Where, k is the initial spring constant, m* = 0.14 x (the mass of the cantilever), 5k is the change in the spring constant, 5m is the change in the mass, and f1 and f2 are the resonance frequencies before and after adsorption (Cherian and Thundat 2002). The parameters f1 and f2 are experimentally measured values; 5m is obtained from the surface excess values and the surface area of one side of the cantilever; and m* is calculated from the dimensions and the density of the cantilever.
In general, theoretical estimations based on commercially available microcantilevers (AC method) show a minimum detectable mass density of 0.67 ng/cm2. When the active area of the structure is taken into account, a minimum detectable mass of 10-15 g can be achieved (Martin et al. 1987). Furthermore, by using NEMS to reduce the dimensions of the mechanical transducer, it is possible to achieve a mass sensitivity of around 10-19 g. However, when a sensor is operated in a liquid with the aid of the resonance mode, the resonance peak and its quality factor, Q, both shift towards lower values because of damping (Butt et al. 1993). This damping considerably reduces the achievable resolution in terms of changes in the minimum detectable mass. To solve this problem, Mehta et al. and Tamayo et al. proposed methods that enhance the Q factor of oscillating cantilevers in liquids and, hence, the resolution.
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