Universal divergenceless scaling between structural relaxation and caged dynamics in glass-forming systems

Abstract

On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbors, whereas its average escape time, the structural relaxation time tau(alpha), increases from a few picoseconds up to thousands of seconds. A thorough study of the correlation between tau(alpha) and the rattling amplitude, expressed by the Debye-Waller factor, was carried out. Molecular-dynamics simulations of both a model polymer system and a binary mixture were performed by varying the temperature, the density rho, the potential and the polymer length to consider the structural relaxation as well as both the rotational and the translation diffusion. The present simulations, together with MD studies on other glassformers, evidence the scaling between the structural relaxation and the caged dynamics. An analytic model of the master curve is developed in terms of two characteristic length scales a(2) (1/2) and sigma(a(2) ) (1/2), pertaining to the distance to be covered by the kinetic unit to reach a transition state. The model does not imply tau(alpha) divergences. The comparison with the experiments supports the numerical evidence over a range of relaxation times as wide as about eighteen orders of magnitude. A comparison with other scaling and correlation procedures is presented. In particular, the density scaling of the length scales a(2) (1/2), sigma(a(2) ) (1/2) proportional to rho(-1/3) is shown to be not supported by the present simulations. The study suggests that the equilibrium and the moderately supercooled states of the glassformers possess key information on the huge slowing-down of their relaxation close to the glass transition. The latter, according to the present simulations, exhibits features consistent with the Lindemann melting criterion and the free-volume model.

Cage rattling does not correlate with the local geometry in molecular liquids

“…One major finding was that states with equal ST-MSD u 2 have equal relaxation times τ α too. For polymers states with equal ST-MSD show also equal chain reorientation rate [53,54] and diffusivity [54]. Diffusion scaling was also observed in atomic mixtures [55].…”

“…Recently, extensive molecular-dynamics (MD) simulations evidencing the universal correlation between the structural relaxation time τ α and u 2 were reported in polymeric systems [52][53][54], binary atomic mixtures [55], colloidal gels [56] and antiplasticized polymers [41] and compared with the experimental data concerning several glassformers in a wide fragility range (20 ≤ m ≤ 191) [52,55,57,59]. One major finding was that states with equal ST-MSD u 2 have equal relaxation times τ α too.…”

Communication: Correlation of the instantaneous and the intermediate-time elasticity with the structural relaxation in glassforming systems

“…It is seen that the subtraction of the vibrational dynamics around IS removes the initial drop and the plateau seen in F s (q max , t) at intermediate times. 25 Note that F s (q max , t) and F I S s (q max , t) coincide only at times a little bit longer than τ α , as it is reported for binary mixtures. 28 Now we investigate if, during the initial mechanical equilibration, transitions between different ISs take place and how they affect both the density and the stress relaxation.…”

“…This was seen by observing the monomer mean square displacement r 2 (t) which exhibits a well-defined minimum of the logarithmic derivative quantity (t) ≡ ∂log r 2 (t) /∂log t at t = 1.023. 12,25 Since this quantity vanishes in the case of perfect trapping, i.e., r 2 (t) ∼ const, the minimum signals the full exploration of the cage and the onset of early escape events (t is independent of the physical state in the present model).…”

Thermodynamic scaling of vibrational dynamics and relaxation

“…Insight into the correlation is offered by the remark that the height of the barrier to be surmounted for structure rearrangement increases with the curvature near the minimum of the potential well temporarily trapping the particles, as first noted by Tobolsky et al [47] via a simple viscoelastic model and put on a firmer ground by Hall and Wolynes who related the barrier height to 1/ u 2 [49]. The correlation was reported in polymeric systems [72][73][74], binary atomic mixtures [39,73,75,79], colloidal gels [76] and antiplasticized polymers [56,78] and compared with the experimental data concerning several glassformers in a wide range of fragility -the steepness m of the temperature-dependence of the logarithm of the structural relaxation time at GT defined by Angell [89] -(20 ≤ m ≤ 191), including polymers, van der Waals and hydrogen-bonded liquids, metallic glasses, molten salts and the strongest inorganic glassformers [72,75,77,80,81,87]. The correlation between structural relaxation and fast mobility is summarized by the universal master curve [72]:…”