A detailed Kinetics of Polycondensation of the polymer with the acid catalyzed and non acid catalyzed reactions.

1. Kinetics of Polycondensation
Sivaprakash S
Department of Polymer Technology
Kamaraj College of Engineering and Technology
+91 99407 33520

2. Introduction
According to Flory, so long as the molecules are
not quite small, the intrinisic reactivity of the
functional groups present in them are
independent of the molecular size.
Similarly, the effect of viscosity of the reaction to
the overall kinetics of a condensation reaction.

3. Non – catalyzed polycondensation
For example, let us take the synthesis of polyester from a dicarboxylic
acid and a diol.
This type of esterification reaction need catalyst like acid.
However no strong acid is required. The dicarboxylic acid itself acts a
reactant and catalyst.
The rate of the polyesterification reaction rate will be propotional to
the square of the concentration of the carboxylic acid and to the first
power of the hydroxyl group concentration.

4. Mathematical representation
When the concentration of –OH and –COOH groups are equal.
i.e., when we take stoichiometric quantities of the functional groups (FG),
We can represent that at a given time t:
[COOH]=[OH]=[FG]
After rearranging and integration

5. Finding the concentration of FG
Where [FG]0 represents the initial
concentration of –COOH or –OH. If p
represents the fraction of the functional group
which has undergone the esterification
reaction (i.e., the extent of reaction) at a time
t, then [FG] could be related to [FG]0 through
the following equations:

6. [FG] = [FG]O (1-P)

8. This implies that a graphical plot of 1/(1 - p)2 versus t must be linear.
Experimentally, this has been found to be the case; Fig. represents a
plot for the reaction between adioic acid and diethylene glycol at
166°C.
For a simple esterification reaction, which proceeds without any side
reaction, the number-average degree of polymerisation may be
related to p, the fraction of the functional groups which has
undergone the esterification at a time t, by the following equation:

9. Acid catalyzed polycondensation
We have said earlier that the condensation
reactions are enhanced by the presence of
strong acids. The acid-catalysed
polycondensation reaction becomes governed
by the following equation:

10. Molecular Weight Distribution
As our assumption that equimolar quantities of reactants AA and BB react and that
the reactivity of groups A or B remains the same at all stages of conversion.
We know that the degree of polymerization varies with the extent of polymerization
that has taken place.
Now, let us see how the probability factor can give an idea about the molecular weight
distribution at a particular conversion p.
Here, p is the extent of reaction, which also gives the probability of reaction occurring
between two functional groups to give a repeat unit of -AB- asper the-reaction.

11. The fraction of unreacted groups is I-p. Now, assume that
a tetramer is formed as a result of the reaction between 4
reactant molecules, 2 of A-A and 2 of B-B, wherein 3 pairs
of reactive groups have reacted.
The probability of a tetramer formation is, therefore, p2.
For that matter, the probability of Occurrence of an n-
mer, I.e., a polymer molecule containing n number of
repeat units, will be pn-l.
Assuming that at a conversion of p, the total number of
polymer molecules formed is N and that of the n-mers
formed is Nn, then N and N; can be related as follows:

12. Nn=Npn-1(1-p)
If N0 is the number of reactant molecules
present to start with, then
N=N0 (1-p)
Now, combining Eqns,
Nn = N0 (1-p) Pn-1(1-p)
Nn = N0 (1-p)2 Pn-1
Wn represents weight fraction

13. For different values of p, the Nn; and Wn
distribution functions are shown in Figs.,
respectively.
The curves in Fig. show that if we consider the
number fraction, an appreciable quantity of very
low molecular weight species will be present at all
stages of conversion, as compared to high
molecular weight spices.
On the other hand, if we consider the weight
fraction.
The very low molecular weight species will be
present in a negligible quantity, as compared to
high molecular weight species.

16. On the other hand, if we consider the weight fraction. The very low
molecular weight species will be present in a negligible quantity, as
compared to high molecular weight species.
Equation which relates the weight-fraction distribution with the extent
of reaction can also be used in determining the extent of reaction that
should be attained if we want to get a maximum yield of a particular
molecular weight species.
Thus. from Eqn. we can derive:

17. Extent of Reaction and Degree of polymerization
We know that
Let us put different values of P and get the corresponding
values of , which are listed in the table.
It may be noted that in order to get a relatively high
degree of polymerization pr a high molecular weight
polymer, the extent of conversion has to be very high.
We can see from table that even for a degree of
polymerization of 100 (which, in fact, corresponds to low
molecular weight polymers), conversion has to be as high
as 99%.

18. Values of p Extent of conversion (%) Degree of polymerization
0.50 50 2
0.90 90 10
0.95 95 20
0.99 99 100
0.999 99.9 1000
0.99999 99.999 100000
Effect of extent of conversion on
degree of polymerization for
polycondensation reaction