# The effect of hydration number on the interfacial transport of sodium ions

## Abstract

Ion hydration and transport at interfaces are relevant to a wide range of applied fields and natural processes1,2,3,4,5. Interfacial effects are particularly profound in confined geometries such as nanometre-sized channels6,7,8, where the mechanisms of ion transport in bulk solutions may not apply9,10. To correlate atomic structure with the transport properties of hydrated ions, both the interfacial inhomogeneity and the complex competing interactions among ions, water and surfaces require detailed molecular-level characterization. Here we constructed individual sodium ion (Na+) hydrates on a NaCl(001) surface by progressively attaching single water molecules (one to five) to the Na+ ion using a combined scanning tunnelling microscopy and noncontact atomic force microscopy system. We found that the Na+ ion hydrated with three water molecules diffuses orders of magnitude more quickly than other ion hydrates. Ab initio calculations revealed that such high ion mobility arises from the existence of a metastable state, in which the three water molecules around the Na+ ion can rotate collectively with a rather small energy barrier. This scenario would apply even at room temperature according to our classical molecular dynamics simulations. Our work suggests that anomalously high diffusion rates for specific hydration numbers of ions are generally determined by the degree of symmetry match between the hydrates and the surface lattice.

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## Change history

• ### 22 August 2018

In this Letter, the links to Supplementary Videos 5, 7, 9 and 10 were incorrect, and there were some formatting errors in the Supplementary Video legends. These errors have been corrected online.

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## Acknowledgements

This work was supported by the National Key R&D Program under grant numbers 2016YFA0300901, 2017YFA0205003, 2016YFA0300903 and 2015CB856801; the National Natural Science Foundation of China under grant numbers 11634001, 11525520, 21573006 and 11290162/A040106; and the Key Research Program of the Chinese Academy of Sciences under grant numbers XDPB08-1 and XDPB08-4. Y.J. acknowledges support by the National Science Fund for Distinguished Young Scholars (grant number 21725302) and the Cheung Kong Young Scholar Program. P.H. and P.J. acknowledge support from the Czech Academy of Sciences project number MSM100101705 and Premium Academiae and GACR project number 18-09914S. J.G. acknowledges support from the National Postdoctoral Program for Innovative Talents. J.P. acknowledges support from the Weng Hongwu Original Research Foundation under grant number WHW201502. We are grateful for the computational resources provided by the TianHe-1A, TianHe II supercomputer, and the High-performance Computing Platform of Peking University. This work is supported in part by Songshan Lake Laboratory for Material Sciences.

### Reviewer information

Nature thanks P. Asinari and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

Y.J. and E.-G.W. designed and supervised the project. J.P. performed the STM/AFM measurements (with J.G. and R.M.). D.C., J.C., X.-Z.L. and L.-M.X. performed ab initio DFT calculations. Z.H., W.J.X. and Y.Q.G. carried out the classical molecular dynamics simulations. P.H. and P.J. carried out the theoretical simulations of the AFM images (in collaboration with D.C. and B.C.). J.P., D.C., Z.H., J.G., W.J.X., X.-Z.L., Y.Q.G., L.-M.X., E.-G.W. and Y.J. analysed the data. Y.J. wrote the manuscript with input from all other authors. The manuscript reflects the contributions of all authors.

### Corresponding authors

Correspondence to Li-Mei Xu or Yi Qin Gao or En-Ge Wang or Ying Jiang.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### 41586_2018_122_MOESM2_ESM.mov

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### 41586_2018_122_MOESM3_ESM.mov

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### 41586_2018_122_MOESM4_ESM.mov

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video. The mobility of Na+·3H2O is more than one order of magnitude larger than that of other clusters.

### 41586_2018_122_MOESM5_ESM.mov

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### 41586_2018_122_MOESM6_ESM.mov

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### 41586_2018_122_MOESM7_ESM.mov

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 1. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. The intermediate transitions during the diffusion can be seen clearly in the video. Na·H2O hops between the bridge sites, accompanied with the rotation of water around the Na+.

### 41586_2018_122_MOESM8_ESM.mov

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 2. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Na+·2H2O hops between the bridge sites, accompanied with the rotation of two water molecules around the Na+.

### 41586_2018_122_MOESM9_ESM.mov

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 3. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. The diffusion of Na+·3H2O is facilitated by a metastable state (Fig. 4f), where the Na+ is located at the top Cl− site of NaCl in contrast to the bridge site in the most stable state (Fig. 4e). See Fig. 4 for detailed discussions.

### 41586_2018_122_MOESM10_ESM.mov

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 4. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Na+·4H2O hops between the top Cl− sites. The diffusion of Na+·4H2O is usually accompanied with the flipping of water molecules, that is, one water molecule climbs onto the top of the Na+ ion, leaving the rest three in contact with the surface. Such a configuration resembles that of Na+·3H2O, leading to the stabilization at the bridge site. See Supplementary Figure 11 for detailed discussions.

### 41586_2018_122_MOESM11_ESM.mov

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 5. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Na+·5H2O hops between the top Cl− sites and shows a similar flipping-assisted diffusion behaviour to Na+·4H2O. See Supplementary Figure 11 for detailed discussions.

### Supplementary Information

This file contains Supplementary Text 1–13 (see contents page for more details), Supplementary Figures S1–S13, Supplementary Tables S1–S3 and references.

### Video 1: Diffusion trajectory of Na+⋅H2O on NaCl(001) surface during a period of 10 ns.

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### Video 2: Diffusion trajectory of Na+⋅2H2O on NaCl(001) surface during a period of 10 ns.

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### Video 3: Diffusion trajectory of Na+⋅3H2O on NaCl(001) surface during a period of 10 ns.

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video. The mobility of Na+·3H2O is more than one order of magnitude larger than that of other clusters.

### Video 4: Diffusion trajectory of Na+⋅4H2O on NaCl(001) surface during a period of 10 ns.

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### Video 5: Diffusion trajectory of Na+⋅5H2O on NaCl(001) surface during a period of 10 ns.

The video was generated by molecular dynamics simulations at 275 K. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Overall diffusion dynamics can be seen clearly in the video.

### Video 6: Diffusion trajectory of Na+⋅H2O during a period of 20 ps.

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 1. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. The intermediate transitions during the diffusion can be seen clearly in the video. Na·H2O hops between the bridge sites, accompanied with the rotation of water around the Na+.

### Video 7: Diffusion trajectory of Na+⋅2H2O during a period of 20 ps.

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 2. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Na+·2H2O hops between the bridge sites, accompanied with the rotation of two water molecules around the Na+.

### Video 8: Diffusion trajectory of Na+⋅3H2O during a period of 20 ps.

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 3. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. The diffusion of Na+·3H2O is facilitated by a metastable state (Fig. 4f), where the Na+ is located at the top Cl− site of NaCl in contrast to the bridge site in the most stable state (Fig. 4e). See Fig. 4 for detailed discussions.

### Video 9: Diffusion trajectory of Na+⋅4H2O during a period of 20 ps.

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 4. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Na+·4H2O hops between the top Cl− sites. The diffusion of Na+·4H2O is usually accompanied with the flipping of water molecules, that is, one water molecule climbs onto the top of the Na+ ion, leaving the rest three in contact with the surface. Such a configuration resembles that of Na+·3H2O, leading to the stabilization at the bridge site. See Supplementary Figure 11 for detailed discussions.

### Video 10: Diffusion trajectory of Na+⋅5H2O during a period of 20 ps.

The video was generated by molecular dynamics simulations at 300 K and played with a 2,000-times higher frame rate than Supplementary Video 5. H, O, Cl, Na atoms are denoted as white, red, green and purple spheres, respectively. Na+·5H2O hops between the top Cl− sites and shows a similar flipping-assisted diffusion behaviour to Na+·4H2O. See Supplementary Figure 11 for detailed discussions.

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Peng, J., Cao, D., He, Z. et al. The effect of hydration number on the interfacial transport of sodium ions. Nature 557, 701–705 (2018). https://doi.org/10.1038/s41586-018-0122-2

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