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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.

Determining mechanical properties of single-stranded DNA film grafted on gold surface is critical for analysis and design of DNA-microcantilever biosensors. However, it remains an open issue to quantify the relations among the disordered packing patterns of DNA chains, the mechanical properties of DNA film and the resultant biodetection signals. In this paper, first, the bending experiment of microcantilever is carried out to provide the basic data for a refined multi-scale model of microcantilever deflection induced by ssDNA immobilization. In the model, the complicated interactions in DNA film (consisting of DNA, water molecules and salt ions) are simplified as effective interactions among coarse-grained soft cylinders, which can reveal the varieties of DNA structure in the circumstances of different lengths and salt concentrations; Ohshima's distribution of net charge density is employed to incorporate compositional variations of salt ions along the thickness direction into the Strey's mesoscopic empirical potential on molecular interactions in DNA solutions, and the related model parameters for ssDNA film on substrate are obtained from the curve fitting with our microcantilever bending experiment. Second, the effect of nanoscopic distribution of DNA chains on elastic modulus of ssDNA film is studied by a thought experiment of uniaxial compression, and the disordered patterns of DNA chains are generated by Monte Carlo method. Simulation results point out that nanoscale ssDNA film shows size effect, gradient and diversity in elastic modulus and can achieve maximum stiffness by preferring a disordered and energetically favorable packing pattern collectively induced by electrostatic force, hydration force and configurational entropy.