Understanding the low-frequency quasilocalized modes in disordered colloidal systems

Revealing the three-component structure of water with principal component analysis (PCA) of X-ray spectra

Combining principal component analysis (PCA) of X-ray spectra with MD simulations, we experimentally reveal the existence of three basic components in water. These components exhibit distinct structures, densities, and temperature dependencies. Among the three, the two major components correspond to the low-density liquid (LDL) and the high-density liquid (HDL) predicted by the two-component model, and the third component exhibits a unique 5-hydrogen-bond configuration with ultra-high local density. As the temperature increases, the LDL component decreases and the HDL component increases, while the third component varies non-monotonically with a peak around 20 °C to 30 °C. The 3D structure of the third component is further illustrated as the uniform distribution of five hydrogen-bonded neighbors on a spherical surface. Our study reveals experimental evidence for water's possible three-component structure, which provides a fundamental basis for understanding water's special properties and anomalies.

Phonon eigenfunctions of inhomogeneous lattices: Can you hear the shape of a cone?

We study the phonon modes of interacting particles on the surface of a truncated cone resting on a plane subject to gravity, inspired by recent colloidal experiments. We derive the ground-state configuration of the particles under gravitational pressure in the small-cone-angle limit and find an inhomogeneous triangular lattice with spatially varying density but robust local order. The inhomogeneity has striking effects on the normal modes such that an important feature of the cone geometry, namely its apex angle, can be extracted from the lattice excitations. The shape of the cone leads to energy crossings at long wavelengths and frequency-dependent quasilocalization at short wavelengths. We analytically derive the localization domain boundaries of the phonons in the limit of small cone angle and check our results with numerical results for eigenfunctions.

Critical point of jamming transition in two-dimensional monodisperse systems

The existence of amorphous packings in two-dimensional monodisperse system is a classical unsolved problem. We get the energy minimum state by the energy minimization method of enthalpy under constant pressure conditions. Firstly, we find that there are two peaks in the experiment, which demonstrate the interesting features of the coexistence of crystals and amorphous crystals. And then, we confirm the critical point of jamming transition of the two-dimensional monodisperse is [Formula: see text]. Finally, we prove that the jamming scaling is still satisfied in two-dimensional monodispersed system: [Formula: see text] and vanishes as [Formula: see text], and the boson peak shifts to lower frequencies for less compressed systems.

Mechanical oscillation accelerating nucleation and nuclei growth in hard-sphere colloidal glass

Crystallization from amorphous solids is generally caused by activating phonons in a wide frequency range during heat treatment. In contrast, the activation of phonons in a narrow frequency range using ultrasonic treatment also causes crystallization below the glass transition temperature. These behaviors indicate that crystallization is related to the atomic motion in the glass state, and it is suggested that the activation of specific atomic motion can cause crystallization without increasing temperature. In this study, we observe nucleation and nuclei growth caused by mechanical oscillation in a hard-sphere colloidal glass and evaluate the effect of mechanical oscillation on the structural evolution in the early stage of the crystallization. Oscillation between 5 and 100 Hz is applied to the colloidal glass, and it is observed that the nucleation rate increases under the 70 Hz oscillation, resulting in formation of stable nuclei in a short amount of time. The nuclei growth is also accelerated by the 70 Hz oscillation, whereas increases in the nucleation rate and nuclei growth were not observed at other frequencies. Finally, activation of the diffusion-based rattling of particles by caging is considered as a possible mechanism of the observations.

A universal state and its relaxation mechanisms of long-range interacting polygons

Using polygonal magnetic particles, we conduct experiments to explore the space-filling properties of anisotropic blocks with long-range interactions. In contrast to previous studies, we obtain the surprising finding that our systems' structures do not depend on the shape of building blocks: a single state, the hexagonal plastic crystal, appears as a universal attractor for a wide range of different polygons. This robust particle-shape independency appears as the interactions go beyond nearest neighbors. Particle shape plays an essential role in system relaxation, and determines the basic relaxation dynamics through a microscopic control parameter, internal roughness, produced by particle vertices. Thus our study reveals a new pattern-forming paradigm, in which particle shape plays little role in the static structure but determines the essential relaxation dynamics. Due to the ubiquity of long-range interactions and anisotropic building blocks, our discovery may shed new light on diverse problems involving structure formation, self-assembly, and packing.

Determining Quiescent Colloidal Suspension Viscosities Using the Green-Kubo Relation and Image-Based Stress Measurements

By combining confocal microscopy and stress assessment from local structural anisotropy, we directly measure stresses in 3D quiescent colloidal liquids. Our noninvasive and nonperturbative method allows us to measure forces ≲50  fN with a small and tunable probing volume, enabling us to resolve the stress fluctuations arising from particle thermal motions. We use the Green-Kubo relation to relate these measured stress fluctuations to the bulk Brownian viscosity at different volume fractions, comparing against simulations and conventional rheometry measurements. We find that the Green-Kubo analysis gives excellent agreement with these prior results, suggesting that similar methods could be applied to investigations of local flow properties in many poorly understood far-from-equilibrium systems, including suspensions that are glassy, strongly sheared, or highly confined.

Experimental studies of vibrational modes in a two-dimensional amorphous solid

The boson peak, which represents an excess of vibrational states compared to Debye’s prediction at low frequencies, has been studied extensively, and yet, its nature remains controversial. In this study, we focus on understanding the nature of the boson peak based on the spatial heterogeneity of modulus fluctuations using a simple model system of a highly jammed two-dimensional granular material. Despite the simplicity of our system, we find that the boson peak in our two-dimensional system shows a shape very similar to that of three-dimensional molecular glasses when approaching their boson peak frequencies. Our finding indicates a strong connection between the boson peak and the spatial heterogeneity of shear modulus fluctuations.

The low-frequency collective vibrational modes, known as the boson peak, characterize many glasses at low temperature, yet its origin remains elusive. Zhang et al. show a correlation between the boson peak and the spatial heterogeneity of shear modulus fluctuation in a two-dimensional granular system.

Accelerated crystallization of colloidal glass by mechanical oscillation

Crystallization of a hard-sphere colloidal glass by mechanical oscillation is investigated, and accelerated crystallization is found at a specific frequency. The crystallization frequency increases as attractive force between particles increases, indicating that interparticle interaction affects the crystallization frequency. Time scale of the mechanical oscillation is different from that of the slow relaxation, and notable relationship with the low-frequency mode is not observed. The experimental results are not explained by the previously proposed model for crystallization by oscillatory shear. Conversely, we speculate that activations of the fast relaxation and particle motion in crystal-like clusters are possible causes of the observations.

Excitation of vibrational soft modes in disordered systems using active oscillation

We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional athermal jammed system by giving a small amplitude of active oscillation to each particle's size with an identical driving frequency. The response is then obtained as the real time displacements of the particles. We show remarkable correlations between the real time displacements and the eigen vectors obtained from conventional normal mode analysis. More importantly, from these real time displacements, we can measure the participation ratio and spatial polarization of particles' vibrations. From these measurements, we find three distinct frequency regimes which characterize the spatial distribution and correlation of particles' vibrations in jammed amorphous solids. Furthermore, we can possibly apply this method to a much larger system to examine the low frequency behaviour of amorphous solids with a much higher resolution of the frequency space.

Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation

By using large-scale molecular dynamics simulations, the dynamics of two-dimensional (2D) supercooled liquids turns out to be dependent on the system size, while the size dependence is not pronounced in three-dimensional (3D) systems. It is demonstrated that the strong system-size effect in 2D amorphous systems originates from the enhanced fluctuations at long wavelengths which are similar to those of 2D crystal phonons. This observation is further supported by the frequency dependence of the vibrational density of states, consisting of the Debye approximation in the low-wave-number limit. However, the system-size effect in the intermediate scattering function becomes negligible when the length scale is larger than the vibrational amplitude. This suggests that the finite-size effect in a 2D system is transient and also that the structural relaxation itself is not fundamentally different from that in a 3D system. In fact, the dynamic correlation lengths estimated from the bond-breakage function, which do not suffer from those enhanced fluctuations, are not size dependent in either 2D or 3D systems.

Evidence for Marginal Stability in Emulsions

We report the first measurements of the effect of pressure on vibrational modes in emulsions, which serve as a model for soft frictionless spheres at zero temperature. As a function of the applied pressure, we find that the density of states D(ω) exhibits a low-frequency cutoff ω^{*}, which scales linearly with the number of extra contacts per particle δz. Moreover, for ω<ω^{*}, our results are consistent with D(ω)∼ω^{2}/ω^{*2}, a quadratic behavior whose prefactor is larger than what is expected from Debye theory. This surprising result agrees with recent theoretical findings [E. DeGiuli, A. Laversanne-Finot, G. A. Düring, E. Lerner, and M. Wyart, Soft Matter 10, 5628 (2014); S. Franz, G. Parisi, P. Urbani, and F. Zamponi, Proc. Natl. Acad. Sci. U.S.A. 112, 14539 (2015)]. Finally, the degree of localization of the softest low frequency modes increases with compression, as shown by the participation ratio as well as their spatial configurations. Overall, our observations show that emulsions are marginally stable and display non-plane-wave modes up to vanishing frequencies.

Vibrational properties of quasi-two-dimensional colloidal glasses with varying interparticle attraction

We measure the vibrational modes and particle dynamics of quasi-two-dimensional colloidal glasses as a function of interparticle interaction strength. The interparticle attractions are controlled via a temperature-tunable depletion interaction. Specifically, the interparticle attraction energy is increased gradually from a very small value (nearly hard-sphere) to moderate strength (∼4k_{B}T), and the variation of colloidal particle dynamics and vibrations are concurrently probed. The particle dynamics slow monotonically with increasing attraction strength, and the particle motions saturate for strengths greater than ∼2k_{B}T, i.e., as the system evolves from a nearly repulsive glass to an attractive glass. The shape of the phonon density of states is revealed to change with increasing attraction strength, and the number of low-frequency modes exhibits a crossover for glasses with weak compared to strong interparticle attraction at a threshold of ∼2k_{B}T. This variation in the properties of the low-frequency vibrational modes suggests a new means for distinguishing between repulsive and attractive glass states.

Probing the Role of Mobility in the Collective Motion of Nonequilibrium Systems

By systematically varying the mobility of self-propelled particles in a 2D lattice, we experimentally study the influence of particle mobility on system's collective motion. Our system is intrinsically nonequilibrium due to the lack of energy equipartition. By constructing the covariance matrix of spatial fluctuations and solving for its eigenmodes, we obtain the collective motions of the system with various magnitudes. Interestingly, our structurally ordered nonequilibrium system exhibits properties almost identical to disordered glassy systems under thermal equilibrium: the modes with large overall motions are spatially correlated and quasilocalized while the modes with small collective motions are highly localized, resembling the low- and high-frequency modes in glass. More surprisingly, a peak similar to the boson peak forms in our nonequilibrium system as the number of mobile particles increases, revealing the possible origin of the boson peak from a dynamic aspect. We further illustrate that the spatially correlated large-movement modes can be produced by the cooperation of highly active particles above a threshold fraction, while the localized small-movement modes can be created by adding individual inactive particles. Our study clarifies the role of mobility in collective motions, and further suggests a promising possibility of extending the powerful mode analysis approach to nonequilibrium systems.

Disordered solids without well-defined transverse phonons: the nature of hard-sphere glasses

We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by calculating the dynamical structure factors. The Ioffe-Regel limit (frequency) is reached when the phonon wavelength is comparable to the mean free path, beyond which phonons are no longer well defined. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamminglike transition and glass transition, respectively. As a consequence, glasses between the glass transition and the jamminglike transition, which are hard-sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.

Dependence of the atomic level Green-Kubo stress correlation function on wavevector and frequency: molecular dynamics results from a model liquid

We report on a further investigation of a new method that can be used to address vibrational dynamics and propagation of stress waves in liquids. The method is based on the decomposition of the macroscopic Green-Kubo stress correlation function into the atomic level stress correlation functions. This decomposition, as was demonstrated previously for a model liquid studied in molecular dynamics simulations, reveals the presence of stress waves propagating over large distances and a structure that resembles the pair density function. In this paper, by performing the Fourier transforms of the atomic level stress correlation functions, we elucidate how the lifetimes of the stress waves and the ranges of their propagation depend on their frequency, wavevector, and temperature. These results relate frequency and wavevector dependence of the generalized viscosity to the character of propagation of the shear stress waves. In particular, the results suggest that an increase in the value of the frequency dependent viscosity at low frequencies with decrease of temperature is related to the increase in the ranges of propagation of the stress waves of the corresponding low frequencies. We found that the ranges of propagation of the shear stress waves of frequencies less than half of the Einstein frequency extend well beyond the nearest neighbor shell even above the melting temperature. The results also show that the crossover from quasilocalized to propagating behavior occurs at frequencies usually associated with the Boson peak.

Soft spots and their structural signature in a metallic glass

In a 3D model mimicking realistic Cu64Zr36 metallic glass, we uncovered a direct link between the quasi-localized low-frequency vibrational modes and the local atomic packing structure. We also demonstrate that quasi-localized soft modes correlate strongly with fertile sites for shear transformations: geometrically unfavored motifs constitute the most flexible local environments that encourage soft modes and high propensity for shear transformations, whereas local configurations preferred in this alloy, i.e., the full icosahedra (around Cu) and Z16 Kasper polyhedra (around Zr), contribute the least.

Phonons in two-dimensional soft colloidal crystals

The vibrational modes of pristine and polycrystalline monolayer colloidal crystals composed of thermosensitive microgel particles are measured using video microscopy and covariance matrix analysis. At low frequencies, the Debye relation for two-dimensional harmonic crystals is observed in both crystal types; at higher frequencies, evidence for van Hove singularities in the phonon density of states is significantly smeared out by experimental noise and measurement statistics. The effects of these errors are analyzed using numerical simulations. We introduce methods to correct for these limitations, which can be applied to disordered systems as well as crystalline ones, and we show that application of the error correction procedure to the experimental data leads to more pronounced van Hove singularities in the pristine crystal. Finally, quasilocalized low-frequency modes in polycrystalline two-dimensional colloidal crystals are identified and demonstrated to correlate with structural defects such as dislocations, suggesting that quasilocalized low-frequency phonon modes may be used to identify local regions vulnerable to rearrangements in crystalline as well as amorphous solids.

String-like cooperative motion in homogeneous melting

Despite the fundamental nature and practical importance of melting, there is still no generally accepted theory of this ubiquitous phenomenon. Even the earliest simulations of melting of hard discs by Alder and Wainwright indicated the active role of collective atomic motion in melting and here we utilize molecular dynamics simulation to determine whether these correlated motions are similar to those found in recent studies of glass-forming (GF) liquids and other condensed, strongly interacting, particle systems. We indeed find string-like collective atomic motion in our simulations of "superheated" Ni crystals, but other observations indicate significant differences from GF liquids. For example, we observe neither stretched exponential structural relaxation, nor any decoupling phenomenon, while we do find a boson peak, findings that have strong implications for understanding the physical origin of these universal properties of GF liquids. Our simulations also provide a novel view of "homogeneous" melting in which a small concentration of interstitial defects exerts a powerful effect on the crystal stability through their initiation and propagation of collective atomic motion. These relatively rare point defects are found to propagate down the strings like solitons, driving the collective motion. Crystal integrity remains preserved when the permutational atomic motions take the form of ring-like atomic exchanges, but a topological transition occurs at higher temperatures where the rings open to form linear chains similar in geometrical form and length distribution to the strings of GF liquids. The local symmetry breaking effect of the open strings apparently destabilizes the local lattice structure and precipitates crystal melting. The crystal defects are thus not static entities under dynamic conditions, such as elevated temperatures or material loading, but rather are active agents exhibiting a rich nonlinear dynamics that is not addressed in conventional "static" defect melting models.

Glassy Interfacial Dynamics of Ni Nanoparticles: Part II Discrete Breathers as an Explanation of Two-Level Energy Fluctuations

Recent studies of the dynamics of diverse condensed amorphous materials have indicated significant heterogeneity in the local mobility and a progressive increase in collective particle motion upon cooling that takes the form of string-like particle rearrangements. In a previous paper (Part I), we examined the possibility that fluctuations in potential energy E and particle mobility μ associated with this 'dynamic heterogeneity' might offer information about the scale of collective motion in glassy materials based on molecular dynamics simulations of the glassy interfacial region of Ni nanoparticles (NPs) at elevated temperatures. We found that the noise exponent associated with fluctuations in the Debye-Waller factor, a mobility related quantity, was directly proportional to the scale of collective motion L under a broad range of conditions, but the noise exponent associated with E(t) fluctuations was seemingly unrelated to L. In the present work, we focus on this unanticipated difference between potential energy and mobility fluctuations by examining these quantities at an atomic scale. We find that the string atoms exhibit a jump-like motion between two well-separated bands of energy states and the rate at which these jumps occur seems to be consistent with the phenomenology of the 'slow-beta' relaxation process of glass-forming liquids. Concurrently with these local E(t) jumps, we also find 'quake-like' particle displacements having a power-law distribution in magnitude so that particle displacement fluctuations within the strings are strikingly different from local E(t) fluctuations. An analysis of these E(t) fluctuations suggests that we are dealing with 'discrete breather' excitations in which large energy fluctuations develop in arrays of non-linear oscillators by virtue of large anharmonicity in the interparticle interactions and discreteness effects associated with particle packing. We quantify string collective motions on a fast caging times scale (picoseconds) and explore the significance of these collective motions for understanding the Boson peak of glass-forming materials.

Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids

There are at least three fundamental states of matter, depending upon temperature and pressure: gas, liquid, and solid (crystal). These states are separated by first-order phase transitions between them. In both gas and liquid phases a complete translational and rotational symmetry exist, whereas in a solid phase both symmetries are broken. In intermediate phases between liquid and solid, which include liquid crystal and plastic crystal phases, only one of the two symmetries is preserved. Among the fundamental states of matter, the liquid state is the most poorly understood. We argue that it is crucial for a better understanding of liquids to recognize that a liquid generally has the tendency to have a local structural order and its presence is intrinsic and universal to any liquid. Such structural ordering is a consequence of many-body correlations, more specifically, bond angle correlations, which we believe are crucial for the description of the liquid state. We show that this physical picture may naturally explain difficult unsolved problems associated with the liquid state, such as anomalies of water-type liquids (water, Si, Ge, ...), liquid-liquid transition, liquid-glass transition, crystallization and quasicrystal formation, in a unified manner. In other words, we need a new order parameter representing a low local free-energy configuration, which is a bond orientational order parameter in many cases, in addition to a density order parameter for the physical description of these phenomena. Here we review our two-order-parameter model of liquid and consider how transient local structural ordering is linked to all of the above-mentioned phenomena. The relationship between these phenomena is also discussed.

Force propagation in isostatic granular packs

We investigate how forces spread through frictionless granular packs at the jamming transition. Previous work has indicated that such packs are isostatic, and thus obey a null stress law which, independent of the packing history, causes rays of stress to propagate away from a point force at oblique angles. Prior verifications of the null stress law have used a sequential packing method which yields packs with anisotropic packing histories. We create packs without this anisotropy, and then later break the symmetry by adding a boundary. Our isotropic packs are very sensitive, and their responses to point forces diverge wildly, indicating that they cannot be described by any continuum stress model. We stabilize the packs by supplying an additional boundary, which makes the response much more regular. The response of the stabilized packs resembles what one would expect in a hyperstatic pack, despite the isostatic bulk. The expected stress rays characteristic of null stress behavior are not present. This suggests that isostatic packs do not need to obey a null stress condition. We argue that the rays may arise instead from more simple geometric considerations, such as preferred contact angles between beads.