Many-Body Correlations Are Non-negligible in Both Fragile and Strong Glassformers.

It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a nontrivial competition between static triplet correlations that work to stabilize the glass state and dynamic higher-order correlations that destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are, in fact, non-negligible in both fragile and strong glassformers.

Glassy dynamics of sticky hard spheres beyond the mode-coupling regime.

Sticky hard spheres, i.e., hard particles decorated with a short-ranged attractive interaction potential, constitute a relatively simple model with highly non-trivial glassy dynamics. The mode-coupling theory of the glass transition (MCT) offers a qualitative account of the complex reentrant dynamics of sticky hard spheres, but the predicted glass transition point is notoriously underestimated. Here we apply an improved first-principles-based theory, referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres. This theoretical framework seeks to go beyond MCT by hierarchically expanding the dynamics in higher-order density correlation functions. We predict the phase diagrams from the first few levels of the GMCT hierarchy and the dynamics-related critical exponents, all of which are much closer to the empirical observations than MCT. Notably, the prominent reentrant glassy dynamics, the glass-glass transition, and the higher-order bifurcation singularity classes (A3 and A4) of sticky hard spheres are found to be preserved within GMCT at arbitrary order. Moreover, we demonstrate that when the hierarchical order of GMCT increases, the effect of the short-ranged attractive interactions becomes more evident in the dynamics. This implies that GMCT is more sensitive to subtle microstructural differences than MCT, and that the framework provides a promising first-principles approach to systematically go beyond the MCT regime.

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

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.

Tagged-particle motion of Percus-Yevick hard spheres from first principles.

We develop a first-principles-based generalized mode-coupling theory (GMCT) for the tagged-particle motion of glassy systems. This theory establishes a hierarchy of coupled integro-differential equations for self-multi-point density correlation functions, which can formally be extended up to infinite order. We use our GMCT framework to calculate the self-nonergodicity parameters and the self-intermediate scattering function for the Percus-Yevick hard-sphere system based on the first few levels of the GMCT hierarchy. We also test the scaling laws in the α- and ß-relaxation regimes near the glass-transition singularity. Furthermore, we study the mean-square displacement and the Stokes-Einstein relation in the supercooled regime. We find that qualitatively our GMCT results share many similarities with the well-established predictions from standard mode-coupling theory, but the quantitative results change, and typically improve, by increasing the GMCT closure level. However, we also demonstrate on general theoretical grounds that the current GMCT framework is unable to account for violation of the Stokes-Einstein relation, underlining the need for further improvements in the first-principles description of glassy dynamics.

Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres.

Mode-coupling theory (MCT) constitutes one of the few first-principles-based approaches to describe the physics of the glass transition, but the theory's inherent approximations compromise its accuracy in the activated glassy regime. Here, we show that microscopic generalized mode-coupling theory (GMCT), a recently proposed hierarchical framework to systematically improve upon MCT, provides a promising pathway toward a more accurate first-principles description of glassy dynamics. We present a comprehensive numerical analysis for Percus-Yevick hard spheres by performing explicitly wavenumber- and time-dependent GMCT calculations up to sixth order. Specifically, we calculate the location of the critical point, the associated non-ergodicity parameters, and the time-dependent dynamics of the density correlators at both absolute and reduced packing fractions, and we test several universal scaling relations in the α- and ß-relaxation regimes. It is found that higher-order GMCT can successfully remedy some of MCT's pathologies, including an underestimation of the critical glass transition density and an overestimation of the hard-sphere fragility. Furthermore, we numerically demonstrate that the celebrated scaling laws of MCT are preserved in GMCT and that the predicted critical exponents manifestly improve as more levels are incorporated in the GMCT hierarchy. Although formally the GMCT equations should be solved up to infinite order to reach full convergence, our finite-order GMCT calculations unambiguously reveal a uniform convergence pattern for the dynamics. We thus argue that GMCT can provide a feasible and controlled means to bypass MCT's main uncontrolled approximation, offering hope for the future development of a quantitative first-principles theory of the glass transition.

Generalized mode-coupling theory of the glass transition. II. Analytical scaling laws.

Generalized mode-coupling theory (GMCT) constitutes a systematically correctable, first-principles theory to study the dynamics of supercooled liquids and the glass transition. It is a hierarchical framework that, through the incorporation of increasingly many particle density correlations, can remedy some of the inherent limitations of the ideal mode-coupling theory (MCT). However, despite MCT's limitations, the ideal theory also enjoys several remarkable successes, notably including the analytical scaling laws for the α- and ß-relaxation dynamics. Here, we mathematically derive similar scaling laws for arbitrary-order multi-point density correlation functions obtained from GMCT under arbitrary mean-field closure levels. More specifically, we analytically derive the asymptotic and preasymptotic solutions for the long-time limits of multi-point density correlators, the critical dynamics with two power-law decays, the factorization scaling laws in the ß-relaxation regime, and the time-density superposition principle in the α-relaxation regime. The two characteristic power-law-divergent relaxation times for the two-step decay and the non-trivial relation between their exponents are also obtained. The validity ranges of the leading-order scaling laws are also provided by considering the leading preasymptotic corrections. Furthermore, we test these solutions for the Percus-Yevick hard-sphere system. We demonstrate that GMCT preserves all the celebrated scaling laws of MCT while quantitatively improving the exponents, rendering the theory a promising candidate for an ultimately quantitative first-principles theory of glassy dynamics.

Influence of physical interactions on spatiotemporal patterns.

Spatiotemporal patterns are often modeled using reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusive motion. Such descriptions neglect physical interactions between constituents, which might affect resulting patterns. To overcome this, we study how physical interactions affect cyclic dominant reactions, like the seminal rock-paper-scissors game, which exhibits spiral waves for ideal diffusion. Generalizing diffusion to incorporate physical interactions, we find that weak interactions change the length- and time scales of spiral waves, consistent with a mapping to the complex Ginzburg-Landau equation. In contrast, strong repulsive interactions typically generate oscillating lattices, and strong attraction leads to an interplay of phase separation and chemical oscillations, like droplets co-locating with cores of spiral waves. Our work suggests that physical interactions are relevant for forming spatiotemporal patterns in nature, and it might shed light on how biodiversity is maintained in ecological settings.

Physical interactions in non-ideal fluids promote Turing patterns.

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction-diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems.

Emergent structural correlations in dense liquids.

The complete quantitative description of the structure of dense and supercooled liquids remains a notoriously difficult problem in statistical physics. Most studies to date focus solely on two-body structural correlations, and only a handful of papers have sought to consider additional three-body correlations. Here, we go beyond the state of the art by extracting many-body static structure factors from molecular dynamics simulations and by deriving accurate approximations up to the six-body structure factor via density functional theory. We find that supercooling manifestly increases four-body correlations, akin to the two- and three-body case. However, at small wave numbers, we observe that the four-point structure of a liquid drastically changes upon supercooling, both qualitatively and quantitatively, which is not the case in two-point structural correlations. This indicates that theories of the structure or dynamics of dense liquids should incorporate many-body correlations beyond the two-particle level to fully capture their intricate behavior.

Dynamical susceptibilities near ideal glass transitions.

Building on the recently derived inhomogeneous mode-coupling theory, we extend the generalized mode-coupling theory of supercooled liquids to inhomogeneous environments. This provides a first-principles-based, systematic, and rigorous way of deriving high-point dynamical susceptibilities from variations of the many-body dynamic structure factors with respect to their conjugate field. This framework allows for a fully microscopic possibility to probe for collective relaxation mechanisms in supercooled liquids near the mode-coupling glass transition. The behavior of these dynamical susceptibilities is then studied in the context of simplified self-consistent relaxation models.

Generalized mode-coupling theory for mixtures of Brownian particles.

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 nontrivial similarity between Brownian and Newtonian MCT is maintained for our multicomponent 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.

Hydroxyl radical-based and sulfate radical-based photocatalytic advanced oxidation processes for treatment of refractory organic matter in semi-aerobic aged refuse biofilter effluent arising from treating landfill leachate.

In this study, three photolytic advanced oxidation processes (AOPs) were applied to the treatment of refractory organic matter in semi-aerobic aged refuse biofilter (SAARB) effluent, and the treatment efficiencies of the three AOPs were systematically compared. The AOPs combined ultraviolet (UV) radiation with either hydrogen peroxide (UV-H2O2), peroxymonosulfate (UV-PMS) or both oxidants (UV-PMS/H2O2). The effects of key parameters on degradation characteristics of refractory organics, and the contribution of reactive oxygen species were systematically studied. Results indicated that UV radiation can greatly enhance treatment efficiencies of both PMS and H2O2. Furthermore, decreasing n(H2O2)/n(PMS) ratio and decreasing the reaction pH can increase treatment efficiency for refractory organics. Compared on the basis of chemical oxygen demand (COD), treatment efficiency followed the order UV-PMS (COD removal 37.39%) > UV-PMS/H2O2 (30.51%) > UV-H2O2 (28.59%) which is consistent with results from ultraviolet-visible spectra analysis. HO• and SO4•- were both identified in the UV-PMS/H2O2 and UV-PMS processes. In the UV-PMS process, SO4•- was the dominant ROS, which suggested that SO4•--based AOPs are better than HO•-based AOPs for degrading refractory organics contained in SAARB effluent. Parallel factor (PARAFAC) analysis indicated that UV-based AOPs were effective in degrading humic- and fulvic-like substances in the SAARB leachate, and the UV-PMS process achieved a much better degradation efficiency of refractory organics in the leachate than did the UV-PMS/H2O2 and the UV-H2O2 processes. Furthermore, the best treatment efficiency was achieved by the UV-PMS process and this process also consumed the least electrical energy. This study provides a theoretical reference for refractory organics degradation in SAARB effluent by UV-catalyzed AOPs.