Strain Pattern in Supercooled Liquids

Abstract

Investigations of strain correlations at the glass transition reveal unexpected phenomena. The shear strain fluctuations show an Eshelby-strain pattern ( ∼ cos (4θ)/r 2 ), characteristic for elastic response, even in liquids at long times [1]. We address this using a mode-coupling theory for the strain fluctuations in supercooled liquids and data from both, video microscopy of a two-dimensional colloidal glass former and simulations of Brownian hard disks. We show that long-ranged and longlived strain-signatures follow a scaling law valid close to the glass transition. For large enough viscosities, the Eshelby-strain pattern is visible even on time scales longer than the structural relaxation time τ and after the shear modulus has relaxed to zero.Glasses behave like isotropic elastic solids under external loads. Their strain fields are long-ranged as captured in elasticity theory. Considering appropriate boundary conditions, Eshelby obtained the elastic strain field surrounding an isolated local deformation [2], which is also the basis for modern theories of plasticity in disordered solids [3]: Plastic deformation proceeds via localized irreversible rearrangements coupled by elastic strain fields.While the relevance of strain in glass at low temperatures originates in the breaking of translational symmetry underlying solidification [4], the proper understanding of the evolution of strains at the crossover from metastable glass to supercooled liquid remains an open topic [5]. The concept of plastic events, which are elastically coupled, has emerged as one candidate rooted in the theory of solids which aims to capture the glass transition from the low temperature side. It suggests that 'supercooled liquids are solids that flow ' [6] and focuses on strain fluctuations and their correlations to probe plastic flow.Lemaître and colleagues found evidence for this concept in molecular dynamics simulations of twodimensional Lennard-Jones mixtures: They observed persistent long-ranged strain fluctuations in supercooled liquid states [1]. Because the time over which strains were accumulated exceeds the structural relaxation time τ of the liquid, observable elastic stresses have decayed. The observation of spatial dependences exhibiting a far-field Eshelby-strain pattern thus can not be a simple consequence of elasticity. It suggests that particle rearrangements in a fluid interact over large distances via strains likely in an underlying elastic structure, the 'inherent states' characterizing the potential energy landscape [7].Strain patterns have been observed experimentally, but not yet in quiescent supercooled liquids. An anisotropic decay of strain was found in a 3D colloidal hard sphere glass under steady shear [8], in 2D simulations [9], and in granular matter [10]. Eshelby-patterns are reported in 2D flowing emulsions [11] and in a 3D colloidal hard sphere glass, where they appear under shear and thermally induced in quiescent state [12]. They are also present in 2D soft hexagonal crystals with dipolar interaction [...

Constructing a Theory for Amorphous Solids

“…In simulations both of granular materials [7,8] and deeply supercooled liquids [9][10][11], the spatial shearstress correlator has quadrapolar anisotropy and a powerlaw decay ∝ 1=r d in d dimensions. Similar observations have been made for strain correlations in experiment, both for colloids [12,13] and granular materials [14]. It was argued in Refs.…”

Nonlinear mechanical response of supercooled melts under applied forces

“…MCT identifies momentum conservation as the microscopic transport mechanism responsible for the long-ranged strain fields observable inside a region of size L in a liquid. It explains this intriguing observation made in molecular dynamics simulations [61] and in measurements on a colloidal system [63]. The possible consequences of the spatial variations on the viscosity, which has been seen to depend on wavevector q in simulations [64][65][66], remain to be investigated.…”

“…We have investigated far-field strain correlations in liquids within MCT and in video-microscopy experiments on a model two-dimensional glass-forming suspension [63]. Results are shown in Figure 4.…”

“…4. Strain pattern in supercooled states as measured by video microscopy on layers of colloidal particles and described by MCT; from [63]. Left panel: experimental rescaled strain correlation data for a fluid state (inverse rescaled temperature Γ = 103 far below the glass transition Γ c ≈ 200) at different times (see legend); the average particle separation a satisfies na 2 = 1.…”

Local versus Global Stretched Mechanical Response in a Supercooled Liquid near the Glass Transition

“…Such a surface contribution is expected to contribute as 1/r c to the shear modulus of the zone. In addition, since the shear transformations in supercooled liquid shows a Eshelby inclusion-like pattern [27,28],the energy barrier of shear transformations can be represented by the Eshelby external field energy [29,30]. For the local region, the displacement field associated with a shear transformation has to vanish at the boundary r c .…”