MATS3004 · Polymer Science and Engineering 1
Ionic and Step-Growth Polymerization
This chapter contrasts the non-radical routes. Anionic polymerization is stabilized by electron-withdrawing groups and cationic by electron-donating groups (the substituent electronics select the mechanism), while step-growth/condensation joins di-functional monomers into polyesters, polyamides and polyurethanes. The examinable calculation is the Carothers equation Xn = 1/(1−p), including the effect of stoichiometric imbalance — a favourite Mid-term and Final item because it shows why high molar mass needs both high conversion and near-perfect stoichiometry.
What this chapter covers
- 01Anionic polymerization: electron-withdrawing groups (ester, nitrile, phenyl) stabilize the carbanion; initiators are nucleophiles/Lewis bases (n-BuLi)
- 02Cationic polymerization: electron-donating groups (alkoxy, alkyl, phenyl) stabilize the carbocation; initiators are electrophiles/Lewis acids (BF₃, AlCl₃)
- 03Monomer-susceptibility logic (Young & Lovell Table 5.1): which monomers go radical / cationic / anionic
- 04Living anionic polymerization: no inherent termination → narrow dispersity and predictable Mn
- 05Step-growth of di-functional monomers: polyester, polyamide, polyurethane, polycarbonate
- 06Carothers equation Xn = 1/(1−p) and dispersity Xw/Xn = 1 + p → 2 at high conversion
- 07Stoichiometric imbalance r = N_A/N_B: Xn = (1+r)/(1+r−2rp); at p = 1, Xn = (1+r)/(1−r)
- 08Applied example: cyanoacrylate 'superglue' cures by rapid anionic polymerization from trace moisture
Carothers degree of polymerization and the cost of stoichiometric imbalance
- +1Balanced case uses the simple Carothers equation Xn = 1/(1−p). At p = 0.99: Xn = 1/(1 − 0.99) = 1/0.01 = 100.
- +1Dispersity for an ideal step-growth polymer is Đ = Xw/Xn = 1 + p = 1 + 0.99 = 1.99, i.e. close to the most-probable value of 2 at high conversion.
- +1Imbalanced case uses Xn = (1+r)/(1+r−2rp). Substitute r = 0.98, p = 0.99: numerator 1 + 0.98 = 1.98; denominator 1.98 − 2(0.98)(0.99) = 1.98 − 1.9404 = 0.0396.
- +1So Xn = 1.98/0.0396 = 50. A mere 2% stoichiometric imbalance halves the chain length (100 → 50) at the same conversion — high molar mass demands both p → 1 and r → 1.
Key terms
- Anionic polymerization
- Chain polymerization through a carbanion active centre, favoured by monomers bearing electron-withdrawing groups (ester, nitrile, phenyl) that stabilize the negative charge. Initiated by nucleophiles/Lewis bases such as n-butyllithium; can be 'living' if impurities are excluded.
- Cationic polymerization
- Chain polymerization through a carbocation active centre, favoured by monomers with electron-donating groups (alkoxy, alkyl, phenyl) that stabilize the positive charge. Initiated by electrophiles/Lewis acids such as BF₃ or AlCl₃.
- Living anionic polymerization
- An anionic polymerization with no inherent termination step, so chains grow until monomer runs out. It gives a very narrow dispersity (Đ → 1), a predictable Mn set by monomer-to-initiator ratio, and access to well-defined block copolymers by sequential monomer addition.
- Extent of reaction (p)
- The fraction of functional groups that have reacted in a step-growth polymerization. Because Xn = 1/(1−p) for balanced stoichiometry, molar mass climbs steeply only as p approaches 1.
- Carothers equation
- For step-growth polymerization the number-average degree of polymerization Xn = 1/(1−p) (balanced stoichiometry), with dispersity Đ = 1 + p → 2 at high conversion. High molar mass requires both high conversion and near-perfect stoichiometry.
- Stoichiometric imbalance (r)
- The ratio r = N_A/N_B (≤ 1) of the two monomers' functional groups. It caps the achievable chain length: Xn = (1+r)/(1+r−2rp), and at full conversion Xn = (1+r)/(1−r), so even a small excess of one reagent sharply limits molar mass.
Ionic and Step-Growth Polymerization FAQ
How do I decide whether a monomer polymerizes anionically or cationically?
Look at the substituent on the C=C. An electron-withdrawing group — an ester, nitrile, carbonyl or phenyl — pulls electron density off the double bond and stabilizes a negative charge, so the monomer is prone to anionic polymerization initiated by a nucleophile or Lewis base. An electron-donating group — an alkoxy, alkyl or phenyl — pushes electron density in and stabilizes a positive charge, so the monomer favours cationic polymerization initiated by a Lewis acid. Some monomers, like styrene and the dienes, are balanced enough to go by all three routes (radical, cationic and anionic).
Why does step-growth need such high conversion for high molar mass?
Because chain length in step-growth is tied directly to conversion by Xn = 1/(1−p). At p = 0.90 you only reach Xn = 10; at p = 0.99, Xn = 100; at p = 0.999, Xn = 1000. The chains only become useful macromolecules in the last fraction of a percent of reaction. This is the opposite of chain polymerization, where individual chains reach high molar mass almost instantly and conversion just increases how many chains exist.
Why does a small excess of one monomer ruin the molar mass?
Because the excess reagent eventually caps every chain end with the same group, and two identical groups cannot react with each other. Once the limiting monomer is used up, growth stops. The Carothers form Xn = (1+r)/(1−r) at full conversion shows this quantitatively: r = 0.99 gives Xn = 199, but r = 0.98 gives only Xn = 99. Getting the stoichiometry as close to 1:1 as possible is therefore just as important as driving the conversion high.
Why does superglue set so fast?
Cyanoacrylate, the monomer in superglue, carries two strong electron-withdrawing groups (an ester and a nitrile) on the same carbon, which makes it extremely susceptible to anionic polymerization. Trace surface moisture or hydroxide — a weak nucleophile — is enough to initiate it, so a thin film polymerizes almost instantly on contact with skin or most surfaces. It is a vivid worked example of the substituent-electronics rule: strong EWGs give an ultra-reactive anionic monomer.
Exam move
Split your revision in two. For the ionic route, drill the substituent-electronics rule until it is reflexive — EWG stabilizes a carbanion (anionic, needs a nucleophile/base); EDG stabilizes a carbocation (cationic, needs a Lewis acid) — and memorise a few worked cases (styrene = all three; cyanoacrylate = anionic; isobutylene = cationic). For the step-growth route, make the Carothers calculations automatic: Xn = 1/(1−p) only when r = 1, otherwise Xn = (1+r)/(1+r−2rp), plus Đ = 1 + p. Practise the sensitivity — carry p to enough decimals and show how a 1-2% imbalance slashes Xn — because that reasoning is the marked insight. Keep the linkage map (polyester/polyamide/polyurethane/polycarbonate) from the previous chapter handy, since step-growth questions often ask you to name the product too. Confirm the assessed formula set on the UNSW course outline / Moodle.
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