Universal L-3 finite-size effects in the viscoelasticity of amorphous systems

We present a theory of viscoelasticity of amorphous media, which takes into account the effects of confinement along one of three spatial dimensions. The framework is based on the nonaffine extension of lattice dynamics to amorphous systems, or nonaffine response theory. The size effects due to the confinement are taken into account via the nonaffine part of the shear storage modulus G'. The nonaffine contribution is written as a sum over modes in k-space. With a rigorous argument based on the analysis of the k-space integral over modes, it is shown that the confinement size L in one spatial dimension, e.g., the z axis, leads to a infrared cutoff for the modes contributing to the nonaffine (softening) correction to the modulus that scales as L-3. Corrections for finite sample size D in the two perpendicular dimensions scale as similar to(L/D)(4), and are negligible for L << D. For liquids it is predicted that G'similar to L-3 is in agreement with a previous more approximate analysis, whereas for amorphous materials G' (similar to)G'(bulk) + beta L-3. For the case of liquids, four different experimental systems are shown to be very well described by the L-3 law. The theory can also explain previous simulation data of confined jammed granular packings.

Automated summary

The theory presents a comprehensive explanation of the viscoelasticity of amorphous media, considering the effects of confinement in one spatial dimension. The confinement-induced size effects are accounted for through the nonaffine contribution to the shear storage modulus, which is written as a sum over modes in k-space. The rigorous argument based on the analysis of the k-space integral shows that confinement size in one spatial dimension leads to an infrared cutoff for the modes contributing to the nonaffine correction to the modulus.