Arrow Lab

Química de Polímeros · Polymerization mechanisms

Polimerização em etapas

Uma lição resolvida gratuita e 40 problemas de prática em que você mesmo desenha cada seta curva.

Travou em polimerização em etapas? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

Escaneie sua lição de graça

O que você vai aprender

  • Draw the bond-forming steps behind polyesters, polycarbonates, polyamides, polyimides, polyurethanes, epoxy networks and phenol–formaldehyde resins.
  • Use the Carothers equation and the Flory distribution to relate conversion to number-average chain length and dispersity.
  • Calculate the chain length set by a stoichiometric imbalance or a monofunctional additive, and choose the imbalance that gives a target molar mass.
  • Predict gelation from average functionality with the Carothers equation and recognise which monomers make networks.
  • Explain why step-growth processes remove by-products, use exact stoichiometry and choose activated monomers or catalysts.

Lição gratuita

O texto da lição resolvida. No Arrow Lab, cada etapa vem com as estruturas e as setas desenhadas.

Ler a aula gratuita (7 partes)

Step growth: any two molecules can react

In step-growth polymerization every molecule carries reactive end groups, and any two molecules with complementary groups can join: monomer with monomer, dimer with trimer, oligomer with oligomer. Adipic acid and hexane-1,6-diamine (drawn) each carry two groups, so each amide link leaves a new acid or amine at the chain end. Monomer is used up early, but chains stay short until almost every group has reacted. If N₀ molecules start and the fraction of groups that has reacted is p, then N₀(1 − p) molecules remain. The number-average degree of polymerization, counted in monomer residues, is therefore the Carothers equation Xn = 1/(1 − p). At p = 0.90, Xn is only 10; at p = 0.99 it is 100, and at p = 0.995 it is 200. Flory's statistics give the weight average Xw = (1 + p)/(1 − p), so the dispersity Đ = Xw/Xn = 1 + p, which approaches 2 at high conversion. Useful step-growth polymers therefore need very pure monomers, reactions that go to more than 99% conversion, and no side reactions that destroy end groups.

Polyesters and polycarbonates: drive off the by-product

Esterification and transesterification have small equilibrium constants (of order 1 to 10), so a polyester grows only if the small molecule that is released keeps leaving. Poly(ethylene terephthalate), PET, is made either by esterifying terephthalic acid directly with ethylene glycol, which releases water and is catalysed by the acid groups themselves, or by ester interchange of dimethyl terephthalate with ethylene glycol, which releases methanol. Both routes give bis(2-hydroxyethyl) terephthalate and short oligomers. These are then polycondensed near 280 °C under high vacuum: each new ester link releases ethylene glycol, which must be pumped away. Bisphenol A polycarbonate is made in the same way, by melt transesterification of bisphenol A with diphenyl carbonate under base catalysis, and phenol is distilled off. A cyclic anhydride needs no by-product removal for its first step. An alcohol opens phthalic anhydride to a half ester that still carries a free carboxylic acid, and that acid is esterified later. With glycerol as the alcohol, this chemistry gives the branched alkyd resins of paints.

Polyamides, polyimides and aramids

Nylon 6,6 is named for its six-carbon diamine and six-carbon diacid. The two monomers are first combined as the 1:1 nylon salt, hexamethylenediammonium adipate, which can be recrystallized; this fixes the stoichiometry exactly. Heating the salt near 270 °C releases water as amide links form. The free amine adds to a carboxylic acid group, and other acid groups in the melt protonate the leaving hydroxyl. Nylon 6 comes from ε-caprolactam. In anionic polymerization a strong base forms the lactamate anion, and an N-acyllactam (drawn) acts as the activator, because its ring carbonyl is an imide carbonyl and is much more electrophilic than the carbonyl of caprolactam. Aromatic amines are weak nucleophiles, so aramids are made at low temperature from diacid chlorides. p-Phenylenediamine and terephthaloyl chloride give the rigid-rod fibre Kevlar, and the meta isomers give Nomex. The HCl released is taken up by an acid acceptor. Polyimides form in two stages. A diamine opens pyromellitic dianhydride at room temperature to give a soluble poly(amic acid). Heating then closes the five-membered imide rings with loss of water.

Addition step growth: urethanes, ureas and epoxy curing

Some step-growth reactions release no by-product. An alcohol adds across the C=N bond of an isocyanate to give a urethane (carbamate) link, so a diisocyanate such as MDI and a diol such as butane-1,4-diol give a polyurethane. Amines add much faster and give ureas. Water adds to give a carbamic acid, which loses CO₂ and leaves an amine. The CO₂ blows polyurethane foams, and the amine reacts with more isocyanate to give urea links. Tertiary amines and tin compounds catalyse urethane formation. With excess isocyanate and heat, urethane and urea N–H groups add to more isocyanate and give allophanate and biuret crosslinks. Anionic catalysts such as potassium acetate trimerize isocyanates to isocyanurate rings, which crosslink rigid foams. Epoxy resins such as the bisphenol A diglycidyl ether drawn here cure with amines. Each N–H attacks the less hindered CH₂ of an epoxide in an SN2 reaction, so a primary amine can open two epoxides and ethylenediamine can open four. The hydroxyl groups formed help to open further epoxides by hydrogen bonding to the epoxide oxygen, so the cure accelerates itself.

Stoichiometric imbalance and end-capping

A small excess of one monomer limits the chain length, because once the minor groups are used up every chain end carries the excess group and cannot react further. With r = NA/NB ≤ 1, the ratio of the minor to the major functional groups, the Carothers equation becomes Xn = (1 + r)/(1 + r − 2rp), where p is the conversion of the minor groups. At complete conversion this is Xn = (1 + r)/(1 − r): r = 0.98 caps the chain at 99 residues, even with a perfect reaction. A monofunctional reagent works the same way, but each of its molecules counts twice: r = NA/(NB + 2NB′), where NB′ is the number of monofunctional molecules. Manufacturers add a little acetic acid to nylon on purpose. The chains end in unreactive groups, so the molar mass and melt viscosity do not keep rising during melt processing. The same arithmetic shows how costly small errors are: a 1% weighing error, or 1 mol% of a monofunctional impurity in one monomer, gives r ≈ 0.99, which caps Xn at 199 even at complete conversion and halves it from 200 to 100 at p = 0.995.

Branching, gelation and thermosets

A monomer with three or more reactive groups makes branches, and the branches link into a network that spans the whole sample at the gel point. For a stoichiometric mixture the Carothers equation predicts gelation at pc = 2/fav, where fav is the average number of functional groups per monomer molecule. Two moles of glycerol (three OH each) with three moles of phthalic anhydride (two acyl groups each) give fav = 12/5 = 2.4 and pc = 0.833. Flory's statistical treatment gives a lower gel point (0.707 for this mixture), because it allows for chains that grow much larger than average. Measured gel points fall between the two estimates. Phenol is trifunctional toward formaldehyde, through its two ortho positions and its para position. In base with excess formaldehyde, phenoxide adds to formaldehyde to give hydroxymethylphenols. These resols cure to networks on heating. In acid with excess phenol, the protonated hydroxymethyl groups lose water, and the benzylic cations alkylate more phenol, giving methylene-bridged novolacs (drawn). Novolacs are thermoplastic until a formaldehyde source such as hexamethylenetetramine is added to crosslink them.

What to carry forward

Step growth joins whole molecules, so chains become long only above about 99% conversion: Xn = 1/(1 − p). Any excess of one group, from a weighing error or a monofunctional impurity, caps Xn at (1 + r)/(1 − r). Condensations need their by-product (water, methanol, ethylene glycol, phenol, HCl) removed or neutralized, while isocyanate and epoxy additions release nothing. Monomers with three or more groups gel at pc = 2/fav and give thermosets.

Problemas de prática (40)

Praticar é grátis com uma conta.

Desenhe o mecanismo 15

Polyesters and polycarbonates

  • Glycerol opens phthalic anhydride: the first step of an alkyd resinDraw the ring opening of phthalic anhydride by a primary hydroxyl of glycerol to give a half ester that still carries a carboxylic acid.
  • Ester interchange of dimethyl terephthalate with ethylene glycolDraw the base-catalysed transesterification in which 2-hydroxyethoxide replaces one methoxy group of dimethyl terephthalate, and show how the catalyst is regenerated.
  • Self-catalysed esterification of terephthalic acid with ethylene glycolDraw the acid-catalysed esterification of terephthalic acid with ethylene glycol in which a second carboxylic acid group acts as the catalyst, ending with loss of water and regeneration of the acid.
  • Melt transesterification of bisphenol A with diphenyl carbonateDraw how bisphenol A phenoxide displaces phenoxide from diphenyl carbonate to form the first carbonate link of polycarbonate, and how the chain end is converted back into an aryloxide.

Urethanes, epoxies and phenolic networks

  • Hydroxyl-assisted epoxide opening by a secondary amine: the branch point of an epoxy networkDraw how a hydroxyl group assists the opening of an epoxide by a secondary amine, giving a tertiary-amine branch point, and explain why epoxy–amine cures accelerate as they proceed.
  • Ethylenediamine opens an epoxide of bisphenol A diglycidyl etherDraw the SN2 opening of a glycidyl ether epoxide by a primary amine at the terminal CH₂ carbon, the key bond-forming step of epoxy curing.
  • Anionic cyclotrimerization of phenyl isocyanate to an isocyanurateDraw the anion-catalysed cyclotrimerization of three isocyanate groups into an isocyanurate ring, the crosslink of polyisocyanurate (PIR) foams, and show that the catalyst is regenerated.
  • Acid-catalysed methylene bridge between two phenols: the novolac linkDraw how a protonated hydroxymethylphenol loses water and alkylates the para position of a second phenol, forming the methylene bridge of a novolac resin.
  • Base-catalysed hydroxymethylation of phenol: the first step of a resol resinDraw how phenoxide adds to formaldehyde through its ortho carbon and is rearomatized to give a hydroxymethylphenoxide, the reactive unit of a resol.
  • Urea link from an amine and an isocyanate in a water-blown foamDraw the addition of an aromatic amine, formed from an isocyanate and water, to a second isocyanate to give the urea link of a polyurethane foam.
  • Urethane link from MDI and butane-1,4-diolDraw the addition of an alcohol to an aryl isocyanate that forms the urethane (carbamate) link of a polyurethane.

Polyamides, polyimides and aramids

  • First amide link of Kevlar from p-phenylenediamine and terephthaloyl chlorideDraw the nucleophilic acyl substitution between p-phenylenediamine and terephthaloyl chloride that forms the first aramid amide link, including removal of the N–H proton by pyridine.
  • Activated anionic polymerization of ε-caprolactam to nylon 6Draw one growth cycle of the activated anionic polymerization of ε-caprolactam: lactamate attack on the N-acyllactam, ring opening, and proton transfer that regenerates lactamate.
  • Amide formation in the nylon 6,6 meltDraw how a free amine group and a carboxylic acid group in the nylon 6,6 melt form an amide, with another carboxylic acid group acting as the acid catalyst and water as the by-product.
  • Poly(amic acid) formation from pyromellitic dianhydride and 4,4′-oxydianilineDraw how an aromatic amine opens one anhydride ring of pyromellitic dianhydride to give the amic acid link of a polyimide precursor.

Preveja o produto 4

Urethanes, epoxies and phenolic networks

  • Where does the amine open a glycidyl ether?Predict the regiochemistry of amine opening of a terminal glycidyl ether under curing conditions.
  • Product of an isocyanate and an alcoholPredict the urethane formed when an alcohol adds to an isocyanate.

Stoichiometric imbalance and gelation

  • Which mixture gels?Predict which monomer mixture forms a crosslinked network before complete conversion from the functionality of its monomers.

Polyesters and polycarbonates

  • The repeat unit of PETPredict the repeat unit of a polyester from its diacid and diol monomers.

Classificar 1

  • Find the chain stopperClassify reagents by their functionality and identify the one that can only end a chain.

Comparar 3

Polyesters and polycarbonates

  • Which acyl monomer reacts fastest with a diol?Rank acyl monomers used in step-growth polymerization by their reactivity toward an alcohol.

Urethanes, epoxies and phenolic networks

  • Who reacts fastest with an isocyanate?Rank nucleophiles by their rate of reaction with an aromatic isocyanate and relate the ranking to urea, urethane and allophanate formation.

Stoichiometric imbalance and gelation

  • Rank four polyamide batches by chain lengthRank step-growth formulations by number-average chain length using the modified Carothers equation.

Calcular 10

Step growth and the Carothers equation

  • Chain length at 99% conversionCalculate the number-average degree of polymerization of a stoichiometric step-growth polymer from the extent of reaction with the Carothers equation.
  • Conversion needed for a target chain lengthRearrange the Carothers equation to find the extent of reaction needed for a target number-average degree of polymerization.
  • Mn from end-group titrationCalculate the number-average molar mass of a polyester from titration of its carboxylic acid end groups.
  • Dispersity of a step-growth polymerCalculate the dispersity of a linear step-growth polymer at a given conversion from the Flory distribution.

Urethanes, epoxies and phenolic networks

  • How much ethylenediamine per 100 g of epoxy resin?Calculate the stoichiometric amine loading for an epoxy resin from its epoxide equivalent weight and the amine hydrogen equivalent weight.

Stoichiometric imbalance and gelation

  • Gel point of an alkyd from the Carothers equationCalculate the average functionality of a monomer mixture and predict its gel point with the Carothers equation.
  • A 2% shortage of diamineCalculate the limiting chain length set by a stoichiometric imbalance at complete conversion of the minor groups.
  • Imbalance and incomplete conversion togetherCombine a stoichiometric imbalance with incomplete conversion in the modified Carothers equation.
  • Capping nylon 6,6 with acetic acidCalculate the limiting chain length when a monofunctional reagent is added to a balanced step-growth polymerization.

Polyamides, polyimides and aramids

  • Molar mass of nylon 6,6 at 99% conversionConvert a Carothers degree of polymerization into a number-average molar mass using the mean residue mass.

Encontre o erro 1

  • Why did the PET stop growing?Diagnose why a PET polycondensation stalls at low molar mass from its process record.

Interprete as evidências 1

  • Is 98% conversion nearly finished?Interpret end-group conversion data to judge how far a step-growth polymerization is from high polymer.

Trabalhe de trás para frente 3

Polyamides, polyimides and aramids

  • Monomers for the meta-aramid NomexWork back from an aramid structure to its diamine and diacid chloride monomers using the ring substitution pattern.
  • Monomers for nylon 6,10Work back from a nylon name to its diamine and diacid monomers.

Polyesters and polycarbonates

  • Monomers for polycarbonate without phosgeneWork back from the carbonate repeat unit of bisphenol A polycarbonate to its monomers in the melt process.

Planeje uma síntese 2

Stoichiometric imbalance and gelation

  • Design an imbalance to cap the chain lengthChoose the stoichiometric ratio that limits a step-growth polymer to a target chain length at complete conversion.

Polyamides, polyimides and aramids

  • Why make the nylon salt first?Plan the monomer preparation for nylon 6,6 so that the stoichiometry is exact.

Travou em polimerização em etapas? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

Escaneie sua lição de graça

Antes deste tópico