Understanding the Stokes–Einstein relation in supercooled liquids using random pinning

Abstract

Breakdown of Stokes-Einstein relation in supercooled liquids is believed to be one of the hallmarks of glass transition. The phenomena is studied in depth over many years to understand the microscopic mechanism without much success. Recently it was found that violation of StokesEinstein relation in supercooled liquids can be tuned very systematically by pinning randomly a set of particles in their equilibrium positions. This observation suggested a possible framework where breakdown of Stokes-Einstein relation in the dynamics of supercooled liquids can be studied with precise control. We have done extensive molecular dynamics simulations to understand this phenomena by analyzing the structure of appropriately defined set of dynamically slow and fast particles clusters. We have shown that the Stokes-Einstein breakdown actually become predominant once the cluster formed by the slow particles percolate the entire system size. Finally we proposed a possible close connection between fractal dimensions of these clusters and the exponents associated with the fractional Stokes-Einstein relation.

Length-Scale Dependence of the Stokes-Einstein and Adam-Gibbs Relations in Model Glass Formers

“…The SEB in the KA model is well documented [12,14,[38][39][40][41][42]. In the KA model, for k = k * (∼ 7.25) (first peak of the static structure factor S(k)), the SE relation breaks down close to the onset temperature of slow dynamics.…”

Time Scales of Fickian Diffusion and the Lifetime of Dynamic Heterogeneity

“…As suggested in [15], the time scales τ F and τ H may be thought of as lower bounds of the lifetime of dynamic heterogeneity. As reported in [41,42], the distribution of diffusion constants is a good measure of dynamic heterogeneity in the system. The distribution of diffusion constants is obtained from the selfpart of the van Hove function using Lucy iteration [43].…”

“…The distribution of diffusion constants is obtained from the selfpart of the van Hove function using Lucy iteration [43]. We have followed the method described in [41,42]. In the top and bottom panels of Figure 9, we show the distribution of diffusion constants for T = 0.450 and T = 1.000, respectively, for different times for the 3dKA model.…”

“…The violation of the Stokes-Einstien relation [26][27][28] between the diffusion coefficient D and the viscosity (or a suitable time scale τ ) in deeply supercooled liquids [41,42] is believed to be closely related to dynamic heterogeneity. It is interesting to examine the extent of violation of the SE relation when one of the time scales studied above is considered to be the relevant time scale τ .…”

Heterogeneous fluid-like movements of chromatin and their implications to transcription

“…This problem was overcome (Ashwin et al 2019) by employing the method of iteration of integral equation introduced by Richardson (Richardson 1972) and Lucy (Lucy 1974) (RL). The RL method has been extensively used for reducing noise in the image "deconvolution" processing and recently applied to the data sampling problem in biophysics (Wang et al 2012) and condensed-matter physics (Bhowmik et al 2016;Bhowmik et al 2018). Here, the underlying idea is to use the profile of particle diffusion as a two-dimensional point spread function; q(r, M) = (1/πM) exp(−r 2 /M).…”