# A review of steric interactions of ions: Why some theories succeed and others fail to account for ion size

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## Abstract

As nanofluidic devices become smaller and their surface charges become larger, the steric interactions of ions in the electrical double layers at the device walls will become more important. The ions’ size prevents them from overlapping, and the resulting correlations between the ions can produce oscillations in the density profiles. Because device properties are determined by the structure of these double layers, it is more important than ever that theories correctly include steric interactions between ions. This review analyzes what features a theory must have in order to accurately account for steric interactions. It also reviews several popular theories and compares them against Monte Carlo simulations to gauge their accuracy. Successful theories of steric interactions satisfy the contact density theorem of statistical mechanics and use locally averaged concentrations. Theories that do not satisfy these criteria, especially those that use local concentrations (instead of averaged concentrations) to limit local packing fraction, produce qualitatively incorrect double layer structure. For which ion sizes, ion concentrations, and surface charges monovalent ions steric effects are important is also analyzed.

## Keywords

Electrical double layer Steric interactions Excluded volume effects Theory## Notes

### Acknowledgments

I am grateful to Jan Eijkel for the discussion that inspired this review and to Martin Bazant for his critical readings of the manuscript. I am also grateful to Claudio Berti, Ali Mani, Aditya Khair, and Peter Kekenes-Huskey for their helpful suggestions for the manuscript. Lastly, I would like to thank Roland Roth not only for his many improvements to the manuscript, but most importantly for introducing me to and teaching me about the contact density, the low-density limit, and the hard-rod model.

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