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.
We report a theoretical investigation of self-assembled nanostructures of polymer-grafted nanoparticles in a block copolymer and explore underlying physical mechanisms by employing the self-consistent field method. By varying the particle concentration or the chain length and density of the grafted polymer, one can not only create various ordered morphologies (e.g., lamellar or hexagonally packed patterns) but also control the positions of nanoparticles either at the copolymer interfaces or in the center of one-block domains. The nanostructural transitions we here report are mainly attributed to the competition between entropy and enthalpy.
