Characterization of Polymers and Particles
by Analytical Ultracentrifugation
Dr. Erik Wischerhoff
Characterization of polymers and particles by analytical ultracentrifugation
Analytical Ultracentrifugation
fractionation of particles and molecules by mass difference
(also possible on preparative scale)
accessible molar mass ranges:
about 103 to 1014 g·mol-1
accessible particle sizes:
about 1 nm to 1 µm
Characterization of polymers and particles by analytical ultracentrifugation
Analytical Ultracentrifuge
Beckman, Optima XL-I
rotor speeds: 1000 to 56000 rpm
g-forces 50 to 3·105 g
detection systems:
• UV/Vis absorption (200 nm - 800 nm)
• interference optics
• schlieren optics
Characterization of polymers and particles by analytical ultracentrifugation
AUC cell
explosion drawing of an AUC cell
high requirements
regarding mechanical
stability and
leak tightness
Characterization of polymers and particles by analytical ultracentrifugation
AUC cell
AUC cell in cross section
need for reduction of molecular impacts at the chamber wall
⇒ sample chambers have the form of a circle segment
Characterization of polymers and particles by analytical ultracentrifugation
Theory of Analytical Ultracentrifugation
centrifugal force: Fs
molar mass:
Avogadro no.:
particle mass:
particle diameter:
friction coefficient:
dynamic viscosity:
sedimentation speed:
density solvent/particle:
partial specific volume:
diffusion coefficient:
Characterization of polymers and particles by analytical ultracentrifugation
buoyancy: Fb
friction: Ff
during centrifugation forces are balanced,
the sedimentation front moves at constant speed u
Theory of Analytical Ultracentrifugation
insertion of
into
:
molar masses
insertion of
and
into
:
particle sizes
Characterization of polymers and particles by analytical ultracentrifugation
Theory of Analytical Ultracentrifugation
absolute method!
but: auxiliary measurements required!
required: partial specific volume, density of solvent, viscosity
Characterization of polymers and particles by analytical ultracentrifugation
Absorbance at 280 nm
Analytical Ultracentrifugation
1.0
analysis of data,
z. B. with Sedfit*
0.5
40.000 rpm
∆t = 8 min
0.4
0.0
Meniscus
6.2
6.4
6.6
6.8
7.0
7.2
Radius (cm)
g(s)
6.0
0.3
Bottom
0.2
0.1
*https://sedfitsedphat.nibib.nih.gov/software/
*www.analyticalultracentrifugation.com/download.htm
Characterization of polymers and particles by analytical ultracentrifugation
0.0
0
2
4
6
8
sapp (Svedberg)
10
12
Molar Mass Calculation by Sedimentation Speed
suited for polymers with medium to very high molar masses
distribution of sedimentation coefficients
(and thereby molar mass distribution) is
(apparently) concentration dependent
cause:
entanglement of polymer chains
⇒ measurements at lowest possible
⇒ polymer concentrations
Characterization of polymers and particles by analytical ultracentrifugation
Molar Mass Calculation by Sedimentation Equilibria
suited for polymers with low molar masses
c −c
M w, app = b m
λ co
c (mg/ml)
1,5
c (d ln c / dx) − c (d ln c / dx)
b m
m
M
= b
z , app
λ (c − c )
b
m
1,0
c01
c02
c03
c04
0,5
0,0
0,0
CellMeniscus
0,2
0,4
0,6
2
2
m
2
2
m
x = (r - r )/(rb - r )
0,8
1,0
CellBottom
Characterization of polymers and particles by analytical ultracentrifugation
2 2 2
with λ = (1 − vρ o ) ⋅ω ⋅ ( rb − rm ) / 2 RT
and extrapolation to c0 → 0 acc. to
1
M app
=
1
+ B ⋅ co
M
(mol/g)
c01 = 0.89 mg/ml
c02 = 0.54 mg/ml
c03 = 0.37 mg/ml
c04 = 0.18 mg/ml
1/Mz , 1/Mw
2,0
4x10-6
3x10-6
Mw = 860 kg/mol
Mz = 2800 kg/mol
B = 8E-4 ml*mol/g2
2x10-6
1x10-6
0
0,0 0,2 0,4 0,6 0,8 1,0 1,2
cc /(mg/ml)
mg/ml
Particle Characterization by AUC
18η s
ρ P − ρ0
D=
particle size calculation
sample with complex composition
Fringe Displacement
(= concentration in arb. Units)
10
Meniscus
Bottom
6000 rpm
∆t = 2 min
8
0,02
6
g(D)
0,01
4
10000 rpm
∆t = 20 min
2
0,00
0
50
100
150
200
Particle Diameter D (nm)
0
6,0
6,2
6,4
6,6
6,8
Cell-Radius (cm)
Characterization of polymers and particles by analytical ultracentrifugation
7,0
7,2
250
300
AUC – Practical Examples
Diff. Volumenfraktion
comparison of particle size distribution
by AUC and by dynamic light scattering (DLS):
Kern-Schale, 0.07 wt%, Interf.
Kern-Schale, 0.07 wt%, Abs.
Kern, 0.07 wt%, Interf.
Kern, 0.07 wt%, Abs
core-shell particles:
core polystyrene
shell poly(butylcyanoacrylate)
provided by Dr. Bernd-Reiner Paulke (IAP)
Median: 91 nm
st.Dev.: 6 nm
Median: 134 nm
St.Dev.: 20 nm
70
80
90
100 110 120 130 140 150 160 170
Durchmesser, d (nm)
25
Kern-Schale, DLS
Kern, DLS
Kern-Schale, AUZ
Kern, AUZ
DLS gives by far too broad distributions
correct differentiation only possible by AUC
Diff. Volumenfraktion
20
15
DLS:
Median: 190 nm
St. Dev.: 60 nm
10
Median: 142 nm
St. Dev.: 55 nm
5
0
0
100
200
300
Durchmesser (d.nm)
Characterization of polymers and particles by analytical ultracentrifugation
400
500
AUC – Practical Examples
DLS often overestimates particle diameters, but not always:
PMMA Partikel, Konz. Stammdisp.: 15 gew%
Volume (a.u.)
0.03 wt%, Median: 55.8 nm, DLS
0.033 wt%, Median: 144 nm, AUZ
20
40
60
80
100 120 140 160 180 200 220
d (nm)
Characterization of polymers and particles by analytical ultracentrifugation
sample: PMMA-Partikel (090528-4L)
density: ρ=1.005 g/cm³
provided by Dr. Bernd-Reiner Paulke (IAP)
AUC – Practical Examples
c(dhydr) (a.u.)
MnL2n polyhedra with metal ions and ligands
Konz..: 2 mM
1.0
0.8
0.6
M60L120-Se, d(50)=8.8nm
M30L60, d(50)=6.1nm
M24L48, d(50)=4.7nm
M12L24, d(50)=3.1nm
0.4
0.2
0.0
2
4
6
8
10
12
dhydr (nm)
provided by Dr. Daishi Fujita (Uni Tokio)
Characterization of polymers and particles by analytical ultracentrifugation
Ligand
d0 [nm]
dpeak [Sved]
dth [nm]
M12L24
3.1
3.1
3.5a
M24L48
5.0
4.4
4.5a
M30L60
6.6
5.3
5.0a
M60L120-Se
9.0
7.7
7.2b
AUC – Practical Examples
analytical question: reason for diverging colors in nanoparticles
sample: ZnO nanoparticles with PEG shell
provided by Dr. Piotr Cywinski (IAP)
quantum confinement or defects in crystal structure
0.20
1.2
Konz: 10mg/ml (ZnO-Nanopart. / DMSO), U=15000 RPM
1.0
Interferenz
Abs: 320nm
Abs: 350nm
Abs: 370nm
0.8
c(r) (a.u.)
Absorbance
0.15
0.10
0.6
0.4
0.05
0.2
0.00
300
320
340
360
380
400
420
λ (nm)
440
0.0
1.5
2.0
2.5
3.0
Hydr. Radius, r (nm)
diverging colors stem from nanoparticles of different sizes
Characterization of polymers and particles by analytical ultracentrifugation
3.5
4.0
4.5
5.0
Summary
Analytical Ultracentrifugation (AUC)
• advantages
• suitable for particles and dissolved macromolecules
• extremly wide dynamic range for molar mass characterisation
• (11 orders of magnitude!)
• absolute method (no need for calibration)
• provides more realistic size distributions than other methods
• potential to solve complex analytical problems
• disadvantages
• laborious method
• auxiliary measurements required
• quality of results dependent on auxiliary measurements
Characterization of polymers and particles by analytical ultracentrifugation