Carbon Nanotube Forest Growth: Catalyst-Controlled Self-Termination (2D)

Growth Recipe

Catalyst nanoparticle diameter 8.0 nm

Carbon feedstock flow 100 sccm

Growth temperature 750 °C

Initial catalyst activity 100 %

Deactivation rate multiplier 1.0×

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 base of its own nanotube and cracks the carbon feedstock, feeding carbon atoms into the growing wall (base-growth CVD, drawn here as a 2D side view). This engine does not use the closed-form height formula directly — it numerically integrates the real per-tube ODE pair every frame, catalyst-activity decay driving growth rate:

da/dt = −a/τ              a(0) = a₀ (initial catalyst activity)
dH/dt = k · a(t)          H(t) computed by forward-Euler integration each frame

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

Catalyst diameter d — sets nanotube thickness 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) — a real trade-off from actual CVD reactors.
Initial catalyst activity a₀ — models a partially pre-poisoned or partially-sintered catalyst batch (e.g. from air exposure before growth); lower a₀ scales the whole run down without changing its timescale.
Deactivation rate multiplier — directly speeds up (Ostwald-ripening / carbon-encapsulation) or slows down catalyst death, shortening or lengthening τ and therefore the self-termination time.
Each of the drawn tubes carries its own random nucleation delay and catalyst-size jitter, so the forest silhouette is uneven exactly as in a real CVD run, even though every tube obeys the same underlying kinetics.

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 (base) Height vs. time curve