Directed self-assembly of colloidal model systems on charge-selective surfaces in external electric fields: theory and numerical analysis.

Membrane electrophoretic deposition has a long-established reputation in delivering high quality nanoparticle compact and coating solutions in the field of high performance nanoparticle architectures made from aqueous nanoparticle suspensions. Although for a long time, it has been common practice in nanoparticle science and particle-based nanotechnology to use membrane electrophoretic shaping of nanoparticles, little is known about long-range electrohydrodynamic manipulation of the engineered assembly of colloidal particles at the nanoscale. Here, we analyze the interfacial field-induced flow of a strong electrolyte and its implications for the directed self-assembly of colloidal nanoparticles on nonuniform charge-selective ion-exchange membrane surfaces as well as on conducting microelectrodes imposed to electrophoretic deposition boundary conditions. Numerical calculations of the vortex streamlines are derived for the case of extreme diffusion limitation, concentration polarization near the limiting current, and induced electric forces acting upon the residual space charge. The system is modeled by coupled mass balances, Ohmic law, Navier-Stokes, and Nernst-Planck equations. Particularly, numerical calculations under bulk electroconvection conditions show that the latter provides an efficient intrinsic interfacial mechanism capable of accounting for the experimentally observed local electrophoretic deposition behavior of nanoparticles at ideal permselective membranes with nonplanar periodic charge discontinuity and metal microelectrodes.