Analytical
Analytical Ultracentrifugation
Ultracentrifugation
of
of Nanoparticles
Nanoparticles
Helmut Cölfen
Max-Planck-Institute of Colloids and Interfaces,
Colloid Chemistry, Am Mühlenberg 2, D-14424 Potsdam
Email: Coelfen@mpikg-golm.mpg.de
Why
Why fractionating
fractionating analytics
analytics in
in solution
solution ??
Light
Light Scattering
Scattering
Microscopy
Microscopy
AUC
AUC // FFF
FFF
No fractionation
Counting of
particles
Drying artifacts
Problem:
Statistics
Sensitive to
bigger particles /
dust as
I∼r6
Problem:
Big particles
Absorption
multiple scattering
Fractionation
Every particle is
detected,
simultaneous
multiple detection
possible
Svedbergs
Svedbergs Colloid
Colloid Research
Research
•
T. Svedberg, J.B. Nichols, J.
Amer. Chem. Soc. 45 (1923)
2910
•
T. Svedberg, H. Rinde, J. Amer.
Chem. Soc. 45 (1923) 943
•
T. Svedberg, H. Rinde, J. Amer.
Chem. Soc. 46 (1924) 2677
•
T. Svedberg, Kolloid-Z.
Zsigmondy Festschrift, Erg.-Bd.
Zu 36 (1925) 53
1925: Nobel prize for
colloid work
1926: First protein work
Principle
Principle of
of AUC
AUC
Radial Detection
Light
Solution
Vapour
ω
ϕ
h
rm
rt
Detector
r
UV/VIS Absorption optics
Δn
Abs.
Rayleigh Interference optics
r
rb
r
Experiments very simple, evaluation not always
Sedimentation velocity
High centrifugal force
Sedimentation stronger than back
diffusion
Absorbance
Different
Different AUC
AUC experiments
experiments
1.0
0.5
50000 RPM
Scaninterval
10 min
0.0
6.2
6.4
6.6
6.8
7.0
7.2
Sedimentation equilibrium
Moderate centrifugal force
Sedimentation in the order of back
diffusion
Absorbance
Radius (cm)
2.0
Sedimentation
1.5
Diffusion
1.0
0.5
0.0
10000 RPM
6.7
6.8
6.9
7.0
7.1
Radius (cm)
Density gradient
High centrifugal force for distribution
of a low molecular salt or a second
solvent
Absorbance
1.0
0.8
50 % CH2Cl2 + 50 % CHCl3
60000 RPM
0.6
0.4
0.2
0.0
6.2
6.4
6.6
6.8
Radius (cm)
7.0
7.2
Lamm
equation
Lamm
equation
⎛
⎞
⎟
∂c 1 d ⎜
dc
2 2
⎜ rD
=
− sω r c ⎟
1
424
3 ⎟
∂t r dr ⎜ 123
dr
Se
dim
entation
term ⎟
⎜ Diffusion term
⎝
⎠
Experiment
Effective term in the
Lamm equation
Characteristics
Sedimentation
velocity
Sedimentation term much
bigger than diffusion term
High rotational
speed
Synthetic boundary
experiment for the
determination of D
Only diffusion term
effective
Synthetic
boundary cell,
low rotational
speed
Sedimentation
velocity
Sedimentation and
diffusion term effective /
equilibrium between
sedimentation and
diffusion
Moderate / low
rotational speed
Density gradient
(special case of
sedimentation
equilibrium)
Sedimentation and diffusion
term effective / equilibrium
between sedimentation and
diffusion
Moderate / high
rotational speed,
locally dependent
solution density
Absorbance
Basic
Basic evaluation
evaluation important
important for
for
nanoparticles
nanoparticles
1 step means
1 component
1.0
0.5
50000 RPM
Scaninterval 10 min
0.0
6.2
6.4
6.6
6.8
7.0
Flat baseline
indicates
purity
7.2
Radius (cm)
a) Determine distance travelled in given time interval
b) Calculate sedimentation coefficient s or its distribution
c) Calculate particle size or distribution
u
s= 2
ωr
s=
ln(r /rm )
ω2 t
18ηs i
di =
ρ2 − ρ
Sedimentation
Sedimentation velocity
velocity
RT
sRT
18ηs i
di =
M=
f=
ρ2 − ρ
N AD
D (1 − vρ )
Sedimentation velocity depends on:
Molar mass / particle size
Density
Shape / Friction
Charge
for given exptl. parameters (temperature, solvent
density & viscosity etc.)
Particle size distributions calculated on a hard sphere basis
Sedimentation
Sedimentation velocity
velocity
1.6
a)
1.4
1.845
1.2
1.0
Data for individual boundaries
Regression line
sw = 480 S
1.840
s=
0.8
ln(r /rm )
0.6
ln(r/rm)
Absorbance
Gold in
H2O at
5000 RPM,
25 °C
1.850
ω t
2
1.835
1.830
0.4
1.825
0.2
6.0
a) Raw data
6.2
6.4
6.6
6.8
7.0
7.2
b)
1.820
4.00E+008
ωt
g*(s)
c(s) diffusion corrected
c)
1.0
1.0
18ηs i
ρ2 − ρ
di =
d)
0.8
g*(d)
g*(s) resp. c(s)
0.8
d) ddistribution
8.00E+008
2
1.2
b) Sevaluation
c) sdistribution
6.00E+008
Radius [cm]
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0
200
400
600
sedimentation coefficient [S]
800
0.0
6.0
6.2
6.4
6.6
6.8
Diameter [nm]
7.0
7.2
Common
Common Problems
Problems
•
Extremely broad s-distributions, Big aggregates or small
impurities are not detected
•
Colloids aggregate or grow during centrifugation
(concentration dependent aggregation)
•
Density of hybrid colloids is unknown to access particle
size
•
Electrostatic stabilization complicates analysis due to
charge contributions
•
Particle polydispersity in size, shape, density and
hydration
•
High particle density often makes density gradients or
density variation methods impossible
•
Often multicomponent mixtures
Fractionation
of
heterogeneous
samples
Fractionation
of
heterogeneous
samples
5
Carrageenan
Absorbance / Fringe shift
Absorption optics
+ iron oxyhydroxide
Interference optics
4
Large aggregates
Carrageenan + iron oxyhydroxide
3
0.55 fringes
Free
Carrageenan
2
2.72 fringes
1
40000 RPM, 25 °C
0
6,0
6,2
6,4
6,6
6,8
7,0
Protected partially
mobile FeOOH
Radius [cm ]
pH 2, κ-carrageenan
Hollow space
+
Fe3+
Fe3+
Fe3+
Fe3+
3+
pH 2, Fe
+ OHpH > 5
crosslinking of κ-carrageenan
Hydrolized Fe3+
F. Jones
Latex
Latex mixture
mixture
1 .0
A. Völkel
60 nm
100 nm
0 .8
164 nm
i
Σc /c
0
0 .6
389 nm
0 .4
0 .2
3400 nm
0 .0
100
d=
•
18 η s
ρP − ρLM
1000
d H [μ m ]
Particles analyzed over colloidal
range in one experiment
given
d [nm] %
60 20
103 20
160 20
347 20
2800 20
reproduced
d [nm] %
60 20
100 20
164 18
389 20
3400 22
Very
Very small
small colloids
colloids
Au
[P(
Phe
)
]
Cl
Au55
[P(Phe)
]
3
12
55
3 12Cl66
Reported to be definite cluster
with 55 Au, Transition between
metal and molecule
1530 counts
0.21
Expt. Data
Sum Gauss Fit
Ind. Gauss Fit
g(dH) [A.U.]
0.14
Species 1: 1.84 +/- 0.15 nm (48.7 %)
Species 2: 1.95 +/- 0.20 nm (26.0 %)
Species 3: 2.34 +/- 0.32 nm (25.3 %)
0.07
0.00
1.5
2.0
2.5
dH [nm]
3.0
1.0
High
High
resolution
resolution PSD
PSD
0.9
Absorbance
0.8
0.7
0.6
0.5
0.4
Pt colloid in MeOH / HAc
0.3
0.2
60000 RPM, 25 °C, 380 nm
Scanint. 2 min
0.1
0.0
6.0
6.2
6.4
6.6
6.8
7.0
7.2
Radius (cm)
1.0
0.1 nm Baseline resolution
1.77 nm
1.6
1.8
1.92 nm
1.59 nm
1.68 nm
0.6
1.50 nm
Differential
1.40 nm
0.8
1.30 nm
Sum of mass fractions
Integral
0.4
0.83 nm
0.2
0.0
0.4
0.6
0.8
1.0
1.2
1.4
Particle diameter [nm]
Problem:
Elimination of diffusion
broadening by selfsharpening effects
is not common
2.0
Baseline resolution > 1 Angström
TEM
TEM
Number frequency %
20
350 counts
15
10
5
0
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
particle diameter [nm]
Particles slightly bigger than from AUC (Density)
Pt
-Colloid growth
Pt-Colloid
growth
Coalescence
Critical
crystal
nucleus
= Stabilizer
= Pt-Particle
Growth
Coalescence until particles Further growth through
are stabilized
reduction of PtCl4 at the
crystal surface
dr
= const. Differences in the particle size after
coalescence are conserved
dt
Mechanism in G.A. Braun, Ph-D dissertation, Aachen 1997
Start of heating defines
start of the reaction
5
0 2
4 6
8 10
Parti
cle d
12 14
iame
ter [n
m]
Problem: AUC has a low time resolution
300
250
200
150
100
50
tim
e[
mi
n]
Dilution 1 : 5 and
Heating to 65 °C
10
Re
ac
tio
n
Zn(Ac)2 (1 mmol/l)
+ 20 mmol/l NaOH
in water free
Isopropanol
ts
Arbitrary uni
Growing
Growing ZnO
ZnO Colloid
Colloid
T. Pauck
Bio
-labeling
Bio-labeling
Au
Au
Au S
Au
S
COO
COO
Differential distribution
+
BSA
etched + transferred to water
attached to protein
0
2
4
6
8
10
Particle size (nm)
12
D.I.Gittins and F.Caruso
Phase
-labeling
Phase transfer
transfer and
and bio
bio-labeling
Au particles in toluene
Au particles in water
BSA labeled Au particles in water
1.0
0.8
Phase transfer agent: 11Mercaptoundecanoic acid
(MUA)
g(s)
0.6
0.4
0.2
0.0
0
500
1000
s25,w [S]
1500
2000
D.I.Gittins and F.Caruso
Dopamine
Dopamine functionalized
functionalized TiO
TiO22
0.10
3
0.09
Absorption
g (d)
0.08
0.07
0.06
2
0.05
0.04
3
1
Particle size
decreases
4
5
6
7
8
9
dH (nm)
Spectra taken at
different
positions in
distribution
0
200 250 300 350 400 450 500 550 600
Wavelength [nm]
M. Niederberger
Concept
Concept of
of turbidimetric
turbidimetric immunoassay
immunoassay
Antibody
(high reactivity)
Antibody
(low reactivity)
Antigen
127 nm
Latex particle
221 nm
Latex particle
Concept
Concept of
of turbidimetric
turbidimetric immunoassay
immunoassay
Big particles
aggregate first,
then the small
ones
TEM
TEM of
of Immunoassay
Immunoassay
0 mg/L CRP
4.28 mg/L CRP
Statistics, drying artifacts ?
25 mg/L CRP
156 mg/L CRP
Scale bars 500 nm
SLS
SLS of
of Immunoassay
Immunoassay
100
50 mg/L CRP
G(dH)
80
•
Fast measurement
without equilibration
needs
•
Kinetic measurements
possible
•
Ambient conditions
without any pressure
effects
•
Low resolution in particle
size
•
Low statistical resolution
(No fractionation)
60
0 min
2 min
5 min
7 min
11 min
15 min
40
20
0
0.1
1
10
dH [μm]
100
G(dH)
80
171 mg/L CRP
60
0 min
2 min
4 min
7 min
11 min
15 min
40
20
0
0.1
1
dH [μm]
10
92 wt-% small latices
AUC
AUC of
of Immunoassay
Immunoassay
1.0
G(dH)
0.8
25 °C
0.6
•
AUC has equilibration time >
10 min before experiment
•
Fractionation enables to
determine correct particle
quantities and sizes by
turbidity detection (MIE
correction) with speed profile
even over decades of svalues
•
92 wt-% small latices in
mixture correctly detected
0.4
Latex mixture
+ 4.28 mg/L CRP
+ 50 mg/L CRP
+ 156 mg/L CRP
0.2
0.0
0.0
0.5
1.0
1.5
dH [μm]
2.0
2.5
3.0
1.0
G(dH)
0.8
0.6
Latex mixture
+ 5 mg/L CRP
+ 10 mg/L CRP
+ 20 mg/L CRP
+ 30 mg/L CRP
+ 40 mg/L CRP
+ 50 mg/L CRP
0.4
0.2
37 °C
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
dH [μm]
1.4
1.6
1.8
2.0
2.2
Microgels
Microgels
Figure from:
H.G. Müller, A.
Schmidt, D. Kranz;
Progr. Colloid
Polym. Sci. 86, 70
(1991)
b ⋅ d ρ P − ρs
Q=
⋅
s
18 ⋅ η
2
h
3
b = mass ratio of soluble parts
PNIPAM
PNIPAM Microgels
Microgels
Fringe shift of crosslinked part: 7.90
Fringe shift of free chains
: 2.37
10
76%
24%
4
Crosslinked 10000 rpm
Not crosslinked
60000 rpm
8
6
4
Fringe shift
Fringe shift
3
7,50
2
2,37
1
2
0
6.0
6.2
6.4
6.6
r [cm]
6.8
7.0
7.2
0
6.3
6.6
6.9
r [cm]
D. Kuckling
1.0
1.0
0.8
0.8
0.6
0.6
G(Q)
G(s)
Swelling
Swelling degree
degree distribution
distribution
0.4
0.2
0.2
Deswollen (40 °C)
Swollen (25 °C)
low crosslinking degree
high crosslinking degree
0.0
0
200
400
600
800
s [Svedberg]
⎛ s unswollen ⎞
⎟⎟
Q = ⎜⎜
⎝ s swollen ⎠
3
1000
0.4
1200
0.0
0
5
10
15
20
25
30
35
40
Q
In principle also possible with soluble fraction b
b ⋅ d 2h ρ P − ρs
Q=
⋅
s
18 ⋅ η
D. Kuckling
Solvent
Solvent density
density variation
variation
PS123-P4VP145 in toluene resp. d-toluene
0,8
0.6
1,5
ρ [g/cm³]
0.8
2,0
1,0
ρTdT for the following data:
==============================
low density:PS-P4VP in toluene
high density:PS-P4VP in tol/tol-d8
Integral distribution
integral distribution
1.0
0,6
18 η s
d=
ρP − ρLM
0.4
0,4
0.2
lower density
higher density
0.0
0
100
200
300
400
sedimentation coefficient [S]
1,0
500
0,5
0,2
0,0
0,0
40
60
80
100
dH [nm]
Combination of 2 s-distributions in 2 chemically identical
solvents yields particle size and density distribution
•
•
•
Density in good agreement with values from density meter
Particle size in agreement with results from DLS or viscosity measurements
Same result for core crosslinked micelles
K. Schilling
PS
-PMAA Latex
PS-PMAA
Latex mixture
mixture 40
40 :: 60
60
1,0
integral psd
differential psd
0,8
ρP = 1.188 g/ml
nP= 1.460
b = 61.5%
0,6
0,4
ρP = 1.054 g/ml
nP = 1.6
b = 38.5%
0,2
0,0
0
50
100
150
18( s2 ηs2− s1 ηs1 )
d=
ρ s1 − ρ s2
200
250
300
350
400
450
s1 ηs1 ρs2 − s2 ηs2 ρs1
ρ =
p
s 1 η s1 − s2 η s2
A. Völkel
Synthetic
Synthetic hybrid
hybrid colloids
colloids
200 nm
A
B
200 nm
Brushite CaHPO4 * 2H2O
TG 18% Mineral
C
100 nm
A: Star like crystals/whisker, d = 17 nm, l = 184 nm
B: Transversal growth, destabilization of filaments, further
densification of core
C: Compact aggregates with periodicity („Chrysanthemun“ structure)
M. Breulmann
Synthetic
Synthetic hybrid
hybrid colloids
colloids
whisker
•
Superposition
of particle size
and density
distribution
•
Densities can
exceed 2 g/ml
1.0
dense structure
0.6
0.4
0.2
400
300
200
0.0
0 10
20
30
s* [S]
40
tim
e[
h]
g(s*)
0.8
100
50
60
70
0
Synthetic
Synthetic hybrid
hybrid colloids
colloids
density increase
PEG-PMAA-C12
1.0
2+
PEG-PMAA-C12 + Ca
"Chrysanthemum" 1 week
Diameter(DLS) = 150 nm
g(s*)
0.8
polydispersity
increase
0.6
• Global Analysis
could reveal
density and molar
mass
0.4
0.2
0.0
0
5
10
15
20
25
30
s* [Svedberg]
35
• Clear monitoring
of density
increase upon
Ca2+ complexation
40
Combination of AUC
with DLS or better
Fl-FFF is highly
desirable
Particle
Particle size
size and
and density
density
CdS
UV : d = 1.65 nm
DLS : d = 1.6 nm
„
AUC: d = 1.25 nm“ (s = 3.6 S)
ρparticle = 3.2 g/cm3
dparticle = 1.6 nm
calculated with ρCdS = 4.83 g/cm3
3
0,03
UV
2
1
0
200 250 300 350 400 450
λAbs [nm]
18ηs
ρp = 2 + ρ s
dp
r*d(r) [a.u.]
I [a.u.]
4
0,02
DLS
0,01
0,00
1
10
2 r [nm]
Density core and
shell are known
With independent size measurement,
hybrid particle is fully characterized
dtotal = 1.6 nm
dcore = 1.1 nm
dshell = 0.5 nm
(Lit.: dshell = 0.4 nm)
Hybrid
Hybrid Colloids
Colloids
Ferrihydrite
Fe2O3 . x H2O
•
Iron storage protein Ferritin
forms robust hollow sphere
from 24 dimeric subunits
•
•
Ferritin oligomerizes
•
Simultaneous particle size and
density distribution
•
•
Size and amount of oligomers ?
Different amounts of
ferrihydrite inside the core (up
to 4500 Fe)
Amount of ferrihydrite inside
the core for the different
oligomers ?
A. Völkel
Ferritin
Ferritin
Fl-FFF separates only according to particle size, AUC
according to particle size and density
4.35x10-7cm2s-1
Dimer
t0 = 0.455min
AUC
0,8
g(s*)
Signal [a.u.]
1,0
Fl-FFF
Monomer
Diffusion corrected g(s*)
Sum of Gauss Fits
Individual Gauss Fits
0,6
0,4
2.93x10-7cm2s-1
Trimer
2.29x10-7cm2s-1
0,2
0,0
0 2 4 6 8 10 12 14 16 18 20 22
t [min]
ret
0
20
40
60
80
100 120 140 160
s* [S]
AUC no baseline separation of oligomers (density distribution)
Global analysis
Monomer
Dimer
Trimer
s* at 25 °C (AUC)
59.8 S
96.9 S
127.9 S
D* at 25 °C (Fl-FFF)
3.68 x 10-7 cm2/s
2.41 x 10-7 cm2/s
1.90 x 10-7 cm2/s
dH (Fl-FFF)
11.9 nm
18.1 nm
23.0 nm
ρP
1.764 g/cm3
1.531 g/cm3
1.436 g/cm3
Mw
586,700 g/mol
954,100 g/mol
1,367,400 g/mol
Oligomer amount
69.4 wt.-%
19.5 wt.-%
11.1 wt.-%
n Fe3+
1476
667
34
Diffusion corrected g(s*)
Sum of Gauss Fits
Individual Gauss Fits
3+
Ferritin low Fe content
1.0
3+
Ferritin high Fe content
0,8
0.8
0,6
0.6
g (s)
g(s*)
1,0
0,4
0.4
0,2
0.2
0,0
Fe
c o rri t
se nte in w
di nt ith
m ha h
en s
ta di ighe
tio ffe r
F
n
be rent e 3+
ha
vio
ur
0.0
0
20
40
60
80
s* [S]
100 120 140 160
0
100
200
300
400
s (S)
500
600
700
800
First
First direct
direct observation
observation of
of near
near critical
critical size
size
clusters
clusters by
by AFM
AFM
S.T. Yau, P.G. Vekilov „Quasi-planar nucleus structure in
apoferritin crystallization“, Nature 406, 494 - 497; 3 August 2000
σ = 1.1
Crystallization
Molecules that
appeared after capture
of the previous frame
Dissolution
Molecules that are
missing in the next frame
D.W. Oxtoby „Catching crystals at birth“, Nature 406, 464 - 465; 3 August 2000:
„Although the first small crystallites involved in nucleation form in the bulk of the
solution, Yau and Vekilov can observe them only once they have fallen to the bottom
of the vessel and attached themselves to the surface there. How can the authors be
sure that they are observing the critical early stages of crystallization described by
nucleation ?“
Synthetic
Synthetic boundary
boundary cell
cell of
of the
the Vinograd
Vinograd Type
Type
Reservoir
Capillaries
Reactant (
) containing solution is layered onto the
second reactant via the capillary ( )
Formation of a sharp reaction boundary
L. Börger
Reaction zone
Particle
Particle formation
formation in
in aa synthetic
synthetic boundary
boundary cell
cell
1 Generation
2 Generation
1) Formed particles sediment out of
the reaction zone, reaction is
quenched
2) Particles diffuse back into the
reaction zone, further growth
3) Sedimentation time >>
reaction time
N-th Generation Sedimentation of particles
Transformation of a
time distribution into a
radial distribution
according to size, Determination
of particle size distribution
possible
Synthetic boundary crystallization ultracentrifugation
1.0
[Cd4SR10]20.5 nm
g(dH)
CdS
+ thio0.8
glycerin
0.6
[CdSR4]20.3 nm
0.4
0.2
8 exptl. Scans
Sum Gauss Fit
Individual Gauss Fits
[Cd10S4SR16]41.0 nm
Structure unknown
literature 1.3 nm
Cd17S4SR26
1.4 nm
Structure unknown
literature 1.6 nm
Cd32S14SR36
1.8 nm
0.0
0.4
0.8
1.2
1.6
2.0
dH [nm]
All known stable CdS growth species simultaneously accessible in one
experiment. Even subcritical clusters detectable in solution
Conclusion
Conclusion
•
AUC is a very versatile instrument for colloid chemistry (Range
of possible methods still not fully explored !!!)
•
Fractionation allows the investigation of complex mixtures or
very polydisperse samples with s ranging over decades (speed
profile)
•
•
•
High statistical accuracy
Critical crystal nuclei and subcritical clusters can be resolved
Crystal growth reactions can be investigated by transformation
of time distribution into radial distribution
BUT:
•
Colloids can express various unfavourable properties which
makes them problematic to investigate
•
Fast multidetection systems together with global analysis can
potentially adress even most complex mixtures with particle
size and VBAR distribution but role of charge still unadressed
Future
Future Perspectives
Perspectives
•
Fast speed profiles and detectors to suppress
diffusion broadening
•
•
Multi-detection systems (RI, UV-Vis, SLS and others)
•
New ultracentrifugation methods could allow to access
new quantities
Global Analysis (promising with SEDVEL &
SEDEQUIL + DLS & Fl-FFF) to obtain s, M, D &
VBAR distributions
Surface tension from phase transfer, particle charge
determination via sedimentation in pH or charge gradient,
Conformational changes in solvent quality gradients, new
synthetic boundary techniques for membrane / crystal growth
investigations or chemical reactions in the AUC, etc.
Recommended
Recommended reading
reading
. Svedberg, K.O. Pedersen, The ultracentrifuge, Clarendon Press, Oxford (1940)
he classical textbook about analytical ultracentrifugation still with much impact
today
.K. Schachman, Ultracentrifugation in biochemistry, Academic Press, New York
(1959)
compact and useful book covering experimental and theoretical aspects
.E. Harding, A.J. Rowe and J.C. Horton; Analytical ultracentrifugation in
biochemistry and polymer science, The royal society of chemistry, Cambridge,
ISBN 0-85186-345-0 (1992)
he most comprehensive modern book about analytical ultracentrifugation. A very
good overview about methods & techniques of analytical ultracentrifugation and a
valuable source of modern applications.