10.569 Synthesis of Polymers Prof. Paula Hammond Lecture 3: Step Growth Polymerization, Types of Monomers, Kinetics and Equilibrium Considerations, Closed vs. Open Systems Kinetics of Step Growth Polymerization (Chapter 2) A + B → polymer + byproduct Rp = rate of polymerization −d ⎡⎣M ⎤⎦ Rp = dt = −d ⎡⎣a⎤⎦ dt = −d ⎡⎣b⎤⎦ dt = k ⎡⎣a⎤⎡ ⎦⎣b⎤⎦ a b ⎡⎣a⎤⎦ = ⎡⎣b⎤⎦ Assume r =1, where r is the stoichiometric ratio. r = Terminology pn varies with t → pn = ( Xn ) −d ⎡⎣a⎤⎦ dt ⎣⎡a⎦⎤o ⎣⎡a⎦⎤ p. 50 2 = k ⎡⎣a⎤⎦ −d ⎡⎣a⎤⎦ = kt 2 ⎡⎣a⎤⎦ 1 1 − = kt ⎡⎣a⎤⎦ ⎡⎣a⎤⎦o ⎡⎣a⎤⎦o − 1 = ⎡⎣a⎤⎦o kt ⎡⎣a⎤⎦ ⎡a⎤ π =1− ⎣ ⎦ ⎡⎣a⎤⎦o in book, π = p (p. 46) ⎡⎣a⎤⎦o 1 = ⎡⎣a⎤⎦ 1 − π 1 − 1 = pn − 1 ⎡⎣ao ⎤⎦ kt = 1− π Notes: 1 1. ⎡⎣M ⎤⎦ ∝ as time ↑, concentration of monomer ↓ t 2. pn increases linearly with time a+b kf kr c+d kf >> kr LeChatlier’s Principle: remove water To drive reaction forward Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date Making esters: O OH COOH + Keq C + H2O O Ester can hydrolyze with water and go backwards (reverse rxn) → drug delivery ⎡COO⎤⎦ ⎡⎣H2O⎤⎦ Keq = ⎣ ⎤⎡OH ⎦⎤ ⎣⎡COOH ⎦⎣ Assume at t = 0 : ⎡⎣M ⎤⎦ = ⎡⎣M ⎤⎦o Put in terms of π: = π ⎡⎣COOH ⎦⎤o = π ⎡⎣OH ⎦⎤o = π ⎡⎣M ⎦⎤o ⎣⎡COO⎦⎤ [OH ] = “ “ ⎣⎡COOH ⎦⎤ = ⎡⎣OH ⎦⎤ = ⎣⎡M ⎤⎦o − π ⎡⎣M ⎦⎤o = ⎡⎣M ⎦⎤o (1 − π ) ( π ⎡⎣M ⎤⎦ ) 2 o K = ⎡⎣M ⎤⎦o (1 − π ) 2 2 π2 K = (1 − π ) 2 1 K2 π= 1+ K In closed system, limited by K (reaction constant). 1 2 That also means rxn and polymer limited by K. pn = 1 1 = 1 + K2 1− π where pn is the # average degree of polymerization (# of units in polymer) Polyesterification: K: 1 ∼ 10 pn ∼ 2 - 5 monomers Polyamidation: K: 100 – 1000 pn : 10 - 40 In between: removing some of the water Open Driven System Removing byproduct - H2O by temperature, low pressure, or N2 blowing of water - Acid like HCl, base neutralization How H2O affects pn ⎡⎣H2O ⎤⎦ ↔ MW pn ( ) 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 3 Page 2 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date O O OH COH + C O + H2O π ⎣⎡H2O⎦⎤ ⎡COO ⎦⎤ ⎣⎡H2O ⎦⎤ = K =⎣ 2 ⎡⎣COOH ⎤⎡ ⎡⎣M ⎤⎦o (1 − π ) ⎦⎣OH ⎤⎦ K = π ⎣⎡H2O⎦⎤eq 1 ⋅ ⋅ 1 − π 1 − π ⎡⎣M ⎤⎦o pn = 1 1− π 1 1− π 1 π = − = − 1 = pn − 1 1− π 1− π 1− π 1− π ( ⎡H2O⎤eq ) ⎣ ⎡⎣M ⎤⎦⎦ K = pn ⋅ pn − 1 o ⎣⎡H2O⎦⎤eq = ⎣⎡M ⎦⎤o K ( only get down to a certain water concentration ) pn pn − 1 → solve for best p n possible Polyesterification Using Acid Catalysis O COH + HA C + k2 Acid catalyst More active than COOH K12 OH k1 OH A OH ⎡ ⎤ ⎢ C OH ⎥ ⎢ + - ⎥ k ⎦ A = 1 =⎣ [HA][COOH ] k2 OH C + OH OH + A OH k3 k4 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond C A + OH OH Slow step (rate-determining step) Lecture 3 Page 3 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date .. .. OH .. OH .. C A + OH Rp = Rp Rp = O k5 C k6 + H2O + HA O catalyst regeneration − d [COOH ] dt Rate of disappearance of carboxylic monomer = k3 ⎡⎣C + ( OH )2 ⎤⎦ ⎡⎣OH ⎤⎦ = k3K12 ⎡⎣HA⎤⎡ ⎦⎣COOH ⎤⎡ ⎦⎣OH ⎤⎦ (from previous page) From equilibrium expression [HA] is constant because it’s regenerated. −d ⎣⎡COOH ⎦⎤ dt = k ' ⎣⎡COOH ⎦⎣ ⎤⎡OH⎤⎦ where k ' = k3 K12 ⎣⎡HA⎦⎤ constant Self-catalyzed: [HA] = [COOH] Rp = Rp = −d ⎡⎣COOH ⎤⎦ dt −d ⎡⎣M ⎤⎦ 3 = k " ⎣⎡M ⎦⎤ dt 2k "t = 1 2 ⎡⎣M ⎤⎦ 2 = k " ⎡⎣COOH ⎤⎦ ⎡⎣OH⎤⎦ − where k " = k3 K12 separate and integrate 1 2 ⎡⎣M ⎤⎦o ⎡⎣M ⎤⎦ = ⎡⎣M ⎤⎦o (1 − π ) (p ) 2 n = 1 2 (1 − π ) 2 = 2 ⎡⎣M ⎤⎦o k 't + 1 Much slower because of time-dependence ( t ) That’s why people add acid to drive reaction. High Temperature - increase k - remove byproduct (evaporate H2O) Bulk or mass conditions (no solvent) - [M]o is maximum - no need to separate product 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 3 Page 4 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date - viscosity η low until high π direct processing Use solvent - monomers are not miscible with each other but miscible with solvent - allow high T - dilute viscous media (carrier for viscous media) → improves processing - improves heat and mass transfer 10.569, Synthesis of Polymers, Fall 2006 Prof. Paula Hammond Lecture 3 Page 5 of 5 Citation: Professor Paula Hammond, 10.569 Synthesis of Polymers Fall 2006 course materials, MIT OpenCourseWare (http://ocw.mit.edu/index.html), Massachusetts Institute of Technology, Date