Document Type

Article

Language

eng

Publication Date

2009

Publisher

American Institute of Physics

Source Publication

Journal of Applied Physics

Source ISSN

0021-8979

Original Item ID

doi: 10.1063/1.3086626

Abstract

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 viscoelastic creep 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 metal coatings. The theoretical results presented here can also be used to extract time-domain viscoelastic properties of the polymer material from beam response data.

Comments

Published version. Journal of Applied Physics, Vol. 105, No. 6 (2009). DOI. © 2009 American Institute of Physics. Used with permission.

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