Ido Regev

Quantitative theory of a time-correlation function in a one-component glass-forming liquid with anisotropic potential.

The Shintani-Tanaka model is a glass-forming system whose constituents interact via an anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits the characteristics of generic relaxation functions during glass transitions. In particular it exhibits a stretched exponential form, with the stretching index beta depending strongly on the temperature. We construct a quantitative theory of this correlation function by analyzing all the physical processes that contribute to it, separating a rotational from a translational decay channel. These channels exhibit different relaxation times, each with its own temperature dependence. Interestingly, the separate decay function of each of these processes is a temperature-independent function, and is shown to scale (exhibit data collapse) at different temperatures. Taken together with temperature-dependent weights determined a priori by statistical mechanics this allows one to generate the observed correlation function in quantitative agreement with simulations at different temperatures. This underlines the danger of concluding anything about glassy relaxation functions without detailed physical scrutiny.

Randomness-induced redistribution of vibrational frequencies in amorphous solids

Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is hardly appropriate for the materials at hand, this created some amount of confusion regarding the existence and universality of the so- called “Boson Peak” which results from such comparisons. We propose that one should pay attention to the different roles played by different aspects of disorder, the first being disorder in the interaction strengths, the second positional disorder, and the third coordination disorder. These have different effects on the low-frequency part of the density of states. We examine the density of states of a number of tractable models in one and two dimensions, and reach a clearer picture of the softening and redistribution of frequencies in such materials. We discuss the effects of disorder on the elastic moduli and the relation of the latter to frequency softening, reaching the final conclusion that the Boson peak is not universal at all. The study of the density of states of solid materials started with attempts to understand the temperature dependence of the specific heat at low temperatures, say CV ≡ (∂U/∂T )V where U is the energy and T the temperature of the system. This called for a microscopic theory for solids, and the first one was developed by Einstein, assuming that in d dimensions each atom is represented as a d-dimensional harmonic oscillator [1] (in the original paper the case d = 3 was considered). In this article Planck’s quantization assumption, which was originally applied to radiation, was extended to solid vibrations [2]. In the case of dN linear oscillators each with its own frequency ω i, Einstein’s result can be expressed as

Aging and relaxation in glass-forming systems

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.

Effective temperature in elastoplasticity of amorphous solids

An effective temperature

Coarse-grained theory of a realistic tetrahedral liquid model

{T}_{\text{eff}}

Rheology and shear band suppression in particle and chain mixtures.

which differs from the bath temperature is believed to play an essential role in the theory of elastoplasticity of amorphous solids. Here, we introduce a natural definition of

Elasticity with arbitrarily shaped inhomogeneity.

{T}_{\text{eff}}

Spontaneous exfoliation of a drying gel

appearing naturally in a Boltzmann-like distribution of measurable structural features without recourse to any questionable assumption. The value of

Onset of irreversibility and chaos in amorphous solids under periodic shear.

{T}_{\text{eff}}

Reversibility and criticality in amorphous solids.

is connected, using theory and scaling concepts, to the flow stress and the mean energy that characterize the elastoplastic flow.