Skip to main content
SpringerLink
Log in

Optimization of charge curve for the extreme inhibition of growing microstructures during electrodeposition

  • Impact Article
  • Published:
MRS Bulletin Aims and scope Submit manuscript

Abstract

The formation of branched microstructures during the electrodeposition is a catastrophic event, which hampers the safe utilization of the metallic electrodes in rechargeable batteries. Focusing on the nonlinear growth dynamics of the dendritic microstructures, we tune the rate of the feeding charge against their growth pace to minimize the amount of the dendritic branching, while maintaining a constant feeding charge. The ultimate morphology of the electrodeposits has been shown to be more compact than the conventional uniform charging in terms of the density of the electrodeposits. Due to analytical derivation and the coupled development of the optimal charge form with respect to the natural kinetics of dendritic evolution in real time, we infer that it prevents the branching of the electrodeposits to the greatest extent, during the stochastic evolution of the dendrites.

Impact statement

Taking into account the runaway behavior in the natural growth rate of the dendritic electrodeposition, which is slowest in the initiation (i.e., triggering) stage and is fastest in the final (i.e., short circuit) stage, we tune the rate of the feeding charge in time, inversely for highest compression of the microstructures, while maintaining a constant total charge. The controlled dendritic growth with the constant speed has analytically been proven to lead to the shortest growth compared with any other runaway growth form, while maintaining the same amount of the total charge. Subsequently, the constant rate of growth has been used as the handle to obtain the charge feeding form leading to such rate of growth. Performing stochastic molecular dynamics (MD) simulations, the ultimate morphology of the electrodeposits has been shown to be more compact than the conventional uniform charging in terms of the density of the electrodeposits. In fact, the charge feeding occurs when the density of the growing structure is the highest, and vice versa, the feeding rate is the least, when the structure is the most branched and sparse. The obtained charging protocol has been successfully tested in our experimental observations, which has visually led to the shorter accumulation of the dendrites with higher packing density. Due to analytical derivation and comparative development of the optimal pulse form with respect to the natural kinetics of dendritic evolution, we infer that it prevents the branching of the electrodeposits almost to the greatest extent, during the stochastic evolution of the dendrites.

GraphicAbstract

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

Similar content being viewed by others

Data availability

The row data for producing the results in this manuscript are freely available upon request from the corresponding author at aryanfar@caltech.edu.

Notes

  1. \(\updelta t=\sum_{i=1}^{n}\updelta t_{i}\) where \(\updelta t_{k}\) is the inter-collision time, typically in the range of fs.

  2. Equivalent to \(Q\approx \left\{ 43,86,174\right\}\) coulombs.

References

  1. S. Suzuki, H. Okada, K. Yabumoto, S. Matsuda, Y. Mima, N. Kimura, K. Kimura, arXiv preprint. arXiv:2010.04489 (2020)

  2. W.H. Sim, H.M. Jeong, Adv. Sci. 8(1), 2002144 (2021)

  3. X. Xu, Y. Liu, J.-Y. Hwang, O.O. Kapitanova, Z. Song, Y.-K. Sun, A. Matic, S. Xiong, Adv. Energy Mater. 10(44), 2002390 (2020)

  4. M. Selvapandiyan, G. Balaji, N. Sivakumar, M. Prasath, S. Sagadevan, Chem. Phys. Lett. 762, 138118 (2021)

  5. Y. Wang, H.-Q. Sang, W. Zhang, Y. Qi, R.-X. He, B. Chen, W. Sun, X.-Z. Zhao, D. Fu, Y. Liu, ACS Appl. Mater. Interfaces 12(46), 51563 (2020)

    Article  CAS  Google Scholar 

  6. T. Gao, C. Rainey, W. Lu, ACS Appl. Mater. Interfaces 12(46), 51448 (2020)

  7. A. Ramasubramanian, V. Yurkiv, T. Foroozan, M. Ragone, R. Shahbazian-Yassar, F. Mashayek, ACS Appl. Energy Mater. 3(11), 10560 (2020)

    Article  CAS  Google Scholar 

  8. J. Qian, S. Wang, Y. Li, M. Zhang, F. Wang, Y. Zhao, Q. Sun, L. Li, F. Wu, R. Chen, Adv. Funct. Mater. 31(7), 2006950 (2020)

  9. Q. Yan, G. Whang, Z. Wei, S.-T. Ko, P. Sautet, S.H. Tolbert, B.S. Dunn, J. Luo, Appl. Phys. Lett. 117(8), 080504 (2020)

  10. D. Tewari, S.P. Rangarajan, P.B. Balbuena, Y. Barsukov, P.P. Mukherjee, J. Phys. Chem. C 124(12), 6502 (2020)

  11. C.-T. Yang, Y.-X. Lin, B. Li, X. Xiao, Y. Qi, ACS Appl. Mater. Interfaces 12(45), 51007 (2020)

    Article  CAS  Google Scholar 

  12. S. Sheng, L. Sheng, L. Wang, N. Piao, X. He, J. Power Sources 476, 228749 (2020)

    Article  CAS  Google Scholar 

  13. T. Witten, L.M. Sander, Phys. Rev. B 27(9), 5686 (1983)

  14. M. Matsushita, K. Honda, H. Toyoki, Y. Hayakawa, H. Kondo, J. Phys. Soc. Jpn. 55(8), 2618 (1986)

    Article  CAS  Google Scholar 

  15. J. Kertész, T. Vicsek, J. Phys. A Math. Gen. 19(5), L257 (1986)

    Article  Google Scholar 

  16. J.N. Chazalviel, Phys. Rev. A 42(12), 7355 (1990)

    Article  CAS  Google Scholar 

  17. V. Fleury, Nature 390(6656), 145 (1997)

    Article  CAS  Google Scholar 

  18. M. Rosso, T. Gobron, C. Brissot, J.-N. Chazalviel, S. Lascaud, J. Power Sources 97, 804 (2001)

    Article  Google Scholar 

  19. C. Monroe, J. Newman, J. Electrochem. Soc. 150(10), A1377 (2003)

    Article  CAS  Google Scholar 

  20. R. Akolkar, J. Power Sources 232, 23 (2013)

    Article  CAS  Google Scholar 

  21. D. Tewari, P.P. Mukherjee, J. Mater. Chem. A 7(9), 4668 (2019)

  22. A. Aryanfar, D. Brooks, B.V. Merinov, W.A. Goddard III, A. Colussi, M.R. Hoffmann, J. Phys. Chem. Lett. 5(10), 1721 (2014)

  23. W. Mu, X. Liu, Z. Wen, L. Liu, J. Energy Storage 26, 100921 (2019)

    Article  Google Scholar 

  24. D.R. Ely, A. Jana, R.E. García, J. Power Sources 272, 581 (2014)

  25. D.A. Cogswell, Phys. Rev. E 92(1), 011301 (2015)

  26. R. Akolkar, J. Power Sources 246, 84 (2014)

    Article  CAS  Google Scholar 

  27. Z. Ahmad, Z. Hong, Venkatasubramanian Viswanathan, Proc. Natl Acad. Sci. U.S.A. 117(43), 26672–26680 (2020)

    Article  CAS  Google Scholar 

  28. W. Huang, P. Feng, C. Gao, X. Shuai, T. Xiao, C. Shuai, S. Peng, Int. J. Polym. Sci. 2015, 132965 (2015)

  29. B. Moorthy, R. Ponraj, J.H. Yun, J.E. Wang, D.J. Kim, D.K. Kim, ACS Appl. Energy Mater. 3(11), 11053 (2020)

  30. T. Gao, C. Rainey, W. Lu, ACS Appl. Mater. Interfaces 12(46), 51448(2020)

    Article  CAS  Google Scholar 

  31. R. Wang, J. Yu, J. Tang, R. Meng, L.F. Nazar, L. Huang, X. Liang, Energy Storage Mater. 32, 178 (2020)

  32. W. Xu, J.L. Wang, F. Ding, X.L. Chen, E. Nasybutin, Y.H. Zhang, J.G. Zhang, Energy Environ. Sci. 7(2), 513 (2014)

    Article  CAS  Google Scholar 

  33. Z. Li, J. Huang, B.Y. Liaw, V. Metzler, J. Zhang, J. Power Sources 254, 168 (2014)

  34. Y. Ren, Y. Shen, Y. Lin, C.-W. Nan, Electrochem. Commun. 57, 27(2015)

    Article  CAS  Google Scholar 

  35. H. Lee, N. Sitapure, S. Hwang, J.S.-I. Kwon, Comput. Chem. Eng. 153, 107415 (2021)

  36. N. Schweikert, A. Hofmann, M. Schulz, M. Scheuermann, S.T. Boles, T. Hanemann, H. Hahn, S. Indris, J. Power Sources 228, 237 (2013)

    Article  CAS  Google Scholar 

  37. R. Younesi, G.M. Veith, P. Johansson, K. Edström, T. Vegge, Energy Environ. Sci. 8(7), 1905 (2015)

  38. M. Zhou, R. Liu, D. Jia, Y. Cui, Q. Liu, S. Liu, D. Wu, Adv. Mater. 33(29), 2100943 (2021)

    Article  CAS  Google Scholar 

  39. C.P. Nielsen, H. Bruus, arXiv preprint. arXiv:1505.07571 (2015)

  40. P.P. Natsiavas, K. Weinberg, D. Rosato, M. Ortiz, J. Mech. Phys. Solids 95, 92 (2016)

    Article  CAS  Google Scholar 

  41. A. Aryanfar, T. Cheng, A.J. Colussi, B.V. Merinov, W.A. Goddard III, M.R. Hoffmann, J. Chem. Phys. 143(13), 134701 (2015)

  42. A. Aryanfar, D.J. Brooks, A.J. Colussi, B.V. Merinov, W.A. Goddard III, M.R. Hoffmann, Phys. Chem. Chem. Phys. 17(12), 8000 (2015)

  43. Y. Fan, Z. Wang, T. Fu, Appl. Therm. Eng. 199, 117541 (2021)

    Article  CAS  Google Scholar 

  44. A.W. Abboud, E.J. Dufek, B. Liaw, J. Electrochem. Soc. 166(4), A667 (2019)

  45. S. Chandrashekar, O. Oparaji, G. Yang, D. Hallinan, J. Electrochem. Soc. 163(14), A2988 (2016)

  46. A. Aryanfar, D.J. Brooks, W.A. Goddard, MRS Adv. 3(22), 1201 (2018)

  47. X. Zhang, Q.J. Wang, K.L. Harrison, K. Jungjohann, B.L. Boyce, S.A. Roberts, P.M. Attia, S.J. Harris, J. Electrochem. Soc. 166(15), A3639 (2019)

  48. C. Monroe, J. Newman, J. Electrochem. Soc. 151(6), A880 (2004)

    Article  CAS  Google Scholar 

  49. M. Klinsmann, F.E. Hildebrand, M. Ganser, R.M. McMeeking, J. Power Sources 442, 227226 (2019)

  50. G. Liu, D. Wang, J. Zhang, A. Kim, W. Lu, ACS Mater. Lett.1(5), 498 (2019)

    Article  CAS  Google Scholar 

  51. P. Wang, W. Qu, W.-L. Song, H. Chen, R. Chen, D. Fang, Adv. Funct. Mater. 29(27), 1900950 (2019)

  52. R. Bhattacharyya, B. Key, H. Chen, A.S. Best, A.F. Hollenkamp, C.P. Grey, Nat. Mater. 9(6), 504 (2010)

  53. S. Chandrashekar, N.M. Trease, H.J. Chang, L.-S. Du, C.P. Grey, A. Jerschow, Nat. Mater. 11(4), 311 (2012)

  54. Y. Li, Y. Qi, Energy Environ. Sci. 12, 1286 (2019)

  55. L.M. Kasmaee, A. Aryanfar, Z. Chikneyan, M.R. Hoffmann, A.J. Colussi, Chem. Phys. Lett. 661, 65 (2016)

  56. G. Yoon, S. Moon, G. Ceder, K. Kang, Chem. Mater. 30(19), 6769 (2018)

    Article  CAS  Google Scholar 

  57. M.Z. Mayers, J.W. Kaminski, T.F. Miller III, J. Phys. Chem. C 116(50), 26214 (2012)

  58. A. Aryanfar, Y. Ghamlouche, W.A. Goddard III, Electrochim. Acta 367, 137469 (2021)

  59. M.Z. Bazant, B.D. Storey, A.A. Kornyshev, Phys. Rev. Lett. 106(4), 046102 (2011)

  60. A. Aryanfar, Y. Ghamlouche, W.A. Goddard III, J. Chem. Phys. 154(19), 194702 (2021)

  61. R. Koerver, W. Zhang, L. de Biasi, S. Schweidler, A.O. Kondrakov, S. Kolling, T. Brezesinski, P. Hartmann, W.G. Zeier, J. Janek, Energy Environ. Sci. 11(8), 2142 (2018)

  62. K. Nishikawa, Y. Fukunaka, T. Sakka, Y.H. Ogata, J.R. Selman, J. Electrochem. Soc. 153(5), A830 (2006)

    Article  CAS  Google Scholar 

  63. J.-H. Kim, N.P.W. Pieczonka, L. Yang, ChemPhysChem 15(10), 1940 (2014)

  64. B.N. Taylor, A. Thompson, The International System of Units (SI). International Bureau of Weights and Measures Publication (US Department of Commerce, Technology Administration, National Institute of Standards and Technology, 2001)

  65. A. Aryanfar, Y. Ghamlouche, W.A. Goddard III, Phys. Rev. E 100(4), 042801 (2019)

  66. J. Philibert, Diffus. Fundam. 4(6), 1 (2006)

    Google Scholar 

  67. R.A. Serway, J.W. Jewett, Physics for Scientists and Engineers (Cengage Learning, Boston, 2018)

  68. A. Aryanfar, US Patent 9,620,808 (April 11, 2017)

  69. N. Otsu, Automatica 11(285–296), 23 (1975)

    Google Scholar 

  70. A. Aryanfar, D.J. Brooks, A.J. Colussi, M.R. Hoffmann, Phys. Chem. Chem. Phys. 16(45), 24965 (2014)

Download references

Acknowledgments

The authors would like to thank and acknowledge the financial support from the Masri Institute (Award No. 103919) and University Research Board (Award No. 103950) at American University of Beirut.

Author information

Authors and Affiliations

  1. American University of Beirut, Beirut, Lebanon

    Asghar Aryanfar & Yara Ghamlouche

  2. Bahçeşehir University, Istanbul, Turkey

    Asghar Aryanfar

  3. California Institute of Technology, Pasadena, USA

    William A. Goddard III

Authors
  1. Asghar Aryanfar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yara Ghamlouche
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. William A. Goddard III
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Asghar Aryanfar.

Ethics declarations

Conflict of interest

The authors declare that they have no competing financial interests to influence the work reported in this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aryanfar, A., Ghamlouche, Y. & Goddard, W.A. Optimization of charge curve for the extreme inhibition of growing microstructures during electrodeposition. MRS Bulletin 47, 665–674 (2022). https://doi.org/10.1557/s43577-022-00307-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/s43577-022-00307-4

Keywords

Search

Navigation