Mode-Coupling Theory of the Glass Transition: A Primer

Abstract

Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the same time undergoes only minute structural changes. Among the numerous theories put forward to rationalize this complex behavior, Mode-Coupling Theory (MCT) stands out as the only framework that provides a fully first-principles-based description of glass phenomenology. This review outlines the key physical ingredients of MCT, its predictions, successes, and failures, as well as recent improvements of the theory. We also discuss the extension and application of MCT to the emerging field of non-equilibrium active soft matter

References in corpus (72)

• Active Particles in Complex and Crowded Environments
• Theoretical perspective on the glass transition and amorphous materials
• Dynamical heterogeneities in a supercooled Lennard-Jones liquid
• A density-independent glass transition in biological tissues
• Theory of Structural Glasses and Supercooled Liquids
• Motility-driven glass and jamming transitions in biological tissues
• Spatial Correlations of Mobility and Immobility in a Glassforming Lennard-Jones Liquid
• The role of local structure in dynamical arrest
• Fragilities of Liquids Predicted from the Random First Order Transition Theory of Glasses
• Higher order glass-transition singularities in colloidal systems with attractive interactions
• Active Jamming: Self-propelled soft particles at high density
• Perspective: The Glass Transition
• Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Mode-Coupling Theory (MCT) Lecture Notes
• Growing length and time scales in glass forming liquids
• Dynamic heterogeneity in amorphous materials
• Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers
• Pushing the glass transition towards random close packing using self-propelled hard spheres
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• Nonequilibrium glassy dynamics of self-propelled hard disks
• Nonperturbative effect of attractive forces in viscous liquids
• A mode coupling theory for Brownian particles in homogeneous steady shear flow
• Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
• Active and Nonlinear Microrheology in Dense Colloidal Suspensions
• Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation
• Solution of the dynamics of liquids in the large-dimensional limit
• Hopping and the Stokes-Einstein relation breakdown in simple glass formers
• The Debye-Waller factor of liquid silica: Theory and simulation
• Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
• Theories of Glass Formation and the Glass Transition
• Increasing the density melts ultrasoft colloidal glasses
• Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
• Glass Transition in Confined Geometry
• How active forces influence nonequilibrium glass transitions
• Colloidal glass transition: Beyond mode-coupling theory
• Cooperativity Beyond Caging: Generalized Mode Coupling Theory
• Mode-Coupling Theory for Active Brownian Particles
• Dynamical field theory for glass-forming liquids, self-consistent resummations and time-reversal symmetry
• Glass transition of hard spheres in high dimensions
• A theory for the dynamics of dense systems of athermal self-propelled particles
• The role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials
• Microscopic dynamics of supercooled liquids from first principles
• Glass Transition for Driven Granular Fluids
• Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles
• A New Theory of Dynamic Arrest in Colloidal Mixtures
• Multiple reentrant glass transitions in confined hard-sphere glasses
• General Non-equilibrium Theory of Colloid Dynamics
• Aging and rejuvenation of active matter under topological constraints
• Aging of a Homogeneously Quenched Colloidal Glass-forming Liquid
• Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids
• Fluids in Extreme Confinement
• Non equilibrium mode coupling theory for supercooled liquids and glasses
• Do current-density nonlinearities cut off the glass transition?
• Quantitative tests of mode-coupling theory for fragile and strong glass-formers
• Structural and conformational dynamics of supercooled polymer melts: Insights from first-principles theory and simulations
• Static triplet correlations in glass-forming liquids: A molecular dynamics study
• Equilibration and aging of dense soft-sphere glass-forming liquids
• Unraveling the success and failure of mode coupling theory from consideration of entropy
• Mode coupling theory for multi-point and multi-time correlation functions
• The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
• The Random First-Order Transition Theory of Glasses: a critical assessment
• Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling Theory
• Mode-coupling theory and beyond: a diagrammatic approach
• Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order
• Single-Particle Dynamics in Dense Granular Fluids under Driving
• Mean-field dynamic criticality and geometric transition in the Gaussian core model
• Glassy Dynamics of Brownian Particles with Velocity-Dependent Friction
• On the Concept of Static Structure Factor
• Dynamics and rheology of active glasses
• Nonequilibrium Glass Transition in Mixtures of Active-Passive Particles
• Random First Order Theory concepts in Biology and Condensed Matter physics

Cited by in corpus (72)

• Classical dynamical density functional theory: from fundamentals to applications
• Active glasses
• Power functional theory for many-body dynamics
• Understanding, predicting, and tuning the fragility of vitrimeric polymers
• Noether's Theorem in Statistical Mechanics
• Projection operators in statistical mechanics: a pedagogical approach
• Experimental evidence of a crossover between cooperative relaxation and liquid growth dynamics
• Soft Metamaterials: Adaptation and Intelligence
• Translational and rotational dynamics of a self-propelled Janus probe in crowded environments
• Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• Perspective: How to overcome dynamical density functional theory
• Cage Length Controls the Non-Monotonic Dynamics of Active Glassy Matter
• Thermodynamic-Dynamic Interrelations in Glass-Forming Polymer Fluids
• Noether-Constrained Correlations in Equilibrium Liquids
• Active Glassy Dynamics is Unaffected by the Microscopic Details of Self-Propulsion
• Many-body correlations are non-negligible in both fragile and strong glassformers
• Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres
• The glass transition in molecules, colloids and grains: universality and specificity
• Combined Description of Pressure-Volume-Temperature and Dielectric Relaxation of Several Polymeric and Low-Molecular-Weight Organic Glass-Formers using 'SL-TS2' Mean-Field Approach
• Active microrheology of a bulk metallic glass
• Mode-coupling theory of lattice dynamics for classical and quantum crystals
• Generalized mode-coupling theory of the glass transition. II. Analytical scaling laws
• Multi-component generalized mode-coupling theory: Predicting dynamics from structure in glassy mixtures
• Waiting-time dependent non-equilibrium phase diagram of simple glass- and gel-forming liquids
• Mode-coupling theory for mixtures of athermal self-propelled particles
• Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism
• From sub-aging to hyper-aging in structural glasses
• Phase separation and dynamical arrest of protein solutions dominated by short-range attractions
• Generalized Mode-Coupling Theory for Mixtures of Brownian Particles
• Connecting real glasses to mean-field models
• Dynamical Susceptibilities Near Ideal Glass Transitions
• Mode-coupling theory of the glass transition for colloidal liquids in slit geometry
• Rheological regimes in agitated granular media under shear
• Glassy dynamics of a binary Voronoi fluid: A mode-coupling analysis
• Dynamical properties of densely packed confined hard-sphere fluids
• Glassy dynamics from generalized mode-coupling theory: existence and uniqueness of solutions for hierarchically coupled integro-differential equations
• Unveiling the anatomy of mode-coupling theory
• A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
• Scaling equations for mode-coupling theories with multiple decay channels
• Glassy dynamics of sticky hard spheres beyond the mode-coupling regime
• Modeling non-linear dielectric susceptibilities of supercooled molecular liquids
• An energy-landscape-based crossover temperature in glass-forming liquids
• Time-resolved thermal lens spectroscopy of glassy dynamics in supercooled liquids: theory and experiments
• Dynamic properties of quasi-confined colloidal hard-sphere liquids near the glass transition
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Computer Simulations and Mode-Coupling Theory of Glass-Forming Confined Hard-Sphere Fluids
• Tagged-particle motion of Percus-Yevick hard spheres from first principles
• Unifying the Concepts of Scattering and Structure Factor in Ordered and Disordered Samples
• Non-equilibrium Onsager-Machlup theory
• Nonequilibrium mixture dynamics: A model for mobilities and its consequences
• Automated characterization of spatial and dynamical heterogeneity in supercooled liquids via implementation of Machine Learning
• A self-consistent current response theory of jamming and vibrational modes in low-temperature amorphous solids
• Not-so-glass-like Caging and Fluctuations of an Active Matter Model
• Glass transition in colloidal monolayers controlled by light-induced caging
• Mobility-induced kinetic effects in multicomponent mixtures
• Mode-coupling theory of the glass transition for a liquid in a periodic potential
• Nonlinear Langevin functionals for a driven probe
• General Two-Parameter Model of Alpha-Relaxation in Glasses
• Pair correlation function based on Voronoi topology
• Modeling the Dielectric Relaxation in Semicrystalline Polymers -- Understanding the Role of the Interphase between the Amorphous and Crystalline Domains
• Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
• Tagged-particle motion in quasi-confined colloidal hard-sphere liquids
• Does mesoscopic elasticity control viscous slowing down in glassforming liquids?
• Time-Varying Energy Landscapes and Temperature paths: Dynamic Transition Rates in locally Ultrametric Complex Systems
• Controlling the Glass Transition through Active Fluctuating Interactions
• Efficient spectra from atomistic simulation: a generalized master equation study of the air-water interface
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment
• Ergodicity in glass relaxation
• Model dielectric functions for fluctuation potential calculations in electron gas: a critical assessment
• Analytical treatment of the structure and thermodynamics of the square-well fluid
• Probing Glass Formation in Perylene Derivatives via Atomic Scale Simulations and Bayesian Regression