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

Abstract

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.Polymer-coated microcantilevers have been extensively investigated for use as chemical sensor platforms. [1][2][3][4] Microcantilevers have shown high sensitivities in chemical vapor detection. In particular, polymer-coated cantilevers are often utilized in the dynamic (resonant) mode for detection in gas.2,5-9 Several investigators have analyzed such devices by considering only the mass loading effect of the chemical analyte without consideration of the coating viscoelastic effects.3,4,10 Others have explicitly included the effects of the coating properties, 2 while assuming operation in a vacuum. In this work, the effects of both the medium and the coating will be taken into account.Application of microcantilevers to liquid-phase detection has mostly focused on static-mode detection because dynamically driven microcantilevers suffer from low frequency stability in viscous liquid media.11 The characteristics of uncoated dynamically driven microcantilevers have previously been investigated in viscous liquid media accounting for the properties of the liquid media, including density and viscosity.12 Recently, work has been done on characterizing the behavior of polymer-coated microcantilevers in a vacuum, which indicated significant chemically induced coating plasticization effects.1 However, the effects of the polymer coating in a viscous liquid environment have not been studied, which includes plasticization and the properties of the viscous liquid. The present derivation extends previous work on uncoated and coated microcantilevers to obtain generalized formulas for the characteristics NOT THE PUBLISHED VERSION; this is the author's final, peer-reviewed manuscript. The published version may be accessed by following the link in the citation at the bottom of the page.Analytical Chemistry, Vol 80, No. 15 (August 1, 2008): pg. 5760-5767...

Timoshenko Beam Model for Lateral Vibration of Liquid-Phase Microcantilever-Based Sensors

“…These studies were motivated by the goal of reducing the detrimental effects of fluid damping and fluid inertia, thus providing higher resonant frequencies, fres, and quality factors, Q, the latter corresponding to sharper resonance peaks. Such improvements in the resonant characteristics of the device translate into corresponding enhancements in sensor sensitivity and limit of detection, especially for liquid-phase detection [6,10]. Some of the previously mentioned studies on the use of the inplane flexural mode demonstrated both theoretically [3,4,8] and experimentally [5,7] that the improvements in the in-liquid resonant characteristics will be most pronounced in microcantilevers that are relatively short and wide.…”

Liquid-Phase Chemical Sensing Using Lateral Mode Resonant Cantilevers

“…The simulation does not account for changes in resonator stiffness due to the analyte absorption; while this is a reasonable assumption for the case of thin polymeric films on top of silicon resonators as studied herein, stiffness effects may substantially change the characteristics of a mass-sensitive sensor for other conditions. 21 If the analyte concentration cA is given in parts per million (v/v), the analyte sensitivity SA may be calculated as accessed by following the link in the citation at the bottom of the page.…”

Lateral-Mode Vibration of Microcantilever-Based Sensors in Viscous Fluids Using Timoshenko Beam Theory

“…The total displacement at the tip is the relevant response quantity for sensor applications that utilize optical (laser) monitoring of the tip position, while the tip's bending-deformation displacement at or near resonance will be approximately proportional to the beam's bending strain, i.e., it will correspond to the output signal of sensors that employ local piezoresistive elements for monitoring beam response (e.g., the piezoresistive Wheatstone bridge employed in [19] [20,[29][30][31]). …”

“…All of these studies were primarily motivated by the desire to reduce the detrimental effects of fluid damping and fluid inertia, thus providing higher resonant frequencies, fres , and quality factors, Q , the latter corresponding to sharper resonant peaks. Within the context of sensing applications, such improvements in the resonant characteristics correspond to enhancements in sensor performance metrics such as mass or chemical sensitivity and limit of detection, especially for liquid-phase detection (e.g., [20,[29][30][31]). …”