Carbon Nanotube Forest Growth: Catalyst-Controlled Self-Termination

Growth Recipe

Catalyst nanoparticle diameter 8.0 nm

Carbon feedstock flow 100 sccm

Growth temperature 750 °C

Simulation speed 6×

Forest State

Forest height

0.0 µm

Growth rate

0.00 nm/s

Catalyst activity

100 %

Process time

0 s

How it works

Each catalyst nanoparticle (Fe/Ni, diameter d) sits at the tip of its own nanotube and cracks the carbon feedstock, feeding carbon atoms into the growing wall (tip-growth CVD). A tube's diameter tracks its catalyst's diameter. As growth proceeds, the catalyst slowly deactivates — subsurface carbon diffusion and Ostwald-ripening-driven sintering bury or coarsen the particle — so growth self-terminates rather than continuing forever:

H(t)  = H∞ (1 − e^(−t/τ))
dH/dt = k · e^(−t/τ)          H∞ = k · τ

k  = k₀·(P/P₀)·exp[−(Ea/R)(1/T − 1/T₀)]   (Arrhenius decomposition rate)
τ = τ₀·(d/d₀)^1.5 · exp[−(T−T₀)/300]       (catalyst-deactivation timescale)

Catalyst diameter d — sets nanotube diameter and, via (d/d₀)^1.5, how long the catalyst survives before deactivating: bigger particles resist encapsulation longer.
Feedstock flow P — scales the carbon-decomposition rate k linearly; more feedstock, faster initial growth.
Temperature T — accelerates decomposition (Arrhenius, faster growth) but also accelerates catalyst sintering/deactivation (shorter τ) — there is a real trade-off, exactly as in real CVD reactors, where an optimal temperature window maximizes final forest height.
The 3D view uses a square-root visual scale on tube height so both stubby and mm-tall forests stay framed at once; the numeric readouts report true heights in micrometres.

Real-world relevance: this self-terminating kinetics model (saturating exponential height vs. time, catalyst-lifetime-limited) is the standard description of vertically aligned carbon nanotube (VACNT) "forest" growth used to engineer CNT arrays for interconnects, thermal interface materials and electron-emission cathodes.

Carbon nanotube Catalyst nanoparticle (tip)

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