Nanomechanical Systems Research Articles

Protein adsorption by nanomechanical mass spectrometry: Beyond the real-time molecular weighting.

During past decades, enormous progress in understanding the mechanisms of the intermolecular interactions between the protein and surface at the single-molecule level has been achieved. These advances could only be possible by the ongoing development of highly sophisticated experimental methods such as atomic force microscopy, optical microscopy, surface plasmon resonance, ellipsometry, quartz crystal microbalance, conventional mass spectrometry, and, more recently, the nanomechanical systems. Here, we highlight the main findings of recent studies on the label-free single-molecule (protein) detection by nanomechanical systems including those focusing on the protein adsorption on various substrate surfaces. Since the nanomechanical techniques are capable of detecting and manipulating proteins even at the single-molecule level, therefore, they are expected to open a new way of studying the dynamics of protein functions. It is noteworthy that, in contrast to other experimental methods, where only given protein properties like molecular weight or protein stiffness can be determined, the nanomechanical systems enable a real-time measurement of the multiple protein properties (e.g., mass, stiffness, and/or generated surface stress), making them suitable for the study of protein adsorption mechanisms. Moreover, we also discuss the possible future trends in label-free detection and analysis of dynamics of protein complexes with these nanomechanical systems.

Chaotic forced vibration analysis of a single-walled carbon nanotube resting on elastic foundations

Chaotic presence in nanotube (CNT) vibration is a potential source of imprecision and instability in nanomechanical systems. It is for this reason that the major focus of this paper is on the subject. The system’s vibration model is developed using the Euler–Bernoulli beam and nonlocal theory with consideration of transverse harmonic force, thermal term, magnetic field, and Pasternak foundation influences. The equation of motion is then solved using the Galerkin decomposition method and the Differential transform method (DTM). The influences of velocity, nonlocal parameters, transverse harmonic force, and length on the nonlinear vibration of the nanotube are analyzed using the simulations contained in this paper. For the purpose of convergence and dynamic response analysis, the obtained results in this study were treated with the use of the Cosine-after treatment technique (CAT). The outcome indicates that the controlling parameters such as harmonic force, nonlocal terms, velocity and all other included terms have considerable effects on the behavior of a CNT and can be used as effective control parameters for avoiding chaos.

Anisotropic crystal orientations dependent mechanical properties and fracture mechanisms in zinc blende ZnTe nanowires.

The orientations of crystal growth significantly affect the operating characteristics of elastic and inelastic deformation in semiconductor nanowires (NWs). This work uses molecular dynamics simulation to extensively investigate the orientation-dependent mechanical properties and fracture mechanisms of zinc blende ZnTe NWs. Three different crystal orientations, including [100], [110], and [111], coupled with temperatures (100 to 600 K) on the fracture stress and elastic modulus, are thoroughly studied. In comparison to the [110] and [100] orientations, the [111]-oriented ZnTe NW exhibits a high fracture stress. The percentage decrease in fracture strength exhibits a pronounced variation with increasing temperature, with the highest magnitude observed in the [100] direction and the lowest magnitude observed in the [110] direction. The elastic modulus dropped by the largest percentage in the [111] direction as compared to the [100] direction. Most notably, the [110]-directed ZnTe NW deforms unusually as the strain rate increases, making it more sensitive to strain rate than other orientations. The strong strain rate sensitivity results from the unusual short-range and long-range order crystals appearing due to dislocation slipping and partial twinning. Moreover, the {111} plane is the principal cleavage plane for all orientations, creating a dislocation slipping mechanism at room temperature. The {100} plane becomes active and acts as another fundamental cleavage plane at increasing temperatures. This in-depth analysis paves the way for advancing efficient and reliable ZnTe NWs-based nanodevices and nanomechanical systems.

Quantifying the local mechanical properties of twisted double bilayer graphene.

Nanomechanical measurements of minimally twisted van der Waals materials remained elusive despite their fundamental importance for device realisation. Here, we use Ultrasonic Force Microscopy (UFM) to locally quantify the variation of out-of-plane Young's modulus in minimally twisted double bilayer graphene (TDBG). We reveal a softening of the Young's modulus by 7% and 17% along single and double domain walls, respectively. Our experimental results are confirmed by force-field relaxation models. This study highlights the strong tunability of nanomechanical properties in engineered twisted materials, and paves the way for future applications of designer 2D nanomechanical systems.

Topological lattices realized in superconducting circuit optomechanics.

Cavity optomechanics enables the control of mechanical motion through the radiation-pressure interaction1, and has contributed to the quantum control of engineered mechanical systems ranging from kilogramme-scale Laser Interferometer Gravitational-wave Observatory (LIGO)mirrors to nanomechanical systems, enabling ground-state preparation2,3, entanglement4,5, squeezing of mechanical objects6, position measurements at the standard quantum limit7 and quantum transduction8. Yet nearly all previous schemes have used single- or few-mode optomechanical systems. By contrast, new dynamics and applications are expected when using optomechanical lattices9, which enable the synthesis of non-trivial band structures, and these lattices have been actively studied in the field of circuit quantum electrodynamics10. Superconducting microwave optomechanical circuits2 are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here we overcome this challenge and demonstrate topological microwave modes in one-dimensional circuit optomechanical chains realizing the Su-Schrieffer-Heeger model11,12. Furthermore, we realize the strained graphene model13,14 in a two-dimensional optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe15,16. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offer an avenue to explore collective17,18, quantum many-body19 and quench20 dynamics, topological properties9,21 and, more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedom22-24.

The conductivity and electrophysical characteristics of Janus-like TaSi2/Si nanoparticles

All applications of single nanoparticles as independent nano-objects are based not on their collective properties, but on their individual properties, which are currently insufficiently studied in the vast majority of cases. The same applies to single Janus-like TaSi2/i-Si nanoparticles, which are independent nano-objects with prominent individual properties. In this regard, a system of single Janus-like TaSi2/i-Si nano-particles with a seven percent weight content of the TaSi2 metal phase is investigated for the first time using atomic force microscopy methods, conductivity, static volt–ampere characteristics (VACs) and the spatial 3D structure of the electrostatics, namely: the thermal emissions and tunneling mechanisms responsible for current transfer through the close-contact area between TaSi2 and i-Si; the effect of a serial resistance of RS = 156 MΩ on the VACs, the barriers ϕbm ( f) = 0.578 eV and ϕbm (r) = 0.648 eV, large values of the ideality indices nf = 3.61 and nr = 5.07 for the VAC reverse and forward branches; the 3D distribution of the electrostatic potential of the surface 4.84 ⩽ Ф(x,y)⩽ 4.90 eV; the electrostatic field | E | = 1.76 × 106 V m−1, and the capacitive contrast ∂C(x, y)/∂z. The values of ϕbm , which are uncharacteristic for commonly used metal/Si Schottky contacts, and the abnormally large values of n and RS confirm the pronounced individual properties of these nanoparticles. The presence of a potential barrier in the close TaSi2/i-Si contact leads to the emergence of a space charge region with a sufficiently strong intrinsic electric field E. The latter contributes to the redistribution of electric charges and the appearance of an electric dipole moment in the particles, which increases the number of their degrees of freedom. All these individual features strongly influence the adhesion and transport properties of the particles and their interactions with electromagnetic radiation, which are of particular interest to specialists in the fields of semiconductor electronics, microwave engineering, nanomechanical systems, catalysis, and biomedicine.

Modulating Directional Movement of Graphene Nanoflake Using a Channel

The graphene-based nano-mechanical systems have attracted a lot of attention due to their unique properties. Owing to its planar shape, it is hard to control the direction of motion of graphene. In this study, a directional system based on graphene with a channel driven by a thermal gradient was examined by means of molecular dynamics simulations. The results showed that the channel could direct the motion and correct the rotation of graphene nanoflakes. The movement of graphene nanoflake not only depended on the interaction between the nanoflake and the substrate, but also the configuration of the graphene in the channel. A larger thermal gradient was needed to drive a hydrogen-passivated graphene nanoflake. However, the movement of a passivated nanoflake was more stable. Our results showed that a passivated graphene nanoflake could move steadily along a direction in a channel, which might shed light on the design of nano-mechanical systems based on graphene.

Mesoscopic physics of nanomechanical systems

Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic physics of nanomechanical systems. Major applications of nanomechanics in science and technology are also outlined. A broad range of phenomena related to the conservative as well as dissipative nonlinearity and fluctuations are discussed within a unifying framework. They include the linear response of single and coupled vibrational modes as well as nonlinear effects of periodic driving. Such driving breaks the continuous time-translation symmetry and the detailed balance, with conspicuous consequences for fluctuations, particularly in the presence of the driving-induced bi- and multistability. Mathematical techniques are described in the appendices to streamline the reading, but also to provide an introduction to the theory. The goal of the review is to show the richness of the physics at work. The continuous experimental and theoretical advances make nanomechanical systems a vibrant area of research, with many new phenomena to discover.

Nonlinear Stiffness and Nonlinear Damping in Atomically Thin MoS2 Nanomechanical Resonators

We report on experimental measurements and quantitative analyses of nonlinear dynamic characteristics in ultimately thin nanomechanical resonators built upon single-layer, bilayer, and trilayer (1L, 2L, and 3L) molybdenum disulfide (MoS2) vibrating drumhead membranes. This synergistic study with calibrated measurements and analytical modeling on observed nonlinear responses has led to the determination of nonlinear damping and stiffness coefficients at cubic and quintic orders for these two-dimensional (2D) resonators operating in the very high frequency (VHF) band (up to ∼90 MHz). We find that the quintic force can be ∼20% of the Duffing force at larger amplitudes, and thus, it generally cannot be ignored in a nonlinear dynamics analysis. This study provides the first quantification of nonlinear damping and frequency detuning characteristics in 2D semiconductor nanomechanical resonators and elucidates their origins and dependency on engineerable parameters, setting a foundation for future exploration and utilization of the rich nonlinear dynamics in 2D nanomechanical systems.

Nano-Optomechanical Resonators Based on Suspended Graphene for Thermal Stress Sensing

Nanomechanical resonators made from suspended graphene combine the properties of ultracompactness and ultrahigh detection sensitivity, making them interesting devices for sensing applications. However, nanomechanical systems can be affected by membrane stress. The present work developed an optomechanical resonator for thermal stress sensing. The proposed resonator consists of a section of hollow core fiber (HCF) and a trampoline graphene-Au membrane. An all-optical system that integrated optical excitation and optical detection was applied. Then, the resonance frequency of the resonator was obtained through this all-optical system. In addition, this system and the resonator were used to detect the membrane's built-in stress, which depended on the ambient temperature, by monitoring the resonance frequency shift. The results verified that the temperature-induced thermal effect had a significant impact on membrane stress. Temperature sensitivities of 2.2646 kHz/°C and 2.3212 kHz/°C were obtained when the temperature rose and fell, respectively. As such, we believe that this device will be beneficial for the quality monitoring of graphene mechanical resonators.

Wrinkle-mediated CVD synthesis of wafer scale Graphene/h-BN heterostructures

The combination of two-dimensional materials (2D) into heterostructures enables their integration in tunable ultrathin devices. For applications in electronics and optoelectronics, direct growth of wafer-scale and vertically stacked graphene/hexagonal boron nitride (h-BN) heterostructures is vital. The fundamental problem, however, is the catalytically inert nature of h-BN substrates, which typically provide a low rate of carbon precursor breakdown and consequently a poor rate of graphene synthesis. Furthermore, out-of-plane deformations such as wrinkles are commonly seen in 2D materials grown by chemical vapor deposition (CVD). Herein, a wrinkle-facilitated route is developed for the fast growth of graphene/h-BN vertical heterostructures on Cu foils. The key advantage of this synthetic pathway is the exploitation of the increased reactivity from inevitable line defects arising from the CVD process, which can act as active sites for graphene nucleation. The resulted heterostructures are found to exhibit superlubric properties with increased bending stiffness, as well as directional electronic properties, as revealed from atomic force microscopy measurements. This work offers a brand-new route for the fast growth of Gr/h-BN heterostructures with practical scalability, thus propelling applications in electronics and nanomechanical systems.

Nonlinear Vibration Movements of the Mid-Supported Micro-Beam

This study analyzes the vibration movements of multi-support micro beams placed in an electrically smooth area using the modified couple stress theory. It has been assumed that the potential voltage that creates the electrical field strength varies harmonically. Large number of experiments in recent years have indicated that classical continuum theory is unable to predict the mechanical behavior of microstructure with small size. However, nonclassical continuum theory should be used to accurately design and analyze the microstructures. Modified couple stress theory models the micro and nanomechanical systems with higher accuracy because they employ additional material parameters to the equation considering size dependent behavior. The most general nonlinear motion equations for multi-support microbeams have been obtained by considering the material size parameter, the number of support and support positions, damping effect, axial stresses, electrical field strength, and nonlinear effects resulting from elongations. The nonlinear equations of motion are obtained according to the Hamilton method using the modified couple stress theory (MCST). The resulting equations of motion are nondimensionalized. In this way, the mathematical model has been made independent of the type and geometric structure of the material. Approximate solutions of the obtained dimensionless motion equation are obtained by the multi-scale method, which is one of the perturbation methods. As a result, an increase occurs in the first mode frequencies ([Formula: see text]) and nonlinear correction effect parameters ([Formula: see text]) with the progress of the center support position gradually towards [Formula: see text] and the increase of the microbeam elasticity coefficient ([Formula: see text]).

Machine learning to probe modal interaction in dynamic atomic force microscopy

Modal interactions are pervasive effects that commonly emerge in nanomechanical systems. The coupling of vibrating modes can be leveraged in many ways, including to enhance sensing or to disclose complex phenomenologies. In this work we show how machine learning and data-driven approaches could be used to capture intermodal coupling. We employ a quasi-recurrent neural network (QRNN) for identifying mode coupling and verify its applicability on experimental data obtained from tapping mode atomic force microscopy (AFM). Hidden units of the QRNN are monitored to trace fingerprints of modes activation and to quantify their contributions over the global distortion of orbits in the phase space. To demonstrate the broad applicability of the method, the trained model is re-applied over different experiments and on diverse materials. Over a range of tip-sample configurations, dynamic AFM possesses features general enough to be seized by the QRNN and it is not required an ad-hoc re-training for the identification of interacting modes. Our study opens up a route for utilizing established machine learning techniques for rapid recognition of nonlinear complex effect such as internal resonances in nanotechnology. The QRNN analysis is meant to assist AFM sensing operations when exploiting modal interaction to enhance the signal-to-noise ratio of higher harmonics and provide high resolution compositional contrast in multi-frequency AFM applications.

Achievable accuracy of resonating nanomechanical systems for mass sensing of larger analytes in GDa range

Measurement of larger analytes such as many chemical and biological structures or viruses in gigadalton (GDa) range is a reminding fundamental task in analytical chemistry and life sciences, which can be possibly resolved with the resonating nanomechanical systems. Common approaches to mass sensing with these systems model the bound analyte as a point particle and assume the analyte does not change the vibrational mode shapes. However, for larger analytes their stiffness and size not only affect the resonant frequencies but also cause the significant changes in the vibrational mode shapes making their measurement highly challenging and still under-explored problem. Here, we develop a 3D model capable to accurately predict the resonant frequencies and vibrational mode shapes of the resonating nanomechanical systems with the bound analyte of arbitrary properties and size. Then, we examine in details the impact of analyte properties, size and its position of attachment on the resonant frequencies and vibrational mode shapes and, correspondingly, resolve a dispute over the achievable detection limits of the nanomechanical systems, especially for mass sensing of larger analytes. Furthermore, we identify three different sensing regimes, that is, the ultra-light, light and heavy, for which the effects of the analyte mass, stiffness, its size and the position of attachment on the accuracy of the determined mass can be separated. For the ultra-light regime (mass ratio < 10−3) the analyte stiffness and its size affect notably the resonant frequencies, the point mass approximation is inaccurate and the analyte can be identified by its mass and stiffness. For the light regime the point mass approximation is accurate, while for the heavy one (mass ratio > 2∙10−2) the mass effect dominates the frequency response and alters the vibrational mode shapes which, for the common approaches, yields the errors in the determined analyte mass. Finally, we also propose an easily accessible approach for the identification of larger analytes (in GDa range) that does not require the advanced computational tools or experimental setup, applicable to the majority of the clamped-clamped ends resonating nanomechanical systems.

Tunable Friction Properties of Periodic Wrinkled BaTiO3 Membranes

AbstractThe wrinkled patterns may find potential applications in the areas that require tunable friction properties, such as flexible electronics, nanomechanical systems, and biomedical devices. However, the regulation of wrinkled patterns and the influence of friction property remain poorly understood, especially in the field of oxides. The epitaxial wrinkled BaTiO3 (BTO) membranes are prepared by the pulsed laser deposition and water‐dissolution process. The patterns, amplitude, and wavelength of the wrinkled BTO membranes are dependent on the thickness, pre‐stretched mechanical stress, and heat treatment. The friction properties of the wrinkled BTO membranes exhibit various anisotropic and periodic features due to the varying wrinkled patterns as applying different mechanical stress, including anisotropy with 180° angular periodicity, anisotropy with 360° angular periodicity, and isotropy, corresponding to the parallel, zigzag, and labyrinth patterns, respectively. Moreover, the heat process can further alter the magnitude of the friction property, showing a downward trend with increasing temperature. These results provide a better understanding of the friction properties of wrinkled patterns and pave a novel way to alter the friction properties for extensive applications.

Thermal-fluctuation gradient induced tangential entropic forces in layered two-dimensional materials

Recent studies on nanomechanical devices based on low-dimensional nanomaterials have revealed several different types of thermal fluctuation gradient induced tangential entropic forces (TEFs), including expulsion force, edge force, thermophoretic force, nanodurotaxis force, etc. While all these forces originate from thermal fluctuation gradients, they can take different forms for different problems and have been treated case-by-case in the literature. Here, we develop a unified theoretical framework for TEFs in layered low-dimensional materials. In particular, we derive explicit analytical solutions for TEFs in layered two-dimensional materials and validate them with molecular dynamics simulations for various bilayers composed of graphene, graphyne, hexagonal-boron nitride (h-BN), boron-carbon-nitride (BCN), and double walled nanotubes. We present also approximate solutions to TEFs in hetero- or substrate-supported-bilayers based on a solution-guided machine learning (SGML) technique. The developed concept for TEFs is unique to nanomechanical systems and may serve as one of the founding pillars of nanomechanics.

On size-dependent thermo-viscoelasticity theory for piezoelectric materials

Nanomechanical systems are widely employed in research and engineering for a variety of purposes. For the design of nanodevices, a comprehensive understanding of these systems’ mechanical compliance is important. One of the most likely alternatives for nanodevices has been the use of viticultural nanomaterials with excellent mechanical, thermal and chemical characteristics. In the framework of the piezoelectric-thermo-viscoelastic solid, a nonlocal systemic formulation is built, sizes-dependent coupling of viscoelastic and thermal deformations. Laplace transforms technique is used. For piezoelectric rod, the obtained formulation is utilized to address one-dimensional problems. The numerical approach for the inversion of the Laplace transforms is used to get numerical results that are visually represented. Some comparisons are shown in the figures to estimate the influences of nonlocal parameters.

Size-dependent thermoelastic damping analysis in nanobeam resonators based on Eringen’s nonlocal elasticity and modified couple stress theories

Thermoelastic damping has emerged as a critical issue in the modeling and design of micro and nanomechanical systems. Therefore, an extensive research interest is being devoted towards the reduction in thermoelastic damping for micro and nanomechanical systems. The present study intends to examine thermoelastic damping in nanobeam resonators using the modified couple stress theory and Eringen’s nonlocal elasticity theory, thus so-called modified nonlocal couple stress theory within the context of the recently proposed Moore–Gibson–Thompson thermoelasticity theory. In order to observe size effects, the size-dependent coupled thermoelastic equations are derived by combining modified couple stress theory and nonlocal elasticity theory in the frame of Moore–Gibson–Thompson thermoelasticity. The coupled governing equations for thermoelastic damping of nanobeam resonators are solved analytically in terms of the inverse quality factor. The size-dependent thermoelastic damping of nanobeams is presented graphically with the help of numerical results predicted by modified nonlocal couple stress theory. The results obtained under the combined effects of modified couple stress theory and nonlocal theory in the present context are further compared to those of the classical, modified couple stress, and nonlocal elasticity theories as special cases of the modified nonlocal couple stress theory. It is observed that thermoelastic damping weakens at the submicron scale under Eringen’s nonlocal elasticity theory, whereas it becomes greater at the submicron scale under modified couple stress theory. However, at the submicron scale, the modeling of nanobeam resonators using modified nonlocal couple stress theory reveals a smaller amount of thermoelastic damping than modified couple stress, nonlocal, and classical theories. In addition, as compared to the Green–Naghdi thermoelasticity theory of type III (GN-III), the Moore–Gibson–Thompson model predicts a higher thermoelastic damping value, while agreeing with the results predicted by the Lord–Shulman (LS) model under modified nonlocal couple stress theory. Some important points highlighted here are believed to be useful in the design of mechanical resonators at micron and submicron scales.

Surface energy effects on thermoelastic vibration of nanomechanical systems under Moore–Gibson–Thompson thermoelasticity and Eringen’s nonlocal elasticity theories

Surface and size effects are frequently important in the design of high-performance nano-sized devices. However, due to the influence of the small-scale impact, the classical theory fails to predict the size-dependent behavior of nanoscale devices. In this regard, the current work attempts to investigate the dynamic and mechanical behaviors of nanobeams using nonlocal elasticity theory and the recently proposed Moore–Gibson–Thompson (MGT) thermoelasticity theory while taking into account the surface effects. In the context of nonlocal elasticity and surface elasticity theories, the governing equation of motion for an Euler–Bernoulli nanobeam that is simply supported at both ends and has a uniform load on the top surface is first derived. Thereafter, the solution for deflection and temperature distribution along the thickness direction of the nanobeam is obtained based on MGT theory using the finite Fourier sine transform and Laplace transform techniques. The influences of nonlocal parameter, phase-lag time, residual surface tension, surface elastic modulus, thickness and length of nanobeam on deflection and temperature over time are systematically analyzed in depth. Some important points are highlighted regarding size dependency and surface effects on thermoelastic vibration of nanobeams in the present context. When surface and small-scale effects are included, this approach may be valuable in understanding the dynamic and mechanical behaviors of nanomechanical systems.

Scrambling and quantum feedback in a nanomechanical system

The question of how swiftly entanglement spreads over a system has attracted vital interest. In this regard, the out-of-time ordered correlator (OTOC) is a quantitative measure of the entanglement spreading process. Particular interest concerns the propagation of quantum correlations in the lattice systems, {\it e.g.}, spin chains. In a seminal paper D. A. Roberts, D. Stanford and L. Susskind, J. High Energy Phys. 03, 051, (2015) the concept of the OTOC's radius was introduced. The radius of the OTOC defines the front line reached by the spread of entanglement. Beyond this radius operators commute. In the present work, we propose a model of two nanomechanical systems coupled with two Nitrogen-vacancy (NV) center spins. Oscillators are coupled to each other directly while NV spins are not. Therefore, the correlation between the NV spins may arise only through the quantum feedback exerted from the first NV spin to the first oscillator and transferred from the first oscillator to the second oscillator via the direct coupling. Thus nonzero OTOC between NV spins quantifies the strength of the quantum feedback. We show that NV spins cannot exert quantum feedback on classical nonlinear oscillators. We also discuss the inherently quantum case with a linear quantum harmonic oscillator indirectly coupling the two spins and verify that in the classical limit of the oscillator, the OTOC vanishes.