Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses

TL;DR

This study shows that in polymer glasses, the local shear modulus heterogeneity remains unaffected by bending rigidity, and vibrational and acoustic properties depend only on the global shear modulus, explaining the scaling of the boson peak.

Contribution

It demonstrates that elastic heterogeneity in polymer glasses is insensitive to bending rigidity, linking vibrational properties solely to the global shear modulus.

Findings

Elastic heterogeneity is unaffected by bending rigidity.

Vibrational properties scale only with the global shear modulus.

Transverse sound wave propagation depends solely on the global shear modulus.

Abstract

Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.