Nanomechanical Sensing for Mass Flow Control in Nanowire-Based Open Nanofluidic Systems.

Open nanofluidic systems, where liquids flow along the outer surface of nanoscale structures, provide otherwise unfeasible capabilities for extremely miniaturized liquid handling applications. A critical step toward fully functional applications is to obtain quantitative mass flow control. We demonstrate the application of nanomechanical sensing for this purpose by integrating voltage-driven liquid flow along nanowire open channels with mass detection based on flexural resonators. This approach is validated by assembling the nanowires with microcantilever resonators, enabling high-precision control of larger flows, and by using the nanowires as resonators themselves, allowing extremely small liquid volume handling. Both implementations are demonstrated by characterizing voltage-driven flow of ionic liquids along the surface of the nanowires. We find a voltage range where mass flow rate follows a nonlinear monotonic increase, establishing a steady flow regime for which we show mass flow control at rates from below 1 ag/s to above 100 fg/s and precise liquid handling down to the zeptoliter scale. The observed behavior of mass flow rate is consistent with a voltage-induced transition from static wetting to dynamic spreading as the mechanism underlying liquid transport along the nanowires.

Square Membrane Resonators Supporting Degenerate Modes of Vibration for High-Throughput Mass Spectrometry of Single Bacterial Cells.

In nanomechanical mass spectrometry, sensing devices are commonly placed in the vacuum environment and a stream of analytes is directed toward the sensor surface for measurement. Beam structures, such as double-clamped nanobeams and nanocantilevers, are commonly used due to their low inertial mass and the simplicity of the analytical models for mass extraction. The drawback of such structures is their low capture areas, compromising the capture efficiency and throughput of this technique. Bi-axisymmetric resonators, such as ultrathin square or circular membranes, arise as an optimal geometry to maximize capture efficiency while minimizing the device inertial mass. However, these structures present degenerate mechanical modes, whose frequency perturbations upon analyte adsorption are not well described by commonly used models. Furthermore, prior knowledge of the vibration mode shapes of the sensor is crucial for the correct calculation of the analyte's mass, and the mode shape of degenerate modes may change significantly after every adsorption event. In this work, we present an accurate analytical theory to describe the effect of mass adsorption on the degenerate modes of square membrane resonators and propose two different methods based on the new theory to update the vibration mode shapes after every adsorption event. Finally, we illustrate the problem experimentally obtaining the mass and adsorption position of individual Escherichia coli K-12 bacterial cells on commercial square silicon nitride membranes fabricated with very small tolerances.

High-throughput determination of dry mass of single bacterial cells by ultrathin membrane resonators.

How bacteria are able to maintain their size remains an open question. Techniques that can measure the biomass (dry mass) of single cells with high precision and high-throughput are demanded to elucidate this question. Here, we present a technological approach that combines the transport, guiding and focusing of individual bacteria from solution to the surface of an ultrathin silicon nitride membrane resonator in vacuum. The resonance frequencies of the membrane undergo abrupt variations at the instants where single cells land on the membrane surface. The resonator design displays a quasi-symmetric rectangular shape with an extraordinary capture area of 0.14 mm2, while maintaining a high mass resolution of 0.7 fg (1 fg = 10-15 g) to precisely resolve the dry mass of single cells. The small rectangularity of the membrane provides unprecedented frequency density of vibration modes that enables to retrieve the mass of individual cells with high accuracy by specially developed inverse problem theory. We apply this approach for profiling the dry mass distribution in Staphylococcus epidermidis and Escherichia coli cells. The technique allows the determination of the dry mass of single bacterial cells with an accuracy of about 1% at an unparalleled throughput of 20 cells/min. Finally, we revisit Koch & Schaechter model developed during 60 s to assess the intrinsic sources of stochasticity that originate cell size heterogeneity in steady-state populations. The results reveal the importance of mass resolution to correctly describe these mechanisms.

High Dynamic Range Nanowire Resonators.

Dynamic range quantifies the linear operation regime available in nanomechanical resonators. Nonlinearities dominate the response of flexural beams in the limit of very high aspect ratio and very small diameter, which leads to expectation of low dynamic range for nanowire resonators in general. However, the highest achievable dynamic range for nanowire resonators with practical dimensions remains to be determined. We report dynamic range measurements on singly clamped silicon nanowire resonators reaching remarkably high values of up to 90 dB obtained with a simple harmonic actuation scheme. We explain these measurements by a comprehensive theoretical examination of dynamic range in singly clamped flexural beams including the effect of tapering, a usual feature of semiconductor nanowires. Our analysis reveals the nanowire characteristics required for broad linear operation, and given the relationship between dynamic range and mass sensing performance, it also enables analytical determination of mass detection limits, reaching atomic-scale resolution for feasible nanowires.

Publisher Correction: Optomechanical detection of vibration modes of a single bacterium.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Optomechanical detection of vibration modes of a single bacterium.

Low-frequency vibration modes of biological particles, such as proteins, viruses and bacteria, involve coherent collective vibrations at frequencies in the terahertz and gigahertz domains. These vibration modes carry information on their structure and mechanical properties, which are good indicators of their biological state. In this work, we harnessed a particular regime in the physics of coupled mechanical resonators to directly measure these low-frequency mechanical resonances of a single bacterium. We deposit the bacterium on the surface of an ultrahigh frequency optomechanical disk resonator in ambient conditions. The vibration modes of the disk and bacterium hybridize when their associated frequencies are similar. We developed a general theoretical framework to describe this coupling, which allows us to retrieve the eigenfrequencies and mechanical loss of the bacterium low-frequency vibration modes (quality factor). Additionally, we analysed the effect of hydration on these vibrational modes. This work demonstrates that ultrahigh frequency optomechanical resonators can be used for vibrational spectrometry with the unique capability to obtain information on single biological entities.

Optical Transduction for Vertical Nanowire Resonators.

We describe an optical transduction mechanism to measure the flexural mode vibrations of vertically aligned nanowires on a flat substrate with high sensitivity, linearity, and ease of implementation. We demonstrate that the light reflected from the substrate when a laser beam strikes it parallel to the nanowires is modulated proportionally to their vibration, so that measuring such modulation provides a highly efficient resonance readout. This mechanism is applicable to single nanowires or arrays without specific requirements regarding their geometry or array pattern, and no fabrication process besides the nanowire generation is required. We show how to optimize the performance of this mechanism by characterizing the split flexural modes of vertical silicon nanowires in their full dynamic range and up to the fifth mode order. The presented transduction approach is relevant for any application of nanowire resonators, particularly for integrating nanomechanical sensing in functional substrates based on vertical nanowires for biological applications.

Spatially Multiplexed Micro-Spectrophotometry in Bright Field Mode for Thin Film Characterization.

Thickness characterization of thin films is of primary importance in a variety of nanotechnology applications, either in the semiconductor industry, quality control in nanofabrication processes or engineering of nanoelectromechanical systems (NEMS) because small thickness variability can strongly compromise the device performance. Here, we present an alternative optical method in bright field mode called Spatially Multiplexed Micro-Spectrophotometry that allows rapid and non-destructive characterization of thin films over areas of mm² and with 1 µm of lateral resolution. We demonstrate an accuracy of 0.1% in the thickness characterization through measurements performed on four microcantilevers that expand an area of 1.8 mm² in one minute of analysis time. The measured thickness variation in the range of few tens of nm translates into a mechanical variability that produces an error of up to 2% in the response of the studied devices when they are used to measure surface stress variations.

Tackling reproducibility in microcantilever biosensors: a statistical approach for sensitive and specific end-point detection of immunoreactions.

In the last decade, microcantilever biosensors have shown enormous potential for highly sensitive label-free detection of nucleic acid and proteins. Despite the enormous advances, the promise of applications of this technology in the biomedical field has been frustrated because of its low reproducibility. Here we tackle the reproducibility issue in microcantilever biosensors and provide the guidelines to minimize the deviations in the biosensor response between different assays. We use as a model system the label-free end-point detection of horseradish peroxidase. We choose the end-point detection mode because of its suitability for implementation in the clinical field that requires simplicity and point-of-care capability. Our study comprises the analysis of 1012 cantilevers with different antibody surface densities, two blocking strategies based on polyethylene-glycol (PEG) and bovine serum albumin (BSA) and stringent controls. The study reveals that the performance of the assay critically depends on both antibody surface density and blocking strategies. We find that the optimal conditions involve antibody surface densities near but below saturation and blocking with PEG. We find that the surface stress induced by the antibody-antigen binding is significantly correlated with the surface stress generated during the antibody attachment and blocking steps. The statistical correlation is harnessed to identify immobilization failure or success, and thus enhancing the specificity and sensitivity of the assay. This procedure enables achieving rates of true positives and true negatives of 90% and 91% respectively. The detection limit is of 10 ng mL(-1) (250 pM) that is similar to the detection limit obtained in our enzyme-linked immunosorbent assay (ELISA) and at least two orders of magnitude smaller than that achieved with well-established label-free biosensors such as a quartz crystal microbalance (QCM) and surface plasmon resonance (SPR) sensor.

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.

Quantification of the surface stress in microcantilever biosensors: revisiting Stoney's equation.

Microcantilever biosensors in the static operation mode translate molecular recognition into a surface stress signal. Surface stress is derived from the nanomechanical cantilever bending by applying Stoney's equation, derived more than 100 years ago. This equation ignores the clamping effect on the cantilever deformation, which induces significant errors in the quantification of the biosensing response. This leads to discrepancies in the surface stress induced by biomolecular interactions in measurements with cantilevers with different sizes and geometries. So far, more accurate solutions have been precluded by the formidable complexity of the theoretical problem that involves solving the two-dimensional biharmonic equation. In this paper, we present an accurate and simple analytical expression to quantify the response of microcantilever biosensors. The equation exhibits an excellent agreement with finite element simulations and DNA immobilization experiments on gold-coated microcantilevers.

A stereovision matching strategy for images captured with fish-eye lenses in forest environments.

We present a novel strategy for computing disparity maps from hemispherical stereo images obtained with fish-eye lenses in forest environments. At a first segmentation stage, the method identifies textures of interest to be either matched or discarded. This is achieved by applying a pattern recognition strategy based on the combination of two classifiers: Fuzzy Clustering and Bayesian. At a second stage, a stereovision matching process is performed based on the application of four stereovision matching constraints: epipolar, similarity, uniqueness and smoothness. The epipolar constraint guides the process. The similarity and uniqueness are mapped through a decision making strategy based on a weighted fuzzy similarity approach, obtaining a disparity map. This map is later filtered through the Hopfield Neural Network framework by considering the smoothness constraint. The combination of the segmentation and stereovision matching approaches makes the main contribution. The method is compared against the usage of simple features and combined similarity matching strategies.

A featured-based strategy for stereovision matching in sensors with fish-eye lenses for forest environments.

This paper describes a novel feature-based stereovision matching process based on a pair of omnidirectional images in forest stands acquired with a stereovision sensor equipped with fish-eye lenses. The stereo analysis problem consists of the following steps: image acquisition, camera modelling, feature extraction, image matching and depth determination. Once the depths of significant points on the trees are obtained, the growing stock volume can be estimated by considering the geometrical camera modelling, which is the final goal. The key steps are feature extraction and image matching. This paper is devoted solely to these two steps. At a first stage a segmentation process extracts the trunks, which are the regions used as features, where each feature is identified through a set of attributes of properties useful for matching. In the second step the features are matched based on the application of the following four well known matching constraints, epipolar, similarity, ordering and uniqueness. The combination of the segmentation and matching processes for this specific kind of sensors make the main contribution of the paper. The method is tested with satisfactory results and compared against the human expert criterion.