A continuum theory of surface piezoelectricity for nanodielectrics

Abstract

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 deformation-dependent 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.