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The probability of forming a pentamer is thus:
It follows by induction that for any n-mer, the weight fraction is:
(This is sometimes called the Kuhn distribution)
Example:
Assume we degrade a polymer (randomly) until
α
equals 0.015. According to
the equation above the reaction mixture contains the following amounts of
monomers, dimers.. etc.
The distribution is broad, the maximum amount being somewhere around
0.5% (calculated for n = 100).
The entire distribution can be represented graphically:
w
5
=
5
α
(1
−
α
)(1
−
α
)(1
−
α
)(1
−
α
)
α
=
5
α
2
(1
−
α
)
4
w
n
=
n
α
2
(1
−
α
)
n
−
1