Spatial Dimensionality Dependence of Heterogeneity, Breakdown of the Stokes–Einstein Relation, and Fragility of a Model Glass-Forming Liquid

Abstract

We investigate the heterogeneity of dynamics, the breakdown of the Stokes−Einstein relation and fragility in a model glass forming liquid, a binary mixture of soft spheres with a harmonic interaction potential for spatial dimensions from 3 to 8. The dynamical heterogeneity is quantified through the dynamical susceptibility χ 4 and the non-Gaussian parameter α 2 . We find that the fragility, the degree of breakdown of the Stokes−Einstein relation, and the heterogeneity of the dynamics decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on the density and use it to resolve an apparent inconsistency with previous results.

Crossover in dynamics in the Kob-Andersen binary mixture glass-forming liquid

“…The time scales shown fall into two groups: The time scales τ α and τ 4 are essentially the same, as previously observed [32,48,[53][54][55]. The remaining time scales, (D/T ) −1 (which has been scaled to match the magnitude of the others at one reference temperature), t * , t peak n M , and t peak L , also exhibit the same temperature dependence, which is milder than that of τ α [35,55]. We note that recent work on a metallic glass former indicates that t peak n M is larger than t * ∼ t peak L and is equal to the time scale associated with the Johari-Goldstein process [25], although all these time scales exhibit a milder temperature dependence than the alpha relaxation time τ α .…”

“…6 shows an Arrhenius plot of the alpha relaxation time τ α (from q(t) and F s (k, t)), the diffusion time scale (D/T ) −1 , the time at which χ 4 , α 2 , the size of mobile particles n M , string length L show maximum values, which are, respectively, τ 4 , t * , t peak n M , and t peak L . The time scales shown fall into two groups: The time scales τ α and τ 4 are essentially the same, as previously observed [32,48,[53][54][55]. The remaining time scales, (D/T ) −1 (which has been scaled to match the magnitude of the others at one reference temperature), t * , t peak n M , and t peak L , also exhibit the same temperature dependence, which is milder than that of τ α [35,55].…”

“…The decoupling of the diffusion time scale and the alpha relaxation time scale have been investigated extensively ( [42,[55][56][57][58][59][60][61][62][63][64][65][66][67][68] and references therein), in the context of the breakdown of the Stokes-Einstein relation, employing τ α as being proportional to the viscosity [42]. We consider the breakdown of the Stokes-Einstein relation in order to investigate whether it reveals any indication of the crossover in dynamics around T M CT , as reported in [25].…”

The dimensional evolution of structure and dynamics in hard sphere liquids

“…Like any spinodal critical point, however, a true dynamical transition can only exist in the mean-field limit of high-spatial dimension, d → ∞. In finite-d systems, activated processes blur the singularity into a crossover, and decouple D and τ α thus giving rise to a breakdown of the Stokes-Einstein relation [8,43]. If activated processes can be screened somehow, or if dimension is sufficiently high, however, traces of criticality may still be distinguished, including the pseudo-critical scaling of Eq.…”

“…overshoot its values beyond even our enlarged error bars (Figure 6a) in the highest d attained. One potential source of discrepancy is the reliance of Mangeat and Zamponi on the Gaussian cage approximation, which is violated in finite-d hard spheres [8,43] and is known to lead to significant 1/d corrections in a related model [49? , 50].…”