Chap 11. Free Radical Copolymerization
 Radical copolymerization
Regular copolymer
Random copolymer
Block copolymer
Graft copolymer
Actual copolymer (case)
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Chap 12. Free Radical Copolymerization
Copolymer Equation
Only Binary Case
Two Monomers; M1 + M2
M1 .
+
M1
M1 .
+
M2
M2 .
+
M1
M2 .
+
M2
k11
M1.
k12
M2.
k21
M1 .
k22
M2.
Steady State Assumption

d [ M 1 ]
d [ M 2 ]

0
dt
dt
and chain transfer & termination compared w/ propagation
k12  [M1 ][M 2 ]  k 21[M 2 ][M1 ]
[M 1 ] k 21[M 1 ]

[M 2 ] k12[M 2 ]
……①
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Copolymer Equation
d[M 1 ]
 k11[ M 1 ][M 1 ]  k 21[ M 2 ][M 1 ]
dt


d[M 2 ]
 k12 [ M 1 ][ M 2 ]  k 22 [ M 2 ][ M 2 ]
dt
d[M 1 ] [M 1 ] k11[M 1 ]  k 21[M 2 ][M 1 ]

d[M 2 ] [M 2 ] k12[M 1 ]  k 21[M 2 ][M 2 ]
……②
Instantaneous ratio of monomers in copolymer
From ① and ②
[M 1 ]
d[M 1 ]
[M 2 ]

[M 2 ]
d[M 2 ]
1  r2
[M 1 ]
1  r1
where
r2 
k
k 22
r1  11
k12
k 21 ,
monomer reactivity ratio
COPOLYMER EQ.
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Meaning of r & Definition of f1, F1
Meaning of r
r1 characterizes the reactivity of the 1 radical with respect to the two monomers 1 and 2
r1  1
then homopolymerization growth is preferred
r1  0
then only reaction with 2 will occur
Define f1, F1
f1, f2 : mole fractions of monomers in feed
F1, F2 : mole fractions of monomers in polymer
f1  1  f 2 
[M1 ]
[M1  M 2 ]
…… ③
From ③, ④
F1 
r1f12  f1f2
r1f12  2f1f2  r2 f2 2 ……⑤
how come? Homework!
F 1 1  F2 
d[M 1 ]
d[M 1 ]  d[M 2 ]
……④
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Ideal Copolymerization
Ideal Copolymerization
d[M 1 ] [M 1 ] r1[M 1 ]  [M 2 ]
r1  r2  1


d[M 2 ] [M 2 ] [M 1 ]  r2 [M 2 ]
1
[M1 ] r1[M1 ]  [M 2 ]
r2 
 r1

r1
[M 2 ] r1[M1 ]  [M 2 ]
r1  r2  1
r1 f1
F1 
r1 f1  f 2
 r1
[M 1 ]
[M 2 ]
k11 k 22

1
k12 k 21
k11 k 21

k12 k 22
Most ionic copolymerizations are characterizes bythe ideal type of behavior
When r1  1  r2 , the two monomers show equal reactivities toward both propagating species
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Ideal Copolymerization
r1  1
r2  1
r1  1
or
r2  1 One of the monomer us nire reactive than
The other toward both propagating speces. The copolymer will contain a larger proportion of
the more reactive monomer in random placement
1
F1
0
f1
Surfing to the internet
For further details about Ideal Copolymerization
Click next homepage.
http://www.chem.rochester.edu/~chem421/copoly.htm
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Alternating Copolymerization
Alternating Copolymerization
r1  r2  0
or
r1r2  0
F1
0.5
r1=0
f1
As r1, r2 approach to zero, alternating tendency can be observed
If r 1 r2  0
→
perfect alternation!
d[M 1 ]
1
d[M 2 ]
If
If
F1  0.5 
d[M 1 ]
d[M 1 ]  d[M 2 ]
r1  1 , r2  1 F1 / f1 plots cross the line representing F1  f1
r1  r2   , then become homopolymer
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Alternating Copolymerization
Mean of Cross-over Point
F1  f1
At these crossover points the copolymer and feed compositions are the same and
copolymerization occurs whthout a change in the feed composition
Such copolymerizaions are termed Azeotropic copolymeriztions.
Condition of Azeotropic copolymeriztion
d[M 1 ] [M 1 ]

and
d[M 2 ] [M 2 ]
∵ F1 
[M 1 ] (r2  1)

[M 2 ] (r1  1)
d[M 1 ]
[M1 ]

 f1
d[M 1 ]  d[M 2 ] [M 1 ]  [M 2 ]
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Alternating Copolymerization
d[M 1 ] [M 1 ] r1[M 1 ]  [M 2 ]


d[M 2 ] [M 2 ] [M 1 ]  r2 [M 2 ]
r1[M1 ]  [M 2 ]  [M1 ]  r2 [M 2 ]
r1
[M 1 ]
[M 1 ]
1 
 r2
[M 2 ]
[M 2 ]
[M1 ] r2  1

[M 2 ] r1  1
f1 
[M 1 ]
[M 1 ]  [M 2 ]
[M 2 ]
r  1 r2  r1  2
1
 1
 1 1

f1
[M1 ]
r2  1
r2  1
∴
f1 
r2  1
1  r2

r2  r1  2 2  r1  r2
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Alternating Copolymerization
r1  r2
(
r1  1 and r1  1 )
Both types of propagating species preferentially add monomer M1. there is a tendency toward
consecutive Homopolymerization of the two monomers.
And then monomer M2 will subsequently homopolymerize.
r1>1
In the result r1r2=1 ideal or random
F1
r1=1
r1<1
f1
fix r2=0.5
r1=2
r1  0 
F1
k11
k12
Addition monimer A and A*
Can not prepare copolymer
r1=0
f1
It’s alternating upto 0.5, and above 0.5
there’s no formation of copolymer
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Alternating Copolymerization
r2=0.5
azeotropic comp
F1
r1=0.5
alternating
f1
r1=2
F1
r2=0.5
r1=1
r1=1 no azeotrope
f1
r1, r2 > 1 Case
F1
tend to be a block copolymerization
f1
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Alternating Copolymerization
Drift:
r1, r2 > 1
r1, r2 <1
r1  1 , r2  1 finally r1r2  1
block azeotrope
alternating
Block COPOLYMERIZATION
HW #6.
Solve S.S. expression for a monomer concentration and substitute into the
original composition equation which contains the active center. You can get eq.
in terms of active center concentrations and if necessary define new kind of new
reactivity ratio in eq.
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Experimental Determination of r1 & r2
Experimental Determination of r1 & r2
1.Mayo and Lewis
rearrange copolymer eq. and can get
r2 
[ M 1 ]  d [ M 2 ]  r1[ M 1 ]  

1 
  1
[M 2 ]  d[M 1 ] 
[M 2 ]  
monomer comp
copolymer comp.
[M1 ] [M 2 ]
d [ M1 ] d [ M 2 ]


then vary r1 value (put) and iterate r 2  r1


experiment 3
experiment
experiment
2
1
This Δ is more for
smaller, r1, r2 value
calculate with accuracy
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Experimental Determination of r1 & r2
2. Finemann and Ross
Recall
r1 f1  f1 f 2
2
F1 
r1 f1  2 f1 f 2  r2 f 2
2
2
f 1(1  2 F 1)
f ( F  1)
 r2  1 1 2  r1
F1 (1  f1 )
F1 (1  f1 )
2
B
A
at low conversion
A
r1
r2
B
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Relationship Between ξand F1, f1
Relationship Between ξand F1, f1
Material Balance for M1
 d ([M ] f1 )  d[M ]F1
where [M] = total # of moles of monomers
decrease of M1 monomer
 d ([M ] f1 )  {d[M ]} F1  f 1d[M ]  [M ]df1
( F1  f1 )d[M ]  [M ]df1
d[M ]
df1

[ M ] F1  f1
f
df1
[M ]
lim

[M 0 ] f1, 0 F1  f1
f
df1
 f1, 0
[M ]
  1
 1  e F1  f1
[ M ]0
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Effect of Reaction Condition
Reaction medium
Depend on Solubility, PH, Viscosity, Polarity
Temperature
r1 
A
( E  E11 )
k11
 11 exp[ 12
]
A12
RT
k12
But the effect of temperature on r is not large
Pressure
d ln r1  (df1V11  V12 )

dP
RT
But the effect of pressure on r is not large
Reactivity
Next page
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Effect of Reaction Condition
Structure and Reactivity
I. Resonance Stabilization
II. Polar Effects
III. Steric Effects
I.Resonance Stabilization
Substituent
on Double Bond
Relative Reactivity
of Monomer
Stabilization Energy, kcal/mole
Olefine
Radical
-H, -OCH3
1
0
0
-OAc, -CH3
1.5-5
2.5
4
-Cl
3-20
-
6
-COO, -COOH
20-60
2.5
-
-CN, -COR
30-60
0
-
-C2H3, -C6H5
50-100
3-4
25
* Walling’s “Free Radicals in Solution”
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Structure and Reactivity
Define
rA, rB : monomer reactivity ratios
RA, RB : active center reactivity ratios
rA 
k AA
k AB
rB 
k BB
k BA
RA 
k AA
k BA
RB 
k BB
k AB
RA 
RB 
k AA
k k
 rB  AA BB
k BB
k BB k BA
k BB
 rA
k AA
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Structure and Reactivity
TABLE I. Propagation Rate Constants, Monomer Reactivity Ratios, and Active
Center Reactivity Ratios for Radical Chain-Growth Polymerizations1
Mon A2
Mon B2
AN
AN
AN
AN
MA
MA
MA
MMA
MMA
STY
MA
MMA
STY
VA
MMA
STY
VA
STY
VA
VA
KAAx10-3
KBBx10-3
1.96
1.96
1.96
1.96
2.09
2.09
2.09
0.515
0.515
0.515
2.09
0.515
0.165
2.30
0.515
0.165
2.30
0.165
2.30
2.30
rA
rB
RA
RB
1.26
0.15
0.04
5.4
0.25
0.20
9.
0.46
20
55
0.67
1.20
0.40
0.050
3.22
0.75
0.1
0.52
0.015
0.01
6.28x10-1
4.57x100
4.8 x100
4.3 x10-2
1.31x101
9.5 x100
9. x10-2
1.6 x100
3.4 x10-3
7. x10-4
1.34 x100
3.94 x10-2
3.4 x10-3
6.3 x100
6.16 x10-2
1.6 x10-2
1. x101
1.5 x10-1
8.9 x101
8. x102
1All values are based on data collected at 60℃
2AN=acrylonitrile; MA=methylacrylate; MMA=methylmetacrylate;
STY=styrene; VA=vinyl acetate
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Structure and Reactivity
Active Center Reactivity Ratios vs. Monomer Reactivity Ratios
d [ A] [ A*]  R A [ A*]  [ B*] 



d [ B] [ B*]  [ A*]  RB [ B*] 
RA 
when
k AA
k BA
RB 
R A  R B then
RA rB

RB rA
when
k BB
k AB
Relative reactivity of the monomer
rA  rB
R A  RB
The effect in relative reactivity of the active center is more stronger than that of monomer.
The monomer reactivity gets affect in opposite way comparing to the active center reactivity.
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Structure and Reactivity
Odian Table 6-3. Relative Reactivities(1/r) of Monomers
Polymer Radical
Monomer
Butadiene
Butadiene
Sty
VAc
VC
MMA
MA
AN
29
4
20
50
100
50
2.2
5.0
25
1.9
67
10
2
6.7
3.4
20
10
1.7
Styrene
0.7
Methyl Metacrylate
1.3
Methyl Vinyl Ketones
1.7
Acrylonitrile
3.3
2.5
20
25
0.82
Methyl Acrylate
1.3
1.3
10
17
0.52
0.67
0.54
10
0.39
1.1
0.059
4.4
0.10
0.25
0.37
0.05
0.11
0.24
Vinylidene Chloride
Vinyl Chloride
Vinyl Acetate
0.11
0.019
0.59
1.2
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Structure and Reactivity
@ Substituent Effects
Φ, CH2=CH- > -C≡N, -COR > -COOH, -COOR > -Cl > -O-COR, -R > -OR, -H
monomers increase relative reactivity by resonance stabilization.
The resonance stability of the monomer increases the reactivity of the monomer.
The resonance stability of the radical is weakened reactivity of the radical.
Table 6-4 Rate Constant(k12) for Radical-Monomer Reactions
Polymer Radical
Monomer(M1)
Butadiene
Styrene
Methyl
_methacrylate
Acrylonitrile
Methyl _acrylate
Vinyl chloride
Vinyl acetate
Butadiene
Styrene
100
70
280
165
130
330
130
11
Methyl
Metacrylate
Acrylo
-nirile
Methyl
Vinyl
Vinyl
Acrylate Acetate Chloride
2,060
1,130
98,000
49,000
41,800
10,045
314
413
515
422
13,100
1,960
4,180
2,510
215
9.7
3.4
268
52
26
1,310
720
230
2,090
520
530
230,000 319,000
154,000 550,000
110,000
46,000 225,000
23,000 187,000
11,000
0,100
6,490
2,300
Q1
e1
2.39
1.00
0.74
0.60
0.42
0.044
0.026
-1.05
-0.80
0.40
1.20
0.60
0.20
-0.22
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Structure and Reactivity
Resonance stabilization of Active Center
H
C C
. C
H2
O.
O
C C C
H2 H
OR
OR
Transition State Theory
AB*
Activated complex
ΔER
A+B
P.E.
compound
ΔHR
Increasing Separation of A & B
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Structure and Reactivity
AB Morse curve
P.E.
A+B repulsion curve
Increasing Separation of A & B
R
P.E.
ΔE1‡ > ΔE3‡
then Rexn III is less stable than Rexn I
ΔHR3‡ < ΔHR1‡
ΔE1‡
R + M
Reaction I R 
ΔE3‡
Rs  + M
Reaction III R 
Increasing Separation of Reactant
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Structure and Reactivity
Resonance stability of Active Center become primary
Resonance stability of Monomer become secondary
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Structure and Reactivity
-ΔH
ΔE‡
R·+ MS → RS·
1.20
0.40
R·+ M → R·
0.95
0.50
RS·+ MS → RS·
0.70
0.70
RS·+ M → R·
0.40
0.80
|-ΔH | ① > ② > ③ > ④
ΔE‡ ④ > ③ > ② > ①
Surfing to the internet
For further details about Free Radical Polymerization
Click next homepage.
http://www.chem.rochester.edu/~chem421/frfull.htm
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Structure and Reactivity
II. Polar Effects
Tend to cause alternation in a copolymerization
i.e.
rA  rB  1 for polar effects
e : tendency to give monomer a polar effects
Alfrey-Price Q,e scheme
(Polarity Values)
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Structure and Reactivity
@ Q-e
scheme of Alfred Price
rB forecast randomness of copolymerization
rA
,
As know r, prediction is possible to polar, resonance effectGuidance to chemists
kij  Pi Q j exp( ei e j )
where P : active center reactivity
Q : monomer reactivity
i, j : active center, monomer, respectively
ri 
k ii
P Q exp(ei ei )
 i i
k ij Pi Q j exp(ei e j )
ri 
Qi
ex p[e i (e i  e j )]
Qj
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Structure and Reactivity
so that, this equation forecast ri
Q 1
Base materials use styrene :
(arbitrary)
e   0 .8
fair results, but not absolute in predicting r using Q-e scheme.
rj 
k jj
k ji
ri  r j 

Pj Q j exp(e j e j )
Pi Q j exp(e j ei )
exp[ei (ei  e j )]
exp[e j (e j  ei )]

Qj
Qi
exp[e j (e j  ei )]
 exp[(ei  e j ) 2 ]
ri  r j  exp[(ei  e j ) 2 ]  1
 (ei  e j ) 2  0  (ei  e j ) 2  0
alternating tendency is correct
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Structure and Reactivity
Active Center Reacting Ratios
d[ A] [ A*] RA [ A*]  [ B*]


d[ B] [ B*] [ A*]  RB [ B*]
P-e scheme
Ri 
Pi Qi exp(ei ei ) k ii

Pj Qi exp(e j ei ) k ji
Ri 
Pi
exp[ei (ei  e j )]
Pj
St
AN
MA
MMA
VAc
P
e
Q
E
1
58.23
21.03
2.413
751.3
-0.8
1.233
0.577
0.397
-0.027
1
0.4
0.42
0.24
0.024
-0.8
1.2
1.2
0.4
-0.22
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Structure and Reactivity
The criticism against Q-e scheme
Reference state arbitrarily set.
Alternating effect was observed due to fixed charges not due to the induced dipole
Exercise)
How to indicate Randoness of Copolymer with Q-e scheme ?
We can forecast alternation or randomness through Q-e scheme, however, why can not forecast
Blockcopolymerization? (algebraic standpoint)
Surfing to the internet
For further details about Free Radical Polymerization
Click next homepage.
http://www.kcpc.usyd.edu.au/resources/notes/gilbertnotes3.pdf
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Structure and Reactivity
III. Steric Effects
1) 1,2-disubstituted ethylene do not homopolymerize readily
H
H
C C
R'
R
2). 1,1-disubstituted ethylene
II. Polar Effects
X X
X
C
X X
C
C
H2
X X
C.
C
C
H2
X
C
H2
planar conformation
tetrahedral conformation
more reactive
+
H2C CX2
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Structure and Reactivity
3) Cis-trans Effect
H
H
H
C C
C C
X
X
X
X
H
The trans is stabilized the cis than thermodynamics(Heat of Hydrogenation)
Planarity! Easier for trans than cis
Steric Effect!
Surfing to the internet
For further details about Free Radical Polymerization
Click next homepage.
http://pslc.ws/macrog/lab/unit1.htm
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Structure and Reactivity
Table 6-5 Rate Constants( k12 ) for Radical-Monomer Reactionsa
Monomer
Polymer Radical
Vinyl
Acetate
Vinyl chloride
Vinylidene chloride
Cis-1,2-Dichloroethylene
Trans-1,2-Dichloroethylene
Trichloroethylene
Tetrachloroethylene
a
10,000
23,000
365
2,320
3,480
338
Styrene
9.7
89
0.79
4.5
10.3
0.83
Acrylonitrile
725
2,150
29
4.2
k12values calculated from data in Table 3-11 and 6-2 and [66]
1,1-disubs.
Mono subs.
Tri subs.
Trans 1,2
Cis 1,2
High reactive
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