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. 2008 Oct 21;105(42):16077-82.
doi: 10.1073/pnas.0808375105. Epub 2008 Oct 16.

Facilitation, complexity growth, mode coupling, and activated dynamics in supercooled liquids

Sarika Maitra Bhattacharyya  1 , Biman Bagchi, Peter G Wolynes
Affiliations

Facilitation, complexity growth, mode coupling, and activated dynamics in supercooled liquids

Sarika Maitra Bhattacharyya et al. Proc Natl Acad Sci U S A. .

Abstract

In low-temperature-supercooled liquids, below the ideal mode-coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. Here, we present a theory that shows explicitly the interplay between the two processes and shows that activated hopping facilitates continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics described here by the mode coupling theory (MCT)] and the activated hopping (described here by the random first-order transition theory). We apply the theory to a specific system, Salol, to show that the theory correctly predicts the temperature dependence of the nonexponential stretching parameter, beta, and the primary alpha relaxation timescale, tau. The study explains why, even below the mean field ergodic to nonergodic transition, the dynamics is well described by MCT. The nonlinear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory correctly predicts the observed variation of the stretching exponent beta with the fragility parameter, D. These two predictions also allow the complexity growth to be predicted, in good agreement with the results of Capaccioli et al. [Capaccioli S, Ruocco G, Zamponi F (2008) J Phys Chem B 112:10652-10658].

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Temperature dependence of the α relaxation timescale for Salol–hopping-induced diffusive dynamics. The timescale for the longtime part of the total structural relaxation, ø(t), obtained from experiments (8) (black circles) and that calculated from the present coupled theory, τtotal (red diamonds) are plotted against temperature. We fit the τtotal to the MCT phenomenological expression, τtotal ∼ [(T−Tcfit/Tcfit]−γ (blue dashed line), we obtain Tcfit = 258 K. (Inset) We plot (τMCT−τtotal)/τtotal as obtained from the theory (red stars). The black dashed line is a guide to the eye. The function shows a jump at approximately T = 258 K. We find that across this temperature the hopping dynamics changes its role and below Tcfit = 258 K it plays a direct role in the dynamics. The scaling times is 1 ps.
Fig. 2.
Fig. 2.
Temperature dependence of the stretching parameter for Salol. The stretching parameter for the longtime part of the total structural relaxation, ø(t), obtained from experiments (6) (black squares) and (7) (black circle) and that calculated from the present coupled theory, βtotal (red diamonds), are plotted against temperature. In the same plot we also present the stretching parameter predicted by the RFOT theory by using the static barrier height distribution, βhopstatic (blue dashed-dot line) and the MCT, βMCT (green dashed line) (which shows no temperature dependence).
Fig. 3.
Fig. 3.
Temperature dependence of the probability distribution of barrier heights which participate in the dynamics, ℘dynamics(ΔF). In this figure we plot the static barrier height distribution, ℘static(ΔF), which is used in the calculation of the total dynamics (black solid curve). From the total dynamics we again estimate the barrier height distribution that actually participates in the dynamics (colored dashed line). This has been done for different MCT relaxation time scale by changing the temperature of the MCT part of the dynamics (T = 240 K, 230 K, 200 K, and 175 K). As the temperature is lowered, the barrier height distribution becomes broader.
Fig. 4.
Fig. 4.
Fragility dependence of the stretching parameter. The stretching parameter for the total structural relaxation, ø(t), obtained from experiments βexpt (3) (black circles) and that calculated from the present coupled theory, βtotal (red solid line) are plotted against the square root of fragility index D. As D decreases, the fragility of the system increases. In the same plot we also present the stretching parameter predicted by the full static barrier height distribution (blue dashed line). The experimental and the theoretical values are at the glass transition temperature T = Tg.
Fig. 5.
Fig. 5.
Relation between alpha relaxation timescale and complexity of dynamically reconfiguring regions. σCRR calculated from the present theory (see footnote ‡‡) (red squares) is plotted against log10 (τtotal/τ0) for Salol by using the analysis of Capaccioli et al. (31). This τ0 is the relaxation time at high temperature and different from the τ0 used to describe the activated dynamics. We also plot the results presented by Capaccioli et al. (31) that they obtained from experimental data (black circles).
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References

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