A Hybrid Orbitrap-Nanoelectromechanical Systems Approach for the 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Photoinduced Electron Transfer in the Strong Coupling Regime: Waveguide-Plasmon Polaritons.

Reversible exchange of photons between a material and an optical cavity can lead to the formation of hybrid light-matter states where material properties such as the work function [ Hutchison et al. Adv. Mater. 2013 , 25 , 2481 - 2485 ], chemical reactivity [ Hutchison et al. Angew. Chem., Int. Ed. 2012 , 51 , 1592 - 1596 ], ultrafast energy relaxation [ Salomon et al. Angew. Chem., Int. Ed. 2009 , 48 , 8748 - 8751 ; Gomez et al. J. Phys. Chem. B 2013 , 117 , 4340 - 4346 ], and electrical conductivity [ Orgiu et al. Nat. Mater. 2015 , 14 , 1123 - 1129 ] of matter differ significantly to those of the same material in the absence of strong interactions with the electromagnetic fields. Here we show that strong light-matter coupling between confined photons on a semiconductor waveguide and localized plasmon resonances on metal nanowires modifies the efficiency of the photoinduced charge-transfer rate of plasmonic derived (hot) electrons into accepting states in the semiconductor material. Ultrafast spectroscopy measurements reveal a strong correlation between the amplitude of the transient signals, attributed to electrons residing in the semiconductor and the hybridization of waveguide and plasmon excitations.

Hollow Microtube Resonators via Silicon Self-Assembly toward Subattogram Mass Sensing Applications.

Fluidic resonators with integrated microchannels (hollow resonators) are attractive for mass, density, and volume measurements of single micro/nanoparticles and cells, yet their widespread use is limited by the complexity of their fabrication. Here we report a simple and cost-effective approach for fabricating hollow microtube resonators. A prestructured silicon wafer is annealed at high temperature under a controlled atmosphere to form self-assembled buried cavities. The interiors of these cavities are oxidized to produce thin oxide tubes, following which the surrounding silicon material is selectively etched away to suspend the oxide tubes. This simple three-step process easily produces hollow microtube resonators. We report another innovation in the capping glass wafer where we integrate fluidic access channels and getter materials along with residual gas suction channels. Combined together, only five photolithographic steps and one bonding step are required to fabricate vacuum-packaged hollow microtube resonators that exhibit quality factors as high as ∼ 13,000. We take one step further to explore additionally attractive features including the ability to tune the device responsivity, changing the resonator material, and scaling down the resonator size. The resonator wall thickness of ∼ 120 nm and the channel hydraulic diameter of ∼ 60 nm are demonstrated solely by conventional microfabrication approaches. The unique characteristics of this new fabrication process facilitate the widespread use of hollow microtube resonators, their translation between diverse research fields, and the production of commercially viable devices.

Viscoelasticity of glycerol at ultra-high frequencies investigated via molecular dynamics simulations.

We present a calculation of the shear and longitudinal moduli of glycerol in the gigahertz frequency regime and temperature range between 273 K and 323 K using classical molecular dynamics simulations. The full frequency spectra of shear and longitudinal moduli of glycerol between 0.5 GHz and 100 GHz at room temperature are computed, which was not previously available from experiments or simulations. We also demonstrate that the temperature dependence of the real parts of the shear and longitudinal moduli agrees well with available experimental counterparts obtained via time-domain Brillouin scattering. This work provides new insights into the response of molecular liquids to ultra-high frequency excitation and opens a new pathway for studying simple liquids at high frequencies and strain rates.

Compressible Viscoelastic Liquid Effects Generated by the Breathing Modes of Isolated Metal Nanowires.

Transient absorption microscopy is used to examine the breathing modes of single gold nanowires in highly viscous liquids. By performing measurements on the same wire in air and liquid, the damping contribution from the liquid can be separated from the intrinsic damping of the nanowire. The results show that viscous liquids strongly reduce the vibrational lifetimes but not to the extent predicted by standard models for nanomaterial-liquid interactions. To explain these results a general theory for compressible viscoelastic fluid-structure interactions is developed. The theory results are in good agreement with experiment, which confirms that compressible non-Newtonian flow phenomena are important for vibrating nanostructures. This is the first theoretical study and experimental measurement of the compressible viscoelastic properties of simple liquids.

Probing silver deposition on single gold nanorods by their acoustic vibrations.

Acoustic vibrations of single gold nanorods coated with silver were investigated. We used single-particle pump-probe spectroscopy to monitor the silver deposition through the particle vibrations. Two vibration modes, the breathing mode and extensional mode, are observed, and the vibrational frequencies are measured as functions of the amount of silver deposited on single gold nanorods. The breathing mode frequency was found to decrease with silver deposition, while the extensional mode frequency was almost constant for silver shells up to 6 nm. The frequency changes agree with a model based on continuum mechanics and on the assumption of a uniform silver coating. The quality factors for the breathing mode and the extensional mode are hardly affected by silver deposition, indicating that the introduced interface between gold and silver contributes negligibly to the damping of the particle vibrations. Finally, we demonstrated that an atomic layer of silver can be detected using the particle acoustic vibrations.

Dynamic similarity of oscillatory flows induced by nanomechanical resonators.

Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure P0 is α times that of a scaled-up microscale resonator at a reduced pressure α P0, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales.

Damping of acoustic vibrations of immobilized single gold nanorods in different environments.

We present measurements of the acoustic vibrations of single gold nanorods deposited on a glass substrate immersed in air and water by ultrafast pump-probe spectroscopy. The nanorods display two vibration modes, the breathing mode and the extensional mode. The damping time of the two modes is influenced by the environment, and a reduction of the quality factor is observed when the particles are immersed in water. The reduced quality factor of the breathing mode is in good agreement with a model that takes into account viscous damping and radiation of sound waves into the medium. The extension mode, however, is heavily damped when the particles are immersed in water, which is attributed to hydrodynamic lubrication forces between the nanoparticle and the glass substrate. Our results identify a new mode of damping in supported nanoparticles and indicate that the immersion medium can have different effects on different modes of vibration.

Self-assembled nanoparticle drumhead resonators.

The self-assembly of nanoscale structures from functional nanoparticles has provided a powerful path to developing devices with emergent properties from the bottom-up. Here we demonstrate that freestanding sheets self-assembled from various nanoparticles form versatile nanomechanical resonators in the megahertz frequency range. Using spatially resolved laser-interferometry to measure thermal vibrational spectra and image vibration modes, we show that their dynamic behavior is in excellent agreement with linear elastic response for prestressed drumheads of negligible bending stiffness. Fabricated in a simple one-step drying-mediated process, these resonators are highly robust and their inorganic-organic hybrid nature offers an extremely low mass, low stiffness, and the potential to couple the intrinsic functionality of the nanoparticle building blocks to nanomechanical motion.

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.

Variational solution to the lattice Boltzmann method for Couette flow.

Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations (PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.