We have investigated both experimentally and theoretically the resonance frequency change of a piezoelectric unimorph cantilever due to the mass loaded at the tip of the cantilever. The piezoelectric cantilever was composed of a lead zirconate titanate (PZT) layer and a stainless steel layer. The dependence of the resonance frequency shift, Δf, with respect to a loaded mass, Δm, on the cantilever length, L, width, w, and the resonance modes was examined. For Δm much smaller than the effective mass of the cantilever, we showed that Δf/Δm increased with an increasing eigen value, νn2, and decreasing length, L, and decreasing width, w, as Δfn/Δm=−(νn2/4π)(1/L3w)(1/0.23612ρ̃)Ẽ/ρ̃, where Ẽ and ρ̃ are the effective Young’s modulus and effective density of the unimorph cantilever that depends on the thickness fraction, Young’s modulus and density of each of the individual layers. Thus, given the same Ẽ and ρ̃ by maintaining the same layer thickness fractions of the individual layers, Δf/Δm is increased by a factor of α−4 when a cantilever is reduced in size by a factor α in proportion in all dimensions. We also showed that the same scaling relationship can be applied to a strip mass loaded at the tip as well as uniformly distributed mass on the cantilever surface provided that the uniformly distributed mass does not form a continuous solid film rigidly bonded to the cantilever surface.

We have investigated piezoelectric lead zirconate titanate (PZT)-stainless steel cantilevers as real-time in-water cell detectors using yeast cells as a model system. Earlier studies have shown that mass changes of a cantilever can be detected by monitoring the resonance frequency shift. In this study, two PZT-stainless steel cantilevers with different sensitivities were used to detect the presence of yeast cells in a suspension. The stainless steel cantilever tip was coated with poly-L-lysine that attracted yeast cells from the suspension, and immobilized them on the cantilever surface. After immersing the poly-L-lysine coated tip in a yeast suspension, the flexural resonance frequency of the cantilever was monitored with time. The flexural resonance frequency decreased with time in agreement with the optical micrographs that showed increasing amount of adsorbed yeast cells with time. The resonance frequency shifts are further shown to be consistent with both the mass of immobilized cells on the poly-L-lysine coated stainless steel surface and that deduced from the optical micrographs. Furthermore, under the present experimental conditions where the cell diffusion distance is smaller than the linear dimension of the adsorption area, it is shown that the rate of resonance frequency shift is linear with the cell concentration and the rate of resonance frequency shift can be used to quantify the cell concentration.

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