Finite-Element Simulation and Verification of Nanoparticle Translocation Through Biogenic Diatom Shells

Biogenic nanoporous shells derived from marine diatoms Coscinodiscus wailesii were used for nanoparticle translocation experiments, and the observed ionic current was compared with results of analytical calculation and finite-element simulation. The lateral size (250 μm) of the shells enabled positioning and immobilization on micromachined silicon substrates. Since these shells have a hierarchical structure with the smallest aperture diameter of 40 nm and length of 50 nm as obtained from scanning electron microscopy, the ionic current reduction of 28.69 ± 4.12 pA could be measured during the translocation of 27-nm diameter polystyrene spheres. Note, this average current of 10 events, measured for 120 s, was comparable with the results of: 1) finite-element simulation as a function of the position of the polystyrene sphere using a simplified geometry of the smallest aperture and 2) analytical calculation from the Coulter Counter theory. The current reduction obtained from the simulation and theory was 28.36 and 29.95 pA, respectively. In addition, a mobility of 1.11 × 10^-8 m² s^-1 V^-1 for the 27-nm polystyrene spheres was used to convert the simulated current from spatial dependence to time dependence in order to match the average experimental translocation time of 155 μs.