Step-Growth vs Chain-Growth Polymerization
Particle simulation · Carothers equation · Natta DPn kinetics · Living vs regular
Step-Growth (Polycondensation / Polyaddition)
Any reactive end + any reactive end · no "active centre"Chain-Growth (Addition)
Regular mode — with terminationCarothers Equation
D̄Pn vs Conversion — Natta equation
Press Play to run both simulations simultaneously.
In the orange/amber step-growth panel, all particles are equivalent A–B monomers. The colour darkens (amber → blue) as chain length increases. Oligomers form first; long chains appear only at very high conversion (p → 1).
In the blue chain-growth panel, the green initiator activates and starts grabbing blue free monomers one by one. Free monomers and long polymer chains coexist from the very first moment.
Toggle Regular / Living to see the effect of termination on chain-length kinetics.
In step-growth polymerization, any reactive A end-group can react with any B end-group, regardless of chain length. No chain is privileged.
- Polycondensation
- –OH + –COOH → ester + H₂O (PET, nylon 6,6)
- Polyaddition
- –OH + –NCO → urethane — no by-product (polyurethanes)
The Carothers equation: X̄n = 1/(1−p)
- p = 0.90
- X̄n = 10 — still mostly oligomers
- p = 0.99
- X̄n = 100 — 99% conversion needed for useful MW
- Dispersity
- Đ → 2 (Flory–Schulz most-probable distribution)
An initiator generates an active centre that adds free monomers one by one. Monomers never react with each other.
- Radical
- R• end; termination by combination (kt > 0) — "regular" mode
- Anionic
- R⁻ end (e.g. BuLi); often living (kt ≈ 0), narrow Đ
- Coordination
- M–C bond at metallocene catalyst; controls tacticity
In living polymerization (kt = 0), D̄Pn increases linearly: D̄Pn = [M]₀·p / [I]₀, with Đ → 1.
The defining contrast appears at p = 0.50 (50% conversion):
- Step-growth X̄n
- X̄n = 2 — average chain is a dimer
- Chain-growth D̄Pn
- Already 10–18 — high-MW polymer present alongside free monomer
- Free monomer?
- Step: none — all monomer locked in oligomers
- Chain: yes — half the monomer still free
- Dispersity
- Step: Đ → 2 · Regular chain: Đ ≈ 1.5–2 · Living: Đ → 1
Isospecific propylene polymerization with C2-symmetric bis(indenyl)-type metallocene catalysts
SBI_polym
●Zr ●C ●Si —η⁵ —Zr–Cchain
π-complex {SBI}Zr…si-C3H6 (favored)
●Zr ●C ●Si —η⁵ —Zr–Cchain - -propene π
π-complex {SBI}Zr…re-C3H6 (disfavored)
●Zr ●C ●Si —η⁵ —Zr–Cchain - -propene π
KIR1177_2
●Ru ●C ●O
KIRVC14
●P ●C ●O ●H
KIR1190
●B ●N ●O ●Si ●C