Scaling equations for mode-coupling theories with multiple decay channels

TL;DR

This paper extends mode-coupling theory to systems with multiple relaxation channels, showing that the standard beta-scaling law still applies and identifying signatures of multiple decay processes in susceptibility spectra.

Contribution

The authors derive asymptotic equations for MCT with multiple relaxation channels, demonstrating the persistence of beta-scaling and validating results with a schematic model.

Findings

Beta-scaling law remains valid with multiple channels

Distinct decay channels leave detectable signatures in susceptibility spectra

Asymptotic analysis applies to confined and nonspherical particle liquids

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.