10.569 Synthesis of Polymers Prof. Paula Hammond Lecture 12: Free Radical Kinetic Chain Length, MWD, Chain Transfer, Energetics Energetics General Equation −E k = Ae RT Eln k = ln A −RT For thermal decomposition of initiator 1 Rp =kp [][ ] M ⋅ =kp ⎜⎜⎛kd ⎟⎞2 f 21 M I 21 M ⎟ [][]kt ⎠⎝ net rate “fudge factor” constant Arrhenius expression: ⎡ E E ⎤⎡ 1⎤ ⎡ 1 ⎤ E + d − t ⎢⎛kd ⎞2 ⎥ ⎢⎛Ad ⎞2 ⎥ ⎣⎢p 2 2 ⎦⎥ ln⎢kp ⎜⎜ k ⎟⎟⎥=ln⎢Ap ⎜⎜ A ⎟⎟⎥− RT ⎢⎝ t ⎠⎥ ⎢⎝ t ⎠⎥ ⎣ ⎦ ⎣ ⎦ constant Ep = activation energy for propag. step w.r.t. Temp ⎡⎢Ep + Ed −Et ⎤⎥is activation energy for polymerization ⎣ 2 2 ⎦ ER = Ep + Ed −Et 2 2 Overall: ⎡ 1 ⎤ R ln⎢A ⎜⎛Ad ⎟⎞2 ⎥+ ln⎡ []21 M ⎤ ER ln p ⎢p ⎜At ⎟⎥ ⎣⎢( )[]⎦⎥−RT = f I ⎢⎝ ⎠⎥ ⎣ ⎦ 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.Sample Values of Ep and Et in kJ/mol Monomers Ep (kJ/mol) Et (kJ/mol) Vinyl chloride 16 17.6 Methyl acrylate 29.7 22.2 Methyl metacrylate 26.4 11.9 Styrene 26.0 8.0 Initiator Ed (kJ/mol) AIBN 123.4 Acetyl Peroxide 136 Benzoyl Peroxide 124.3 On Average: Ep ∼ 20 – 30 Et ∼ 10 - 15 Ed ∼ 100 – 150 ⇒ ER = Ep + Ed/2 - Et/2 is dominated by Ed ER ∼ 80 – 90 kJ/mol Because Rp is a positive number → positive activation energy If T ↑, k ↑ e.g. if T ↑ ∼ 10oC, Rp ↑ by 2-3x (rate of polymerization increases by 2 or 3 times) What about pn ? (assume no chain transfer) pn = 2aν let a = 1 (coupling) kp []M Large value p = 2ν= n 1 (fkd kt []2 I )⎡ A ⎤ ⎡[]⎤ ⎡Ep −E 2 d −E 2 t ⎥⎤ ⎦ ln pn = ln⎢⎢ p 1 ⎥⎥+ln⎢⎢ M 1 ⎥⎥− ⎢⎣ RT ⎣(Ad At )2 ⎥⎦ ⎣ f I )2 ⎦ ⎢ ([]⇒ on average, get negative value for [ ] E term [E p]⇒ n is negative RT 10.569, Synthesis of Polymers, Fall 2006 Lecture 12 Prof. Paula Hammond 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.ln pnlnln pnpn(das(da hed shed line) line)ln R (solid line)ln R (solid line)pp111TTThigh T low Thigh T low TThermodynamics ΔG = ΔH - TΔS should be negative for polymerization to take place 1. ΔH → strongly exothermic rxns ΔHp (enthalpy of propagation) → ∼ -160 to -60 kJ/mol 2. ΔS → lose entropy with polymerization ΔS → ∼ -90 to -120 J/(mol⋅K) or -0.09 to -0.12 kJ/(mol⋅K) Usually ΔH is much larger than T ΔS term ⇒ negative ΔG (thermodynamically favorable to polymerize) At certain Temp range, its possible for ΔG → 0 ⇒ get near equilibria conditioning kpM +M MMkdp depropagation rate constant At equilibrium (or near): d[]MM −dp [ ]− =(kp []k )M ⋅ dt at equilibrium = 0 [Mn+1 ⋅]Keq =[ ]⋅[ ][Mn+1⋅] and [Mn ⋅] approx. equalMn M 1 kp= = [] kdpM 10.569, Synthesis of Polymers, Fall 2006 Lecture 12 Prof. Paula Hammond 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.[] M =kdp = 1 eq k Kp eq equilibrium monomer concentration at a given temp Will always define with respect to monomer conc or temperature. Standard States Defns: ΔGo = ΔHo − TΔSo = −RT ln Keq ΔG = ΔGo + RT ln K = 0eq 1ΔHo − TΔSo = −RTc ln M[]eq = RTc ln[]M eq Solve for T: ΔHo T =coΔS + R ln[]M eq Equilibrium monomer conc “ceiling [M]eq defined as ratio: [M ]e Motemp” []s Standard state monomer conc = highest T for polymerization to occur [M]os = 1 M soln (or bulk conc’n) M Ho o ⇒ln[] oe = ln[]eq =Δ −ΔSM []s cR M RT determine [M]e from T ceiling temperature term when no monomer conc is specified, is usually assuming that [M]c = [M]bulk 10.569, Synthesis of Polymers, Fall 2006 Lecture 12 Prof. Paula Hammond 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.(at 25oC) Examples [M]c (M) Tc (assuming bulk monomer) Vinyl acetate 1x10-4 --Methyl methacrylate -- 220oC α-methyl styrene 2.2 61oC 10.569, Synthesis of Polymers, Fall 2006 Lecture 12 Prof. Paula Hammond 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,