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 (2)

• Glassy dynamics of kinetically constrained models
• Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory

Cited by in corpus (37)

• Theoretical perspective on the glass transition and amorphous materials
• Growing length and time scales in glass forming liquids
• Spatial correlations in the dynamics of glassforming liquids: Experimental determination of their temperature dependence
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• The building blocks of dynamical heterogeneities in dense granular media
• Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Nonlinear rheology of colloidal dispersions
• Glass Transition in Confined Geometry
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition
• Multiple length and time scales of dynamic heterogeneities in model glass-forming liquids: A systematic analysis of multi-point and multi-time correlations
• Mode-coupling theory of the glass transition for confined fluids
• Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes
• Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime
• Confinement effects on glass forming liquids probed by DMA
• Static triplet correlations in glass-forming liquids: A molecular dynamics study
• Colloidal suspensions in modulated light fields
• Multiple time scales hidden in heterogeneous dynamics of glass-forming liquids
• Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis
• Static replica approach to critical correlations in glassy systems
• Non-affine deformations of inherent structure as signature of cooperativity in supercooled liquids
• Dynamic heterogeneities in attractive colloids
• Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
• Lower bound on the four-point dynamical susceptibility: Direct experimental test on a granular packing
• Direct measurements of the dynamical correlation length indicate its divergence at an athermal glass transition
• Deformation of inherent structures to detect long-range correlations in supercooled liquids
• Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approach
• Dynamics of k-core percolation in a random graph
• A small subset of normal modes mimics the properties of dynamical heterogeneity in a model supercooled liquid
• Time reparametrization symmetry in spin glass models
• Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach
• Theory of simple glasses
• Scale-free patterns at a saddle-node bifurcation in a stochastic system
• Three-point susceptibilities ${\chi }_n(k;t)$ and ${\chi }_n^s(k;t)$: mode-coupling approximation
• Spatiotemporal structures in aging and rejuvenating glasses