Michael J. Wenzel

Sorption-induced Static Bending of Microcantilevers Coated with Viscoelastic Material

Absorption of a chemical analyte into a polymer coating results in an expansion governed by the concentration and type of analyte that has diffused into the bulk of the coating. When the coating is attached to a microcantilever, this expansion results in bending of the device. Assuming that absorption (i.e., diffusion across the surface barrier into the bulk of the coating) is Fickian, with a rate of absorption that is proportional to the difference between the absorbed concentration and the equilibrium concentration, and the coating is elastic, the bending response of the coated device should exhibit a first-order behavior. However, for polymer coatings, complex behaviors exhibiting an overshoot that slowly decays to the steady-state value have been observed. A theoretical model of absorption-induced static bending of a microcantilever coated with a viscoelastic material is presented, starting from the general stress/strain relationship for a viscoelastic material. The model accounts for viscoelastic str...

Online Drift Compensation for Chemical Sensors Using Estimation Theory

Sensor drift from slowly changing environmental conditions and other instabilities can greatly degrade a chemical sensors 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.

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 layers loss and storage moduli, changes in the moment of inertia, and changes in the medium of operations 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.

Near Real-Time Monitoring of Organophosphate Pesticides in the Aqueous-Phase Using SH-SAW Sensors Including Estimation-Based Signal Analysis

The sensor response times for the absorption of organophosphate pesticides (phosmet and parathion) from aqueous solution into partially selective coatings [poly(epichlorohydrin) (PECH) and polyurethane (PU)], are investigated using guided shear horizontal surface acoustic wave (SH-SAW) devices on LiTaO3 as the sensing platform. A study of the response time (absorption time constant) reveals that it is possible to decrease the sensor response time by increasing temperature and/or decreasing film thickness. However, these approaches reduced device sensitivity. A second approach involving nonlinear estimation-based sensor signal analysis is also investigated in an attempt to decrease the time required for identification and quantification without decreasing sensitivity. Specifically, the extended Kalman filter is employed for online analysis of the sensor data during the detection process. To achieve this, the sensor response was first represented by a state-space model which includes all relevant contributions to the polymer-coated device response. This allows for the steady-state sensor response and absorption time constant to be extracted online well before the steady-state is reached, thus reducing the time required for quantification. Extracting the absorption time, which is often unique to a class of analyte-coating pairs, will make it possible to improve analyte recognition in sensor array design.

An analytical model for transient deformation of viscoelastically coated beams: Applications to static-mode microcantilever chemical sensors

The problem governing the transient deformation of an elastic cantilever beam with viscoelastic coating, subjected to a time-dependent coating eigenstrain, is mathematically formulated. An analytical solution for an exponential eigenstrain history, exact within the context of beam theory, is obtained in terms of the coating and base layer thicknesses, the elastic modulus of the base material, the initial coating modulus, the coating relaxation percentage (0%–100%), and the time constants of the coating’s relaxation process and its eigenstrain history. Approximate formulas, valid for thin coatings, are derived as special cases to provide insight into system behavior. Main results include (1) the time histories of the beam curvature and the coating stresses, (2) a criterion governing the response type (monotonic or “overshoot” response), and (3) simple expressions for the overshoot ratio, defined as the peak response scaled by the steady-state response, and the time at which the peak response occurs. Applic...

Liquid-Phase Detection of Organophosphate Pesticides Using Guided SH-SAW Sensor

It has been established that a polymer-coated SH-SAW sensor on 36deg rotated Y-cut LiTaO3 is a very sensitive platform for direct liquid-phase chemical sensing. In this work, two partially selective coatings, poly(epichlorohydrin) and polyurethane are investigated for the detection of organophosphate pesticides (phosmet and parathion) in aqueous solutions. Moreover, in order to meet the need for sensitive and selective chemical detection systems, novel signal processing techniques are employed in the detection process. First, the sensor response is modeled in terms of all relevant contributions (mass loading and viscoelasticity) using a state-space approach. Transient information, often unique to a given analyte/coating pair, is then extracted using nonlinear estimation theory and used to distinguish between chemical species, explain observed sensor responses, and decrease detection time. A detection limit in the ppb range can be achieved from the current experimental measurements.

Design of a portable guided SH-SAW chemical sensor system for liquid environments

Following successful application in gas sensing, acoustic wave liquid sensors attracted considerable attention due to the need for real-time, rapid and direct detection where the device is in direct contact with the solution. More importantly, there is a need for field measurement capability with portable devices. Challenges include a physical layout of the RF circuitry to minimize parasitic and spurious noise, continuous and realtime measurements capability, and obtaining vector network analyzer (VNA) performance in a portable RF unit, especially since the sensor signal noise dictates the limit of detection (LOD). Polymer-guided shear horizontal surface acoustic wave (SH-SAW) sensor platforms operating around 105 MHz on 36deg rotated Y-cut LiTaO 3 are investigated as portable detectors in liquid environments. The described system is self-contained including RF signal source, sensor input/output signal conditioning, and sensor signal amplitude and phase measuring capabilities. Amplitude and phase signals from the sensor are differentially compared with concomitant signals available directly from the RF signal source. The two primary outputs from the system are voltages related to the detected amplitude and phase changes that are caused by the sensors response to analyte sorption by the coated device. Several devices, coated with chemically sensitive polymers, are investigated in the detection of low concentrations (10-60 ppm) of ethylbenzene and xylenes in water using the RF portable unit. The units were tested for both reproducibility and repeatability, and the results matched very well with VNA measurements

Rapid Detection of Analytes with Improved Selectivity Using Coated Microcantilever Chemical Sensors and Estimation Theory

Rapid detection of analytes with improved selectivity is achieved though the use of estimation theory to analyze the response of polymer-coated microcantilever chemical sensors. In general, chemical sensors exhibit partial selectivity and can have relatively long response times. Using estimation theory, it is possible to make short-term response predictions from past data. This makes it possible to use the transient information (response time), often unique to an analyte/coating pair, to achieve an improvement in analyte species recognition while simultaneously allowing for a reduction in the time required for identification and quantification. An extended Kalman filter is used as a recursive online approach to refine the estimate of the sensors future response. Both identification and quantification are thus possible as soon as the filter estimate achieves a high confidence level. Also, with improved selectivity, identification is possible using fewer sensors in an array.

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.

Generalized Characteristics 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 coating has on the device sensitivity when used in liquid-phase chemical sensing applications. The derived expressions are shown to reduce to well-known formulas for the case of an uncoated cantilever in an invisicid medium and the case of a coated cantilever in air. The theoretical results are compared to existing chemical sensor data in aqueous and viscous solutions.