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2.2.15. Determination of
the persistence
length
from
experimental data
The persistence length can be determined from experimental data, for
example R
G
-M or [
η
]-M data for polymer fractions. In contrast to the simpler
equations used previously, the mathematical expressions are here more
complicated. The simplest is the expression for R
G
developed by Porod and
Kratky in 1949:
Note that the only parameter beside the persistence length is the mass per
unit length (M
L
).
The expression cannot be simplified or linearized in the same way as for the
exponential equations used earlier, for example the R
G
-M equation. Instead,
data are fitted to experimentally data by systematically varying the
parameters. Here is an example from the literature (T. Sato et al.
Macromolecules 1984, 17, 2696-2700), showing data for xanthan. The best fit
is obtained for q = 120 nm.
R
G
2
=
qM
3
M
L
−
q
2
+
2
q
3
M
L
M
1
−
qM
L
M
1
−
e
−
M
qM
L
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
M
L
=
M
L
c
mass per unit length
(
)
L
c
=
nl
contour length
(
)