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Register a new userBond formation and slow heterogeneous dynamics in adhesive spheres with long--ranged repulsion: Quantitative test of Mode Coupling Theory
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A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).
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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 -- an approach that may become exact if sufficiently many correlations are taken into account. 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 ($A_3$ and $A_4$) 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.
Within the mode-coupling theory (MCT) of the glass transition, we reconsider the numerical schemes to evaluate the MCT functional. Here we propose nonuniform discretizations of the wave number, in contrast to the standard equidistant grid, in order to decrease the number of grid points without losing accuracy. We discuss in detail how the integration scheme on the new grids has to be modified from standard Riemann integration. We benchmark our approach by solving the MCT equations numerically for mono-disperse hard disks and hard spheres and by computing the critical packing fraction and the nonergodicity parameters. Our results show that significant improvements in performance can be obtained by employing a nonuniform grid.
We theoretically study thermally activated elementary dynamical processes that precede full structural relaxation in ultra-dense particle liquids interacting via strong short range attractive forces. Our approach is based on a microscopic theory formulated at the particle trajectory level built on the dynamic free energy concept and an explicit treatment of how attractions control physical bonding. Mean time scales for bond breaking, the early stage of cage escape, and a fixed non-Fickian displacement are analyzed in the repulsive glass, bonded repulsive (attractive) glass, fluid, and dense gel regimes. The theory predicts a strong length-scale-dependent growth of these time scales with attractive force strength at fixed packing fraction, a much weaker slowing down with density at fixed attraction strength, and a strong decoupling of the shorter bond breaking time with the other two time scales that are controlled mainly by perturbed steric caging. All results are in good accord with simulations, and additional testable predictions are made. The classic statistical mechanical projection approximation of replacing all bare attractive and repulsive forces with a single effective force determined by pair structure incurs major errors for describing processes associated with thermally activated escape from transiently localized states.
A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_cpropto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $phi$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $phitophi_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $chi_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6leqphileq 0.805$, and to become increasingly long-ranged as $phitophi_c$. Finite size scaling of $chi_4(t)$ provides a consistency check for the previously analyzed divergences of $chi_4(t)propto (phi-phi_c)^{-gamma_{chi}}$ and the correlation length $xipropto (phi-phi_c)^{-gamma_{xi}}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $phitophi_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.
Normal dynamics in a quasi-one-dimensional channel of length L (toinfty) of N hard spheres are analyzed. The spheres are heterogeneous: each has a diffusion coefficient D that is drawn from a probability density function (PDF), W D^(-{gamma}), for small D, where 0leq{gamma}<1. The initial spheres density {rho} is non-uniform and scales with the distance (from the origin) l as, {rho} l^(-a), 0leqaleq1. An approximation for the N-particle PDF for this problem is derived. From this solution, scaling law analysis and numerical simulations, we show here that the mean square displacement for a particle in such a system obeys, <r^2>~t^(1-{gamma})/(2c-{gamma}), where c=1/(1+a). The PDF of the tagged particle is Gaussian in position. Generalizations of these results are considered.
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