Lecture 11: Radical Polymerization, Homogeneous Reaction Rate Kinetics

10.569 Synthesis of Polymers Prof. Paula Hammond Lecture 11: Radical Polymerization, Homogeneous Reaction Rate Kinetics How to determine MW in free radical polymerization Kinetic Chain Length ν = # of monomers added per effective free radical ν = ν= rate of chain growth rate of chain growth = rate of chain initiation rate of chain termination Rp Ri = Rp Rt = k p [M ] 1 2( fk d k t [I ]) 2 p n = ν if termination is by disproportionation process p n = 2ν if termination is by coupling Generally, (if no chain transfer): p n = 2aν where ½ ≤ a ≤ 1 100% disproportionation 100% disproportionation M n = M n ⋅ pn molecular weight of vinyl monomer unit What happens more often? • Coupling usually greater than disproportionation • Percent of coupling increases if: steric factors prevent effective coupling: CH3 CH3 C C CH3 CH3 or if: β-hydrogens are more reactive: Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. H C + C C H ν= Consider k p [M ] 1 2( fk d k t [I ]) 2 1 ⎛ fk p [I ] ⎞ 2 ⎟ [M ] R p = k p ⎜⎜ ⎟ ⎝ kt ⎠ Increase Rp by: [M]↑, [I]↑ But increase ν → [M]↑, [I]↓ Thus you want to increase [M] Chain Transfer 1. ktr Mn + X' Y Rtr = d [Y ⋅] = k tr [M ⋅][X '−Y ] dt Mn ktr = transfer constant X' + Y Chain transfer can occur when there are solvent impurities. But sometimes using chain transfer can be advantageous. 2. Y + M ka YM 3. YM + M kp Chain transfer agent → CTA Used to decrease MW in polymerization YMn kp >> ktr and kp ≈ ka ⇒ Rp is the same pn ↓ slightly – moderately depending on CTA kp << ktr and kp ≈ ka ⇒ Rp ∼ same p n ↓ dramatically kp >> ktr and ka < kp ⇒ Rp↓ slightly and p n ↓ slightly kp << ktr and ka < kp ⇒ Rp↓ drastically and p n ↓ drastically Transfer Types: 1. to monomer: ktr,m Mn⋅ + M → Mn + M⋅ 2. to solvent or impurity Mn⋅ + S → Mn + S⋅ ktr,s 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 11 Page 2 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. or CTA 3. to initiator: Mn⋅ + I → Mn + I⋅ ktr,I All act to decrease p n : (assume coupling) pn = Rp Rp = Rt Rt + Rtr,m + Rtr,s + Rtr,I + k tr,m [M ⋅][M ] + k tr,s [M ⋅][S ] + k tr,I [M ⋅][I ] 2 2 Use resistor analogy: (resistors in series) C = transfer constant = relative rate const vs. Rp Cm = k tr,m kp , CS = k tr,S kp , CI = k tr,I kp since Rp = kp[M⋅][M] 1 pn = Ri [S ] + C [I ] + Cm + C S [M ] I [M ] 2R p Additive effect of each constant Rt 2R p ⎛ 1 ⎞ ⎟ ↔ 1 ⎜ ⎜p ⎟ 2ν ⎝ n ⎠o Often only have transfer to CTA (or impurity) 1 pn = Ri [S ] + CS [M ] 2R p 1 ( fk d k t [I ]) 2 k p [M ] = 1 2ν 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 11 Page 3 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. For a given amount of initiator [I] and monomer [M] ⎛ 1 ⎞ ⎟ + C S [S ] =⎜ ⎜ [M ] p n ⎝ p n ⎟⎠ o 1 1 pn Increase Increas e MW Cs 1 pn o [S] [M] Useful to control MW is free radical with high kp and/or really low kt Cs values for different compounds: π orbitals • alkanes (weakest) • cyclic hydrocarbons • benzenes, aromatics H unstable negative charge → H- extraction unlikely Increasing radical stability < < weakest < share e- cloud with other C atoms CH2 resonance stabilization CH2 High Cs values: • weak C—H bonds • stabilized by conjugation O O N C • weak C—Cl, C—Br, C—I 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 11 Page 4 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date. R R C R Cl + R R H C + RCl H • weak S—S bonds, S—H weakest largest CS CTA (chain-transfer-agents) CS x 104 CS x 104 For styrene Vinyl acetate Benzene 0.023 1.2 Cyclohexane 0.031 7.0 0.42 17.0 n-butyl alcohol 1.6 20.0 CHCl3 (chloroform) 3.4 150.0 Tri-methyl amine 7.1 370 210,000 480,000 Heptane n-butyl mercaptan SH 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 11 Page 5 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date.