Flexible nanomechanical bit based on few-layer graphene.

Mechanical computers have gained intense research interest at size scales ranging from nano to macro as they may complement electronic computers operating in extreme environments. While nanoscale mechanical computers may be easier to integrate with traditional electronic components, most current nanomechanical computers are based on volatile resonator systems that require continuous energy input. In this study, we propose a non-volatile nanomechanical bit based on the quasi-stable configurations of few-layer graphene with void defects, and demonstrate its multiple quasi-stable states by deriving an analytic relationship for the void configuration based on a competition between the bending energy and the cohesive energy. Using this nanomechanical bit, typical logic gates are constructed to perform Boolean calculations, including NOT, AND, OR, NAND and NOR gates, and demonstrate reprogrammability between these logic gates. We also study the accuracy and the stability of the nanomechanical bits based on the few-layer graphene. These findings provide a novel approach to realize the nanomechanical computing process.

Surface Adatom Diffusion-Assisted Dislocation Nucleation in Metal Nanowires.

We employ a hybrid diffusion- and nucleation-based kinetic Monte Carlo model to elucidate the significant impact of adatom diffusion on incipient surface dislocation nucleation in metal nanowires. We reveal a stress-regulated diffusion mechanism that promotes preferential accumulation of diffusing adatoms near nucleation sites, which explains the experimental observations of strong temperature but weak strain-rate dependence as well as temperature-dependent scatter of the nucleation strength. Furthermore, the model demonstrates that a decreasing rate of adatom diffusion with an increasing strain rate will lead to stress-controlled nucleation being the dominant nucleation mechanism at higher strain rates. Overall, our model offers new mechanistic insights into how surface adatom diffusion directly impacts the incipient defect nucleation process and resulting mechanical properties of metal nanowires.

Efficient snap-through of spherical caps by applying a localized curvature stimulus.

In bistable actuators and other engineered devices, a homogeneous stimulus (e.g., mechanical, chemical, thermal, or magnetic) is often applied to an entire shell to initiate a snap-through instability. In this work, we demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, thereby decreasing the energy input required to actuate the shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimulus-responsive material. We rely on the effective curvature stimulus, i.e., the natural curvature induced by the non-mechanical stimulus, which ensures that our results are entirely stimulus-agnostic. To validate our numerics and demonstrate this generality, we also perform two sets of experiments, wherein we use residual swelling of bilayer silicone elastomers-a process that mimics differential growth-as well as a magneto-elastomer to induce curvatures that cause snap-through. Our results elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through.

Elastic Instabilities Govern the Morphogenesis of the Optic Cup.

Because the normal operation of the eye depends on sensitive morphogenetic processes for its eventual shape, developmental flaws can lead to wide-ranging ocular defects. However, the physical processes and mechanisms governing ocular morphogenesis are not well understood. Here, using analytical theory and nonlinear shell finite-element simulations, we show, for optic vesicles experiencing matrix-constrained growth, that elastic instabilities govern the optic cup morphogenesis. By capturing the stress amplification owing to mass increase during growth, we show that the morphogenesis is driven by two elastic instabilities analogous to the snap through in spherical shells, where the second instability is sensitive to the optic cup geometry. In particular, if the optic vesicle is too slender, it will buckle and break axisymmetry, thus, preventing normal development. Our results shed light on the morphogenetic mechanisms governing the formation of a functional biological system and the role of elastic instabilities in the shape selection of soft biological structures.

Erratum: Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning [Phys. Rev. Lett. 121, 255304 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.255304.

Atomistic Simulation of the Rate-Dependent Ductile-to-Brittle Failure Transition in Bicrystalline Metal Nanowires.

The mechanical properties and plastic deformation mechanisms of metal nanowires have been studied intensely for many years. One of the important yet unresolved challenges in this field is to bridge the gap in properties and deformation mechanisms reported for slow strain rate experiments (∼10-2 s-1), and high strain rate molecular dynamics (MD) simulations (∼108 s-1) such that a complete understanding of strain rate effects on mechanical deformation and plasticity can be obtained. In this work, we use long time scale atomistic modeling based on potential energy surface exploration to elucidate the atomistic mechanisms governing a strain-rate-dependent incipient plasticity and yielding transition for face centered cubic (FCC) copper and silver nanowires. The transition occurs for both metals with both pristine and rough surfaces for all computationally accessible diameters (<10 nm). We find that the yield transition is induced by a transition in the incipient plastic event from Shockley partials nucleated on primary slip systems at MD strain rates to the nucleation of planar defects on non-Schmid slip planes at experimental strain rates, where multiple twin boundaries and planar stacking faults appear in copper and silver, respectively. Finally, we demonstrate that, at experimental strain rates, a ductile-to-brittle transition in failure mode similar to previous experimental studies on bicrystalline silver nanowires is observed, which is driven by differences in dislocation activity and grain boundary mobility as compared to the high strain rate case.

Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning.

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks, commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of ∼4×10^{6} candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.

Negative Thermal Expansion of Ultrathin Metal Nanowires: A Computational Study.

Most materials expand upon heating because the coefficient of thermal expansion (CTE), the fundamental property of materials characterizing the mechanical response of the materials to heating, is positive. There have been some reports of materials that exhibit negative thermal expansion (NTE), but most of these have been in complex alloys, where NTE originates from the transverse vibrations of the materials. Here, we show using molecular dynamics simulations that some single crystal monatomic FCC metal nanowires can exhibit NTE along the length direction due to a novel thermomechanical coupling. We develop an analytic model for the CTE in nanowires that is a function of the surface stress, elastic modulus, and nanowire size. The model suggests that the CTE of nanowires can be reduced due to elastic softening of the materials and also due to surface stress. For the nanowires, the model predicts that the CTE reduction can lead to NTE if the nanowire Young's modulus is sufficiently reduced while the nanowire surface stress remains sufficiently large, which is in excellent agreement with the molecular dynamics simulation results. Overall, we find a "smaller is smaller" trend for the CTE of nanowires, leading to this unexpected, surface-stress-driven mechanism for NTE in nanoscale materials.

Electro-elastocapillary Rayleigh-plateau instability in dielectric elastomer films.

We demonstrate, using both finite element simulations and a linear stability analysis, the emergence of an electro-elastocapillary Rayleigh-plateau instability in dielectric elastomer (DE) films under 2D, plane strain conditions. When subject to an electric field, the DEs exhibit a buckling instability for small elastocapillary numbers. For larger elastocapillary numbers, the DEs instead exhibit the Rayleigh-plateau instability. The stability analysis demonstrates the critical effect of the electric field in causing the Rayleigh-plateau instability, which cannot be induced solely by surface tension in DE films. Overall, this work demonstrates the effects of geometry, boundary conditions, and multi-physical coupling on a new example of Rayleigh-plateau instability in soft solids.

Kirigami actuators.

Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single non-propagating crack in a sheet, we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift. Our analytical model shows that these deformations are only weakly dependent on thickness, which we confirm with experiments on centimeter-scale objects and molecular dynamics simulations of graphene and MoS2 nanoscale sheets. We show how the interactions between non-propagating cracks can enable either lift or rotation, and we use a combination of experiments, theory, continuum computational analysis, and molecular dynamics simulations to provide mechanistic insights into the geometric and topological design of kirigami actuators.

Negative Poisson's Ratio in Single-Layer Graphene Ribbons.

The Poisson's ratio characterizes the resultant strain in the lateral direction for a material under longitudinal deformation. Though negative Poisson's ratios (NPR) are theoretically possible within continuum elasticity, they are most frequently observed in engineered materials and structures, as they are not intrinsic to many materials. In this work, we report NPR in single-layer graphene ribbons, which results from the compressive edge stress induced warping of the edges. The effect is robust, as the NPR is observed for graphene ribbons with widths smaller than about 10 nm, and for tensile strains smaller than about 0.5% with NPR values reaching as large as -1.51. The NPR is explained analytically using an inclined plate model, which is able to predict the Poisson's ratio for graphene sheets of arbitrary size. The inclined plate model demonstrates that the NPR is governed by the interplay between the width (a bulk property), and the warping amplitude of the edge (an edge property), which eventually yields a phase diagram determining the sign of the Poisson's ratio as a function of the graphene geometry.

Intrinsic Negative Poisson's Ratio for Single-Layer Graphene.

Negative Poisson's ratio (NPR) materials have drawn significant interest because the enhanced toughness, shear resistance, and vibration absorption that typically are seen in auxetic materials may enable a range of novel applications. In this work, we report that single-layer graphene exhibits an intrinsic NPR, which is robust and independent of its size and temperature. The NPR arises due to the interplay between two intrinsic deformation pathways (one with positive Poisson's ratio, the other with NPR), which correspond to the bond stretching and angle bending interactions in graphene. We propose an energy-based deformation pathway criteria, which predicts that the pathway with NPR has lower energy and thus becomes the dominant deformation mode when graphene is stretched by a strain above 6%, resulting in the NPR phenomenon.

Cofilin reduces the mechanical properties of actin filaments: approach with coarse-grained methods.

An actin filament is an essential cytoskeleton protein in a cell. Various proteins bind to actin for cell functions such as migration, division, and shape control. ADF/cofilin is a protein that severs actin filaments and is related to their dynamics. Actin is known to have excellent mechanical properties. Binding cofilin reduces its mechanical properties, and is related to the severing process. In this research, we applied a coarse-grained molecular dynamics simulation (CGMD) method to obtain actin filaments and cofilin-bound actin (cofilactin) filaments. Using these two obtained models, we constructed an elastic network model-based structure and conducted a normal mode analysis. Based on the low-frequency normal modes of the filament structure, we applied the continuum beam theory to calculate the mechanical properties of the actin and cofilactin filaments. The CGMD method provided structurally accurate actin and cofilactin filaments in relation to the mechanical properties, which showed good agreement with the established experimental results.

ß-sheet-like formation during the mechanical unfolding of prion protein.

Single molecule experiments and simulations have been widely used to characterize the unfolding and folding pathways of different proteins. However, with few exceptions, these tools have not been applied to study prion protein, PrP(C), whose misfolded form PrP(Sc) can induce a group of fatal neurodegenerative diseases. Here, we apply novel atomistic modeling based on potential energy surface exploration to study the constant force unfolding of human PrP at time scales inaccessible with standard molecular dynamics. We demonstrate for forces around 100 pN, prion forms a stable, three-stranded ß-sheet-like intermediate configuration containing residues 155-214 with a lifetime exceeding hundreds of nanoseconds. A mutant without the disulfide bridge shows lower stability during the unfolding process but still forms the three-stranded structure. The simulations thus not only show the atomistic details of the mechanically induced structural conversion from the native α-helical structure to the ß-rich-like form but also lend support to the structural theory that there is a core of the recombinant PrP amyloid, a misfolded form reported to induce transmissible disease, mapping to C-terminal residues ≈160-220.

Fermi-Pasta-Ulam physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling.

Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta, and Ulam. Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for Fermi-Pasta-Ulam physics. We find the thermalization rate Γ to be independent of radius and scaling as Γ∼T*/εpre2, where T* and εpre are effective resonator temperature and prestrain.

Atomistic simulations of electric field effects on the Young's modulus of metal nanowires.

We present a computational, atomistic study of electric field effects on the Young's modulus of metal nanowires. The simulations are electromechanically coupled, where the mechanical forces on the atoms are obtained from realistic embedded atom method potentials, and where the electrostatic forces on the atoms are obtained using a point dipole electrostatic model that is modified to account for the different polarizability and bonding environment of surface atoms. By considering three different nanowire axial orientations (left angle bracket 100 right angle bracket, left angle bracket 110 right angle bracket and right angle bracket 111 right angle bracket) of varying cross sectional sizes and aspect ratios, we find that the Young's modulus of the nanowires differs from that predicted for the purely mechanical case due to the elimination of nonlinear elastic stiffening or softening effects due to the electric field-induced positive relaxation strain relative to the relaxed mechanical configuration. We further find that left angle bracket 100 right angle bracket nanowires are most sensitive to the applied electric field, with Young's moduli that can be increased more than 20% with increasing aspect ratio. Finally, while the orientation of the transverse surfaces does impact the Young's modulus of the nanowires under applied electric field, the key factor controlling the magnitude of the stiffness change of the nanowires is the distance between atomic planes along the axial direction of the nanowire bulk.

Adsorbate migration effects on continuous and discontinuous temperature-dependent transitions in the quality factors of graphene nanoresonators.

We perform classical molecular dynamics simulation to investigate the mechanisms underpinning the unresolved, experimentally observed temperature-dependent scaling transition in the quality factors of graphene nanomechanical resonators (GNMRs). Our simulations reveal that the mechanism underlying this temperature scaling phenomenon is the out-of-plane migration of adsorbates on GNMRs. Specifically, the migrating adsorbate undergoes frequent collisions with the GNMR, which strongly influences the resulting mechanical oscillation, and thus the quality factors. We also predict a discontinuous transition in the quality factor at a lower critical temperature, which results from the in-plane migration of the adsorbate. Overall, our work clearly demonstrates the strong effect of adsorbate migration on the quality factors of GNMRs.

How graphene slides: measurement and theory of strain-dependent frictional forces between graphene and SiO2.

Strain, bending rigidity, and adhesion are interwoven in determining how graphene responds when pulled across a substrate. Using Raman spectroscopy of circular, graphene-sealed microchambers under variable external pressure, we demonstrate that graphene is not firmly anchored to the substrate when pulled. Instead, as the suspended graphene is pushed into the chamber under pressure, the supported graphene outside the microchamber is stretched and slides, pulling in an annulus. Analyzing Raman G band line scans with a continuum model extended to include sliding, we extract the pressure dependent sliding friction between the SiO2 substrate and mono-, bi-, and trilayer graphene. The sliding friction for trilayer graphene is directly proportional to the applied load, but the friction for monolayer and bilayer graphene is inversely proportional to the strain in the graphene, which is in violation of Amontons' law. We attribute this behavior to the high surface conformation enabled by the low bending rigidity and strong adhesion of few layer graphene.

Origin of size dependency in coherent-twin-propagation-mediated tensile deformation of noble metal nanowires.

Researchers have recently discovered ultrastrong and ductile behavior of Au nanowires (NWs) through long-ranged coherent-twin-propagation. An elusive but fundamentally important question arises whether the size and surface effects impact the twin propagation behavior with a decreasing diameter. In this work, we demonstrate size-dependent strength behavior of ultrastrong and ductile metallic NWs. For Au, Pd, and AuPd NWs, high ductility of about 50% is observed through coherent twin propagation, which occurs by a concurrent reorientation of the bounding surfaces from {111} to {100}. Importantly, the ductility is not reduced with an increase in strength, while the twin propagation stress dramatically increases with decreasing NW diameter from 250 to 40 nm. Furthermore, we find that the power-law exponent describing the twin propagation stress is fundamentally different from the exponent describing the size-dependence of the yield strength. Specifically, the inverse diameter-dependence of the twin propagation stress is directly attributed to surface reorientation, which can be captured by a surface energy differential model. Our work further highlights the fundamental role that surface reorientations play in enhancing the size-dependent mechanical behavior and properties of metal NWs that imply the feasibility of high efficiency mechanical energy storage devices suggested before.

Resonant tunneling in graphene pseudomagnetic quantum dots.

Realistic relaxed configurations of triaxially strained graphene quantum dots are obtained from unbiased atomistic mechanical simulations. The local electronic structure and quantum transport characteristics of y-junctions based on such dots are studied, revealing that the quasi-uniform pseudomagnetic field induced by strain restricts transport to Landau level- and edge state-assisted resonant tunneling. Valley degeneracy is broken in the presence of an external field, allowing the selective filtering of the valley and chirality of the states assisting in the resonant tunneling. Asymmetric strain conditions can be explored to select the exit channel of the y-junction.