The polarization of a nanoparticle surrounded by a thick electric double layer

The polarization of a charged, dielectric, nanoparticle enveloped by a thick electric double layer and subjected to a uniform, alternating electric field is studied theoretically with the standard model (the Poisson-Nernst-Planck PNP equations). The dipole coefficient (f) is calculated as a function of the electric field's frequency and the double layer's thickness (lambda(D)). For a weakly charged particle with a small zeta potential zeta, an approximate, analytic expression for the dipole moment coefficient, accurate within O(zeta(2)), is derived. Two processes contribute to the dipole moment: the ion transport in the electric double layer under the action of the electric field and the particle's electrophoretic motion. As the thickness of the electric double layer increases so does the importance of the latter. In contrast to the case of the thin electric double layer, the particle with the thick double layer exhibits only high-frequency dispersion. The theoretical predictions are compared and favorably agree with experimental data, leading one to conclude that the standard, PNP based-model adequately represents the behavior of nanoparticles subject to electric fields.