MATS3004 · Polymer Science and Engineering 1
Polymerization Thermodynamics and Ceiling Temperature
Lecture 4 explains why polymerization is feasibility-limited: the ΔG = ΔH − TΔS balance, the ceiling temperature Tc = ΔH/ΔS at which propagation and depropagation cancel, and the Trommsdorff (autoacceleration) effect. It also compares the practical free-radical processes — bulk, solution, suspension and emulsion. A recurring exam item gives a monomer's ΔH and ΔS and asks you to compute Tc and judge whether a target molar mass is achievable at a stated temperature.
What this chapter covers
- 01Gibbs free energy of polymerization ΔG = ΔH − TΔS; chain polymerization of a C=C is exothermic (ΔH < 0) but loses entropy (ΔS < 0)
- 02Ceiling temperature Tc = ΔH/ΔS: above Tc depropagation dominates and no high-molar-mass polymer forms
- 03Reading a monomer ΔH/ΔS table to rank ceiling temperatures (α-methylstyrene is low, vinyl acetate high)
- 04Temperature effect on kinetics: raising T increases Rp but decreases Xn (shorter chains)
- 05Autoacceleration / Trommsdorff (gel) effect — kt falls at high conversion, so rate and molar mass surge
- 06Bulk polymerization: monomer + soluble initiator; simple but poor heat removal, high viscosity
- 07Solution polymerization: solvent lowers viscosity but lowers rate/DP and adds chain transfer
- 08Suspension (filterable beads) and emulsion (a latex; high rate and high molar mass together)
Compute a ceiling temperature and judge feasibility
- +1At the ceiling temperature propagation and depropagation are in balance, so ΔG = 0 and ΔH = Tc·ΔS, giving Tc = ΔH/ΔS. Keep units consistent: convert ΔH to J·mol⁻¹ so it matches ΔS in J·K⁻¹·mol⁻¹.
- +1Substitute: Tc = (−35 000 J·mol⁻¹) / (−104 J·K⁻¹·mol⁻¹) = 336.5 K. Convert: 336.5 − 273.15 ≈ 63 °C.
- +1Compare the run temperature to Tc: 80 °C = 353 K, which is above Tc = 336.5 K (≈ 63 °C).
- +1Above Tc the free energy of propagation ΔG = ΔH − TΔS becomes positive (TΔS outweighs ΔH), so depropagation dominates over propagation. The student will not obtain high-molar-mass polymer at 80 °C — they must run below about 63 °C.
Key terms
- Gibbs free energy of polymerization (ΔG)
- ΔG = ΔH − TΔS for adding monomer to a chain. Polymerization proceeds only while ΔG < 0. A C=C addition is exothermic (ΔH < 0) but orders the monomer into a chain (ΔS < 0), so the entropy term opposes it and grows with temperature.
- Ceiling temperature (Tc)
- The temperature at which propagation and depropagation balance, ΔG = 0, so Tc = ΔH/ΔS. Below Tc high polymer forms; above Tc depropagation dominates and only monomer or short chains survive.
- Autoacceleration (Trommsdorff/gel effect)
- At high conversion the medium becomes very viscous, so diffusion-controlled bimolecular termination slows (kt drops sharply) while kp is little affected. Rate and molar mass surge suddenly, which can cause a runaway exotherm in bulk polymerization.
- Bulk polymerization
- Polymerization of neat monomer with a monomer-soluble initiator. It is simple and gives a pure product, but heat removal is poor and the viscosity becomes very high, making the Trommsdorff effect a hazard.
- Suspension polymerization
- Monomer plus initiator suspended as droplets in an inert (usually aqueous) medium; each droplet is a mini bulk reactor. The product is filterable beads, though it may carry traces of the dispersion stabilizer.
- Emulsion polymerization
- Initiator is soluble in the medium but not in the monomer, and polymerization occurs in surfactant micelles to give a latex (a stable aqueous dispersion). Uniquely, it can deliver high rate and high molar mass at the same time.
Polymerization Thermodynamics and Ceiling Temperature FAQ
What is the ceiling temperature and why does it exist?
The ceiling temperature Tc is the temperature above which a monomer will not form high-molar-mass polymer. Adding a C=C monomer to a chain releases heat (ΔH < 0) but reduces disorder (ΔS < 0), so the free energy ΔG = ΔH − TΔS has a favourable enthalpy term fighting an unfavourable entropy term that grows with T. At Tc = ΔH/ΔS the two exactly cancel (ΔG = 0); above it the entropy term wins, ΔG turns positive, and depropagation (chains shedding monomer) dominates over propagation.
Does raising temperature always speed polymerization up?
It speeds the rate but shortens the chains, and only up to the ceiling. Higher temperature raises Rp (initiation and propagation accelerate), yet it lowers the degree of polymerization Xn because chains terminate sooner — so you trade molar mass for speed. And once you cross Tc, depropagation takes over and you get essentially no high polymer at all. That is why molar-mass-sensitive polymerizations are run cool and well below the monomer's ceiling temperature.
Which polymerization process should I choose, and why?
It depends on the trade-off you need. Bulk is simplest and purest but suffers poor heat removal and high viscosity. Solution cuts the viscosity but lowers rate and molar mass and adds chain transfer to solvent. Suspension gives easily filtered beads in water. Emulsion is the standout when you want both high rate and high molar mass simultaneously, delivering a latex. Matching process to the required product form, purity and molar mass is the examinable reasoning.
How is thermodynamics examined in MATS3004?
Most often as a ceiling-temperature calculation-and-judgement: you are given ΔH and ΔS, asked to compute Tc = ΔH/ΔS, then to decide whether a run at a stated temperature can make high polymer. Marks reward consistent units (convert kJ to J), the correct comparison to Tc, and a ΔG-based explanation. You may also be asked to compare processes or to explain the Trommsdorff effect. Confirm the assessed scope on the UNSW course outline / Moodle.
Exam move
Drill the ceiling-temperature routine until it is automatic: convert ΔH to joules, divide by ΔS, convert Tc to °C, compare to the run temperature, and justify with ΔG = ΔH − TΔS. Keep a mental ranking from the monomer ΔH/ΔS table — low-|ΔH| monomers like α-methylstyrene have low, easily-exceeded ceilings, while vinyl acetate sits very high — so you can sanity-check a computed Tc. Pair the thermodynamics with the temperature-kinetics rule (hotter = faster Rp but shorter Xn) because the exam likes to combine them. Be able to contrast bulk/solution/suspension/emulsion on viscosity, heat removal, product form and molar mass in a sentence each, and to explain the Trommsdorff effect as a fall in kt at high conversion. Confirm the examinable data and any provided constants on the UNSW course outline / Moodle.
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