Nonmonotonic Dynamical Correlations beneath the Surface of Glass-Forming Liquids

Hailong Peng, Huashan Liu, and Thomas Voigtmann

Phys. Rev. Lett. 129, 215501 – Published 16 November 2022

Abstract

Collective motion over increasing length scales is a signature of the vitrification process of liquids. We demonstrate how distinct static and dynamic length scales govern the dynamics of vitrifying films. In contrast to a monotonically growing static correlation length, the dynamical correlation length that measures the extent of surface-dynamics acceleration into the bulk displays a striking nonmonotonic temperature evolution that is robust also against changes in detailed interatomic interaction. This nonmonotonic change defines a crossover temperature $T_{*}$ that is distinct from the critical temperature $T_{c}$ of mode-coupling theory. We connect this nonmonotonic change to a morphological change of cooperative rearrangement regions of fast particles, and to the point where the decoupling of fast-particle motion from the bulk relaxation is most sensitive to fluctuations. We propose a rigorous definition of this new crossover temperature $T_{*}$ within a recent extension of mode-coupling theory, the stochastic $β$ -relaxation theory.

Received 12 July 2021
Revised 20 December 2021
Accepted 27 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.215501

Physics Subject Headings (PhySH)

Dynamical phase transitions Glass transition

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Hailong Peng ^1,*, Huashan Liu¹, and Thomas Voigtmann^2,3,†

¹School of Materials Science and Engineering, Central South University, 932 South Lushan Rd, 410083 Changsha, China
²Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany
³Department of Physics, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf, Germany

^*Corresponding author. hailong.peng@csu.edu.cn
^†Corresponding author. thomas.voigtmann@dlr.de

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Vol. 129, Iss. 21 — 18 November 2022

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Images

Figure 1
(a) Snapshot of the simulation setup (CuZr system, colors indicating atomic species). (b) Static density profiles $ρ (z)$ as a function of distance $z$ from the surface along the normal into the bulk for the CuZr liquid and the Lennard-Jones binary mixture (LJBM) (in units of the average atomic radius $σ$ , each curve shifted vertically in steps of $0.4 / σ^{3}$ for clarity). Solid lines are fits to extract the static correlation length. (c) Decay of the overlap correlation function $q_{c} (z, t)$ (CuZr; $T = 810 K$ ). Dashed lines in the inset exemplify stretched-exponential fits of the structural decay, Eq. (1). (d) Static and dynamic parameters characterizing the overlap correlation function (CuZr; $T = 850 K$ ). The normalized static overlap $q_{c} (z, \infty) / q_{c} (\infty, \infty)$ (crosses) follows the normalized density profile $ρ (z) / ρ (\infty)$ (line). The normalized change in the relaxation time $τ_{ov} (z) / τ_{ov} (0)$ (squares) is shown in comparison to the corresponding quantity obtained from the $z$ -resolved SISF (circles). (e), (f): Position-dependent relative mobility enhancement $τ (\infty) / τ (z) - 1$ (from the layer-resolved SISF) for CuZr and the LJBM.
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Figure 2
Temperature-dependent statical $ξ_{stat} (T)$ and dynamical correlation lengths $ξ_{dyn} (T)$ near a free surface for the CuZr (top panel) and the LJBM liquids (bottom panel). The static correlation length $ξ_{stat}$ is extracted from the exponential decay of $ρ (z)$ . Values from the self- ( $ξ_{dyn}^{s}$ ) and collective- ( $ξ_{dyn}^{c}$ ) intermediate scattering functions are shown in systems of two different sizes (S: small systems; L: large systems). The evolution is nonmonotonic around a peak temperature $T_{*}$ indicated by the dashed vertical lines.
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Figure 3
Characterization of the CRR shape in the bulk liquids. (a) Aspect ratio of fast-particle clusters in the bulk simulations, $ξ_{cl} / R_{s}$ . Vertical dashed lines are $T_{*}$ from Fig. 2. (b), (c), (d) denote the temperature points at which fast-particle clusters are exemplified in the respective panels. Particles in blue correspond to the core of the cluster (having more than two fast nearest neighbors); red particles are those with only one or two fast particles as their nearest neighbors.
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Figure 4
Diffusivity $D$ versus viscosity $η$ for the bulk liquids (symbols), compared with the prediction from stochastic $β$ -relaxation theory (solid line, using the MCT exponent parameter $λ = 0.75$ ). $μ_{0}$ and $η_{0}$ are scaling factors, and are ones for LJBM. Dotted lines are the SBR asymptotes for the SE relation, $D / T \sim η^{- 1}$ , at high temperatures, and a fractional law, $D / T \sim η^{- 0.56}$ , at low temperatures. Red circles mark the MCT- $T_{c}$ , and $T_{*}$ predicted from SBR (maximum slope in the inset); arrows indicate the $T_{*}$ from $ξ_{dyn}$ in Fig. 2.
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