Basic HTML Version
88
2.1.9. The Kuhn distribution
Distributions similar to the one shown above are surprisingly common among
polysaccharides. It is often called the Kuhn distribution, and is a result of
random depolymerization of a very long chain (See section 5.4 for details).
The weight fraction of an i-mer (DP = i) is given by:
w
i
=
i
α
2
1
−
α
(
)
i
−
1
Here,
α
is the degree of chain scission, which is equivalent to the fraction of
broken linkages.
α
is directly related to DP
n
:
α
=
1
DP
n
To illustrate: If one out of 10 linkages (between monomers) are on average
cleaved, then
α
= 1/10. The number average chain length is of course 10
when 1 out of 10 linkages are cleaved. Hence DP
n
= 10 = 1/
α
.
The figure above actually corresponds to a Kuhn distribution having DP
n
=
100 and DP
w
= 200 (M
0
= 198 as in alginates).
2.1.10 Practical examples
Example 1