Polymer-Coated and Polymer-Based Microcantilever Chemical Sensors: Analysis and Sensor Signal Processing
Abstract
The responses of polymer-coated and/or polymer-based microcantilever chemical sensors are analyzed. Viscoelastic stress relaxation and creep that occur in polymeric materials are taken into account to derive differential equations that accurately model the polymer-coated and polymer-based microcantilever chemical sensors. The results show that, upon sorption, viscoelastic stress relaxation in the coating (or creep in the base layer) can lead to an overshoot (or creeping response) that has been observed in experimental microcantilever sensor data, but not predicted by elastic models such as Stoney's equation or Timoshenko's analysis. Additionally, the derived models indicate that viscoelastic behavior in the coating (or base layer) can greatly effect the response time of a microcantilever sensor. This phenomenon is not predicted by elastic models which indicate that the transient response, hence the response time, is governed only by the sorption kinetics. The response time of the polymer-coated and/or polymer-based microcantilever chemical sensor is found to depend on the ratio of the relaxation and sorption time constants and the percent relaxation that the polymer undergoes. By appropriate choice of the polymeric materials (coating or base layer), one can minimize the increase in response time caused by viscoelasticity. The response of a polymer-coated microcantilever, for example, can be faster or slower than absorption, depending on the material properties of the coating. On the other hand, a polymeric cantilever (e.g. SU-8) increases sensitivity more than ten fold, but creep may occur after analyte sorption has reached equilibrium, thereby increasing the response time of the device. In these cases, the transient response is such that creep (or stress relaxation) can be confused with continued sorption (or desorption), thus compromising sensor signal analysis.
The derived models are used in combination with nonlinear estimation theory to realize novel sensor signal/data processing techniques. Assuming the sorption kinetics are known (monitoring for a known analyte), the Extended Kalman Filter (EKF) is used to recursively estimate the steady-state response before the steady-state is achieved, thus significantly reducing the time required to quantify an analyte. If the sorption kinetics are unknown (analyte identification), a similar technique consisting of a bank of second-order Extended Kalman Filters (SOEKF) is used to perform online estimation of the sorption time constant and steady-state response. The sorption time constant, unique to a class of analyte/coating pairs, can be used to improve the identification potential of a sensor array. The SOEKFs are also used to recursively calculate the probability that a given analyte is causing the response using only the available measured sensor data. These online identification techniques exhibit a significantly lower identification error rate compared to using only steady-state information, and can identify the analyte in less than 5% of the time required for the response to reach its steady-state. Finally, a technique for online baseline drift correction using a bank of EKFs is demonstrated.