Effect of surface charge state on the surface stress of a microcantilever

The surface charge state at a liquid-solid interface is important to the variations in the physical/chemical properties of adsorbate film such as surface stress and the ensuing tip deflection of the microcantilever. The well-known Stoney's equation, derived more than 100 years ago, conceals the film electrical properties with the replacement of substrate deformation induced by adsorptions of particles. This implicit expression provides a shortcut to circumvent the difficulty in identifying some film properties, however, it limits the capacity to ascertain the relation between surface stress variation and the surface charge state. In this paper, we present an analytical expression to quantify the cantilever deflection/surface stress and the film potential difference by combining the piezoelectric theory and Poisson-Boltzmann equation for electrolyte solution. This updated version indicates that the two linear correlations between surface stress and surface charge density or the bias voltage are not contradictory, but two aspects of one thing under different conditions. Based on Parsegian's mesoscopic interaction potential, a multiscale prediction for the piezoelectric coefficient of double-stranded DNA (dsDNA) film is done, and the results show that the distinctive size effect with variations in salt concentration and nucleotide number provides us with an opportunity to obtain a more sensitive potential-actuated microcantilever sensor by careful control of packing conditions.