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

Abstract

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 = τ 0 exp(τ LD /k B T).

Local-Average Free Volume Correlates with Dynamics in Glass Formers

“…Particles with a high μ i,t (in the top 25%) tend to form stringlike clusters. , This is observed for both the long-time interval t = τ α (Figure a) and short-time interval t = 0.1τ α (Figure S3a). This observation is in good agreement with our recent study based on the long-range particle group concept, where stringlike clusters were found to move cooperatively over a long time scale . To quantitatively describe the stringlike feature, we evaluate the percentage of particles that have both themselves and at least one but at most two of their neighbors belonging in the high-μ i ,τ α group.…”

“…This observation is in good agreement with our recent study based on the long-range particle group concept, where stringlike clusters were found to move cooperatively over a long time scale. 52 To quantitatively describe the stringlike feature, we evaluate the percentage of particles that have both themselves and at least one but at most two of their neighbors belonging in the high-μ i,τ α group. Using φ(μ) to denote this percentage of stringlike particles, which describes clusters that are strictly stringlike in shape, we find φ(μ) = 57.33%.…”

“…(iii) The top 25% high- D i ,τ α particles are determined by particle displacements between two configurations, at t = 0 and t = τ α . However, on the basis of the recent concept of a long-range particle group, all particles evolve over time and the members in the group do not maintain their ranking, because a particle that has moved a larger distance at an earlier time can be overtaken by another particle at a later time. Because large rearrangement motions of the particles are stochastic and discontinuous, i.e., they can take place at any moment between t = 0 and t = τ α , we define a threshold value D min to be the minimum of D i ,τ α among the top HRCPs.…”

Size and Dynamics of a Tracer Ring Polymer Embedded in a Linear Polymer Chain Melt Matrix

“…The Stokes–Einstein relationship is usually written as Dτ = C for supercooled liquids, − where D is the self-diffusion coefficient, τ is the structural relaxation time, and C is a constant which is independent of temperature. For a Rouse chain, D ∼ N –1 and τ ∼ N 2 .…”

Experimental Tests of a Theoretically Predicted Noncausal Correlation between Dynamics and Thermodynamics in Glass-forming Polymer Melts

“…In the macroscopic thermodynamic class, these include various measures of free volume, , excess entropy, different definitions of configurational entropy, − and configurational internal energy and enthalpy. , In the equilibrium structural class, ,,− the length-scale-dependent pair correlation function, g ( r ), and its Fourier space analogue, the static structure factor, S ( k ), or specific scalar metrics such as the intensity of the first cage peak of S ( k ) or local aspect(s) of g ( r ) are often advocated. Surprising correlations between the alpha process and short time/distance dynamical properties have also been proposed, including the high-frequency shear modulus ,− and Debye–Waller factor, and in the intermediate time/length scale class the concentration of dilute mobile excitations (e.g., string length − and facilitating defect concentration). Many of the proposed order parameters are difficult or impossible to uniquely define and/or experimentally measure, especially for real-world chemically complex molecules and polymers.…”