Towards single-molecule nanomechanical mass spectrometry

Charge and heat transport in soft nanosystems in the presence of time-dependent perturbations

BACKGROUND

Soft nanosystems are electronic nanodevices, such as suspended carbon nanotubes or molecular junctions, whose transport properties are modulated by soft internal degrees of freedom, for example slow vibrational modes. Effects of the electron-vibration coupling on the charge and heat transport of soft nanoscopic systems are theoretically investigated in the presence of time-dependent perturbations, such as a forcing antenna or pumping terms between the leads and the nanosystem. A well-established approach valid for non-equilibrium adiabatic regimes is generalized to the case where external time-dependent perturbations are present. Then, a number of relevant applications of the method are reviewed for systems composed by a quantum dot (or molecule) described by a single electronic level coupled to a vibrational mode.

RESULTS

Before introducing time-dependent perturbations, the range of validity of the adiabatic approach is discussed showing that a very good agreement with the results of an exact quantum calculation is obtained in the limit of low level occupation. Then, we show that the interplay between the low frequency vibrational modes and the electronic degrees of freedom affects the thermoelectric properties within the linear response regime finding out that the phonon thermal conductance provides an important contribution to the figure of merit at room temperature. Our work has been stimulated by recent experimental results on carbon nanotube electromechanical devices working in the semiclassical regime (resonator frequencies in the megahertz range compared to an electronic hopping frequency of the order of tens of gigahertz) with extremely high quality factors. The nonlinear vibrational regime induced by the external antenna in such systems has been discussed within the non-perturbative adiabatic approach reproducing quantitatively the characteristic asymmetric shape of the current-frequency curves. Within the same set-up, we have proved that the antenna is able to pump sufficient charge close to the mechanical resonance making single-parameter adiabatic charge pumping feasible in carbon nanotube resonators. The pumping mechanism that we observe is different from that acting in the two parameter pumping and, instead, it is based on an important dynamic adjustment of the mechanical motion of the nanotube to the external drive in the weakly nonlinear regime. Finally, stochastic forces induced by quantum and thermal fluctuations due to the electron charging of the quantum dot are shown to affect in a significant way a Thouless charge pump realized with an elastically deformable quantum dot. In this case, the pumping mechanism is also shown to be magnified when the frequency of the external drive is resonant with the proper frequency of the deformable quantum dot. In this regime, the pumping current is not strongly reduced by the temperature, giving a measurable effect.

CONCLUSION

Aim of this review has been to discuss common features of different soft nanosystems under external drive. The most interesting effects induced by time-dependent perturbations are obtained when the external forcing is nearly resonant with the slow vibrational modes. Indeed, not only the external forcing can enhance the electronic response, but it also induces nonlinear regimes where the interplay between electronic and vibrational degrees of freedom plays a major role.

Ultrasensitive Characterization of Mechanical Oscillations and Plasmon Energy Shift in Gold Nanorods

Mechanical vibrational resonances in metal nanoparticles are intensively studied because they provide insight into nanoscale elasticity and for their potential application to ultrasensitive mass detection. In this paper, we use broadband femtosecond pump-probe spectroscopy to study the longitudinal acoustic phonons of arrays of gold nanorods with different aspect ratios, fabricated by electron beam lithography with very high size uniformity. We follow in real time the impulsively excited extensional oscillations of the nanorods by measuring the transient shift of the localized surface plasmon band. Broadband and high-sensitivity detection of the time-dependent extinction spectra enables one to develop a model that quantitatively describes the periodic variation of the plasmon extinction coefficient starting from the steady-state spectrum with only one additional free parameter. This model allows us to retrieve the time-dependent elongation of the nanorods with an ultrahigh sensitivity and to measure oscillation amplitudes of just a few picometers and plasmon energy shifts on the order of 10(-2) meV.

Built-in Electric Field Induced Mechanical Property Change at the Lanthanum Nickelate/Nb-doped Strontium Titanate Interfaces

The interactions between electric field and the mechanical properties of materials are important for the applications of microelectromechanical and nanoelectromechanical systems, but relatively unexplored for nanoscale materials. Here, we observe an apparent correlation between the change of the fractured topography of Nb-doped SrTiO₃ (Nb:STO) within the presence of a built-in electric field resulting from the Schottky contact at the interface of a metallic LaNiO₃ thin film utilizing cross-sectional scanning tunneling microscopy and spectroscopy. The change of the inter-atomic bond length mechanism is argued to be the most plausible origin. This picture is supported by the strong-electric-field-dependent permittivity in STO and the existence of the dielectric dead layer at the interfaces of STO with metallic films. These results provided direct evidence and a possible mechanism for the interplay between the electric field and the mechanical properties on the nanoscale for perovskite materials.

Proposition of a Silica Nanoparticle-Enhanced Hybrid Spin-Microcantilever Sensor Using Nonlinear Optics for Detection of DNA in Liquid

We theoretically propose a method based on the combination of a nonlinear optical mass sensor using a hybrid spin-microcantilever and the nanoparticle-enhanced technique, to detect and monitor DNA mutations. The technique theoretically allows the mass of external particles (ssDNA) landing on the surface of a hybrid spin-microcantilever to be detected directly and accurately at 300 K with a mass responsivity 0.137 Hz/ag in situ in liquid. Moreover, combined with the nanoparticle-enhanced technique, even only one base pair mutation in the target DNA sequence can be identified in real time accurately, and the DNA hybridization reactions can be monitored quantitatively. Furthermore, in situ detection in liquid and measurement of the proposed nonlinear optical spin resonance spectra will minimize the experimental errors.

High-frequency nano-optomechanical disk resonators in liquids

Nano- and micromechanical resonators are the subject of research that aims to develop ultrasensitive mass sensors for spectrometry, chemical analysis and biomedical diagnosis. Unfortunately, their merits generally diminish in liquids because of an increased dissipation. The development of faster and lighter miniaturized devices would enable improved performances, provided the dissipation was controlled and novel techniques were available to drive and readout their minute displacement. Here we report a nano-optomechanical approach to this problem using miniature semiconductor disks. These devices combine a mechanical motion at high frequencies (gigahertz and above) with an ultralow mass (picograms) and a moderate dissipation in liquids. We show that high-sensitivity optical measurements allow their Brownian vibrations to be resolved directly, even in the most-dissipative liquids. We investigate their interaction with liquids of arbitrary properties, and analyse measurements in light of new models. Nano-optomechanical disks emerge as probes of rheological information of unprecedented sensitivity and speed, which opens up applications in sensing and fundamental science.

Graphene as a Massless Electrode for Ultrahigh-Frequency Piezoelectric Nanoelectromechanical Systems

Designing "ideal electrodes" that simultaneously guarantee low mechanical damping and electrical loss as well as high electromechanical coupling in ultralow-volume piezoelectric nanomechanical structures can be considered to be a key challenge in the NEMS field. We show that mechanically transferred graphene, floating at van der Waals proximity, closely mimics "ideal electrodes" for ultrahigh frequency (0.2 GHz < f0 < 2.6 GHz) piezoelectric nanoelectromechanical resonators with negligible mechanical mass and interfacial strain and perfect radio frequency electric field confinement. These unique attributes enable graphene-electrode-based piezoelectric nanoelectromechanical resonators to operate at their theoretically "unloaded" frequency-limits with significantly improved electromechanical performance compared to metal-electrode counterparts, despite their reduced volumes. This represents a spectacular trend inversion in the scaling of piezoelectric electromechanical resonators, opening up new possibilities for the implementation of nanoelectromechanical systems with unprecedented performance.

Binding assay for low molecular weight analytes based on reflectometry of absorbing molecules in porous substrates

Small molecule sensing is of great importance in pharmaceutical research. While there exist well established screening methods such as EMSA (electrophoretic motility shift assay) or biointeraction chromatography to report on successful binding interactions, there are only a few techniques that allow studying and quantifying the interaction of low molecular weight analytes with a binding partner directly. We report on a binding assay for small molecules based on the reflectivity change of a porous transparent film upon immobilisation of an absorbing substance on the pore walls. The porous matrix acts as a thin optical transparent film to produce interference fringes and accumulates molecules at the inner wall to amplify the sensor response. The benefits and limits of the assay are demonstrated by investigating the binding of biotin labelled with an atto dye to avidin physisorbed within an anodic aluminium oxide membrane.

Whispering gallery mode sensors

We present a comprehensive overview of sensor technology exploiting optical whispering gallery mode (WGM) resonances. After a short introduction we begin by detailing the fundamental principles and theory of WGMs in optical microcavities and the transduction mechanisms frequently employed for sensing purposes. Key recent theoretical contributions to the modeling and analysis of WGM systems are highlighted. Subsequently we review the state of the art of WGM sensors by outlining efforts made to date to improve current detection limits. Proposals in this vein are numerous and range, for example, from plasmonic enhancements and active cavities to hybrid optomechanical sensors, which are already working in the shot noise limited regime. In parallel to furthering WGM sensitivity, efforts to improve the time resolution are beginning to emerge. We therefore summarize the techniques being pursued in this vein. Ultimately WGM sensors aim for real-world applications, such as measurements of force and temperature, or alternatively gas and biosensing. Each such application is thus reviewed in turn, and important achievements are discussed. Finally, we adopt a more forward-looking perspective and discuss the outlook of WGM sensors within both a physical and biological context and consider how they may yet push the detection envelope further.

Mass and Force Sensing of an Adsorbate on a Beam Resonator Sensor

The mass sensing superiority of a micro-/nano-mechanical resonator sensor over conventional mass spectrometry has been, or at least is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors, such as position and axial force, can also cause the shifts of resonant frequencies. The in situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated, and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of a mechanical resonator sensor for two reasons: reducing extra experimental equipment and achieving better mass sensing by considering more factors.

Nonlinear optical response of cavity optomechanical system with second-order coupling

We theoretically investigate the optical response of a cavity optomechanical system via the nonlinear coupling between optical and mechanical resonators, which is expected to be strong. Our results show that the nonlinear coupling will significantly influence the optical bistability. We compare the transmission spectrum of linear coupling with that of nonlinear coupling up to the second order and observe a shift between the transmission peak, which indicates the energy-level modification induced by the nonlinear coupling. Based on this nonlinear optomechanical phenomenon, we propose a theoretical method to determine the mechanical frequency and the second-order coupling constant. This means will eliminate the influence caused by the first-order coupling, which enables much easier detection of second-order coupling constant.

Wavelength-division multiplexing of nano-optomechanical doubly clamped beam systems

Wavelength-division multiplexing is demonstrated for a set of two doubly clamped beams. Using a single input/output waveguide in a nanophotonic detection system, the two mechanical beams are independently addressable using different wavelength channels as determined by their respective racetrack resonator detection cavities. The two cavities slightly overlap, which also enables the mechanical frequency of both beams to be detected simultaneously with a single wavelength. Finally, to physically map which wavelength channel corresponds to which specific device, a heating laser is targeted individually on each beam to create a reversible mechanical frequency shift. This multiplexing method would allow for the simpler detection of large arrays of nanomechanical devices in a sensor system.

Modeling biomolecular site dynamics in immunoreceptor signaling systems

The immune system plays a central role in human health. The activities of immune cells, whether defending an organism from disease or triggering a pathological condition such as autoimmunity, are driven by the molecular machinery of cellular signaling systems. Decades of experimentation have elucidated many of the biomolecules and interactions involved in immune signaling and regulation, and recently developed technologies have led to new types of quantitative, systems-level data. To integrate such information and develop nontrivial insights into the immune system, computational modeling is needed, and it is essential for modeling methods to keep pace with experimental advances. In this chapter, we focus on the dynamic, site-specific, and context-dependent nature of interactions in immunoreceptor signaling (i.e., the biomolecular site dynamics of immunoreceptor signaling), the challenges associated with capturing these details in computational models, and how these challenges have been met through use of rule-based modeling approaches.

Ultrasensitive room-temperature piezoresistive transduction in graphene-based nanoelectromechanical systems

The low mass and high quality factors that nanomechanical resonators exhibit lead to exceptional sensitivity in the frequency domain. This is especially appealing for the design of ultrasensitive force and mass sensors. The sensitivity of a nanomechanical mass and force sensor depends on its mass and quality factor; a low resonator mass and a higher quality factor reduce both the minimum resolvable mass and force. Graphene, a single atomic layer thick membrane is an ideal candidate for nanoelectromechanical resonators due to its extremely low mass and high stiffness. Here, we show that by employing the intrinsic piezoresistivity of graphene to transduce its motion in nanoelectromechanical systems, we approach a force resolution of 16.3 ± 0.8 aN/Hz(1/2) and a minimum detectable mass of 1.41 ± 0.02 zeptograms (10(-21) g) at ambient temperature. Quality factors of the driven response of the order of 10(3) at pressures ∼10(-6) Torr on several devices are also observed. Moreover, we demonstrate this at ambient temperature on chemical-vapor-deposition-grown graphene to allow for scale-up, thus demonstrating its potential for applications requiring exquisite force and mass resolution such as mass spectroscopy and magnetic resonance force microscopy.

Inertial imaging with nanomechanical systems

Mass sensing with nanoelectromechanical systems has advanced significantly during the last decade. With nanoelectromechanical systems sensors it is now possible to carry out ultrasensitive detection of gaseous analytes, to achieve atomic-scale mass resolution and to perform mass spectrometry on single proteins. Here, we demonstrate that the spatial distribution of mass within an individual analyte can be imaged--in real time and at the molecular scale--when it adsorbs onto a nanomechanical resonator. Each single-molecule adsorption event induces discrete, time-correlated perturbations to all modal frequencies of the device. We show that by continuously monitoring a multiplicity of vibrational modes, the spatial moments of mass distribution can be deduced for individual analytes, one-by-one, as they adsorb. We validate this method for inertial imaging, using both experimental measurements of multimode frequency shifts and numerical simulations, to analyse the inertial mass, position of adsorption and the size and shape of individual analytes. Unlike conventional imaging, the minimum analyte size detectable through nanomechanical inertial imaging is not limited by wavelength-dependent diffraction phenomena. Instead, frequency fluctuation processes determine the ultimate attainable resolution. Advanced nanoelectromechanical devices appear capable of resolving molecular-scale analytes.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Neutral particle mass spectrometry with nanomechanical systems

Current approaches to mass spectrometry (MS) require ionization of the analytes of interest. For high-mass species, the resulting charge state distribution can be complex and difficult to interpret correctly. Here, using a setup comprising both conventional time-of-flight MS (TOF-MS) and nano-electromechanical systems-based MS (NEMS-MS) in situ, we show directly that NEMS-MS analysis is insensitive to charge state: the spectrum consists of a single peak whatever the species' charge state, making it significantly clearer than existing MS analysis. In subsequent tests, all the charged particles are electrostatically removed from the beam, and unlike TOF-MS, NEMS-MS can still measure masses. This demonstrates the possibility to measure mass spectra for neutral particles. Thus, it is possible to envisage MS-based studies of analytes that are incompatible with current ionization techniques and the way is now open for the development of cutting-edge system architectures with unique analytical capability.

The smallest resonator arrays in atmosphere by chip-size-grown nanowires with tunable Q-factor and frequency for subnanometer thickness detection

A chip-size vertically aligned nanowire (NW) resonator arrays (VNRs) device has been fabricated with simple one-step lithography process by using grown self-assembled zinc oxide (ZnO) NW arrays. VNR has cantilever diameter of 50 nm, which breakthroughs smallest resonator record (>100 nm) functioning in atmosphere. A new atomic displacement sensing method by using atomic force microscopy is developed to effectively identify the resonance of NW resonator with diameter 50 nm in atmosphere. Size-effect and half-dimensional properties of the NW resonator have been systematically studied. Additionally, VNR has been demonstrated with the ability of detecting nanofilm thickness with subnanometer (<10(-9)m) resolution.

Focused-ion-beam induced rayleigh-plateau instability for diversiform suspended nanostructure fabrication

A novel method for fabricating diversiform suspended nanostructures is reported. The method utilizes focused-ion-beam (FIB) induced material redistribution and Rayleigh-Plateau instability, which determine the resulting shapes of formed nanostructures. By choosing target materials, their predefined patterns as well as FIB settings, we have achieved parallel nanofabrication of various kinds including nanostrings, nanobead chains and nanopore membranes with smooth surfaces due to the self-perfection effect of the material redistribution upon the minimization of system free energy. The diameters of the nanostrings and nanopores reach about 10 nm and 200 nm, respectively. The average period of the nanobead chains is 250 nm.

Hybrid spin-microcantilever sensor for environmental, chemical, and biological detection

Nowadays hybrid spin-micro/nanomechanical systems are being actively explored for potential quantum sensing applications. In combination with the pump-probe technique or the spin resonance spectrum, we theoretically propose a realistic, feasible, and an exact way to measure the cantilever frequency in a hybrid spin-micromechanical cantilever system which has a strong coherent coupling of a single nitrogen vacancy center in the single-crystal diamond cantilever with the microcantilever. The probe absorption spectrum which exhibits new features such as mechanically induced three-photon resonance and ac Stark effect is obtained. Simultaneously, we further develop this hybrid spin-micromechanical system to be an ultrasensitive mass sensor, which can be operated at 300 K with a mass responsivity 0.137 Hz ag(-1), for accurate sensing of gaseous or aqueous environments, chemical vapors, and biomolecules. And the best performance on the minimum detectable mass can be [Formula: see text] in vacuum. Finally, we illustrate an in situ measurement to detect Angiopoietin-1, a marker of tumor angiogenesis, accurately with this hybrid microcantilever at room temperature.

Enhanced resolution of low molecular weight poly(ethylene glycol) in nanopore analysis

A design with conjugation of DNA hairpin structure to the poly(ethylene glycol) molecule was presented to enhance the temporal resolution of low molecular weight poly(ethylene glycol) in nanopore studies. By the virtue of this design, detection of an individual PEG with molecular weight as low as 140 Da was achieved at the single-molecule level in solution, which provides a novel strategy for characterization of an individual small molecule within a nanopore. Furthermore, we found that the current duration time of poly(ethylene glycol) was scaled with the relative molecular weight, which has a potential application in single-molecule detection.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Monitoring sessile droplet evaporation on a micromechanical device

A bulk acoustic mode micro-electro-mechanical dual resonator platform is utilised to study the evaporation of sub-microliter water droplets from the surface of the resonator. An analytical formulation for the observed frequency shift and the measure dependence of resonant frequency on the modes of evaporation which is consistent with the optically derived data. The resonators access only a thin layer of the liquid through shear contact and, hence, the response is not affected by the bulk mass of the droplet to first order. A relationship between the droplet contact area and the elapsed time was established for the evaporation process and is used to derive a value of the diffusion coefficient of water in air that is found to be in reasonable agreement with literature values. This work introduces a new tool for the electro-mechanical monitoring of droplet evaporation with relevance to applications such as biosensing in liquid samples of sub-microliter volumes.

VHF NEMS-CMOS piezoresistive resonators for advanced sensing applications

This work reports on top-down nanoelectromechanical resonators, which are among the smallest resonators listed in the literature. To overcome the fact that their electromechanical transduction is intrinsically very challenging due to their very high frequency (100 MHz) and ultimate size (each resonator is a 1.2 μm long, 100 nm wide, 20 nm thick silicon beam with 100 nm long and 30 nm wide piezoresistive lateral nanowire gauges), they have been monolithically integrated with an advanced fully depleted SOI CMOS technology. By advantageously combining the unique benefits of nanomechanics and nanoelectronics, this hybrid NEMS-CMOS device paves the way for novel breakthrough applications, such as NEMS-based mass spectrometry or hybrid NEMS/CMOS logic, which cannot be fully implemented without this association.

Femtogram-scale photothermal spectroscopy of explosive molecules on nanostrings

We demonstrate detection of femtogram-scale quantities of the explosive molecule 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) via combined nanomechanical photothermal spectroscopy and mass desorption. Photothermal spectroscopy provides a spectroscopic fingerprint of the molecule, which is unavailable using mass adsorption/desorption alone. Our measurement, based on thermomechanical measurement of silicon nitride nanostrings, represents the highest mass resolution ever demonstrated via nanomechanical photothermal spectroscopy. This detection scheme is quick, label-free, and is compatible with parallelized molecular analysis of multicomponent targets.

Detecting the mass and position of an adsorbate on a drum resonator

The resonant frequency shifts of a circular membrane caused by an adsorbate are the sensing mechanism for a drum resonator. The adsorbate mass and position are the two major (unknown) parameters determining the resonant frequency shifts. There are infinite combinations of mass and position which can cause the same shift of one resonant frequency. Finding the mass and position of an adsorbate from the experimentally measured resonant frequencies forms an inverse problem. This study presents a straightforward method to determine the adsorbate mass and position by using the changes of two resonant frequencies. Because detecting the position of an adsorbate can be extremely difficult, especially when the adsorbate is as small as an atom or a molecule, this new inverse problem-solving method should be of some help to the mass resonator sensor application of detecting a single adsorbate. How to apply this method to the case of multiple adsorbates is also discussed.

Stabilization of a linear nanomechanical oscillator to its thermodynamic limit

The rapid development of micro- and nanomechanical oscillators in the past decade has led to the emergence of novel devices and sensors that are opening new frontiers in both applied and fundamental science. The potential of these devices is however affected by their increased sensitivity to external perturbations. Here we report a non-perturbative optomechanical stabilization technique and apply the method to stabilize a linear nanomechanical beam at its thermodynamic limit at room temperature. The reported ability to stabilize a nanomechanical oscillator to the thermodynamic limit can be extended to a variety of systems and increases the sensitivity range of nanomechanical sensors in both fundamental and applied studies.

Graphene-based nanoresonator with applications in optical transistor and mass sensing

Graphene has received significant attention due to its excellent properties currently. In this work, a nano-optomechanical system based on a doubly-clamped Z-shaped graphene nanoribbon (GNR) with an optical pump-probe scheme is proposed. We theoretically demonstrate the phenomenon of phonon-induced transparency and show an optical transistor in the system. In addition, the significantly enhanced nonlinear effect of the probe laser is also investigated, and we further put forward a nonlinear optical mass sensing that may be immune to detection noises. Molecules, such as NH₃ and NO₂, can be identified via using the nonlinear optical spectroscopy, which may be applied to environmental pollutant monitoring and trace chemical detection.

Detecting both the mass and position of an accreted particle by a micro/nano-mechanical resonator sensor

In the application of a micro-/nano-mechanical resonator, the position of an accreted particle and the resonant frequencies are measured by two different physical systems. Detecting the particle position sometimes can be extremely difficult or even impossible, especially when the particle is as small as an atom or a molecule. Using the resonant frequencies to determine the mass and position of an accreted particle formulates an inverse problem. The Dirac delta function and Galerkin method are used to model and formulate an eigenvalue problem of a beam with an accreted particle. An approximate method is proposed by ignoring the off-diagonal elements of the eigenvalue matrix. Based on the approximate method, the mass and position of an accreted particle can be decoupled and uniquely determined by measuring at most three resonant frequencies. The approximate method is demonstrated to be very accurate when the particle mass is small, which is the application scenario for much of the mass sensing of micro-/nano-mechanical resonators. By solving the inverse problem, the position measurement becomes unnecessary, which is of some help to the mass sensing application of a micro-/nano-mechanical resonator by reducing two measurement systems to one. How to apply the method to the general scenario of multiple accreted particles is also discussed.

Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser

Optical whispering-gallery-mode resonators (WGMRs) have emerged as promising platforms for label-free detection of nano-objects. The ultimate sensitivity of WGMRs is determined by the strength of the light-matter interaction quantified by quality factor/mode volume, Q/V, and the resolution is determined by Q. To date, to improve sensitivity and precision of detection either WGMRs have been doped with rare-earth ions to compensate losses and increase Q or plasmonic resonances have been exploited for their superior field confinement and lower V. Here, we demonstrate, for the first time to our knowledge, enhanced detection of single-nanoparticle-induced mode splitting in a silica WGMR via Raman gain-assisted loss compensation and WGM Raman microlaser. In particular, the use of the Raman microlaser provides a dopant-free, self-referenced, and self-heterodyned scheme with a detection limit ultimately determined by the thermorefractive noise. Notably, we detected and counted individual nanoparticles with polarizabilities down to 3.82 × 10(-6) μm(3) by monitoring a heterodyne beatnote signal. This level of sensitivity is achieved without exploiting plasmonic effects, external references, or active stabilization and frequency locking. Single nanoparticles are detected one at a time; however, their characterization by size or polarizability requires ensemble measurements and statistical averaging. This dopant-free scheme retains the inherited biocompatibility of silica and could find widespread use for sensing in biological media. The Raman laser and operation band of the sensor can be tailored for the specific sensing environment and the properties of the targeted materials by changing the pump laser wavelength. This scheme also opens the possibility of using intrinsic Raman or parametric gain for loss compensation in other systems where dissipation hinders progress and limits applications.

Physics of nanomechanical spectrometry of viruses

There is an emerging need of nanotools able to quantify the mechanical properties of single biological entities. A promising approach is the measurement of the shifts of the resonant frequencies of ultrathin cantilevers induced by the adsorption of the studied biological systems. Here, we present a detailed theoretical analysis to calculate the resonance frequency shift induced by the mechanical stiffness of viral nanotubes. The model accounts for the high surface-to-volume ratio featured by single biological entities, the shape anisotropy and the interfacial adhesion. The model is applied to the case in which tobacco mosaic virus is randomly delivered to a silicon nitride cantilever. The theoretical framework opens the door to a novel paradigm for biological spectrometry as well as for measuring the Young's modulus of biological systems with minimal strains.

Harnessing vacuum forces for quantum sensing of graphene motion

Position measurements at the quantum level are vital for many applications but also challenging. Typically, methods based on optical phase shifts are used, but these methods are often weak and difficult to apply to many materials. An important example is graphene, which is an excellent mechanical resonator due to its small mass and an outstanding platform for nanotechnologies, but it is largely transparent. Here, we present a novel detection scheme based upon the strong, dispersive vacuum interactions between a graphene sheet and a quantum emitter. In particular, the mechanical displacement causes strong changes in the vacuum-induced shifts of the transition frequency of the emitter, which can be read out via optical fields. We show that this enables strong quantum squeezing of the graphene position on time scales that are short compared to the mechanical period.

Ultrasensitive nanomechanical mass sensor using hybrid opto-electromechanical systems

Nanomechanical resonators provide an unparalleled mass sensitivity sufficient to detect single biomolecules, viruses and nanoparticles. In this work we propose a scheme for mass sensing based on the hybrid opto-electromechanical system, where a mechanical resonator is coupled to an optical cavity and a microwave cavity simultaneously. When the two cavities are driven by two pump fields with proper frequencies and powers, a weak probe field is used to scan across the optical cavity resonance frequency. The mass of a single baculovirus landing onto the surface of the mechanical resonator can be measured by tracking the resonance frequency shift in the probe transmission spectrum before and after the deposition. We also propose a nonlinear mass sensor based on the measurement of the four-wave mixing (FWM) spectrum, which can be used to weigh a single 20-nm-diameter gold nanoparticle with sub-femtogram resolution.

Remote sensing in hybridized arrays of nanostrings

We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas isolated individual resonators exhibit sinusoidal vibrational modes with an almost perfectly harmonic spectrum, the modes of the interacting strings are substantially hybridized. Even far-separated strings can show significantly correlated displacement. This remote coupling property is exploited to quantify the deposition of femtogram-scale masses with string-by-string positional discrimination based on measurements of one string only.

Extraordinary dynamic mechanical response of vanadium dioxide nanowires around the insulator to metal phase transition

Nanomechanical resonators provide a compelling platform to investigate and exploit phase transitions coupled to mechanical degrees of freedom because resonator frequencies and quality factors are exquisitely sensitive to changes in state, particularly for discontinuous changes accompanying a first-order phase transition. Correlated scanning fiber-optic interferometry and dual-beam Raman spectroscopy were used to investigate mechanical fluctuations of vanadium dioxide (VO2) nanowires across the first order insulator to metal transition. Unusually large and controllable changes in resonator frequency were observed due to the influences of domain wall motion and anomalous phonon softening on the effective modulus. In addition, extraordinary static and dynamic displacements were generated by local strain gradients, suggesting new classes of sensors and nanoelectromechanical devices with programmable discrete outputs as a function of continuous inputs.

Optical racetrack resonator transduction of nanomechanical cantilevers

Optomechanical transduction has demonstrated its supremacy in probing nanomechanical displacements. In order to apply nano-optomechanical systems (NOMS) as force and mass sensors, knowledge about the transduction responsivity (i.e. the change in measured optical transmission with nanomechanical displacement) and its tradeoffs with system design is paramount. We compare the measured responsivities of NOMS devices with varying length, optomechanical coupling strength gom, and optical cavity properties. Cantilever beams 1.5 to 5 μm long are fabricated 70 to 160 nm from a racetrack resonator optical cavity and their thermomechanical (TM) noise signals are measured. We derive a generic expression for the transduction responsivity of the NOMS in terms of optical and mechanical system parameters such as finesse, optomechanical coupling constant, and interaction length. The form of the expression holds direct insight as to how these parameters affect the responsivity. With this expression, we obtain the optomechanical coupling constants using only measurements of the TM noise power spectra and optical cavity transmission slopes. All optical pump/probe operation is also demonstrated in our side-coupled cantilever-racetrack NOMS. Finally, to assess potential operation in a gas sensing environment, the TM noise signal of a device is measured at atmospheric pressure.

Resolution enhancement of suspended microchannel resonators for weighing of biomolecular complexes in solution

We introduce the use of correlation analysis to extend the dynamic range of suspended micro- and nanochannel resonator (SMR/SNR) mass sensors by over five orders of magnitude. This method can analyze populations of particles flowing through an embedded channel micromechanical resonator, even when the individual particle masses are far below the noise floor. To characterize the method, we measured the mass of polystyrene nanoparticles with 300 zg resolution. As an application, we monitored the time course of insulin amyloid formation from pre-fibrillar aggregates to mature fibrils of 15 MDa average mass. Results were compared with thioflavin-T (ThT) assays and electron microscopy (EM). Mass measurements offer additional information over ThT during the fluorescent inaccessible lag period, and the average fibril dimensions calculated from the mass signal are in good accordance with EM. In the future, we envision that more detailed modeling will allow the computational deconvolution of multicomponent samples, enabling the mass spectrometric characterization of a variety of biomolecular complexes, small organelles, and nanoparticles in solution.

Weighing nanoparticles in solution at the attogram scale

Physical characterization of nanoparticles is required for a wide range of applications. Nanomechanical resonators can quantify the mass of individual particles with detection limits down to a single atom in vacuum. However, applications are limited because performance is severely degraded in solution. Suspended micro- and nanochannel resonators have opened up the possibility of achieving vacuum-level precision for samples in the aqueous environment and a noise equivalent mass resolution of 27 attograms in 1-kHz bandwidth was previously achieved by Lee et al. [(2010) Nano Lett 10(7):2537-2542]. Here, we report on a series of advancements that have improved the resolution by more than 30-fold, to 0.85 attograms in the same bandwidth, approaching the thermomechanical noise limit and enabling precise quantification of particles down to 10 nm with a throughput of more than 18,000 particles per hour. We demonstrate the potential of this capability by comparing the mass distributions of exosomes produced by different cell types and by characterizing the yield of self-assembled DNA nanoparticle structures.

Analytical approaches for size and mass analysis of large protein assemblies

Analysis of the size and mass of nanoparticles, whether they are natural biomacromolecular or synthetic supramolecular assemblies, is an important step in the characterization of such molecular species. In recent years, electrospray ionization (ESI) has emerged as a technology through which particles with masses up to 100 MDa can be ionized and transferred into the gas phase, preparing them for accurate mass analysis. Here we review currently used methodologies, with a clear focus on native mass spectrometry (MS). Additional complementary methodologies are also covered, including ion-mobility analysis, nanomechanical mass sensors, and charge-detection MS. The literature discussed clearly demonstrates the great potential of ESI-based methodologies for the size and mass analysis of nanoparticles, including very large naturally occurring protein assemblies. The analytical approaches discussed are powerful tools in not only structural biology, but also nanotechnology.

Detection of molecular binding via charge-induced mechanical response of optical fibers

We report a charge sensitive optical detection technique for label-free study of molecular interactions. Traditional label-free optical detection techniques largely rely on the detection of the mass of a molecule, which are insensitive to small molecules. In contrast, the present technique detects the charge of a molecule, where the signal does not diminish with the size of the molecule, thus capable for studying small molecules. In addition, the technique is compatible with the standard microplate platform, making it suitable for high-throughput screening of drug candidates. Using the technique, we have detected 0.2 nM anti-BSA and 15 μM anti-cancer drug (imatinib) with an enzyme modified surface. The achieved effective charge detection limit is ~0.25 electron charge/μm², corresponding to ~0.3 fg/mm² for imatinib, which is orders of magnitude better than traditional label-free optical detection methods.

Functional nanoprobes for ultrasensitive detection of biomolecules: an update

With the rapidly increasing demands for ultrasensitive biodetection, the design and applications of functional nanoprobes have attracted substantial interest for biosensing with optical, electrochemical, and various other means. In particular, given the comparable sizes of nanomaterials and biomolecules, there exists plenty of opportunities to develop functional nanoprobes with biomolecules for highly sensitive and selective biosensing. Over the past decade, numerous nanoprobes have been developed for ultrasensitive bioaffinity sensing of proteins and nucleic acids in both laboratory and clinical applications. In this review, we provide an update on the recent advances in this direction, particularly in the past two years, which reflects new progress since the publication of our last review on the same topic in Chem. Soc. Rev. The types of probes under discussion include: (i) nanoamplifier probes: one nanomaterial loaded with multiple biomolecules; (ii) quantum dots probes: fluorescent nanomaterials with high brightness; (iii) superquenching nanoprobes: fluorescent background suppression; (iv) nanoscale Raman probes: nanoscale surface-enhanced Raman resonance scattering; (v) nanoFETs: nanomaterial-based electrical detection; and (vi) nanoscale enhancers: nanomaterial-induced metal deposition.

Programmable mechanical resonances in MEMS by localized joule heating of phase change materials

A programmable micromechanical resonator based on a VO2 thin film is reported. Multiple mechanical eigenfrequency states are programmed using Joule heating as local power source, gradually driving the phase transition of VO2 around its Metal-Insulator transition temperature. Phase coexistence of domains is used to tune the stiffness of the device via local control of internal stresses and mechanical properties. This study opens perspectives for developing mechanically configurable nanostructure arrays.

Enabling systems biology approaches through microfabricated systems

With the experimental tools and knowledge that have accrued from a long history of reductionist biology, we can now start to put the pieces together and begin to understand how biological systems function as an integrated whole. Here, we describe how microfabricated tools have demonstrated promise in addressing experimental challenges in throughput, resolution, and sensitivity to support systems-based approaches to biological understanding.

Real-time single airborne nanoparticle detection with nanomechanical resonant filter-fiber

Nanomechanical resonators have an unprecedented mass sensitivity sufficient to detect single molecules, viruses or nanoparticles. The challenge with nanomechanical mass sensors is the direction of nano-sized samples onto the resonator. In this work we present an efficient inertial sampling technique and gravimetric detection of airborne nanoparticles with a nanomechanical resonant filter-fiber. By increasing the nanoparticle momentum the dominant collection mechanism changes from diffusion to more efficient inertial impaction. In doing so we reach a single filter-fiber collection efficiency of 65 ± 31% for 28 nm silica nanoparticles. Finally, we show the detection of single 100 nm silver nanoparticles. The presented method is suitable for environmental or security applications where low-cost and portable monitors are demanded. It also constitutes a unique technique for the fundamental study of single filter-fiber behavior. We present the direct measurement of diffusive nanoparticle collection on a single filter-fiber qualitatively confirming Langmuir's model from 1942.

Biosensors based on nanomechanical systems

The advances in micro- and nanofabrication technologies enable the preparation of increasingly smaller mechanical transducers capable of detecting the forces, motion, mechanical properties and masses that emerge in biomolecular interactions and fundamental biological processes. Thus, biosensors based on nanomechanical systems have gained considerable relevance in the last decade. This review provides insight into the mechanical phenomena that occur in suspended mechanical structures when either biological adsorption or interactions take place on their surface. This review guides the reader through the parameters that change as a consequence of biomolecular adsorption: mass, surface stress, effective Young's modulus and viscoelasticity. The mathematical background needed to correctly interpret the output signals from nanomechanical biosensors is also outlined here. Other practical issues reviewed are the immobilization of biomolecular receptors on the surface of nanomechanical systems and methods to attain that in large arrays of sensors. We then describe some relevant realizations of biosensor devices based on nanomechanical systems that harness some of the mechanical effects cited above. We finally discuss the intrinsic detection limits of the devices and the limitation that arises from non-specific adsorption.