Correlation of the Elastic Properties in Steady-State Flow and Vibrational Experiments

Abstract

A comparison between steady‐state and vibrational techniques for measuring the elastic properties of polymer solutions has shown an unexpected anomaly at high frequencies. The steady‐state technique used was flowbirefringence which relates elasticity (recoverable shear, s) to the extinction angle χ: s=2 cot 2χ. The vibrational technique used, both the ultrasonic crystal and the Birnboim instruments, relates elasticity to the loss angle, δ′: cot δ m ′=η2/(η1−η solv). The solutions investigated included a monodisperse polystyrene, S111, at concentrations of 2% and 4% in a chlorinated biphenyl (Aroclor 1248), a polydisperse polystyrene, PF‐139 and polyisobutylenes in oil. The same solutions were used in both kinds of instruments. In the lower range of frequencies (taken as equivalent to low shear rates) the steady‐state and dynamic instruments showed excellent agreement for the monodisperse polystyrene. In this range the curve agreed with the Zimm theory. But at higher frequencies the results from the two techniques diverged rapidly. The steady‐state measurements showed s to increase continually, whereas the dynamic measurements showed cot δ m ′ to pass through a flat maximum and then decrease slowly out to 2×106 sec−1. This lack of agreement was unexpected and is unexplained. It does show that steady‐state elasticity cannot always be predicted from high‐frequency dynamic experiments. The steady‐state viscosity could be satisfactorily predicted from η1 using Pao's theory, but only for the monodisperse polymers.