Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well studied examples of glass formers in two dimensions. In this context we demonstrate here: (i) a direct evidence for a diverging length scale at the glass transition (ii) an identification of the glass transition with the disappearance of fluid-like regions and (iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively.

The statistical mechanics of simple glass forming systems in two dimensions is worked out. The glass disorder is encoded via a Voronoi tesselation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, T(g) and T(c) , the first associated with jamming and the second associated with crystallization at very low temperatures.

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with anisotropic potential. This system is interesting per-se and as a model of liquids like glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them). The theory provides a full explanation of the glass transition phenomenology, including the identification of a diverging length scale and a relation between the structural changes and the diverging relaxation times.The study of associated liquids like glycerol as glass formers has a long and rich history [1], but until now the role of the anisotropic hydrogen bonds, while clearly important in frustrating crystallization, has not been made explicit. Recently a model of one component liquids with anisotropic interaction potential was introduced [2], together with numerical simulations in two-dimensions that demonstrated clearly the importance of the anisotropic interaction in frustrating crystallization and allowing the formation of a glassy state of matter. This model is important in stressing the fact that even simple onecomponent liquids may not crystallize if the local symmetry of the interaction potential does not perfectly match the symmetry of the equilibrium crystal. It is worthwhile therefore to analyze further this example of glass formation and put it in the general context of the glass transition. In this Letter we present a theory of this model, constructing its statistical mechanics and providing an understanding of the phenomenology of its glass transition, including an identification of a diverging length and explaining the diverging time scales. Our analysis allows putting this interesting example of glass formation on the same footing as other classical glass formers such as binary mixtures with central potentials [3,4], stressing the generality of the approach [5,6] and of the glass transition phenomenon at the same time.Particles of mass m in this model interact viawhere r ij is the distance between the two particles i and j. The first term on the RHS of (1) is the standard isotropic Lennard-Jones potentialwhereas the anisotropic part of the potential is given byh(x) = (1 − x 2 ) 3 for |x| < 1 ; h(x) = 0 for |x| ≥ 1 .Here θ i (θ j ) is the included angle between the relative vector r ij ≡ r i − r j and a unit vector u i (u j ) (referred to below as 'spin') which represents the orientation of the axis of particle i (j). The function h((θ − θ 0 )/θ c ) (with θ 0 = 126 o and θ c = 53.1 o ) has a maximum at θ = θ 0 , and thus θ 0 is a favored value of θ i . Thus the anisotropic term in the potential favors structures of five-fold symmetry. The parameter ∆ controls the tendency of fivefold symmetry, and therefore of the frustration against crystallization. The units of mass, length, time and temperature are m, σ, τ = σ m/ǫ and ǫ/k B , respectively, with k B being Boltzmann's constant.Accordin...

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