Frequency-dependent moduli in a supercooled liquid in the close vicinity of the glass transition by molecular dynamics

Amorphous materials have a rich relaxation spectrum which is usually described in terms of alpha, beta, and possibly more complex relaxation mechanism. In this work, we investigate the local dynamic modulus spectrum in a model glass just above glass transition temperature by performing a mechanical spectroscopy analysis using molecular dynamics. We find that the spectrum, at the local as well as on the global scale, can be well depicted by Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. Furthermore, we find that the size dependence of local relaxation time and modulus can be well explained by the elastic shoving model.