Comparative analysis of nonlinear elastic moduli of polystyrene, polycarbonate and PMMA

TL;DR

This study compares the frequency-dependent linear and nonlinear elastic moduli of polystyrene, polycarbonate, and PMMA using acousto-elastic measurements, revealing distinct variations and trends across the polymers.

Contribution

It provides the first detailed experimental analysis of the frequency dependence of both linear and nonlinear elastic moduli in these polymers.

Findings

PMMA shows the highest linear and nonlinear elastic moduli.

Nonlinear Murnaghan moduli are significantly frequency-dependent, especially below 1 MHz.

PMMA's elastic moduli are higher than those of PC and PS, which are similar to each other.

Abstract

We present the comparative experimental analysis of frequency dependencies of linear (Lam\'e) and nonlinear (Murnaghan) elastic moduli of polystyrene, PMMA and polycarbonate. The measurement methodology, based on the acousto-elastic effect, provided data on variations of these moduli in block samples of the polymers in the frequency range of 0.45-3 MHz. In all the three polymers the linear Lam\'e moduli demonstrated moderate rise with frequency, most pronounced rise was observed in modulus $\lambda$ of PMMA in about 35%. The frequency dependencies of Murnaghan moduli were considerably nonlinear. At higher frequencies above ~1 MHz no significant variations of the Murnaghan moduli occurred, while at lower frequencies the absolute values of the moduli $l$ and $m$ demonstrated rapid rise, more pronounced for the modulus $l$. At the same time the absolute values of the modulus $n$ decreased and demonstrated a tendency to become positive at lower frequencies. Both linear and nonlinear moduli of PMMA had higher values than those of PC and PS, with the latter two demonstrating close values of both types of moduli. The potential origins of the differences in nonlinear elastic properties of the three polymers are discussed.