Molecular Weight Distributions
(Rodriguez-52)
Before getting into the math of everything, we will first contrast
addition and condensation polymerization with graphs and "movies."
Below is a graph representing molecular weight distributions with
respect to time (red is time one, orange is time two, and yellow is
time three) for condensation polymerization:
In the 381 notes, this picture is provided in the section about Gel
Permeation Chromatography (GPC). From GPC you can construct a plot
showing the molecular weight distribution. The idea of 'distribution'
made seem obscure to you if you haven't covered probability and
normalization in P-Chem (or elsewhere.) When you click on the
link to the movie, immediately look up to the
title bar because there you will see a line of periods, with
each period representing a monomer. When a monomer has taken part
in polymerization, it is then represented as a star.
Below we show periods to represent unreacted monomers:
....................
and now we show a D.P.=10 oligomer in the monomer.
: In the notation
below a * indicates that a reaction has taken place. There are only nine
stars because nine reactions form a D.P.=10 oligomer.
.....**********.....
The
Condensation Polymerization "Movie".
We now look at a distribution graph for addition polymerization:
The
Addition Polymerization "Movie".
Let's now look at both distributions graphs at the same time:
Start with the condensation graph. There are several ideas in this
cartoon:
- As time passes, the average molecular weight increases
- As time passes, the difference between the molecular weight of the
largest molecule, and then smallest increases
- Toward the end of the experiment, there aren't as many polymer
molecules. If I were to redo this graph I would make the yellow peak
height much small than it now is.
This can be rationalized by noting that if there are 1000 monomers in
the starting solution, the maximum possible D.P.=10 species is 100,
the maximum possible D.P.=25 is 40, and so on.
- IMPORTANT! Don't assume the time scale going from red to orange
is the same as going from orange to yellow. It's not! With regard
to extent of reaction, it takes as long to go from the start to extent
of reaction=0.98 as it does to go from extent of reaction= 0.98 to
extent of reaction= 1.0.
We now examine the Addition Polymerization "cartoon":
- We DON'T see a gradual increase in molecular weight!
This is where the theory gets interesting. We must consider the timescale of
the experiment vs. the timescale of the polymerization of a single
molecule. Maybe it takes an hour for all the monomer to convert to
polymer, but once a chain is initiated, it is fractions of a second
before termination occurs. It might work to view the system as a sea of
monomers with terminated polymer chains, and all of a sudden an
iniator fragments into two radicals and two polymers grow and what seems
to be an instant, it is over. If you are running the "film" at a super slow
speed at which you can watch the polymerization, then it will take what
seems to be an eternity before another polymerization starts.
If you quench your reaction (i.e., you stop all polymerizations in progress
and prevent any further polymerizations), the concentration of polymer
quenched while growing will be much less than the concentration of monomer
and and terminated polymers (monomer concentration is not shown on the
graphs.)
- The molecular weight of all formed polymer chains is about the same.
This assumes that the rate of termination (the sum of the rates for all
possible modes of termination) and the rate of propagation remain the
same relative to each other. This is an inaccurate assumption if the
system is heating up, for molecular weight studies for systems at
higher temperatures show a decrease in molecular weight, indicating
that increased temperature increases the probability of termination more
so than the probability of propagation, but that is another story.
Last Update- October 29, 1995- wld