The characteristics of microcantilevers vibrating laterally in viscous liquid media are investigated and compared to those of similar microcantilevers vibrating in the out-of-plane direction. The hydrodynamic loading on the vibrating beam is first determined using a numerical model. A semi-analytical expression for the hydrodynamic forces in terms of the Reynolds number and the aspect ratio (beam thickness over beam width) is obtained by introducing a correction factor to Stokes' solution for a vibrating plate of infinite area to account for the effects of the thickness. The results enable the effects of fluid damping and effective fluid mass on the resonant frequency and the quality factor (Q) to be investigated as a function of both the beam's geometry and liquid medium's properties and compared to experimentally determined values given in the literature. The resonant frequency and Q are found to be higher for laterally vibrating microcantilevers compared to those of similar geometry experiencing transverse (out-of-plane) vibration. Compared to transversely vibrating beams, the resonant frequency of laterally vibrating beams is shown to decrease at a slower rate (with respect to changes in viscosity) in media having higher viscosities than water. The theoretical results are compared to experimental data obtained for cantilevers completely immersed in solutions of varying aqueous percent glycerol. The increases in resonant frequency and Q are expected to yield much lower limits of detection in liquid-phase chemical sensing applications.

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...

The characteristics of microcantilevers vibrating in the in-plane flexural mode (also known as lateral vibration) in viscous liquid media are investigated. A numerical model was utilized to determine a correction to Stokes' solution for an infinite plate to obtain an analytical expression for the hydrodynamic forces acting on a laterally vibrating microcantilever as a function of both Reynolds number and aspect ratio (thickness over width). The results allowed for the resonant frequency and quality factor to be investigated as a function of both beam geometry and medium properties. Trends in these characteristics can be used to optimize device geometry and maximize the frequency stability. As the thickness of a microcantilever is increased, both its stiffness and the medium's viscous damping increase. This will lead to an optimum quality factor in terms of the thickness. The characteristics of laterally and transversely vibrating microcantilevers with similar geometries are also compared. It is found that the resonant frequency and quality factor are higher for laterally vibrating microcantilevers (at least by a factor of 2 to 3 or higher for the Q-factor depending on the geometry) compared to those of similar beams under transverse (or out-of-plane) vibration. The improvement in sensitivity (due to the increase in frequency) and in the quality factor (thus a reduced frequency noise) are expected to yield much lower limits of detection in liquid-phase chemical sensing applications.

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