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

Step Growth Polymerizations Bifunctional monomers AB monomers

Example Polymers via Step Growth Reactions DacronTM, MylarTM

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—B + A—ba—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 = ————————————————

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—B + A—ba—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

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

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

Weight Average and Number Average Molar Masses

Accessibility of mutually reacting groups 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

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

Direct Reaction “Le Chatelier’s Principle”

Mechanism

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

Equilibrium Considerations: Closed System [ester] [H2O] [RCOOH] [ROH] Keq = ———————— 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 ( p [M]0)2 ( [M]0 – p [M]0)2 Keq = ———————— p2 [M]02 [M]02 ( 1– p )2 = ———————— p2 ( 1– p )2 = ————

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

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

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 Polymer K Polyesters 1 - 10 Polycarbonates 15 Transesterifications 0.1 – 1.0 Polyamidation 102 - 103

Open System 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 ( p [M]0)2 ( [M]0 – p [M]0)2 Keq = ———————— p [H2O] [M]0 ( 1– p )2 = —————— p [H2O] (Xn)2 [M]0 = —————— 1 Xn2 [H2O] —— K [M]0 Xn ( Xn – 1) [H2O] = —————

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

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

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