Scaling equations for mode-coupling theories with multiple decay channels

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 $\beta$-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 (16)

• 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
• Active and Nonlinear Microrheology in Dense Colloidal Suspensions
• Logarithmic Relaxation in Glass-Forming Systems
• Glass Transition in Confined Geometry
• 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
• Multiple reentrant glass transitions in confined hard-sphere glasses
• Mode-coupling theory of the glass transition for confined fluids
• The Cole-Cole Law for Critical Dynamics in Glass-Forming Liquids
• The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
• Persistent anti-correlations in Brownian dynamics simulations of dense colloidal suspensions revealed by noise suppression
• Long-time limit of correlation functions

Cited by in corpus (1)

• Dynamical properties of densely packed confined hard-sphere fluids