Analysis on the Propagation and Assembly of Metallic Nanoparticles through Subwavelength Apertures with Overlapping Electrical Double Layers

Hybrid nanoplasmonic structures composed of subwavelength apertures in metallic films and nanoparticles have recently been demonstrated as ultrasensitive plasmonic sensors. This work investigates the electrokinetically driven propagation of the assembly mechanism of the metallic nanoparticles through nanoapertures. The Debye-Hückel approximation for a symmetric electrolyte solution with overlapping electrical double layers (EDLs) is used to obtain an analytical solution to the problem. The long-term silver nanoparticle concentration response is derived using the homogenization method and a multiscale analysis. The results indicate that uncharged nanoparticles will flow through the nanohole array if the nanochannel height is larger than the Debye length (<i>h</i> ₀ > λ_D), while a trapping mechanism occurs, due to the overlapping of the EDL, when <i>h</i> ₀ ∼ 3.8λ_D. For charged nanoparticles, the response to the electric field occurs locally with the walls of the nanochannel, regardless of its height. For a critical value of the nanochannel length, the leading order of the concentration field becomes purely diffusive.