From dynamic modulus via different relaxation spectra to relaxation and creep functions

Abstract

The main goal of the paper is to compare predictive power of relaxation spectra found by different methods of calculations. The experimental data were obtained for a new family of propylene random copolymers with 1-pentene as a comonomer. The results of measurements include flow curves, viscoelastic properties, creep curves and rubbery elasticity of copolymer melts. Different relaxation spectra were calculated using independent methods based on different ideas. It lead to various distributions of relaxation times and their “weights”. However, all of them correctly describe the frequency dependencies of dynamic modulus. Besides, calculated spectra were used for finding integral characteristics of viscoelastic behaviour of a material (Newtonian viscosity, the normal stress coefficient, steady-state compliance). In this sense all approaches are equivalent, though it appears impossible to estimate instantaneous modulus. The most crucial arguments in estimating the results of different approaches is calculating the other viscoelastic function and predicting behaviour of a material in various deformation modes. It is the relaxation and creep functions. The results of relaxation curve calculations show that all methods used give rather similar results in the central part of the curves, but the relaxation curves begin to diverge when approaching the high-time (low-frequency) boundary of the relaxation curves. The distributions of retardation times calculated through different approaches also appear very different. Meanwhile, predictions of the creep curves based on these different retardation spectra are rather close to each other and coincide with the experimental points in the wide time range. Relatively slight divergences are observed close to the upper boundary of the experimental window. All these results support the conclusion about a rather free choice of the relaxation time spectrum in fitting experimental data and predicting viscoelastic behaviour of a material in different deformation modes.