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Colloidal hard-sphere glasses represent a useful model system to investigate the physics of amorphous solids both experimentally and theoretically. We recently developed a bottom-up framework to analytically describe the deformation of colloidal glasses, in terms of the free energy of deformation. In the standard theory of solids, the starting point to describe their lattice dynamics is to develop the free energy as a Taylor expansion in the particles displacements (Born-Huang expansion). As already emphasized by Alexander [1], this approach fails with disordered solids, principally because of the nonaffine component of displacements. Nonaffine displacements arise due to structural disorder because nearest-neighbor forces acting on every particle do not cancel by center-inversion symmetry, and therefore trigger additional (nonaffine) particle motions to re-establish mechanical equilibrium [2]. Our new free energy expansion, which includes nonaffinity, is able to correctly predict the vanishing of shear rigidity of amorphous solids as a function of connectivity, as a result of the elastic free energy that gets wasted in nonaffine motions. This can be understood as a transition between a still predominantly affine response regime (where the affine contribution to free energy is larger, in absolute value, than nonaffine) and a fully nonaffine liquid-like regime (where the nonaffine contribution is larger than affine). In sheared colloidal glasses, it can be shown, by combining theory with novel experiments by the Schall group where the free energy is measured directly, that nonlinear deformation starts early on due to the decrease of connectivity induced by shear-distortion of the glassy cage. As a consequence of connectivity decreasing with strain, the response becomes increasingly more nonaffine up to the yielding point where the affine (positive) and the nonaffine (negative) contributions to free energy become equal and the shear modulus vanishes. At that point, the response becomes predominantly viscous and the Newtonian plateau is reached at large strains. This theoretical framework has been applied with success to analytically describe yielding of bulk metallic glasses, where only physically measurable parameters are involved in the theory [3].
[1] S. Alexander, Phys. Rep. 296, 65 (1998). [2] A. Zaccone and E. M. Terentjev, Phys. Rev. Lett. 110, 178002 (2013). [3] A. Zaccone, P. Schall, E. M. Terentjev, Phys. Rev. B 90, 140203(R) (2014). |