A Mechano-Electro-Chemical Coupling Model for Bending Analysis of Single-Stranded DNA Microbeam Biosensors Due to Flexoelectricity

Abstract

Highly compliant structures such as microbeams can deform substantially in response to interactions between molecules adsorbed on their surface. To understand such systems and improve their detection signals, a mechano-electro-chemical coupling model for mechanical deformations of the microbeams immobilized single-stranded DNA (ssDNA) is established due to flexoelectricity. The governing equations and corresponding boundary conditions of ssDNA microbeams are derived by using the variational principle. The bending deformations of ssDNA microbeams (one for cantilever beam and another for simply supported beam) are derived. The electric potential in the regions inside and outside the ssDNA layer is obtained by linear Poisson–Boltzmann equation for different electrolyte solutions. The analytical expressions to quantify the beam deflection and the potential difference of ssDNA layer are presented. The theoretical predictions are compared with the experimental data to validate the applicability of the present model. Numerical results reveal that the solution types, thickness, and elastic modulus of substrate materials have an obvious influence on the deflections of ssDNA microbeams. Therefore, the present model can help to improve the reading of the bending deformation signal of the microbeam biosensors.