Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids

Abstract

We extend Mode-Coupling Theory (MCT) to inhomogeneous situations, relevant for supercooled liquid in pores, close to a surface, or in an external field. We compute the response of the dynamical structure factor to a static inhomogeneous external potential and provide the first direct evidence that the standard formulation of MCT is associated with a diverging length scale. We find in particular that the so called ``cages'' are in fact extended objects. Although close to the transition the dynamic length grows as |T-T_c|^-1/4 in _both_ the beta and alpha regimes, our results suggest that the fractal dimension of correlated clusters is larger in the alpha regime. We also derive inhomogeneous MCT equations valid to second order in gradients.

4 pages

References in corpus (18)

• String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid
• Direct experimental evidence of a growing length scale accompanying the glass transition
• Glassy dynamics of kinetically constrained models
• Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems
• Dynamics of Highly Supercooled Liquids:Heterogeneity, Rheology, and Diffusion
• Mode-Coupling Theory (MCT) Lecture Notes
• Dynamical Heterogeneity close to the Jamming Transition in a Sheared Granular Material
• Time and length scales in supercooled liquids
• Stripe glasses: self generated randomness in a uniformly frustrated system
• On nonlinear susceptibility in supercooled liquids
• Dynamic criticality in glass-forming liquids
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• Democratic particle motion for meta-basin transitions in simple glass-formers
• Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Mode-coupling theory and the fluctuation-dissipation theorem for nonlinear Langevin equations with multiplicative noise
• Do current-density nonlinearities cut off the glass transition?
• Finite-range spin glasses in the Kac limit: free energy and local observables

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