The size of an ion affects everything from the structure of water to life itself. In this report, to gauge their size, ions dissolved in water are forced electrically through a sub-nanometer- diameter pore spanning a thin membrane and the current is measured. The measurements reveal an ion-selective conductance that vanishes in pores <0.24 nm in diameter—the size of a water molecule—indicating that permeating ions have a grossly distorted hydration shell. Analysis of the current noise power spectral density exposes a threshold, below which the noise is independent of current, and beyond which it increases quadratically. This depen- dence proves that the spectral density, which is uncorrelated below threshold, becomes correlated above it. The onset of correlations for Li+, Mg2+, Na+ and K+-ions extrapolates to pore diameters of 0.13 ± 0.11nm, 0.16 ± 0.11nm, 0.22 ± 0.11nm and 0.25 ± 0.11nm, respectively—consonant with diameters at which the conductance vanishes and consistent with ions moving through the sub-nanopore with distorted hydration shells in a correlated way.
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