Chemical Engineering 160/260 Polymer Science and Engineering LectureLecture 66 -- MechanismMechanism andand KineticsKinetics ofof FreeFree RadicalRadical ChainChain PolymerizationPolymerization JanuaryJanuary 29,29, 20012001 Outline ! Mechanism of Radical Chain Polymerization " Fundamental steps (initiation, propagation, termination) " Kinetic chain length and molecular weight ! Chain Transfer ! Energetic Characteristics " Activation energies and frequency factors " Rate of polymerization " Degree of polymerization ! Autoacceleration General Comments on Chain Reactions ! Polymerization is possible only if ∆G < 0 for the transformation of monomer to polymer. This will depend only upon the initial and final states, not the nature of the intermediate (free radical, anion, cation). ! Substituents on a vinyl group will influence reactivity through inductive, resonance,and steric effects. ! Susceptibility to a particular chain mechanism depends on the degree of stabilization of the propagating center. ! Radicals are “free” species, but anionic and cationic end groups have counterions that influence reactivity. ! High polymer is formed immediately in a chain reaction. Increasing the reaction time simply increases the amount of high polymer produced. Effect of Substituents on Chain Mechanism Monomer Radical Anionic Cationic Hetero. Ethylene + - + + Propylene - - - + 1-Butene - - - + Isobutene - - + - 1,3-Butadiene + + - + Isoprene + + - + Styrene + + + + Vinyl chloride + - - + Acrylonitrile + + - + Methacrylate + + - + esters • Almost all substituents allow resonance delocalization. • Electron-withdrawing substituents lead to anionic mechanism. • Electron-donating substituents lead to cationic mechanism. Mechanism of Radical Chain Polymerization Initiation: (thermal or photochemical bond cleavage) k d always the slow I → 2R • H | same identity fast R• + CH2=CHY → RCH2C • and reactivity | for head-to-tail Propagation: Y reaction (addition of hundreds or H thousands of monomers) H | | RCH2C • + CH2=CHY → RCH2CHYCH2C • | | Y Y H H | | RCH2CHYCH2C • + CH2=CHY → R(CH2CHY)2CH2C • | | Y Y Mechanism of Radical Chain Polymerization Termination: (Reactions are similar for radical and cationic.) Coupling (molecular weight is effectively doubled) H H H k H | | tc | | ~CH2C • + • CCH2~ → ~CH2C-CCH2~ | | | | Y Y Y Y Disproportionation (molecular weight is unchanged) H H H H | | ktd | | ~CH2C • + • CCH2~ → ~CH2CH + C=CH~ | | | | Y Y Y Y Most anionic reactions have no inherent termination step. Mechanism of Radical Chain Polymerization Initiation: Azonitriles: kd M • + RN=NR → M R + N + R • I → 2R • n n 2 Peroxides: dI[] − ==RkIi d [] dt Mn • + RO-OR → MnOR + RO • Propagation: kp k ~ 102 - 104 liter/mole sec Mn • + M → M n+1 • p dM[] − ==RkMM[][] • dt pp Termination: k = k + k kt t tc td Mn • + Mm • → dead polymer 2 RkMtt=•2 [] [M •] ~ 10-7 - 10-9 mole/liter Note: [M+], [M-] ~10-2- 6 8 kt ~ 10 -10 liter/mole sec 10-3 mole/liter Magnitudes of Reaction Parameters G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 274. Rate of Polymerization Define the rate of polymerization based upon monomer loss. dM[] dM[] − =+RR − ==RkMM[][] • dt ip dt pp ~ 0 Assume that kp and kt are independent of size of radical. Steady-state assumption: The net rate of production of free radicals is zero so that the initiation and termination rates are equal. This is usually true after about 1 minute reaction. 12/ Ri 2 []M•= RRit==2 kM t[] • 2kt 12/ Ri RkMpp= [] 2kt Rate of Initiation Unimolecular decomposition: [II ]= [o ]exp(− ktd ) dI[] − ==RkIdd[] []I o dt ln = ktd []I I Half life: 1 []o 0. 693 t12/ ==ln k []I o k d 2 d In actual reactions, not all initiator decompositions are effective in initiating polymerization. An efficiency factor f is introduced to account for this. RfkIdd= 2[] RRi = d 12/ 12/ fk[] I Ri d RkM[] RkMpp= [] pp= k 2kt t Kinetic Chain Length ν = average number of monomer molecules consumed for each radical that initiates a polymer chain Rp Rp kMM[][]• kM[] ν == ν = p = p Ri Rt 2 22kMt []• kMt []• 2 2 kMp [] RkMMpp=•[][] ν = 2kRtp For initiation by thermal homolysis: kM[] ν = p Typically, the initiator 12/ efficiency f is about 0.5. 2([])fkd kt I Relationship Between Kinetic Chain Length and Molecular Weight Coupling: This is the most common mode for styrene, methyl acrylate, and acrylonitrile. X 2 (true only if there is no n = ν chain transfer) Disproportionation: Methyl methacrylate (MMA) has a combination of coupling and disproportionation. At 70 °C, MMA termination is almost 100% by disproportionation. X = ν (true only if there is no n chain transfer) Chain Transfer Chain transfer is a chain breaking reaction leading to a decrease in the size of the propagating polymer chain. The active center is transferred from the growing chain to a different species (chain transfer agent, initiator, monomer, or polymer). The new species may initiate polymerization or may truncate it. ktr Mn• + XA → Mn-X + A• dead can initiate a new reaction ka A• + M → M • RkMXAtr=• tr[][] Effect of Chain Transfer on Molecular Weight Use the kinetic chain length approach to obtain the ratio of the polymerization rate to the sum of all termination rates: R X p n = R t +•+•+•kMMkMSkMI[][] [][][][] 2 trM trS trI Define chain transfer constants: k ktrM ktrS trI CM ≡ CS ≡ CI ≡ kp kp kp 1 2Rp []S []I =++CCMS +C I Xn Ri []M []M 2 1 kRtp []S kRtp =+++2 2 CCMSC I2 3 Xn kMp [] []M kfkMp d [] Chain Transfer to Polymer Consider a terminal free radical of polyethylene: 6 5 4 Size of side chain after backbiting • ~CH2CH2CH2CH2 CH2 | | CH2 CH2 CH2 Short branches decrease crystallinity and are 20 - 50 times more prevalent than long branches. A typical polyethylene has 5 n-butyl branches and 1 - 2 each of ethyl, n-amyl, and n-hexyl branches per 1000 carbons. Long branches, formed by normal chain transfer to polymer, affect melt flow properties. Transfer to Chain Transfer Agent 11 []S 1 kR kR2 = + C tp tp S =++2 2 CCMI2 3 XXnn []M X kM kfkM o n o p []p d [] • Strong C-H bonds of aliphatics lead to small CS. • Acids, carbonyls, ethers, amines, and alcohols have higher CS values than aliphatics due to stabilization by O, N, C=O. • Weak S-S bonds lead to large CS. • Carbon-halogen bonds are very weak, with excellent radical stabilization. • Thiols have the highest CS due to the weak S-H bond. Energetic Characteristics: Activation Energies and Frequency Factors Assume that all rate constants (kd, kp, kt) are Arrhenius-like. E A = frequency factor kA= exp(− ) RT E = activation energy G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 277. Energetic Characteristics: Activation Energies and Frequency Factors G. Odian, Principles of Polymerization, 3rd. Ed., 1991, p 275. Methyl methacrylate is sterically hindered, leading to low Ap. Energetics: Rate of Polymerization 12/ 12/ fkd [] I kd This is RkM= [] kp pp the key. kt kt EE 12// 12 d t −Ep + − kd Ad 22 lnkp = lnAp = k A RT t t EE composite activation energy, EE≡ + d − t Rp22 usually ~80-90 kJ/mole 12/ Ad 12/ ER lnRApp= ln + ln (fI [ ]) [ M ] − A {}RT t Energetics: Degree of Polymerization kM[] kp This is ν = p 12/ kk 12/ the key. 2([])fkd kt I ()d t EEd t Ep −− kp Ap 22 ln 12// = ln 12 − ()kkd t ()AAd t RT EEd t composite or overall EE≡−−p Xn 22activation energy Xn = 2ν A E p []M Xn coupling lnXn = ln 12// + ln 12 − ()AAd t ([])fI RT Temperature Dependence of Rate of Polymerization and Degree of Polymerization Rate of Weight-average polymerization molecular weight 1 T Autoacceleration (Trommsdorff effect) 12/ Normally, Rp decreases with time fkd [] I RkMpp= [] because [M] and [I] drop with kt extent of conversion. G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 289..