Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

What Does Instantaneous Normal Mode Spectrum Tell Us About Dynamical Heterogeneity in Glass-Forming Fluids?



Jack F. Douglas, Wengang Zhang, Francis W. Starr


We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum (UL modes) and find that the particles that make the dominant contribution to the participation ratio form clusters, and that these clusters grow on cooling. This finding is similar to the observation of dynamic heterogeneity in glass-forming fluids, i.e. that highly mobile (or immobile) particles tend to form clusters which grow upon cooling; however, a comparison of the UL mode clusters to mobile and immobile particle clusters shows that they are distinct entities. We also show that the size of clusters can be used as an alternate method to distinguish localized and delocalized modes, which offers a significant practical advantage over the finite-size scaling approach. By examining the trajectory of the dominant particles in the UL mode, we find that they have slightly enhanced mobility as compared to the average, and determine a characteristic time for the persistence of the excess mobility. We find that the excess mobility persists for a time scale that is proportional to the structural relaxation time τα of the fluid, in accord with a prediction by Zwanzig. Evidently, excitations defined in terms of UL modes, serve to facilitate relaxation, but do not actually participate in the large scale displacement processes leading to diffusion and structural relaxation of fluids. These collective excitations thus serve as a possible concrete realization of the “facilitation” clusters postulated in previous modeling of glass-forming liquids.
The Journal of Chemical Physics


Instantaneous normal modes, collective excitations, stable and unstable modes, localized and delocalized modes


Douglas, J. , Zhang, W. and Starr, F. (2019), What Does Instantaneous Normal Mode Spectrum Tell Us About Dynamical Heterogeneity in Glass-Forming Fluids?, The Journal of Chemical Physics (Accessed April 14, 2024)
Created November 14, 2019, Updated April 27, 2020