Deflection of a Viscoelastic Cantilever under a Uniform Surface Stress: Applications to Static-mode Microcantilever Sensors Undergoing Adsorption

The equation governing the curvature of a viscoelastic microcantilever beam loaded with a uniform surface stress is derived. The present model is applicable to static-mode microcantilever sensors made with a rigid polymer, such as SU-8. An analytical solution to the differential equation governing the curvature is given for a specific surface stress representing adsorption of analyte onto the viscoelastic beam’s surface. The solution for the bending of the microcantilever shows that, in many cases, the use of Stoney’s equation to analyze stress-induced deflection of viscoelastic microcantilevers (in the present case due to surface analyte adsorption) can lead to poor predictions of the beam’s response. It is shown that using a viscoelastic substrate can greatly increase sensitivity (due to a lower modulus), but at the cost of a longer response time due to viscoelasticcreep in the microcantilever. In addition, the effects of a coating on the cantilever are considered. By defining effective moduli for the coated-beam case, the analytical solution for the uncoated case can still be used. It is found that, unlike the case of a silicon microcantilever, the stress in the coating due to bending of a polymer cantilever can be significant, especially for metalcoatings. The theoretical results presented here can also be used to extract time-domain viscoelasticproperties of the polymermaterial from beam response data

Characterization of Epoxy Resin (SU-8) Film Using Thickness-Shear Mode (TSM) Resonator under Various Conditions

Characterization of an epoxy resin film, commonly known as SU-8, is presented using thickness shear mode (TSM) quartz resonator. The impedance-admittance characteristics of the equivalent circuit models of the unperturbed and coated resonators are analyzed to extract the storage modulus and loss modulus (G\u27 and G\u27\u27). Those parameters are needed to establish SU-8 film as an effective wave-guiding layer in the implementation of guided shear-horizontal surface acoustic wave (SH-SAW) sensor platforms. Both cured and uncured polymer films are studied at the fundamental and third harmonic frequencies of the TSM resonators. The storage modulus (G\u27) and loss modulus (G\u27\u27) of the SU-8 film approach constant values of 1.66 × 1010 dyne/cm2 and 6.0 × 108 dyne/cm2, respectively, for relatively thicker films (\u3e20 μm) at a relatively low frequency of 9 MHz. The most accurate values for the extracted shear moduli G (G = G\u27 + jG\u27\u27) are obtained at high thickness where the viscoelastic contribution to the TSM response is substantial. The effect of temperature on the storage and loss moduli is determined for the range of −75 to 40 °C. It is found that the polymer approaches a totally glassy state below −60 °C. Exposure to water appears to follow Fickian diffusion behavior at short times and this exposure also results in changes to both G\u27 and G\u27\u27. However, stability is rapidly reached with exposure to water, indicating relatively lower water absorption, consistent with the extracted diffusion coefficient

Resonant Microcantilevers for the Determination of the Loss Modulus of Thin Polymer Films

The increasing interest in polymer materials creates the need for accurate tools to characterize their mechanical properties. Due to energy dissipation in polymers during deformation, these materials exhibit viscoelastic behavior. Accurate determination of these viscoelastic properties and, more specifically, viscous losses, remains challenging and mainly unknown for thin polymer films. In this paper, a straightforward method to determine the loss modulus of organic materials using resonating microcantilevers has been developed. The extracted results for polyisobutylene show the variation of viscous losses over a large range of frequencies (7-350 kHz)

Analysis of Liquid-Phase Chemical Detection Using Guided Shear Horizontal-Surface Acoustic Wave Sensors

Direct chemical sensing in liquid environments using polymer-guided shear horizontal surface acoustic wave sensor platforms on 36° rotated Y-cut LiTaO3 is investigated. Design considerations for optimizing these devices for liquid-phase detection are systematically explored. Two different sensor geometries are experimentally and theoretically analyzed. Dual delay line devices are used with a reference line coated with poly (methyl methacrylate) (PMMA) and a sensing line coated with a chemically sensitive polymer, which acts as both a guiding layer and a sensing layer or with a PMMA waveguide and a chemically sensitive polymer. Results show the three-layer model provides higher sensitivity than the four-layer model. Contributions from mass loading and coating viscoelasticity changes to the sensor response are evaluated, taking into account the added mass, swelling, and plasticization. Chemically sensitive polymers are investigated in the detection of low concentrations (1-60 ppm) of toluene, ethylbenzene, and xylenes in water. A low-ppb level detection limit is estimated from the present experimental measurements. Sensor properties are investigated by varying the sensor geometries, coating thickness combinations, coating properties, and curing temperature for operation in liquid environments. Partition coefficients for polymer-aqueous analyte pairs are used to explain the observed trend in sensitivity for the polymers PMMA, poly(isobutylene), poly(epichlorohydrin), and poly(ethyl acrylate) used in this work

Cantilever-based Resonant Microsensors with Integrated Temperature Modulation for Transient Chemical Analysis

This work introduces a resonant cantilever platform with integrated temperature modulation for real-time chemical sensing. Embedded heaters allow for rapid thermal cycling of individual sensors, thereby enabling real-time transient signal analysis without the need for a microfluidic setup to switch between analyte and reference gases. Compared to traditional mass-sensitive microsensors operating in steady state, the on-chip generation of signal transients provides additional information for analyte discrimination

Transient Analysis of Analyte Desorption Due to Thermal Cycling with Varying Pulse Duration

This paper introduces heating pulse duration modulation on a chemically sensitive, polymer-coated resonant cantilever platform for analyte discrimination during the desorption phase. As in our previous work, the embedded heaters enable real-time measurements of analyte sorption into the polymer film, without the need for traditional valve systems and reference gases [1-2]. This work particularly looks at the effects of varying pulse lengths on the sensor responses, while holding the heating power constant. A model differential equation is developed for the sensor response based on both the device sensitivity and transient response. This model can then be used together with estimation theory for analyte identification and quantification, even in mixtures

Generalized Model of Resonant Polymer-Coated Microcantilevers in Viscous Liquid Media

Expressions describing the resonant frequency and quality factor of a dynamically driven, polymer-coated microcantilever in a viscous liquid medium have been obtained. These generalized formulas are used to describe the effects the operational medium and the viscoelastic coating have on the device sensitivity when used in liquid-phase chemical sensing applications. Shifts in the resonant frequency are normally assumed proportional to the mass of sorbed analyte in the sensing layer. However, the expression for the frequency shift derived in this work indicates that the frequency shift is also dependent on changes in the sensing layer’s loss and storage moduli, changes in the moment of inertia, and changes in the medium of operation’s viscosity and density. Not accounting for these factors will lead to incorrect analyte concentration predictions. The derived expressions are shown to reduce to well-known formulas found in the literature for the case of an uncoated cantilever in a viscous liquid medium and the case of a coated cantilever in air or in a vacuum. The theoretical results presented are then compared to available chemical sensor data in aqueous and viscous solutions

Online Drift Compensation for Chemical Sensors Using Estimation Theory

Sensor drift from slowly changing environmental conditions and other instabilities can greatly degrade a chemical sensor\u27s performance, resulting in poor identification and analyte quantification. In the present work, estimation theory (i.e., various forms of the Kalman filter) is used for online compensation of baseline drift in the response of chemical sensors. Two different cases, which depend on the knowledge of the characteristics of the sensor system, are studied. First, an unknown input is considered, which represents the practical case of analyte detection and quantification. Then, the more general case, in which the sensor parameters and the input are both unknown, is studied. The techniques are applied to simulated sensor data, for which the true baseline and response are known, and to actual liquid-phase SH-SAW sensor data measured during the detection of organophosphates. It is shown that the technique is capable of estimating the baseline signal and recovering the true sensor signal due only to the presence of the analyte. This is true even when the baseline drift changes rate or direction during the detection process or when the analyte is not completely flushed from the system

A Multi-Modal Continuous-Systems Model of a Novel High-Q Disk Resonator in a Viscous Liquid

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ATR-FTIR Spectroscopic Analysis of Sorption of Aqueous Analytes into Polymer Coatings Used with Guided SH-SAW Sensors

Attenuated total internal reflectance Fourier transform infrared (ATR-FTIR) spectroscopy was used for the investigation of sorption of aqueous solutions of analytes into polymer coatings. A series of simple model polymers, such as poly(dimethylsiloxane), poly(epichlorhydrin), and poly(isobutylene), and films and analytes, such as aqueous solutions of ethylbenzene, xylenes, toluene, and nitrobenzene, were used to evaluate the use of ATR-FTIR spectroscopy as a screening tool for sensor development. The ratios of integrated infrared absorption bands provided a simple and efficient method for predicting trends in partition coefficients. Responses of polymer-coated guided shear horizontal surface acoustic wave (SH-SAW) sensor platforms to the series of analytes, using polymer coatings with similar viscoelastic properties, were consistent with ATR-FTIR predictions. Guided SH-SAW sensor responses were linear in all cases with respect to analyte concentration in the tested range. Comparison of ATR-FTIR data with guided SH-SAW sensor data identifies cases where mass loading is not the dominant contribution to the response of the acoustic wave sensor. ATR-FTIR spectra of nitrobenzene, coupled with computational chemistry, provided additional insight into analyte/polymer interactions