A Hybrid Orbitrap-Nanoelectromechanical Systems Approach to Analysis of Individual, Intact Proteins in Real Time.

Nanoelectromechanical systems (NEMS)-based mass spectrometry (MS) is an emerging technique that enables determination of the mass of individual adsorbed particles, by driving nanomechanical devices at resonance and monitoring the real-time changes in their resonance frequencies induced by each single molecule adsorption event. We incorporate NEMS into an Orbitrap mass spectrometer and report our progress towards leveraging the single-molecule capabilities of the NEMS to enhance the dynamic range of conventional MS instrumentation and to offer new capabilities for performing deep proteomic analysis of clinically relevant samples. We use the hybrid instrument to deliver E. coli GroEL molecules (801 kDa) to the NEMS devices in their native, intact state. Custom ion optics are used to focus the beam down to 40 µm diameter with a maximum flux of 25 molecules/second. The mass spectrum obtained with NEMS-MS shows good agreement with the known mass of GroEL.

Nanomechanical mass measurements through feature-based time series clustering.

Recent years have seen explosive growth in miniaturized sensors that can continuously monitor a wide variety of processes, with applications in healthcare, manufacturing, and environmental sensing. The time series generated by these sensors often involves abrupt jumps in the detected signal. One such application uses nanoelectromechanical systems (NEMS) for mass spectrometry, where analyte adsorption produces a quick but finite-time jump in the resonance frequencies of the sensor eigenmodes. This finite-time response can lead to ambiguity in the detection of adsorption events, particularly in high event-rate mass adsorption. Here, we develop a computational algorithm that robustly eliminates this often-encountered ambiguity. A moving-window statistical test together with a feature-based clustering algorithm is proposed to automate the identification of single-event jumps. We validate the method using numerical simulations and demonstrate its application in practice using time-series data that are experimentally generated by molecules adsorbing onto NEMS sensors at a high event rate. This computational algorithm enables new applications, including high-throughput, single-molecule proteomics.

Optical measurement of the picosecond fluid mechanics in simple liquids generated by vibrating nanoparticles: a review.

Standard continuum assumptions commonly used to describe the fluid mechanics of simple liquids have the potential to break down when considering flows at the nanometer scale. Two common assumptions for simple molecular liquids are that (1) they exhibit a Newtonian response, where the viscosity uniquely specifies the linear relationship between the stress and strain rate, and (2) the liquid moves in tandem with the solid at any solid-liquid interface, known as the no-slip condition. However, even simple molecular liquids can exhibit a non-Newtonian, viscoelastic response at the picosecond time scales that are characteristic of the motion of many nanoscale objects; this viscoelasticity arises because these time scales can be comparable to those of molecular relaxation in the liquid. In addition, even liquids that wet solid surfaces can exhibit nanometer-scale slip at those surfaces. It has recently become possible to interrogate the viscoelastic response of simple liquids and associated nanoscale slip using optical measurements of the mechanical vibrations of metal nanoparticles. Plasmon resonances in metal nanoparticles provide strong optical signals that can be accessed by several spectroscopies, most notably ultrafast transient-absorption spectroscopy. These spectroscopies have been used to measure the frequency and damping rate of acoustic oscillations in the nanoparticles, providing quantitative information about mechanical coupling and exchange of mechanical energy between the solid particle and its surrounding liquid. This information, in turn, has been used to elucidate the rheology of viscoelastic simple liquids at the nanoscale in terms of their constitutive relations, taking into account separate viscoelastic responses for both shear and compressible flows. The nanoparticle vibrations have also been used to provide quantitative measurements of slip lengths on the single-nanometer scale. Viscoelasticity has been shown to amplify nanoscale slip, illustrating the interplay between different aspects of the unconventional fluid dynamics of simple liquids at nanometer length scales and picosecond time scales.

Squeeze-Film Effect on Atomically Thin Resonators in the High-Pressure Limit.

The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.

Inertial and viscous flywheel sensing of nanoparticles.

Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. In the context of inertial sensing, which can measure mass with atomic precision, rotational dynamics are normally considered a complication hindering measurement interpretation. Here, we exploit the rotational dynamics of a microfluidic device to develop a modality in inertial sensing. Combining theory with experiments, we show that this modality measures the volume of a rigid particle while normally being insensitive to its density. Paradoxically, particle density only emerges when fluid viscosity becomes dominant over inertia. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a 'viscous flywheel'. This modality now enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement.

Measurement of Navier Slip on Individual Nanoparticles in Liquid.

The Navier slip condition describes the motion of a liquid relative to a neighboring solid surface, with its characteristic Navier slip length being a constitutive property of the solid-liquid interface. Measurement of this slip length is complicated by its small magnitude, expected to be in the nanometer range based on molecular simulations. Here, we report an experimental technique that interrogates the Navier slip length on individual nanoparticles immersed in liquid with subnanometer precision. Proof-of-principle experiments on individual, citrate-stabilized, gold nanoparticles in water give a constant slip length of 2.7 ± 0.6 nm (95% C.I.), independent of particle size. Achieving this feature of size independence is central to any measurement of this constitutive property, which is facilitated through the use of individual particles of varying radii. This demonstration motivates studies that can now validate the wealth of existing molecular simulation data on slip.

Highly Spherical Nanoparticles Probe Gigahertz Viscoelastic Flows of Simple Liquids Without the No-Slip Condition.

Simple liquids are conventionally described by Newtonian fluid mechanics, based on the assumption that relaxation processes in the flow occur much faster than the rate at which the fluid is driven. Nanoscale solids, however, have characteristic mechanical response times on the picosecond scale, which are comparable to mechanical relaxation times in simple liquids; as a result, viscoelastic effects in the liquid must be considered. These effects have been observed using time-resolved optical measurements of vibrating nanoparticles, but interpretation has often been complicated by finite velocity slip at the liquid-solid interface. Here, we use highly spherical gold nanoparticles to drive flows that are theoretically modeled without the use of the no-slip boundary condition at the particle surface. We obtain excellent agreement with this analytical theory that considers both the compression and shear relaxation properties of the liquid.

Viscoelasticity Enhances Nanometer-Scale Slip in Gigahertz-Frequency Liquid Flows.

The interaction between flowing liquids and solid surfaces underpins many physical phenomena and technologies, such as the ability of an airfoil to generate lift and the mixing of liquids for industrial applications. These phenomena are often described using the Navier-Stokes equations and the no-slip boundary condition: the assumption that the liquid immediately adjacent to a solid surface does not move relative to the surface. Herein, we observe violation of the no-slip condition with strong enhancement of slip due to intrinsic viscoelasticity of the bulk liquid. This is achieved by measuring the 20 GHz acoustic vibrations of gold nanoparticles in glycerol/water mixtures, for which the underlying physics is explored using rigorous, theoretical models. The reported enhancement of slip revises current understanding of ultrafast liquid flows, with implications for technologies ranging from membrane filtration to nanofluidic devices and biomolecular sensing.

Acoustic Vibrations of Al Nanocrystals: Size, Shape, and Crystallinity Revealed by Single-Particle Transient Extinction Spectroscopy.

Acoustic vibrations in plasmonic nanoparticles, monitored by an all-optical means, have attracted significant increasing interest because they provide unique insight into the mechanical properties of these metallic nanostructures. Al nanostructures are a recently emerging alternative to noble metal nanoparticles, because their broad wavelength tunability and high natural abundance make them ideal for many potential applications. Here, we investigate the acoustic vibrations of individual Al nanocrystals using a combination of electron microscopy and single-particle transient extinction spectroscopy, made possible with a low-pulse energy, high sensitivity, and probe-wavelength-tunable, single-particle transient extinction microscope. For chemically synthesized, faceted Al nanocrystals, the observed vibration frequency scales with the inverse particle diameter. In contrast, triangularly shaped Al nanocrystals support two distinct frequencies, corresponding to their in- and out-of-plane breathing modes. Unlike ensemble measurements, which measure average properties, measuring the damping time of the acoustic vibrations for individual particles enables us to investigate variations of the quality factor on the particle-to-particle level. Surprisingly, we find a large variation in quality factors even for nanocrystals of similar size and shape. This observed heterogeneity appears to result from substantially varying degrees of nanoparticle crystallinity even for chemically synthesized nanocrystals.

Origin of spurious oscillations in lattice Boltzmann simulations of oscillatory noncontinuum gas flows.

Oscillatory noncontinuum gas flows at the micro and nanoscales are characterized by two dimensionless groups: a dimensionless molecular length scale, the Knudsen number Kn, and a dimensionless frequency θ, relating the oscillatory frequency to the molecular collision frequency. In a recent study [Shi et al., Phys. Rev. E 89, 033305 (2014)10.1103/PhysRevE.89.033305], the accuracy of the lattice Boltzmann (LB) method for simulating these flows at moderate-to-large Kn and θ was examined. In these cases, the LB method exhibits spurious numerical oscillations that cannot be removed through the use of discrete particle velocities drawn from higher-order Gauss-Hermite quadrature. Here, we identify the origin of these spurious effects and formulate a method to minimize their presence. This proposed method splits the linearized Boltzmann Bhatnagar-Gross-Krook (BGK) equation into two equations: (1) a homogeneous "gain-free equation" that can be solved directly, containing terms responsible for the spurious oscillations; and (2) an inhomogeneous "remainder equation" with homogeneous boundary conditions (i.e., stationary boundaries) that is solved using the conventional LB algorithm. This proposed "splitting method" is validated using published high-accuracy numerical solutions to the linearized Boltzmann BGK equation where excellent agreement is observed.

Large-scale parallelization of nanomechanical mass spectrometry with weakly-coupled resonators.

Nanomechanical mass spectrometry is a recent technological breakthrough that enables the real-time analysis of single molecules. In contraposition to its extreme mass sensitivity is a limited capture cross-section that can hinder measurements in a practical setting. Here we show that weak-coupling between devices in resonator arrays can be used in nanomechanical mass spectrometry to parallelize the measurement. This coupling gives rise to asymmetric amplitude peaks in the vibrational response of a single nanomechanical resonator of the array, which coincide with the natural frequencies of all other resonators in the same array. A rigorous theoretical model is derived that explains the physical mechanisms and describes the practical features of this parallelization. We demonstrate the significance of this parallelization through inertial imaging of analytes adsorbed to all resonators of an array, with the possibility of simultaneously detecting resonators placed at distances a hundred times larger than their own physical size.

Strong vibrational coupling in room temperature plasmonic resonators.

Strong vibrational coupling has been realized in a variety of mechanical systems. However, there have been no experimental observations of strong coupling of the acoustic modes of plasmonic nanostructures, due to rapid energy dissipation in these systems. Here we realized strong vibrational coupling in ultra-high frequency plasmonic nanoresonators by increasing the vibrational quality factors by an order of magnitude. We achieved the highest frequency quality factor products of f × Q = 1.0 × 1013 Hz for the fundamental mechanical modes, which exceeds the value of 0.6 × 1013 Hz required for ground state cooling. Avoided crossing was observed between vibrational modes of two plasmonic nanoresonators with a coupling rate of g = 7.5 ± 1.2 GHz, an order of magnitude larger than the dissipation rates. The intermodal strong coupling was consistent with theoretical calculations using a coupled oscillator model. Our results enabled a platform for future observation and control of the quantum behavior of phonon modes in metallic nanoparticles.

Publisher Correction: Interatomic force laws that evade dynamic measurement.

In the version of this Comment originally published, equation (4) was incorrect; see the correction notice for details. This has now been corrected in the online versions of the Comment.

Interatomic force laws that evade dynamic measurement.

Measurement of the force between two atoms is performed routinely with the atomic force microscope. The shape of this interatomic force law is now found to directly regulate this capability: rapidly varying interatomic force laws, which are common in nature, can corrupt their own measurement.

Solvent-Engineered Stress in Nanoscale Materials.

Nanoscale materials are frequently coated with surface stabilization layers during growth that prevent flocculation in solution and facilitate processing technologies such as ink-jet device printing. Here, we show that few-nanometer-thick stabilization layers typically used swell in the presence of certain solvents and impart significant stresses to the nanomaterial that remains even after the solvent has evaporated. Solvent swelling of the surface layer dramatically enhances nanomaterial-substrate adhesion via the collapse of the stabilization layer during solvent evaporation, preventing stress relaxation. We demonstrate the stress modulation of Ag, Au, and Si nanowires functionalised with surface polymers and surfactant layers and detect strain levels between 0.1 and 0.6% using atomic force microscopy mechanical measurement and Raman spectroscopy. Dry-transferred nanowires exhibit poor adhesion and show no evidence of incorporated stress but become stressed immediately following solvent exposure. Strain engineering is demonstrated by coating nanowires with few-nanometer-thick solvent-responsive polymer layers.

On the measurement of relaxation times of acoustic vibrations in metal nanowires.

The mechanical resonances of metal nanostructures are strongly affected by their environment. In this paper the way the breathing modes of single metal nanowires are damped by liquids with different viscosities was studied by ultrafast pump-probe microscopy experiments. Both nanowires supported on a glass substrate and nanowires suspended over trenches were investigated. The measured quality factors for liquid damping for the suspended nanowires are in good agreement with continuum mechanics calculations for an inviscid fluid that assume continuity in stress and displacement at the nanowire-liquid interface. This shows that liquid damping is controlled by radiation of sound waves into the medium. For the nanowires on the glass surface the quality factors for liquid damping are approximately 60% higher than those for the suspended nanowires. This is attributed to a shadowing effect. The nanowires in our measurements have pentagonal cross-sections. This produces two different breathing modes and also means that one of the faces for the supported nanowires is blocked by the substrate, which reduces the amount of damping from the liquid. Comparing the supported and suspended nanowires also allows us to estimate the effect of the substrate on the acoustic mode damping. We find that the substrate has a weak effect, which is attributed to poor mechanical contact between the nanowires and the substrate.

Polycrystallinity of Lithographically Fabricated Plasmonic Nanostructures Dominates Their Acoustic Vibrational Damping.

The study of acoustic vibrations in nanoparticles provides unique and unparalleled insight into their mechanical properties. Electron-beam lithography of nanostructures allows precise manipulation of their acoustic vibration frequencies through control of nanoscale morphology. However, the dissipation of acoustic vibrations in this important class of nanostructures has not yet been examined. Here we report, using single-particle ultrafast transient extinction spectroscopy, the intrinsic damping dynamics in lithographically fabricated plasmonic nanostructures. We find that in stark contrast to chemically synthesized, monocrystalline nanoparticles, acoustic energy dissipation in lithographically fabricated nanostructures is solely dominated by intrinsic damping. A quality factor of Q = 11.3 ± 2.5 is observed for all 147 nanostructures, regardless of size, geometry, frequency, surface adhesion, and mode. This result indicates that the complex Young's modulus of this material is independent of frequency with its imaginary component being approximately 11 times smaller than its real part. Substrate-mediated acoustic vibration damping is strongly suppressed, despite strong binding between the glass substrate and Au nanostructures. We anticipate that these results, characterizing the optomechanical properties of lithographically fabricated metal nanostructures, will help inform their design for applications such as photoacoustic imaging agents, high-frequency resonators, and ultrafast optical switches.

Mass Spectrometry Using Nanomechanical Systems: Beyond the Point-Mass Approximation.

The mass measurement of single molecules, in real time, is performed routinely using resonant nanomechanical devices. This approach models the molecules as point particles. A recent development now allows the spatial extent (and, indeed, image) of the adsorbate to be characterized using multimode measurements ( Hanay , M. S. , Nature Nanotechnol. , 10 , 2015 , pp 339 - 344 ). This "inertial imaging" capability is achieved through virtual re-engineering of the resonator's vibrating modes, by linear superposition of their measured frequency shifts. Here, we present a complementary and simplified methodology for the analysis of these inertial imaging measurements that exhibits similar performance while streamlining implementation. This development, together with the software that we provide, enables the broad implementation of inertial imaging that opens the door to a range of novel characterization studies of nanoscale adsorbates.

Vibrational coupling in plasmonic molecules.

Plasmon hybridization theory, inspired by molecular orbital theory, has been extremely successful in describing the near-field coupling in clusters of plasmonic nanoparticles, also known as plasmonic molecules. However, the vibrational modes of plasmonic molecules have been virtually unexplored. By designing precisely configured plasmonic molecules of varying complexity and probing them at the individual plasmonic molecule level, intramolecular coupling of acoustic modes, mediated by the underlying substrate, is observed. The strength of this coupling can be manipulated through the configuration of the plasmonic molecules. Surprisingly, classical continuum elastic theory fails to account for the experimental trends, which are well described by a simple coupled oscillator picture that assumes the vibrational coupling is mediated by coherent phonons with low energies. These findings provide a route to the systematic optical control of the gigahertz response of metallic nanostructures, opening the door to new optomechanical device strategies.

Optomechanics of Single Aluminum Nanodisks.

Aluminum nanostructures support tunable surface plasmon resonances and have become an alternative to gold nanoparticles. Whereas gold is the most-studied plasmonic material, aluminum has the advantage of high earth abundance and hence low cost. In addition to understanding the size and shape tunability of the plasmon resonance, the fundamental relaxation processes in aluminum nanostructures after photoexcitation must be understood to take full advantage of applications such as photocatalysis and photodetection. In this work, we investigate the relaxation following ultrafast pulsed excitation and the launching of acoustic vibrations in individual aluminum nanodisks, using single-particle transient extinction spectroscopy. We find that the transient extinction signal can be assigned to a thermal relaxation of the photoexcited electrons and phonons. The ultrafast heating-induced launching of in-plane acoustic vibrations reveals moderate binding to the glass substrate and is affected by the native aluminum oxide layer. Finally, we compare the behavior of aluminum nanodisks to that of similarly prepared and sized gold nanodisks.