Multi-component generalized mode-coupling theory: predicting dynamics from structure in glassy mixtures

Abstract

The emergence of glassy dynamics and the glass transition in dense disordered systems is still not fully understood theoretically. Mode-coupling theory (MCT) has shown to be effective in describing some of the non-trivial features of glass formation, but it cannot explain the full glassy phenomenology due to the strong approximations on which it is based. Generalized mode-coupling theory (GMCT) is a hierarchical extension of the theory, which is able to outclass MCT by carefully describing the dynamics of higher-order correlations in its generalized framework. Unfortunately, the theory has so far only been developed for single-component systems and as a result works poorly for highly polydisperse materials. In this paper, we solve this problem by developing GMCT for multi-component systems. We use it to predict the glassy dynamics of the binary Kob–Andersen Lennard-Jones mixture, as well as its purely repulsive Weeks–Chandler–Andersen analogue. Our results show that each additional level of the GMCT hierarchy gradually improves the predictive power of GMCT beyond its previous limit. This implies that our theory is able to harvest more information from the static correlations, thus being able to better understand the role of attraction in supercooled liquids from a first-principles perspective. Graphic abstract

Generalized Mode-Coupling Theory for Mixtures of Brownian Particles

“…To summarize, we have demonstrated that a multi-component GMCT formalism can be constructed for Brownian systems governed by a many-body Smoluchowski equation. A comparison of our presented results with recent work on multi-component Newtonian GMCT [24] shows that in the overdamped limit both hierarchies of equations are completely identical. This demonstrates that the non-trivial similarity between Brownian and Newtonian systems witnessed for standard MCT is maintained for GMCT.…”

“…Despite remarkable successes of MCT [1,16,18,45], several discrepancies between the theory and simulations or experiments still persist [31,[46][47][48][49], most notably an overestimation of the glass transition. Inspired by previous studies [19][20][21][22][23][24][25][26][27], we therefore seek to improve and generalize the theory by developing a separate equation for the 4point dynamic density correlations (and later on continuing the process for even higher order correlations). Since we believe the factorization to be the most severe approximation, we will retain the 4-point density correlations and only replace the irreducible evolution operator by a full one.…”

“…Considering that an appreciable amount of studied glassy materials, including polydisperse colloidal suspensions, is comprised of particles experiencing overdamped dynamics, it becomes apparent that a complete GMCT framework for multi-component systems governed by Brownian dynamics is desired. For standard MCT it is known that deriving the theory from either Newtonian or Brownian principles yields the same results [24,29]. This subtle and non-trivial equivalency might be attributed to the fact that in MCT all 'fast' variables are projected out and the differences between overdamped and underdamped dynamics seem to be covered within these 'fast' variables.…”

“…Unfortunately, MCT often fails to reach full quantitative accuracy; the primary reason for this resides in the theory's ad hoc Gaussian factorization and disregard of higher-order correlation functions. In recent years so-called generalized mode-coupling theory (GMCT) has therefore been introduced as a means to limit the effect of this uncontrolled approximation, with results that improve upon predictions of standard MCT in a systematic, seemingly convergent manner [19][20][21][22][23][24][25][26][27][28]. The basic notion of this theory is to develop separate equations of motion for higher-order correlation functions, instead of immediately applying a factorization approximation at the lowest possible order.…”

“…As a proof of principle, we also employ our theory to study some features, primarily the critical temperature, of the Kob-Andersen binary Lennard-Jones mixture [30]. This model system has been extensively studied in the context of glassy physics and earlier comparisons with MCT have shown that the theory strongly overestimates the critical temperature [24,[31][32][33]. We confirm the improved predictive power of GMCT by demonstrating that, upon including more levels of the hierarchy of equations, the critical temperature lowers in a seemingly convergent manner towards the simulation results.…”