CHEM2522 · Sustainable Chemical Manufacture
Step-Growth Polymerisation
Week 8 covers step-growth (condensation) polymerisation: how difunctional monomers react in stepwise fashion so that chains grow slowly and high molar mass appears only at very high conversion. The Carothers equation, DP = 1/(1 - p), and its stoichiometric-imbalance form are the examinable quantitative core, and you meet the commodity polymers made this way — PET, the nylons, Kevlar, polycarbonate and polyurethane. Exam questions combine a Carothers calculation with mechanism and polymer-identification parts.
What this chapter covers
- 01Step-growth vs chain-growth: all chain sizes coexist and grow slowly (no fast active centre)
- 02Polycondensation (loses a small molecule, e.g. water) vs polyaddition (no by-product, e.g. polyurethane)
- 03The Carothers equation: DPn = 1/(1 - p), where p is the fractional conversion of functional groups
- 04Dispersity for step-growth: Đ = 1 + p, approaching 2 at high conversion
- 05Stoichiometric imbalance: DPn = (1 + r)/(1 + r - 2rp); an excess of one monomer caps the DP
- 06Polyesters (PET) and their reversible hydrolytic depolymerisation; polyamides (Nylon-6, Nylon-6,6, Kevlar)
- 07Polycarbonate (BPA + phosgene) and polyurethane (isocyanate + alcohol, no by-product; CO2-blown foams)
- 08Polymerisation processes: bulk (gel effect), solution, suspension, emulsion
Carothers equation: conversion, dispersity and stoichiometric imbalance
- +1Balanced case, DP from Carothers: DPn = 1/(1 - p) = 1/(1 - 0.99) = 1/0.01 = 100.
- +1Dispersity at that conversion: Đ = 1 + p = 1 + 0.99 = 1.99 (step-growth dispersity approaches 2 at high conversion).
- +1Imbalanced case at full conversion: put p = 1 into DPn = (1 + r)/(1 + r - 2rp) = (1 + r)/(1 - r) = (1 + 0.98)/(1 - 0.98) = 1.98/0.02 = 99.
- +1Comment: with a 2% imbalance, even complete conversion caps DPn at 99 (each chain runs out because the deficient monomer is exhausted). High molar mass in step-growth therefore needs BOTH near-perfect stoichiometry AND very high conversion — either alone is not enough.
Key terms
- Step-growth polymerisation
- Polymerisation in which difunctional monomers react stepwise (e.g. esterification, amidation), so all chain sizes coexist and molar mass climbs only near full conversion — unlike chain-growth, which has fast, low-concentration active centres.
- Carothers equation
- DPn = 1/(1 - p), relating the number-average degree of polymerisation to the fractional conversion p of functional groups; high DP demands p very close to 1.
- Stoichiometric imbalance (r)
- The ratio of the two monomers' functional groups; a deviation from 1:1 caps molar mass via DPn = (1 + r)/(1 + r - 2rp), because the deficient monomer is used up first.
- Polycondensation vs polyaddition
- Polycondensation loses a small molecule each bond-forming step (e.g. water in polyester formation); polyaddition forms bonds with no by-product (e.g. the isocyanate + alcohol reaction of polyurethane).
- PET (poly(ethylene terephthalate))
- A polyester of terephthalic acid and ethylene glycol, made industrially in two stages; its ester bonds are reversible, allowing hydrolytic or enzymatic depolymerisation back to monomer.
- Kevlar
- Poly(p-phenylene terephthalamide), an aramid made from terephthaloyl chloride and p-phenylenediamine; its strength comes from extensive hydrogen bonding and aromatic pi-stacking between rigid chains.
Step-Growth Polymerisation FAQ
Why does step-growth need such high conversion for high molar mass?
Because in step-growth every functional group has to react to link chains, and the Carothers equation DPn = 1/(1 - p) is brutally sensitive near p = 1: p = 0.90 gives DP = 10, p = 0.99 gives DP = 100, p = 0.999 gives DP = 1000. Below ~99% conversion you only have oligomers. That is very different from chain-growth, where high molar mass appears almost immediately.
How does a stoichiometric imbalance limit the chain length?
If one monomer is in excess, chains eventually have that monomer's group on both ends and cannot grow further once the deficient monomer is exhausted. The imbalance form DPn = (1 + r)/(1 + r - 2rp) captures this: even at p → 1 the DP is capped at (1 + r)/(1 - r). A 1% excess (r = 0.99) caps DP near 199; a 2% excess near 99. So you need to weigh the monomers very accurately, and a monofunctional impurity has the same capping effect.
What is the difference between polycondensation and polyaddition?
Both are step-growth, but polycondensation expels a small molecule at each linkage (water in polyester and polyamide formation), whereas polyaddition forms the bond with no by-product. Polyurethane (isocyanate + alcohol) is the classic polyaddition — 100% atom economy for the linkage — while PET and the nylons are polycondensations. Naming the right category and its by-product is a common short-answer mark.
Can Sia help me with Carothers calculations and step-growth mechanisms?
Yes. Sia can walk you through DPn = 1/(1 - p) and the stoichiometric-imbalance form, tabulate DP and Đ against conversion, and check your esterification or amidation mechanism arrows. It explains the method and checks your reasoning step by step; it does not do graded assessment for you, and University of Sydney academic-integrity rules apply.
Exam move
Make the Carothers equation reflexive: DPn = 1/(1 - p) for the balanced case, Đ = 1 + p for the dispersity, and DPn = (1 + r)/(1 + r - 2rp) when the monomers are off stoichiometry. Practise both levers — a table of DP against p (0.90, 0.99, 0.999) and against r — so you can instantly see why step-growth needs high conversion and near-perfect stoichiometry. Alongside the maths, keep a compact map of the commodity step-growth polymers: monomers, whether it is polycondensation (by-product) or polyaddition (none), and one structural feature (Kevlar's H-bonding, polyurethane's CO2-blown foam). Exam questions typically bolt a Carothers calculation onto a 'name the polymer and draw the linkage' part, so rehearse the two together from the Week 8 tutorial.
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