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COPOLYMERIZATION

POLYMERIZATION OF TWO OR MORE

Examples: Poly(-co-propylene) (EP) Poly(-co-) (SBR) ® Poly(vinylidine chloride-co-vinyl chloride) (Saran )

Microstructure depends on method of Random -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

Examples: High Impact (HIPS) / Butadiene / Styrene (ABS)

Dissolve A in a solvent Add 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 k ___11 ___22 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.