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260
M
2
[
η
]
⎛
⎝⎜
⎞
⎠⎟
1/ 3
=
A
η
+
B
η
M
1/ 2
A
η
=
A
0
M
L
Φ
0,
∞
−
1/ 3
B
η
=
B
0
Φ
0,
∞
−
1/ 3
2
q
M
L
⎛
⎝⎜
⎞
⎠⎟
-1/2
Φ
0,∞
is the limiting value of the Flory viscosity constant, and equals 2.86
⋅
10
23
.
A
0
and B
0
are known functions of the reduced hydrodynamic diameter (d
r
) and
B
0
can in practise be replaced by a mean value (1.05). q is the persistence
length, and M
L
is the molar mass per unit contour length.
Plots of (M
2
/[
η
])
1/3
as a function of M
1/2
are given in the figure below (overlay
of several chitosan samples).
Fitting a straight line to these data provides the slope and the intercept, from
which we obtain the persistence length using the equations above (q = 7.5 nm
in the present case).
More examples are found in the following articles:
Christensen, B.E., Vold, I.M.N., Vårum, K.M. (2008) Chain stiffness and extension of chitosans and periodate
oxidised chitosans studied by size exclusion chromatography combined with light scattering and viscosity detector.
Carbohydr. Polym. 74, 559-565
Inger Mari N. Vold, Kåre A. Kristiansen and Bjørn E. Christensen (2006) A study of the chain stiffness in epimerised
and periodate-oxidised alginates using size-exclusion chromatography combined with light-scattering and viscosity
detectors. Biomacromolecules, 7, 2136-2146.
0
200
400
600
800
1,000
0
200
400
600
800 1,000
M
1/
(M
2
/[
!
])
1/