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

Abstract

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 $G^{\prime }$. 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 cut-off 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 $\sim (L/D{)}^4$, and are negligible for $L\ll D$. For liquids it is predicted that $G^{\prime }\sim L^{-3}$ in agreement with a previous more approximate analysis, whereas for amorphous materials $G^{\prime }\sim G_{bulk}^{\prime }+\beta L^{-3}$. For the case of liquids, four different experimental systems are shown to be very well described by the $L^{-3}$ law.

arXiv commentPhysical Review Materials, accepted, in press

References in corpus (24)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Local elasticity map and plasticity in a model Lennard-Jones glass
• Approximate analytical description of the nonaffine response of amorphous solids
• Finite-Size Scaling at the Jamming Transition
• Jamming of Deformable Polygons
• Measuring Spatial Distribution of Local Elastic Modulus in Glasses
• Gapped momentum states
• Emergence and evolution of $k$-gap in spectra of liquid and supercritical states
• Nonlinear viscoelastic dynamics of nano-confined water
• Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time
• Long-lived neighbors determine the rheological response of glasses
• Microscopic origin of nonlinear non-affine deformation and stress overshoot in bulk metallic glasses
• Revealing the three-dimensional structure of liquids using four-point correlation functions
• Explaining the low-frequency shear elasticity of confined liquids
• Local versus global stretched mechanical response in a supercooled liquid near the glass transition
• Collective modes and gapped momentum states in liquid Ga: experiment, theory and simulation
• Rigidity in Condensed Matter and its Origin in Configurational Constraint
• $q$-independent slow-dynamics in atomic and molecular systems
• Identifying non-affine softening modes in glassy polymer networks: A pathway to chemical design
• Nonmonotonic dependence of polymer glass mechanical response on chain bending stiffness
• Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz
• Confinement-induced demixing and crystallization
• Particle rearrangement and softening contributions to the nonlinear mechanical response of glasses

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