Scaling equations for mode-coupling theories with multiple decay channels
arXiv:2005.13347 · doi:10.1088/1742-5468/ab9e61
Abstract
Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in lateral and longitudinal direction to the walls are very different, or fluids of nonspherical particles with distinct relaxation patterns for translational and rotational degrees of freedom. Here, we perform an asymptotic analysis of the slow structural relaxation close to kinetic arrest as described by mode-coupling theory (MCT) with several relaxation channels. Compared to standard MCT, the presence of multiple relaxation channels significantly changes the structure of the underlying equations of motion and leads to additional, non-trivial terms in the asymptotic solution. We show that the solution can be rescaled, and thus prove that the well-known -scaling equation of MCT remains valid even in the presence of multiple relaxation channels. The asymptotic treatment is validated using a novel schematic model. We demonstrate that the numerical solution of this schematic model can indeed be described by the derived asymptotic scaling laws close to kinetic arrest. Additionally, clear traces of the existence of two distinct decay channels are found in the low-frequency susceptibility spectrum, suggesting that clear footprints of the additional relaxation channels can in principle be detected in simulations or experiments of confined or molecular liquids.
Accepted by J. Stat. Mech.: Theory and Experiments, https://iopscience.iop.org/journal/1742-5468
References in corpus (42)
- Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
- Scaling behavior in the -relaxation regime of a supercooled Lennard-Jones mixture
- Theory of nonlinear rheology and yielding of dense colloidal suspensions
- Mode-Coupling Theory of the Glass Transition: A Primer
- Broadband Dielectric Spectroscopy on Glass-Forming Propylene Carbonate
- Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules
- Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
- Glass Rheology: From mode-coupling theory to a dynamical yield criterion
- A mode coupling theory for Brownian particles in homogeneous steady shear flow
- Supercooled Water and the Kinetic Glass Transition II: Collective Dynamics
- Anomalous dynamics of intruders in a crowded environment of mobile obstacles
- Active and Nonlinear Microrheology in Dense Colloidal Suspensions
- The Debye-Waller factor of liquid silica: Theory and simulation
- Logarithmic Relaxation in Glass-Forming Systems
- Glass Transition in Confined Geometry
- Colloidal glass transition: Beyond mode-coupling theory
- Molecular mode-coupling theory for supercooled liquids: Application to water
- Mode-Coupling Theory for Active Brownian Particles
- Dense colloidal suspensions under time-dependent shear
- Glass Transition for Driven Granular Fluids
- Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles
- Universal and non-universal features of glassy relaxation in propylene carbonate
- Slow Dynamics in Ion-Conducting Sodium Silicate Melts: Simulation and Mode-Coupling Theory
- Multiple reentrant glass transitions in confined hard-sphere glasses
- Mode-coupling theory of the glass transition for confined fluids
- Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom
- Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators
- A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid
- Molecular Dynamics Computer Simulation of the Dynamics of Supercooled Silica
- Mode-coupling theory predictions for the dynamical transitions of the partly pinned fluid systems
- Reorientational relaxation of a linear probe molecule in a simple glassy liquid
- Completely monotone solutions of the mode-coupling theory for mixtures
- The Cole-Cole Law for Critical Dynamics in Glass-Forming Liquids
- Dynamics in a supercooled molecular liquid: Theory and Simulations
- Molecular mode-coupling theory applied to a liquid of diatomic molecules
- The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
- Observation of strongly heterogeneous dynamics at the depinning transition in a colloidal glass
- Mode-coupling theory for multiple decay channels
- Structural relaxation in orthoterphenyl: a schematic mode coupling theory model analysis
- Nonergodicity parameters of confined hard-sphere glasses
- Persistent anti-correlations in Brownian dynamics simulations of dense colloidal suspensions revealed by noise suppression
- Long-time limit of correlation functions
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- Mode-Coupling Theory for Tagged-Particle Motion of Active Brownian Particles
- Dynamical properties of densely packed confined hard-sphere fluids
- Tagged-particle dynamics in confined colloidal liquids
- Computer Simulations and Mode-Coupling Theory of Glass-Forming Confined Hard-Sphere Fluids
- Mode-coupling theory of the glass transition for a liquid in a periodic potential
- Tagged-particle motion in quasi-confined colloidal hard-sphere liquids