This report presents a fundamental study of nanoparticle transport phenomena in conical-shaped pores contained within glass membranes. The electrophoretic translocation of charged polystyrene (PS) nanoparticles (80- and 160-nm-radius) was investigated using the Coulter counter principle (or "resistive-pulse" method) in which the time-dependent nanopore current is recorded as the nanoparticle is driven across the membrane. Particle translocation through the conical-shaped nanopore results in a direction-dependent and asymmetric triangular-shaped resistive pulse. Because the sensing zone of conical-shaped nanopores is localized at the orifice, the translocation of nanoparticles through this zone is very rapid, resulting in pulse widths of ~200 μs for the nanopores used in this study. A linear dependence between translocation rate and nanoparticle concentration was observed from 10(7) to 10(11) particles/mL for both 80- and 160-nm-radius particles, and the magnitude of the resistive pulse scaled approximately in proportion to the particle volume. A finite-element simulation based on continuum theory to compute ion fluxes was combined with a dynamic electric force-based nanoparticle trajectory calculation to compute the position- and time-dependent nanoparticle velocity as the nanoparticle translocates through the conical-shaped nanopore. The computational results were used to compute the resistive pulse current-time response for conical-shaped pores, allowing comparison between experimental and simulated pulse heights and translocation times. The simulation and experimental results indicate that nanoparticle size can be differentiated based on pulse height, and to a lesser extent based on translocation time.

This paper describes a fundamental study of the effect of electrostatic interactions on the resistive pulse waveshape associated with translocation of charged nanoparticles through a conical-shaped, charged glass nanopore. In contrast to single-peak resistive pulses normally associated with resistive-pulse methods, biphasic pulses, in which the normal current decrease is preceded by a current increase, were observed in the current–time recordings when a high negative potential (lower than −0.4 V) is applied between the pore interior and the external solution. The biphasic pulse is a consequence of the offsetting effects of an increased ion conductivity induced by the surface charge of the translocating particle and the current decrease due to the volume exclusion of electrolyte solution by the particle. Finite-element simulations based on the coupled Poisson–Nernst–Planck equations and a particle trajectory calculation successfully capture the evolution of the waveshape from a single resistive pulse to a biphasic response as the applied voltage is varied. The simulation results demonstrate that the surface charges of the nanopore and the particle are responsible for the voltage-dependent shape evolution. Additionally, the use of high ionic strength solution or high pressures to drive particle translocation was found to eliminate the biphasic response. The former is due to the screening of the electrical double layer, while the latter results from the solution flow preventing formation of an equilibrium double layer ion distribution within the nanopore, similar to the previously reported elimination of ion current rectification when solution flows through a nanopore.

Ion current rectification that occurs in conical-shaped glass nanopores in low ionic strength solutions is shown to be dependent on the rate of pressure-driven electrolyte flow through the nanopore, decreasing with increasing flow rate. The dependence of the i-V response on pressure is due to the disruption of cation and anion distributions at equilibrium within the nanopore. Because the flow rate is proportional to the third power of the nanopore orifice radius, the pressure-driven flow can eliminate rectification in nanopores with radii of ∼200 nm but has a negligible influence on rectification in a smaller nanopore with a radius of ∼30 nm. The experimental results are in qualitative agreement with predictions based on finite-element simulations used to solve simultaneously the Nernst-Planck, Poisson, and Navier-Stokes equations for ion fluxes in a moving electrolyte within a conical nanopore.

The development of nanopore fabrication methods during the past decade has led to the resurgence of resistive-pulse analysis of nanoparticles. The newly developed resistive-pulse methods enable researchers to simultaneously study properties of a single nanoparticle and statistics of a large ensemble of nanoparticles. This review covers the basic theory and recent advances in applying resistive-pulse analysis and extends to more complex transport motion (e.g., stochastic thermal motion of a single nanoparticle) and unusual electrical responses (e.g., resistive-pulse response sensitive to surface charge), followed by a brief summary of numerical simulations performed in this field. We emphasize the forces within a nanopore governing translocation of low-aspect-ratio, nondeformable particles but conclude by also considering soft materials such as liposomes and microgels.

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