Graph Theory Ideas Reveal Long Range Proton Conduction Pathways

Acceptor doped barium zirconate shows great potential for proton conduction in fuel cell applications. Finding long range conduction pathways is challenging when the system includes both fast frequency modes needing short time step force integration and slow frequency modes requiring long time samples. Methods such as kinetic Monte Carlo avoid the integration of steps and instead use probabilities to choose the next moves and advance the clock based on the move chosen. Centrality methods based on the number of steps to return to key sites or vertices in a graph have been used to identify the most central areas in a graph. However, physical systems with traps and highways have steps with distinctly different barriers, making steps non-equivalent. This contribution reviews both traditional and new graph theory schemes for finding long range pathways, with a special focus on time-based centrality measures which provide a single image of traps and highways [1] and applications of these to proton conduction in doped perovskites where correlated proton motion is important.[2] Our recent work including a small electric field, and a catalog of tuple moves is included.

[1] Gomez-Haibach, K; Gomez, M. A., Revised Centrality Measures Tell a Robust Story of Ion Conduction in Solids. J. Phys. Chem. B 2023, 127, 43, 9258–9266. https://doi.org/10.1021/acs.jpcb.3c03886
[2] Pan, Y.; Hoang, M.T.; Mansoor, S.; Gomez, M.A. Inorganics 2023, 11, 160. https://doi.org/10.3390/inorganics11040160