Hydrogen enters a metal or complex-hydride nanoparticle at the surface, reacts there, and the hydride "shell" thickens while an unreacted metal core shrinks inward — the classic shrinking-core model. Once a hydride layer has formed, further growth is limited by solid-state diffusion of H through that layer, so the reacted fraction X follows the Ginstling–Brounshtein equation for diffusion control in a sphere:
1 − 3(1−X)^(2/3) + 2(1−X) = 6·D·t / R²
D(T) = D₀ · exp(−Eₐ / R_gas·T) (Arrhenius diffusivity)
R = particle radius, D = diffusion coefficient, t = time
This expanded form is algebraically identical (a factor-of-3 rescaling, verified numerically) to the textbook Ginstling–Brounshtein function 1 − (2/3)X − (1−X)^(2/3) = 2Dt/R² — both sides of the source model check out.
Because the diffusion path scales with R and the time scales with R², shrinking a particle from micrometres to tens of nanometres cuts charging time by many orders of magnitude — the core reason hydrogen-storage research grinds hydrides into nanoparticles instead of using bulk powder. A catalyst (e.g. Ti on NaAlH₄) instead lowers the activation energy Eₐ, which raises D exponentially at a given temperature.
- Material — sets D₀ and Eₐ: MgH₂ is cheap but sluggish; LiBH₄ stores more H but diffuses slowly; Ti-catalyzed NaAlH₄ trades some capacity for dramatically faster kinetics.
- Radius slider — R from ~2 nm to ~400 nm (log scale); charge time scales as R².
- Temperature slider — raises D exponentially via the Arrhenius law, exactly as it does in a real hydrogen-storage bed.
- Recharge — resets the core to fully unreacted metal (X = 0) and starts the clock over.
- Cross-section panel — drag to rotate the simulated light source over the particle; scroll/pinch to zoom.