Elasticity of arrested short-ranged attractive colloids: homogeneous and heterogeneous glasses.

We evaluate the elasticity of arrested short-ranged attractive colloids by combining an analytically solvable elastic model with a hierarchical arrest scheme. This new approach allows us to discriminate the microscopic (primary particle-level) from the mesoscopic (cluster-level) contribution to the macroscopic shear modulus. The results quantitatively predict experimental data in a wide range of volume fractions and indicate in which cases the relevant contribution is due to mesoscopic structures. On this basis we propose that different arrested states of short-ranged attractive colloids can be meaningfully distinguished as homogeneous or heterogeneous colloidal glasses in terms of the length scale which controls their elastic behavior.