1. Chapter 3 Free Radical Copolymerization

2. 1 Introduction

3. 1.1 Concept Homopolymerization
—— polymerization of one kind of monomer;
Copolymerization (addition polymerization)
—— polymerization of more than one kind of monomer;
New kinds of copolymer can be synthesized by copolymerization of different combination of various monomers.
Copolymer generated from same monomers can have different compositions and topologies.

4. Examples Styrene Styrene + Acrylonitrile Styrene + Butadiene
Styrene + Acrylonitrile+ Butadiene PS
SAN
SBR
ABS
Brittle, transparent, poor solvent toleration
High impact, good solvent toleration
High elasticity
Engineering plastics
Maleic anhydride
Styrene + maleic anhydride
No polymer
SMA

5. 1.2 Type of copolymer also obtained by other methods
Normally prepared by other methods

6. 1.3 Nomenclature of copolymer
poly(ethylene-co-propylene) 乙烯-丙烯共聚物
poly(ethylene-r-propylene) 乙烯-丙烯无规共聚物
poly(ethylene-b-propylene) 乙烯-丙烯嵌段共聚物
poly(ethylene-g-propylene) 乙烯-丙烯接枝共聚物
poly(ethylene-a-styrene) 乙烯-苯乙烯交替共聚物

7. Key topics in copolymerization
-ABABBAABABBAAABABA-
Composition distribution
the relative amounts of each monomer unit incorporated into the copolymer, A% or B%
Sequence distribution
the way in which these monomer units are arranged within a polymer chain; AA or AB

8. 2. Copolymer composition

9. Essential Point
The composition of a copolymer does not necessarily match the composition of the comonomers used in the reaction ( feed ratio 投料比).
Ethylene-vinyl acetate copolymer
vinyl acetate % property
10 ~ plastic
30 ~ 40 adhesive
rubber

10. Possible propagation sequences in free-radical copolymerization

11. Assumptions in copolymerization
the rate of the propagation be chain-length-independent.
only the terminal unit of the polymer radical can affect its reactivity
no side reactions, such as depropagation, monomer partitioning, and various forms of complex formation

12. Reactions in copolymerization

13. 2.1 Copolymer composition equation
The overall rates of consumption of monomers [M1],[M2] then follow these expressions:
ignore the initiation
The expression for instantaneous copolymer composition (F1/F2)
molar fraction of M1
molar fraction of M2

14. Steady-state assumption

15. Mayo-Lewis Equation

16. Reactivity ratio （竞聚率）
The ratio of rate constant of homopolymerization to copolymerization 1
homopolymerizaiton
copolymerizaiton r
Special cases:
r1=0 and r2=0
Each comonomer prefers to react with the other.
Perfectly alternating copolymer.
r1 > 1 and r2 > 1
Each comonomer prefers to react with others of its own kind.
Tendency to form block copolymers.
r1 * r2=1
There is no preference due to the chain ends.
Random incorporation of comonomers; “Ideal” copolymerization.

17. Examples Neither monomer homopolymerizes very well.
Forms almost perfectly alternating copolymer of high MW.
Alternating copolymerization is common in free radical reactions when one monomer has electron withdrawing groups and the other has electron donating groups.

18. Influnece of polymerization mechanism on r
St(M1)-MMA(M2)
Radical ： r1=0.52, r2=0.46;
Cationic： r1=10, r2=0.1;
Ionic: r1=0.1, r2=6;

19. Copolymer equation in terms of mole fraction
Copolymer composition depends on not only the monomer feed, but the reactivity ratio as well.

20. 2.2 Copolymer composition curve
Variation of reactivity ratio
r1= 0 or k11= 0
only copolymn.
r1<1 or k11<k12 tend to co- than homopolymn.
r1>1 or k11>k12 tend to homo- than copolymn.
r1= or k11>>k12 only homopolymn. 1 r1
F is the function of both r and f

21. Typical copolymer composition curves
1. Ideal copolymerization (r1*r2=1)
0.1
0.2
0.5 1 2 5 10
r1>1
r1<1
butadiene r1 = 1.39, styrene r2 = 0.78

22. A. r1=r2=1 B. r1<1, r2>1 C. r1>1, r2<1
azeotropic copolymerization
恒比共聚
copolymer composition equals to monomer feed
A. r1=r2=1
VDC (偏氯乙烯)- MMA, r1 = 1.0, r2 = 1.0
Acrylamide(丙烯酰胺)-丙烯酸甘油酯, r1 = 1.0, r2 = 1.0
Ethylene-VAc r1 = 1.07, r2 = 1.08
B. r1<1, r2>1
C. r1>1, r2<1

23. Characteristics of ideal copolymerization
r1*r2=1
There is no preference due to the chain ends.
Random incorporation of comonomers.
"Ideal" copolymerization

24. St/MMA initiated by BPO/AlR3
Typical copolymer composition curves
2. Alternative copolymerization (r1=r2=0)
St/MMA initiated by BPO/AlR3
Each comonomer prefers to react with the other.
Perfectly alternating copolymer.
copolymer composition independent on monomer feed
If r2=0 and r1  0
[M2]>>[M1]
[M2]~[M1]

25. Typical copolymer composition curves
3. Others
r1<1 and r2 <1
r1>1 and r2 <1
r1>1 and r2 >1
block

26. Summary r1 > 1, r2 < 1 close to random r1 r2 = 1 random
r1 = r2 = alternative
r1 < 1, r2 < random
r1 > 1, r2 > block or mixture of homopolymer
r1 > 1, r2 < close to random

27. Azeotropic composition 恒比组成
Definition:
To get solution, it should be that r1 and r2>1 or r1 and r2<1

28. Independent on feed ratio

29. 2.3 Copolymer composition with conversion
r1 > 1，r2 < 1
r1 < 1，r2 > 1   f1 or F1
conversion f1 or F1
conversion

30. r1< 1，r2 < 1 r1>1，r2>1 conversion conversion f1 or F1 f1

31. Copolymer composition with conversion
Since f varies with conversion, F1 also varies with conversion. Therefore, the average copolymer composition should be obtained by integration
Monomer before polym.
Polymerized monomer
Monomer after polym.

32. Average copolymer composition
M0=1 M
F1=f1=0.484
St-MMA
f10=0.8, f20=0.2,
r1=0.53, r2=0.56

33. Controlling copolymer composition
By adjusting feed ratio
When the f10 is close to azeotropic point, the copolymer composition slightly varies with conversion (<90%).
When the f10 is far from azeotropic point, the copolymer composition greatly varies with conversion.
Adding relatively active comonomer during polymerization.
苯乙烯-反丁烯二酸二乙酯共聚物瞬时组成与转化率的关系(r1=0.30, r2=0.07)

34. Controlling copolymer composition
By controlling monomer conversion
St-Bd copolymer composition with conversion
Bd-AN copolymer composition with conversion

35. 2.4 Copolymer microstructure and composition distribution
-ABABBAABABBAAABABA- 1 2 3 4 An
N(An)/W(An) %
AAA
AAB
ABA
ABB
BAB
BBB 1 4 3
Chain-length distribution
Monomer sequence distribution

36. Monomer distribution and polymer propertiy
A：random copolymer average of both polymer A and B
….AAABBABBAABBBABAAB…
B：block copolymer mixture of polymer A and B
…AAAAAAAABBBBBBBBBBBAAAAAAAAAAA…..

37. Chain-length distribution by Probability
For formation of M1M1 from M1· so
The probability to find block M2(M1)xM2
The probability to find block M1(M2)xM1

38. Number-fraction distribution
Weight-fraction distribution

39. Number-average chain length
On the other hand,

40. When r1 , r2 >>1, and [M1]~[M2]
Special examples
When r1 = r2 = 0
When r1 , r2 >>1, and [M1]~[M2]

41. Derivation of copolymer composition equation
Terminal effect vs penultimate effect
M1M1 vs M2M1
Depolymerization effect
For copolymerization involving α-methyl styrene

42. 3. Multi-component copolymerization

43. Ethylene-propylene-vinylidene norbornene
Terpolymerization
Three initiation reactions
Nine propagation reactions
Six termination reactions
Six reactivity ratios
Ethylene-propylene-vinylidene norbornene

44. 4. Experimental evaluation of reactivity ratios

45. 4.1 Method for measurement of reactivity ratio
By fitting copolymer composition curve with various r1 and r2
Since the F is not sensitive to the variation of r, this method is not so good

46. Line cross
Plot r2vs r1 with different [M1]/[M2] and F1/F2

47. Fineman-Ross method

48. 4.2 Variation of reactivity ratio
Effect of temperature
Active energy of homopolymerization
Active energy of copolymerization
Since E11 and E12 are low, their difference is also low.
So the reactivity ratio varies slightly with temperature.
In the case of r1<1, indicating E11 > E12, as temperature increases, k11 increase more faster than k12, so r1 increases and approach to unit.
In the case of r1>1, as as temperature increases, r1 decreases and approach to unit.

49. Effect of Pressure
Same as temperature.
Effect of solvent
Effect of pH

50. 5. Monomer structure and the copolymerization reactivity

51. 5.1 Relative reactivity of monomer
With respect to same radical, the monomer reactivity can be evaluated.
To compare the reactivity of AN (M1), VAc (M2), St (M3)
The reactivity of VAc is one fourth of that of AN
The reactivity of St is 25 times of that of AN
The reactivity of St is 100 times of that of VAc

52. The monomer reactivity decreases in the order of :
St>AN>VAc (100: 4:1)
So the 1/r1 can be applied to estimate the monomer reactivity.
The larger the reciprocal of r1, the higher the reactivity of M1 compared to M2.

53. 5.2 Relative reactivity of radical
With respect to same monomer, the radical reactivity can be evaluated.
To compare the reactivity of St· and VAc·
k11 = 145 L/mols
k22 = 2300 L/mols
The reactivity of VAc· is 1586 times of that of St·

54. General rules
Monomer with low reactivity (VAc) generates corresponding radical with high reactivity(VAc)
Monomer with high reactivity (St) generates corresponding radical with low reactivity(St).
The rate of copolymerization is mainly determined by the reactivity of the radical

55. 5.3 Influence of substitute on the monomer/radical reactivity
From Table 3-8 in the textbook
Monomer reactivity
Radical reactivity
The substitute group affects reactivity of radical stronger than monomer

56. Resonance effect For CH2=CHX Resonance effect: strong weak
Monomer reactivity: high low
Radical reactivity: low high

57. Reaction tendency： RS· + M < RS· + MS < R· + M < R· + MS
S: With resonance effect
RS· + MS(•)< R· + M(•)
Homopolymerization of monomer without resonance effect is faster than monomer with resonance effect    
RS· + M(•) < < R· + MS (•)
Copolymerization of M-M or Ms-Ms is better than M-Ms
Reaction tendency： RS· + M < RS· + MS < R· + M < R· + MS

58. Can VAc and St be well copolymerized?
Good!
Poor!

59. Polarity effects
Monomer with electron-withdrawing substitute has tendency to copolymerize with monomer with electron-donating substitute, in favor of forming alternative copolymer

60. Charge-transfer interaction
Homopolymerization of the charge-transfer complex or donor-acceptor complex

61. Steric effect
no influence on mono- or 1,1-disubstituted vinyl monomer
1,2-disubstituted monomer can be copolymerized with monomer with less steric effect.
Steric effect plays a more important role in homopolymerization than copolymerization.

62. 6. Q-e concept

63. Q-e scheme
To simplify the process of determine reactivity ratios, a semiempirical relationship has been developed that expresses the ratios in terms of constants that are characteristic of each monomer but independent of comonomer.
P1 and Q2 are measures of the reactivity of radical and monomer related to resonance stabilization,
e1 and e2 are measures of the polarity of the radical and monomer

64. Assuming the e value of monomer and radical are same,
Styrene was chosen as the standard and assigned value of Q=1.00 and e=
Value of Q increase with increasing resonance stabilization, while e value become less negative as groups attached to the double bond become more electron attracting.
The bigger the (e1-e2), the smaller the r1*r2.

65. Application of Q-e equation
Anticipate the reactivity ratio of monomer by Q-e equation.
Compare the reactivity of monomer by Q value:
High Q value --- high reactivity
Compare the polarity of monomer by e:
With electron-withdrawing group, +e;
With electron-donating group, -e;
Anticipate the copolymerization results by Q-e value
Copolymerization is difficult for monomer pair with big Q
Copolymerization is easy and becomes ideal when Q and e values of monomer are close
alternative copolymerization occurs when monomer pair with big e

66. 7. Copolymerization rate

67. Chemically controlled termination
Diffusion controlled termination

68. kp of copolymerization

70. Summary Nomenclature of copolymer
Reactivity ratio and copolymer composition equation
Copolymer composition curve
Copolymer composition with conversion
Control of copolymer composition
Copolymer composition distribution
The reactivity of monomer and radical
Q-e equation