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

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.