Scaling of the glassy dynamics of soft repulsive particles: a mode-coupling approach

We combine the hyper-netted chain approximation of liquid state theory with the mode-coupling theory of the glass transition to analyze the structure and dynamics of soft spheres interacting via harmonic repulsion. We determine the locus of the fluid-glass dynamic transition in a temperature -- volume fraction phase diagram. The zero-temperature (hard sphere) glass transition influences the dynamics at finite temperatures in its vicinity. This directly implies a form of dynamic scaling for both the average relaxation time and dynamic susceptibilities quantifying dynamic heterogeneity. We discuss several qualitative disagreements between theory and existing simulations at equilibrium. Our theoretical results are, however, very similar to numerical results for the driven athermal dynamics of repulsive spheres, suggesting that `mean-field' mode-coupling approaches might be good starting points to describe these nonequilibrium dynamics.Comment: 11 pages, 8 figure

Dynamic criticality at the jamming transition

We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, phi = phi_J). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near phi_J is divided in three different regimes separated by a characteristic temperature scale T*(phi) that vanishes quadratically with the distance to phi_J. While two of them, (T < T*(phi), phi > phi_J) and (T < T*(phi), phi < phi_J), are described by harmonic theories developed in the zero temperature limit, the third one for T > T*(phi) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T*(phi) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specifically-dedicated experiments.Comment: 18 pages; submitted to J. Chem. Phys. for "Special Topic Issue on the Glass Transition

Theory for Swap Acceleration near the Glass and Jamming Transitions

Swap algorithms can shift the glass transition to lower temperatures, a recent unexplained observation constraining the nature of this phenomenon. Here we show that swap dynamic is governed by an effective potential describing both particle interactions as well as their ability to change size. Requiring its stability is more demanding than for the potential energy alone. This result implies that stable configurations appear at lower energies with swap dynamics, and thus at lower temperatures when the liquid is cooled. \maa{ The magnitude of this effect is proportional to the width of the radii distribution, and decreases with compression for finite-range purely repulsive interaction potentials.} We test these predictions numerically and discuss the implications of these findings for the glass transition.We extend these results to the case of hard spheres where swap is argued to destroy meta-stable states of the free energy coarse-grained on vibrational time scales. Our analysis unravels the soft elastic modes responsible for the speed up swap induces, and allows us to predict the structure and the vibrational properties of glass configurations reachable with swap. In particular for continuously poly-disperse systems we predict the jamming transition to be dramatically altered, as we confirm numerically. A surprising practical outcome of our analysis is new algorithm that generates ultra-stable glasses by simple descent in an appropriate effective potential.Comment: 8 pages, 7 figures in the main text, 3 pages 4 figures in the supplemental material. We improved the theoretical discussion in the v3. In particular, we added a section with an extended discussion of the implications of our findings for the glass transitio

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling

Liquids relax extremely slowly upon approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.Comment: 4+23 pages, 3+12 figures; v2: final version, with various changes made. Data relevant to this work can be accessed at http://dx.doi.org/10.7924/G8ZG6Q9

Structure and dielectric properties of polar fluids with extended dipoles: results from numerical simulations

The strengths and short-comings of the point-dipole model for polar fluids of spherical molecules are illustrated by considering the physically more relevant case of extended dipoles formed by two opposite charges $\pm q$ separated by a distance $d$ (dipole moment $\mu=q d$). Extensive Molecular Dynamics simulations on a high density dipolar fluid are used to analyse the dependence of the pair structure, dielectric constant \eps and dynamics as a function of the ratio $d/\sigma$ (\sig is the molecular diameter), for a fixed dipole moment $\mu$. The point dipole model is found to agree well with the extended dipole model up to d/\sig \simeq 0.3. Beyond that ratio, \eps shows a non-trivial variation with d/\sig. When d/\sig>0.6, a transition is observed towards a hexagonal columnar phase; the corresponding value of the dipole moment, \mu^2/\sig^3 k T=3, is found to be substantially lower than the value of the point dipole required to drive a similar transition.Comment: 10 pages, 11 figures; Paper submitted to Molecular Physic

The contact dynamics method for granular media

In this paper we review the simulation method of the non-smooth contact dynamics. This technique was designed to solve the unilateral and frictional contact problem for a large number of rigid bodies and has proved to be especially valuable in research of dense granular materials during the last decade. We present here the basic principles compared to other methods and the detailed description of a 3D algorithm. We point out an artifact manifesting itself in spurious sound waves and discuss the applicability of the method.Comment: for the proceedings of the 7th Granada Seminar, 23 pages, 8 figure