Thawed matrix method for computing local mechanical properties of amorphous solids.

We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly penalizes large nonaffine displacements. With increasing strength of the field, plastic deformation can be localized. We characterize the distribution of local plastic yield stresses (residual local stresses to instability) with our approach and assess the correlation of their spatial maps with plastic activity in a model two-dimensional amorphous solid. Our approach reduces artifacts inherent in a previous method known as the "frozen matrix" approach that enforces fully affine deformation and improves the prediction of plastic rearrangements from structural information.

Understanding the Role of Entropy in High Entropy Oxides.

The field of high entropy oxides (HEOs) flips traditional materials science paradigms on their head by seeking to understand what properties arise in the presence of profound configurational disorder. This disorder, which originates from multiple elements sharing a single lattice site, can take on a kaleidoscopic character due to the vast numbers of possible elemental combinations. High configurational disorder appears to imbue some HEOs with functional properties that far surpass their nondisordered analogs. While experimental discoveries abound, efforts to characterize the true magnitude of the configurational entropy and understand its role in stabilizing new phases and generating superior functional properties have lagged behind. Understanding the role of configurational disorder in existing HEOs is the crucial link to unlocking the rational design of new HEOs with targeted properties. In this Perspective, we attempt to establish a framework for articulating and beginning to address these questions in pursuit of a deeper understanding of the true role of entropy in HEOs.

Dynamic phase diagram of plastically deformed amorphous solids at finite temperature.

The yielding transition that occurs in amorphous solids under athermal quasistatic deformation has been the subject of many theoretical and computational studies. Here, we extend this analysis to include thermal effects at finite shear rate, focusing on how temperature alters avalanches. We derive a nonequilibrium phase diagram capturing how temperature and strain rate effects compete, when avalanches overlap, and whether finite-size effects dominate over temperature effects. The predictions are tested through simulations of an elastoplastic model in two dimensions and in a mean-field approximation. We find a scaling for temperature-dependent softening in the low-strain rate regime when avalanches do not overlap, and a temperature-dependent Herschel-Bulkley exponent in the high-strain rate regime when avalanches do overlap.

Exploring glassy dynamics with Markov state models from graph dynamical neural networks.

Using machine learning techniques, we introduce a Markov state model (MSM) for a model glass former that reveals structural heterogeneities and their slow dynamics by coarse-graining the molecular dynamics into a low-dimensional feature space. The transition timescale between states is larger than the conventional structural relaxation time τ_{α}, but can be obtained from trajectories much shorter than τ_{α}. The learned map of states assigned to the particles corresponds to local excess Voronoi volume. These results resonate with classic free volume theories of the glass transition, singling out local packing fluctuations as one of the dominant slowly relaxing features.

Molecular simulations and hydrodynamic theory of nonlocal shear-stress correlations in supercooled fluids.

A supercooled fluid close to the glass transition develops nonlocal shear-stress correlations that anticipate the emergence of elasticity. We performed molecular dynamics simulations of a binary Lennard-Jones mixture at different temperatures and investigated the spatiotemporal autocorrelation function of the shear stress for different wavevectors, q, from a locally measured and Fourier-transformed stress tensor. Anisotropic correlations are observed at non-zero wavevectors, exhibiting strongly damped oscillations with a characteristic frequency ω(q). A comparison with a recently developed hydrodynamic theory [Maier et al., Phys. Rev. Lett. 119, 265701 (2017)] shows a remarkably good quantitative agreement between particle-based simulations and theoretical predictions.

Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids.

Amorphous solids are yield stress materials that flow when a sufficient load is applied. Their flow consists of periods of elastic loading interrupted by rapid stress drops, or avalanches, coming from microscopic rearrangements known as shear transformations (STs). Here we show that the spatial extent of avalanches in a steadily sheared amorphous solid has a profound effect on the distribution of local residual stresses that in turn determines the stress drop statistics. As reported earlier, the most unstable sites are located in a flat "plateau" region that decreases with system size. While the entrance into the plateau is set by the lower cutoff of the mechanical noise produced by individual STs, the departure from the usually assumed power-law (pseudogap) form of the residual stress distribution comes from far field effects related to spatially extended rearrangements. Interestingly, we observe that the average residual stress of the weakest sites is located in an intermediate power-law regime between the pseudogap and the plateau regimes, whose exponent decreases with system size. Our findings imply a new scaling relation linking the exponents characterizing the avalanche size and residual stress distributions.

Residual stress distributions in amorphous solids from atomistic simulations.

The distribution of local residual stresses (threshold to instability) that controls the statistical properties of plastic flow in athermal amorphous solids is examined with an atomistic simulation technique. For quiescent configurations, the distribution has a pseudogap (power-law) form with an exponent that agrees well with global yielding statistics. As soon as deformation sets in, the pseudogap region gives way to a system size dependent plateau at small residual stresses that can be understood from the statistics of local residual stress differences between plastic events. Results further suggest that the local yield stress in amorphous solids changes even if the given region does not participate in plastic activity.

Kinetic Pathways of Block Copolymer Directed Self-Assembly: Insights from Efficient Continuum Modeling.

We introduce a computationally efficient continuum technique to simulate the complex kinetic pathways of block copolymer self-assembly. Subdiffusive chain dynamics is taken into account via nonlocal Onsager coefficients. An application to directed self-assembly of thin films of diblock copolymers on patterned substrates reveals the conditions under which experimentally observed metastable structures intervene in the desired thin-film morphology. The approach generalizes easily to multiblock copolymers and more complex guiding patterns on the substrate, and its efficiency allows for the systematic optimization of guiding patterns and process conditions.

Poisson-Boltzmann modeling and molecular dynamics simulations of polyelectrolyte gel diodes in the static regime.

We present molecular dynamics (MD) simulations of a model polyelectrolyte gel diode formed by a junction of two oppositely charged crosslinked polyelectrolyte networks, and compare the ion densities and electrostatic field to a corresponding continuum Poisson-Boltzmann (PB) model. At low electrostatic coupling strength (i.e. low Bjerrum lengths), the PB model reproduces the MD simulation results for density and electric field throughout the gel very well. At higher electrostatic coupling (i.e. large Bjerrum lengths) and higher degrees of ionization, the standard PB fails to predict the MD profiles at the diode interface due to counterion condensation, network collapse and field-induced gel deformation. In fact MD simulations predict that the rectifying behavior of diodes operating in such regimes will be much reduced. We develop a modified PB model that accounts for these effects, and show that it produces better agreement with the MD results. The updated PB model can be used for improved modeling of experimental results on PE gel diodes.

Local versus Global Stretched Mechanical Response in a Supercooled Liquid near the Glass Transition.

Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model.

Molecular mobility in driven monomeric and polymeric glasses.

We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress σ while being deformed with strain rate ε[over ̇], the microscopic structural relaxation time τ_{str} is given by the universal relation σ/G_{∞}ε[over ̇] with G_{∞} a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxation time and τ_{str} is in fact further reduced even though σ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

Orientation of plastic rearrangements in two-dimensional model glasses under shear.

The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods to extract the size and orientation of these shear transformations in simulations of a two-dimensional athermal model glass under simple shear. We find that the shear angles are broadly distributed around the macroscopic shear direction, with a more or less Gaussian distribution with a standard deviation of around 20^{∘}. The distributions of sizes and orientations of shear transformations display no substantial sensitivity to the shear rate. These results can notably be used to refine the description of rearrangements in elastoplastic models.

Molecular simulations of the piezoionic effect.

We present a molecular dynamics study of two polyelectrolyte gels with different degrees of ionization coupled in a slab geometry. Our simulations show that a pressure gradient emerges between the two gels that results in the buildup of a Nernst-Donnan potential. This methodology is reverse to experiments of the piezoionic or mechanoelectric effect, in which an electric potential gradient appears upon application of a pressure gradient to a hydrogel. The Nernst-Donnan potential at the interface is found to scale linearly with temperature with the coefficient of proportionality given by the fraction of concentrations of the uncondensed counterions. We show that the potential difference can also be expressed as a linear function of the lateral pressure, thus providing a molecular interpretation of the piezoionic effect.

Soft Vibrational Modes Predict Breaking Events during Force-Induced Protein Unfolding.

We investigate the correlation between soft vibrational modes and unfolding events in simulated force spectroscopy of proteins. Unfolding trajectories are obtained from molecular dynamics simulations of a Go model of a monomer of a mutant of superoxide dismutase 1 protein containing all heavy atoms in the protein, and a normal mode analysis is performed based on the anisotropic network model. We show that a softness map constructed from the superposition of the amplitudes of localized soft modes correlates with unfolding events at different stages of the unfolding process. Soft residues are up to eight times more likely to undergo disruption of native structure than the average amino acid. The memory of the softness map is retained for extensions of up to several nanometers, but decorrelates more rapidly during force drops.

Dewetting during Terahertz Vibrations of Nanoparticles.

We use molecular simulations to demonstrate the formation of a vacuum layer around a vibrating nanoparticle in a liquid. This vacuum layer forms readily for high frequencies with respect to the characteristic vibrational (Einstein) frequency of the fluid, even with small amplitude vibrations. The opposite is true for low frequencies, where large amplitudes are required to demonstrate the vacuum layer. With the vacuum layer forming, the quality factor of the oscillations increases substantially. The findings provide an interpretation of our recent experiments that show the onset of high-quality resonances of nanoparticles in water ( Xiang et al. Nano Lett. 2016 , 16 , 3638 ) in the gigahertz to terahertz range.

The unfolding mechanism of monomeric mutant SOD1 by simulated force spectroscopy.

Mechanical unfolding of mutated apo, disulfide-reduced, monomeric superoxide dismutase 1 protein (SOD1) has been simulated via force spectroscopy techniques, using both an all-atom (AA), explicit solvent model and a coarse-grained heavy-atom Go (HA-Go) model. The HA-Go model was implemented at two different pulling speeds for comparison. The most-common sequence of unfolding in the AA model agrees well with the most-common unfolding sequence of the HA-Go model, when the same normalized pulling rate was used. Clustering of partially-native structures as the protein unfolds shows that the AA and HA-Go models both exhibit a dominant pathway for early unfolding, which eventually bifurcates repeatedly to multiple branches after the protein is about half-unfolded. The force-extension curve exhibits multiple force drops, which are concomitant with jumps in the local interaction potential energy between specific ß-strands in the protein. These sudden jumps in the potential energy coincide with the dissociation of specific pairs of ß-strands, and thus intermediate unfolding events. The most common sequence of ß-strand dissociation in the unfolding pathway of the AA model is ß-strands 5, 4, 8, 7, 1, 2, then finally ß-strands 3 and 6. The observation that ß-strand 5 is among the first to unfold here, but the last to unfold in simulations of loop-truncated SOD1, could imply the existence of an evolutionary compensation mechanism, which would stabilize ß-strands flanking long loops against their entropic penalty by strengthening intramolecular interactions. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

As Simple As Possible, but Not Simpler: Exploring the Fidelity of Coarse-Grained Protein Models for Simulated Force Spectroscopy.

Mechanical unfolding of a single domain of loop-truncated superoxide dismutase protein has been simulated via force spectroscopy techniques with both all-atom (AA) models and several coarse-grained models having different levels of resolution: A Go model containing all heavy atoms in the protein (HA-Go), the associative memory, water mediated, structure and energy model (AWSEM) which has 3 interaction sites per amino acid, and a Go model containing only one interaction site per amino acid at the Cα position (Cα-Go). To systematically compare results across models, the scales of time, energy, and force had to be suitably renormalized in each model. Surprisingly, the HA-Go model gives the softest protein, exhibiting much smaller force peaks than all other models after the above renormalization. Clustering to render a structural taxonomy as the protein unfolds showed that the AA, HA-Go, and Cα-Go models exhibit a single pathway for early unfolding, which eventually bifurcates repeatedly to multiple branches only after the protein is about half-unfolded. The AWSEM model shows a single dominant unfolding pathway over the whole range of unfolding, in contrast to all other models. TM alignment, clustering analysis, and native contact maps show that the AWSEM pathway has however the most structural similarity to the AA model at high nativeness, but the least structural similarity to the AA model at low nativeness. In comparison to the AA model, the sequence of native contact breakage is best predicted by the HA-Go model. All models consistently predict a similar unfolding mechanism for early force-induced unfolding events, but diverge in their predictions for late stage unfolding events when the protein is more significantly disordered.

Threshold for Terahertz Resonance of Nanoparticles in Water.

Nanoparticle vibrations are coupled to light through electrostriction, which gives nonlinear optical scattering. We investigated the acoustic response of 2 nm gold nanoparticles using a nearly degenerate four-wave mixing experimental configuration and show that the nonlinear response suddenly turns on at low powers (<100 mW) for continuous-wave (CW) lasers. The observed nonlinear response is a million times larger than typical electronic nonlinearities. The threshold implies a dramatic change in the quality factor of the vibrating nanoparticles, 4 orders of magnitude larger than usual hydrodynamic theory predicts. It is as if the water is removed altogether, which we speculate is the result of the vibrating particle pushing away the water molecules to form a stable cavity. Because these acoustic vibrations extend to terahertz frequencies, there is potential to harness this effect for high speed optical data processing, as well as to probe the dynamics of proteins all having acoustic modes in this range.

Effects of Inertia on the Steady-Shear Rheology of Disordered Solids.

We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping strength ζ in the low-temperature limit, we identify two well-defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number Wi∝ζγ[over ˙]; the macroscopic stress Σ follows the frequently encountered Herschel-Bulkley law Σ=Σ_{0}+ksqrt[Wi], with yield stress Σ_{0}>0. In the underdamped (inertial) regime, dramatic changes in the rheology are observed for low damping: the flow curve becomes nonmonotonic. This change is not caused by longer-lived correlations in the particle dynamics at lower damping; instead, for weak dissipation, the sample heats up considerably due to, and in proportion to, the driving. By thermostating more or less underdamped systems, we are able to link quantitatively the rheology to the kinetic temperature and the shear rate, rescaled with Einstein's vibration frequency.