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Química de Polímeros · Polymerization mechanisms

Polimerização em cadeia

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O que você vai aprender

  • Draw initiation, propagation and termination of a radical chain polymerization with fishhook arrows.
  • Explain how chain transfer, inhibitors and termination mode set the chain length of a radical polymer.
  • Choose cationic, anionic or radical conditions for a vinyl monomer from the stability of its propagating species.
  • Use the steady-state rate law, the kinetic chain length and the ceiling temperature to predict how conditions change rate and chain length.
  • Calculate number- and weight-average molar mass and dispersity, and relate dispersity to the polymerization mechanism.

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Chain growth: one active end adds monomer after monomer

In chain-growth polymerization an active species (a radical, a carbocation or a carbanion) adds one monomer at a time and stays at the chain end. Unless the chains are living (see below), each chain grows to full length within a fraction of a second to a few seconds, so high-molar-mass polymer is present from the start, while unreacted monomer is still in the flask. Step growth is different: any two molecules can react, and long chains appear only at very high conversion. Vinyl monomers CH₂=CHX add head to tail. The growing end attacks the unsubstituted CH₂ carbon, which is less hindered, and the new active centre sits on the carbon that carries X, where X stabilizes it. Substituents therefore end up on alternate carbons. In poly(vinyl chloride) the chlorines sit 1,3 to each other, and in polystyrene every second carbon carries a phenyl ring. Each addition turns a C=C π bond into a stronger C–C σ bond, so propagation is exothermic, about −93 kJ/mol for ethylene.

Radical initiation, propagation and termination

An initiator supplies a slow trickle of radicals. Dibenzoyl peroxide (drawn) breaks its weak O–O bond on heating, giving two benzoyloxy radicals, and some of these lose CO₂ to become phenyl radicals. AIBN loses N₂ and gives two 2-cyano-2-propyl radicals; it has a 10-hour half-life near 65 °C. A redox pair such as persulfate and Fe²⁺ makes radicals by single-electron transfer, and it works even at 5 °C. Not every initiator radical starts a chain. Some recombine inside the solvent cage before they separate, so the initiator efficiency f is usually 0.3–0.8. Each initiator radical adds to a monomer, and the new radical adds to monomer again and again; these propagation steps are drawn with fishhook arrows. Chains stop when two radicals meet. In combination the two chain ends bond to each other, so one dead chain contains both kinetic chains; polystyrene terminates mainly this way. In disproportionation one radical takes a β-hydrogen from the other, giving one saturated and one unsaturated chain end; poly(methyl methacrylate) terminates largely this way. Oxygen and phenolic inhibitors such as 4-methoxyphenol (MEHQ) trap radicals and stop polymerization during storage.

Chain transfer and branching

In chain transfer the growing radical takes an atom, usually H, from another molecule. One chain stops growing and a new radical starts another. The number of radicals does not change, so the rate is about the same, but the chains are shorter. Thiols such as 1-dodecanethiol are added on purpose: the weak S–H bond gives up its hydrogen readily, and the thiyl radical adds quickly to monomer. The Mayo equation gives the effect: 1/Xn = 1/Xn,0 + C_S[S]/[M], where C_S is the chain-transfer constant. If the new radical cannot restart a chain, transfer stops the reaction instead. Propene gives an allylic radical that is too stable to add to monomer, so free-radical polypropylene does not form (degradative chain transfer). Transfer to polymer causes branching. In high-pressure polyethylene the chain-end radical curls back and takes a hydrogen from the fifth carbon along its own chain through a six-membered cyclic transition state (backbiting), which leaves butyl branches. Abstraction of H from another, finished chain starts long branches.

Rate, chain length and ceiling temperature

The steady-state approximation sets the rate at which radicals form (Ri = 2fkd[I]) equal to the rate at which they are destroyed (Rt = 2kt[M•]²). This gives [M•] = (fkd[I]/kt)^½, typically about 10⁻⁸ mol/L, and Rp = kp[M](fkd[I]/kt)^½. The rate is first order in monomer and half order in initiator, because termination is bimolecular in radicals. The kinetic chain length ν = Rp/Ri, the number of monomers added per radical, falls as [I]^−½. Doubling the initiator speeds the reaction by √2 but shortens the chains by the same factor. Without chain transfer, Xn = 2ν for combination and Xn = ν for disproportionation. In bulk methyl methacrylate the viscosity rises with conversion, so the large chain radicals diffuse together more slowly and kt falls. The rate and the molar mass then jump (the gel or Trommsdorff effect). Polymerization also has a large negative entropy, so above the ceiling temperature Tc = ΔHp/ΔSp depropagation wins. Crowded 1,1-disubstituted monomers release much less heat on polymerizing: α-methylstyrene gives only about −35 kJ/mol and has a ceiling temperature of about 61 °C in bulk.

Cationic and anionic chain growth

Monomers with electron-donating groups polymerize cationically: isobutylene (drawn) and vinyl ethers. A protic acid, or a Lewis acid such as BF₃ with a trace of water as co-initiator, protonates the CH₂ end and gives a tertiary carbocation or an oxocarbenium ion, which then adds to more monomer. Loss of a β-proton to monomer (chain transfer) has a higher activation energy than propagation, so high polymer needs low temperature: isobutylene is polymerized near −100 °C. Monomers with electron-withdrawing groups polymerize anionically, and the weaker the base that can start the reaction, the more stabilized the propagating carbanion. Styrene needs butyllithium. Methyl methacrylate gives an ester enolate. Methyl 2-cyanoacrylate (superglue) is set off by traces of moisture, because its carbanion is stabilized by both a nitrile and an ester. Carefully dried anionic polymerizations have no termination step: the chains stay living until a proton source is added. All chains start together and grow equally, so Xn = [M]consumed/[I]0, the dispersity is close to 1 and adding a second monomer gives a block copolymer.

Molar-mass averages and dispersity

A polymer sample is a mixture of chain lengths. Mn = ΣNiMi/ΣNi is an average over molecules. Mw = ΣNiMi²/ΣNiMi is an average over mass, so heavy chains count more and Mw ≥ Mn. The dispersity Đ = Mw/Mn measures the breadth of the distribution. It is about 1.01–1.1 for living anionic polymers (Poisson distribution, Đ ≈ 1 + 1/Xn), about 1.5 for ideal radical termination by combination and about 2 for disproportionation or transfer; branching and the gel effect broaden it further. Size-exclusion chromatography separates chains by size: the largest chains elute first. End-group analysis gives Mn directly. If every chain carries a known number of initiator fragments, the mass fraction of an element found only in those fragments fixes the mass per chain.

What to carry forward

Find the active end (radical, cation or anion) and let it add head to tail. Then ask what stops it: radical–radical termination, transfer of an atom, or nothing at all in a living system. Rp ∝ [M][I]^½, ν ∝ [I]^−½, and transfer shortens chains without slowing the reaction. Living ionic chains grow evenly and give Đ near 1; radical chains give Đ of 1.5–2 or more.

Problemas de prática (40)

Praticar é grátis com uma conta.

Desenhe o mecanismo 12

Radical initiation and propagation

  • AIBN radicals start a poly(methyl methacrylate) chainDraw the addition of the 2-cyano-2-propyl radical from AIBN to methyl methacrylate and the first propagation step, placing each new radical on the carbon that carries the ester.
  • Benzoyloxy radical starts a polystyrene chainDraw the addition of a benzoyloxy radical to styrene and the next head-to-tail propagation step, and describe how the benzylic radical is stabilized.
  • Dibenzoyl peroxide gives benzoyloxy and phenyl radicalsDraw the homolysis of the O–O bond of dibenzoyl peroxide and the loss of CO₂ from a benzoyloxy radical, using one-electron (fishhook) arrows.
  • Head-to-tail propagation of vinyl chlorideDraw two radical propagation steps of vinyl chloride and show why the chlorines end up on alternate carbons of poly(vinyl chloride).

Ionic chain growth

  • n-Butyllithium starts a living polystyrene chainDraw initiation and propagation of the anionic polymerization of styrene by butyllithium and explain why the chain ends stay active.
  • Moisture sets off superglue: anionic polymerization of methyl 2-cyanoacrylateDraw hydroxide initiation and the first propagation step of methyl 2-cyanoacrylate, and explain why such a weak base is enough.
  • BF₃ and water start the cationic polymerization of isobutyleneDraw how BF₃ and water generate a proton, how the proton gives the tert-butyl cation, and how that cation adds head to tail to a second isobutylene.
  • Triflic acid starts the cationic polymerization of ethyl vinyl etherDraw protonation of ethyl vinyl ether, the oxocarbenium resonance form of the resulting cation, and its head-to-tail addition to a second monomer.

Termination and chain transfer

  • Termination by disproportionation of PMMA chain endsDraw disproportionation of two tertiary ester-stabilized chain-end radicals by transfer of a β-hydrogen, and identify the two chain ends it creates.
  • Backbiting makes butyl branches in low-density polyethyleneDraw the intramolecular 1,5-hydrogen transfer of a polyethylene chain-end radical and the next ethylene addition, and explain why it produces butyl branches.
  • Termination by combination of two polystyryl radicalsDraw combination termination of two benzylic chain-end radicals and relate it to the length of the dead polymer chain.
  • Chain transfer to 1-dodecanethiol in styrene polymerizationDraw hydrogen-atom transfer from a thiol to a polystyryl radical and the addition of the thiyl radical to styrene that starts a new chain.

Preveja o produto 3

Radical initiation and propagation

  • What does AIBN leave on the chain?Predict the initiator-derived end group of polystyrene made with AIBN.
  • Head-to-tail polyacrylonitrilePredict the head-to-tail placement of substituents in a radical vinyl polymer from the regiochemistry of radical addition.

Rate and thermodynamics

  • Faster but shorterPredict how doubling the initiator concentration changes both the rate and the chain length of a radical polymerization.

Classificar 4

Ionic chain growth

  • Which monomer suits cationic polymerization?Match a vinyl monomer to cationic chain growth from the electronic effect of its substituents.
  • Pick the initiator for a living polystyreneChoose the initiator that gives living anionic polymerization of styrene and classify the others by mechanism.

Radical initiation and propagation

  • Spot the chain-growth signatureClassify a polymerization as chain growth from how molar mass develops with conversion.

Termination and chain transfer

  • What keeps the monomer bottle from polymerizing?Identify a phenolic inhibitor and distinguish it from initiators and chain-transfer agents.

Comparar 3

Ionic chain growth

  • How weak a base can start the chain?Rank vinyl monomers by the weakest base able to initiate their anionic polymerization, using the stability of the propagating carbanion.

Rate and thermodynamics

  • Rank the heat released on polymerizationRank vinyl monomers by the heat released on polymerization and relate the order to conjugation and steric strain.

Molar mass and dispersity

  • Rank the molar-mass averagesOrder the number-, viscosity-, weight- and z-average molar masses of a polydisperse polymer.

Calcular 10

Rate and thermodynamics

  • Ceiling temperature of α-methylstyreneCalculate a ceiling temperature from the enthalpy and entropy of polymerization.
  • Half-life of AIBNCalculate the half-life of a first-order initiator from its decomposition rate constant.
  • Quadruple the initiatorUse the half-order dependence of the radical polymerization rate on initiator concentration.

Molar mass and dispersity

  • Dispersity of an equal-mass blendCalculate Mn, Mw and the dispersity of a blend given by mass.
  • Mn from nitrogen analysisCalculate Mn from elemental analysis of initiator end groups, accounting for the termination mode.
  • Number-average of a two-component blendCalculate the number-average molar mass of a mixture of two polymer fractions from their amounts in moles.
  • Dispersity of a living polymerCalculate the degree of polymerization and the Poisson dispersity of an ideal living polymerization.

Termination and chain transfer

  • Chain length from ratesCalculate the number-average degree of polymerization from the rates of propagation and initiation for termination by combination.
  • How much does a thiol shorten the chains?Use the Mayo equation to calculate the degree of polymerization in the presence of a chain-transfer agent.

Ionic chain growth

  • Molar mass of a living polystyreneCalculate Mn of a living anionic polymer from the amounts of monomer consumed and initiator.

Encontre o erro 1

  • Why is the polystyrene too long?Diagnose the effect of protic impurities on initiator and molar mass in an anionic polymerization.

Interprete as evidências 2

Termination and chain transfer

  • Where do the branches in LDPE come from?Assign the short and long branches of low-density polyethylene to intramolecular and intermolecular chain transfer.

Molar mass and dispersity

  • Reading a size-exclusion chromatogramInterpret elution volume in size-exclusion chromatography in terms of chain size.

Trabalhe de trás para frente 1

  • Which monomer makes PMMA?Work back from the repeat unit of poly(methyl methacrylate) to its vinyl monomer.

Planeje uma síntese 1

  • Order of addition for a block copolymerPlan the order of monomer addition in a sequential living anionic synthesis of a block copolymer.

Explique por quê 3

Rate and thermodynamics

  • Runaway in bulk methyl methacrylateExplain autoacceleration in bulk radical polymerization from diffusion-controlled termination.

Termination and chain transfer

  • Why no free-radical polypropylene?Explain degradative chain transfer to monomer using the stability of the allylic radical.

Radical initiation and propagation

  • Radicals at 5 °C from persulfate and iron(II)Explain how a redox pair generates initiating radicals at temperatures where thermal homolysis is negligible.

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