Emergence of long-ranged stress correlations at the liquid to glass transition

Abstract

A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time $\tau$ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length $\xi \propto \tau$ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow to connect to fluidity and elasto-plastic models.

arXiv comment5 pages plus 1 page SI

References in corpus (17)

• Dynamics of Viscoplastic Deformation in Amorphous Solids
• Rheology of Soft Glassy Materials
• A kinetic theory of plastic flow in soft glassy materials
• Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow
• A mode-coupling theory for the pasty rheology of soft glassy materials
• Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids
• On the Microscopic Foundations of Elasticity
• Non-local rheology in dense granular flows -- Revisiting the concept of fluidity
• A simple model for heterogeneous flows of yield stress fluids
• Relaxation in yield stress systems through elastically interacting activated events
• Experimental measurements of stress redistribution in flowing emulsions
• Shear stress relaxation and ensemble transformation of shear stress autocorrelation functions revisited
• Long Range Stress Correlations in the Inherent Structures of Liquids at Rest
• Long-range spatial correlations of particle displacements and the emergence of elasticity
• Rigidity in Condensed Matter and its Origin in Configurational Constraint
• Shear modulus and shear-stress fluctuations in polymer glasses
• Goldstone fluctuations in the amorphous solid state

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• Aging in a mean field elastoplastic model of amorphous solids
• Edwards field theory for glasses and granular matter
• Long-range strain correlations in 3D quiescent glass forming liquids
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• Yielding is an absorbing phase transition with vanishing critical fluctuations
• Brittle yielding in supercooled liquids below the critical temperature of mode coupling theory
• Renormalization of elastic quadrupoles in amorphous solids
• Testing theories of the glass transition with the same liquid, but many kinetic rules
• Correlations of tensor field components in isotropic systems with an application to stress correlations in elastic bodies
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• Decoupling of rotation and translation at the colloidal glass transition
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• A crossover in spatio-temporal correlations of strain fluctuations in glass forming liquids
• Spatial correlation functions for non-ergodic stochastic processes of macroscopic system
• Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity
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• Simple models for strictly non-ergodic stochastic processes of macroscopic systems
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