Generalized Mode-Coupling Theory for Mixtures of Brownian Particles

Abstract

Generalized mode-coupling theory (GMCT) has recently emerged as a promising first-principles theory to study the poorly understood dynamics of glass-forming materials. Formulated as a hierarchical extension of standard mode-coupling theory (MCT), it is able to systematically improve its predictions by including the exact dynamics of higher-order correlation functions into its hierarchy. However, in contrast to Newtonian dynamics, a fully generalized version of the theory based on Brownian dynamics is still lacking. To close this gap, we provide a detailed derivation of GMCT for colloidal mixtures obeying a many-body Smoluchowski equation. We demonstrate that a hierarchy of coupled equations can again be established and show that these, consistent with standard MCT, are identical to the ones obtained from Newtonian GMCT when taking the overdamped limit. Consequently, the non-trivial similarity between Brownian and Newtonian MCT is maintained for our newly developed multi-component GMCT. As a proof of principle, we also solve the generalized mode-coupling equations for the binary Kob-Andersen Lennard-Jones mixture undergoing Brownian dynamics, and confirm the improved predictive power of the theory upon using more levels of the GMCT hierarchy of equations.

References in corpus (37)

• Theoretical perspective on the glass transition and amorphous materials
• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• Mode-Coupling Theory (MCT) Lecture Notes
• Mode-Coupling Theory of the Glass Transition: A Primer
• Nature of the Breakdown in the Stokes-Einstein Relationship in a Hard Sphere Fluid
• A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
• Relaxation in a glassy binary mixture: Comparison of the mode-coupling theory to a Brownian dynamics simulation
• 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
• Colloidal glass transition: Beyond mode-coupling theory
• Active glasses
• Cooperativity Beyond Caging: Generalized Mode Coupling Theory
• A critical test of the mode-coupling theory of the glass transition
• Mode-Coupling Theory for Active Brownian Particles
• Active glass: ergodicity breaking dramatically affects response to self-propulsion
• 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
• Understanding, predicting, and tuning the fragility of vitrimeric polymers
• Topological persistence and dynamical heterogeneities near jamming
• Microscopic dynamics of supercooled liquids from first principles
• Anatomy of cage formation in a 2D glass-forming liquid
• Attractive versus truncated repulsive supercooled liquids: The dynamics is encoded in the pair correlation function
• Quantitative tests of mode-coupling theory for fragile and strong glass-formers
• Nonmonotonic behavior in the dense assemblies of active colloids
• Microscopic Theory for the Role of Attractive Forces in the Dynamics of Supercooled Liquids
• Mode-coupling theory for the steady-state dynamics of active Brownian particles
• A Microscopic Model of the Stokes-Einstein Relation in Arbitrary Dimension
• Glassy dynamics of partially pinned fluids: an alternative mode-coupling approach
• Relaxation Patterns in Supercooled Liquids from Generalized Mode-Coupling Theory
• Generalized mode-coupling theory of the glass transition: schematic results at finite and infinite order
• Mode-Coupling Theory for Tagged-Particle Motion of Active Brownian Particles
• Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres
• 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
• Glassy dynamics from generalized mode-coupling theory: existence and uniqueness of solutions for hierarchically coupled integro-differential equations
• Tagged-particle motion of Percus-Yevick hard spheres from first principles
• Scaling behavior of the self diffusion coefficients: dependence on the mass ratio of a binary mixture

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• Dynamical Susceptibilities Near Ideal Glass Transitions
• A deep learning approach to the measurement of long-lived memory kernels from Generalised Langevin Dynamics
• Scaling the glassy dynamics of active particles: Tunable fragility and reentrance