Optimum Determination of Parameters in Differential and Integral Viscoelastic Models and Study on Reliability of the Models for Polymer Melts. 2. Determination of Nonlinear Parameters from Both Shear and Elongational Flow Data.

Abstract

A nonlinear regression program to determine the material constants for differential and integral viscoelastic models was applied to the determination of nonlinear model parameters from both shear and elongational flow data. The availability of this program and reliability of the viscoelastic models were also discussed. The viscoelastic models employed were the Phan Thien-Tanner (PTT), Larson and K-BKZ models with damping functions of the PSM and Wagner types. The determination of the nonlinear parameters for several polymer melts with extension-thinning uni-axial elongational viscosity was successful and all models could predict the steady shear and elongational flow data well. For a low density polyethylene (LDPE) melt with extension-thickening uni-axial elongational viscosity, the K-BKZ model with a PSM damping function succeeded if we used multiple nonlinear parameters and enough number of relaxation modes in the optimization. On the other hand, the program could not determine physically realistic values of the parameters for the other models even if multiple nonlinear parameters were used. The failure of optimization by the program was due to the strong dependence on initial guesses. We confirmed by manual trial and error fitting that the PTT and the K-BKZ with Wagner damping function models could predict both the shear and elongational flow data if we successfully determined the relaxation spectrum. However, the Larson model could not predict both shear and elongational flow data.