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Published November 2019 | Published
Journal Article Open

Two-step relaxation and the breakdown of the Stokes-Einstein relation in glass-forming liquids


It is well known that glass-forming liquids exhibit a number of anomalous dynamical phenomena, most notably a two-step relaxation in the self-intermediate scattering function and the breakdown of the Stokes-Einstein (SE) relation, as they are cooled toward the glass transition temperature. While these phenomena are generally ascribed to dynamic heterogeneity, specifically to the presence of slow- and fast-moving particles, a quantitative elucidation of the two-step relaxation and the violation of the SE relation in terms of these concepts has not been successful. In this work, we propose a classification of particles according to the rank order of their displacements (from an arbitrarily defined origin of time), and we divide the particles into long-distance (LD), medium-distance, and short-distance (SD) traveling particle groups. Using molecular-dynamics simulation data of the Kob-Andersen model, we show quantitatively that the LD group is responsible for the fast relaxation in the two-step relaxation process in the intermediate scattering function, while the SD group gives rise to the slow (α) relaxation. Furthermore, our analysis reveals that τ_α is controlled by the SD group, while the ensemble-averaged diffusion coefficient D is controlled by both the LD and SD groups. The combination of these two features provides a natural explanation for the breakdown in the SE relation at low temperature. In addition, we find that the α-relaxation time, τ_α, of the overall system is related to the relaxation time of the LD particles, τ_(LD), as τ_α = τ₀exp(Ωτ_(LD)/k_BT).

Additional Information

© 2019 American Physical Society. Received 30 August 2019; published 15 November 2019. This work was supported by the Science Challenge Project (Grant No. TZ2018004), the National Natural Science Foundation of China (Grants No. 21674113 and No. 21790340), the Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-SSW-SLH027), the International Partnership Program of CAS (Grant No. 121522KYSB20160015), and Jilin Scientific and Technological Development Program (Grant No. 20180519001JH). Y.L. acknowledges the Youth Innovation Promotion Association of CAS (Grant No. 2016204) for financial support.

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Published - PhysRevE.100.052607.pdf


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