Shear moduli of two dimensional binary glasses

The shear moduli of two-component glasses in two dimensions are studied within mode coupling theory. Varying the concentration, strong mixing effects are observed along the glass transition lines for two interaction potentials. Nonoverlapping disks with size ratios between 0.3 and 0.9, and point particles interacting with (magnetic) dipoles of strength ratio between 0.1 and 0.6 are considered. Equilibrium structure factors (partially obtained from Monte Carlo simulations) and glass form factors, and perturbative calculations show that a softening of the elastic shear constant of glass upon adding another component arises from a dilution effect of the majority component. For very disparate mixtures, an anomalous elastic strenghtening results from what we interpret as clustering of the smaller particles in the voids between the larger ones. This might point to a glass–glass transition. We include simulation data on hard disk mixtures which show that the theory underestimates the moduli by around 50%, but otherwise captures the qualitative trends (within the rather large simulational error bars).