Universal law for the vibrational density of states of liquids.

An analytical derivation of the vibrational density of states (DOS) of liquids, and, in particular, of its characteristic linear in frequency low-energy regime, has always been elusive because of the presence of an infinite set of purely imaginary modes-the instantaneous normal modes (INMs). By combining an analytic continuation of the Plemelj identity to the complex plane with the overdamped dynamics of the INMs, we derive a closed-form analytic expression for the low-frequency DOS of liquids. The obtained result explains, from first principles, the widely observed linear in frequency term of the DOS in liquids, whose slope appears to increase with the average lifetime of the INMs. The analytic results are robustly confirmed by fitting simulations data for Lennard-Jones liquids, and they also recover the Arrhenius law for the average relaxation time of the INMs, as expected.

Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding.

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, ϕRCP, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find ϕRCP to increase monotonically with the relative standard deviation, sσ, of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for ϕRCP that quantitatively captures a distribution-independent regime for sσ < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.

Explaining the low-frequency shear elasticity of confined liquids.

Experimental observations of unexpected shear rigidity in confined liquids, on very low frequency scales on the order of 0.01 to 0.1 Hz, call into question our basic understanding of the elasticity of liquids and have posed a challenge to theoretical models of the liquid state ever since. Here we combine the nonaffine theory of lattice dynamics valid for disordered condensed matter systems with the Frenkel theory of the liquid state. The emerging framework shows that applying confinement to a liquid can effectively suppress the low-frequency modes that are responsible for nonaffine soft mechanical response, thus leading to an effective increase of the liquid shear rigidity. The theory successfully predicts the scaling law [Formula: see text] for the low-frequency shear modulus of liquids as a function of the confinement length L, in agreement with experimental results, and provides the basis for a more general description of the elasticity of liquids across different time and length scales.

Explicit Analytical Solution for Random Close Packing in d=2 and d=3.

We present an analytical derivation of the volume fractions for random close packing (RCP) in both d=3 and d=2, based on the same methodology. Using suitably modified nearest neighbor statistics for hard spheres, we obtain ϕ_{RCP}=0.658 96 in d=3 and ϕ_{RCP}=0.886 48 in d=2. These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This statistical derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammed state and dictates ϕ_{RCP} via the coordination number z, (iii) disordered packings with ϕ>ϕ_{RCP} are possible at the expense of creating some order, and z=12 at the fcc limit acts as a boundary condition.

Erratum: Explicit Analytical Solution for Random Close Packing in d=2 and d=3 [Phys. Rev. Lett. 128, 028002 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.028002.

Combined description of pressure-volume-temperature and dielectric relaxation of several polymeric and low-molecular-weight organic glass-formers using SL-TS2 approach.

We apply our recently-developed mean-field "SL-TS2" (two-state Sanchez-Lacombe) model to simultaneously describe dielectric α-relaxation time, τα, and pressure-volume-temperature (PVT) data in four polymers (polystyrene, poly(methylmethacrylate), poly(vinyl acetate) and poly(cyclohexane methyl acrylate)) and four organic molecular glass formers (ortho-terphenyl, glycerol, PCB-62, and PDE). Previously, it has been shown that for all eight materials, the Casalini-Roland thermodynamical scaling, τα = f(Tvγsp) (where T is temperature and vsp is specific volume) is satisfied (R. Casalini and C. M. Roland, Phys. Rev. E, 2004, 69(6), 62501). It has also been previously shown that the same scaling emerges naturally (for sufficiently low pressures) within the "SL-TS2" framework (V. V. Ginzburg, Soft Matter, 2021, 17, 9094-9106). Here, we fit the ambient pressure curves for the relaxation time and the specific volume as functions of temperature for the eight materials and observe a good agreement between theory and experiment. We then use the Casalini-Roland scaling to convert those results into "master curves", thus enabling predictions of relaxation times and specific volumes at elevated pressures. The proposed approach can be used to describe other glass-forming materials, both low-molecular-weight and polymeric.

Plasticity in Amorphous Solids Is Mediated by Topological Defects in the Displacement Field.

The microscopic mechanism by which amorphous solids yield plastically under an externally applied stress or deformation has remained elusive in spite of enormous research activity in recent years. Most approaches have attempted to identify atomic-scale structural "defects" or spatiotemporal correlations in the undeformed glass that may trigger plastic instability. In contrast, in this Letter we show that the topological defects that correlate with plastic instability can be identified, not in the static structure of the glass, but rather in the nonaffine displacement field under deformation. These dislocation-like topological defects (DTDs) can be quantitatively characterized in terms of Burgers circuits (and the resulting Burgers vectors) that are constructed on the microscopic nonaffine displacement field. We demonstrate that (i) DTDs are the manifestation of incompatibility of deformation in glasses as a result of violation of Cauchy-Born rules (nonaffinity); (ii) the resulting average Burgers vector displays peaks in correspondence of major plastic events, including a spectacular nonlocal peak at the yielding transition, which results from self-organization into shear bands due to the attractive interaction between antiparallel DTDs; and (iii) application of Schmid's law to the DTDs leads to prediction of shear bands at 45° for uniaxial deformations, as widely observed in experiments and simulations.

Theory of Pressure-Induced Rejuvenation and Strain Hardening in Metallic Glasses.

We theoretically investigate high-pressure effects on the atomic dynamics of metallic glasses. The theory predicts compression-induced rejuvenation and the resulting strain hardening that have been recently observed in metallic glasses. Structural relaxation under pressure is mainly governed by local cage dynamics. The external pressure restricts the dynamical constraints and slows down the atomic mobility. In addition, the compression induces a rejuvenated metastable state (local minimum) at a higher energy in the free-energy landscape. Thus, compressed metallic glasses can rejuvenate and the corresponding relaxation is reversible. This behavior leads to strain hardening in mechanical deformation experiments. Theoretical predictions agree well with experiments.

Physics of phonon-polaritons in amorphous materials.

The nature of bosonic excitations in disordered materials has remained elusive due to the difficulties in defining key concepts such as quasi-particles in the presence of disorder. We report on an experimental observation of phonon-polaritons in glasses, including a prominent boson peak (BP), i.e., excess of THz modes over the Debye law. A theoretical framework based on the concept of diffusons is developed to describe the broadening linewidth of the polariton due to disorder-induced scattering. It is shown here for the first time that the BP frequency and the Ioffe-Regel (IR) crossover frequency of the polariton collapse onto the same power-law decay with the diffusivity of the bosonic excitation. This analysis dismisses the hypothesis of the BP being caused by a relic of the van Hove singularity. The presented framework establishes a new methodology to analyze bosonic excitations in amorphous media, well beyond the traditional case of acoustic phonons, and establishes the IR crossover as the fundamental physical mechanism behind the BP.

Live-cell super-resolution microscopy reveals a primary role for diffusion in polyglutamine-driven aggresome assembly.

The mechanisms leading to self-assembly of misfolded proteins into amyloid aggregates have been studied extensively in the test tube under well-controlled conditions. However, to what extent these processes are representative of those in the cellular environment remains unclear. Using super-resolution imaging of live cells, we show here that an amyloidogenic polyglutamine-containing protein first forms small, amorphous aggregate clusters in the cytosol, chiefly by diffusion. Dynamic interactions among these clusters limited their elongation and led to structures with a branched morphology, differing from the predominantly linear fibrils observed in vitro Some of these clusters then assembled via active transport at the microtubule-organizing center and thereby initiated the formation of perinuclear aggresomes. Although it is widely believed that aggresome formation is entirely governed by active transport along microtubules, here we demonstrate, using a combined approach of advanced imaging and mathematical modeling, that diffusion is the principal mechanism driving aggresome expansion. We found that the increasing surface area of the expanding aggresome increases the rate of accretion caused by diffusion of cytosolic aggregates and that this pathway soon dominates aggresome assembly. Our findings lead to a different view of aggresome formation than that proposed previously. We also show that aggresomes mature over time, becoming more compacted as the structure grows. The presence of large perinuclear aggregates profoundly affects the behavior and health of the cell, and our super-resolution imaging results indicate that aggresome formation and development are governed by highly dynamic processes that could be important for the design of potential therapeutic strategies.

Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder.

The damping or attenuation coefficient of sound waves in solids due to impurities scales with the wavevector to the fourth power, also known as Rayleigh scattering. In amorphous solids, Rayleigh scattering may be enhanced by a logarithmic factor although computer simulations offer conflicting conclusions regarding this enhancement and its microscopic origin. We present a tensorial replica field-theoretic derivation based on heterogeneous or fluctuating elasticity (HE), which shows that long-range (power-law) spatial correlations of the elastic constants, is the origin of the logarithmic enhancement to Rayleigh scattering of phonons in amorphous solids. We also consider the case of zero spatial fluctuations in the elastic constants, and of power-law decaying fluctuations in the internal stresses. Also in this case the logarithmic enhancement to the Rayleigh scattering law can be derived from the proposed tensorial HE framework.

Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity.

A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D([Formula: see text]) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form [Formula: see text] is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a [Formula: see text] regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory.

Nanoparticle amount, and not size, determines chain alignment and nonlinear hardening in polymer nanocomposites.

Polymer nanocomposites-materials in which a polymer matrix is blended with nanoparticles (or fillers)-strengthen under sufficiently large strains. Such strain hardening is critical to their function, especially for materials that bear large cyclic loads such as car tires or bearing sealants. Although the reinforcement (i.e., the increase in the linear elasticity) by the addition of filler particles is phenomenologically understood, considerably less is known about strain hardening (the nonlinear elasticity). Here, we elucidate the molecular origin of strain hardening using uniaxial tensile loading, microspectroscopy of polymer chain alignment, and theory. The strain-hardening behavior and chain alignment are found to depend on the volume fraction, but not on the size of nanofillers. This contrasts with reinforcement, which depends on both volume fraction and size of nanofillers, potentially allowing linear and nonlinear elasticity of nanocomposites to be tuned independently.

Universal Origin of Boson Peak Vibrational Anomalies in Ordered Crystals and in Amorphous Materials.

The vibrational spectra of solids, both ordered and amorphous, in the low-energy regime, control the thermal and transport properties of materials, from heat capacity to heat conduction, electron-phonon couplings, conventional superconductivity, etc. The old Debye model of vibrational spectra at low energy gives the vibrational density of states (VDOS) as proportional to the frequency squared, but in many materials the spectrum departs from this law which results in a peak upon normalizing the VDOS by frequency squared, which is known as the "boson peak." A description of the VDOS of solids (both crystals and glasses) is presented starting from first principles. Without using any assumptions whatsoever of disorder in the material, it is shown that the boson peak in the VDOS of both ordered crystals and glasses arises naturally from the competition between elastic mode propagation and diffusive damping. The theory explains the recent experimental observations of boson peak in perfectly ordered crystals, which cannot be explained based on previous theoretical frameworks. The theory also explains, for the first time, how the vibrational spectrum changes with the atomic density of the solid, and explains recent experimental observations of this effect.

Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz.

A lattice dynamical formalism based on nonaffine response theory is derived for noncentrosymmetric crystals, accounting for long-range interatomic interactions using the Ewald method. The framework takes equilibrated static configurations as input to compute the elastic constants in excellent agreement with both experimental data and calculations under strain. Besides this methodological improvement, which enables faster evaluation of elastic constants without the need of explicitly simulating the deformation process, the framework provides insights into the nonaffine contribution to the elastic constants of α-quartz. It turns out that, due to the noncentrosymmetric lattice structure, the nonaffine (softening) correction to the elastic constants is very large, such that the overall elastic constants are at least 3-4 times smaller than the affine Born-Huang estimate.

Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics.

We study the viscoelastic response of amorphous polymers using theory and simulations. By accounting for internal stresses and considering instantaneous normal modes (INMs) within athermal non-affine theory, we make parameter-free predictions of the dynamic viscoelastic moduli obtained in coarse-grained simulations of polymer glasses at non-zero temperatures. The theoretical results show very good correspondence with rheology data collected from molecular dynamics simulations over five orders of magnitude in frequency, with some instabilities that accumulate in the low-frequency part on approach to the glass transition. These results provide evidence that the mechanical glass transition itself is continuous and thus represents a crossover rather than a true phase transition. The relatively sharp drop of the low-frequency storage modulus across the glass transition temperature can be explained mechanistically within the proposed theory: the proliferation of low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy excitations) is directly responsible for the rapid growth of a negative non-affine contribution to the storage modulus.

Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids.

The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.

Interatomic repulsion softness directly controls the fragility of supercooled metallic melts.

We present an analytic scheme to connect the fragility and viscoelasticity of metallic glasses to the effective ion-ion interaction in the metal. This is achieved by an approximation of the short-range repulsive part of the interaction, combined with nonaffine lattice dynamics to obtain analytical expressions for the shear modulus, viscosity, and fragility in terms of the ion-ion interaction. By fitting the theoretical model to experimental data, we are able to link the steepness of the interionic repulsion to the Thomas-Fermi screened Coulomb repulsion and to the Born-Mayer valence electron overlap repulsion for various alloys. The result is a simple closed-form expression for the fragility of the supercooled liquid metal in terms of few crucial atomic-scale interaction and anharmonicity parameters. In particular, a linear relationship is found between the fragility and the energy scales of both the screened Coulomb and the electron overlap repulsions. This relationship opens up opportunities to fabricate alloys with tailored thermoelasticity and fragility by rationally tuning the chemical composition of the alloy according to general principles. The analysis presented here brings a new way of looking at the link between the outer shell electronic structure of metals and metalloids and the viscoelasticity and fragility thereof.

Fluorescence Self-Quenching from Reporter Dyes Informs on the Structural Properties of Amyloid Clusters Formed in Vitro and in Cells.

The characterization of the aggregation kinetics of protein amyloids and the structural properties of the ensuing aggregates are vital in the study of the pathogenesis of many neurodegenerative diseases and the discovery of therapeutic targets. In this article, we show that the fluorescence lifetime of synthetic dyes covalently attached to amyloid proteins informs on the structural properties of amyloid clusters formed both in vitro and in cells. We demonstrate that the mechanism behind such a "lifetime sensor" of protein aggregation is based on fluorescence self-quenching and that it offers a good dynamic range to report on various stages of aggregation without significantly perturbing the process under investigation. We show that the sensor informs on the structural density of amyloid clusters in a high-throughput and quantitative manner and in these aspects the sensor outperforms super-resolution imaging techniques. We demonstrate the power and speed of the method, offering capabilities, for example, in therapeutic screenings that monitor biological self-assembly. We investigate the mechanism and advantages of the lifetime sensor in studies of the K18 protein fragment of the Alzheimer's disease related protein tau and its amyloid aggregates formed in vitro. Finally, we demonstrate the sensor in the study of aggregates of polyglutamine protein, a model used in studies related to Huntington's disease, by performing correlative fluorescence lifetime imaging microscopy and structured-illumination microscopy experiments in cells.