In this paper, a phenomenological continuum theory of surface piezoelectricity accounting for the linear superficial interplay between electricity and elasticity is formulated primarily for elastic dielectric materials. This theory is inspired by the physical idea that once completely relaxed, an insulating free dielectric surface will sustain a nontrivial spontaneous surface polarization in the normal direction together with a tangential self-equilibrated residual surface stress field. Under external loadings, the surface Helmholtz free energy density is identified as the characteristic function of such surfaces, with the in-plane strain tensor of surface and the surface free charge density as the independent state variables. New boundary conditions governing the surface piezoelectricity are derived through the variational method. The resulting concepts of charge-dependent surface stress and deformationdependent surface electric field reflect the linear electromechanical coupling behavior of nanodielectric surfaces. As an illustrative example, an infinite radially polarizable piezoelectric nanotube with both inner and outer surfaces grounded is investigated. The novel phenomenon of possible surface-induced polarity inversion is predicted for thin enough nanotubes.surface effects, piezoelectricity, nanodielectrics, surface stress, spontaneous surface polarization PACS: 62.25.+g, 68.35.Md, 77.22.Ej

This paper studies the surface instability of an elastic thin solid film lying on a rigid substrate and subjected to van der Waals-like surface interactions. The effect of film–substrate interfacial slippage is accounted for by using a simplified linear cohesive interface model. It is found that the interfacial slippage generally plays a destabilizing role in the surface instability of the thin film. For highly compressible films with Poisson's ratio smaller than 0.25, the surface wrinkling behaviour previously inconceivable in the case of a perfectly bonded interface is now feasible if film–substrate interface slipping is permitted. In addition, our linear perturbation analysis shows that the critical conditions for the onset of surface instability can be modulated by adjusting the slippery stiffness of the interface. The result might be helpful for developing novel techniques to create micro-/nanosized surface patterns.

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Physisorption may cause a dimple on a deformable solid surface due to adsorbate-substrate interaction. The interactive force between the adsorbate and the crystal atoms depends on their distances, which may change with substrate deformation. This feature of displacement-dependence indicates that the equilibrium problem is a force-deformation coupled nonlinear procedure. In the present study, a continuum mechanics model, in which the force is considered as a function of the displacement field of the medium, is presented to calculate the physisorption-induced deformation in a semi-infinite elastic medium. It is found that the nonlinear effect due to force-deformation coupling should be taken in consideration in the adsorbate-substrate interaction analysis.