Understanding the boson peak in glasses and glassy polymers

The density of states of the vibrational modes (VDOS) plays a central role in determining macroscopic physical quantities of solids, such as specific heat, thermal conductivity and the critical temperature towards a superconducting phase. Also, the VDOS is directly linked to the elastic and viscoelastic moduli of the solid. For glasses, the VDOS at low frequency is not simply behaving quadratically in frequency as predicted long ago by Debye, but presents an excess of modes above some frequency where the quadratic Debye law breaks down. Upon normalizing the VDOS by the Debye law a peak is visible, known as the boson peak (BP). Consensus is emerging to explain the origin of the BP in terms of a (Ioffe-Regel type) crossover between ballistic phonon propagation and diffusive-like propagation dominated by randomness and scattering. The diffusive propagation shows up in a damping coefficient which is quadratic in the wavevector [1]. A theoretical description leads to the possibility of studying the VDOS in semi-analytical form as a function of physical parameters [2].

In glassy polymers, the BP has been shown to anti-corrleate with the bending rigidity of the polymer chain [3,4], in spite of the BP occurring in a band of the VDOS spectrum dominated by Lennard-Jones type interactions [5]. This can be explained as due to redistribution of modes across the spectrum. The BP is shown to scale with the square root of the shear modulus [4], as predicted by theory [2]. The BP also controls the nonaffine contribution to the viscoleastic moduli [6] and thus is the central input to numerical predictions of mechanics [7], recently also at the atomistic level [8], thus leading to material design principles.

[1] Phys. Rev. B 87, 134203 (2013)
[2] Phys. Rev. Lett. 122, 145501 (2019)
[3] Macromolecules 51, 1559-1572 (2018)
[4] arXiv:1907.10899
[5] J. Chem. Phys. 120, 9371 (2004)
[6] Phys. Rev. B 83, 184205 (2011)
[7] Soft Matter 14, 8475 (2018)
[8] ACS Macro Lett. 8, 9, 1160-1165 (2019)