Clamped nano-beams as adsorption induced sensors: Linear and non-linear effects

This work analyzes the deflection of clamped nano-beam due to stochastic surface stresses, induced by adsorption/desorption of surrounding particles. Both linear and non-linear effects (mid-plane stretching) are considered. A mechanical model for 1D nano-beam is first introduced and includes the surface effects via their effective cross sectional residual force and moment. The model considers local non-stationary surface residual stresses, governed by Langmuir's interaction model. Local adsorption relations are described by non-deterministic model, from which the statistics of the surface residual stresses are extracted and their time-space correlations are calculated. A straightforward perturbation method is used to evaluate the non-linear effects. In each order of the approximated solution, the nano-beam deflections are governed by a stochastic differential operator with a non-deterministic load. Equations are solved analytically by the Functional Perturbation method (FPM) and validated by Monte-Carlo simulations. It is found that the non-deterministic nature of the nano-beam deflections can be used for in situ sensing applications, in cases of very fast or slow adsorption schemes, for which the microscopic sensors are not sufficient. Geometric non-linear effects can be used in order to achieve fine tuning of the sensitivity.