High Polymer Synthesis: Importance of Equal Reactivity in Step-Growth Reactions

1. Reading (Odian Book): Chapter 2-1, 2-2, 2-4

2. Step Growth Polymerizations • Bifunctional monomers • AB monomers

3. Example Polymers via Step Growth Reactions DacronTM, MylarTM

4. Importance of Equal Reactivity A—B + A—B + A—B + A—B + A—B + A—B + A—B + A—B + A—B A—B + A—ba—B + A—ba—B + A—B + A—ba—B + A—ba—B + A—B FA°= # of A groups at the beginning FA = # of A groups at any given time p= conversion = 1 – FA /FA° = 1 – (6/10) Xn = average degree of polymerization total # of molecules present initially total # of molecules present at time t Xn = ————————————————

5. Importance of Equal Reactivity A—B + A—B + A—B + A—B + A—B + A—B + A—B + A—B + A—B A—B + • p = 0.0 Xn = 1 A—ba—B + A—ba—B + A—B + A—ba—B + A—ba—B + A—B • p = 0.4 Xn = 1.67 A—ba—ba—ba—B + A—ba—B + A—ba—ba—B + A—B • p = 0.6 Xn = 2.5 A—ba—ba—ba—B + A—ba—ba—ba—ba—B + A—B • p = 0.7 Xn = 3.33 A—ba—ba—ba—B + A—ba—ba—ba—ba—ba—B • p = 0.8 Xn = 5

6. MW and Conversion Rewriting: 1[M]0 (1 – p)[M] Knowing: [M]0 [M] = Xn = Xn = Given that: [M]= [M]0 - [M]0 p Rewriting: [M]= [M]0 (1 – p) 1 (1 – p)

7. Implications of Carothers Equation 1 (1 – p) • Conversion Xn • 50% 2 • 80% 5 • 90% 10 • 95% 20 • 99% 100 • 99.5% 200 Xn =

8. Weight Average and Number Average Molar Masses

9. Factors Involved in the Synthesis of High MW Linear Polymers via Step-Growth Reactions • High purity monomers • Di-functionality • Proper stoichiometry • Very high conversions • No side reactions • Accessibility of mutually reacting groups • In general: • Suitable for bulk reactions • Moderate viscosity during much of the reaction • Incredible effort ($$) goes to pushing the reaction forward in last stages

10. Methods for Polyester Synthesis • Direct reaction • Acid halide / hydroxyl • Transesterification • Melt acidolysis

11. Direct Reaction • “Le Chatelier’s Principle”

12. Mechanism

13. Overall Reaction • Self-catalyzed Rp [OH] [COOH] [COOH] • Catalyzed by added acid ( [H+] = constant)

14. Equilibrium Considerations:Closed System [ester] [H2O] ( p [M]0)2 p2 [M]02 p2 Keq = ———————— Keq = ———————— = ———————— = ———— [RCOOH] [ROH] ( [M]0 – p [M]0)2 [M]02 ( 1– p )2 ( 1– p )2 • Initial hydroxyl and carboxyl concentrations are [M]0 • Concentration of ester groups @ equilibrium is p [M]0 where p = extent of reaction @ equilibrium • The concentrations of hydroxyl and carboxyl groups @ equilibrium must therefore be:( [M]0 – p [M]0) • Therefore

15. Equilibrium Considerations:Closed System [ester] [H2O] Keq = ———————— [RCOOH] [ROH] K½ p = ———— 1+ K½ Xn 1 + K½ = • Solve for p yields: • Knowing that: 1 (1 – p) Xn =

16. Effect of Equilibrium Constant on “p” and Degree of Polymerization:Closed System

17. Effect of Equilibrium Constant on “p” and Degree of Polymerization:Closed System • Indicates the limitation imposed by equilibrium on the synthesis of high MW polymer • @ Xn = 100 (corresponding to Mn≈ 10k) can be obtained in a closed system only if K is 104!!! • Can not be done in a closed system for most polymers… • Therefore must drive the equilibrium

18. Open System ( p [M]0)2 p [H2O] p [H2O] (Xn)2 Keq = ———————— = —————— = —————— ( [M]0 – p [M]0)2 [M]0 ( 1– p )2 [M]0 1 K [M]0 [H2O] —— [H2O] = ————— Xn2 Xn ( Xn – 1) • Extent to which one must drive the system in the forward reaction • can be seen by calculating the lowering of the small molecule condensate concentration that is necessary to achieve a particular MW • Knowing that • Solve for [H2O] 1 (1 – p) Xn = [H2O] = p [M]0

19. Drive the Equilibrium • Need to remove the small molecule condensate • H2O • HCl • Small molecule condensate needs to diffuse through and eventually out of the reaction mixture • Not easy because of high viscosity • Can lead to reactions becoming diffusion controlled

20. Effect of Water Concentration on Degree of Polymerization:Open, Driven System

21. How best to drive the Equilibrium? • Mixing is energy and capital intensive • Wiped film reactors to increase surface area • Increase diffusivity of the condensate • Raise the temperature to lower the viscosity of the melt • Potential for side reactions • Swell the melt with solvents • Supercritical CO2