Vibrational dynamics and boson peak in a supercooled polydisperse liquid

Abstract

Vibrational density of states (VDOS) in a supercooled polydisperse liquid is computed by diagonalizing the Hessian matrix evaluated at the potential energy minima for systems with different values of polydispersity. An increase in polydispersity leads to an increase in the relative population of localized high-frequency modes. At low frequencies, the density of states shows an excess compared to the Debye squared-frequency law, which has been identified with the boson peak. The height of the boson peak increases with polydispersity and shows a rather narrow sensitivity to changes in temperature. While the modes comprising the boson peak appear to be largely delocalized, there is a sharp drop in the participation ratio of the modes that exist just below the boson peak indicative of the quasilocalized nature of the low-frequency vibrations. Study of the difference spectrum at two different polydispersity reveals that the increase in the height of boson peak is due to a population shift from modes with frequencies above the maximum in the VDOS to that below the maximum, indicating an increase in the fraction of the unstable modes in the system. The latter is further supported by the facilitation of the observed dynamics by polydispersity. Since the strength of the liquid increases with polydispersity, the present result provides an evidence that the intensity of boson peak correlates positively with the strength of the liquid, as observed earlier in many experimental systems.

Theory of sparse random matrices and vibrational spectra of amorphous solids

“…The numerical values of the participation ratio for vibrational modes P (ω) in various glasses according to the data obtained by molecular dynamics methods usually are in the range 0.2 P (ω) 0.6 [3][4][5][6][7][8][9] . This is in a good agreement with the results of random matrix theory.…”

“…The same behavior of g(ω) was found in the soft-sphere glass 4 , and in amorphous Se 5 . In other glasses the density of states has a broad maximum around ω D and then decays to zero [6][7][8][9] .…”

“…They were called diffusons, having in mind that they spread in space by means of diffusion (from one atom to another) 11 . Many computer simulations of real and model glasses show that the most part of vibrational modes are indeed delocalized [3][4][5][6][7][8][9] .…”

Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies

“…This is very similar to the P R (ω) ∼ ω curve of a supercooled polydispersed liquid. [27] While P R (ω) increases with increasing s when ω is smaller than ω + , it also suggests that the size disorder can decrease the degree of localization in low frequency modes (ω < ω + ). (iii) The P R (ω) in the whole region of ω never exceeds 0.4, which indicates that the system is still very heterogeneous on the length scale of the simulation box.…”