F R A U N H O F E R I N S T I T U T E F O R A P P L I E D P O LY M E R R E S E A R C H I A P
MOLAR MASS DETERMINATION
FROM SEDIMENTATION DIFFUSION
EQUILIBRIUM
With moderate rotor speed at sufficiently
long run time of the centrifuge an equilibrium between sedimentation and backdiffusion of the dissolved macromolecules is
reached. One distinguishes between “high
c [mg/mL]
2.0
1.5
1.0
c01
speed” or “meniscus depletion” equilibrium,
where the polymer concentration at the
meniscus comes to zero, and “low speed”
0.5
c02
c03
c04
equilibrium (Fig. 1) which is more adequate
0.0
0.0
for samples with broad mass distribution.
Cell-Meniscus
From the equilibrium concentration distri-
0.2
0.4
0.6
0.8
x = (r2-rm2)/(rb2- rm2)
c01 = 0.89 mg/mL
c02 = 0.54 mg/mL
bution between cell meniscus and bottom
1.0
Cell-Bottom
c03 = 0.37 mg/mL
c04 = 0.18 mg/mL
which is detected by UV-absorbance or in-
Fig. 1 Concentration distribution at ­
terference optics the average molar masses
„low speed“ sedimentation equilibrium.
MW (weight average) and MZ (centrifuge average) can be calculated after an appropriate
extrapolation to zero concentration (Fig. 2).
Fraunhofer Institute for
Applied Polymer Research IAP
M w, app =
Science Park Potsdam-Golm
M
z , app
=
cb − cm
Contact
1x10-6
λ co
cb (d ln c / dx)b − cm (d ln c / dx)m
Geiselbergstr. 69
14476 Potsdam-Golm
λ (cb − cm )
Phone +49 331 568-1508
[email protected]
www.iap.fraunhofer.com
0
0.0
0.2
λ =(1−vρo)⋅ω 2 ⋅(rb2 −rm2 )/2 RT
1
1
=
+ B ⋅ co
Mapp M
0.4
0.6
0.8
1.0
1.2
c [mg/mL]
with
and extrapolation to c0 = 0 according ­to
Dr. Erik Wischerhoff
[mol/g]
2x10-6
Mz = 2800 kg/mol
Mw = 860 kg/mol
B = 8E-4 mL*mol/g2
Fig. 2 Extrapolation of the apparent molar
masses to c = 0.