We present a complete theoretical study of the relationship between the structure (tip shape and dimensions) and function (selectivity and rectification) of asymmetric nanopores on the basis of previous experimental studies. The theoretical model uses a continuum approach based on the Nernst-Planck equations. According to our results, the nanopore transport properties, such as current-voltage (I-V) characteristics, conductance, rectification ratio, and selectivity, are dictated mainly by the shape of the pore tip (we have distinguished bullet-like, conical, trumpet-like, and hybrid shapes) and the concentration of pore surface charges. As a consequence, the nanopore performance in practical applications will depend not only on the base and tip openings but also on the pore shape. In particular, we show that the pore opening dimensions estimated from the pore conductance can be very different, depending on the pore shape assumed. The results obtained can also be of practical relevance for the design of nanopores, nanopipettes, and nanoelectrodes, where the electrical interactions between the charges attached to the nanostructure and the mobile charges confined in the reduced volume of the inside solution dictate the device performance in practical applications. Because single tracks are the elementary building blocks for nanoporous membranes, the understanding and control of their individual properties should also be crucial in protein separation, water desalination, and bio-molecule detection using arrays of identical nanopores.

Single- and multiple-nanopore membranes are both highly interesting for biosensing and separation processes, as well as their ability to mimic biological membranes. The density of pores, their shape, and their surface chemistry are the key factors that determine membrane transport and separation capabilities. Here, we report silicon nitride (SiN) membranes with fully controlled porosity, pore geometry, and pore surface chemistry. An ultrathin freestanding SiN platform is described with conical or double-conical nanopores of diameters as small as several nanometers, prepared by the track-etching technique. This technique allows the membrane porosity to be tuned from one to billions of pores per square centimeter. We demonstrate the separation capabilities of these membranes by discrimination of dye and protein molecules based on their charge and size. This separation process is based on an electrostatic mechanism and operates in physiological electrolyte conditions. As we have also shown, the separation capabilities can be tuned by chemically modifying the pore walls. Compared with typical membranes with cylindrical pores, the conical and double-conical pores reported here allow for higher fluxes, a critical advantage in separation applications. In addition, the conical pore shape results in a shorter effective length, which gives advantages for single biomolecule detection applications such as nanopore-based DNA analysis.