Resonance Frequency Of Microcantilevers Research Articles

Development of a microcantilever-based biosensor for detecting Programmed Death Ligand 1

The ongoing global concern of cancer worldwide necessitates the development of advanced diagnostic and therapeutic strategies. The majority of recent detection strategies involve the employment of biomarkers. A critical biomarker for cancer immunotherapy efficacy and patient prognosis is Programmed Death Ligand 1 (PD-L1), which is a key immune checkpoint protein. PD-L1 can be particularly linked to cancer progression and therapy response. Current detection methods, such as enzyme-linked immunosorbent assay (ELISA), face limitations like high cost, time consumption, and complexity. This study introduces a microcantilever-based biosensor designed for the detection of soluble PD-L1 (sPD-L1), which has a specific association with PD-L1. The biosensor utilizes anti-PD-L1 as the sensing layer, capitalizing on the specific binding affinity between anti-PD-L1 and sPD-L1. The presence of the sensing layer was confirmed through Atomic Force Microscopy (AFM) and contact angle measurements. Binding between sPD-L1 and anti-PD-L1 induces a shift in the microcantilever's resonance frequency, which is proportional to the PD-L1 concentration. Notably, the resonance frequency shift demonstrates a robust linear relationship with the increasing biomarker concentration, ranging from 0.05 ng/ml to 500 ng/ml. The detection limit of the biosensor was determined to be approximately 10 pg/ml. The biosensor demonstrates excellent performance in detecting PD-L1 with high specificity even in complex biological matrices. This innovative approach not only provides a promising tool for early cancer diagnosis but also holds potential for monitoring immunotherapy efficacy, paving the way for personalized and effective cancer treatments.

Torsional Vibration and Sensitivity Analysis of Microcantilever in Liquid

Development of microsystems and ever-increasing advances of nanotechnology have resulted in growing applications of microcantilevers (MCs), including Atomic Force Microscopy (AFM). In AFM, transverse vibration of microfiber from a liquid medium results in resonance of unwanted hydrodynamic and electrostatic forces, which can be minimized by torsional mode. In the present study, the differential equation of the vibrational motion is extracted by acquiring the hydrodynamic force applied to MCs aiming to investigate the torsional vibration behavior of MCs in a liquid medium; and the extracted equation is solved to study the behavior of MCs in a liquid medium. Considering the significant effect of MC geometry on its torsional vibrations in a liquid medium, Sobol's variance-based sensitivity analysis method was utilized to investigate the effectiveness of MC geometry on torsional vibration. The sensitivity analysis results show that length and width have the most significant effects on the quality factor and the resonance frequency of MCs.

Rapid and Sensitive Detection of Severe Acute Respiratory Syndrome Coronavirus 2 in Label-Free Manner Using Micromechanical Sensors.

Coronavirus (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has been identified as a deadly pandemic. The genomic analysis of SARS-CoV-2 is performed using a reverse transcription-polymerase chain reaction (RT-PCR) technique for identifying viral ribonucleic acid (RNA) in infected patients. However, the RT-PCR diagnostic technique is manually laborious and expensive; therefore, it is not readily accessible in every laboratory. Methodological simplification is crucial to combat the ongoing pandemic by introducing quick, efficient, and affordable diagnostic methods. Here, we report how microcantilever sensors offer promising opportunities for rapid COVID-19 detection. Our first attempt was to capture the single-stranded complementary DNA of SARS-CoV-2 through DNA hybridization. Therefore, the microcantilever surface was immobilized with an oligonucleotide probe and detected using complementary target DNA hybridization by a shift in microcantilever resonance frequency. Our results show that microcantilever sensors can discriminate between complementary and noncomplementary target DNA on a micro to nanoscale. Additionally, the microcantilever sensors’ aptitude toward partial complementary DNA determines their potential to identify new variants of coronavirus. Therefore, microcantilever sensing could be a vital tool in the effort to extinguish the spreading COVID-19 pandemic.

Regulation of thermoelastic properties of concave-packaged DNA adsorption films and its relevant microcantilever detection signals

The packing patterns have close correlation with the thermoelastic properties of DNA adsorption films and the relevant detection signals of microcantilevers. In this paper, we investigate the influence of packing patterns on the thermoelastic properties of DNA adsorption films, the detection signals of microcantilevers and their temperature dependence. First, the Parsegian’s empirical potential based on a mesoscopic liquid crystal theory is employed to describe the interaction energy among coarse-grained DNA cylinders; then, the thought experiment method and the force balance method of nonlinear elastic network nodes are combined to characterize the elastic modulus, prestress and thermal expansion coefficient of DNA adsorption films; finally, based on an effective macroscopic continuum model for DNA microbeam deformation, we study the microcantilever resonance frequency shifts caused by DNA adsorptions and the temperature effect on the microcantilever static deflections, respectively. Results show that, compared with the convex-packaged, the re-entrant honeycomb packing pattern endows DNA adsorption films with a larger adjustable range of the elastic modulus and prestress, so as to make DNA-microcantilevers having an enhanced dynamic detection signal whereas a weaker response to temperature variation. These results are expected to provide a new option for the regulation design of DNA composite materials and microbeam sensors. Packing patterns play a key role in thermoelastic properties of DNA adsorption films and detection signals of microcantilevers. By constructing multiscale relations between DNA mesoscopic free energy and continuum microcantilever deformation, resonant frequency shift, the influence of packing patterns on thermoelastic properties of DNA adsorption films and detection signals of microcantilevers is investigated. Compared with the convex-packaged DNA adsorption film, the concave-packaged one endows a stronger dynamic biodetection signal, whereas a weaker response to ambient temperature variation due to a larger adjustable range of thermoelastic property.

Dynamic mechanical characterization of two-photon-polymerized SZ2080 photoresist

Two-photon polymerization (2PP) is a material processing technique employed for the production of high-resolution microstructures. The high potential of this technique in the fabrication of structured materials, or metamaterials, has recently attracted significant research interest. To proceed toward real applications, the mechanical properties of the material obtained by 2PP should be known. These properties depend on all the process parameters, which affect the cross-linking between the polymeric chains, and very few results are available in the literature. In this work, we perform a systematic characterization of the elastic properties of femtosecond laser-polymerized SZ2080 (hybrid organic–inorganic photoresist) by combining dynamic experimental tests and numerical simulations on properly designed microstructures. Studying the resonance frequencies of micro-cantilevers, we demonstrate the possibility of tailoring the mechanical properties of the material by changing the laser irradiation conditions. This result paves the way to the use of 2PP for the fabrication of microdevices operating in a dynamic regime with optimized material properties.

Exact Mode Shapes of T-shaped and Overhang-shaped Microcantilevers

Resonance frequencies and mode shapes of microcantilevers are of important interest in micro-mechanical systems for enhancing the functionality and applicable range of the cantilevers in vibration transducing, energy harvesting, and highly sensitive measurement. In this study, using the Euler-Bernoulli theory for beam, we figured out the exact mode shapes of cantilevers of varying widths such as the overhang- or T-shaped cantilevers. The obtained mode shapes have been shown to significantly deviate from the approximate forms of a rectangular cantilever that are commonly used in mechanics and physics. They were then used to figure out the resonance frequencies of the cantilever. The analytical solutions have been confirmed by using the finite element method simulations with very low deviation. This study suggested a method for correctly obtaining the resonance frequency of microcantilevers with complicated dimensions, such as the doubly clamped cantilever with the undercut, with the overhangs at the clamped positions, or with an attached mass in the middle.

Effect of surface patterning using femtosecond laser on micromechanical and structural properties of micromechanical sensors

A femtosecond laser can be used to fabricate microstructures on a silicon microcantilever surface with high precession and minimal sidewall defects. The aim of this study is to investigate the effect of the creation of microgrooves and sub-microgrooves on the resonance frequency, quality factor, and spring constant of a silicon microcantilever. A single pass of a femtosecond laser with a wavelength of 1026 nm was used to fabricate microgrooves on the microcantilever surface. Different numbers of microgrooves were fabricated on each microcantilever using the femtosecond laser micromachining technique. The separation distance between the center of the two microgrooves was 7 μm. The microstructure of the fabricated microgrooves was investigated through field emission electron microscopy. The resonance frequency increased with the number of microgrooves, but the quality factor of the patterned microcantilever was higher than that of the unpatterned microcantilever. The spring constant increased with the number of microgrooves, increasing from 18.96 to 38.04 mN/m for microcantilevers with 1 and 7 microgrooves, respectively.

Ultrahigh sensitive and ultrafast relative humidity sensing using surface enhanced microcantilevers

Active control of relative humidity (RH) and real-time monitoring in a sustained manner are of paramount importance in numerous fields and it is necessary to develop state-of-the-art RH sensors with high sensitivity and fast response times. In the present work, we propose and experimentally demonstrate a high-performance RH sensor using SiO2 microcantilevers (MCs) with controlled micro-patterns on their surface. SiO2 MCs with and without controlled surface micro-patterns were fabricated using direct laser writer and wet chemical etching methods. RH sensing experiments were performed, by measuring the shift in resonance frequency of MCs, when RH is varied between 20% and 90%. RH sensitivity of micro-patterned MCs was found to be significantly higher than the unpatterned ones and is explained on the basis of gel-like water layer formation inside the micro-patterns which facilitates the enhanced uptake of water molecules. Micro-patterned MCs exhibited an unprecedented RH sensitivity (10.45 Hz/% RH), ultrafast response/recovery times (∼ 1 s) and outstanding stability (variation < 5%) along with low hysteresis error (< 3%RH). These superior characteristics of micro-patterned MCs allowed the real-time monitoring of human respiration during normal and slow inhale/exhale cycles. Introduction of controlled micro-patterns on MC surface provides a simple and efficient way to enhance the sensitivity of MC based sensors without compromising other sensor characteristics such as response and recovery times.

Effect of biaxial curvature on the resonance frequency of uncoated microcantilevers

Microcantilevers (MCs) are extensively studied as physical, chemical and biological sensors in dynamic mode, where the shift in resonance frequency due to the adsorption of target analytes/biomolecules on their surface is measured. However, surface stress generated during adsorption or microfabrication induced curvature inherently present in MCs can influence the observed frequency shift, introducing significant errors in the quantification of the analyte sensing response. In spite of several studies over the past four decades, the role of surface stress/curvature on the stiffness and thus resonance frequency of MCs is not well established. Interestingly, this effect also depends on MC dimensions and is not completely understood. In the present work, we address this problem and demonstrate that the presence of transverse curvature significantly influences the resonance frequency and this effect critically depends on width by length ratio (W/L) of MCs. For this purpose, we have fabricated uncoated SiO2 MCs of various dimensions with inherent biaxial curvature. Our experiments on these devices revealed that when W/L of MCs is < 0.16, resonance frequency shift is independent of curvature whereas it is directly proportional to the same when W/L is between 0.16 and 0.35. These results are explained on the basis of curvature induced nonlinear stiffening of MCs and clamping geometric effects. Interestingly, a further increase in W/L (>0.4) was found to marginally reduce the observed frequency shift and is attributed to the presence of competing non-linear plate softening effects at these dimensions. Finally, we have compared our results with various experimental studies and theoretical models reported in the literature.

Investigation of the Photothermal Excited Microcantilevers Based on Modified Couple Stress Theory

In microscale and sub-micron scale, scale effect highlights and the classical continuum mechanics cannot describe microstructure-dependent size effects. So many non-classical theories were put forward. The modified couple stress theory was established by introducing a material parameter to characterize the scale effect. In this paper, the dynamic responses of microcantilever under photothermal excitation are studied using the modified couple stress theory. The microcantilever deflection governing equation was given, and deflections were obtained numerically using relaxation method. Comparison was made between numerical results with that obtained with experimental measurement and showed a good agreement. According to the numerical results, the scale effect becomes remarkable as the ratio of thickness to the material parameter changes from zero to one. Also, the results showed that this ratio has prominent effect on the resonant frequency of microcantilever.

Thermomechanical Response of a Representative Porin for Biomimetics.

The thermomechanical response of Omp2a, a representative porin used for the fabrication of smart biomimetic nanomembranes, has been characterized using microcantilever technology and compared with standard proteins. For this purpose, thermally induced transitions involving the conversion of stable trimers to bigger aggregates, local reorganizations based on the strengthening or weakening of intermolecular interactions, and protein denaturation have been detected by the microcantilever resonance frequency and deflection as a function of the temperature. Measurements have been carried out on arrays of 8-microcantilevers functionalized with proteins (Omp2a, lysozyme and bovine serum albumin). To interpret the measured nanofeatures, the response of proteins to temperature has been also examined using other characterization techniques, including real time wide angle X-ray diffraction. Results not only demonstrate the complex behavior of porins, which exhibit multiple local thermal transitions before undergoing denaturation at temperatures higher than 105 °C, but also suggest a posttreatment to control the orientation of immobilized Omp2a molecules in functionalized biomimetic nanomembranes and, thus, increase their efficacy in ion transport.

Young’s modulus of multi-layer microcantilevers

A theoretical model for calculating the Young’s modulus of multi-layer microcantilevers with a coating is proposed, and validated by a three-dimensional (3D) finite element (FE) model using ANSYS parametric design language (APDL) and atomic force microscopy (AFM) characterization. Compared with typical theoretical models (Rayleigh-Ritz model, Euler-Bernoulli (E-B) beam model and spring mass model), the proposed theoretical model can obtain Young’s modulus of multi-layer microcantilevers more precisely. Also, the influences of coating’s geometric dimensions on Young’s modulus and resonant frequency of microcantilevers are discussed. The thickness of coating has a great influence on Young’s modulus and resonant frequency of multi-layer microcantilevers, and the coating should be considered to calculate Young’s modulus more precisely, especially when fairly thicker coating is employed.

CO Gas-Induced Resonance Frequency Shift of ZnO-Functionalized Microcantilever in Humid Air

Resonance frequency shift of a zinc oxide- (ZnO-) functionalized microcantilever as a response to carbon monoxide (CO) gas has been investigated. Here, ZnO microrods were grown on the microcantilever surface by a hydrothermal method. The measurement of resonance frequency of the microcantilever vibrations due to the gas was carried out in two conditions, that is, gas flow with and without air pumping into an experiment chamber. The results show that the resonance frequency of the ZnO-functionalized microcantilever decreases because of CO in air pumping condition, while it increases when CO is introduced without air pumping. Such change in the resonance frequency is influenced by water vapor condition, and a possible model based on water-CO combination was proposed.

Nanoscale Mapping of Dielectric Properties of Nanomaterials from Kilohertz to Megahertz Using Ultrasmall Cantilevers.

Electrostatic force microscopy (EFM) is often used for nanoscale dielectric spectroscopy, the measurement of local dielectric properties of materials as a function of frequency. However, the frequency range of atomic force microscopy (AFM)-based dielectric spectroscopy has been limited to a few kilohertz by the resonance frequency and noise of soft microcantilevers used for this purpose. Here, we boost the frequency range of local dielectric spectroscopy by 3 orders of magnitude from a few kilohertz to a few megahertz by developing a technique that exploits the high resonance frequency and low thermal noise of ultrasmall cantilevers (USCs). We map the frequency response of the real and imaginary components of the capacitance gradient (∂C(ω)/∂z) by using second-harmonic EFM and a theoretical model, which relates cantilever dynamics to the complex dielectric constant. We demonstrate the method by mapping the nanoscale dielectric spectrum of polymer-based materials for organic electronic devices. Beyond offering a powerful extension to AFM-based dielectric spectroscopy, the approach also allows the identification of electrostatic excitation frequencies which affords high dielectric contrast on nanomaterials.

Frequency response of curved bilayer microcantilevers with applications to surface stress measurement

Bilayer microcantilevers are normally curved because of fabrication-induced stresses. When used in biological/chemical sensing applications, the absorption of target agents onto the functionalized surface of the microcantilever creates a surface stress that shifts its resonance frequency. Despite numerous efforts, the mechanisms of surface stress-induced shift in the resonance frequency of microcantilevers remain elusive. To address this problem, this work presents a detailed analysis of the frequency response of microcantilevers, with different width-to-thickness ratios and curvature levels, using classical lamination theory and the Rayleigh–Ritz method. Based on the results of this analysis, a new relationship between resonance frequency shift and curvature variation due to differential surface stress loading is established. By comparing the strain energies associated with the in-plane and out-of-plane displacements of the microcantilever at different curvature levels, a new implicit model for surface stress-induced resonance frequency shift in microcantilevers is presented. Verified against the results of experiments carried out on gold/polysilicon microcantilevers, the new model is expected to provide a better understanding of surface stress-microcantilever resonator interaction, which is critical to systematic optimization of resonance-based micro sensors.

Role of surface morphology on desorption kinetics of water molecules from uncoated silicon microcantilever

Desorption kinetics of water molecules from uncoated silicon microcantilevers (MC) is studied, by measuring resonance frequency, with Relative Humidity (RH) varying in the range of 50–15%. Shift in resonance frequency of MC was used to estimate the desorbed mass, which over-estimated the number of monolayers desorbed between the RH values of interest and followed a single exponential decay model. Moreover, desorption rate is found to be higher for RH>25% compared to RH<25%. However, the Q factor describing the sensitivity of the MC and computed from the resonance spectrum is found to decrease by ∼3%. These results are explained on the basis of complex surface coverage during desorption of water molecules and is supported by topographical image of MC surface clearly showing quasi 3D nanofeatures. The bending of uncoated MC during desorption, due to the generation of differential surface stress, further confirms the presence of these surface features.

Feedback-Controlled MEMS Force Sensor for Characterization of Microcantilevers

This paper outlines the design and characterization of a setup used to measure the stiffness of microcantilevers and other small mechanical devices. Due to the simplicity of fabrication, microcantilevers are used as the basis for a variety of mechanical sensor designs. In a range of applications, knowledge of the stiffness of microcantilevers is essential for the accurate calibration of the sensors in which they are used. Stiffness is most commonly identified through measurement of the microcantilever's resonance frequency, which is applied to an empirically derived model. This paper uses a microelectromechanical system (MEMS)-based force sensor to measure the forces produced by a microcantilever when deformed and a piezoelectric tube-based nanopositioner to displace the microcantilever. A method of calibrating the force sensor is presented that takes advantage of the lumped nature of the mechanical system and the nonlinearity of MEMS electrostatic drives.

Effect of surface stress on microcantilever resonance frequency during water adsorption: influence of microcantilever dimensions.

This paper reports the effect of dimensions of microcantilever (MC) on its resonance frequency and bending upon adsorption of water molecules. Study is conducted on three MCs having the dimensions of 450 × 40 × 2.5 μm(3) (MC1), 225 × 30 × 3 μm(3) (MC2) and 125 × 35 × 4.5 μm(3) (MC3). The measured resonant frequency showed the expected negative shift in MC1, initially positive followed by a negative shift in MC2 and only positive shift in MC3 during adsorption. This behavior is attributed to changes in the stiffness of the MC associated with the surface stress. The surface stress generated on the MC has been derived from its bending measurements upon water adsorption. The change in the stiffness of MC evaluated from an independent estimate of expected frequency shift showed that the relative stiffness change of MC increases linearly with the surface stress scaled with cube of width to height ratio of MCs, confirming the dimensional dependence of adsorption induced stiffness change.

Gas chemical sensitivity of a CMOS MEMS cantilever functionalized via evaporation driven assembly

This work demonstrates an electrostatically actuated resonant microcantilever fabricated in a complementary metal oxide semiconductor process and functionalized with a chemically sorbent polymer layer for the detection of volatile organic compounds. Deposition of the chemically sorbent layer is controlled through evaporation-driven assembly. Analytical and finite element analysis models of the deposited polymer layer on the microcantilever resonant frequency and mass sensitivity are presented. Fabrication of the chemical sensor, including a description of polymer deposition through evaporation-driven assembly within a capillary, is detailed. The completely functionalized resonator demonstrates a limit of detection of 1.6 ppm for toluene. An optimal polymer sensitive layer deposition of 42% of the total beam length is measured from frequency instability and sensitivity tests.

Preliminary results of the feasibility of hydrogen detection by the use of uncoated silicon microcantilever-based sensors

Hydrogen is a key parameter to monitor radioactive disposal facility such as the envisioned French geological repository for nuclear wastes. The use of microcantilevers as chemical sensors usually involves a sensitive layer whose purpose is to selectively sorb the analyte of interest. The sorbed substance can then be detected by monitoring either the resonant frequency shift (dynamic mode) or the quasi-static deflection (static mode). The objective of this paper is to demonstrate the feasibility of eliminating the need for the sensitive layer in the dynamic mode, thereby increasing the long-term reliability. The microcantilever resonant frequency allows probing the mechanical properties (mass density and viscosity) of the surrounding fluid and, thus, to determine the concentration of a species in a binary gaseous. Promising preliminary work has allowed detecting concentration of 200 ppm of hydrogen in air with non-optimized geometry of silicon microcantilever with integrated actuation and read-out.