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108
The virtual bond length,
β
.
We introduce a virtual bond length (
β
) to describe the stiffness of the random
coil polymer by defining it as:
<r
2
> = n
β
2
We easily see, since <r
2
> = C
∞
nl
2
, that
C
∞
=
β
2
/l
2
.
The Kuhn length (l
k
).
This is another way of creating a virtual random coil, and the ratio between
the Kuhn length and the actual segment length (l
k
/l) expresses the chain
stiffness. The Kuhn chain has n
k
segments of length l
k
, and obeys the
expression for perfect random coils:
<r
2
> = n
k
l
k
2
(= C
∞
nl
2
)
This means that the Kuhn chain has the same end-to-end distance as the real
chain. At the same time the contour length of the Kuhn chain is the same as
for the real chain:
n
k
l
k
= nl
These equations immediately yield that:
l
k
= C
∞
l
n
k
= n/C
∞