COPOLYMERIZATION POLYMERIZATION OF TWO OR MORE MONOMERS Examples: Poly(ethylene-co-propylene) (EP) Poly(styrene-co-butadiene) (SBR) ® Poly(vinylidine chloride-co-vinyl chloride) (Saran ) Microstructure depends on method of polymerization Random Copolymers -A-B-B-B-A-A-B-A-B-A-A-A-B-A-B-B- Alternating Copolymers A B A B B A A A B A A -A-B-A-B-A-B-A-B-A-B-A-B-A-B-A-B- B B B A A A B A A B R* B R* A B A B A B A A B A R* A Block Copolymers A B A-A-A-A-A-A-A-A-B-B-B-B-B-B-B-B-B-A-A-A-A-A-A POST POLYMERIZATION OR HOW TO MAKE A GRAFT COPOLYMER Examples: High Impact Polystyrene (HIPS) Acrylonitrile / Butadiene / Styrene (ABS) Dissolve polymer A in a solvent Add monomer B and initiator Polymerize B -A-A-A-A-A-A-A-A-A-A- -A-A-A-A-A-A-A-A-A-A--B-B-B-B-B-B B R* B -A-A-A-A-A-A-A-A-A-A- B -B-B-B-B B R* B B -A-A-A-A-A-A-A-A-A-A--B-B-B-B-B-B B B -A-A-A-A-A-A-A-A-A-A- B B B B B B-B-B-B-B-B B B -A-A-A-A-A-A-A-A-A-A- B-B-B-B-B B B R* FREE RADICAL COPOLYMERIZATION ARE "RANDOM" COPOLYMERS REALLY RANDOM ? ~~~~~~~~~~~A -- A* A ~~~~~~~~~~~ A* B ~~~~~~~~~~~A -- B* ~~~~~~~~~~~ B -- A* A ~~~~~~~~~~~ B* B ~~~~~~~~~~~ B --B* DO A's ADD TO A's AS EASILY AS B's ADD TO A's ? (and vice - versa) POSSIBLE PRODUCTS COPOLYMERIZATION OF MONOMERS M 1 AND M 2 •Homopolymers •Alternating copolymers •”Ideal" or truly random copolymers •Non ideal copolymers - tendency to "blockiness” or alternating KINETICS OF COPOLYMERIZATION k 11 ~~~~~~~~ M 1. + M 1 ~~~~~~~~ M 1 . k 12 ~~~~~~~~ M 1. + M 2 ~~~~~~~~ M 2 . k 21 ~~~~~~~~ M 2. + M 1 ~~~~~~~~ M 1 . k22 ~~~~~~~~ M 2. + M 2 ~~~~~~~~ M 2 . TENDENCIES 1. BLOCKS AND / OR HOMOPOLYMER IF k 11 > k 12 AND k 22 > k 21 2. ALTERNATING IF k 12 > k 11 AND k 21 > k22 3. RANDOM COPOLYMERS IF k 11 = k 12 AND k 22 = k 21 REACTIVITY RATIOS DEFINE k k ___11 ___22 r1 = r2 = k 12 k 21 WHAT IF r1 , r2 >> 1 ? r1 , r2 << 1 ? r1 = r2 = 1 ? r r1 2 = 1 ? KINETICS OF COPOLYMERIZATION M d[____ 1 ] . k . - = k 11[ M 1 ][ M 1 ] + 21 [ M 2 ][ M 1 ] dt M ____d[ 2 ] . k . - = k22 [ M 2 ][ M 2 ] + 12 [ M 1 ][ M 2 ] dt Divide and eliminate [ M ]. terms using STEADY STATE ASSUMPTION . - M , 1 M generated2 and consumed at equal rates. we only need focus on one . type of radical; e.g. M 1 k . 12 [ M 1 ][ M 2 ] = k 21 [ M 2 ][ M 1 ] COPOLYMER EQUATION d[ M 1 ] [M 1 ] r1[ M 1 ] + [ M 2 ] ______ = ___ _____________ d[ M 2 ] [ M 2 ] { [M 1 ] + r 2 [ M 2 ]} or d[ M 1 ] ( r1[ M 1 ] / [ M 2 ]+1 ) _____ = ________________ d[ M 2 ] ( r2 [ M 2 ]/[M 1 ]+1 ) remember k 11 k22 ___ ___ r1 = r2 = k 12 k 21 COPOLYMER EQUATION It is often more convenient to work in terms of mole fractions. d[ M 1 ] F = 1 - F = _____________ 1 2 d[ M ] + d[ M ] define : 1 2 F 1 = mole fraction of monomer 1 in the polymer at some instant of [ M ] f = 1- f = __________1 time 1 2 [M 1 ] + [ M 2 ] f1 = mole fraction of monomer 1 in the feed at the same instant of time COPOLYMER EQUATION 2 ( r 1 - 1 f 1) + f1 F1 = _________________________________ 2 r f r ( r 1 + r2 - 2 )f1 + 2 (1 - 2 ) 1+ 2 1 r1 > 1 ; r2 < 1 r < 1 ; r < 1 Note that this equation 1 2 describes the instantaneous F 1 copolymer composition Azeotrope r1 = r2 = 1 0 0 f1 1 In a batch copolymerization composition will "drift " with conversion . to treat this properly we need to first do some statistics,but here we will just give a couple of illustrations DETERMINATION OF REACTIVITY RATIOS There are some older methods based on rearrangements of the copolymer equation [M ] d[M ] 1 1 r LET = x and = y 2 [M2] d[M2] 1 + r x y = 1 THEN r2 1 + x x(r x + 1) 1 r r = - x 1 2 y MAYO - LEWIS PLOT 1 x(1 - y ) 2 r 1 x 2 (intercept) x 1 - = r - r (5.16) ( y ) 1( y ) 2 x2 ( y ) r 1 ( - slope) FINEMAN - ROSS PLOT DETERMINATION OF REACTIVITY RATIOS ALSO; KELEN TUDOS PLOT Q - e SCHEME APPLICATION OF PROBABILITY THEORY AND nmr SPECTROSCOPY POLYMER SYNTHESIS—COPOLYMERIZATION THE COPOLYMER EQUATION [A] 1 + rAx x = Composition of the Feed = y = [B] P [A] rB y = Composition of the Instaneously Formed Polymer = 1 P [B] 1 + x 1 Copolymer Composition as a Function of Conversion 1.0 VDC 0.8 0.6 0.4 0.2 VC Polymer Composition 0.0 0 20 40 60 80 100 Degree of Conversion Compositional variation for vinylidine chloride/vinyl chloride copolymers..