Alladi Ramakrishnan Hall

In pursuit of a universal model for molecular diffusion in glass-formers

Harish Srinivasan

BARC, Mumbai

The issue of diffusion in supercooled liquids and glasses is a key element in understanding glass transitions. These systems don't follow typical Brownian motion principles, such as linear timedependent mean-squared displacement (MSD) and Gaussian displacement distribution. The extent of these deviations depends on the length and time scales considered, leading to shifts between different diffusion mechanisms. Specifically, molecular motion in glassy systems demonstrates subdiffusion, resulting in a non-linear variation of MSD with time. Additionally, molecular/polymeric glass formers exhibit a universal crossover from non-Gaussian to Gaussian subdiffusion across small to large length scales [1]. Despite extensive research, a fundamental model capturing this behaviour, including the universal signature of exponential tails in the radial part of the van Hove self-correlation function [2-3], remains elusive. To address this gap, we introduce a model called non-Gaussian fractional Brownian motion (nGfBm) [4], extending the concept of fractional Brownian motion (fBm) to incorporate non-Gaussian features via a jump-kernel that accounts for sudden jumps during subdiffusion. By utilizing the Fokker-Planck equation for this model, we elucidate the subdiffusion crossover in molecular and polymeric glass formers, corroborating our findings with incoherent quasielastic neutron scattering (IQENS) data. Furthermore, our model proves useful in explaining the phenomenon of Fickian yet Non-Gaussian diffusion observed in colloidal glass formers [3, 5]. This work represents one of the initial efforts to develop a model that effectively captures stochastic processes featuring a blend of pronounced historical dependencies and sudden jumps.

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[2] F. Rusciano, R. Pastore, F. Greco, Phys. Rev. Lett. 128, 2022, 168001
[3] Eli Barkai, Stanislav Burov, Phys. Rev. Lett. 124, 2020, 060603
[4] H. Srinivasan, V. K. Sharma, V. G. Sakai, S. Mitra, Phys. Rev. Lett. 132, 2024, 058202.
[5] Bo Wang, James Kuo, Sung Chul Bae, Steve Granick, Nat. Mat. 11, 2012, 481