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CHAPTER 9: Kinetics of chain and step growth polymerization

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INTRODUCTION TO POLYMER (THIRD YEAR)

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CHE 305 Introduction to Polymer Chemistry Chapter 9: Kinetics of chain and step growth polymerization β€’ Name: Winnie Hung β€’ E-mail: r61042i@gmail.com 1
Outline 1. Step-growth mechanism 2. Kinetics of step-growth polymerization 3. Chain-growth mechanism 4. Kinetics of chain-growth polymerization 2
Polymer synthesis 3 β€’ Polymers may be formed by two major kinetic schemes. 1.Step polymerization 2.Chain polymerization (Faster) β€’ Free radical polymerization Initiation ο‚‚Propagation Termination β€’ Anionic polymerization β€’ Cationic polymerization
Step-growth mechanism 4
Step-growth polymerization 5 +𝐻𝐢𝑙
6 Chain growth 1. Uncontrolled (Popcorn) 2. Controlled/ Living (Grass) Controlled chain-growth
Polyamide-I 7 A B A BA BA B
Polyamide-II 8 Diacid Diamina Polyamide A BA B A BA BA A
Assume all functional groups equally reactive 9 β€’ Xn: Number average chain length β€’ Imagine 16 monomers (or 32 functional groups) Xn= 8Γ—1+4Γ—2 12 = 1.3 25% reaction Xn= 4Γ—1+1Γ—2+2Γ—3+1Γ—4 8 = 2 50% reaction Xn=? 75% reaction 4 Still very low
Step-growth 10 For high molecular weight β€’ the reaction must go toward completion! β€’ ( >99% reaction rate)
Carother's Equation 11 β€’ N0 ≑ # of monomers originally present in system β€’ N ≑ # of molecules present in system at any time t β€’ (N0-N) ≑ Total # of functional groups of either A or B that have reacted at t β€’ 𝑝 ≑ 𝐸π‘₯𝑑𝑒𝑛𝑑 π‘œπ‘“ π‘Ÿπ‘’π‘Žπ‘π‘‘π‘–π‘œπ‘› = 𝑁0 βˆ’ 𝑁 𝑁0 β†’ 𝑁 = 𝑁0 1 βˆ’ 𝑝 β€’ Since 𝑋 𝑛 = 𝑁0 𝑁 Xn = 1 1 βˆ’ 𝑝 Carother's Equation
Carother's Equation 12 p Xn 0.95 20 0.99 100 0.999 1000 Example: Good fibers of nylon 6-6 (fishing line), Mn=12,000 g/mol, Xn~ 110, so p should be more than? Ans: >0.99
How to control the MW 13 If the Mw ‒ Too low→ Poor properties ‒ Too high→ Difficult to process (Melt/ solubilize) Nylon rope trick ‒ A.Q. phase (Hexine diamine)+Organic phase (Adipoyl chloride)
How to control the MW 14 Control β€’ Heat+Pressure
How to control the MW 15 Control β€’ Stoichiometric imbalance β€’ Excess of one reactant in A-A/B-B system to limit MW 𝑋 𝑛 = 1 + π‘Ÿ 1 + π‘Ÿ βˆ’ 2π‘Ÿπ‘ , r = 𝑁0𝐴－𝐴 𝑁0𝐡－B = 𝑁0𝐴 𝑁0𝐡 # of unreacted functional groups Excess goes to denominator, r<1
How to control the MW 16 For β€œquantitative” reaction, P=0.999 N0AA N0BB r Xn 1 1 1 1000 1 1.05 0.952 39 𝑋 𝑛 = 1 + π‘Ÿ 1 + π‘Ÿ βˆ’ 2π‘Ÿπ‘ , r = 𝑁0𝐴－𝐴 𝑁0𝐡－B = 𝑁0𝐴 𝑁0𝐡
Kinetics of step-growth 17
Polyesterification 18 A-B type Polyester RCOOH + OH β†’ COOR + H2O H+ (cat) Self-catalyzed βˆ’π‘‘[𝐢𝑂𝑂𝐻] 𝑑𝑑 = π‘˜ 𝐢𝑂𝑂𝐻 2[𝑂𝐻]
Polyesterification 19 Self-catalyzed βˆ’π‘‘[𝐢𝑂𝑂𝐻] 𝑑𝑑 = π‘˜ 𝐢𝑂𝑂𝐻 2[𝑂𝐻] If [COOH]=[OH] β†’ C Then βˆ’π‘‘πΆ 𝑑𝑑 = π‘˜πΆ3 β†’βˆ’ 𝐢0 𝐢 𝑑𝐢 𝐢3 = π‘˜ 0 𝑑 𝑑𝑑 β†’2kt= 1 𝐢2 βˆ’ 1 𝐢0 2 𝑋 𝑛 = 𝐢0 𝐢 = 1 1 βˆ’ 𝑝 β†’C=C0(1-P) Then, 2C0 2kt=[ 1 1βˆ’π‘ƒ 2] βˆ’ 1 Xn 2
Polyesterification 20 Acid-catalyzed βˆ’π‘‘[𝐢𝑂𝑂𝐻] 𝑑𝑑 = π‘˜β€² 𝐢𝑂𝑂𝐻 [𝑂𝐻] If [COOH]=[OH] β†’ C Then βˆ’π‘‘πΆ 𝑑𝑑 = π‘˜β€²πΆ2 β†’βˆ’ 𝐢0 𝐢 𝑑𝐢 𝐢2 = π‘˜β€² 0 𝑑 𝑑𝑑 →𝐢0 π‘˜β€² 𝑑 = 1 1βˆ’π‘ βˆ’ 1
Polyesterification 21 Self-catalyzed Acid-catalyzed 1 1 βˆ’ 𝑝 2 = Xn2 t 1 1 βˆ’ 𝑝 = Xn t 𝐢0 π‘˜β€² 𝑑 = 1 1 βˆ’ 𝑝 βˆ’ 12C0 2kt=[ 1 1βˆ’π‘ƒ 2] βˆ’ 1
Practice 22 Q: 80 moles of monomers react to prepare Nylon 12. After completion of 8 h, 4 moles of monomers are still left. What is the number average molecular weight of polymer system? (the molecular weights of the repeating units of polymer Nylon 12 is 197) The extent of reaction is p= (80-4)/80 = 0.95 Xn=1/(1-p) = 1/(1-0.95)= 20 Mn=20*197=3940
Practice 23 Q: If the value of C0 and k are 10 mol L-1 and 10-3 L mol s-1, respectively, how long would it take to obtain a Xn of 37? Assume it’s self-catalyzed 2C0 2kt=[ 1 1βˆ’π‘ƒ 2] βˆ’ 1 β†’2C0 2kt=Xn 2βˆ’1 β†’t=68400 s
Flory distribution 24 Molar mass/ Degree of polymerization distribution β†’ Calculate the probability P(x) of finding a chain comprising x units also know as the mole fraction P(x) P(x)= 𝑁 π‘₯ 𝑁 = # π‘‹βˆ’π‘šπ‘’π‘Ÿπ‘  π‘‡π‘œπ‘‘π‘Žπ‘™ # π‘šπ‘œπ‘™π‘’π‘π‘’π‘™π‘’π‘  (X=1 for monomer, 2 for dimer, 3 for trimer)
Flory distribution 25  Step 1: Probability of random molecule being a monomer P(x=1)=(1-p)  Step 2: Probability of random molecule being a dimer P(x=2)=p(1-p) The first molecule reacted The adjacent is unreacted At extent of reaction p for either 1. x A-A + x B-B β†’ A-A[B-BA-A]x-1B-B 2. x A-B β†’ A[BA]x-1B Note: β€’ A, B are functional groups β€’ β€œMolecules” are either monomers or polymer chains
Flory distribution 26 P(x=2) =p(1-p), P(x=3) =p2(1-p) β†’P(x)=px-1(1-p) Since probability of x=P(x)=Mol. Fraction= 𝑁 π‘₯ 𝑁 𝑃 π‘₯ = 𝑁 π‘₯ 𝑁 = 𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝 →𝑁 π‘₯ = 𝑁𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝
Flory distribution 27 Since Xn= 𝑁0 𝑁 β†’ N = 𝑁0 𝑋 𝑛 = 𝑁0(1 βˆ’ 𝑝) β†’ 𝑁 π‘₯ = 𝑁0 𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝 2 In terms of mass fraction of x-mers, Wx β†’ π‘Š π‘₯ = π‘₯𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝 2 Where Wx= π‘₯𝑁 π‘₯ 𝑁0 = π‘‡π‘œπ‘‘π‘Žπ‘™ # π‘œπ‘“ π‘šπ‘œπ‘›π‘œπ‘šπ‘’π‘Ÿπ‘  π‘–π‘›π‘π‘œπ‘Ÿπ‘π‘Žπ‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘–π‘›π‘‘π‘œ π‘šπ‘œπ‘™π‘’π‘π‘’π‘™π‘’π‘  π‘€π‘–π‘‘β„Ž π‘™π‘’π‘›π‘”π‘‘β„Ž π‘₯ π‘‡π‘œπ‘‘π‘Žπ‘™ π‘šπ‘œπ‘›π‘œπ‘šπ‘’π‘Ÿπ‘  𝑖𝑛 π‘‘β„Žπ‘’ π‘ π‘¦π‘ π‘‘π‘’π‘š 𝑁 π‘₯ = 𝑁𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝
Flory distribution here 28 Number-fraction distribution Weight-fraction distribution 𝑁 π‘₯ 𝑁 X 50 100 150 200 Wx= π‘₯𝑁 π‘₯ 𝑁0 X 50 100 150 200 p=0.96 p=0.9875 p=0.9950 p=0.96 p=0.9875 p=0.9950
Note 29 β€’ Average molecular weight Mn and Mw as function of p for step-growth 𝑀0 ≑ π‘šπ‘œπ‘™π‘Žπ‘Ÿ π‘šπ‘Žπ‘ π‘  π‘œπ‘“ π‘Ÿπ‘’π‘π‘’π‘Žπ‘‘ 𝑒𝑛𝑖𝑑 𝑋 𝑛 = 𝑀 𝑛 𝑀0 = 1 1 βˆ’ 𝑝 β†’ 𝑀 𝑛 = 𝑀0 1 βˆ’ 𝑝 β†’Mw= 𝑀0 (1+𝑝) 1βˆ’π‘ β€’ Dispersity (PDI) PDI=Đ= 𝑀 π‘Š 𝑀 𝑛 = 1 + 𝑝 As pβ†’1 (reaction ↑) Đ→2
Major stepwise polymer classes 30
Nature product polymers 31 β€’ Living organisms make many polymers enzymatically. β€’ Most such natural polymers strongly resemble step- polymerized materials. β€’ The structure ultimately being controlled by DNA.
Commercialization dates 32
Chain-growth By radical polymerization by unpaired electrons traveling down the chain and add new monomers as they go! Or made by ionic polymerization (anionic or cationic) 33
Free radical polymerization 34 1. Initiation 2. Propagation
Free Radical Polymerization οΌ©ο‚˜ + C=C οΌ©ο‚˜ + C － C Ｉ－C－C 35
Free radical polymerization 36 3. Termination
Radical initiators 37 benzoyl peroxide
Radical intiators 38 𝐻2 𝑂2 + 𝐹𝑒2 + β†’ 𝐹𝑒3 + +𝑂𝐻 βˆ’ +𝑂𝐻● Redox
Initiation + Propagation 39
Termination I 40 (a) Combination (Two chain ends couple)  Double molecular weight  2 initiator fragments
Termination II 41 (b) Disproportionation  One initiator fragment per chain  Predicted molecular weight
Kinetic of chain-growth 42 β€’ Steady-state kinetics β€’ Assume rate of radical formation = rate of radical destruction Initiation, 2-step 1. Decombination of initiator 𝐼 β†’ π‘˜ 𝑑 2𝑅● 2. Attack on the monomer 𝑅● + M β†’ π‘˜π‘– 𝑅𝑀● β†’Rate of thermal initiation 𝑣𝑖 = 𝑑[𝑅𝑀●] 𝑑𝑑 = 2π‘˜π‘‘π‘“[𝐼] Slow-rate determining step 2 initiators per I Initiators efficiency, the ability of 𝑅● to propagate chains 0.3-0.8
Kinetic of chain-growth 43 Propagation 𝑅𝑀 𝑛● + 𝑀 β†’ π‘˜ 𝑝 𝑅𝑀 𝑛 + 1● 𝑣 𝑝 = π‘˜π‘ 𝑀 [𝑀●] β€’ [M] : concentration of monomers β€’ [𝑀●]: concentration of the growing chains (active centers)
Kinetic of chain-growth 44 Termiation 𝑣𝑑 = 2π‘˜π‘‘ 𝑀● 𝑀● 2 radicals cost for each termination step kt=ktc+ktd β€’ ktc: combination β€’ ktd: disproportionation
Kinetic of chain-growth 45 Steady state≑ 𝑣𝑖 = 𝑣𝑑 2π‘˜π‘‘π‘“ 𝐼 = 2kt M● 2 M● = π‘˜ 𝑑 𝑓[𝐼] π‘˜π‘‘ 𝑣 𝑝 = π‘˜π‘[𝑀] π‘˜ 𝑑 𝑓[𝐼] π‘˜π‘‘ Too low to measure experimentally
Kinetic of chain-growth 46 β€’ 𝐷𝑒𝑓𝑖𝑛𝑒 𝑣 ≑ π‘˜π‘–π‘›π‘’π‘‘π‘–π‘ π‘β„Žπ‘Žπ‘–π‘› π‘™π‘’π‘›π‘”π‘‘β„Ž β€’ Average # of monomers reacting with active center during its lifetime β†’ 𝑣＝ π‘šπ‘œπ‘›π‘œπ‘šπ‘’π‘Ÿπ‘  π‘Žπ‘‘π‘‘π‘’π‘‘/𝑠𝑒𝑐 # π‘œπ‘“ π‘β„Žπ‘Žπ‘–π‘›π‘  π‘“π‘œπ‘Ÿπ‘šπ‘’π‘‘/𝑠𝑒𝑐 = 𝑣 𝑝 𝑣𝑑 1. For combination: Xn=2 𝑣 2. For disproportionation: Xn= 𝑣
Kinetic of chain-growth 47 β€’ Under steady state 𝑣＝ 𝑣 𝑝 𝑣𝑑 = 𝑣 𝑝 𝑣𝑖 = π‘˜ 𝑝 𝑀 [𝑀●] 2π‘˜π‘‘ 𝑀● 2 = π‘˜ 𝑝 𝑀 2π‘˜π‘‘ 𝑀● = π‘˜ 𝑝 2 𝑀 2 2π‘˜π‘‘π‘£π‘ β˜… 𝑀● = 𝑣 𝑝 π‘˜π‘[𝑀]
Practice 48 The following are data for the polymerization of styrene in benzene at 60Β°C with benzoyl peroxide as the initiator. [M] = 3.34 Γ— 103 mol/m3 [I] = 4.0 mol/m3 kp 2/kt = 0.95 Γ— 10–6 m3/mol-s If the spontaneous decomposition rate of benzoyl peroxide is 3.2 Γ— 10–6 m3/mol-s, calculate the initial rate of polymerization. Assume the initiator efficiency f=1
Answer 49 𝑣 𝑝 = π‘˜π‘ 𝑀 π‘˜ 𝑑 𝑓 𝐼 π‘˜π‘‘ β†’ 𝑣 𝑝 2 = π‘˜π‘‘ π‘˜ 𝑝 2 π‘˜π‘‘ 𝐼 𝑀 2 β†’ 𝑣 𝑝 2 = (3.2 Γ— 10–6)Γ—( 0.95 Γ— 10–6) Γ— 4 Γ— (3.34 Γ— 103)2 →𝑣 𝑝 2 = 1.357 Γ— 10–4 →𝑣 𝑝=0.0116 mol/m3-s
Practice 50 For vinyl acetate polymerized at 50 α΅’C, the value of the ratio kp 2/kt is 0.0138 l/mol-s. What is the value of chain length, when monomer concentration is 6.53 mol/l and rate of polymerization is 2.0Γ—10-4 mol/l-s? The expression for kinetic chain length is 𝑣 = π‘˜ 𝑝 2 𝑀 2 2π‘˜π‘‘π‘£π‘ = 0.0138 Γ— 6.532 2 Γ— (2.0 Γ— 10βˆ’4) = 1471
Thermodynamics 51 βˆ†πΊ 𝑝 = βˆ†H 𝑝 βˆ’ Tβˆ†π‘† 𝑝 β€’ βˆ†H 𝑝: negative, because from πœ‹ π‘π‘œπ‘›π‘‘ π‘‘π‘œ 𝜎 π‘π‘œπ‘›π‘‘ 𝑖𝑠 𝑒π‘₯π‘‘β„Žπ‘œπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘–π‘ β€’ βˆ’βˆ†π» 𝑝 β‰ˆ 30 βˆ’ 150𝐾𝐽/π‘šπ‘œπ‘™ β€’ βˆ†π‘† 𝑝: negative, because we are confining monomers to the chain β€’ βˆ’βˆ†π‘† 𝑝 β‰ˆ 100 βˆ’ 130𝐽 π‘šπ‘œπ‘™πΎ βˆ†πΊ 𝑝 < 0 at normal temp.
Polymerization processes 52 1. Block (monomers only, no solvent) -Efficient, eco-friendly, optically transparent -Susceptible to auto acceleration, explosion 2. Solution (In a solvent) -Heat dissipation, but susceptible to reaction with solvent -Ungreen 3. Suspension (of monomers in AQ phase) -Effectively bulk, Droplets 0.1-5mm -Reaction must be stable to water 4. Emulsion (Much smaller particles 50nm-5πœ‡m) -Use Micelles with a surfactant to control Mw
Features of free radical polymerization 53 1. High Mw formed immediately The average of molecular weight in the beginning is low 2. Steady decrease in [M] thru out the reaction 3. Only the active center (the growing chain ) is reactive toward other monomers 4. Long reaction time increase the yield of polymer produce but not Mw 5. Increasing temp. increases the rate but decreases Mw
Chain-growth 54 1. The rate of propagation is proportional to the concentration of the monomer and the square root of the concentration of the initiator. 2. The rate of termination is proportional to the concentration of the initiator. 3. The average molecular weight is proportional to the concentration of the monomer and inversely proportional to the square root of the concentration of initiator. 4. The first chain that is initiated rapidly produces a high molecular weight polymer. 5. The monomer concentration decreases steadily throughout the reaction and approaches zero at the end. 6. The increases in rates of initiation, propagation, and termination with increases in temperature are in accord with the Arrhenius equation. The energies of activation of initiation, propagation, and termination are approximately 35, 5, and 3kcal/mol, respectively. Data for typical energies of activation are given in Tables8.3 and 8.4. 7. Increasing the temperature increases the concentration of free radicals and thus the rate of reactions, but it decreases the average molecular weight. 8. If the temperature exceeds the ceiling temperature (Tc), the polymer will decompose and no propagation will take place at temperatures above the ceiling temperature.
Chain growth V.S. Step growth 55 Step growth Chain growth Reactive sites All molecules (monomer, oligomer, polymer) Only monomer react to the β€œactive site” Reaction process No termination 3 steps 1. Initiation 2. Propagation 3. Termination Reaction speed Slower Faster (Initiator↑) Final product Oligomers of many sizes Polymer+monomer+very few growing chains
56
Chain polymer strucutre 59
Chain polymer structure-ABS 60 3D printing, Tg? m.p.? Acrylonitrile Butadiene Styrene
Thanks for your attention 62

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CHAPTER 9: Kinetics of chain and step growth polymerization

  • 1. CHE 305 Introduction to Polymer Chemistry Chapter 9: Kinetics of chain and step growth polymerization β€’ Name: Winnie Hung β€’ E-mail: r61042i@gmail.com 1
  • 2. Outline 1. Step-growth mechanism 2. Kinetics of step-growth polymerization 3. Chain-growth mechanism 4. Kinetics of chain-growth polymerization 2
  • 3. Polymer synthesis 3 β€’ Polymers may be formed by two major kinetic schemes. 1.Step polymerization 2.Chain polymerization (Faster) β€’ Free radical polymerization Initiation ο‚‚Propagation Termination β€’ Anionic polymerization β€’ Cationic polymerization
  • 6. 6 Chain growth 1. Uncontrolled (Popcorn) 2. Controlled/ Living (Grass) Controlled chain-growth
  • 9. Assume all functional groups equally reactive 9 β€’ Xn: Number average chain length β€’ Imagine 16 monomers (or 32 functional groups) Xn= 8Γ—1+4Γ—2 12 = 1.3 25% reaction Xn= 4Γ—1+1Γ—2+2Γ—3+1Γ—4 8 = 2 50% reaction Xn=? 75% reaction 4 Still very low
  • 10. Step-growth 10 For high molecular weight β€’ the reaction must go toward completion! β€’ ( >99% reaction rate)
  • 11. Carother's Equation 11 β€’ N0 ≑ # of monomers originally present in system β€’ N ≑ # of molecules present in system at any time t β€’ (N0-N) ≑ Total # of functional groups of either A or B that have reacted at t β€’ 𝑝 ≑ 𝐸π‘₯𝑑𝑒𝑛𝑑 π‘œπ‘“ π‘Ÿπ‘’π‘Žπ‘π‘‘π‘–π‘œπ‘› = 𝑁0 βˆ’ 𝑁 𝑁0 β†’ 𝑁 = 𝑁0 1 βˆ’ 𝑝 β€’ Since 𝑋 𝑛 = 𝑁0 𝑁 Xn = 1 1 βˆ’ 𝑝 Carother's Equation
  • 12. Carother's Equation 12 p Xn 0.95 20 0.99 100 0.999 1000 Example: Good fibers of nylon 6-6 (fishing line), Mn=12,000 g/mol, Xn~ 110, so p should be more than? Ans: >0.99
  • 13. How to control the MW 13 If the Mw β€’ Too lowβ†’ Poor properties β€’ Too highβ†’ Difficult to process (Melt/ solubilize) Nylon rope trick β€’ A.Q. phase (Hexine diamine)+Organic phase (Adipoyl chloride)
  • 14. How to control the MW 14 Control β€’ Heat+Pressure
  • 15. How to control the MW 15 Control β€’ Stoichiometric imbalance β€’ Excess of one reactant in A-A/B-B system to limit MW 𝑋 𝑛 = 1 + π‘Ÿ 1 + π‘Ÿ βˆ’ 2π‘Ÿπ‘ , r = 𝑁0𝐴－𝐴 𝑁0𝐡－B = 𝑁0𝐴 𝑁0𝐡 # of unreacted functional groups Excess goes to denominator, r<1
  • 16. How to control the MW 16 For β€œquantitative” reaction, P=0.999 N0AA N0BB r Xn 1 1 1 1000 1 1.05 0.952 39 𝑋 𝑛 = 1 + π‘Ÿ 1 + π‘Ÿ βˆ’ 2π‘Ÿπ‘ , r = 𝑁0𝐴－𝐴 𝑁0𝐡－B = 𝑁0𝐴 𝑁0𝐡
  • 18. Polyesterification 18 A-B type Polyester RCOOH + OH β†’ COOR + H2O H+ (cat) Self-catalyzed βˆ’π‘‘[𝐢𝑂𝑂𝐻] 𝑑𝑑 = π‘˜ 𝐢𝑂𝑂𝐻 2[𝑂𝐻]
  • 19. Polyesterification 19 Self-catalyzed βˆ’π‘‘[𝐢𝑂𝑂𝐻] 𝑑𝑑 = π‘˜ 𝐢𝑂𝑂𝐻 2[𝑂𝐻] If [COOH]=[OH] β†’ C Then βˆ’π‘‘πΆ 𝑑𝑑 = π‘˜πΆ3 β†’βˆ’ 𝐢0 𝐢 𝑑𝐢 𝐢3 = π‘˜ 0 𝑑 𝑑𝑑 β†’2kt= 1 𝐢2 βˆ’ 1 𝐢0 2 𝑋 𝑛 = 𝐢0 𝐢 = 1 1 βˆ’ 𝑝 β†’C=C0(1-P) Then, 2C0 2kt=[ 1 1βˆ’π‘ƒ 2] βˆ’ 1 Xn 2
  • 20. Polyesterification 20 Acid-catalyzed βˆ’π‘‘[𝐢𝑂𝑂𝐻] 𝑑𝑑 = π‘˜β€² 𝐢𝑂𝑂𝐻 [𝑂𝐻] If [COOH]=[OH] β†’ C Then βˆ’π‘‘πΆ 𝑑𝑑 = π‘˜β€²πΆ2 β†’βˆ’ 𝐢0 𝐢 𝑑𝐢 𝐢2 = π‘˜β€² 0 𝑑 𝑑𝑑 →𝐢0 π‘˜β€² 𝑑 = 1 1βˆ’π‘ βˆ’ 1
  • 21. Polyesterification 21 Self-catalyzed Acid-catalyzed 1 1 βˆ’ 𝑝 2 = Xn2 t 1 1 βˆ’ 𝑝 = Xn t 𝐢0 π‘˜β€² 𝑑 = 1 1 βˆ’ 𝑝 βˆ’ 12C0 2kt=[ 1 1βˆ’π‘ƒ 2] βˆ’ 1
  • 22. Practice 22 Q: 80 moles of monomers react to prepare Nylon 12. After completion of 8 h, 4 moles of monomers are still left. What is the number average molecular weight of polymer system? (the molecular weights of the repeating units of polymer Nylon 12 is 197) The extent of reaction is p= (80-4)/80 = 0.95 Xn=1/(1-p) = 1/(1-0.95)= 20 Mn=20*197=3940
  • 23. Practice 23 Q: If the value of C0 and k are 10 mol L-1 and 10-3 L mol s-1, respectively, how long would it take to obtain a Xn of 37? Assume it’s self-catalyzed 2C0 2kt=[ 1 1βˆ’π‘ƒ 2] βˆ’ 1 β†’2C0 2kt=Xn 2βˆ’1 β†’t=68400 s
  • 24. Flory distribution 24 Molar mass/ Degree of polymerization distribution β†’ Calculate the probability P(x) of finding a chain comprising x units also know as the mole fraction P(x) P(x)= 𝑁 π‘₯ 𝑁 = # π‘‹βˆ’π‘šπ‘’π‘Ÿπ‘  π‘‡π‘œπ‘‘π‘Žπ‘™ # π‘šπ‘œπ‘™π‘’π‘π‘’π‘™π‘’π‘  (X=1 for monomer, 2 for dimer, 3 for trimer)
  • 25. Flory distribution 25  Step 1: Probability of random molecule being a monomer P(x=1)=(1-p)  Step 2: Probability of random molecule being a dimer P(x=2)=p(1-p) The first molecule reacted The adjacent is unreacted At extent of reaction p for either 1. x A-A + x B-B β†’ A-A[B-BA-A]x-1B-B 2. x A-B β†’ A[BA]x-1B Note: β€’ A, B are functional groups β€’ β€œMolecules” are either monomers or polymer chains
  • 26. Flory distribution 26 P(x=2) =p(1-p), P(x=3) =p2(1-p) β†’P(x)=px-1(1-p) Since probability of x=P(x)=Mol. Fraction= 𝑁 π‘₯ 𝑁 𝑃 π‘₯ = 𝑁 π‘₯ 𝑁 = 𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝 →𝑁 π‘₯ = 𝑁𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝
  • 27. Flory distribution 27 Since Xn= 𝑁0 𝑁 β†’ N = 𝑁0 𝑋 𝑛 = 𝑁0(1 βˆ’ 𝑝) β†’ 𝑁 π‘₯ = 𝑁0 𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝 2 In terms of mass fraction of x-mers, Wx β†’ π‘Š π‘₯ = π‘₯𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝 2 Where Wx= π‘₯𝑁 π‘₯ 𝑁0 = π‘‡π‘œπ‘‘π‘Žπ‘™ # π‘œπ‘“ π‘šπ‘œπ‘›π‘œπ‘šπ‘’π‘Ÿπ‘  π‘–π‘›π‘π‘œπ‘Ÿπ‘π‘Žπ‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘–π‘›π‘‘π‘œ π‘šπ‘œπ‘™π‘’π‘π‘’π‘™π‘’π‘  π‘€π‘–π‘‘β„Ž π‘™π‘’π‘›π‘”π‘‘β„Ž π‘₯ π‘‡π‘œπ‘‘π‘Žπ‘™ π‘šπ‘œπ‘›π‘œπ‘šπ‘’π‘Ÿπ‘  𝑖𝑛 π‘‘β„Žπ‘’ π‘ π‘¦π‘ π‘‘π‘’π‘š 𝑁 π‘₯ = 𝑁𝑝 π‘₯βˆ’1 1 βˆ’ 𝑝
  • 28. Flory distribution here 28 Number-fraction distribution Weight-fraction distribution 𝑁 π‘₯ 𝑁 X 50 100 150 200 Wx= π‘₯𝑁 π‘₯ 𝑁0 X 50 100 150 200 p=0.96 p=0.9875 p=0.9950 p=0.96 p=0.9875 p=0.9950
  • 29. Note 29 β€’ Average molecular weight Mn and Mw as function of p for step-growth 𝑀0 ≑ π‘šπ‘œπ‘™π‘Žπ‘Ÿ π‘šπ‘Žπ‘ π‘  π‘œπ‘“ π‘Ÿπ‘’π‘π‘’π‘Žπ‘‘ 𝑒𝑛𝑖𝑑 𝑋 𝑛 = 𝑀 𝑛 𝑀0 = 1 1 βˆ’ 𝑝 β†’ 𝑀 𝑛 = 𝑀0 1 βˆ’ 𝑝 β†’Mw= 𝑀0 (1+𝑝) 1βˆ’π‘ β€’ Dispersity (PDI) PDI=Đ= 𝑀 π‘Š 𝑀 𝑛 = 1 + 𝑝 As pβ†’1 (reaction ↑) Đ→2
  • 31. Nature product polymers 31 β€’ Living organisms make many polymers enzymatically. β€’ Most such natural polymers strongly resemble step- polymerized materials. β€’ The structure ultimately being controlled by DNA.
  • 33. Chain-growth By radical polymerization by unpaired electrons traveling down the chain and add new monomers as they go! Or made by ionic polymerization (anionic or cationic) 33
  • 34. Free radical polymerization 34 1. Initiation 2. Propagation
  • 35. Free Radical Polymerization οΌ©ο‚˜ + C=C οΌ©ο‚˜ + C － C Ｉ－C－C 35
  • 38. Radical intiators 38 𝐻2 𝑂2 + 𝐹𝑒2 + β†’ 𝐹𝑒3 + +𝑂𝐻 βˆ’ +𝑂𝐻● Redox
  • 40. Termination I 40 (a) Combination (Two chain ends couple)  Double molecular weight  2 initiator fragments
  • 41. Termination II 41 (b) Disproportionation  One initiator fragment per chain  Predicted molecular weight
  • 42. Kinetic of chain-growth 42 β€’ Steady-state kinetics β€’ Assume rate of radical formation = rate of radical destruction Initiation, 2-step 1. Decombination of initiator 𝐼 β†’ π‘˜ 𝑑 2𝑅● 2. Attack on the monomer 𝑅● + M β†’ π‘˜π‘– 𝑅𝑀● β†’Rate of thermal initiation 𝑣𝑖 = 𝑑[𝑅𝑀●] 𝑑𝑑 = 2π‘˜π‘‘π‘“[𝐼] Slow-rate determining step 2 initiators per I Initiators efficiency, the ability of 𝑅● to propagate chains 0.3-0.8
  • 43. Kinetic of chain-growth 43 Propagation 𝑅𝑀 𝑛● + 𝑀 β†’ π‘˜ 𝑝 𝑅𝑀 𝑛 + 1● 𝑣 𝑝 = π‘˜π‘ 𝑀 [𝑀●] β€’ [M] : concentration of monomers β€’ [𝑀●]: concentration of the growing chains (active centers)
  • 44. Kinetic of chain-growth 44 Termiation 𝑣𝑑 = 2π‘˜π‘‘ 𝑀● 𝑀● 2 radicals cost for each termination step kt=ktc+ktd β€’ ktc: combination β€’ ktd: disproportionation
  • 45. Kinetic of chain-growth 45 Steady state≑ 𝑣𝑖 = 𝑣𝑑 2π‘˜π‘‘π‘“ 𝐼 = 2kt M● 2 M● = π‘˜ 𝑑 𝑓[𝐼] π‘˜π‘‘ 𝑣 𝑝 = π‘˜π‘[𝑀] π‘˜ 𝑑 𝑓[𝐼] π‘˜π‘‘ Too low to measure experimentally
  • 46. Kinetic of chain-growth 46 β€’ 𝐷𝑒𝑓𝑖𝑛𝑒 𝑣 ≑ π‘˜π‘–π‘›π‘’π‘‘π‘–π‘ π‘β„Žπ‘Žπ‘–π‘› π‘™π‘’π‘›π‘”π‘‘β„Ž β€’ Average # of monomers reacting with active center during its lifetime β†’ 𝑣＝ π‘šπ‘œπ‘›π‘œπ‘šπ‘’π‘Ÿπ‘  π‘Žπ‘‘π‘‘π‘’π‘‘/𝑠𝑒𝑐 # π‘œπ‘“ π‘β„Žπ‘Žπ‘–π‘›π‘  π‘“π‘œπ‘Ÿπ‘šπ‘’π‘‘/𝑠𝑒𝑐 = 𝑣 𝑝 𝑣𝑑 1. For combination: Xn=2 𝑣 2. For disproportionation: Xn= 𝑣
  • 47. Kinetic of chain-growth 47 β€’ Under steady state 𝑣＝ 𝑣 𝑝 𝑣𝑑 = 𝑣 𝑝 𝑣𝑖 = π‘˜ 𝑝 𝑀 [𝑀●] 2π‘˜π‘‘ 𝑀● 2 = π‘˜ 𝑝 𝑀 2π‘˜π‘‘ 𝑀● = π‘˜ 𝑝 2 𝑀 2 2π‘˜π‘‘π‘£π‘ β˜… 𝑀● = 𝑣 𝑝 π‘˜π‘[𝑀]
  • 48. Practice 48 The following are data for the polymerization of styrene in benzene at 60Β°C with benzoyl peroxide as the initiator. [M] = 3.34 Γ— 103 mol/m3 [I] = 4.0 mol/m3 kp 2/kt = 0.95 Γ— 10–6 m3/mol-s If the spontaneous decomposition rate of benzoyl peroxide is 3.2 Γ— 10–6 m3/mol-s, calculate the initial rate of polymerization. Assume the initiator efficiency f=1
  • 49. Answer 49 𝑣 𝑝 = π‘˜π‘ 𝑀 π‘˜ 𝑑 𝑓 𝐼 π‘˜π‘‘ β†’ 𝑣 𝑝 2 = π‘˜π‘‘ π‘˜ 𝑝 2 π‘˜π‘‘ 𝐼 𝑀 2 β†’ 𝑣 𝑝 2 = (3.2 Γ— 10–6)Γ—( 0.95 Γ— 10–6) Γ— 4 Γ— (3.34 Γ— 103)2 →𝑣 𝑝 2 = 1.357 Γ— 10–4 →𝑣 𝑝=0.0116 mol/m3-s
  • 50. Practice 50 For vinyl acetate polymerized at 50 α΅’C, the value of the ratio kp 2/kt is 0.0138 l/mol-s. What is the value of chain length, when monomer concentration is 6.53 mol/l and rate of polymerization is 2.0Γ—10-4 mol/l-s? The expression for kinetic chain length is 𝑣 = π‘˜ 𝑝 2 𝑀 2 2π‘˜π‘‘π‘£π‘ = 0.0138 Γ— 6.532 2 Γ— (2.0 Γ— 10βˆ’4) = 1471
  • 51. Thermodynamics 51 βˆ†πΊ 𝑝 = βˆ†H 𝑝 βˆ’ Tβˆ†π‘† 𝑝 β€’ βˆ†H 𝑝: negative, because from πœ‹ π‘π‘œπ‘›π‘‘ π‘‘π‘œ 𝜎 π‘π‘œπ‘›π‘‘ 𝑖𝑠 𝑒π‘₯π‘‘β„Žπ‘œπ‘‘β„Žπ‘’π‘Ÿπ‘šπ‘–π‘ β€’ βˆ’βˆ†π» 𝑝 β‰ˆ 30 βˆ’ 150𝐾𝐽/π‘šπ‘œπ‘™ β€’ βˆ†π‘† 𝑝: negative, because we are confining monomers to the chain β€’ βˆ’βˆ†π‘† 𝑝 β‰ˆ 100 βˆ’ 130𝐽 π‘šπ‘œπ‘™πΎ βˆ†πΊ 𝑝 < 0 at normal temp.
  • 52. Polymerization processes 52 1. Block (monomers only, no solvent) -Efficient, eco-friendly, optically transparent -Susceptible to auto acceleration, explosion 2. Solution (In a solvent) -Heat dissipation, but susceptible to reaction with solvent -Ungreen 3. Suspension (of monomers in AQ phase) -Effectively bulk, Droplets 0.1-5mm -Reaction must be stable to water 4. Emulsion (Much smaller particles 50nm-5πœ‡m) -Use Micelles with a surfactant to control Mw
  • 53. Features of free radical polymerization 53 1. High Mw formed immediately The average of molecular weight in the beginning is low 2. Steady decrease in [M] thru out the reaction 3. Only the active center (the growing chain ) is reactive toward other monomers 4. Long reaction time increase the yield of polymer produce but not Mw 5. Increasing temp. increases the rate but decreases Mw
  • 54. Chain-growth 54 1. The rate of propagation is proportional to the concentration of the monomer and the square root of the concentration of the initiator. 2. The rate of termination is proportional to the concentration of the initiator. 3. The average molecular weight is proportional to the concentration of the monomer and inversely proportional to the square root of the concentration of initiator. 4. The first chain that is initiated rapidly produces a high molecular weight polymer. 5. The monomer concentration decreases steadily throughout the reaction and approaches zero at the end. 6. The increases in rates of initiation, propagation, and termination with increases in temperature are in accord with the Arrhenius equation. The energies of activation of initiation, propagation, and termination are approximately 35, 5, and 3kcal/mol, respectively. Data for typical energies of activation are given in Tables8.3 and 8.4. 7. Increasing the temperature increases the concentration of free radicals and thus the rate of reactions, but it decreases the average molecular weight. 8. If the temperature exceeds the ceiling temperature (Tc), the polymer will decompose and no propagation will take place at temperatures above the ceiling temperature.
  • 55. Chain growth V.S. Step growth 55 Step growth Chain growth Reactive sites All molecules (monomer, oligomer, polymer) Only monomer react to the β€œactive site” Reaction process No termination 3 steps 1. Initiation 2. Propagation 3. Termination Reaction speed Slower Faster (Initiator↑) Final product Oligomers of many sizes Polymer+monomer+very few growing chains
  • 56. 56
  • 58. Chain polymer structure-ABS 60 3D printing, Tg? m.p.? Acrylonitrile Butadiene Styrene
  • 59. Thanks for your attention 62