Metal Hydride Nanoparticle Charging Kinetics

Hydride Material

Particle & Bed Conditions

Particle radius R 50 nm

Bed temperature T 400 K

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Hydrogenation X = 0%Core 100%

Diffusion coeff. D

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Elapsed time

0 s

Characteristic charge time τ (X→~100%)

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How it works

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

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 ~300 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.

Unreacted metal core Absorbed hydrogen (hydride shell)

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