Organic Chemistry · Synthetic Polymers

Step-Growth Polymers

9 min read

Lab safety note: diacids, diamines, and diols can be corrosive or irritating; polymerization at elevated temperature requires proper ventilation, heat control, and PPE per institutional rules (general principles only). The Carothers equation and its conversion dependence, the balanced-stoichiometry requirement, and the PET/nylon-6,6 monomer identities are standard textbook polymer chemistry (W. H. Carothers, DuPont, 1930s). The approximate non-stoichiometric DP estimate in Example 2 is a textbook limiting-reagent treatment; actual industrial processes control stoichiometry far more tightly.

On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

builds polymers by the stepwise reaction of functional groups: any molecule bearing the right functional groups can react with any other, dimer forming trimer, trimer adding to pentamer, and so on. The classic reactions are esterification (a diacid + a diol → ) and amidation (a diacid + a diamine → ). — made from adipic acid and hexamethylenediamine — and PET (polyethylene terephthalate, from terephthalic acid and ethylene glycol) are the flagship products, alongside polycarbonates and polyurethanes.

The defining contrast with chain growth (Topic 1) is kinetics. In step growth, molecular weight builds up slowly and only becomes high at very high conversion: a chain of 100 units requires 99 successful coupling events, each depending on the same statistical coupling of functional groups. Early in the reaction the mixture is full of short oligomers; only when 99%+ of the functional groups have reacted do chains become long. The relationship between conversion p (fraction of functional groups that have reacted) and the average degree of polymerization is the :

$DP = 1 1 - p$

This single equation is the heart of the topic: it says that to reach DP = 100, you need p = 0.99 — 99% conversion. It also explains why step-growth polymers are almost always made with exactly balanced stoichiometry and why industrial processes drive water (or other small molecules) out of the reaction to push conversion higher.

Why this matters

The fibers and bottles of everyday life. Nylon (stockings, ropes, parachutes, carpets) and PET (drink bottles, polyester clothing) are step-growth products. Knowing how they form explains their strength (amide and ester linkages, hydrogen bonding in nylon) and their recycling codes (PET is #1).
Stoichiometry is everything. If the diacid and diol are not exactly equimolar, the extra monomer caps the chains and the polymer is uselessly short. This is a real industrial constraint that the Carothers equation makes quantitative.
Kevlar and engineering polymers. Step growth also makes high-performance aramids (Kevlar) and polycarbonates (shatter-resistant glazing, CDs). The rigid aromatic units give strength and heat resistance.
Exam staples. Carothers-equation calculations, identifying the monomers from a repeat unit, and explaining why high conversion is required are among the most-tested polymer concepts.

The college version

Core Concepts

How chains grow: any two species can react

A step-growth reaction mixture contains monomers, dimers, trimers, and longer chains simultaneously, and any pair bearing complementary functional groups can couple. Monomer + monomer → dimer; dimer + monomer → trimer; dimer + dimer → tetramer; trimer + pentamer → octamer; and so on. Because every coupling is the same chemistry (e.g., esterification), the rate of each step is similar, and the distribution of chain lengths broadens steadily. No reactive "center" exists — that is the essential difference from chain growth.

The Carothers equation: conversion controls chain length

If p is the fraction of functional groups that have reacted, the average degree of polymerization is:

$DP = 1 1 - p$

The consequences are dramatic:

p = 0.90 → DP = 10 (a useless oligomer).
p = 0.99 → DP = 100 (a useful low polymer).
p = 0.999 → DP = 1000 (a high polymer).

High molecular weight demands near-quantitative conversion, which is why step-growth reactions are run with catalysts, elevated temperature, and removal of the byproduct (water) to drive the equilibrium.

Stoichiometry: the one-to-one requirement

If the two monomers are not present in exactly equal amounts, the excess monomer terminates chains. With a 1% excess of diacid over diamine, the diamine runs out while diacid remains, and every chain ends with an unreactive acid group. The Carothers equation for non-stoichiometric feeds is modified (the excess acts as a limiting "capping" group), but the lesson is simple: balance the monomers, or the DP collapses. This is why industrial nylon manufacture meters the two monomers with great precision.

Polyesters and polyamides: the two flagship families

PET: terephthalic acid (HOOC–C₆H₄–COOH) + ethylene glycol (HO–CH₂CH₂–OH) → polyester with repeat unit –O–CH₂CH₂–O–C(=O)–C₆H₄–C(=O)–, releasing water. PET's ester groups are susceptible to hydrolysis at high temperature and are recyclable by depolymerization.
Nylon-6,6: adipic acid (HOOC–(CH₂)₄–COOH) + hexamethylenediamine (H₂N–(CH₂)₆–NH₂) → polyamide with repeat unit –NH–(CH₂)₆–NH–C(=O)–(CH₂)₄–C(=O)–, releasing water. The "6,6" names the six-carbon diamine and six-carbon diacid. Nylon's strength comes from dense hydrogen bonding between amide groups in aligned chains.

Condensation chemistry and byproducts

Most step-growth reactions are condensation polymerizations: each coupling eliminates a small molecule (water, methanol, HCl). The byproduct must be removed to drive the equilibrium toward polymer (Le Chatelier's principle). Note that the term "condensation" describes the byproduct release, while "step-growth" describes the mechanism — a distinction that matters because some condensation reactions are not step-growth and some step-growth reactions (e.g., ring-opening) release no byproduct.

Branched and cross-linked step growth

If a monomer has more than two functional groups (e.g., glycerol, a triol), the polymer can branch and eventually cross-link into a network — the basis of alkyd resins and epoxy thermosets. Cross-linked networks do not melt or dissolve, which is why thermosets cannot be recycled like thermoplastics.

Common Confusions

Do Not Confuse	With	Difference
Step growth	Chain growth	Step growth: any two species couple, MW builds at the end (Carothers); chain growth: monomer adds to a reactive end, high MW appears early
Condensation	Step growth	Condensation = small molecule eliminated (byproduct view); step growth = mechanism (any-species coupling). Not all condensations are step growth and vice versa
Conversion p	Yield	p is the fraction of functional groups reacted, not the isolated yield of polymer; DP depends on p, not on yield
Nylon-6,6	Nylon-6	Nylon-6,6 = two monomers (diacid + diamine, both 6 carbons); nylon-6 = one monomer (caprolactam, ring-opening chain growth)
Polyester	Polyamide	Ester links (–COO–) vs amide links (–CONH–); nylon's amides hydrogen-bond, making it stronger than most polyesters

Eli explains

The same idea, in plain words

Explain it like I’m 10

Step-growth polymerization is like building a paper chain by linking any two pieces you have: two single links join, then that pair joins another pair, and the chain grows a little at a time. You need almost every link to be joined before you get a long chain — if even a few links are missing, you're stuck with lots of short chains.

Worked example

Example 1: Carothers equation in action

Problem. A polyesterification is run to 95% conversion. What is the average degree of polymerization, and how many repeat units would a DP of 200 require?

Step 1 — Apply the Carothers equation at p = 0.95.

$DP = 1 1 - p = 1 1 - 0.95 = 1 0.05 = 20$

Step 2 — Solve for the conversion needed at DP = 200. Rearrange:

$200 = 1 1 - p \Rightarrow 1 - p = 1200 = 0.005 \Rightarrow p = 0.995$

Answer. At 95% conversion, DP = 20 (an oligomer). A DP of 200 requires p = 0.995 — 99.5% of all functional groups must react, showing why industrial step growth is pushed to near-completion.

Example 2: The cost of unbalanced stoichiometry

Problem. A nylon-6,6 polymerization is charged with 100.0 mol of adipic acid and 99.0 mol of hexamethylenediamine. Explain qualitatively what happens to the molecular weight and why.

Step 1 — Identify the limiting reagent. The diamine (99.0 mol) is the limiting reagent; 1.0 mol of diacid is in excess.

Step 2 — Trace the consequence. Every chain that forms an amide at both ends of a diamine unit eventually terminates: once the diamine is consumed, the remaining diacid cannot couple with anything — it caps every chain end with an unreacted –COOH group.

Step 3 — State the result. The average chain length is severely limited (roughly, DP ≈ (2 × 99.0)/(100.0 − 99.0) + 1 ≈ 199 by the standard non-stoichiometric formula, far below the thousands needed for fiber-grade nylon). The polymer is too short to draw into strong fibers.

Answer. The 1% excess of diacid caps the chains, collapsing molecular weight; balanced stoichiometry is essential for useful nylon.

Example 3: Identifying monomers from a repeat unit

Problem. A polyester has the repeat unit –O–CH₂CH₂–O–C(=O)–C₆H₄–C(=O)–. Identify the two monomers and the byproduct.

Step 1 — Split the repeat unit at the ester links. The unit contains an –O–CH₂CH₂–O– fragment (from a diol) and a –C(=O)–C₆H₄–C(=O)– fragment (from a diacid).

Step 2 — Name the monomers. Ethylene glycol (HO–CH₂CH₂–OH) and terephthalic acid (HOOC–C₆H₄–COOH).

Step 3 — State the byproduct. Each ester link releases one water molecule.

Answer. PET from ethylene glycol + terephthalic acid, eliminating water — the polyester of bottles and polyester fabric.

Key takeaways

Step growth: any two species with complementary functional groups couple; no reactive chain end; molecular weight builds slowly and needs very high conversion.
Carothers equation: DP = 1/(1-p). p = 0.99 → DP = 100; p = 0.999 → DP = 1000.
Stoichiometry must be exactly balanced — a small excess of one monomer caps chains and collapses molecular weight.
Flagship products: PET (terephthalic acid + ethylene glycol, a polyester) and Nylon-6,6 (adipic acid + hexamethylenediamine, a polyamide).
Step growth is usually condensation (small molecule eliminated); the byproduct must be removed to drive the equilibrium.
Multifunctional monomers (triols, triacids) give branched/cross-linked thermosets that cannot be remelted.
Contrast: chain growth gives high MW early; step growth gives high MW only at the end.

Check yourself

6 review questions from the chapter. Try each one, then open the answer.

Write the Carothers equation and compute DP at p = 0.98.
Show answer
DP = 1/(1-p); at p = 0.98, DP = 1/0.02 = 50.
Why does step-growth molecular weight stay low until very high conversion?
Show answer
Because chain length grows by statistical coupling of functional groups: reaching DP = 1000 requires 999 successive couplings, and the average length only climbs when nearly all functional groups have reacted.
What happens to nylon molecular weight if the diamine is charged 2% short, and why?
Show answer
The diamine runs out first, leaving excess diacid to cap every chain end with –COOH; the average chain length is severely limited and the polymer is too short for strong fibers.
Name the monomers and repeat-unit linkage of PET and of nylon-6,6.
Show answer
PET: ethylene glycol + terephthalic acid, ester links (–C(=O)–O–). Nylon-6,6: hexamethylenediamine + adipic acid, amide links (–C(=O)–NH–).
Why must the condensation byproduct be removed during the reaction?
Show answer
Esterification and amidation are equilibria; removing the small-molecule byproduct (water) shifts the equilibrium toward polymer (Le Chatelier), raising conversion and therefore DP.
What structural feature converts a step-growth polymer into a ?
Show answer
Monomers with more than two functional groups (e.g., a triol) allow branching that links chains into a cross-linked network, which cannot melt or dissolve.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

Step-growth polymerization: Polymerization by random coupling of functional groups on any two molecules
Condensation polymerization: Step growth that eliminates a small molecule per coupling
Carothers equation: DP = 1/(1-p), relating conversion to chain length
Conversion p: Fraction of functional groups that have reacted
Polyester: Polymer with –C(=O)–O– links (diacid + diol)
Polyamide: Polymer with –C(=O)–NH– links (diacid + diamine)
Nylon-6,6: Polyamide of adipic acid + hexamethylenediamine
Thermoset: Cross-linked network polymer that cannot be remelted

Sources & references

openstax.org — Organic Chemistry

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