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The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

Accepted version
Peer-reviewed

Type

Article

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Authors

Milkus, R 
Zaccone, A 

Abstract

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-dependent elastic modulus, etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition in this model), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents 0.56<β<0.65, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.

Description

Keywords

glasses, Boson peak, dielectric relaxation, stretched-exponential, Kohlrausch, jamming

Journal Title

Physics Letters A

Conference Name

Journal ISSN

0375-9601
1873-2429

Volume Title

381

Publisher

Elsevier