Abstract
Over the last decades, nanomechanical sensors have received significant attention from the scientific community, as they find plenty of applications in many different research fields, ranging from fundamental physics to clinical diagnosis. Regarding biological applications, nanomechanical sensors have been used for characterizing biological entities, for detecting their presence, and for characterizing the forces and motion associated with fundamental biological processes, among many others. Thanks to the continuous advancement of micro- and nano-fabrication techniques, nanomechanical sensors have rapidly evolved towards more sensitive devices. At the same time, researchers have extensively worked on the development of theoretical models that enable one to access more, and more precise, information about the biological entities and/or biological processes of interest. This paper reviews the main theoretical models applied in this field. We first focus on the static mode, and then continue on to the dynamic one. Then, we center the attention on the theoretical models used when nanomechanical sensors are applied in liquids, the natural environment of biology. Theory is essential to properly unravel the nanomechanical sensors signals, as well as to optimize their designs. It provides access to the basic principles that govern nanomechanical sensors applications, along with their intrinsic capabilities, sensitivities, and fundamental limits of detection.
Highlights
Advances in nanotechnology have led to the development of plenty of novel functional devices that are revolutionizing science and their applications at all levels
We have explored the main theories and models that are the base of nanomechanical sensors and that are used on a daily basis by researchers all over the world regarding this field
For the nanomechanical sensors in static mode, we have presented the main theories regarding the effect of differential surface stress on the bending of a rectangular cantilever plate, starting from the well-known Stoney’s equation, the improved solution proposed by Sader et al, and the simplified averaged curvatures expressions obtained by Tamayo et al The effect of surface stress can modify the dynamic properties of the sensor, allowing for quantifying the stress by measuring changes in the resonance frequencies of the nanomechanical resonator
Summary
Advances in nanotechnology have led to the development of plenty of novel functional devices that are revolutionizing science and their applications at all levels. Optomechanics provide access to mechanical modes that possess extraordinary properties, in terms of sensitivity and speed, even when immersed in the most dissipative fluids Since their origin, experimentalists and theorists have worked closely, aiming at the implementation of more sensitive, rapid, effective, robust, and integrable devices. In 2000, Ilic et al demonstrated the detection of Escherichia coli bacteria using an array of low-stress silicon nitride resonant cantilevers [60], where they used simple formulas to relate the change in frequency to the mass of the analyte This change was inversely proportional to the mass of the sensor and directly proportional to the mass of the analyte, and it was calculated for a homogeneous layer of material adsorbed on the cantilever surface. The theoretical models increase in complexity, in the same way as they evolve along the history
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