On the other hand, inter-adsorbate interactions between charged adsorbates are usually repulsive, as described by electrostatic forces, and will induce compressive surface stresses on the surface layers of nanomechanical sensors. The strong adsorbate-substrate interactions occur because of chemical bond formation or chemical reaction. This interaction often leads to surface charge redistribution. A substrate gaining electrons from the adsorbates often results in tensile surface stresses, while transferring charges to the adsorbates often gives rise to compressive surface stresses. The overall adsorption-induced surface stresses are the net effect of the aforementioned mechanisms.Quantitative analysis of the displacement and stress fields of a nanomechanical sensor due to the adsorption-induced surface stress remains a theoretical challenge [9].

The complexity of the competing mechanisms requires detailed molecular modeling. On the other hand, device-level calculations of the displacement and stress fields are beyond the reach of molecular modeling, but can be satisfactorily described by continuum mechanics. For example, analytical formulas for the displacement of the cantilever subjected to surface stress have been derived [12�C14]. It thus naturally calls for multiscale modeling to couple the molecular model with the continuum description. Dareing and Thundat developed a semi-analytical model for calculating adsorption-induced surface stresses based on atomic interactions [15]. To simplify the derivation, the model was restricted to the case of a single atomic layer adsorption with a simple Lennard-Jones potential.

Chen et al. [16�C18] derived a multiscale method to couple a continuum description with first-principles density functional theory (DFT) calculations. This method linked atomic contributions with kinematic constraints imposed by continuum mechanics and provided a pathway to study detailed physics of adsorption-induced surface stresses. However, one drawback of this multiscale method is that the deformation field of the devices needs to be known a priori. The aim of this paper is to generalize the method by removing the kinematic constraints imposed on the device deformation field.In this study, we propose a multiscale simulation framework for nanomechanical cantilever sensors based on DFT calculations Dacomitinib and finite element method (FEM) analysis.

DFT calculations are used to compute the induced surface stress of molecular adsorption on the molecular recognition layer. The calculated surface stresses are then used in the FEM analysis to resolve the deformation and stress fields of the nanomechanical sensors. A gold-coated cantilever sensor exposed to alkanethiolate self-assembled monolayers (SAM) is used to demonstrate the applicability of the proposed multiscale framework.2.