$$\delta(t) \approx \delta_0 + k\sqrt{t}$$

Equation 9 · Materials Science

How Materials Discovery and Degradation Actually Work

This equation gives an approximation: it relates the quantities while allowing an approximation.

Diffusion-limited SEI thickening is commonly modeled with a square-root-of-time growth law, $\delta(t) \approx \delta_0 + k\sqrt{t}$. where $\delta(t)$ is film thickness, $\delta_0$ an initial thickness, and k a rate constant set by species diffusivity through the existing film — a direct consequence of assuming the rate-limiting step is diffusion across a film whose own thickness is the barrier [ 2 ] . This is a model, not a universal law : the review is explicit that mixed kinetic-and-transport regimes, porous or cracked SEI, and side reactions all produce departures from a clean square-root trend, and reconciling model and experiment remains an open problem [ 2 ] .

Meanings in this article

• $\delta$: film thickness.
• $\delta_0$: the initial thickness.

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