Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T. In an Arrhenius plot, ln η vs 1/T, a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel-Fulcher-Tammann law. Here we analyze existing data of the transport coefficients of 84 glass-forming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover η(×), where η(×) has the same value, η(×) ≈ 10(3) Poise, for all 84 liquids. The crossover temperature, T(×), located well above the calorimetric glass transition temperature T(g), marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T(×) to Arrhenius behavior below T(×). We also show that below T(×) the familiar Stokes-Einstein relation D/T ～ η(-1) breaks down and is replaced by a fractional form D/T ～ η(-ζ), with ζ ≈ 0.85.     

Universal spectrum of normal modes in low-temperature glasses

We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way toward a detailed analytical understanding of the vibrational spectrum of low-temperature glasses.Low-energy excitations in disordered glassy systems have received a great deal of attention because of their multiple interesting features and their importance for thermodynamic and transport properties of low-temperature glasses. Much debate has been concentrated around the deviation of the spectrum from the Debye law for solids, due to an excess of low-energy excitations, known as the “boson peak” (1).The vibrational spectrum of glasses is a natural problem of random matrix theory. In fact, the Hessian of a disordered system is a random matrix due to the random position of particles in the sample. The distribution of the particles induces nontrivial correlations between the matrix elements. Many attempted to explain the observed spectrum of eigenvalues by replacing the true statistical ensemble with some simpler ones, in which correlations are neglected or treated in approximate ways (2–11). However, most of these models are not microscopically grounded, thus making it difficult to assess which of the proposed mechanisms are the most relevant and understand their interplay.In this work we will focus on two ways of inducing a boson peak in random matrix models. First, it has been suggested that the boson peak is due to the vicinity to the jamming transition where glasses are isostatic (12, 13). Isostaticity means that the number of degrees of freedom is exactly equal to the number of interactions. Isostaticity implies marginal mechanical stability (MMS): cutting one particle contact induces an unstable soft mode that allows particles to slide without paying any energy cost (14, 15). From this hypothesis, scaling laws have been derived that characterize the spectrum as a function of the distance from an isostatic point (11, 12, 16). Second, it has been proposed that low-temperature glasses have a complex energy landscape with a hierarchical distribution of energy minima and barriers (17). Minima are marginally stable (18) and display anomalous soft modes (11, 19) related to the lowest energy barriers (20–22). We will denote this second kind of marginality as landscape marginal stability (LMS).Both mechanisms described above are highly universal. LMS is a generic property of mean-field strongly disordered models (18). MMS holds for a broad class of simple random matrix models (6, 10, 11, 16) and for realistic glass models (12, 23, 24) at the isostatic point. Universality motivates the introduction of a broad class of continuous constraint satisfaction problems (CCSP) (25), in which a set of constraints is imposed on a set of continuous variables. In the satisfiable (SAT) phase, all of the constraints can be satisfied, whereas this is impossible in the unsatisfiable (UNSAT) phase. A sharp SAT–UNSAT transition separates the two phases: jamming can be seen as a particular instance of this transition. In fact, (i) jamming properties are within numerical precision superuniversal, i.e., independent of the spatial dimension d for all d ≥ 2 (26, 27), (ii) they can be analytically predicted through the exact solution in d → ∞ (17, 28), and (iii) the perceptron model of neural networks, a prototypical CCSP, displays a jamming transition with the same exponents (25). Based on universality, both for analytical and numerical computations, the perceptron appears to be the simplest model^† where low-temperature glassy behavior can be studied (25).Here, we exploit this simplicity and characterize analytically the vibrational spectrum of the perceptron at zero temperature in the glass phase. Our main results are (i) the spectrum is given by a Marchenko–Pastur law with parameters that can be computed analytically; (ii) it closely resembles the one of soft sphere glass models in all d ≥ 2; (iii) it displays soft modes coming from marginal stabilities of both kinds (LMS and MMS), allowing us to unify both contributions and understand their interplay. Our results are based on the replica method and random matrix theory, and for the first time, to our knowledge, we are able to derive all of the critical properties of jamming within the analytic solution of a well-defined microscopic model.     

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.Understanding the mechanism which governs the emergence of mechanical stability at the glass transition of supercooled metallic liquids (1) calls for deeper insights into the connection between the fragility index and the interatomic interaction. As previous work suggested (2–4), mechanical stability in amorphous solids is crucially linked to the repulsive part of the interatomic interaction potential. However, no consensus has been reached on whether interatomic repulsion softness correlates with strong glasses (5) or with fragile glasses (6). We derive an analytical closed-form relation between the fragility index of metallic glass formers and the short-ranged repulsive part of the interatomic interaction given by pseudopotential theory. This fundamental relation is obtained from a one-parameter theory fit to experimental rheological data of supercooled metallic melts. Resorting to this combination of theory and experiments, it is established that interatomic repulsion softness in metals goes along with strong glasses and low fragility. Surprisingly, given the difference in energy scale of many orders of magnitude and the nature of the microscopic interaction, this finding is in full agreement with the correlation observed experimentally for soft colloidal glasses by Mattsson, Weitz, and coworkers (5). Finally, we establish a quantitative link between our analysis and the theory of shear transformation zones to estimate the size of the cooperatively rearranging regions in good agreement with the findings in ref. 7.     

Unique elastic properties of the spectrin tetramer as revealed by multiscale coarse-grained modeling

The force-extension profile of tetrameric spectrin is determined by using multiscale computer simulation. Fluctuation results of atomistic simulations of double spectrin repeat units (DSRU) are used to systematically build a coarse-grained (CG) model for the tetrameric form of spectrin. It is found that the spectrin tetramer can be modeled as a soft polymer with a unique flat force-extension profile over the range of biologically important lengths. It is also concluded that in the cytoskeletal network of the red blood cell the tetramer is in an "overcompressed" state. These findings are in contrast to the commonly used models of spectrin tetramer elasticity, namely the "entropic spring" polymer models. From these results, it is concluded that stable intact helical linker regions are needed to maintain the soft elasticity of the spectrin tetramer.     

PR65, the HEAT-repeat scaffold of phosphatase PP2A,is an elastic connector that links force and catalysis

PR65 is the two-layered (α-α solenoid) HEAT-repeat (Huntingtin, elongation factor 3, a subunit of protein phosphatase 2A, PI3 kinase target of rapamycin 1) scaffold of protein phosphatase PP2A. Molecular dynamics simulations predict that, at forces expected in living systems, PR65 undergoes (visco-)elastic deformations in response to pulling/pushing on its ends. At lower forces, smooth global flexural and torsional changes occur via even redistribution of stress along the hydrophobic core of the molecule. At intermediate forces, helix–helix separation along one layer (“fracturing”) leads to global relaxation plus loss of contact in the other layer to unstack the affected units. Fracture sites are determined by unusual sequences in contiguous interhelix turns. Normal mode analysis of the heterotrimeric PP2A enzyme reveals that its ambient conformational fluctuations are dominated by elastic deformations of PR65, which introduce a mechanical linkage between the separately bound regulatory and catalytic subunits. PR65-dominated fluctuations of PP2A have the effect of opening and closing the enzyme’s substrate binding/catalysis interface, as well as altering the positions of certain catalytic residues. These results suggest that substrate binding/catalysis are sensitive to mechanical force. Force could be imposed from the outside (e.g., in PP2A’s response to spindle tension) or arise spontaneously (e.g., in PP2A’s interaction with unstructured proteins such as Tau, a microtubule-associated Alzheimer’s-implicated protein). The presented example supports the view that conformation and function of protein complexes can be modulated by mechanical energy inputs, as well as by chemical energy inputs from ligand binding. Given that helical-repeat proteins are involved in many cellular processes, the findings also encourage the view that mechanical forces may be of widespread importance.     

A regular pattern of Ig super-motifs defines segmental flexibility as the elastic mechanism of the titin chain

Myofibril elasticity, critical to muscle function, is dictated by the intrasarcomeric filament titin, which acts as a molecular spring. To date, the molecular events underlying the mechanics of the folded titin chain remain largely unknown. We have elucidated the crystal structure of the 6-Ig fragment I65-I70 from the elastic I-band fraction of titin and validated its conformation in solution using small angle x-ray scattering. The long-range properties of the chain have been visualized by electron microscopy on a 19-Ig fragment and modeled for the full skeletal tandem. Results show that conserved Ig-Ig transition motifs generate high-order in the structure of the filament, where conformationally stiff segments interspersed with pliant hinges form a regular pattern of dynamic super-motifs leading to segmental flexibility in the chain. Pliant hinges support molecular shape rearrangements that dominate chain behavior at moderate stretch, whereas stiffer segments predictably oppose high stretch forces upon full chain extension. There, librational entropy can be expected to act as an energy barrier to prevent Ig unfolding while, instead, triggering the unraveling of flanking springs formed by proline, glutamate, valine, and lysine (PEVK) sequences. We propose a mechanistic model based on freely jointed rigid segments that rationalizes the response to stretch of titin Ig-tandems according to molecular features.