Surface stress induced by interactions of adsorbates and its effect on deformation and frequency of microcantilever sensors

Surface stress is widely used to characterize the adsorption effect on the mechanical response of nanomaterials and nanodevices. However, quantitative relations between continuum-level descriptions of surface stress and molecular-level descriptions of adsorbate interactions are not well established. In this paper, we first obtain the relations between the adsorption-induced surface stress and the van der Waals and Coulomb interactions in terms of the physical and chemical interactions between adsorbates and solid surfaces. Then, we present a theoretical framework to predict the deflection and resonance frequencies of microcantilevers with the simultaneous effects of the eigenstrain, surface stress and adsorption mass. Finally, the adsorption-induced deflection and resonance frequency shift of microcantilevers are numerically analyzed for the van der Waals and Coulomb interactions. The present theoretical framework quantifies the mechanisms of the adsorption-induced surface stress, and thus provides guidelines to the analysis of the sensitivities, and the identification of the detected substance in the design and application of micro- and nanocantilever sensors.