Chemical Engineering 160/260 Science and Engineering

LectureLecture 66 -- MechanismMechanism andand KineticsKinetics ofof FreeFree RadicalRadical ChainChain PolymerizationPolymerization JanuaryJanuary 29,29, 20012001 Outline

! Mechanism of Chain " Fundamental steps (initiation, propagation, termination) " Kinetic chain length and molecular weight ! ! 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 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- - - - + Isobutene - - + - 1,3- + + - + Isoprene + + - + + + + + Vinyl chloride + - - + + + - + Methacrylate + + - + • 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 Y Propagation: reaction (addition of hundreds or H thousands of ) 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/  R i  RR kM2 []M•=  it==2 t[] •  2k t

12/  Ri  RkMpp= []   2kt  Rate of Initiation Unimolecular decomposition: [II ]= [o ]exp(− ktd ) dI[] RkI []I − ==dd[] ln o =kt dt []I d 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 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:

kMp[] Typically, the initiator ν = 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 , 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 :

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 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. • 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 lnkp  = lnAp  =  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[] k p This is ν = p ([])fk k I 12/ ()12/ the key. 2 d t kkd 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, R decreases with time  fk[] I  p RkM= [] d because [M] and [I] drop with pp k   t  extent of conversion.

G. Odian, Principles of Polymerization, 3rd Ed., 1991, p 289.