Small Spring Constant Research Articles

A Sub-1 Hz Resonance Frequency Resonator Enabled by Multi-Step Tuning for Micro-Seismometer.

We propose a sub-1 Hz resonance frequency MEMS resonator that can be used for seismometers. The low resonance frequency is achieved by an electrically tunable spring with an ultra-small spring constant. Generally, it is difficult to electrically fine-tune the resonance frequency at a near-zero spring constant because the frequency shift per voltage will diverge at the limit of zero spring constant. To circumvent this issue, we propose a multi-step electrical tuning method. We show by simulations that the resonance frequency can be tuned by 0.008 Hz/mV even in the sub-1 Hz region. The small spring constant, however, reduces the shock robustness and dynamic range of the seismometer. To prevent this, we employ a force-balanced method in which the mass displacement is nulled by the feedback force. We show that the displacement can be obtained from the voltage that generates the feedback force.

High performance thermal link with small spring constant for cryogenic applications

We developed a soft and high thermal conductive thermal link for cryogenic applications. The measured maximum thermal conductivity was approximately 18500 W/m/K at 10 K. This spring constant was 1/43 of that of a single thick wire with the same cross-sectional area at room temperature. We reached these performances by utilizing high purity aluminum (99.9999%, 6 N) and by stranding many thin wires that are 0.15 mm in diameter. The electrical Residual Resistivity Ratio was also measured and used to estimate the thermal conductivity by the Wiedemann–Franz law. We observed the size effect on the electrical conductivity, and evaluated the effect of mechanical deformation to the RRR. These evaluations allow us to design a pragmatic thermal link for cryogenic application.

A Flexible PI/Si/SiO2 Piezoresistive Microcantilever for Trace-Level Detection of Aflatoxin B1.

In this paper, a polyimide (PI)/Si/SiO2-based piezoresistive microcantilever biosensor was developed to achieve a trace level detection for aflatoxin B1. To take advantage of both the high piezoresistance coefficient of single-crystal silicon and the small spring constant of PI, the flexible piezoresistive microcantilever was designed using the buried oxide (BOX) layer of a silicon-on-insulator (SOI) wafer as a bottom passivation layer, the topmost single-crystal silicon layer as a piezoresistor layer, and a thin PI film as a top passivation layer. To obtain higher sensitivity and output voltage stability, four identical piezoresistors, two of which were located in the substrate and two integrated in the microcantilevers, were composed of a quarter-bridge configuration wheatstone bridge. The fabricated PI/Si/SiO2 microcantilever showed good mechanical properties with a spring constant of 21.31 nN/μm and a deflection sensitivity of 3.54 × 10−7 nm−1. The microcantilever biosensor also showed a stable voltage output in the Phosphate Buffered Saline (PBS) buffer with a fluctuation less than 1 μV @ 3 V. By functionalizing anti-aflatoxin B1 on the sensing piezoresistive microcantilever with a biotin avidin system (BAS), a linear aflatoxin B1 detection concentration resulting from 1 ng/mL to 100 ng/mL was obtained, and the toxic molecule detection also showed good specificity. The experimental results indicate that the PI/Si/SiO2 flexible piezoresistive microcantilever biosensor has excellent abilities in trace-level and specific detections of aflatoxin B1 and other biomolecules.

Atomic-Scale Friction on Monovacancy-Defective Graphene and Single-Layer Molybdenum-Disulfide by Numerical Analysis.

Using numerical simulations, we study the atomic-scale frictional behaviors of monovacancy-defective graphene and single-layer molybdenum-disulfide (SLMoS2) based on the classical Prandtl–Tomlinson (PT) model with a modified interaction potential considering the Schwoebel–Ehrlich barrier. Due to the presence of a monovacancy defect on the surface, the frictional forces were significantly enhanced. The effects of the PT model parameters on the frictional properties of monovacancy-defective graphene and SLMoS2 were analyzed, and it showed that the spring constant of the pulling spring cx is the most influential parameter on the stick–slip motion in the vicinity of the vacancy defect. Besides, monovacancy-defective SLMoS2 is found to be more sensitive to the stick–slip motion at the vacancy defect site than monovacancy-defective graphene, which can be attributed to the complicated three-layer-sandwiched atomic structure of SLMoS2. The result suggests that the soft tip with a small spring constant can be an ideal candidate for the observation of stick–slip behaviors of the monovacancy-defective surface. This study can fill the gap in atomic-scale friction experiments and molecular dynamics simulations of 2D materials with vacancy-related defects.

Absolute negative mobility of the chain of Brownian particles in steady laminar flows

Transport of the chain of Brownian particles driven by a constant force is investigated in steady laminar flow. Within tailored parameter regimes, this system exhibits absolute negative mobility (ANM), which means that the chain travels in a direction opposite to the external force. When the constant force is applied to all particles, the phenomenon of ANM is observed for large spring constant. When the force is applied to the first particle of the chain, the emergence of ANM can occur for both small and large spring constant. In addition, we can obtain multiple current reversals by suitably changing the spring constant.

The interplay between drift and electrical measurement in conduction atomic force microscopy.

In Conduction Atomic Force Microscopy (CAFM), it is sometimes required to monitor electrical data at a single location over an extended period of time. However, thermal drift of the microscope will cause the tip to move with respect to the sample and thus limit the collection of data. We investigate a method to prolong the time a tip dwells at a location by choosing the AFM cantilever to have small spring constants in the lateral directions. The basis of the approach is that the tip can only move (or slip) once the lateral forces caused by drift overcome the friction force pinning the tip to the surface. We demonstrate the effect experimentally using platinum wire tips and diamond coated tips on SiO2 and HfO2 dielectric films. Simultaneous measurement of the current flow and lateral force signals show that the onset of tip slipping correlates with the beginning of a decrease in the measured current flow, and the onset of slip is prolonged for blunt tips or cantilevers having soft lateral spring constants. The approach not only provides a way to improve the CAFM method for time dependent measurements but also assists in interpreting CAFM data in the presence of drift.

Parameter Optimization of a Vertical Spring‐Viscous Damper‐Coulomb Friction System

A vertical spring‐viscous damper‐concave Coulomb friction isolation system was firstly proposed, and their parameters were firstly optimized to achieve the best performance under earthquakes. An incremental dynamic analysis method (IDA) and a performance‐based assessment framework were used to calculate the system and assess its seismic vulnerability, respectively. Results show that both the friction force and the horizontal component of spring force gradually increase when an earthquake enforce the isolator to slide from its central location. Although other papers propose that an increase of spring force and a decrease of friction force can reduce the structural residual displacement, this paper can minimize the residual displacement value to be 0 by using a super lubrication in the middle of contact surface and a variable increment ratio of concave friction distribution. The reason is that the horizontal component of spring force is always greater than the friction force within any relative displacement between the structure and the ground in this paper. As for the peak relative displacement and peak acceleration of structure, one is reduced while the other is increased when selecting the optimal isolation parameters. If the structure is very sensitive to the acceleration response, a low friction parameter, a small spring constant, and a small and even zero damping constant could be adopted to yield a small peak acceleration of system. The tightness of vertical spring can be adjusted to be appropriately loose to continuously reduce the structural acceleration response.

Synthesis of a Helical Analogue of Kekulene: A Flexible π-Expanded Helicene with Large Helical Diameter Acting as a Soft Molecular Spring.

A π-expanded helicene that is the helically twisted analogue of kekulene was synthesized using a 6-fold ring-closing olefin metathesis (RCM) reaction as a key step. The π-expanded geometry with large helical diameter ( dh = 10.2 Å), consisting only of carbon and hydrogen atoms (C54H30), was unambiguously determined by single-crystal X-ray analysis. We found that the π-expanded helicene with large helical diameter will act as a soft molecular spring with a small spring constant. Interestingly, the mechanical properties of the molecular springs roughly satisfied a physical formula for macroscopic spring materials; i.e., the force constant of the elongation of a molecular spring ( k) is inversely proportional to the third power of the helical diameter ( k ∝ dh-3).

Modified cantilevers to probe unambiguously out-of-plane piezoresponse

We demonstrate and investigate the coupling of contributions from both in-plane (IP) polarization and out-of-plane (OP) components in ${\mathrm{BiFeO}}_{3}$ (BFO) thin-film polarization probed by piezoresponse force microscopy (PFM). Such coupling leads to image artifacts which prevent the correct determination of OP polarization vector directions and the corresponding piezoelectric coefficient ${d}_{33}$. Using material strength theory with a one-dimensional modeling of the cantilever oscillation amplitude under electrostatic and elastic forces as a function of the tip length, we have evidenced the impact of IP piezoresponse to the OP signal for tip length longer than 4 \ensuremath{\mu}m. The IP polarization vector induces a significant longitudinal bending of the cantilever, due to the small spring constant of long tips, which provokes a normal deviation superimposed to the OP piezoresponse. These artifacts can be reduced by increasing the longitudinal spring constant of the cantilever by shortening the tip length. Standard cantilevers with 15-\ensuremath{\mu}m-long tips were modified to reach the desired tip length, using focused ion-beam techniques and tested using PFM on the same BFO thin film. Tip length shortening has strongly reduced IP artifacts as expected, while the impact of nonlocal electrostatic forces, becoming predominant for tips shorter than 1 \ensuremath{\mu}m, has led to a non-negligible deflection offset. For shorter tips, a strong electric field from a cantilever beam can induce polarization switching as observed for a 0.5-\ensuremath{\mu}m-long tip. Tip length ranging from 1 to 4 \ensuremath{\mu}m allowed minimizing both artifacts to probe unambiguously OP piezoresponse and quantify the ${d}_{33}$ piezoelectric coefficient.

Design and analysis of Outside-Deployed Lamina Emergent Joint (OD-LEJ)

Lamina emergent mechanisms (LEMs) can be fabricated in plane, while achieve motion that emerges out of fabrication plane. This paper presents a new flexure hinge called Outside-Deployed Lamina Emergent Joint (OD-LEJ) with a small equivalent spring constant and a large angular displacement. The closed-form model is given and a finite element analysis (FEA) model is created. The FEA results show that this joint can achieve nearly 170.17˚ of rotation without plastic deformation. Stress analysis is done and the results gotten from theoretical calculation and FEA coincide with each other very well. Safety analysis and fatigue analysis are done as well. An Inside-Deployed Lamina Emergent Joint (ID-LEJ) is also proposed. The joint is analyzed through FEA and theoretical calculation. The joint shows a similar bending property as OD-LEJ. Comparisons between these two joints and Lamina Emergent Torsional (LET) joint are made. OD-LEJ and ID-LEJ do better than LET joint in large angular displacement and have a smaller equivalent spring constant. Finally, the movement of the center of rotation and some other problems are discussed.

Bimodal frequency-modulated atomic force microscopy with small cantilevers.

Small cantilevers with ultra-high resonant frequencies (1-3 MHz) have paved the way for high-speed atomic force microscopy. However, their potential for multi-frequency atomic force microscopy is unexplored. Because small cantilevers have small spring constants but large resonant frequencies, they are well-suited for the characterisation of delicate specimens with high imaging rates. We demonstrate their imaging capabilities in a bimodal frequency modulation mode in constant excitation on semi-crystalline polypropylene. The first two flexural modes of the cantilever were simultaneously excited. The detected frequency shift of the first eigenmode was held constant for topographical feedback, whereas the second eigenmode frequency shift was used to map the local properties of the specimen. High-resolution images were acquired depicting crystalline lamellae of approximately 12 nm in width. Additionally, dynamic force curves revealed that the contrast originated from different interaction forces between the tip and the distinct polymer regions. The technique uses gentle forces during scanning and quantified the elastic moduli Eam = 300 MPa and Ecr = 600 MPa on amorphous and crystalline regions, respectively. Thus, multimode measurements with small cantilevers allow one to map material properties on the nanoscale at high resolutions and increase the force sensitivity compared with standard cantilevers.

A barometric pressure sensor based on the air-gap scale effect in a cantilever

The most common structure for a conventional barometric pressure sensor consists of a vacuum-sealed cavity and a diaphragm. However, we hypothesize that a simple structure with an unsealed cavity and an ultra-thin cantilever can provide more sensitive measurements. We produced a 300-nm-thick cantilever with a small spring constant, which made the cantilever sensitive to low pressures. We demonstrated that miniaturizing the air-gap of the cantilever enables the sensor to measure barometric pressure changes at a low pressure change rate with a high resolution, which was 1 Pa at 0.05 Hz, and for a gap size of 1.7 μm.

Stick-slip statistics in atomic friction

We theoretically study atomic friction experiments in the stick-slip regime within the framework of the Prandtl-Tomlinson model. We derive a differential equation describing the force probability distribution. Approximate analytical solutions of this equation are found for the asymptotic cases of high and low effective spring constant, but for arbitrary pulling velocities. Excellent accuracy of these approximate expressions is demonstrated numerically. In particular, the result for the mean force, although obtained for small spring constants, is shown to be accurate also somewhat outside of its expected validity range.

Bounds and optimization of the minimum eigenvalue for a vibrating system

We consider the problem of the oscillation of a string fixed at one end with a mass connected to a spring at the other end. The problem of minimizing the first eigenvalue of the system subject to a fixed total mass constraint is investigated. We discuss both a Sturm‐Liouville and a Stieltjes integral formulation of the boundary value problem. For small spring constant, the minimum eigenvalue for both formulations is obtained by concentrating all the mass at the end with the spring. For large spring constants, the Stieltjes eigenvalue is minimized by a point mass at an interior point. We also formulate the problem with an -norm constraint on the density in which case the optimal eigenpair satisfies a nonlinear boundary value problem. Numerical evidence suggests that this case tends to the point-mass case at the end as ! 1 +: AMS subject classifications (2010): 34B08, 34B24, 34L05, 34L15, 49K15, 49R05.

Characterization of silver–gallium nanowires for force and mass sensing applications

We investigate the mechanical properties of cantilevered silver–gallium (Ag2Ga) nanowires using laser Doppler vibrometry. From measurements of the resonantfrequencies and associated operating deflection shapes, we demonstrate that theseAg2Ga nanowires behave as ideal Euler–Bernoulli beams. Furthermore, radial asymmetriesin these nanowires are detected through high resolution measurements of thevibration spectra. These crystalline nanowires possess many ideal characteristics fornanoscale force and mass sensing, including small spring constants (as low as10 − 4 N m − 1), high frequency bandwidth with resonance frequencies in the0.02–10 MHz range, small suspended mass (picograms), and relatively highQ-factors(∼2–50) under ambient conditions. We evaluate the utility ofAg2Ga nanowires for nanocantilever applications, including ultrasmall mass and high frequencybandwidth piconewton force detection.

Ultra flexible SiGe/Si/Cr nanosprings

The electrical and mechanical properties of Si/SiGe rolled-up nanosprings have been investigated. Micromanipulation has been employed to investigate the mechanical properties. For nanosprings under investigation, a linear dependence between applied force and extention is found until the spring is extended to 91% of its original length, moreover, the springs could be reproducibly extended to more than 180% of their original length. An extremely small spring constant of 0.003N/m has been determined, which is an order of magnitude smaller than that of the most flexible available atomic force microscope (AFM) cantilever (∼10−2N/m). Thus, it is expected that these springs can be used as ultra-sensitive force sensors. A simple estimation assuming an imaging resolution of approximately 1nm is adopted for displacement measurement and reveals that using a nanospring fabricated from a 300nm wide mesa as a visual-based force sensor, a resolution of 3pN/nm can be provided. The conductivity of nanospirals was analysed and current densities up to 530kA/cm2 were measured. Structures with metallic wires on top of the mesa structures were successfully employed to activate mechanical movements of the structure.

Elastic coefficient of a single polymer chain by using Brownian dynamics analysis

The elastic coefficient of a single polystyrene chain has been experimentally evaluated by using Brownian dynamics analysis. The Brownian motion of the chain is probed using a particle trapped by optical tweezers with a negligibly small spring constant. The displacement of the particle due to Brownian motion is measured by an interferometer assembled using the same laser beam as the optical tweezers. Two methods are employed for Brownian dynamics analysis: (1) the analysis of the time course of the displacement of the particle and (2) the fitting of the power spectrum of Brownian motion with a Lorentzian. The elastic constant of a polystyrene chain in dichloromethane at 21 degrees C is estimated to be 6.4 x 10(-6) and 1.1 x 10(-5) N/m when methods (1) and (2) are employed, respectively. The elastic constant obtained by approximating the polystyrene chain to a freely jointed chain is in agreement with the experimentally evaluated elastic constant.

Piezoresistive cantilevers in a commercial CMOS technology for intermolecular force detection

We report the development of piezoresistive cantilevers for intermolecular force detection in biochemical sensing, by using a commercial CMOS technology. The detection of the small forces involved in molecular recognition requires cantilevers with a small spring constant and high force sensitivity. We have fabricated polycrystalline silicon cantilevers by using the two polysilicon layers of a commercial CMOS process with minimum design rule widths. The cantilevers have been released by post-process micromachining. The upper polysilicon layer has been used as a piezoresistor. CMOS amplifying circuits have been integrated on-chip with the cantilever structures. The cantilevers have small spring constants ranging from 1.5 to 12 mN/m. The complete system has been successfully tested by applying a known transverse displacement with an AFM tip. A force sensitivity of 8 μV/pN and resolution of 50 pN has been obtained. This high resolution is obtained with CMOS polysilicon, which has a relatively low piezoresistive coefficient, but this is compensated by the integration of signal-processing circuitry.

Versatility of Self-Oscillation Technique with Mechanical-Acoustic Excitations for Frequency Modulation Atomic Force Microscope in Liquids

We demonstrated that a cantilever with a small spring constant could be self-oscillated in liquids using a commercial atomic force microscope (AFM) employing a mechanical-acoustic excitation and that the present AFM system can image biological samples such as protein and deoxyribonucleic acid (DNA) in an aqueous solution in regions of slight contact. The present study together with the previous one [T. Okajima et al., Appl. Surf. Sci. 210 (2003) 68.] indicate that a self-oscillation technique with mechanical-acoustic excitations is a versatile method for frequency modulation (FM)-AFM in liquids, although the vibration properties of the cantilever in liquids, which affect the sensitivity of FM detection, have to be more optimized. It was also demonstrated that a noncontact force such as an electrostatic force was detected by the present FM-AFM.

Silicon Tip Cantilevers for Force Microscopy in Water with Resonance of 20 kHz or Above

Silicon nitride cantilevers with a silicon probe have been developed for force microscopy of soft samples in water. The cantilevers were soft with a small spring constant of from 0.05 to 0.11 N/m and some showed resonance of 20 kHz or higher in water. The typical dimensions of a cantilever were 40 µm ×15 µm ×0.19 µm. Autofluorescent light emissions from the resulting cantilever and probe were studied. Autofluorescence of the silicon nitride cantilever was smaller than that of a conventional silicon nitride cantilever. Autofluorescence of the silicon probe was small and of negligible intensity for fluorescence optical microscopy. The cantilever probe less disturbs fluorescence optical microscopy than conventional soft cantilever probes.