Spring 2008
Chap 11. Free Radical Copolymerization
 Radical copolymerization
Regular copolymer
Random copolymer
Block copolymer
Graft copolymer
Actual copolymer (case)
Hanyang Univ.
Spring 2008
Copolymer Equation
Only Binary Case
Two Monomers; M1 + M2
M1 .
+
M1
M1 .
+
M2
M2 .
+
M1
M2 .
+
M2
k11
k12
k21
k22
M1.
M2.
M1 .
M2.
Steady State Assumption

d [ M 1 ]
d [ M 2 ]

0
dt
dt
and chain transfer & termination compared w/ propagation
k12 [M1][M 2 ]  k21[M 2 ][M1 ]
[M 1 ] k 21[M 1 ]

[M 2 ] k12[M 2 ]
……①
Hanyang Univ.
Spring 2008
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.
Hanyang Univ.
Spring 2008
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
[M1 ]
f1  1  f 2 
[M1  M 2 ]
From ③, ④
F1 
…… ③
F 1 1  F2 
r1f12  f1f2
r1f12  2f1f2  r2 f2 2
……⑤
d[M 1 ]
d[M 1 ]  d[M 2 ]
How come?
Hanyang Univ.
……④
Spring 2008
Ideal Copolymerization
Ideal Copolymerization
d[M 1 ] [M 1 ] r1[M 1 ]  [M 2 ]


d[M 2 ] [M 2 ] [M 1 ]  r2 [M 2 ]
F1 
 r1
[M1 ] r1[M1 ]  [M 2 ]

[M 2 ] r1[M1 ]  [M 2 ]
 r1
[M 1 ]
[M 2 ]
r1 f1
r1 f1  f 2
k11 k 22

1
k12 k 21
where r1  r2  1
r2 
1
r1
k11 k 21

k12 k 22
Most ionic copolymerizations are characterizes by the ideal type of behavior
When r1  1  r2 , the two monomers show equal reactivity toward both propagating species
random copolymer
Hanyang Univ.
Spring 2008
Ideal Copolymerization
r1  1
r2  1
or
r1  1
r2  1 One of the monomer us nire reactive than
The other toward both propagating spices. The copolymer will contain a larger
proportion of
the more reactive monomer in random placement
1
F1
0
f1
1
Surfing to the internet
For further details about Ideal Copolymerization
Click next homepage.
http://www.chem.rochester.edu/~chem421/copoly.htm
Hanyang Univ.
Spring 2008
Alternating Copolymerization
Alternating Copolymerization
1
r1  r2  0
or
r1r2  0
F1
0.5
r1=0
0
Cross-over point
f1
1
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
F1  0.5 
d[M1 ]
d[M1 ]  d[M 2 ]
r1  1 , r2  1 F1 / f1 plots cross the line representing F1  f1
If r1  r2   ,
then, become a homopolymer
Hanyang Univ.
Spring 2008
Alternating Copolymerization
Mean of Cross-over Point
F1  f1
At these crossover points the copolymer and feed compositions are the same
and copolymerization occurs without 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 ]
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
Spring 2008
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
It’s alternating up to 0.5, and above
0.5 there’s no formation of copolymer
f1
Hanyang Univ.
Spring 2008
Alternating Copolymerization
r2=0.5
azeotropic comp
F1
r1=0.5
alternating
f1
r1=2
r2=0.5
F1
r1=1
r1=1
no azeotrope
f1
r1, r2 > 1 Case
F1
tend to be a block copolymerization
f1
Hanyang Univ.
Spring 2008
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.
Hanyang Univ.
Spring 2008
Experimental Determination of r1 & r2
Experimental Determination of r1 & r2
1.Mayo and Lewis
rearrange copolymer eq. and can get
[ M 1 ]  d [ M 2 ]  r1[ M 1 ]  
r2 

1 
  1
[M 2 ]  d[M 1 ] 
[M 2 ]  
copolymer comp.
monomer 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
Hanyang Univ.
Spring 2008
Experimental Determination of r1 & r2
2. Finemann and Ross
r1 f1  f1 f 2
2
Recall
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
A
const.
B
const.
at low conversion
A
r1
Slope : r1
Intersection : r2
r2
B
Hanyang Univ.
Spring 2008
Relationship Between ξand F1, f1
Relationship Between ξ and 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
ln
f
[M ]
df1

[ M 0 ] f1, 0 F1  f1
f
df1
 f1, 0
[M ]
  1
 1  e F1  f1
[ M ]0
Hanyang Univ.
Spring 2008
Effect of Reaction Condition
Reaction medium
Depend on Solubility, PH, Viscosity, and Polarity
Temperature
A
( E  E11 )
k11
 11 exp[ 12
]
A12
RT
k12
But the effect of temperature on r is not large
r1 
Pressure
d ln r1  (df1V11  V12 )

dP
RT
But the effect of pressure on r is not large
Reactivity
Next page
Hanyang Univ.
Spring 2008
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”
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
Spring 2008
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 
RA R B
RA rB

RB rA
when
then
k BB
k AB
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.
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
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
Spring 2008
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
P.E.
A+B
ΔHR
compound
Increasing Separation of A & B
Hanyang Univ.
Spring 2008
Structure and Reactivity
AB Morse curve
P.E.
A+B repulsion curve
Increasing Separation of A & B
R
P.E.
ΔE1‡
ΔE3‡
R + M
Rs  + M
ΔE1‡ > ΔE3‡
then Rxn III is less stable than Rxn I
ΔHR3‡ < ΔHR1‡
Reaction I
Reaction III
R
R
Increasing Separation of Reactant
Hanyang Univ.
Spring 2008
Structure and Reactivity
Resonance stability of Active Center becomes primary
Resonance stability of Monomer becomes secondary
Hanyang Univ.
Spring 2008
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 the link below.
http://www.chem.rochester.edu/~chem421/frfull.htm
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
Spring 2008
Structure and Reactivity
@ Q-e
scheme of Alfred Price
rA , rB forecast randomness of copolymerization
As know r, prediction is possible to polar, resonance effect
Guidance 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
Hanyang Univ.
Spring 2008
Structure and Reactivity
So that, this equation forecasts
ri
Base materials use styrene : Q  1
(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
Hanyang Univ.
Spring 2008
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
Hanyang Univ.
Spring 2008
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 Randomness 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 the link below
http://www.kcpc.usyd.edu.au/resources/notes/gilbertnotes3.pdf
Hanyang Univ.
Spring 2008
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
+
H2C CX2
planar conformation
tetrahedral conformation
more reactive
Hanyang Univ.
Spring 2008
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 the link below.
http://pslc.ws/macrog/lab/unit1.htm
Hanyang Univ.
Spring 2008
Structure and Reactivity
Table 6-5 Rate Constants( k12 ) for Radical-Monomer Reactionsa
Monomer
Vinyl chloride
Vinylidene chloride
Cis-1,2-Dichloroethylene
Trans-1,2-Dichloroethylene
Trichloroethylene
Tetrachloroethylene
a
Polymer Radical
Vinyl
Acetate
Styrene
10,000
23,000
365
2,320
3,480
338
9.7
89
0.79
4.5
10.3
0.83
Acrylonitrile
725
2,150
29
4.2
k12Values were 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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