Step-Growth vs Chain-Growth Polymerization

Two ways to build the same long molecule

A polymer is just a long chain of repeating units. There are two completely different ways to assemble that chain, and which one you use decides almost everything about the process — the temperature, how long it takes, what the molar mass does over time, and which plastic falls out the other end.

Step-growth is democratic. Every molecule in the pot carries reactive ends, and any two of them can couple: a monomer with another monomer, a dimer with a trimer, an oligomer with an oligomer. The chain grows in steps, doubling and tripling at random, and you only get truly long chains when nearly every reactive end has found a partner.

Chain-growth is aristocratic. A handful of active centers — radicals, cations, or anions — are created, and monomer can only add to one of those active ends, one unit at a time, thousands of times per second. A chain that starts goes from monomer to a 5,000-mer in under a second, then dies. While it grows, the rest of the flask is still unreacted monomer.

STEP-GROWTH (any-to-any):
  M–M  +  M–M     →  M–M–M–M           (monomer + monomer = dimer/tetramer)
  M–M–M  +  M–M–M–M → M–M–M–M–M–M–M    (oligomer + oligomer)
  ...everything reacts with everything; long chains only near 100%

CHAIN-GROWTH (monomer-to-active-end only):
  R•  +  M → R–M•                       (initiation)
  R–M•  +  M → R–M–M•                   (propagation, ×thousands)
  R–M–(M)ₙ•  +  •M–R → dead chain       (termination)
  ...a few live chains eat monomer; full length from the start

That single difference — can any two species combine, or only monomer-with-an-active-end — propagates into two distinct molar-mass histories, two dispersity limits, and two different shopping lists of monomers.

Step-growth: difunctional monomers condensing end-to-end

Step-growth needs monomers with two (or more) reactive functional groups. The classic pairings are a diacid with a diol (giving a polyester) or a diacid with a diamine (giving a polyamide / nylon). Each coupling is an ordinary organic condensation — esterification or amidation — that you could run on a single small molecule. Polymerization is just that same reaction repeated until the chains run out of ends.

Nylon 6,6 is the canonical example: hexamethylenediamine (a diamine) reacts with adipic acid (a diacid), expelling one water per amide bond:

n H₂N–(CH₂)₆–NH₂  +  n HOOC–(CH₂)₄–COOH
        diamine                 diacid
   →  H–[ NH–(CH₂)₆–NH–CO–(CH₂)₄–CO ]ₙ–OH  +  (2n−1) H₂O
                    nylon 6,6

Mechanistically each step is nucleophilic acyl substitution: the amine lone pair attacks the carbonyl carbon of the acid (or its activated derivative), a tetrahedral intermediate forms, and the −OH leaves as water. Critically, the product still has reactive ends — an amine on one terminus, a carboxyl on the other — so it is itself a monomer for the next step. There is no privileged "growing end"; a 50-mer and a 50-mer can fuse into a 100-mer just as readily as two monomers form a dimer.

Because every condensation here splits out water, step-growth is usually (not always) a condensation polymerization. To push conversion past 99% you must drag that water out — industrial nylon and PET are finished under vacuum at 250–285 °C precisely to strip the by-product and shift the equilibrium toward chain.

Chain-growth: an active end eating monomer

Chain-growth needs monomers with a reactive π bond — overwhelmingly a vinyl group, C=C. The mechanism runs in three distinct kinetic stages, shown here for free-radical polymerization of styrene with a peroxide or AIBN initiator:

INITIATION    I → 2 R•                       (kd ≈ 10⁻⁵ s⁻¹, slow)
              R•  +  CH₂=CHPh → R–CH₂–CHPh•

PROPAGATION   ~CH₂–CHPh•  +  CH₂=CHPh
                  → ~CH₂–CHPh–CH₂–CHPh•       (kp ≈ 10²–10³ M⁻¹s⁻¹)
              ...repeats 10³–10⁴ times in well under a second

TERMINATION   2 ~CHPh•  →  dead polymer        (kt ≈ 10⁷–10⁸ M⁻¹s⁻¹)
                  (combination or disproportionation)

The radical adds to the less-substituted carbon of the alkene, generating the more stabilized radical on the substituted carbon (the same Markovnikov-style regioselectivity that gives head-to-tail chains). Each addition consumes the monomer's double bond and regenerates an active end, so the chain keeps eating monomer until two radicals meet and quench each other.

The numbers tell the whole story. Termination (kt ≈ 10⁷–10⁸ M⁻¹s⁻¹) is roughly a million times faster than propagation (kp ≈ 10²–10³ M⁻¹s⁻¹), so the steady-state radical concentration is tiny (~10⁻⁸ M). A given chain lives about one second, during which it adds thousands of monomers, then dies forever. At any instant the flask is a mix of finished high polymer and untouched monomer — there is essentially no oligomer in between. That is the kinetic fingerprint that distinguishes chain-growth from step-growth at a glance.

The Carothers equation: why step-growth molar mass crawls

The single most useful equation in step-growth is Wallace Carothers' relation between the number-average degree of polymerization Xₙ and the fractional conversion p of functional groups:

Xₙ = 1 / (1 − p)        (equal stoichiometry)

p = 0.50  →  Xₙ = 2      (mostly dimers)
p = 0.90  →  Xₙ = 10     (short oligomers, brittle goo)
p = 0.95  →  Xₙ = 20
p = 0.99  →  Xₙ = 100    (usable fiber)
p = 0.999 →  Xₙ = 1000   (high-strength)

Read that table again: getting from a useless oligomer (Xₙ = 10) to a fiber-grade polymer (Xₙ = 100) means dragging conversion from 90% to 99% — the last 9% of reactions does as much for chain length as the first 90% did. This is the defining hardship of step-growth and the reason every commercial process obsesses over driving the reaction to completion.

Stoichiometry is just as unforgiving. If the two monomers are present in a ratio r < 1, the corrected expression is:

Xₙ = (1 + r) / (1 + r − 2rp)

At full conversion (p = 1):   Xₙ = (1 + r)/(1 − r)
  r = 1.00  →  Xₙ = ∞ (in principle)
  r = 0.99  →  Xₙ = 199    (1% imbalance caps it)
  r = 0.98  →  Xₙ = 99
  r = 0.95  →  Xₙ = 39

A mere 1% excess of one monomer ceilings the chain at ~200 units no matter how long you cook it, because the chains end up capped on both ends by the excess group. Chain-growth has no analogue of this — its molar mass is set by the ratio of propagation to termination/transfer, not by mixing two feeds in exact balance.

Side-by-side: step-growth vs chain-growth

	Step-growth	Chain-growth
What can react	Any two molecules with reactive ends	Monomer + one active center only
Monomer type	Difunctional (diol, diacid, diamine, diisocyanate)	Vinyl C=C or strained ring
Active species	None — all ends equivalent	Radical, cation, or anion
Molar mass vs time	Rises slowly; high only near 100% conversion	High from the first percent of conversion
Mid-reaction mixture	Broad spread of oligomers, little monomer left	Finished polymer + untouched monomer; little oligomer
Governing law	Carothers Xₙ = 1/(1−p)	Kinetic chain length ν = kp[M]/(2(fkdkt[I])^½)
Ideal dispersity Đ	→ 2.0 (Flory most-probable)	1.5–2 (radical); ~1.05 (living/anionic)
By-product	Often a small molecule (H₂O, HCl, CH₃OH)	None — atoms conserved
Stoichiometry	Must be balanced to <0.1% for high Mn	Insensitive — no second feed to balance
Typical T / time	200–285 °C, hours, vacuum to remove by-product	40–90 °C, seconds–minutes per chain
Examples	Nylon, PET, polycarbonate, polyurethane, epoxy	Polyethylene, PVC, polystyrene, PMMA, PP

Real numbers behind the two molar-mass curves

The contrast is sharpest if you watch molar mass against conversion. In step-growth, average molar mass tracks 1/(1−p): negligible until p > 0.9, then it shoots up. In chain-growth, the instantaneous chains formed at 2% conversion are essentially as long as those formed at 80% — what changes with time is how many dead chains you have accumulated, not their individual length.

A worked free-radical kinetic chain length, ν, the average number of monomers added before termination:

ν = kp[M] / (2·(f·kd·kt·[I])^½)

Take styrene at 60 °C:
  kp = 176 M⁻¹s⁻¹,  kt = 7.2×10⁷ M⁻¹s⁻¹
  kd(AIBN) = 9.1×10⁻⁶ s⁻¹,  f = 0.6
  [M] = 8.7 M (bulk),  [I] = 0.01 M

  ν = 176 · 8.7 / (2·(0.6 · 9.1×10⁻⁶ · 7.2×10⁷ · 0.01)^½)
    = 1531 / (2 · (3.93)^½)
    = 1531 / (2 · 1.98)
    ≈ 386 monomers per chain (before transfer)

Lower the initiator and ν climbs (the denominator shrinks with [I]^½); raise the temperature and the radicals are made faster but also die faster — the trade-offs all live inside that one square root. None of these levers appear in step-growth, where molar mass is dictated by p and r alone.

Dispersity: the Flory limit and the living exception

Step-growth at full conversion converges on the Flory most-probable distribution. The probability a chain has exactly i units is (1−p)·pⁱ⁻¹, which makes the dispersity Đ = Mw/Mn = 1 + p. As p → 1, Đ → exactly 2.0. There is no way around this for a simple step-growth — broadness is baked into the statistics of random pairing.

Chain-growth dispersity depends on how chains die. Termination by combination gives Đ ≈ 1.5; by disproportionation, Đ ≈ 2.0; chain transfer broadens it further; and the autoacceleration (Trommsdorff–Norrish) gel effect — where rising viscosity throttles termination but not propagation — can balloon real radical polymers to Đ = 5–10.

The dramatic exception is living polymerization: anionic chains (initiated by butyllithium on styrene, for instance) and controlled-radical methods (ATRP, RAFT, NMP) start every chain at nearly the same instant and let them all grow for the same time with no termination. The result is a Poisson-narrow distribution with Đ as low as 1.02–1.05 — the basis of block copolymers and precision materials. Living polymerization is what lets you set the molar mass simply by the monomer-to-initiator ratio: Xₙ = [M]/[I].

Where each mechanism shows up

• Step-growth in your clothes and bottles. Polyester (PET) — diacid + diol, ~70 million tonnes/year — is step-growth, finished at 280 °C under vacuum to reach Mn ≈ 20,000. Nylon 6,6 (diamine + diacid) makes carpet and airbags. Polycarbonate (bisphenol A + phosgene, losing HCl) makes eyewear and CD substrates.
• Step-growth without losing a small molecule. Polyurethane (diisocyanate + diol) is step-growth but not a condensation — the −N=C=O simply adds across the −OH, conserving every atom. Epoxy resins (epichlorohydrin + bisphenol A) cure the same way. This is why "step-growth" and "condensation" are not synonyms.
• Chain-growth in packaging. Polyethylene (~110 million tonnes/year) and polypropylene are chain-growth additions of ethylene and propylene; PVC (vinyl chloride), polystyrene, and PMMA (Plexiglas) are radical chain-growth of vinyl monomers. None of them lose a by-product — the C=C simply opens.
• Coordination chain-growth. Ziegler–Natta and metallocene catalysts run chain-growth at a metal center, inserting one monomer at a time with stereocontrol — that is how isotactic polypropylene and HDPE are made, and why Ziegler–Natta catalysis earned a Nobel Prize.

Common misconceptions and pitfalls

• Equating step-growth with condensation. The mechanism axis (step vs chain) and the by-product axis (condensation vs addition) are independent. Polyurethane is step-growth addition; most chain-growth is addition too. Don't assume "loses water" — check whether any two molecules can couple.
• Thinking step-growth makes long chains early. At 90% conversion you still only have Xₙ = 10. Beginners expect a "polymer" to form fast; step-growth spends most of the run as a sticky oligomer soup and only becomes useful in the last fraction of a percent.
• Ignoring stoichiometric balance. A 2% monomer imbalance or a trace of monofunctional impurity caps step-growth molar mass at a few hundred. Chain-growth doesn't care about feed balance because there is only one monomer adding to active ends.
• Assuming higher temperature always helps. In chain-growth, hotter means faster initiation and faster termination, so ν (and molar mass) usually drops with temperature. In step-growth, heat mainly serves to drive off by-product and raise conversion — opposite intuitions.
• Confusing degree of polymerization with molar mass. Xₙ counts repeat units; Mn = Xₙ × M₀ where M₀ is the repeat-unit mass (or the average of the two monomer residues in step-growth). Reporting "Xₙ = 100" without the repeat mass tells you nothing about whether it is a fiber or a wax.
• Believing dispersity is a quality defect. Đ = 2 is the statistical floor for simple step-growth and the norm for radical chain-growth — it is physics, not sloppiness. Only living methods beat it, and even then narrow Đ is a feature you pay for, not a baseline expectation.