Analyte concentration at the tip of a nanopipette

Concentration of molecules within the tips of nanopipettes when applying a DC voltage is herein investigated using finite-element simulations. The ion concentrations and fluxes due to diffusion, electro-migration, and electro-osmotic flow, and the electric potential are determined by the simultaneous solution of the Nernst-Planck, Poisson, and Navier-Stokes equations within the water solution containing sodium and chloride ions and negatively charged molecules. The electric potential within the pipette glass wall is at the same time determined by the Poisson equation together with appropriate boundary conditions and accounts for a field effect through the wall. Fixed negative surface charge on both the internal and external glass surfaces of the nanopipette is included together with the field effect through the glass wall to account for the electric double layer and the electro-osmosis. The inclusion of the field effect through the pipette wall is new compared to previous modeling of similar structures and is shown to be crucial for the behavior at the tip. It is demonstrated that the concentration of molecules is a consequence of ionic charge accumulation at the tip screening the electric field, thereby slowing down the electrophoretic motion of the molecules, which is further slowed down or stopped by the oppositely directed electro-osmosis. It is also shown that the trapping is very sensitive to the properties of the molecule, that is, its electrophoretic mobility and diffusion coefficient, the properties of the pipette, the ionic strength of the solution, and the applied electric field.