Theory and experiment for one-dimensional directed self-assembly of nanoparticles

A promising method of particle self-assembly using patterned surfaces is described. A set of long order of millimeters , nanoscale-width grooves is etched into a substrate, and an aqueous solution containing particles of 50or 80-nm diameter is deposited on the surface. Upon the evaporation of the solution, the particles are dragged into the grooves by the receding contact line. A partial differential equation, incorporating screening, is constructed to investigate the final distribution of particles in the grooves. A complete analysis of the stationary states for the density equation in one and two dimensions is performed. Additionally, the nonlinear evolution of the density is studied numerically and the results compare well with both the analytic results and the experiments. © 2005 American Institute of Physics. DOI: 10.1063/1.1999029