Chemistry · Organic chemistry · Year 3

Polymer synthesis and kinetics

Why does adding more initiator make the polymer form faster, yet with shorter chains?

The situation

At the Ustyurt gas chemical complex, ethane and propane from natural gas are turned into ethylene and propylene, and from these hundreds of thousands of tonnes of polyethylene and polypropylene granules are made every year. A polymer is also “born” in a university laboratory: in a dilatometer in a thermostat, styrene slowly contracts, methyl methacrylate turns into organic glass, and a nylon thread is pulled from the boundary between two liquids. Why, when there is more initiator, does the polymer form faster but with shorter chains, whereas in polycondensation long chains appear only when the reaction is almost complete?

Topic

Polymer synthesis: polymerisation and polycondensation. Shurtan and Ustyurt gas-chemical complexes: polyethylene and polypropylene granules from natural gas; in the laboratory, styrene and methyl methacrylate polymerise in ampoules,…

Key ideas

Radical polymerisation
Mayo–Lewis equation
Carothers equation

Formulas

R_{p} = k_{p} [M] {(\frac{f k_{d} [I]}{k_{t}})}^{1 / 2}

Rate of radical polymerisation: first order in monomer, order 0.5 in initiator (radicals terminate in pairs).

ν = \frac{R_{p}}{R_{i}} = \frac{k_{p} [M]}{2 {(f k_{d} k_{t} [I])}^{1 / 2}}, \frac{1}{{\overline{X}}_{n}} = \frac{2 - c}{2 ν} + C_{M} + C_{S} \frac{[S]}{[M]}

Kinetic chain length and the Mayo equation ( $c$ — fraction of recombination, $C$ — chain-transfer constants).

F_{1} = \frac{r_{1} f_{1}^{2} + f_{1} f_{2}}{r_{1} f_{1}^{2} + 2 f_{1} f_{2} + r_{2} f_{2}^{2}}

Mayo–Lewis equation: instantaneous copolymer composition $F_{1}$ from the mixture composition $f_{1}$ .

{\overline{X}}_{n} = \frac{1 + r}{1 + r - 2 r p} \overset{\overset{}{r = 1}}{\to} \frac{1}{1 - p}

Carothers equation; $r = N_{A} / N_{B}$ < 1 — non-equivalence (Korshak rule), $p$ — fraction of groups that have reacted.

T_{c} = \frac{Δ H_{p}}{Δ S_{p}^{\circ} + R \ln [M]}

Ceiling temperature: above it, depolymerisation predominates.

Theory

Polymers: basic concepts and classification

A monomer is a small molecule that forms a polymer; a macromolecule is a chain made of thousands of repeating units; the degree of polymerisation $n$ (or ${\overline{X}}_{n}$ ) is the number of units in the chain, $M = n M_{0}$ . If $n$ ≈ 2–20, it is an oligomer; hundreds to thousands — a polymer. In living nature, proteins, nucleic acids, cellulose and starch are polymers (in cotton cellulose $n$ is from a few thousand to ten thousand). Classification: by origin — natural (rubber, cellulose), artificial (modified natural ones: acetate and viscose fibres) and synthetic; by composition — organic, inorganic (polyphosphazenes, silicates) and organoelement (polysiloxanes −Si(CH₃)₂−O−); by shape — linear, branched and crosslinked (network); by the number of monomer types — homopolymer and copolymer (statistical, alternating, block and graft); by the group in the main chain — polyesters (−COO−), polyacetals (−CH₂O−), polyamides (−CONH−), polyurethanes (−NHCOO−). There are two kinds of synthesis: chain polymerisation (an active centre adds hundreds of monomers in an instant; the mixture contains monomer and large polymer) and step-growth — polycondensation and polyaddition (any two molecules react; the chain lengthens slowly). Compare the two in the molecular window. The school of polymer chemistry in Uzbekistan was begun by Academician Kh. U. Usmonov (chemistry of cotton cellulose); at the Institute of Polymer Chemistry and Physics of the Academy of Sciences of the Republic of Uzbekistan in Tashkent, Academician S. Sh. Rashidova worked on chitosan and polymer composites. Molar mass and the physics of solutions are covered in the “Physics of macromolecules” experiment; a school-level introduction is in the “Polymers, rubber and fibres” experiment.

Radical polymerisation: mechanism, kinetics, thermodynamics

Initiation: the initiator decomposes into radicals — thermally (AIBN: half-life ≈ 10 hours at 65 °C; benzoyl peroxide), by redox pairs (K₂S₂O₈ + NaHSO₃ — low activation energy, works at room temperature), photochemically (UV light + photoinitiator) and by radiation (γ-rays); styrene also initiates itself when heated. $R_{i} = 2 f k_{d} [I]$ , $f$ ≈ 0.5–0.8 — efficiency (the “cage” effect). Propagation: $R - M_{n}^{∙} + M \to R - M_{n + 1}^{∙}$ , $k_{p}$ ≈ 10²–10³ L/(mol·s). Termination: two radicals by recombination (styrene) or disproportionation (mainly MMA); $k_{t}$ ≈ 10⁷–10⁸ L/(mol·s). In the quasi-steady state $R_{i} = 2 k_{t} {[P^{∙}]}^{2}$ , so $R_{p} = k_{p} [M] {(f k_{d} [I] / k_{t})}^{1 / 2}$ — if [I] increases 4 times, the rate increases 2 times, while the kinetic chain length $ν = R_{p} / R_{i}$ decreases 2 times. Chain transfer to monomer, to solvent (with telogens such as CCl₄ — telomerisation, short-chain telomers), to initiator and to regulators (mercaptans, $C$ ≈ 21) only reduces ${\overline{X}}_{n}$ , without changing the rate (Mayo equation). Inhibitors (benzoquinone, hydroquinone, DPPH) capture radicals: until they are used up there is an induction period — from it $R_{i} = z {[Z]}_{0} / t_{i n d}$ is found; retarders (nitrobenzene) reduce the rate. Temperature: the overall activation energy $E = E_{p} + E_{d} / 2 - E_{t} / 2$ ≈ 80–90 kJ/mol (the rate increases), for ${\overline{X}}_{n}$ it is $E_{p} - E_{d} / 2 - E_{t} / 2$ < 0 — it decreases; but $R_{p} ν = k_{p}^{2} {[M]}^{2} / (2 k_{t})$ , and it depends on temperature only through $k_{p}^{2} / k_{t}$ . Thermodynamics: since a π bond becomes a σ bond, $Δ H_{p}$ < 0 (styrene −73, MMA −56, α-methylstyrene −35 kJ/mol; steric crowding of substituents and conjugation of the double bond reduce $| Δ H_{p} |$ ), and since free monomers are assembled into an ordered chain, $Δ S_{p}$ < 0. Therefore a ceiling temperature $T_{c} = Δ H / (Δ S^{\circ} + R \ln [M])$ exists: for pure monomer α-methylstyrene ≈ 61 °C, MMA ≈ 220 °C, styrene ≈ 310 °C (Odian; reference books differ slightly — it depends on the standard state and the measurement method). High conversion: in MMA above 20–30 % the viscosity rises and large radicals cannot meet — $k_{t}$ drops sharply, the rate and ${\overline{X}}_{n}$ increase (the gel or Trommsdorff effect, risk of overheating); when the glass transition temperature of the mixture reaches the reaction temperature, the chain “freezes” — a limiting conversion (MMA at 60 °C ≈ 85 %).

Ionic and coordination polymerisation, industrial methods

Cationic polymerisation is typical of monomers with electron-donating substituents (isobutylene, styrene, vinyl ethers): the catalyst is a Lewis acid (SnCl₄, BF₃, AlCl₃), the co-catalyst is a proton source (traces of water): $S n C l_{4} + H_{2} O \to H^{+} {[S n C l_{4} O H]}^{-}$ . The carbocation adds monomer, with the counter-ion moving alongside; two cations do not terminate each other — the chain ends by combination with the counter-ion or by transfer to monomer. $R_{p} \propto [C] {[M]}^{2}$ , $1 / {\overline{X}}_{n} = C_{M} + k_{t} / (k_{p} [M])$ ; the activation energy of transfer is greater than that of propagation, so when the temperature falls ${\overline{X}}_{n}$ rises sharply (butyl rubber at −100 °C). Anionic polymerisation works with monomers having electron-withdrawing or conjugated (phenyl, vinyl) substituents (acrylonitrile, MMA; styrene, dienes): initiators are n-BuLi, sodium naphthalenide, amides. In a pure (water-free, air-free) medium there is no termination — “living” polymers (M. Szwarc, 1956): all chains start at the same time and grow equally, ${\overline{X}}_{n} = x {[M]}_{0} / {[I]}_{0}$ , the distribution is narrow (Poisson, ${\overline{M}}_{w} / {\overline{M}}_{n} \approx 1 + 1 / {\overline{X}}_{n}$ ); if a second monomer is added, a block copolymer forms (SBS thermoplastic elastomers). Coordination-ionic polymerisation: Ziegler–Natta catalysts (TiCl₄/MgCl₂ + AlEt₃) “insert” the monomer into the Ti–C bond (Cossee–Arlman mechanism) and control the spatial structure of the chain: isotactic (all CH₃ on one side), syndiotactic (alternating), atactic (random) polypropylene; metallocenes (+ MAO) have only one type of active centre. Low-pressure (Ziegler) polyethylene is linear and dense (0.94–0.97 g/cm³), high-pressure (150–300 MPa, 200–300 °C, radical) polyethylene is branched and soft (0.91–0.93). Configuration is covered in detail in the “Stereochemistry and conformations” experiment. Industrial methods: bulk (mass) — pure polymer, but heat is hard to remove (organic glass); solution — heat is easy to remove, transfer to solvent occurs; suspension — monomer droplets in water (polyvinyl alcohol as stabiliser), beads of 0.1–2 mm; emulsion — in micelles (Smith–Ewart), latex particles of 0.05–0.5 µm, fast and long-chain at the same time; gas phase (polyethylene, fluidised bed) and solid phase. Polycondensation is also carried out in the melt, in solution and at an interface (between two immiscible liquids). The Shurtan (2001) gas chemical complex produces polyethylene, and the Ustyurt (2016) complex produces polyethylene from ethylene and polypropylene from propylene. Obtaining methanol and ethanol from synthesis gas, viscose and acetate fibres, moulding of polymers, injection moulding, extrusion and calendering are covered in the “Chemistry of polymer materials” and “Chemical plant: reactors and workshops” experiments.

Copolymerisation: Mayo–Lewis, r₁, r₂ and Q–e

When two monomers polymerise together, which monomer the unit at the chain end prefers is determined by the reactivity ratios $r_{1} = k_{11} / k_{12}$ , $r_{2} = k_{22} / k_{21}$ . The Mayo–Lewis equation follows from the quasi-steady state: $F_{1} = (r_{1} f_{1}^{2} + f_{1} f_{2}) / (r_{1} f_{1}^{2} + 2 f_{1} f_{2} + r_{2} f_{2}^{2})$ ; the copolymerisation diagram is the curve $F_{1} (f_{1})$ . $r_{1} r_{2}$ ≈ 1 — ideal (statistical), $r_{1} r_{2}$ → 0 — alternating (styrene + maleic anhydride), $r_{1}, r_{2}$ > 1 — tends towards blocks. If $r_{1}, r_{2}$ < 1, the curve crosses the diagonal at the azeotropic point: $f_{1} = (1 - r_{2}) / (2 - r_{1} - r_{2})$ — such a mixture gives a copolymer of unchanging composition. At any other composition the more reactive monomer is used up faster — composition drift (Skeist equation $d X / d f_{1} = (1 - X) / (f_{1} - F_{1})$ ) and compositional heterogeneity of the copolymer; for a homogeneous copolymer, the azeotropic mixture is used or the more reactive monomer is added continuously during the reaction. Determining the constants: copolymerise at different $f_{1}$ up to low (< 10 %) conversion and find the composition by elemental analysis for an element present in only one monomer (O in MMA, N in acrylonitrile), by IR or by titration of carboxyl groups (in styrene–butadiene both are hydrocarbons: C % changes only from 88.8 to 92.3 % over the whole composition range, so the double bonds in the butadiene units are titrated — the iodine value), then use the Fineman–Ross ( $G = r_{1} H - r_{2}$ , $x = f_{1} / f_{2}$ , $y = F_{1} / F_{2}$ , $G = x (y - 1) / y$ , $H = x^{2} / y$ ) or Kelen–Tüdős lines. Chain microstructure: the mean sequence length is ${\overline{n}}_{1} = 1 + r_{1} f_{1} / f_{2}$ . Alfrey–Price Q–e scheme: each monomer is given a resonance stability $Q$ and a polarity $e$ (styrene $Q = 1$ , $e = - 0.8$ ): $r_{1} = (Q_{1} / Q_{2}) e^{- e_{1} (e_{1} - e_{2})}$ — empirical, with a large error, but a good estimate for an unknown pair (styrene–MMA: 0.52 and 0.46). The solvent (hydrogen bonding) changes the reactivity of acidic monomers.

Polycondensation and new methods of synthesis

In polycondensation, functional groups (−COOH + −OH, −NH₂ + −COCl …) react and a small molecule (H₂O, HCl) is released. Types: linear (polyesters, polyamides) from bifunctional monomers, three-dimensional (glyptal, phenol–formaldehyde resins) from trifunctional ones; homo- and heteropolycondensation. Any two molecules can join, so the monomer disappears quickly, but long chains appear only at the end: the Carothers equation ${\overline{X}}_{n} = 1 / (1 - p)$ — 100 at $p$ = 0.99, 1000 at $p$ = 0.999. Non-equivalence $r = N_{A} / N_{B}$ < 1 or a monofunctional additive (acetic acid) stops chain growth: ${\overline{X}}_{n} = (1 + r) / (1 + r - 2 r p)$ , at $p \to 1$ it is $(1 + r) / (1 - r)$ — the Korshak rule (a way of controlling molar mass). Kinetics (Flory): the reactivity of the groups does not depend on chain length; in catalysed polyesterification ${\overline{X}}_{n} = 1 + k {[A]}_{0} t$ , uncatalysed (the acid itself is the catalyst) ${\overline{X}}_{n}^{2} = 1 + 2 k {[A]}_{0}^{2} t$ . Equilibrium polycondensation: the esterification constant $K$ ≈ 1–10, for amidation ≈ 300; in a closed vessel ${\overline{X}}_{n} = 1 + \sqrt{K}$ (≈ 3 for a polyester), so the water is removed with a stream of nitrogen or by vacuum: ${\overline{X}}_{n} \approx \sqrt{K / n_{w}}$ . Destructive reactions (hydrolysis, acidolysis, aminolysis, exchange) establish equilibrium and bring the distribution to the Flory distribution. Network and gel point: if the average functionality $\overline{f}$ > 2, then $p_{c} = 2 / \overline{f}$ (Carothers) or $p_{c} = 1 / \sqrt{r (f - 1)}$ (Flory–Stockmayer); for glyptal 0.833 and 0.707, experimentally ≈ 0.765. Step (migration) polymerisation — polyaddition: polyurethanes (diisocyanate + diol), epoxides; no small molecule is released. Polymerisation by ring opening — nylon-6 from caprolactam, polyethylene glycol from ethylene oxide, polylactic acid from lactide (biodegradable): a cyclic compound becomes a linear polymer. New methods: dendrimers (stepwise from the core, exact structure) and hyperbranched polymers (in one step from AB₂ monomers), green chemistry (solvent-free, in water, renewable raw materials, enzymes), synthesis in ionic liquids (non-volatile, reusable). Nylon-6,6 melts at ≈ 265 °C — fibre is spun from it directly from the melt.

Lab work, safety and the model

30 lab works are in the “Lab work” list: the aim, reagents, procedure, equation and what is measured for each; on the bench the following have been recreated: dilatometer (L1–L5, L8–L10, Kimtex L20), acrylonitrile flask (L6), ampoules and titration (L12–L17), polyester flask (L18–L21), nylon thread (L23), resin test tube (L22, L24–L27, Kimtex L18–L19), suspension and ionic polymerisation (L7, L11). Dilatometry: the polymer is denser than the monomer, so the volume decreases: $x = Δ h S / (V_{0} K)$ , $K = 1 - ρ_{M} / ρ_{P}$ (at 60 °C styrene ≈ 0.17, MMA ≈ 0.24). Safety: styrene, MMA, acrylonitrile (toxic, carcinogenic), phenol, formalin, epichlorohydrin, diisocyanates, adipoyl chloride, polysulfide for thiokol — only in a fume cupboard, with gloves and safety goggles; do not hit or heat peroxides (they explode); SnCl₄ and n-BuLi fume or ignite in humid air; open a sealed ampoule only after it has cooled; if phenol gets on the skin — plenty of water and alcohol; if alkali gets in the eyes — plenty of water. Never taste anything. Model: classical kinetics (radicals quasi-steady); $k_{p}$ — IUPAC PLP values (styrene, MMA), other constants — model numbers of the order found in the literature; the gel and glass effects are semi-empirical; copolymerisation — terminal model; the rates for acidic monomers, cationic and anionic polymerisation, resins and polycondensation are model values; the molecular window is schematic (chains ≈ 1000 times shorter, time accelerated).

Did you know?

Wallace Carothers synthesised nylon-6,6 in 1935 in the laboratory of the DuPont company; nylon stockings went on general sale in 1940.
Hermann Staudinger received the Nobel Prize in Chemistry in 1953 for proving that polymers are not a crowd of small molecules but long covalent chains.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

The aromatic ring and azo dyes — Year 3
Carbonyl compounds and synthesis — Year 3
Heterocycles and DNA — Year 3
Amino acids and proteins — Year 3
Physics of macromolecules — Year 3
Chemistry of polymer materials — Year 3