A theory of localized excitations in supercooled liquids

Abstract

A new connection between the structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by the dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in the DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as Jσ, is obtained as a function of inherent-state elastic moduli and the radial distribution function. The energy barrier from the current theory is compared to the one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.

Inherent-State Melting and the Onset of Glassy Dynamics in Two-Dimensional Supercooled Liquids

“…This Arrhenius form of c eq (T ) is found in kinetically constrained models [39,40], used by DF theory to model hierarchical relaxation between excitations [21]. It is also consistent with the rate of particle-hopping events c σ (T ), which is a proxy for c eq (T ) in molecular simulations for DF theory, since c σ (T ) is empirically observed to be of Arrhenius form [17,19].…”

“…The IS trajectory coarse-grains the vibrational motion, and hopping in particle motions are reflected as jumps in the IS positions at t = τ jump [26]. Within the perspective of DF theory [17,21], recent work [19] indicates that jumps in the inherent states correspond to excitation events, which induce localized pure-shear deformation [19,27] (inset of Fig. 1(c)).…”

“…We determine C and d c following the mapping between bound geometric dipoles and localized pure-shear excitations (SM, Sec. 3.3), which were modeled previously via a force-dipole formalism [19]. This mapping ensures equivalency between the average energy barrier and the spatial stress distributions corresponding to excitations, and yields (SM, Sec.…”

“…where R exc = a dpl / √ 2, and the eigenstrain, c , are determined from the knowledge of local structure; see Eqs. ( 34)- (35) in [19].…”

“…The supercooled liquid, i.e., liquid below T o , is further characterized by dynamical heterogeneity [16], where particles initially move in sparse 'mobile' regions that spread over time [17,18]. These initial mobile regions are spatially localized and can be classified as excitations [17,19] that drive particle hopping dynamics, while the rest of the system vibrates around its initial state (inset of Fig. 1(b)).…”