Fig. 2
From: Measurements of the size and correlations between ions using an electrolytic point contact
Electrolytic ion transport through sub-nanopores. a A juxtaposition of the current-voltage characteristics acquired from the same sub-nanopore with a 0.50 nm mean-diameter using different concentrations of NaCl electrolyte. The dotted lines reflect FESs. Inset: The conductance of a pore with a mean-diameter of 0.52 nm as a function of NaCl concentration, illustrating a minimum conductance for concentrations <100 mM. The dotted-line represents a match to the data assuming a surface charge of −0.19e nm-2. b Like a, but acquired from pores with 0.30 nm × 0.40 nm→)0.35 nm, (0.50 nm × 0.55 nm→)0.52 nm and (0.80 nm × 0.85 nm→)0.82 nm mean-diameters at the waist in 250 mM NaCl. Inset: Like b, but for a pore with a (0.95 nm × 1.00 nm→)0.97 nm mean-diameter. c The current–voltage characteristic of a sub-nanopore with a mean-diameter of (0.35 nm × 0.40 nm→)0.37 nm measured with 250 mM NaCl on both sides of the membrane (open circles), and then with a gradient across the membrane with only 1 mM NaCl on the trans-side (half-filled circles). The asymmetric conductance indicates that >97% of the current was carried by Na+. Inset: Like c, but for a pore with a mean-diameter of (0.75 nm × 0.85 nm→)0.80 nm. Here, 90% of the current was carried by Na+. d The dependences of the diffusivity extracted from FES on the mean-diameter of sub-nanopores for Na+ in 250 mM NaCl (open circles). The best-fit (black dotted) line extrapolates to zero diffusivity near a 0.22 nm-mean-diameter. For comparison, juxtaposed on the same plot is the diffusivity extracted from MD using model sub-nanopores with 0.30 nm and 0.50 nm diameters (gray circles). e Like a, but acquired from two sub-nanopores with (0.80 nm × 0.85 nm→) 0.82 nm (gray lasso) and 0.30 nm (black lasso) mean-diameters using different electrolytes at 500 mM. f The dependences of the conductance on the mean-diameter of sub-nanopores for four different electrolytes at 250 mM. The best-fit lines for the metal ions extrapolate to zero conductance at 0.21 ± 0.11 nm for Na+; 0.24 ± 0.11 nm for K+; 0.26 ± 0.11 nm for Li+ and 0.23 ± 0.11 nm for Mg2+, near to a 0.24 nm-diameter. For comparison, juxtaposed on the same plot are the conductances extracted from MD simulations performed using model sub-nanopores with 0.30 and 0.50 nm diameters in LiCl and NaCl. The error bars are typical of the standard deviation of the empirical data
