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212
5.3.4. Random depolymerisation of
linear
(unbranched)
polymers: The
chain
length distribution
(W
n
)
The main equations for random depolymerisation may be supplemented and
extended to determine the distribution of different chain lengths obtained, i.e.
determining the relative amount of any n-mer in the reaction mixture.
The degree of scission (
α
) is related to the reaction time (t) and the pseudo
first order rate constant:
ln 1
−
α
(
)
= −
kt
Again, note the link between
α
and DP
n
(or M
n
):
α
=
1
DP
n
=
M
0
M
n
We can determine the relative amount of any n-mer by a simple
consideration:
The degree of scission (
α
) is also the
probability
that a specific linkage is
broken. Consequently, 1-
α
is the probability that a specific linkage is intact.
We first pick a monomer at random and consider possibilities for this
monomer to be part of a n-mer (n possibilities). Let us take a pentamer as
example, where there are 5 possibilities for a monomer (light blue) to be part
of the oligomer:
The probability of forming a pentamer corresponds to its weight fraction. A
pentamer is a result of the following independent events:
First linkage: cleaved
Second to fifth linkage: intact
Last linage: cleaved
!