Shear-transformation-zone theory of viscosity, diffusion, and stretched exponential relaxation in amorphous solids

Abstract

The shear-transformation-zone (STZ) theory has been remarkably successful in accounting for broadly peaked, frequency-dependent, viscoelastic responses of amorphous systems near their glass temperatures T_{g}. This success is based on the theory's first-principles prediction of a wide range of internal STZ transition rates. Here, I show that the STZ rate distribution causes the Newtonian viscosity to be strongly temperature dependent; and I propose that it is this temperature dependence, rather than any heterogeneity-induced enhancement of diffusion, that is at least in part responsible for Stokes-Einstein violations near T_{g}. I also show that stretched-exponential relaxation of density fluctuations emerges naturally from the same distribution of STZ transition rates that predicts the viscoelastic behavior. To be consistent with observations of Fickian diffusion near T_{g}, however, an STZ-based diffusion theory somehow must include the cascades of correlated displacement events that are seen in low-temperature numerical simulations.

Shear-transformation-zone theory of yielding in athermal amorphous materials

“…This is in contrast to my argument in Ref. [25] where I considered self diffusion of particles and set equal to the size of the STZ core. Here, I am considering diffusion of energy or perhaps, in the spirit of Refs.…”

Observation of the Anomalously Slow Relaxation of a Nonergodic System of Interacting Liquid Nanoclusters in a Disordered Confinement of a Random Porous Medium

“…The states and properties of disordered media such as glasses, colloids, polymers, and loose materials have been actively studied in recent years [1][2][3][4][5][6][7][8][9][10][11][12]. Numerical investigations are performed [6,7,16,18], and phenomenological models such as shear transformation zone (STZ) [1,4,9,13,19], dynamic heterogeneity (DH) [2,5,21], random first order transition theory (RFOT), topological bond-oriented local configuration [1,6,7,16,18,27,28], etc. (see, e.g., [1-3, 10, 14, 20]) were introduced and discussed.…”

“…(4). In this case, the time dependence of the volume fraction of the liquid remaining in the porous medium upon reduction of the pressure at times 10 pore volume distribution function.…”

“…(6) and (19) with the dependence () T  from [71], as well as  and its temperature dependence determined by the method described in [57], give It follows from Eqs. (4) and (9) that the character of relaxation of the state formed at the reduction of excess pressure to 0 p  is determined by the potential barrier  . Figure 8 shows the dependence of the potential barrier  for the system under consideration at the time recondensation, i.e., capillary evaporation and subsequent capillary condensation at the interface between the porous medium and environment liquid considered in [58,59].…”

Mechanical annealing in the flow of supercooled metallic liquid

“…Vast works, including theoretical modeling, [17][18][19][20] physical experiments, [21][22][23] and computer simulations, 24,25 have been carried out to uncover the elementary deformation events of metallic glasses and the origin of shear banding, [26][27][28] which is the dominant plastic deformation mode of metallic glasses at temperature below T g . Incorporating the picture of structural relaxation processes on the potential energy landscape, 29 it was proposed that the flow of supercooled metallic liquids could be recognized as stress-driven structural a-relaxation and the elementary deformation event could be thought of as stress-driven b relaxation, 3 where structural a-relaxation refers to a large scale irreversible atomic rearrangement process in supercooled metallic liquids, while b relaxation is a local reversible atomic rearrangement process.…”