1. Molecular weight control in linear polymerization
2.6 Molecular weight control and molecular weight distribution in linear polymerization
Molecular weight control in linear polymerization
Molecular weight distribution in linear polymerization

2. Molecular weight control in linear polymerization
Molecular weight control in linear polymerization is
the main content of the study of kinetics
There are many influence factors on the molecular
weight of polycondensations.

3. 1. The effects of the balanced characteristic
Closed system： = 由式(2-23)得
Unclossed system： =
由式(2-24)得
Nw是体系中残留水的量

4. 2. The effects of the Catalyzed system
Self-Catalyzed system： = 2k t + 1
External Catalysis system： = k2C0t + 1

5. 3. The effects of the degree of the reaction
基团是等摩尔比的条件下：
The groups is the same mole ratio： =

6. 2.6.1 Molecular weight control in linear polymerization
Making the functional groups not react is a effective method of controlling molecular weight.
The method of stabilizing molecular
weight is used to control the molecular weight.

7. Two kind of the methods:
非化学计量的
The concentrations of the two monomers or two groups are slightly non-stoichiometric. One of the reactants is present in slight excess. Another reactant is completely used up and all the chain ends posses the same functional group.
相同官能团
Another method is adding a small amount of a monofunctional monomer. 单官能团

8. （1）The concentrations of the groups of monomer are non-stoichiometric
The method fits for the systems of a-R-a + b-R‘-b, but not for the systems of a-R-b
The numbers of A and B functional groups are given by Na and Nb, respectively.
And b-groups is present in excess.
The stoichiometric imbalance r of the two functional groups is given by r=Na/Nb ( r≤1).

9. Non-stoichiometric a-R-a b-R'-b t=0 The number of monomer
The number of group A is Na
The number of group B is Nb
The number of monomer
molecules (a-R-a) is given
by Na/2
The number of monomer mole-cules (b-R-b) is given by Nb/2
The total number of monomer molecules(namely the total number of construction unit)is given by
（Na＋Nb）/ 2

10. The total number of polymer molecules
t = t the degree of reaction of group A is given by Pa
Reacted a ： NaPa b : NaPa
Unreacted a ：Na(1－ Pa) b : Nb－ NaPa
The total number of unreacted a and b is given by: Na＋Nb－2NaPa
The total number of polymer molecules is :
(Na＋Nb－2NaPa ) /2

11. The moles of the two groups are equal（r=1）
Thus
Substitute r=Na/Nb
The group A is used up ( Pa=1)
The moles of the two groups are equal（r=1）
If r =1

12. If the equal mole ratio of the two monomers or two functional groups can always be kept，and if the reaction tends to the end, the average degree of the condensation polymer will reach the maximum.

13. Excessive mole-percent q
r=Na/Nb ( r≤1)
Excessive mole-percent q
Besides r，the Excessive percentage q of b-R‘-b molecule is often used.
The q is defined as:
namely

14. （2） Adding a small amount of a monofunctional monomer(R"-b) for locking the end group
R”-b can reacts with group A in the polymer.
Then this method can lock the end group and stabilize molecular weight.
The molecular weight of polymer can be adjusted
by the number of R”-b.

15. This method not only fits the system of bifunctional monomer a-R-a and b-R’-b where mole values of a-R-a and b-R’-b are equal，but also fits the system of a-R-b.

16. ① The systems of a-R-a + b-R‘-b with the same mole ratio
The number of the R"-b is NC
The coefficient 2 in front of Nc
is required since one B molecule has the same quantitative effect as one excess B-B molecule on limiting the growth of a polymer chain.

17. ② The system of a-R-b
The number of the R"-b is NC

18. If the numbers of r and P are substituted
for the equation （2-32） , the
average degree of polymerization will be obtained.

19. Example：
1 mol aRa + 1mol bR’b %R”b

20. The high purity of monomer
Exact measurement
Proper temperature
惰性气体
Protecting by inert gas, using catalytic agent and evacuating the system
排出系统

21. 2.6.2 Molecular Weight Distributions in linear condensation polymers
Molecular Weight Distributions is：
The ratio of molecules of different to the total
(the number of molecules and the weight) of
polymers.
Three kinds of expression methods:
Tabulation, Distribution Curve and Distribution index
分子量分布指数
作表格
分布曲线

22. MWD is determined by the experiment.
MWD can be derived by the theory of probability statistics.

23. Example
As an example the amino acids whose construction is H2NRCOOH forms the polyamide.
This is a kind of the system of homogeneous polycondensation whose functional group is always in the same mole.
The construction unit is only －NHRCO－in the chains of polymer.
均缩聚

24. The results derived from this system suit
the system of a-R-a～b-R-b , too.

25. This is a problem of probability.
Consider the probability of finding a polymer molecule containing x structural units.
X个结构单元
In other words, if the end group is amino group(NH2)，it has a probability of making up x structural units.

26. Expanding the meaning of degree of the reaction(P)
The P is the percentage of the end groups which have reacted at time t.
the percentage of the end groups unreacted
is 1－P.

27. The probability that the groups have reacted by time t is defined as the extent of reaction, P.
The probability of the groups being unreacted
is 1 - P.

28. The course of forming polyamide
molecular formula
分子式
The number of structural units
The number of the reacted groups COOH 1 2 3 4 x
x-1
The course of forming polyamide

29. The reaction begins from the terminal group(－NH2 )
The reaction begins from the terminal group(－NH2 ). （x－1）carboxyl groups(－ COOH) have reacted and one carboxyl group (－ COOH) has not reacted as the end group.
Thus：The probability that (x-1) carboxyl groups
have reacted is Px-1
The probability of a carboxyl group
unreacted is 1－P

30. The probability that the molecule has exactly x units, P(x), is :
P(x)=Px-1(1－P)
P(x) is synonymous with the mole or number
fraction of molecules in the polymer mixture
which are X-mers, then
Nx/N =Px-1 (1-P)
where N is the total number of polymer mole-
cules and Nx is the number of X-mers.
Nx =NPx-1 (1-P)
The total number of structural units present
initially is N0 , then N＝N0（1－P）
Nx=N0Px-1 (1-P)2

31. Nx=N0P x-1 (1-P)2
The equation gives the number-distribution function for linear step polymerizations at the extent of reaction P.
It is seen that on a number when X=1 basis there are more monomer molecules than in any polymer species regardless of the extent of the reaction.
不论反应程度如何，单体分子比任何X-聚体大分子都要多，这是分子量数量分布的特征。

32. Nx=N0P x-1 (1-P)2
The Molecular Wight Distribution becomes broad and the average molecular weight increases as the extent of reaction goes.

33. Number fraction distribution curve for linear polymerization

34. The weight of the end-group( H and OH) can be neglected. –如果忽略端基的质量
Thus: Mx=xM0
Where: (M0 is the molecular weight of a structural unit)
The number average molecular weight:

35. Where:
The result:

36. The weight fraction Wx of X-mers
The Wx is the weight of all X-mers in the weight of all units
Because

37. The weight average molecular weight
since

38. Polydispersity Index The breadth of the molecular weight distri-
bution (also called Polydispersity Index) is then
given by:

39. The value of D increases with increase of he extent of
As P→1，D approaches two.
The value of D increases with increase of he extent of
reaction.
The breadth of the molecular weight distribution is
broader，the molecular weight is not uniformer.