Mermin-Wagner fluctuations in 2D amorphous solids

Is the glassy dynamics same in 2D as in 3D? The Adam Gibbs relation test

It has been recognized of late that even amorphous, glass-forming materials in two dimensions (2D) are affected by Mermin-Wagner-type long wavelength thermal fluctuation, which is inconsequential in three dimensions (3D). We consider the question of whether the effect of spatial dimension on dynamics is only limited to such fluctuations or if the nature of glassy dynamics is intrinsically different in 2D. To address it, we study the relationship between dynamics and thermodynamics using the Adam-Gibbs (AG) relation and the random first order transition (RFOT) theory. Using two model glass-forming liquids, we find that even after removing the effect of long wavelength fluctuations, the AG relation breaks down in two dimensions. Next, we consider the effect of anharmonicity of vibrational entropy-a second factor that affects the thermodynamics but not dynamics. Using the potential energy landscape formalism, we explicitly compute the configurational entropy, both with and without the anharmonic correction. We show that even with both the corrections, the AG relation still breaks down in 2D. The extent of deviation from the AG relation crucially depends on the attractive vs repulsive nature of interparticle interactions, choice of representative timescale (diffusion coefficient vs α-relaxation time), and implies that the RFOT scaling exponents also depend on these factors. Thus, our results suggest that some differences in the nature of glassy dynamics between 2D and 3D remain that are not explained by long wavelength fluctuations.

Unified Understanding of Nonlinear Rheology near the Jamming Transition Point

When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening or melting emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasistatic shear γ. We find the universal scaling behavior for the ratio of the shear stress σ and the pressure P, independent of the preparation protocol of the initial configurations. In particular, we reveal shear softening σ/P∼γ^{1/2} over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize.

Direct Numerical Analysis of Dynamic Facilitation in Glass-Forming Liquids

We propose a computational strategy to quantify the temperature evolution of the timescales and length scales over which dynamic facilitation affects the relaxation dynamics of glass-forming liquids at low temperatures, which requires no assumption about the nature of the dynamics. In two glass models, we find that dynamic facilitation depends strongly on temperature, leading to a subdiffusive spreading of relaxation events which we characterize using a temperature-dependent dynamic exponent. We also establish that this temperature evolution represents a major contribution to the increase of the structural relaxation time.

Anisotropic-Isotropic Transition of Cages at the Glass Transition

Characterizing the local structural evolution is an essential step in understanding the nature of glass transition. In this work, we probe the evolution of Voronoi cell geometry in simple glass models by simulations and colloid experiments, and find that the individual particle cages deform anisotropically in supercooled liquid and isotropically in glass. We introduce an anisotropy parameter k for each Voronoi cell, whose mean value exhibits a sharp change at the mode-coupling glass transition ϕ_{c}. Moreover, a power law of packing fraction ϕ∝q_{1}^{d} is discovered in the supercooled liquid regime with d>D, in contrast to d=D in the glass regime, where q_{1} is the first peak position of structure factor, and D is the space dimension. This power law is qualitatively explained by the change of k. The active motions in supercooled liquid are spatially correlated with long axes rather than short axes of Voronoi cells. In addition, the dynamic slowing down approaching the glass transition can be well characterized through a modified free-volume model based on k. These findings reveal that the structural parameter k is effective in identifying the structure-dynamics correlations and the glass transition in these systems.

Compression and fracture of ordered and disordered droplet rafts

We simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. Finally, we also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. These results are in good agreement with previously published experiments.

Interfacial Fluid Rheology of Soft Particles

In situ interfacial rheology and numerical simulations are used to investigate microgel monolayers in a wide range of packing fractions, ζ_{2D}. The heterogeneous particle compressibility determines two flow regimes characterized by distinct master curves. To mimic the microgel architecture and reproduce experiments, an interaction potential combining a soft shoulder with the Hertzian model is introduced. In contrast to bulk conditions, the elastic moduli vary nonmonotonically with ζ_{2D} at the interface, confirming long-sought predictions of reentrant behavior for Hertzian-like systems.

Front propagation in ultrastable glasses is dynamically heterogeneous

Upon heating, ultrastable glassy films transform into liquids via a propagating equilibration front, resembling the heterogeneous melting of crystals. A microscopic understanding of this robust phenomenology is, however, lacking because experimental resolution is limited. We simulate the heterogeneous transformation kinetics of ultrastable configurations prepared using the swap Monte Carlo algorithm, thus allowing a direct comparison with experiments. We resolve the liquid-glass interface both in space and in time as well as the underlying particle motion responsible for its propagation. We perform a detailed statistical analysis of the interface geometry and kinetics over a broad range of temperatures. We show that the dynamic heterogeneity of the bulk liquid is passed on to the front that propagates heterogeneously in space and intermittently in time. This observation allows us to relate the averaged front velocity to the equilibrium diffusion coefficient of the liquid. We suggest that an experimental characterization of the interface geometry during the heterogeneous devitrification of ultrastable glassy films could provide direct experimental access to the long-sought characteristic length scale of dynamic heterogeneity in bulk supercooled liquids.

Direction-dependent dynamics of colloidal particle pairs and the Stokes-Einstein relation in quasi-two-dimensional fluids

Hydrodynamic interactions are important for diverse fluids, especially those with low Reynolds number such as microbial and particle-laden suspensions, and proteins diffusing in membranes. Unfortunately, while far-field (asymptotic) hydrodynamic interactions are fully understood in two- and three-dimensions, near-field interactions are not, and thus our understanding of motions in dense fluid suspensions is still lacking. In this contribution, we experimentally explore the hydrodynamic correlations between particles in quasi-two-dimensional colloidal fluids in the near-field. Surprisingly, the measured displacement and relaxation of particle pairs in the body frame exhibit direction-dependent dynamics that can be connected quantitatively to the measured near-field hydrodynamic interactions. These findings, in turn, suggest a mechanism for how and when hydrodynamics can lead to a breakdown of the ubiquitous Stokes-Einstein relation (SER). We observe this breakdown, and we show that the direction-dependent breakdown of the SER is ameliorated along directions where hydrodynamic correlations are smallest. In total, the work uncovers significant ramifications of near-field hydrodynamics on transport and dynamic restructuring of fluids in two-dimensions.

Dynamic Gardner cross-over in a simple glass

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.

Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a "universal" evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Two-step devitrification of ultrastable glasses

The discovery of ultrastable glasses raises novel challenges about glassy systems. Recent experiments studied the macroscopic devitrification of ultrastable glasses into liquids upon heating but lacked microscopic resolution. We use molecular dynamics simulations to analyze the kinetics of this transformation. In the most stable systems, devitrification occurs after a very large time, but the liquid emerges in two steps. At short times, we observe the rare nucleation and slow growth of isolated droplets containing a liquid maintained under pressure by the rigidity of the surrounding glass. At large times, pressure is released after the droplets coalesce into large domains, which accelerates devitrification. This two-step process produces pronounced deviations from the classical Avrami kinetics and explains the emergence of a giant lengthscale characterizing the devitrification of bulk ultrastable glasses. Our study elucidates the nonequilibrium kinetics of glasses following a large temperature jump, which differs from both equilibrium relaxation and aging dynamics, and will guide future experimental studies.

Long-Wavelength Fluctuations in Quasi-2D Supercooled Liquids

We use molecular simulation to characterize the dynamics of supercooled liquids confined in quasi-2D slit geometries. Similar to bulk supercooled liquids, the confined systems exhibit subdiffusive dynamics on intermediate time scales arising from particle localization inside their neighbor cages, followed by an eventual crossover to diffusive behavior as cage rearrangement occurs. The quasi-2D confined liquids also exhibit signatures of long-wavelength fluctuations (LWFs) in the lateral directions parallel to the confining walls, reminiscent of the collective displacements observed in 2D but not 3D systems. The magnitude of the LWFs increases with the lateral dimensions of systems with the same particle volume fraction and confinement length scale, consistent with the logarithmic scaling predicted for 2D Mermin-Wagner fluctuations. The amplitude of the fluctuations is a nonmonotonic function of the confinement length scale because of a competition between caging and strengthening LWFs upon approaching the 2D limit. Our findings suggest that LWFs may play an important role in understanding the behavior of confined supercooled liquids due to their prevalence over a surprisingly broad range of particle densities and confinement length scales.

Breaking through the Mermin-Wagner limit in 2D van der Waals magnets

The Mermin-Wagner theorem states that long-range magnetic order does not exist in one- (1D) or two-dimensional (2D) isotropic magnets with short-ranged interactions. Here we show that in finite-size 2D van der Waals magnets typically found in lab setups (within millimetres), short-range interactions can be large enough to allow the stabilisation of magnetic order at finite temperatures without any magnetic anisotropy. We demonstrate that magnetic ordering can be created in 2D flakes independent of the lattice symmetry due to the intrinsic nature of the spin exchange interactions and finite-size effects. Surprisingly we find that the crossover temperature, where the intrinsic magnetisation changes from superparamagnetic to a completely disordered paramagnetic regime, is weakly dependent on the system length, requiring giant sizes (e.g., of the order of the observable universe ~ 1026 m) to observe the vanishing of the magnetic order as expected from the Mermin-Wagner theorem. Our findings indicate exchange interactions as the main ingredient for 2D magnetism.

Surface melting of a colloidal glass

Despite their technological relevance, a full microscopic understanding of glasses is still lacking. This applies even more to their surfaces whose properties largely differ from that of the bulk material. Here, we experimentally investigate the surface of a two-dimensional glass as a function of the effective temperature. To yield a free surface, we use an attractive colloidal suspension of micron-sized particles interacting via tunable critical Casimir forces. Similar to crystals, we observe surface melting of the glass, i.e., the formation of a liquid film at the surface well below the glass temperature. Underneath, however, we find an unexpected region with bulk density but much faster particle dynamics. It results from connected clusters of highly mobile particles which are formed near the surface and deeply percolate into the underlying material. Because its thickness can reach several tens of particle diameters, this layer may elucidate the poorly understood properties of thin glassy films which find use in many technical applications.

Evidence for growing structural correlation length in colloidal supercooled liquids

Using video microscopy, we measure the long-time diffusion coefficients of colloidal particles at different concentrations. The measured diffusion coefficients start to deviate from theoretical predictions based on random collision models upon entering the supercooled regime. The theoretical diffusion relation is recovered by assigning an effective mass proportional to the size of structurally correlated clusters to the diffusing particles, providing an indirect method to probe the growth of static correlation length scales approaching the glass transition. This method is tested and validated in the crystallization of mono-disperse colloids in quasi-two-dimensional experiments. The correlation length obtained for a binary colloidal liquid increases by a power law toward a critical packing fraction of ∼0.79. The system relaxation time exhibits a power-law dependence on the correlation length in agreement with dynamical facilitation theories.

Enhanced short time peak in four-point dynamic susceptibility in dense active glass-forming liquids

Active glassy systems are simple model systems that imitate complex biological processes. Sometimes, it becomes crucial to estimate the amount of activity present in such biological systems, such as predicting the progression rate of the cancer cells or the healing time of the wound, etc. In this work, we study a model active glassy system to quantify the degree of activity from the collective, long-wavelength fluctuations in the system. These long-wavelength fluctuations present themselves as an additional peak in the four-point dynamic susceptibility (χ₄(t)) apart from the usual peak at structural relaxation time. We then show how the degree of the activity at such a small timescale can be obtained by measuring the variation in χ₄(t) due to changing activity. A Detailed finite size analysis of the peak height of χ₄(t) suggests the existence of an intrinsic dynamic length scale that grows with increasing activity. Finally, we show that this peak height is a unique function of effective activity across all system sizes, serving as a possible parameter for characterizing the degree of activity in a system.

Disordered Collective Motion in Dense Assemblies of Persistent Particles

We explore the emergence of nonequilibrium collective motion in disordered nonthermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompanied by collective motion, whose nature evolves from near-equilibrium spatially heterogeneous dynamics at small persistence, to a qualitatively different intermittent dynamics when persistence is large. This latter regime involves a complex time evolution of the correlated displacement field.

Local Plastic Response and Slow Heterogeneous Dynamics of Supercooled Liquids

We demonstrate, via numerical simulations, that the relaxation dynamics of supercooled liquids correlates well with a plastic length scale measuring a particle's response to impulsive localized perturbations and weakly to measures of local elasticity. We find that the particle averaged plastic length scale vanishes linearly in temperature and controls the super-Arrhenius temperature dependence of the relaxation time. Furthermore, we show that the plastic length scale of individual particles correlates with their typical displacement at the relaxation time. In contrast, the local elastic response only correlates with the dynamics on the vibrational timescale.

Hard Ferromagnetism Down to the Thinnest Limit of Iron-Intercalated Tantalum Disulfide

Two-dimensional (2D) magnetic crystals hold promise for miniaturized and ultralow power electronic devices that exploit spin manipulation. In these materials, large, controllable magnetocrystalline anisotropy (MCA) is a prerequisite for the stabilization and manipulation of long-range magnetic order. In known 2D magnetic crystals, relatively weak MCA typically results in soft ferromagnetism. Here, we demonstrate that ferromagnetic order persists down to the thinnest limit of Fe_xTaS₂ (Fe-intercalated bilayer 2H-TaS₂) with giant coercivities up to 3 T. We prepare Fe-intercalated TaS₂ by chemical intercalation of van der Waals-layered 2H-TaS₂ crystals and perform variable-temperature transport, transmission electron microscopy, and confocal Raman spectroscopy measurements to shed new light on the coupled effects of dimensionality, degree of intercalation, and intercalant order/disorder on the hard ferromagnetic behavior of Fe_xTaS₂. More generally, we show that chemical intercalation gives access to a rich synthetic parameter space for low-dimensional magnets, in which magnetic properties can be tailored by the choice of the host material and intercalant identity/amount, in addition to the manifold distinctive degrees of freedom available in atomically thin, van der Waals crystals.

Low-dimensional physics of clay particle size distribution and layer ordering

Clays are known for their small particle sizes and complex layer stacking. We show here that the limited dimension of clay particles arises from the lack of long-range order in low-dimensional systems. Because of its weak interlayer interaction, a clay mineral can be treated as two separate low-dimensional systems: a 2D system for individual phyllosilicate layers and a quasi-1D system for layer stacking. The layer stacking or ordering in an interstratified clay can be described by a 1D Ising model while the limited extension of individual phyllosilicate layers can be related to a 2D Berezinskii–Kosterlitz–Thouless transition. This treatment allows for a systematic prediction of clay particle size distributions and layer stacking as controlled by the physical and chemical conditions for mineral growth and transformation. Clay minerals provide a useful model system for studying a transition from a 1D to 3D system in crystal growth and for a nanoscale structural manipulation of a general type of layered materials.

Are strongly confined colloids good models for two dimensional liquids?

Quasi-two-dimensional (quasi-2D) colloidal hard-sphere suspensions confined in a slit geometry are widely used as two-dimensional (2D) model systems in experiments that probe the glassy relaxation dynamics of 2D systems. However, the question to what extent these quasi-2D systems indeed represent 2D systems is rarely brought up. Here, we use computer simulations that take into account hydrodynamic interactions to show that dense quasi-2D colloidal bi-disperse hard-sphere suspensions exhibit much more rapid diffusion and relaxation than their 2D counterparts at the same area fraction. This difference is induced by the additional vertical space in the quasi-2D samples in which the small colloids can move out of the 2D plane, therefore allowing overlap between particles in the projected trajectories. Surprisingly, this difference in the dynamics can be accounted for if, instead of using the surface density, one characterizes the systems by means of a suitable structural quantity related to the radial distribution function. This implies that in the two geometries, the relevant physics for glass formation is essentially identical. Our results provide not only practical implications on 2D colloidal experiments but also interesting insights into the 3D-to-2D crossover in glass-forming systems.

Aging or DEAD: Origin of the non-monotonic response to weak self-propulsion in active glasses

Among amorphous states, glass is defined by relaxation times longer than the observation time. This nonergodic nature makes the understanding of glassy systems an involved topic, with complex aging effects or responses to further out-of-equilibrium external drivings. In this respect, active glasses made of self-propelled particles have recently emerged as a stimulating systems, which broadens and challenges our current understanding of glasses by considering novel internal out-of-equilibrium degrees of freedom. In previous experimental studies we have shown that in the ergodicity broken phase, the dynamics of dense passive particles first slows down as particles are made slightly active, before speeding up at larger activity. Here, we show that this nonmonotonic behavior also emerges in simulations of soft active Brownian particles and explore its cause. We refute that the deadlock by emergence of active directionality model we proposed earlier describes our data. However, we demonstrate that the nonmonotonic response is due to activity enhanced aging and thus confirm the link with ergodicity breaking. Beyond self-propelled systems, our results suggest that aging in active glasses is not fully understood.

Multiscale heterogeneous dynamics in two-dimensional glassy colloids

On approaching the glass transition, a dense colloid exhibits a dramatic slowdown with minute structural changes. Most microscopy experiments directly follow the motion of individual particles in real space, whereas scattering experiments typically probe the collective dynamics in reciprocal space, at variable wavevector q. Multiscale studies of glassy dynamics are experimentally demanding and thus seldom performed. By using two-dimensional hard-sphere colloids at various area fractions φ, we show here that Differential Dynamic Microscopy (DDM) can be effectively used to measure the collective dynamics of a glassy colloid in a range of q within a single experiment. As φ is increased, the single decay of the intermediate scattering functions is progressively replaced by a more complex relaxation that we fit to a sum of two stretched-exponential decays. The slowest process, corresponding to the long-time particle escapes from caging, has a characteristic time τs = 1/(DLq2 ) with diffusion coefficient DL ∼ (φc −φ)2.8 , and φc ≈ 0.81. The fast process exhibits, instead, a non-Brownian scaling of the characteristic time τf(q) and a relative amplitude a(q) that monotonically increases with q. Despite the non-Brownian nature of τf(q), we succeed in estimating the short-time diffusion coefficient Dcage, whose φ-dependence is practically negligible compared to the one of DL. Finally, we extend DDM to measure the q-dependent dynamical susceptibility χ4(q,t), a powerful yet hard-to-access multiscale indicator of dynamical heterogeneities. Our results show that DDM is a convenient tool to study the dynamics of colloidal glasses over a broad range of time and length-scales.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the interaction between a pair of liquid crystalline (LC) particles. The underlying substrate potential with which the GB particles interact varies sinusoidally in one direction only. At a given temperature and density of the GB system, we varied the substrate's periodicity (a_s) but fixed the substrate strength. We observed that with a small value of a_s, an underlying substrate helps to stabilize a disordered LC nematic phase to a 2D solid phase. However, for an intermediate range of a_s, the system melts and transitions to a modulate-smectic. Finally, with a further increase in a_s, the system undergoes a structural depinning transition and returns to an LC nematic phase like a free system with no substrate. We argue that a three-way interplay of the energies arising from orientation-dependent particle-particle and particle-substrate interaction makes it possible for the system to undergo substrate-periodicity-dependent multiple phase transitions in the GB LC system.

Translation-rotation decoupling of tracers reflects medium-range crystalline order in two-dimensional colloid glasses

The dynamic heterogeneity and the translation-rotation decoupling are the dynamic signatures of glasses and supercooled liquids. Whether and how the dynamic heterogeneity would relate to the local structure of glasses has been a puzzle for decades. In this work we perform molecular dynamics simulations for tracers in both two-dimensional polydisperse colloids (2DPC) and two-dimensional binary colloids (2DBC). In 2DPC glasses, hexatic local structures develop at low enough temperatures and grow quickly along with the dynamic correlation length of the 2DPC, which is well known as the medium-range crystalline order (MRCO). In 2DBC glasses, on the other hand, any explicit local structure has not been reported to grow significantly with the dynamic correlation length at low temperatures. We introduce two different types of tracers into colloidal systems: A diamond tracer that resembles the MRCO of 2DPC glasses and a square tracer that is dissimilar to any local structure of glasses. The translation-rotation decoupling of the diamond tracer in 2DPC glasses is much more significant than that of the square tracer in the same 2DPC glasses. On the other hand, such a tracer shape-dependence of the decoupling is not observed in 2DBC glasses where the local hexatic structure does not develop significantly. We introduce a shape-dependency parameter of the decoupling and find that the shape-dependency parameter grows along with the dynamic correlation length in 2DPC glasses but not in 2DBC glasses. This illustrates that the dynamic heterogeneity and the translation-rotation decoupling of tracers could reveal the local structure that develops in glasses.

Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.

Tracer dynamics in crowded active-particle suspensions

We discuss the dynamics of active Brownian particles (ABPs) in crowded environments through the mean-squared displacement (MSD) of active and passive tracer particles in both active and passive host systems. Exact equations for the MSD are derived using a projection operator technique, extending to dense systems the known solution for a single ABP. The interaction of the tracer particle with the host particles gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for active Brownian particles (ABP-MCT), we discuss the various dynamical regimes that emerge: While self-propelled motion gives rise to super-diffusive MSD, at high densities, this competes with an interaction-induced sub-diffusive regime. The predictions of the theory are shown to be in good agreement with results obtained from an event-driven Brownian dynamics (ED-BD) simulation scheme for the dynamics of two-dimensional active Brownian hard disks.

Ultrahigh Molecular Weight Polyethylene Lamellar-Thin Framework on Square Meter Scale

A new member of low-dimensional structures with a high aspect ratio (LDHA) is introduced. For the first time, commodity polymer is processed into LDHA, which has long been stagnated by the lack of suitable processing techniques. The key to solve the current bottleneck is to overcome the trade-off between kinetic processability and thermodynamic stability. These two factors are both highly determined by intermolecular interaction level (IIL). Thus with a wide tuning range of IIL, ultrahigh molecular weight polyethylene (UHMWPE) is selected and investigated to break through the trade-off. Polymeric LDHA preparation needs both thinning and stiffening. By focusing on one then the other sequentially, they are realized simultaneously. Thus the over sixty-year-old material is finally thinned down by seven orders of magnitude into a 65.5 nm thick and 0.64 m² large lamellar-thin framework (LTF). LTF exhibits a series of exceptional properties such as over-95% transparency, and seven times higher specific strength referred to steel. For the first time, cryogenic electron microscopy (Cryo-EM) is utilized to observe commodity polymers directly. This new LDHA material is promising to expand the scale boundaries of both fundamental research and practical applications, not only for UHMWPE, but also for more commodity polymers to come.

Mode-coupling theory for tagged-particle motion of active Brownian particles

We derive a mode-coupling theory (MCT) to describe the dynamics of a tracer particle that is embedded in a dense system of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian motion and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density-correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a single active particle in a glass-forming passive host suspensions, that of a passive colloidal particle in a suspension of ABP, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We confirm in the simulations a peculiar feature of the transient and stationary dynamical density-correlation functions regarding their lack of symmetry under time reversal, demonstrating the nonequilibrium nature of the system and how it manifests itself in the theory.

Unveiling unconventional magnetism at the surface of Sr2RuO4

Materials with strongly correlated electrons often exhibit interesting physical properties. An example of these materials is the layered oxide perovskite Sr₂RuO₄, which has been intensively investigated due to its unusual properties. Whilst the debate on the symmetry of the superconducting state in Sr₂RuO₄ is still ongoing, a deeper understanding of the Sr₂RuO₄ normal state appears crucial as this is the background in which electron pairing occurs. Here, by using low-energy muon spin spectroscopy we discover the existence of surface magnetism in Sr₂RuO₄ in its normal state. We detect static weak dipolar fields yet manifesting at an onset temperature higher than 50 K. We ascribe this unconventional magnetism to orbital loop currents forming at the reconstructed Sr₂RuO₄ surface. Our observations set a reference for the discovery of the same magnetic phase in other materials and unveil an electronic ordering mechanism that can influence electron pairing with broken time reversal symmetry.

Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τ_ατ_D between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τ_ατ_D∝⟨t_p⟩⟨t_c⟩, where ⟨t_p⟩ and ⟨t_c⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τ_α∝⟨t_p⟩⟨Δr_J ²⟩ and τ_D∝⟨t_c⟩⟨Δr_J ²⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨Δr_J ²⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

Structural and short-time vibrational properties of colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition

We investigate the short-time vibrational properties and structure of two-dimensional, bidisperse, colloidal glasses and supercooled liquids in the vicinity of the re-entrant glass transition, as a function of interparticle depletion attraction strength. The long-time spatiotemporal dynamics of the samples are measured to be non-monotonic, confirming that the suspensions evolve from repulsive glass to supercooled liquid to attractive glass with increasing depletion attraction. Here, we search for vibrational signatures of the re-entrant behavior in the short-time spatiotemporal dynamics, i.e., dynamics associated with particle motion inside its nearest-neighbor cage. Interestingly, we observe that the anharmonicity of these in-cage vibrations varies non-monotonically with increasing attraction strength, consistent with the non-monotonic long-time structural relaxation dynamics of the re-entrant glass. We also extract effective spring constants between neighboring particles; we find that spring stiffness involving small particles also varies non-monotonically with increasing attraction strength, while stiffness between large particles increases monotonically. Last, from study of depletion-dependent local structure and vibration participation fractions, we gain microscopic insight into the particle-size-dependent contributions to short-time vibrational modes in the glass and supercooled liquid states.

Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode Coupling Temperature

As liquids approach the glass transition temperature, dynamical heterogeneity emerges as a crucial universal feature of their behavior. Dynamic facilitation, where local motion triggers further motion nearby, plays a major role in this phenomenon. Here we show that long-ranged, elastically mediated facilitation appears below the mode coupling temperature, adding to the short-range component present at all temperatures. Our results suggest deep connections between the supercooled liquid and glass states, and pave the way for a deeper understanding of dynamical heterogeneity in glassy systems.

Mobilization upon Cooling

Phase transitions between different aggregate states are omnipresent in nature and technology. Conventionally, a crystalline phase melts upon heating as we use ice to cool a drink. Already in 1903, Gustav Tammann speculated about the opposite process, namely melting upon cooling. So far, evidence for such "inverse" transitions in real materials is rare and limited to few systems or extreme conditions. Here, we demonstrate an inverse phase transition for molecules adsorbed on a surface. Molybdenum tetraacetate on copper(111) forms an ordered structure at room temperature, which dissolves upon cooling. This transition is mediated by molecules becoming mobile, i.e., by mobilization upon cooling. This unexpected phenomenon is ascribed to the larger number of internal degrees of freedom in the ordered phase compared to the mobile phase at low temperatures.

Mechanisms of Spontaneous Curvature Inversion in Compressed Graphene Ripples for Energy Harvesting Applications via Molecular Dynamics Simulations

Electrically conductive, highly flexible graphene membranes hold great promise for harvesting energy from ambient vibrations. For this study, we built numerous three-dimensional graphene ripples, with each featuring a different amount of compression, and performed molecular dynamics simulations at elevated temperatures. These ripples have a convex cosine shape, then spontaneously invert their curvature to concave. The average time between inversion events increases with compression. We use this to determine how the energy barrier height depends on strain. A typical convex-to-concave curvature inversion process begins when the ripple's maximum shifts sideways from the normal central position toward the fixed outer edge. The ripple's maximum does not simply move downward toward its concave position. When the ripple's maximum moves toward the outer edge, the opposite side of the ripple is pulled inward and downward, and it passes through the fixed outer edge first. The ripple's maximum then quickly flips to the opposite side via snap-through buckling. This trajectory, along with local bond flexing, significantly lowers the energy barrier for inversion. The large-scale coherent movement of ripple atoms during curvature inversion is unique to two-dimensional materials. We demonstrate how this motion can induce an electrical current in a nearby circuit.

2D Colloidal Crystals with Anisotropic Impurities

We report a study of 2D colloidal crystals with anisotropic ellipsoid impurities using video microscopy. It is found that at low impurity densities, the impurity particles behave like floating disorder with which the quasi-long-range orientational order survives and the elasticity of the system is actually enhanced. There is a critical impurity density above which the 2D crystal loses the quasi-long-range orientational order. At high impurity densities, the 2D crystal breaks into polycrystalline domains separated by grain boundaries where the impurity particles aggregate. This transition is accompanied by a decrease in the elastic moduli, and it is associated with strong heterogeneous dynamics in the system. The correlation length vs impurity density in the disordered phase exhibits an essential singularity at the critical impurity density.

Translational dynamics of a rod-like probe in supercooled liquids: an experimentally realizable method to study Stokes-Einstein breakdown, dynamic heterogeneity, and amorphous order

The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and in experiments. A lot of important information which is not immediately accessible from bulk measurements can be accessed via these local measurements. Still, a detailed understanding of how a probe particle dynamics is affected by the surrounding liquid medium is lacking, especially in the supercooled temperature regime. This work shows how the translational dynamics of a rod-like particle immersed in a supercooled liquid can give us information on the growth of the correlation length scales associated with dynamical heterogeneity and the multi-body static correlations in the medium. This work also provides an understanding of the breakdown of Stokes-Einstein and Stokes-Einstein-Debye relations in supercooled liquids along with a unified scaling theory that rationalizes all the observed results. Finally, this work proposes a novel yet simple method accessible in experiments to measure the growth of these important length scales in molecular glass-forming liquids.

Neglecting polydispersity degrades propensity measurements in supercooled liquids

We conduct molecular dynamics simulations of a bidisperse Kob-Andersen (KA) glass former, modified to add in additional polydispersity. The original KA system is known to exhibit dynamical heterogeneity. Prior work defined propensity, the mean motion of a particle averaged over simulations reconstructing the initial positions of all particles but with randomized velocities. The existence of propensity shows that structure and dynamics are connected. In this paper, we study systems which mimic problems that would be encountered in measuring propensity in a colloidal glass former, where particles are polydisperse (they have slight size variations). We mimic polydispersity by altering the bidisperse KA system into a quartet consisting of particles both slightly larger and slightly smaller than the parent particles in the original bidisperse system. We then introduce errors into the reconstruction of the initial positions that mimic mistakes one might make in a colloidal experiment. The mistakes degrade the propensity measurement, in some cases nearly completely; one no longer has an iso-configurational ensemble in any useful sense. Our results show that a polydisperse sample is suitable for propensity measurements provided one avoids reconstruction mistakes.

Mechanical properties of 2D aggregates of oil droplets as model mono-crystals

We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

Connecting relaxation time to a dynamical length scale in athermal active glass formers

Supercooled liquids display dynamics that are inherently heterogeneous in space. This essentially means that at temperatures below the melting point, particle dynamics in certain regions of the liquid can be orders of magnitude faster than other regions. Often dubbed dynamical heterogeneity, this behavior has fascinated researchers involved in the study of glass transition for over two decades. A fundamentally important question in all glass transition studies is whether one can connect the growing relaxation time to a concomitantly growing length scale. In this paper, we go beyond the realm of ordinary glass forming liquids and study the origin of a growing dynamical length scale ξ in a self-propelled "active" glass former. This length scale, which is constructed using structural correlations, agrees well with the average size of the clusters of slow-moving particles that are formed as the liquid becomes spatially heterogeneous. We further report that the concomitantly growing α-relaxation time exhibits a simple scaling law, τ_{α}∼exp(μξ/T_{eff}), with μ as an effective chemical potential, T_{eff} as the effective temperature, and μξ as the growing free energy barrier for cluster rearrangements. The findings of our study are valid over four decades of persistence times, and hence they could be very useful in understanding the slow dynamics of a generic active liquid such as an active colloidal suspension, or a self-propelled granular medium.

Cooperatively rearranging regions change shape near the mode-coupling crossover for colloidal liquids on a sphere

The structure and dynamics of liquids on curved surfaces are often studied through the lens of frustration-based approaches to the glass transition. Competing glass transition theories, however, remain largely untested on such surfaces and moreover, studies hitherto have been entirely theoretical/numerical. Here we carry out single particle-resolved imaging of dynamics of bi-disperse colloidal liquids confined to the surface of a sphere. We find that mode-coupling theory well captures the slowing down of dynamics in the moderate to deeply supercooled regime. Strikingly, the morphology of cooperatively rearranging regions changed from string-like to compact near the mode-coupling crossover—a prediction unique to the random first-order theory of glasses. Further, we find that in the limit of strong curvature, Mermin–Wagner long-wavelength fluctuations are irrelevant and liquids on a sphere behave like three-dimensional liquids. A comparative evaluation of competing mechanisms is thus an essential step towards uncovering the true nature of the glass transition.

The static and dynamic behavior of condensed phases residing on curved surfaces can be fundamentally different from their counterparts in Euclidean space. Singh et al. test several competing glass theories on colloidal liquids confined to the surface of a sphere and show they behave like 3D bulk liquids.

Pattern detection in colloidal assembly: A mosaic of analysis techniques

Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.

Hierarchical glass transition of hard hemidisks with local assemblies

Using computer simulation, we investigate the glass transition of a two-dimensional hard-hemidisk system. Upon increasing the packing fraction of the system, we find that the system vitrifies into a glass with local assembled discal "dimers", which are free to rotate in a collective way. The rotational mean square displacement does not exhibit the typical plateau (slowdown) like what occurs in the translational mean square displacement. This effect induces a pronounced violation of the rotational Stokes-Einstein relationship compared with the translational degree of freedom at the supercooled region. However, the obtained glass transition points in these two freedom degrees are found to be the same within the numerical accuracy, which is due to the strong positive spatial and dynamic correlation between translational and rotational slow-moving particles. Moreover, we find that the locally assembled dimers can serve as fast rotating gears facilitating the orientational relaxation in the system, and this suggests that the locally favored finite structures play an important role in the hierarchical glass transition of anisotropic colloids.

Dense hard disk ordering: influence of bidispersity and quenched disorder

Using Monte Carlo simulations, the impact on structural ordering in two-dimensional systems via the interplay of size bidispersity and quenched disorder in the form of an externally applied spatially random potential, is studied for a system of hard disks. By scanning across a wide range of dense packing fractions, size ratios and roughness of the applied potential, the phase diagram is constructed, which demonstrates that both quenched and size disorders shift the onset of translational order to higher packings, while maintaining the presence of the intermediate hexatic phase. At larger disorder strengths, the signatures of structural order are absent within the range of investigated packing fractions. Further, the dynamics with increasing potential strength is analysed for the mono-component system to obtain a spatio-temporal description of the melting process. Finally, the influence of the externally rough field on the Mermin-Wagner fluctuations, characteristic to two-dimensional systems, is investigated.

Role of Attractive Interactions in Structure Ordering and Dynamics of Glass-Forming Liquids

A key question in glass physics is what the origin of slow glassy dynamics is. The liquid structure is a natural candidate; however, an apparently severe counterexample has been known. Two model glass-forming liquids, with the standard Lennard-Jones interaction potential and its Weeks-Chandler-Andersen variation without the attractive tail, exhibit very similar structures at the two-body level but drastically different dynamical behaviors in the supercooled states. Here we look at the liquid structure through a (many-body) structural order parameter Θ characterizing the packing capability of local particle arrangements. We show that the structures of these two systems seen by Θ are actually very different at a many-body level, but, quite surprisingly, the macroscopic structure (Θ)-dynamics (τ_{α}) relationships commonly follow a Vogel-Fulcher-Tammann-like function. Furthermore, the mutual information analysis reveals strong local structure-dynamics correlations. Therefore, we conclude that attractive interactions affect the liquid structure in a nonperturbative manner, but a general structural origin of slow dynamics holds for these systems.

Long-time self-diffusion in quasi-two-dimensional colloidal fluids of paramagnetic particles

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r^{3}, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D_{L}^{★}=D_{L}/(D_{0}Γ^{1/2}), with D_{0} the self-diffusion coefficient at infinite dilution and D_{L} the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r^{3} long-ranged DI, the reduced quantity D_{L}^{★} is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.