Erratum: General theory of the viscosity of liquids and solids from nonaffine particle motions [Phys. Rev. E 108, 044101 (2023)].

This corrects the article DOI: 10.1103/PhysRevE.108.044101.

Shear flow of non-Brownian rod-sphere mixtures near jamming.

We use the discrete element method, taking particle contact and hydrodynamic lubrication into account, to unveil the shear rheology of suspensions of frictionless non-Brownian rods in the dense packing fraction regime. We find that, analogously to the random close packing volume fraction, the shear-driven jamming point of this system varies in a nonmonotonic fashion as a function of the rod aspect ratio. The latter strongly influences how the addition of rodlike particles affects the rheological response of a suspension of frictionless non-Brownian spheres to an external shear flow. At fixed values of the total (rods plus spheres) packing fraction, the viscosity of the suspension is reduced by the addition of "short"(≤2) rods but is instead increased by the addition of "long"(≥2) rods. A mechanistic interpretation is provided in terms of packing and excluded-volume arguments.

Anharmonic theory of superconductivity and its applications to emerging quantum materials.

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

General theory of the viscosity of liquids and solids from nonaffine particle motions.

A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.

Molecular-Level Relation between the Intraparticle Glass Transition Temperature and the Stability of Colloidal Suspensions.

In many colloidal suspensions, the dispersed colloidal particles are amorphous solids, resulting from vitrification. A crucial open problem is understanding how colloidal stability is affected by the intraparticle glass transition. By dealing with the latter process from a solid-state perspective, we estabilish a proportionality relation between the intraparticle glass transition temperature, Tg, and the Hamaker constant, AH, of a generic suspension of nanoparticles. It follows that Tg can be used as a convenient parameter (alternative to AH) for controlling the stability of colloidal systems. Within the Derjaguin-Landau-Verwey-Overbeek theory, we show that the novel relationship, connecting Tg to AH, implies the critical coagulation ionic strength to be a monotonically decreasing function of Tg. We connect our predictions to recent experimental findings.

Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian.

We provide a first-principles derivation of the Langevin equation with shear flow and its corresponding fluctuation-dissipation theorems. Shear flow of simple fluids has been widely investigated by numerical simulations. Most studies postulate a Markovian Langevin equation with a simple shear drag term in the manner of Stokes. However, this choice has never been justified from first principles. We start from a particle-bath system described by a classical Caldeira-Leggett Hamiltonian modified by adding a term proportional to the strain-rate tensor according to Hoover's DOLLS method, and we derive a generalized Langevin equation for the sheared system. We then compute, analytically, the noise time-correlation functions in different regimes. Based on the intensity of the shear rate, we can distinguish between close-to-equilibrium and far-from-equilibrium states. According to the results presented here, the standard, simple, and Markovian form of the Langevin equation with shear flow postulated in the literature is valid only in the limit of extremely weak shear rates compared to the effective vibrational temperature of the bath. For even marginally higher shear rates, the (generalized) Langevin equation is strongly non-Markovian, and nontrivial fluctuation-dissipation theorems are derived.

Reply to "Comment on 'Explaining the specific heat of liquids based on instantaneous normal modes'".

We reply to the Comment by Schirmacher et al. [Phys. Rev. E, 106, 066101 (2022)PREHBM2470-004510.1103/PhysRevE.106.066101]. We disagree that the heat capacity of liquids is not a mystery since a widely accepted theoretical derivation based on simple physical assumptions is still missing. We also disagree about the lack of evidence for a linear in frequency scaling of the liquid density of states, which is indeed reported in uncountable simulations and recently also in experiments. We emphasize that our theoretical derivation does not assume any Debye density of states. We agree that such an assumption would be incorrect. Finally, we remark that the Bose-Einstein distribution naturally tends to the Boltzmann distribution in the classical limit, which makes our results valid also for classical liquids. We hope that this scientific exchange will bring more attention to the description of the vibrational density of states and thermodynamics of liquids, which still present many open puzzles.

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.

Possible enhancement of the superconductingTcdue to sharp Kohn-like soft phonon anomalies.

Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constantλ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperatureTc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.

Microscopic theory for the pair correlation function of liquidlike colloidal suspensions under shear flow.

We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction η and the Péclet (Pe) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered values of Pe, we observe a very good agreement between theoretical findings and numerical results from the literature, up to rather large values of η. The theory predicts a consistent enhancement of the structure factor S(k) at k→0, upon increasing the Pe number. We argue this behavior may signal the onset of a phase transition from the isotropic phase to a nonuniform one, induced by the external shear flow.

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.

Reply to "Comment on 'Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory' ".

We reply to the Comment by Bryk et al. [Phys Rev. E 106, 036601 (2022)10.1103/PhysRevE.106.036601] on our paper [Phys. Rev. E 105, 024602 (2022)2470-004510.1103/PhysRevE.105.024602].

Direct observation of heterogeneous formation of amyloid spherulites in real-time by super-resolution microscopy.

Protein misfolding in the form of fibrils or spherulites is involved in a spectrum of pathological abnormalities. Our current understanding of protein aggregation mechanisms has primarily relied on the use of spectrometric methods to determine the average growth rates and diffraction-limited microscopes with low temporal resolution to observe the large-scale morphologies of intermediates. We developed a REal-time kinetics via binding and Photobleaching LOcalization Microscopy (REPLOM) super-resolution method to directly observe and quantify the existence and abundance of diverse aggregate morphologies of human insulin, below the diffraction limit and extract their heterogeneous growth kinetics. Our results revealed that even the growth of microscopically identical aggregates, e.g., amyloid spherulites, may follow distinct pathways. Specifically, spherulites do not exclusively grow isotropically but, surprisingly, may also grow anisotropically, following similar pathways as reported for minerals and polymers. Combining our technique with machine learning approaches, we associated growth rates to specific morphological transitions and provided energy barriers and the energy landscape at the level of single aggregate morphology. Our unifying framework for the detection and analysis of spherulite growth can be extended to other self-assembled systems characterized by a high degree of heterogeneity, disentangling the broad spectrum of diverse morphologies at the single-molecule level.

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.

Predicting plasticity of amorphous solids from instantaneous normal modes.

We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the VDOS of affinely strained configurations at varying strain values. The affine strain, found analytically on the static (undeformed) snapshot of the glass, leads to configurations that are rich with soft low-energy modes as well as unstable modes (negative eigenvalues) that are otherwise completely "washed out" and lost if one lets the system fully relax after strain. This procedure is consistent with the structure of NALD. The INM spectrum of deformed states allows for the analytical prediction of the stress-strain curve of a model glass. Good parameter-free quantitative agreement is shown between the prediction and simulations of athermal quasistatic shear of a coarse-grained polymer glass.

Solution to the two-body Smoluchowski equation with shear flow for charge-stabilized colloids at low to moderate Péclet numbers.

We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed partial differential equation problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wave vectors k and its dependence on Pe is a simple power law. At increasing Pe, the main peak of the structure factor displays a broadening and shift toward lower k in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift toward high k is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.

The ω3 scaling of the vibrational density of states in quasi-2D nanoconfined solids.

The vibrational properties of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic ω2 low-frequency scaling of the vibrational density of states. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the vibrational density of states of amorphous ice confined inside graphene oxide membranes and we observe a crossover from the Debye ω2 scaling to an anomalous ω3 behaviour upon reducing the confinement size L. Additionally, using molecular dynamics simulations, we confirm the experimental findings and prove that such a scaling appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency ω3 law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency ω× = vL/2π, with v the speed of sound of the material, and we confirm this quantitative estimate with simulations.

Local symmetry predictors of mechanical stability in glasses.

The mechanical properties of crystals are controlled by the translational symmetry of their structures. But for glasses with a disordered structure, the link between the symmetry of local particle arrangements and stability is not well established. In this contribution, we provide experimental verification that the centrosymmetry of nearest-neighbor polyhedra in a glass strongly correlates with the local mechanical stability. We examine the distribution of local stability and local centrosymmetry in a glass during aging and deformation using microbeam x-ray scattering. These measurements reveal the underlying relationship between particle-level structure and larger-scale behavior and demonstrate that spatially connected, coordinated local transformations to lower symmetry structures are fundamental to these phenomena. While glassy structures lack obvious global symmetry breaking, local structural symmetry is a critical factor in predicting stability.

Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory.

We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses, and liquids based on nonaffine displacements and the consequent Goldstone phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field-nonaffinity-which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave vector in liquids, thus giving a formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the α relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a nonequilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids, and glasses has to be identified with the associated generalized higher-form global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).

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.