Skip to main content
SpringerLink
Log in

Anomalous diffusion of lithium-anion clusters in ionic liquids

  • Regular Article – Flowing Matter
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract

Lithium-ion transport is significantly retarded in ionic liquids (ILs). In this work, we performed extensive molecular dynamics simulations to mimic the kinetics of lithium ions in ILs using [N-methyl-N-propylpyrrolidium (pyr\(_{13}\))][bis(trifluoromethanesulfonyl)imide (Ntf\(_{2}\))] with added LiNtf\(_{2}\) salt. And we analyzed their transport, developing a two-state model and comparing it to the machine learning-identified states. The transport of lithium ions involves local shell exchanges of the Ntf\(_{2}\) in the medium. We calculated train size distributions over various time scales. The train size distribution decays as a power law, representing non-Poissonian bursty shell exchanges. We analyzed the non-Poissonian processes of lithium ions transport as a two-state (soft and hard) model. We analytically calculated the transition probability of the two-state model, which fits well to the lifetime autocorrelation functions of LiNtf\(_{2}\) shells. To identify two states, we introduced the graph neutral network incorporating local molecular structure. The results reveal that the shell-soft state mainly contributes to the transport of the lithium ions, and their contribution is more important in low temperatures. Hence, it is the key for enhanced lithium ion transport to increase the fraction of the shell-soft state.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability

This manuscript has associated data in a data repository. [Authors’ comment: The authors will provide data on reasonable request.]

References

  1. N. Molinari, J.P. Mailoa, B. Kozinsky, General trend of a negative li effective charge in ionic liquid electrolytes. J. Phys. Chem. Lett. 10(10), 2313–2319 (2019). https://doi.org/10.1021/acs.jpclett.9b00798

    Article  Google Scholar 

  2. N. Molinari, J.P. Mailoa, N. Craig, J. Christensen, B. Kozinsky, Transport anomalies emerging from strong correlation in ionic liquid electrolytes. J. Power Sources 428, 27–36 (2019). https://doi.org/10.1016/j.jpowsour.2019.04.085

    Article  ADS  Google Scholar 

  3. M. McEldrew, Z.A.H. Goodwin, N. Molinari, B. Kozinsky, A.A. Kornyshev, M.Z. Bazant, Salt-in-ionic-liquid electrolytes: ion network formation and negative effective charges of alkali metal cations. J. Phys. Chem. B 125(50), 13752–13766 (2021). https://doi.org/10.1021/acs.jpcb.1c05546. (PMID: 34902256)

    Article  Google Scholar 

  4. M. McEldrew, Z.A.H. Goodwin, S. Bi, M.Z. Bazant, A.A. Kornyshev, Theory of ion aggregation and gelation in super-concentrated electrolytes. J. Chem. Phys. 152(23), 234506 (2020). https://doi.org/10.1063/5.0006197

    Article  ADS  Google Scholar 

  5. M. McEldrew, Z.A.H. Goodwin, H. Zhao, M.Z. Bazant, A.A. Kornyshev, Correlated ion transport and the gel phase in room temperature ionic liquids. J. Phys. Chem. B 125(10), 2677–2689 (2021). https://doi.org/10.1021/acs.jpcb.0c09050. (PMID: 33689352)

    Article  Google Scholar 

  6. Z.A.H. Goodwin, M. McEldrew, B. Kozinsky, M.Z. Bazant, Theory of cation solvation and ionic association in nonaqueous solvent mixtures. PRX Energy 2, 013007 (2023). https://doi.org/10.1103/PRXEnergy.2.013007

    Article  Google Scholar 

  7. C. Fang, D.M. Halat, N.P. Balsara, R. Wang, Dynamic heterogeneity of solvent motion and ion transport in concentrated electrolytes. J. Phys. Chem. B 127(8), 1803–1810 (2023). https://doi.org/10.1021/acs.jpcb.2c08029. (PMID: 36800550)

    Article  Google Scholar 

  8. A. Choudhary, D. Dong, D. Bedrov, Li+ transport in ethylene carbonate based comb-branched solid polymer electrolyte: a molecular dynamics simulation study. ACS Appl. Polym. Mater. 4(11), 8496–8507 (2022). https://doi.org/10.1021/acsapm.2c01416

    Article  Google Scholar 

  9. D. Dong, D. Bedrov, Charge transport in [li(tetraglyme)][bis(trifluoromethane) sulfonimide] solvate ionic liquids: Insight from molecular dynamics simulations. J. Phys. Chem. B 122(43), 9994–10004 (2018). https://doi.org/10.1021/acs.jpcb.8b06913. (PMID: 30299097)

    Article  Google Scholar 

  10. Z. Li, O. Borodin, G.D. Smith, D. Bedrov, Effect of organic solvents on li+ ion solvation and transport in ionic liquid electrolytes: A molecular dynamics simulation study. J. Phys. Chem. B 119, 3085–3096 (2015). https://doi.org/10.1021/jp510644k

    Article  Google Scholar 

  11. V. Lesch, Z. Li, D. Bedrov, O. Borodin, A. Heuer, The influence of cations on lithium ion coordination and transport in ionic liquid electrolytes: A md simulation study. Phys. Chem. Chem. Phys. 18, 382–392 (2016). https://doi.org/10.1039/c5cp05111h

    Article  Google Scholar 

  12. J.B. Haskins, W.R. Bennett, J.J. Wu, D.M. Hernández, O. Borodin, J.D. Monk, C.W. Bauschlicher, J.W. Lawson, Computational and experimental investigation of li-doped ionic liquid electrolytes: [pyr14][tfsi], [pyr13][fsi], and [emim][bf4]. J. Phys. Chem. B 118, 11295–11309 (2014). https://doi.org/10.1021/jp5061705

    Article  Google Scholar 

  13. Z. Li, G.D. Smith, D. Bedrov, Li+ solvation and transport properties in ionic liquid/lithium salt mixtures: a molecular dynamics simulation study. J. Phys. Chem. B 116, 12801–12809 (2012). https://doi.org/10.1021/jp3052246

    Article  Google Scholar 

  14. Z. Li, O. Borodin, G.D. Smith, D. Bedrov, Effect of organic solvents on li+ ion solvation and transport in ionic liquid electrolytes: a molecular dynamics simulation study. J. Phys. Chem. B 119(7), 3085–3096 (2015). https://doi.org/10.1021/jp510644k. (PMID: 25592777)

    Article  Google Scholar 

  15. J.B. Haskins, W.R. Bennett, J.J. Wu, D.M. Hernández, O. Borodin, J.D. Monk, C.W.J. Bauschlicher, J.W. Lawson, Computational and experimental investigation of li-doped ionic liquid electrolytes: [pyr14][tfsi], [pyr13][fsi], and [emim][bf4]. J. Phys. Chem. B 118(38), 11295–11309 (2014). https://doi.org/10.1021/jp5061705. (PMID: 25159701)

    Article  Google Scholar 

  16. D.M. Seo, O. Borodin, D. Balogh, M. O’Connell, Q. Ly, S.-D. Han, S. Passerini, W.A. Henderson, Electrolyte solvation and ionic association III. Acetonitrile–lithium salt mixtures-transport properties. J. Electrochem. Soc. 160(8), 1061 (2013). https://doi.org/10.1149/2.018308jes

    Article  Google Scholar 

  17. L. Kahle, A. Musaelian, N. Marzari, B. Kozinsky, Unsupervised landmark analysis for jump detection in molecular dynamics simulations. Phys. Rev. Mater. 3, 055404 (2019). https://doi.org/10.1103/PhysRevMaterials.3.055404

    Article  Google Scholar 

  18. N. Molinari, Y. Xie, I. Leifer, A. Marcolongo, M. Kornbluth, B. Kozinsky, Spectral denoising for accelerated analysis of correlated ionic transport. Phys. Rev. Lett. 127, 025901 (2021). https://doi.org/10.1103/PhysRevLett.127.025901

    Article  ADS  Google Scholar 

  19. V. Bapst, T. Keck, A. Grabska-Barwińska, C. Donner, E.D. Cubuk, S.S. Schoenholz, A. Obika, A.W.R. Nelson, T. Back, D. Hassabis, P. Kohli, Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 16, 448–454 (2020). https://doi.org/10.1038/s41567-020-0842-8

    Article  Google Scholar 

  20. N.N. Rajput, V. Murugesan, Y. Shin, K.S. Han, K.C. Lau, J. Chen, J. Liu, L.A. Curtiss, K.T. Mueller, K.A. Persson, Elucidating the solvation structure and dynamics of lithium polysulfides resulting from competitive salt and solvent interactions. Chem. Mater. 29, 3375–3379 (2017). https://doi.org/10.1021/acs.chemmater.7b00068

    Article  Google Scholar 

  21. C. Schröder, Comparing reduced partial charge models with polarizable simulations of ionic liquids. Phys. Chem. Chem. Phys. 14, 3089–3102 (2012). https://doi.org/10.1039/c2cp23329k

    Article  Google Scholar 

  22. I. Pethes, A comparison of classical interatomic potentials applied to highly concentrated aqueous lithium chloride solutions. J. Mol. Liq. 242, 845–858 (2017). https://doi.org/10.1016/j.molliq.2017.07.076

    Article  Google Scholar 

  23. T. Köddermann, D. Paschek, R. Ludwig, Molecular dynamic simulations of ionic liquids: A reliable description of structure, thermodynamics and dynamics. ChemPhysChem 8, 2464–2470 (2007). https://doi.org/10.1002/cphc.200700552

    Article  Google Scholar 

  24. O. Borodin, G.D. Smith, W. Henderson, Li+ cation environment, transport, and mechanical properties of the litfsi doped n-methyl-n-alkylpyrrolidinium+tfsi- ionic liquids. J. Phys. Chem. B 110, 16879–16886 (2006). https://doi.org/10.1021/jp061930t

  25. L. Martinez, R. Andrade, E.G. Birgin, J.M. Martínez, Packmol: a package for building initial configurations for molecular dynamics simulations. J. Comput. Chem. 30, 2157–2164 (2009). https://doi.org/10.1002/jcc.21224

    Article  Google Scholar 

  26. O. Borodin, Polarizable force field development and molecular dynamics simulations of ionic liquids. J. Phys. Chem. B 113, 11463–11478 (2009). https://doi.org/10.1021/jp905220k

    Article  Google Scholar 

  27. G.J. Martyna, D.J. Tobias, M.L. Klein, Constant pressure molecular dynamics algorithms. J. Chem. Phys. 101, 4177–4189 (1994). https://doi.org/10.1063/1.467468

    Article  ADS  Google Scholar 

  28. O. Borodin, G.D. Smith, Mechanism of ion transport in amorphous poly(ethylene oxide)/litfsi from molecular dynamics simulations. Macromolecules 39(4), 1620–1629 (2006). https://doi.org/10.1021/ma052277v

    Article  ADS  Google Scholar 

  29. O. Borodin, G.D. Smith, P. Fan, Molecular dynamics simulations of lithium alkyl carbonates. J. Phys. Chem. B 110(45), 22773–22779 (2006). https://doi.org/10.1021/jp0639142. (PMID: 17092027)

    Article  Google Scholar 

  30. O. Borodin, G.V. Zhuang, P.N. Ross, K. Xu, Molecular dynamics simulations and experimental study of lithium ion transport in dilithium ethylene dicarbonate. J. Phys. Chem. C 117(15), 7433–7444 (2013). https://doi.org/10.1021/jp4000494

    Article  Google Scholar 

  31. M. Karsai, H.-H. Jo, K. Kaski et al., Bursty Human Dynamics (Springer, Cham, 2018)

    Book  Google Scholar 

  32. G. Feng, M. Chen, S. Bi, Z.A.H. Goodwin, E.B. Postnikov, N. Brilliantov, M. Urbakh, A.A. Kornyshev, Free and bound states of ions in ionic liquids, conductivity, and underscreening paradox. Phys. Rev. X (2019). https://doi.org/10.1103/PhysRevX.9.021024

    Article  Google Scholar 

  33. Github repository for the GNNs. https://github.com/deepmind/deepmind-research.git

  34. Webpage for the GNNs by Google Deepmind. https://www.deepmind.com/blog/towards-understanding-glasses-with-graph-neural-networks

Download references

Acknowledgements

This research was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) 2018M3D1A1058624, 2021R1A2C1014562, and 2022R1A4A1030660.

Author information

Authors and Affiliations

  1. Department of Physics, Gyeongsang National University, Jinjudae-ro 501, Jinju, Gyeongsangnam-do, 52828, Republic of Korea

    YeongKyu Lee, Junseong Kim & YongSeok Jho

  2. School of Chemical and Biological Engineering, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    JunBeom Cho & Won Bo Lee

Authors
  1. YeongKyu Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JunBeom Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junseong Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Won Bo Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. YongSeok Jho
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

YSJ and WBL designed the project. YSJ and YKL developed the theoretical formula and performed numerical calculations. YKL, JBC, and JSK performed simulations. YSJ, YKL, JBC, and WBL analyzed data and wrote the manuscript.

Corresponding authors

Correspondence to Won Bo Lee or YongSeok Jho.

Additional information

Festschrift in honor of Philip (Fyl) Pincus. Guest editors: Jean-Marc Di Meglio, David Andelman, Cyrus R. Safinya Dedication: “We dedicate this article to Fyl Pincus, our lifelong mentor and a pioneer in the field of soft matter. His research, leadership, and guidance have inspired many scientists, including us.”.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 4480 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, Y., Cho, J., Kim, J. et al. Anomalous diffusion of lithium-anion clusters in ionic liquids. Eur. Phys. J. E 46, 105 (2023). https://doi.org/10.1140/epje/s10189-023-00365-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/s10189-023-00365-9

Search

Navigation