molecular weight between entanglements.