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We have produced single, synthetic nanometer-diameter pores by using a tightly focused, high-energy electron beam to sputter atoms in 10-nm-thick silicon nitride membranes. Subsequently, we measured the ionic conductance as a function of time, bath concentration, and pore diameter to infer the conductivity and ionic mobility through the pores. The pore conductivity is found to be much larger than the bulk conductivity for dilute bath concentrations, where the Debye length is larger than the pore radius, whereas it is comparable with or less than the bulk for high bath concentrations. We interpret these observations by using multiscale simulations of the ion transport through the pores. Molecular dynamics is used to estimate the ion mobility, and ion transport in the pore is described by the coupled Poisson-Nernst-Planck and the Stokes equations that are solved self-consistently for the ion concentration and velocity and electrical potential. We find that the measurements are consistent with the presence of fixed negative charge in the pore wall and a reduction of the ion mobility because of the fixed charge and the ion proximity to the pore wall.
Ho et al. (Thu,) studied this question.