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

Phillips, Anthony E.; Baggioli, Matteo; Sirk, Timothy W.; Trachenko, Kostya; Zaccone, Alessio

doi:10.1103/physrevmaterials.5.035602

Title: Universal $L^{- 3}$ finite-size effects in the viscoelasticity of amorphous systems

Journal Article · Mon Mar 01 00:00:00 EST 2021 · Physical Review Materials

DOI:https://doi.org/10.1103/physrevmaterials.5.035602· OSTI ID:1849659

^[1]; Baggioli, Matteo ^[2];

^[3]; Trachenko, Kostya ^[1];

^[4]

Queen Mary Univ. of London (United Kingdom)
Shanghai Jiao Tong Univ. (China); Shanghai Research Center for Quantum Sciences, Shanghai (China); Univ. Autonoma de Madrid (Spain)
Army Research Lab., Aberdeen Proving Ground, MD (United States)
Univ. of Milan (Italy); Univ. of Cambridge (United Kingdom). Cavendish Lab.

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 ~(L/D)⁴, and are negligible for L«D. For liquids it is predicted that G'~L^-3 is in agreement with a previous more approximate analysis, whereas for amorphous materials G'~G'_bulk+βL^-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.

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Research Organization:: Univ. of Florida, Gainesville, FL (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-05ER46236

OSTI ID:: 1849659

Journal Information:: Physical Review Materials, Vol. 5, Issue 3; ISSN 2475-9953

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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