Static triplet correlations in glass-forming liquids: A molecular dynamics study

We present a numerical evaluation of the three-point static correlations functions of the Kob-Andersen Lennard-Jones binary mixture and of its purely repulsive, Weeks-Chandler-Andersen variant. In the glassy regime, the two models possess a similar pair structure, yet their dynamics differ markedly. The static triplet correlation functions S^(3) indicate that the local ordering is more pronounced in the Lennard-Jones model, an observation consistent with its slower dynamics. A comparison of the direct triplet correlation functions c^(3) reveals that these structural differences are due, to a good extent, to an amplification of the small discrepancies observed at the pair level. We demonstrate the existence of a broad, positive peak at small wave-vectors and angles in c^(3). In this portion of k-space, slight, systematic differences between the models are observed, revealing "genuine" three-body contributions to the triplet structure. The possible role of the low-k features of c^(3) and the implications of our results for dynamic theories of the glass transition are discussed.Comment: 9 pages, 8 figures, contribution to the JCP Special Issue on the Glass Transitio

Locally preferred structures and many-body static correlations in viscous liquids

We investigate the influence of static correlations beyond the pair level on the dynamics of selected model glass-formers. We compare the pair structure, angular distribution functions, and statistics of Voronoi polyhedra of two well-known Lennard-Jones mixtures as well as of the corresponding Weeks-Chandler-Andersen variants, in which the attractive part of the potential is truncated. By means of the Voronoi construction we identify the atomic arrangements corresponding to the locally preferred structures of the models. We find that the growth of domains formed by interconnected locally preferred structures signals the onset of the slow dynamics regime and allows to rationalize the different dynamic behaviors of the models. At low temperature, the spatial extension of the structurally correlated domains, evaluated at fixed relaxation time, increases with the fragility of the models and is systematically reduced by truncating the attractions. In view of these results, proper inclusion of many-body static correlations in theories of the glass transition appears crucial for the description of the dynamics of fragile glass-formers.Comment: 9 pages, 8 figures, added two tables, minor revisions to the tex

Non-linear dynamic response of glass-forming liquids to random pinning

We use large scale computer simulations of a glass-forming liquid in which a fraction c of the particles has been permanently pinned. We find that the relaxation dynamics shows an exponential dependence on c. This result can be rationalized by means of a simple theoretical Ansatz and we discuss its implication for thermodynamic theories for the glass-transition. For intermediate and low temperatures we find that the slowing down of the dynamics due to the pinning saturates and that the cooperativity decreases with increasing c, results which indicate that in glass-forming liquids there is a dynamic crossover at which the shape of the relaxing entities changes

Cluster and reentrant anomalies of nearly Gaussian core particles

We study through integral equation theory and numerical simulations the structure and dynamics of fluids composed of ultrasoft, nearly Gaussian particles. Namely, we explore the fluid phase diagram of a model in which particles interact via the generalized exponential potential u(r)=\epsilon exp[-(r/\sigma)^n], with a softness exponent n slightly larger than 2. In addition to the well-known anomaly associated to reentrant melting, the structure and dynamics of the fluid display two additional anomalies, which are visible in the isothermal variation of the structure factor and diffusivity. These features are correlated to the appearance of dimers in the fluid phase and to the subsequent modification of the cluster structure upon compression. We corroborate these results through an analysis of the local minima of the potential energy surface, in which clusters appear as much tighter conglomerates of particles. We find that reentrant melting and clustering coexist for softness exponents ranging from 2^+ up to values relevant for the description of amphiphilic dendrimers, i.e., n=3.Comment: 10 pages, 8 figure

Hopping and microscopic dynamics of ultrasoft particles in cluster crystals

We have investigated the slow dynamics of ultrasoft particles in crystalline cluster phases, where point particles interact through the generalized exponential potential u(r) = \epsilon \exp[-(r/\sigma)^n], focusing on the cluster fcc phase of this model with n=4. In an effort to elucidate how the mechanisms of mass transport depend on the microscopic dynamics and in order to mimic a realistic scenario in a related experiment we have performed molecular dynamics, Brownian dynamics, and Monte Carlo simulations. In molecular dynamics simulations the diffusion of particles proceeds through long-range jumps, guided by strong correlations in the momentum direction. In Monte Carlo and Brownian dynamics simulations jump events are short-ranged, reflecting the purely configurational nature of the dynamics. In contrast to what was found in models of glass-forming liquids, the effect of Newtonian and stochastic microscopic dynamics on the long-time relaxation cannot be accounted for by a temperature-independent rescaling of the time units. From the obvious qualitative discrepancies in the short time behavior between the three simulation methods and the non-trivial difference in jump length distributions, long time relaxation, and dynamic heterogeneity, we learn that a more complex modeling of the dynamics in realistic systems of ultrasoft colloids is required.Comment: 12 pages, 18 figures, added results of Brownian dynamics simulation

Structure and dynamics of coupled viscous liquids

We perform Monte-Carlo simulations to analyse the structure and microscopic dynamics of a viscous Lennard-Jones liquid coupled to a quenched reference configuration of the same liquid. The coupling between the two replicas is introduced via a field epsilon conjugate to the overlap Q between the two particle configurations. This allows us to study the evolution of various static and dynamic correlation functions across the (epsilon, T) equilibrium phase diagram. As the temperature is decreased, we identify increasingly marked precursors of a first-order phase transition between a low-Q and a high-Q phase induced by the field epsilon. We show in particular that both static and dynamic susceptibilities have a maximum at a temperature-dependent value of the coupling field, which defines a `Widom line'. We also show that, in the high-overlap regime, diffusion and structural relaxation are strongly decoupled because single particle motion mostly occurs via discrete hopping on the sites defined by the reference configuration. These results, obtained using conventional numerical tools, provide encouraging signs that an equilibrium phase transition exists in coupled viscous liquids, but also demonstrate that important numerical challenges must be overcome to obtain more conclusive numerical evidence.Comment: 14 pages, 8 figures. Accepted for publication in Molecular Physics (Special Issue in honour of J.-P. Hansen

Models and algorithms for the next generation of glass transition studies

Successful computer studies of glass-forming materials need to overcome both the natural tendency to structural ordering and the dramatic increase of relaxation times at low temperatures. We present a comprehensive analysis of eleven glass-forming models to demonstrate that both challenges can be efficiently tackled using carefully designed models of size polydisperse supercooled liquids together with an efficient Monte Carlo algorithm where translational particle displacements are complemented by swaps of particle pairs. We study a broad range of size polydispersities, using both discrete and continuous mixtures, and we systematically investigate the role of particle softness, attractivity and non-additivity of the interactions. Each system is characterized by its robustness against structural ordering and by the efficiency of the swap Monte Carlo algorithm. We show that the combined optimisation of the potential's softness, polydispersity and non-additivity leads to novel computer models with excellent glass-forming ability. For such models, we achieve over ten orders of magnitude gain in the equilibration timescale using the swap Monte Carlo algorithm, thus paving the way to computational studies of static and thermodynamic properties under experimental conditions. In addition, we provide microscopic insights into the performance of the swap algorithm which should help optimizing models and algorithms even further.Comment: 22 pages, 15 fig

Impact of random obstacles on the dynamics of a dense colloidal fluid

Using molecular dynamics simulations we study the slow dynamics of a colloidal fluid annealed within a matrix of obstacles quenched from an equilibrated colloidal fluid. We choose all particles to be of the same size and to interact as hard spheres, thus retaining all features of the porous confinement while limiting the control parameters to the packing fraction of the matrix, {\Phi}m, and that of the fluid, {\Phi}f. We conduct detailed investigations on several dynamic properties, including the tagged-particle and collective intermediate scattering functions, the mean-squared displacement, and the van Hove function. We show the confining obstacles to profoundly impact the relaxation pattern of various quantifiers pertinent to the fluid. Varying the type of quantifier (tagged-particle or collective) as well as {\Phi}m and {\Phi}f, we unveil both discontinuous and continuous arrest scenarios. Furthermore, we discover subdiffusive behavior and demonstrate its close connection to the matrix structure. Our findings partly confirm the various predictions of a recent extension of mode-coupling theory to the quenched-annealed protocol.Comment: 16 pages, 20 figures, minor revision

Exploring the jamming transition over a wide range of critical densities

We numerically study the jamming transition of frictionless polydisperse spheres in three dimensions. We use an efficient thermalisation algorithm for the equilibrium hard sphere fluid and generate amorphous jammed packings over a range of critical jamming densities that is about three times broader than in previous studies. This allows us to reexamine a wide range of structural properties characterizing the jamming transition. Both isostaticity and the critical behavior of the pair correlation function hold over the entire range of jamming densities. At intermediate length scales, we find a weak, smooth increase of bond orientational order. By contrast, distorted icosahedral structures grow rapidly with increasing the volume fraction in both fluid and jammed states. Surprisingly, at large scale we observe that denser jammed states show stronger deviations from hyperuniformity, suggesting that the enhanced amorphous ordering inherited from the equilibrium fluid competes with, rather than enhances, hyperuniformity. Finally, finite size fluctuations of the critical jamming density are considerably suppressed in the denser jammed states, indicating an important change in the topography of the potential energy landscape. By considerably stretching the amplitude of the critical "J-line", our work disentangles physical properties at the contact scale that are associated with jamming criticality, from those occurring at larger length scales, which have a different nature.Comment: 19 pages, 11 figures, resubmission to SciPos

Dynamic arrest of colloids in porous environments: disentangling crowding and confinement

Using numerical simulations we study the slow dynamics of a colloidal hard-sphere fluid adsorbed in a matrix of disordered hard-sphere obstacles. We calculate separately the contributions to the single-particle dynamic correlation functions due to free and trapped particles. The separation is based on a Delaunay tessellation to partition the space accessible to the centres of fluid particles into percolating and disconnected voids. We find that the trapping of particles into disconnected voids of the matrix is responsible for the appearance of a nonzero long-time plateau in the single-particle intermediate scattering functions of the full fluid. The subdiffusive exponent $z$, obtained from the logarithmic derivative of the mean-squared displacement, is observed to be essentially unaffected by the motion of trapped particles: close to the percolation transition, we determined $z \simeq 0.5$ for both the full fluid and the particles moving in the percolating void. Notably, the same value of $z$ is found in single-file diffusion and is also predicted by mode-coupling theory along the diffusion-localisation line. We also reveal subtle effects of dynamic heterogeneity in both the free and the trapped component of the fluid particles, and discuss microscopic mechanisms that contribute to this phenomenon.Comment: 18 pages, 12 figures, minor change