Theories of the Glass Transition Based on Local Excitations

Abstract

The dramatic slowdown of dynamics in supercooled liquids approaching the glass transition remains one of the central unresolved problems in condensed matter physics. We review approaches that attribute this slowdown to growing thermodynamic or structural length scales and discuss their difficulties in accounting for recent numerical results. These limitations motivate the present review, which critically examines alternative theories in which the glassy slowdown is instead controlled by localized excitations and their elastic interactions. After reviewing key phenomenology with a focus on the fragility of liquids, dynamical heterogeneities, thermodynamics-dynamics correlation, and the effect of kinetic rules and swap algorithms, we compare elastic descriptions based on homogeneous and local heterogeneous elasticity to excitation-based theories incorporating nonlinear responses. Results are compiled to relate global and local elastic moduli, the Debye-Waller factor, and the density of excitations, leading to a quantitative theory testable in experiments. The thermal evolution of the excitation spectrum provides a parameter-free account of the activation energy, while their elastic interactions quantitatively reproduce dynamical heterogeneities via thermal avalanche processes. Synthesized together, these results lead to a framework where the evolution of the excitation spectrum, rather than the growth of a thermodynamic length scale, governs fragility in simple glass-forming liquids -- yet mean-field concepts of dynamical transitions remain central to describing excitations and building a real-space picture of relaxation.

Figures (27)

• Figure 1: Different scenarios for the glass transition. Left: In many popular views, the growth of a dynamical length scale $\xi$ when cooling, associated with an increasing number $N(\xi)$ of particles participating in structural relaxation, is responsible for the growth upon cooling of the activation energy $E_a$. Right: In alternative scenarios central to this review, local barriers tied to elementary rearrangements govern the change in activation energy $\Delta E_a$ under cooling.
• Figure 2: The classical Angell plot showing the super Arrhenius temperature dependence of the viscosity of several glass-forming liquids (reproduced from Ref. ang85). The x-axis gives the inverse temperature normalized to unity at the glass transition temperature $T_{\rm g}$, the y-axis gives the logarithm (base 10) of the viscosity. As is customary, $T_{\rm g}$ is here defined as the temperature at which the equilibrium (metastable) liquid has viscosity $10^{12}$ Pa$\cdot$s. Reprinted with permission.
• Figure 3: a--c: Rearranging regions (in red) at successive times in a molecular dynamics (MD) simulation of a supercooled liquid gui22. Reproduced from: arXiv:2103.01569. d: From tah23. Comparison between MD results (symbols) for the coarsening length $\ell_{\rm c}(t,T)$ in Ref. sca22 and the theoretical prediction based on interacting excitations (curves) of Eq. (\ref{['eq:ellc']}) presented in Sec. \ref{['S8']} below.
• Figure 4: Correlation between the fragility (Eq. (\ref{['eq:frag_def']})) and the specific-heat jump at $T_{\rm g}$ relative to the melting entropy, $\Delta C_p/\Delta S_m$, for 53 non-polymeric glass-forming liquids (redrawn from Ref. wan06). The dashed line marks the empirical relation $m=40\Delta C_p/\Delta S_m$. The open symbols are selenium, toluene, triphenylphosphite (TPP), and decalin (decahydronaphthalene); many mono-alcohols and polymers also deviate from the line (data not shown).
• Figure 5: Kinetic rules greatly affect the glass transition: the glass transition packing fraction of a poly-disperse hard sphere system is indicated in color as a function of both the fraction $f_P$ of particles whose motions are restricted on arbitrary planes and the fraction $f_R$ of particles not allowed to swap. All these different kinetic rules preserve thermal equilibrium and lead to identical static properties. Yet, gigantic difference in the time (and also length, see Section \ref{['S8']}) scales characterizing relaxation appears, which cannot be explained within theories based on thermodynamic properties alone. The normal kinetic rule is just one point in this diagram, $f_P=0,f_R=1$, which these theories do not distinguish from other points. From gav24, with permission.