Direct Measurements of the Size and Correlations between Single Ions Impelled through a Sub-Nanometer-Diameter Pore

Abstract

The size and charge of an ion affects everything from the structure of water to life itself. To gauge their size, metal alkali and alkali earth ions, and protons dissolved in water were forced through a sub-nanometer-diameter pore spanning an ultra-thin silicon nitride membrane and the current was measured. Except for protons, the measurements revealed a conductance selective to positive ions that vanished when extrapolated to pores smaller than about 0.25 nm in diameter, which was comparable to the diameter of a water molecule (0.28 nm). On the other hand, the proton conductance persisted, extrapolating to zero only when the pore diameter was about 0.15 nm. Furthermore, an analysis of the low frequency (pink) noise power spectral density exposed a threshold, below which the noise was independent of the current, and beyond which it increased quadratically. This dependence on current proved that the spectral density components of the noise, which were uncorrelated below threshold, became nearly perfectly correlated above it. Coincidently, the onset of correlations in the noise current for Li+, Mg2+, Na+and K+ ions extrapolates to pore diameters of 0.12 ± 0.11 nm, 0.12 ± 0.11 nm, 0.21 ± 0.11 nm and 0.23 ± 0.11 nm, respectively. Altogether, these data were consistent with the correlated motion of (at least partially) unscreened metal ions with a grossly distorted hydration shell permeating the smallest pores at high current.