The remarkable strength of glasses is examined using the random first order transition theory of the glass transition. The theory predicts that strength depends on elastic modulus but also on the configurational energy frozen in when the glass is prepared. The stress catalysis of cooperative rearrangements of the type responsible for the supercooled liquid's high viscosity account quantitatively for the measured strength of a range of metallic glasses, silica, and a polymer glass.elasticity | elastic shear modulus | Frenkel strength A fundamental question about solid matter is what ultimately determines its mechanical strength. Glasses, in the popular mind, are easy to break, but in fact, if surface cracks are carefully avoided, glasses turn out to be intrinsically quite strong. Nearly a century ago, Frenkel provided an elegant argument for the maximum stress that a solid could withstand (1). Crystalline metals were found to be hundreds to thousands of times weaker than the Frenkel estimate (2). This observation inspired the extremely fruitful ideas of dislocations and grain boundaries that provide easy ways for polycrystalline metals to rearrange and plastically deform (3-6). Glasses come much closer to the Frenkel limit but still fall short in strength (7). In this paper we explore quantitatively the notion that the mechanical failure of glassy materials ultimately arises from strain catalyzed rearrangements of the same kind as those responsible for the high supercooled liquid viscosity. The idea that there is a relation of yield strength to the glass transition itself is not new and has been examined in various ways (6,(8)(9)(10)(11)(12)). Here we go further by exploiting the current quantitative understanding of cooperatively rearranging regions that has emerged from the random first order transition (RFOT) theory of glasses (13-19) in order to make some specific predictions. RFOT theory describes the microscopic origin of cooperatively rearranging regions and predicts they are compact, containing a few hundred molecular units near the laboratory glass transition temperature T g . These regions become more fractal, resembling strings or percolation clusters (20) at higher temperatures where flow is no longer thermally activated (21) but rather dominantly collisional. The quantitative predictions of RFOT theory concerning the well-established thermodynamic/kinetic correlations in the viscous liquid state, dynamical heterogeneity in supercooled liquids (18), and the aging (22) and rejuvenating (19) properties of the glassy state proper agree quite well with observations (23). It is thus natural to enquire as to what the theory predicts for the material strength of glasses.We begin by reviewing how activated events occur in liquids and glasses in the absence of stress. The easiest way to conceptualize activated events in the RFOT theory is through what is called the landscape library construction by Lubchenko and Wolynes (22). This construction has also been used to define point-to-set correlation lengths (24,...

In the context of the random first order transition theory we use an extended mode coupling theory of the glass transition that includes activated events to account for spatiotemporal structures in rejuvenating glasses. We numerically solve fluctuating dynamical equations for mobility and fictive temperature fields which capture both mobility generation through activated events and facilitation effects. Upon rejuvenating, a source of high mobility at a glass surface initiates a growth front of mobility which propagates into the unstable low mobility region. The speed of the front quantitatively agrees with experiments on the rejuvenation of ultrastable glasses, which "melt" from their surface.

We compare dynamical heterogeneities in equilibrated supercooled liquids and in the nonequilibrium glassy state within the framework of the random first order transition theory. Fluctuating mobility generation and transport in the glass are treated by numerically solving stochastic continuum equations for mobility and fictive temperature fields that arise from an extended mode coupling theory containing activated events. Fluctuating spatiotemporal structures in aging and rejuvenating glasses lead to dynamical heterogeneity in glasses with characteristics distinct from those found in the equilibrium supercooled liquid. The non-Gaussian distribution of activation free energies, the stretching exponent β, and the growth of characteristic lengths are studied along with the four-point dynamical correlation function. Asymmetric thermodynamic responses upon heating and cooling are predicted to be the result of the heterogeneity and the out-of-equilibrium behavior of glasses below Tg. Our numerical results agree with experimental calorimetry. We numerically confirm the prediction of Lubchenko and Wolynes in the glass that the dynamical heterogeneity can lead to noticeably bimodal distributions of local fictive temperatures during some histories of preparation which explains in a unified way recent experimental observations that have been interpreted as coming from there being two distinct equilibration mechanisms in glasses.