We present a method to detect with high sensitivity the viscoelastic property changes of sensor coatings on microcantilever arrays due to radiation, analyte binding, or adsorption. The method uses higher order flexural eigenmodes to identify the location and magnitude of the nonuniform elasticity changes in the microcantilever coating. We demonstrate the method by monitoring the time evolution of resonance frequencies and Q factors of different flexural eigenmodes of microcantilevers functionalized with a small drop of a photosensitive polymer as it is exposed to ultraviolet radiation. The method is particularly well suited for measuring quantitatively the time varying viscoelastic properties of thin films or biological materials attached to microcantilevers.

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7.
The ith eigenmode of a uniform microcantilever has been scaled such that 0Lψi,xx2dx=1.
8.

Experiments showed that applying the coating to the microcantilever caused the first three resonant frequencies to drop by 38%, 32%, and 23%, respectively. Thus, the added mass effect was the dominant effect observed, as is fairly common in practice where the coatings are very thin or in liquid state as in the experiments described.

9.

The total quality factor includes the effects of air and material damping in the microcantilever, which are assumed constant over the entire experiment in this case. The experimentally measured Q̃i, values were 55, 13, and 18 for the first, second, and third eigenmodes, respectively.

10.

CSC 12 tipless silicon (E=112.4GPa, ρ=2329kgm3) microcantilevers from μMasch, Inc. Microcantilever E (341μm long, 35μm wide, and 1μm thick) was used in these experiments.

11.

The α̂, value corresponds to the manufacturer’s specified dynamic viscosity of 0.3Pas, and the value of α̃, was chosen based on experimental data and corresponds to a dynamic viscosity of 7080Pas.

12.
Norland Optical Adhesive
(NOA) 61, Norland Products, Inc., Cranbury, NJ. The elastic modulus of the polymer after complete curing is given as 1.03GPa.
13.

The coated section was modeled as a composite beam with a constant cross section over the entire coated portion.

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