Ultrasonic attenuation of polymer solutions. II. Concentrated solutions

Abstract

In the framework of the Edwards‐Grant model, the ultrasonic attenuation of concentrated polymer solutions is calculated. Entanglements between the chains change the frequency behaviour of the ultrasonic attenuation from ∼ω−1/2zu∼ω−3/4

Frequency dispersion of sound propagation in Rouse polymer melts via generalized dynamic random phase approximation

“…1, the ω-dependence of the absorption coefficient in log-log co-ordinates becomes steeper when the frequency increases, which is in a qualitative agreement both with the experiments reported in Ref. [2], [5] and preceding theories [3], [4].…”

“…Berger and Straube [3] have calculated the sound absorption coefficient by solving the diffusion equation for the distribution function of the structural units (segments) of a single polymer chain interacting with a solvent (dilute solution) and found, in the megahertz range, the Rouse-type behavior α/f 2 ~ f −1/2 . They also concluded [4] that the temporary entanglements present between the chains in concentrated solutions change the dependence of α/f 2 to f −3/4 . However, all the mentioned theoretical studies neglect the inter-chain interactions and, thus, are in principle not capable of studying the frequency dispersion of the sound velocity v directly related to the system compressibility.…”

“…In terms of the final output, we deal here with the sound (ultrasonic) propagation via the monodisperse melt of homopolymer linear chains and calculate the dependence of both the acoustic attenuation coefficient α and sound velocity v on the sound frequency f. Such a calculation is interesting by itself and important to interpret the results of ultrasonic measurements in a due way. Indeed, a substantial frequency dispersion of the sound absorption coefficient α/f 2 in polymer melts was predicted theoretically [1][2][3][4] and found experimentally in the ultrasonic range [5]. Gotlib and Salikhov [1] modeled the behavior of a concentrated solution by a three-dimensional network of polymer subchains immersed in a solvent.…”

“…Berger and Straube [3] have calculated the sound absorption coefficient by solving the diffusion equation for the distribution function of the structural units (segments) of a single polymer chain interacting with a solvent (dilute solution) and found, in the megahertz range, the Rouse-type behavior α/f 2 ~ f −1/2 . They also concluded [4] that the temporary entanglements present between the chains in concentrated solutions change the dependence of α/f 2 to f −3/4 .…”

“…Indeed, a substantial frequency dispersion of the sound absorption coefficient α/f 2 in polymer melts was predicted theoretically [1][2][3][4] and found experimentally in the ultrasonic range [5]. Gotlib and Salikhov [1] modeled the behavior of a concentrated solution by a three-dimensional network of polymer subchains immersed in a solvent.…”