Diffusion–reaction modelling of modulated hydrogen loading

Marcel Simhofer, Philipp Brunner, Jörg Weissmüller, Roland Würschum*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the present work the bulk-diffusion problem of electrochemically inserted solute particles, e.g. hydrogen, in planar or cylindrical electrodes is treated with a boundary condition, which considers simultaneously both a sinusoidal modulation of the particle flux as well as the reaction rate of particle insertion into the electrode. By solving this diffusion–reaction model with superimposed modulation the solute concentration inside the sample as well as the particle flux is obtained. For application to electrochemical charging, this flux is related to that which follows from the Butler-Volmer equation. The phase shift between the surface solute concentration modulated by electrochemical means and the bulk particle concentration provides information whether the particle flux through the electrode-electrolyte interface is influenced more strongly by the insertion reaction or the subsequent diffusion inside the electrode. The spatial and temporal concentration evolution within the sample is analysed. The present model catches not only the modulation behaviour in a stationary state but also the transient behaviour. Furthermore, the faradaic impedance, derived from the current density across the interface, intrinsically contains both, the interfacial transfer resistance and the diffusion impedance. The presented diffusion–reaction model is not only suitable to study solute insertion in electrodes and subsequent diffusion phenomena in the field of electrochemistry, but can also be applied for other types of loading, e.g. from the gas phase, and to other measuring techniques, e.g. dilatometry.
Original languageEnglish
JournalPhilosophical Magazine
Early online date4 Apr 2024
Publication statusE-pub ahead of print - 4 Apr 2024


  • Diffusion–reaction model
  • Faradaic impedance
  • hydrogen in metals
  • modulation
  • transient behaviour

ASJC Scopus subject areas

  • Condensed Matter Physics

Fields of Expertise

  • Advanced Materials Science


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