---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '23087'
abstract:
- lang: eng
  text: Disordered materials such as glasses are promising candidates as solid-state
    electrolytes for batteries, but they tend to exhibit low ionic conductivity and
    current methods for investigating and predicting the ionic conductivity of electrolyte
    materials are inefficient. Here, we propose a framework that summarizes the topological
    properties of the electrolyte material’s atomic structure with a weighted graph
    based on periodic boundary conditions. We then compute a variation of the max-flow
    algorithm, a commonly used model in continuum models of transportation and liquid
    flow, on this summary and show that it is compatible with the simulated periodic
    atomic structures. Using molecular dynamics simulations of various glassy solid-state
    electrolyte families including both mobile lithium and sodium ions, we validate
    the approach by showing a positive correlation between the area-normalized maximum
    flow predicted from the static glass structures and the ionic conductivity as
    obtained from the simulations, especially in the case of high-conductivity sulfide
    glass electrolytes. We envision that the developed methodology, which only relies
    on static atomic structure, will accelerate the discovery of highly conductive
    sulfide glassy electrolytes for high-performance all-solid-state batteries.
acknowledgement: We thank the Danish e-Infrastructure Cooperation (DeiC) for access
  to computational resources at Sophia and LUMI-C (DeiC-AAU-N5-202200005). This work
  was supported by the Independent Research Fund Denmark (1026-00037), European Union
  (ERC, NewGLASS, 101044664), and Danish Data Science Academy, which in turn is funded
  by the Novo Nordisk Foundation (NNF21SA0069429) and VILLUM FONDEN (40516). Y.B.B.
  acknowledges support from the Austrian Science Fund (FWF) 10.55776/ESP9584724.
article_number: '10343'
article_processing_charge: Yes
article_type: original
author:
- first_name: Matteo
  full_name: Pegoraro, Matteo
  last_name: Pegoraro
- first_name: Rasmus
  full_name: Christensen, Rasmus
  last_name: Christensen
- first_name: Søren S.
  full_name: Sørensen, Søren S.
  last_name: Sørensen
- first_name: Anders R.
  full_name: Lindbjerg, Anders R.
  last_name: Lindbjerg
- first_name: Tao
  full_name: Du, Tao
  last_name: Du
- first_name: Yossi
  full_name: Bleile, Yossi
  id: 920a7385-7995-11ef-9bfd-8c434cd8f3c2
  last_name: Bleile
  orcid: 0000-0002-4861-9174
- first_name: Anne Marie
  full_name: Svane, Anne Marie
  last_name: Svane
- first_name: Christophe A.N.
  full_name: Biscio, Christophe A.N.
  last_name: Biscio
- first_name: Lisbeth
  full_name: Fajstrup, Lisbeth
  last_name: Fajstrup
- first_name: Morten M.
  full_name: Smedskjaer, Morten M.
  last_name: Smedskjaer
citation:
  ama: Pegoraro M, Christensen R, Sørensen SS, et al. Predicting ionic conductivity
    of sulfide glass solid-state electrolytes using max-flow methodology. <i>Nature
    Communications</i>. 2026;17. doi:<a href="https://doi.org/10.1038/s41467-026-77363-w">10.1038/s41467-026-77363-w</a>
  apa: Pegoraro, M., Christensen, R., Sørensen, S. S., Lindbjerg, A. R., Du, T., Bokor
    Bleile, Y., … Smedskjaer, M. M. (2026). Predicting ionic conductivity of sulfide
    glass solid-state electrolytes using max-flow methodology. <i>Nature Communications</i>.
    Springer Nature. <a href="https://doi.org/10.1038/s41467-026-77363-w">https://doi.org/10.1038/s41467-026-77363-w</a>
  chicago: Pegoraro, Matteo, Rasmus Christensen, Søren S. Sørensen, Anders R. Lindbjerg,
    Tao Du, Yossi Bokor Bleile, Anne Marie Svane, Christophe A.N. Biscio, Lisbeth
    Fajstrup, and Morten M. Smedskjaer. “Predicting Ionic Conductivity of Sulfide
    Glass Solid-State Electrolytes Using Max-Flow Methodology.” <i>Nature Communications</i>.
    Springer Nature, 2026. <a href="https://doi.org/10.1038/s41467-026-77363-w">https://doi.org/10.1038/s41467-026-77363-w</a>.
  ieee: M. Pegoraro <i>et al.</i>, “Predicting ionic conductivity of sulfide glass
    solid-state electrolytes using max-flow methodology,” <i>Nature Communications</i>,
    vol. 17. Springer Nature, 2026.
  ista: Pegoraro M, Christensen R, Sørensen SS, Lindbjerg AR, Du T, Bokor Bleile Y,
    Svane AM, Biscio CAN, Fajstrup L, Smedskjaer MM. 2026. Predicting ionic conductivity
    of sulfide glass solid-state electrolytes using max-flow methodology. Nature Communications.
    17, 10343.
  mla: Pegoraro, Matteo, et al. “Predicting Ionic Conductivity of Sulfide Glass Solid-State
    Electrolytes Using Max-Flow Methodology.” <i>Nature Communications</i>, vol. 17,
    10343, Springer Nature, 2026, doi:<a href="https://doi.org/10.1038/s41467-026-77363-w">10.1038/s41467-026-77363-w</a>.
  short: M. Pegoraro, R. Christensen, S.S. Sørensen, A.R. Lindbjerg, T. Du, Y. Bokor
    Bleile, A.M. Svane, C.A.N. Biscio, L. Fajstrup, M.M. Smedskjaer, Nature Communications
    17 (2026).
das_tickbox: '1'
dataavailabilitystatement: All data supporting the findings of this study are available
  within the article and Supplementary Information files. Source data are provided
  with this paper. The developed code to perform the max-flow calculations is available
  as part of the Topological Materials Analysis (ToMA) library, which is available
  at Zenodo (https://doi.org/10.5281/zenodo.10781424) and Github (https://github.com/yossibokorbleile/TopologicalMaterialAnalysis),
  with documentation available at https://yossi.eu/toma/. To enhance usability, we
  have included a brief documentation on how to compile ToMA as well as a minimal
  working example of the code together with an example trajectory directly in the
  ToMA repository. LAMMPS is an open-source code available at https://lammps.sandia.gov.
date_created: 2026-10-11T22:02:03Z
date_published: 2026-09-30T00:00:00Z
date_updated: 2026-10-12T09:03:58Z
day: '30'
ddc:
- '500'
department:
- _id: HeEd
doi: 10.1038/s41467-026-77363-w
external_id:
  pmid:
  - '42811056'
file:
- access_level: open_access
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fulldoi: https://doi.org/10.1038/s41467-026-77363-w
has_accepted_license: '1'
intvolume: '        17'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 9106a876-16d5-11f0-9cad-bbf11c9952f9
  grant_number: ESP 9584724
  name: Quantitative Unbiased Shape Analysis with Geometry &amp; Topology
publication: Nature Communications
publication_identifier:
  eissn:
  - 2041-1723
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Predicting ionic conductivity of sulfide glass solid-state electrolytes using
  max-flow methodology
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 17
year: '2026'
...