Dynamic heterogeneities above and below the mode-coupling temperature: Evidence of a dynamic crossover

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.

Dehydration induced dynamical heterogeneity and ordering mechanism of lipid bilayers

Understanding the influence of dehydration on the membrane structure is crucial to control membrane functionality related to domain formation and cell fusion under anhydrobiosis conditions. To this end, we perform all-atom molecular dynamic simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dimyristoylphosphatidylcholine lipid membranes at different hydration levels at 308 K. As dehydration increases, the lipid area per head group decreases with an increase in bilayer thickness and lipid order parameters indicating bilayer ordering. Concurrently, translational and rotational dynamics of interfacial water (IW) molecules near membranes slow down. On the onset of bilayer ordering, the IW molecules exhibit prominent features of dynamical heterogeneity evident from non-Gaussian parameters and one-dimensional van Hove correlation functions. At a fully hydrated state, diffusion constants (D) of the IW follow a scaling relation, D∼τ_α ^-1, where the α relaxation time (τ_α) is obtained from self-intermediate scattering functions. However, upon dehydration, the relation breaks and the D of the IW follows a power law behavior as D∼τ_α ^-0.57, showing the signature of glass dynamics. τ_α and hydrogen bond lifetime calculated from intermittent hydrogen bond auto-correlation functions undergo a similar crossover in association with bilayer ordering on dehydration. The bilayer ordering is accompanied with an increase in fraction of caged lipids spanned over the bilayer surface and a decrease in fraction of mobile lipids due to the non-diffusive dynamics. Our analyses reveal that the microscopic mechanism of lipid ordering by dehydration is governed by dynamical heterogeneity. The fundamental understanding from this study can be applied to complex bio-membranes to trap functionally relevant gel-like domains at room temperature.

Connecting real glasses to mean-field models

We propose a novel model for a glass-forming liquid, which allows us to switch in a continuous manner from a standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducing k additional particle-particle interactions, which thus augments the effective number of neighbors of each particle. Our computer simulations of this system show that the structure of the liquid does not change with the introduction of these pseudo-neighbors and by means of analytical calculations, and we determine the structural properties related to these additional neighbors. We show that the relaxation dynamics of the system slows down very quickly with the increase in k and that the onset and the mode-coupling temperatures increase. The systems with high values of k follow the mode-coupling theory power law behavior for a larger temperature range compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamic heterogeneity decreases with the increase in k, whereas the non-Gaussian parameter is independent of it. Thus, we conclude that with the increase in the number of pseudo-neighbors, the system becomes more mean-field-like. By comparing our results with previous studies on mean-field-like systems, we come to the conclusion that the details of how the mean-field limit is approached are important since they can lead to different dynamical behavior in this limit.

MD simulations of charged binary mixtures reveal a generic relation between high- and low-temperature behavior

Experimental studies of the glassy slowdown in molecular liquids indicate that the high-temperature activation energy E_∞ of glass-forming liquids is directly related to their glass transition temperature T_g. To further investigate such a possible relation between high- and low-temperature dynamics in glass-forming liquids, we analyze the glassy dynamics of binary mixtures using molecular dynamics simulations. We consider a binary mixture of charged Lennard-Jones particles and vary the partial charges of the particles and, thus, the high-temperature activation energy and the glass transition temperature of the system. Based on previous results, we introduce a phenomenological model describing relaxation times over the whole temperature regime from high temperatures to temperatures well inside the supercooled regime. By investigating the dynamics of both particle species on molecular and diffusive length scales along isochoric and isobaric pathways, we find a quadratic charge dependence of both E_∞ and T_g, resulting in an approximately constant ratio of both quantities independent of the underlying observable, the thermodynamic ensemble, and the particle species, and this result is robust against the actual definition of T_g. This generic relation between the activation energy and the glass transition temperature indicates that high-temperature dynamics and the glassy slowdown are related phenomena, and the knowledge of E_∞ may allow us to approximately predict T_g.

Solvable Models of Supercooled Liquids in Three Dimensions

We introduce a supercooled liquid model and obtain parameter-free quantitative predictions that are in excellent agreement with numerical simulations, notably in the hard low-temperature region characterized by strong deviations from mode-coupling-theory behavior. The model is the Fredrickson-Andersen kinetically constrained model on the three-dimensional M-layer lattice. The agreement has implications beyond the specific model considered because the theory is potentially valid for many more systems, including realistic models and actual supercooled liquids.

Static and dynamic correlation lengths in supercooled polymers

A key point to understand the glass transition is the relationship between structural and dynamic behavior experienced by a glass former when it approaches T_g. In this work, the relaxation in a simple bead-spring polymer system in the supercooled regime near its glass transition temperature was investigated with molecular dynamic simulations. We develop a new manner to look at the dynamic length scales in a supercooled polymeric system, focusing on correlated motion of particles in an isoconfigurational ensemble (that is, associated with the structure), as measured by Pearson's correlation coefficient. We found that while the usual dynamic four-point correlation length deviates from the structural (mosaic or point-to-set) length scale at low temperatures, Pearson's length behaves similarly to the static length in the whole temperature range. The results lead to a consensus of similar scaling of structural and dynamical length scales, reinforcing the idea of the theories of Adam-Gibbs and random first order transition.

The race to the bottom: approaching the ideal glass?

Key to resolving the scientific challenge of the glass transition is to understand the origin of the massive increase in viscosity of liquids cooled below their melting temperature (avoiding crystallisation). A number of competing and often mutually exclusive theoretical approaches have been advanced to describe this phenomenon. Some posit a bona fide thermodynamic phase to an 'ideal glass', an amorphous state with exceptionally low entropy. Other approaches are built around the concept of the glass transition as a primarily dynamic phenomenon. These fundamentally different interpretations give equally good descriptions of the data available, so it is hard to determine which-if any-is correct. Recently however this situation has begun to change. A consensus has emerged that one powerful means to resolve this longstanding question is to approach the putative thermodynamic transition sufficiently closely, and a number of techniques have emerged to meet this challenge. Here we review the results of some of these new techniques and discuss the implications for the existence-or otherwise-of the thermodynamic transition to an ideal glass.

Dynamic and thermodynamic crossover scenarios in the Kob-Andersen mixture: Insights from multi-CPU and multi-GPU simulations

The physical behavior of glass-forming liquids presents complex features of both dynamic and thermodynamic nature. Some studies indicate the presence of thermodynamic anomalies and of crossovers in the dynamic properties, but their origin and degree of universality is difficult to assess. Moreover, conventional simulations are barely able to cover the range of temperatures at which these crossovers usually occur. To address these issues, we simulate the Kob-Andersen Lennard-Jones mixture using efficient protocols based on multi-CPU and multi-GPU parallel tempering. Our setup enables us to probe the thermodynamics and dynamics of the liquid at equilibrium well below the critical temperature of the mode-coupling theory, [Formula: see text]. We find that below [Formula: see text] the analysis is hampered by partial crystallization of the metastable liquid, which nucleates extended regions populated by large particles arranged in an fcc structure. By filtering out crystalline samples, we reveal that the specific heat grows in a regular manner down to [Formula: see text] . Possible thermodynamic anomalies suggested by previous studies can thus occur only in a region of the phase diagram where the system is highly metastable. Using the equilibrium configurations obtained from the parallel tempering simulations, we perform molecular dynamics and Monte Carlo simulations to probe the equilibrium dynamics down to [Formula: see text]. A temperature-derivative analysis of the relaxation time and diffusion data allows us to assess different dynamic scenarios around [Formula: see text]. Hints of a dynamic crossover come from analysis of the four-point dynamic susceptibility. Finally, we discuss possible future numerical strategies to clarify the nature of crossover phenomena in glass-forming liquids.

Measurements of growing surface tension of amorphous-amorphous interfaces on approaching the colloidal glass transition

There is mounting evidence indicating that relaxation dynamics in liquids approaching their glass transition not only become increasingly cooperative, but the relaxing regions also become more compact in shape. Of the many theories of the glass transition, only the random first-order theory—a thermodynamic framework—anticipates the surface tension of relaxing regions to play a role in deciding both their size and morphology. However, owing to the amorphous nature of the relaxing regions, even the identification of their interfaces has not been possible in experiments hitherto. Here, we devise a method to directly quantify the dynamics of amorphous–amorphous interfaces in bulk supercooled colloidal liquids. Our procedure also helped unveil a non-monotonic evolution in dynamical correlations with supercooling in bulk liquids. We measure the surface tension of the interfaces and show that it increases rapidly across the mode-coupling area fraction. Our experiments support a thermodynamic origin of the glass transition.

The existence of interfaces, separating distinct relaxing regions, has been predicted in glass  theory, but a direct proof remains challenging due to the amorphous nature of glasses. Ganapathi et al. identify and measure the surface tension of these interfaces in bulk supercooled colloidal liquids.

Nonmonotonic dynamic correlations in quasi-two-dimensional confined glass-forming liquids

It has been broadly accepted that the behavior of glass-forming liquids, where their relaxation dynamics exhibit a pronounced slowdown as they are cooled toward the glass transition temperature, is caused by the increase in one or more correlation lengths. However, the role of length scales in the dynamics of glass-forming liquids is not clearly established, and past simulation work that suggests a surprising nonmonotonic temperature evolution of spatial dynamical correlations near the mode-coupling crossover temperature has been both questioned and supported by subsequent work. Here, using molecular dynamics simulation, we also show a striking maximum in the dynamic length scale ξ_{c}^{dyn} at a given temperature, but the temperature of this maximum is found to shift as the size of the confined system increases. Furthermore, we find that such a maximum disappears for all geometry sizes considered when a rough wall is replaced with a smooth, hard wall, suggesting that the nature of the nonmonotonic temperature dependence of ξ_{c}^{dyn} does not reflect an intrinsic property of bulk liquids, but originates from wall effects. Our results provide new insights into the dynamics of glass-forming liquids, particularly for quasi-two-dimensional systems.

The nonequilibrium glassy dynamics of self-propelled particles

We study the glassy dynamics taking place in dense assemblies of athermal active particles that are driven solely by a nonequilibrium self-propulsion mechanism. Active forces are modeled as an Ornstein-Uhlenbeck stochastic process, characterized by a persistence time and an effective temperature, and particles interact via a Lennard-Jones potential that yields well-studied glassy behavior in the Brownian limit, which is obtained as the persistence time vanishes. By increasing the persistence time, the system departs more strongly from thermal equilibrium and we provide a comprehensive numerical analysis of the structure and dynamics of the resulting active fluid. Finite persistence times profoundly affect the static structure of the fluid and give rise to nonequilibrium velocity correlations that are absent in thermal systems. Despite these nonequilibrium features, for any value of the persistence time we observe a nonequilibrium glass transition as the effective temperature is decreased. Surprisingly, increasing departure from thermal equilibrium is found to promote (rather than suppress) the glassy dynamics. Overall, our results suggest that with increasing persistence time, microscopic properties of the active fluid change quantitatively, but the general features of the nonequilibrium glassy dynamics observed with decreasing the effective temperature remain qualitatively similar to those of thermal glass-formers.

Mean-field dynamic criticality and geometric transition in the Gaussian core model

We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the mode-coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by large energy barriers, as expected from the lack of activated, hopping dynamics, and display features compatible with a geometric transition. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.

Heterogeneous dynamics and its length scale in simple ionic liquid models: a computational study

We numerically investigate the dynamic heterogeneity and its length scale found in coarse-grained ionic liquid model systems.

Correlation between crystalline order and vitrification in colloidal monolayers

We investigate experimentally the relationship between local structure and dynamical arrest in a quasi-2d colloidal model system which approximates hard discs. We introduce polydispersity to the system to suppress crystallisation. Upon compression, the increase in structural relaxation time is accompanied by the emergence of local hexagonal symmetry. Examining the dynamical heterogeneity of the system, we identify three types of motion: 'zero-dimensional' corresponding to β-relaxation, 'one-dimensional' or stringlike motion and '2D' motion. The dynamic heterogeneity is correlated with the local order, that is to say locally hexagonal regions are more likely to be dynamically slow. However, we find that lengthscales corresponding to dynamic heterogeneity and local structure do not appear to scale together approaching the glass transition.

Long-range correlations in glasses and glassy fluids

We argue that the existence of a non-decaying part of the self-intermediate scattering function implies a small wave-vector divergence of a four-point structure factor defined in terms of the microscopic self-intermediate scattering function. This divergence indicates long-range correlations of density fluctuations in direct space. We show that a signature of the divergence and the long-range correlations can be observed in computer simulations of glasses. Interestingly, remnants of this divergence can be easily observed in computer simulations of supercooled fluids. They manifest themselves as transient dynamic correlations with a very large correlation length; much larger than the correlation length characterizing the size of dynamic heterogeneities.

Rotational dynamics of simple asymmetric molecules

Molecular dynamic simulations were carried out on rigid diatomic molecules, which exhibit both α (structural) and β (secondary) dynamics. The relaxation scenarios range from onset behavior, in which a distinct α process emerges on cooling, to merging behavior, associated with two relaxation peaks that converge at higher temperature. These properties, as well as the manifestation of the β peak as an excess wing, depend not only on thermodynamic conditions, but also on both the symmetry of the molecule and the correlation function (odd or even) used to analyze its dynamics. These observations help to reconcile divergent results obtained from different experiments. For example, the β process is more intense and the α-relaxation peak is narrower in dielectric relaxation spectra than in dynamic light scattering or NMR measurements. In the simulations herein, this follows from the weaker contribution of the secondary relaxation to even-order correlation functions, related to the magnitude of the relevant angular jumps.

Mutual information reveals multiple structural relaxation mechanisms in a model glass former

Among the key challenges to our understanding of solidification in the glass transition is that it is accompanied by little apparent change in structure. Recently, geometric motifs have been identified in glassy liquids, but a causal link between these motifs and solidification remains elusive. One 'smoking gun' for such a link would be identical scaling of structural and dynamic lengthscales on approaching the glass transition, but this is highly controversial. Here we introduce an information theoretic approach to determine correlations in displacement for particle relaxation encoded in the initial configuration of a glass-forming liquid. We uncover two populations of particles, one inclined to relax quickly, the other slowly. Each population is correlated with local density and geometric motifs. Our analysis further reveals a dynamic lengthscale similar to that associated with structural properties, which may resolve the discrepancy between structural and dynamic lengthscales.

Long-range spatial correlations of particle displacements and the emergence of elasticity

We examine correlations of transverse particle displacements and their relationship to the shear modulus of a glass and the viscosity of a fluid. To this end we use computer simulations to calculate a correlation function of the displacements, S_{4}(q;t), which is similar to functions used to study heterogeneous dynamics in glass-forming fluids. We show that in the glass the shear modulus can be obtained from the long-time, small-q limit of S_{4}(q;t). By using scaling arguments, we argue that a four-point correlation length ξ_{4}(t) grows linearly in time in a glass and grows as sqrt[t] at long times in a fluid, and we verify these results by analyzing S_{4}(q;t) obtained from simulations. For a viscoelastic fluid, the simulation results suggest that the crossover to the long-time sqrt[t] growth of ξ_{4}(t) occurs at a characteristic decay time of the shear stress autocorrelation function. Using this observation, we show that the amplitude of the long-time sqrt[t] growth is proportional to sqrt[η] where η is the viscosity of the fluid.

Nonlinear 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 assuming that the configurational entropy of the pinned liquid decreases linearly upon increasing of c. This behavior is discussed in the context of thermodynamic theories for the glass transition, notably the Adam-Gibbs picture and the random first order transition theory. 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.

Potential energy landscape and inherent dynamics of a hard-sphere fluid

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential energy landscape) correctly predict the occurrence of dynamic heterogeneity and nonzero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.

Variation of the dynamic susceptibility along an isochrone

Koperwas et al. showed in a recent paper [Phys. Rev. Lett. 111, 125701 (2013)] that the dynamic susceptibility χ4 as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: Measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known noninvariance of the isothermal bulk modulus. Considering the version of χ4 defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

Novel approach to numerical measurements of the configurational entropy in supercooled liquids

The configurational entropy is among the key observables to characterize experimentally the formation of a glass. Physically, it quantifies the multiplicity of metastable states in which an amorphous material can be found at a given temperature, and its temperature dependence provides a major thermodynamic signature of the glass transition, which is experimentally accessible. Measurements of the configurational entropy require, however, some approximations that have often led to ambiguities and contradictory results. Here we implement a novel numerical scheme to measure the configurational entropy Σ(T) in supercooled liquids, using a direct determination of the free-energy cost to localize the system within a single metastable state at temperature T. For two prototypical glass-forming liquids, we find that Σ(T) disappears discontinuously above a temperature Tc, which is slightly lower than the usual estimate of the onset temperature for glassy dynamics. This observation is in good agreement with theoretical expectations but contrasts sharply with alternative numerical methods. While the temperature dependence of Σ(T) correlates with the glass fragility, we show that the validity of the Adam-Gibbs relation (relating configurational entropy to structural relaxation time) established in earlier numerical studies is smaller than previously thought, potentially resolving an important conflict between experiments and simulations.

Crossovers in the dynamics of supercooled liquids probed by an amorphous wall

We study the relaxation dynamics of a binary Lennard-Jones liquid in the presence of an amorphous wall generated from equilibrium particle configurations. In qualitative agreement with the results presented by Kob et al. [Nat. Phys. 8, 164 (2012).] for a liquid of harmonic spheres, we find that our binary mixture shows a saturation of the dynamical length scale close to the mode-coupling temperature T(c). Furthermore we show that, due to the broken symmetry imposed by the wall, signatures of an additional change in dynamics become apparent at a temperature well above T(c). We provide evidence that this modification in the relaxation dynamics occurs at a recently proposed dynamical crossover temperature T(s) > T(c), which is related to the breakdown of the Stokes-Einstein relation. We find that this dynamical crossover at T(s) is also observed for the harmonic spheres as well as a WCA liquid, showing that it may be a general feature of glass-forming systems.

Structural signatures of (two) characteristic dynamical temperatures in lithium metasilicate

We report on the dynamic and structural characterization of lithium metasilicate Li2SiO3, a network-forming ionic glass, by means of molecular dynamics simulations. The system is characterized by a network of SiO4 tetrahedra disrupted by Li ions which diffuse through the network. Measures of mean square displacement and the diffusion constant of Si and O atoms allow us to identify the mode-coupling temperature, Tc ≈ 1500 K. At a much lower temperature, a change in the slope of the specific volume versus temperature singles out the glass transition at Tg ≈ 1000 K, the temperature below which the system goes out of equilibrium. We find signatures of both dynamical temperatures in structural order parameters related to the orientation of the tetrahedra. At lower temperatures we find that a set of order parameters which measure the relative orientation of neighbouring tetrahedra cease to increase and stay constant below Tc. Nevertheless, the bond orientational order parameter, which in this system measures local tetrahedral order, is found to continue growing below Tc until Tg, below which it remains constant. Although these structural signatures of the two dynamical temperatures do not imply any real thermodynamic transition in terms of the order parameters, they do give insight into the relaxation processes that occur between Tc and Tg, in particular they allow us to characterize the nature of the crossover happening around Tc.

Universal features of dynamic heterogeneity in supercooled liquids

A few years ago it was shown that some systems that have very similar local structure, as quantified by the pair correlation function, exhibit vastly different slowing down upon supercooling. Recently, a more subtle structural quantity, the so-called "point-to-set" length, was found to reliably correlate with the average dynamics. Here we use computer simulations to examine the behavior of fluctuations around the average dynamics, i.e., dynamic heterogeneity. We study five model glass-forming liquids: three model liquids used in previous works and two additional model liquids with finite range interactions. Some of these systems have very similar local structure but vastly different dynamics. We show that for all these systems the spatial extent and the anisotropy of dynamic heterogeneity have the same correlation with the average dynamics. This result complements a recent experimental finding of a universal correlation between the number of correlated particles and the apparent activation enthalpy.

Simple picture of supercooled liquid dynamics: dynamic scaling and phenomenology based on clusters

Although it is now well established that in glassy liquids, slow structural relaxation accompanies a correlated structural rearrangement, the role of such a correlation in the transport anomaly, and thus in the slow dynamics, remains unclear. In this paper, we argue from a hydrodynamic viewpoint that a correlated structure (cluster) with a characteristic size ξ sustains the long-lived stress and dynamically couples with the hydrodynamic fluctuations; therefore, the dynamics of this cluster is the origin of the mesoscopic nature of anomalous hydrodynamic transport. Based on this argument, we derive a dynamic scaling law for τ(α) (or η, where η is the macroscopic shear viscosity) as a function of ξ: τ(α)([proportionality]η)[proportionality]ξ(4). We provide a simple explanation for basic features of anomalous transport, such as the breakdown of the Stokes-Einstein relation and the length-scale-dependent decoupling between viscosity and diffusion. The present study further suggests a different physical picture: Through the coarse graining of smaller-scale fluctuations (</~ξ), the supercooled liquid dynamics can be regarded as the dynamics of normal (cluster) liquids composed of units with a typical size of ξ. Although the correlation length of hydrodynamic transport ξ and the dynamic heterogeneity size ξ(DH), which is determined by the usual four-point correlation function, reflect some aspects of the cooperative effects, the correspondence between ξ and ξ(DH) is not one to one. We highlight the possibility that ξ(DH) overestimates the actual collective transport range at a low degree of supercooling.

Decorrelation of the static and dynamic length scales in hard-sphere glass formers

We show that, in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in the dynamics unambiguously decorrelate. The former grow at a much slower rate than the latter when density increases. This observation is valid for the dynamical range that is accessible to computer simulations, which roughly corresponds to that accessible in colloidal experiments. We also find that, in this same range, no one-to-one correspondence between relaxation time and point-to-set correlation length exists. These results point to the coexistence of several relaxation mechanisms in the dynamically accessible regime of three-dimensional hard-sphere glass formers.