Analytical Ultracentrifugation of Nanoparticles

Analytical Ultracentrifugation Analytical Ultracentrifugation of of NanoparticlesNanoparticles

Helmut Cölfen

Max-Planck-Institute of Colloids and Interfaces,Colloid Chemistry, Am Mühlenberg 2, D-14424 Potsdam

Email: Coelfen@mpikg-golm.mpg.de

Why fractionating analytics in solution ?Why fractionating Why fractionating analytics in analytics in solutionsolution ??

AUC / FFFAUC / FFFAUC / FFF

Sensitive to bigger particles /

dust asI ∼ r 66

Problem:Problem:Big Big particlesparticlesAbsorptionAbsorption

multiple multiple scatteringscattering

Light ScatteringLight ScatteringLight Scattering

EveryEvery particle isdetected,

simultaneousmultiple detection

possible

MicroscopyMicroscopyMicroscopy

Counting ofparticles

Drying artifacts

Problem: Problem: StatisticsStatistics

NoNo fractionationfractionation FractionationFractionation

Svedbergs Colloid ResearchSvedbergs Colloid Svedbergs Colloid ResearchResearch• 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

1926: First 1926: First protein workprotein work

1925: Nobel 1925: Nobel prizeprize forforcolloidcolloid workwork

h

ϕ

rr r r

t m

VapourSolution

ω

b

Radial Detection

Rayleigh Interference optics UV/VIS Absorption opticsΔn

Abs

.

r r

Light

Detector

Principle of AUCPrinciple Principle of AUCof AUC

Experiments very simple, evaluation not always

Sedimentation Sedimentation velocityvelocity

Sedimentation Sedimentation equilibriumequilibrium

Density gradientDensity gradient

High centrifugal forceSedimentation stronger than back diffusion

50000 RPMScaninterval10 min

6.2 6.4 6.6 6.8 7.0 7.2

0.0

0.5

1.0

Abs

orba

nce

Radius (cm)

6.7 6.8 6.9 7.0 7.10.0

0.5

1.0

1.5

2.0

Abs

orba

nce

Radius (cm)

Moderate centrifugal forceSedimentation in the order of back diffusion

Sedimentation

Diffusion

10000 RPM

6.2 6.4 6.6 6.8 7.0 7.20.0

0.2

0.4

0.6

0.8

1.0A

bsor

banc

e

Radius (cm)

50 % CH2Cl2 + 50 % CHCl360000 RPM

Different AUC experimentsDifferent AUC Different AUC experimentsexperiments

High centrifugal force for distributionof a low molecular salt or a second solvent

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

ω−=∂∂

43421321 termentationdimSe

22

termDiffusion

crsdrdcDr

drd

r1

tc

Lamm equationLamm Lamm equationequation

Experiment Effective term in the Lamm equation

Characteristics

Sedimentationvelocity

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

Sedimentationvelocity

Sedimentation and diffusion term effective / equilibrium between sedimentation and diffusion

Moderate / low rotational speed

Density gradient(special case ofsedimentation equilibrium)

Sedimentation and diffusion term effective / equilibrium between sedimentation and diffusion

Moderate / highrotational speed,locally dependent solution density

50000 RPMScaninterval 10 min

6.2 6.4 6.6 6.8 7.0 7.2

0.0

0.5

1.0

Abs

orba

nce

Radius (cm)

Basic evaluation important for nanoparticles

Basic Basic evaluation important for evaluation important for nanoparticlesnanoparticles

a) Determine distance travelled in given time intervalb) Calculate sedimentation coefficient s or its distributionc) Calculate particle size or distribution

ρ−ρη

=2

ii

s18dr

us 2ω=

t)r/rln(s 2

m

ω=

1 step means1 component

Flat baseline indicates purity

( )MsRT

D v=

−1 ρf

RTN DA

=

Sedimentation velocitySedimentation Sedimentation velocityvelocity

ρ−ρη

=2

ii

s18d

Sedimentation velocity depends on:

Molar Molar mass mass / / particle sizeparticle sizeDensityDensityShape Shape / / FrictionFrictionChargeCharge

for given exptl. parameters (temperature, solvent density & viscosity etc.)

Particle size distributions calculated Particle size distributions calculated on a on a hard sphere basishard sphere basis

Sedimentation velocitySedimentation Sedimentation velocityvelocity

6.0 6.2 6.4 6.6 6.8 7.0 7.2

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

a)

Abs

orba

nce

Radius [cm]4.00E+008 6.00E+008 8.00E+008

1.820

1.825

1.830

1.835

1.840

1.845

1.850

b)

sw = 480 S

Data for individual boundaries Regression line

ln(r

/r m)

ω2t

0 200 400 600 8000.0

0.2

0.4

0.6

0.8

1.0

1.2

c) g*(s) c(s) diffusion corrected

g*(s

) res

p. c

(s)

sedimentation coefficient [S]

6.0 6.2 6.4 6.6 6.8 7.0 7.20.0

0.2

0.4

0.6

0.8

1.0 d)

g*(d

)

Diameter [nm]

t)r/rln(s 2

m

ω=

ρ−ρη

=2

ii

s18d

Gold in H2O at 5000 RPM, 25 °C

a) Raw data

b) S-evaluation

c) s-distribution

d) d-distribution

Common ProblemsCommon ProblemsCommon 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 samplesFractionation Fractionation of of heterogeneous samplesheterogeneous samples

6,0 6,2 6,4 6,6 6,8 7,00

1

2

3

4

5 Carrageenan

+ iron oxyhydroxide

Large aggregates

Free

Carrageenan

Carrageenan + iron oxyhydroxide

2.72 fringes

0.55 fringes

40000 RPM, 25 °C

Absorption optics

Interference opticsA

bsor

banc

e / F

ring

e sh

ift

Radius [cm]pH 2, κ-carrageenan

pH > 5

pH 2, Fe3+ crosslinking of κ-carrageenan

Hollow space

Protected partiallymobile FeOOH

Hydrolized Fe3+

+ OH-+ Fe3+ Fe3+

Fe3+

Fe3+

F. Jones

1 0 0 1 0 0 0

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

d H [μ m ]

3 4 0 0 n m

3 8 9 n m

1 6 4 n m

1 0 0 n m6 0 n m

Σci/c

0

given reproducedd [nm] % d [nm] %

60 20 60 20103 20 100 20160 20 164 18347 20 389 202800 20 3400 22

Latex mixtureLatex Latex mixturemixture

LMP

s18dρ−ρη

=

•• Particles analyzed over colloidal Particles analyzed over colloidal range range in in one experimentone experiment

A. Völkel

1.5 2.0 2.5 3.0

0.00

0.07

0.14

0.21

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 %)

Expt. Data Sum Gauss Fit Ind. Gauss Fit

g(d H

) [A

.U.]

dH [nm]

Au55[P(Phe)3]12Cl6AuAu5555[P([P(PhePhe))33]]1212ClCl66Reported Reported to to bebe definitedefinite cluster cluster withwith 55 Au, 55 Au, Transition betweenTransition between

metal andmetal and moleculemolecule1530 counts

Very small colloidsVery small colloidsVery small colloids

6.0 6.2 6.4 6.6 6.8 7.0 7.20.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

60000 RPM, 25 °C, 380 nmScanint. 2 min

Abso

rban

ce

Radius (cm)

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.92

nm

1.77

nm

1.68

nm

1.59

nm

1.50

nm

1.40

nm

1.30

nm

0.83 nm

Integral Differential

Sum

of m

ass

frac

tions

Particle diameter [nm]

High resolution PSD

High High resolutionresolution PSDPSDPt colloid in MeOH / HAc

Baseline resolution > 1 Angström

0.1 nm Baseline resolution

Problem: Elimination of diffusion broadening by self-sharpening effectsis not common

Particles slightly bigger than from Particles slightly bigger than from AUC (AUC (DensityDensity))

0.80.8 1.21.2 1.61.6 2.02.0 2.42.4 2.82.8 3.23.2 3.63.600

55

1010

1515

2020350350 countscounts

particle diameterparticle diameter [nm][nm]

Num

ber f

requ

ency

%TEMTEMTEM

Pt-Colloid growthPtPt--ColloidColloid growthgrowth

Critical crystal

nucleus

Coalescence until particles are stabilized

Further growth through reduction of PtCl4 at the

crystal surfacedrdt

const= . DifferencesDifferences in in thethe particleparticle sizesize afteraftercoalescence are conservedcoalescence are conserved

Mechanism in G.A. Braun, Ph-D dissertation, Aachen 1997

= Stabilizer = Pt-Particle

CoalescenceCoalescence GrowthGrowth

0 2 4 6 8 10 12 1450

100150

200250300

0

5

10

Arbi

trar

y un

its

Reac

tion

time [

min

]

Particle diameter [nm]

Growing ZnO ColloidGrowing ZnO ColloidGrowing ZnO Colloid

Zn(Ac)2 (1 mmol/l)+ 20 mmol/l NaOHin water freeIsopropanol

Dilution 1 : 5 andHeating to 65 °C

Start of heating defines start of the reaction

Problem: AUC has a Problem: AUC has a lowlow time time resolutionresolution T. Pauck

0 2 4 6 8 10 12

etched + transferred to waterattached to protein

Diff

eren

tiald

istr

ibut

ion

Particle size (nm)

AuAu

AuAu

S

SCOO

COO

+BSA

D.I.Gittins and F.Caruso

Bio-labelingBioBio--labelinglabeling

0 500 1000 1500 20000.0

0.2

0.4

0.6

0.8

1.0 Au particles in toluene Au particles in water BSA labeled Au particles in water

s25,w [S]

g(s)

Phase transfer agent: 11-Mercaptoundecanoic acid(MUA)

Phase transfer and bio-labelingPhase Phase transfer transfer and bioand bio--labelinglabeling

D.I.Gittins and F.Caruso

Dopamine functionalized TiO2DopamineDopamine functionalizedfunctionalized TiOTiO22

200 250 300 350 400 450 500 550 6000

1

2

3

Abs

orpt

ion

Wavelength [nm]

3 4 5 6 7 8 90.04

0.05

0.06

0.07

0.08

0.09

0.10

g (d

)dH (nm)Particle sizeParticle size

decreasesdecreases Spectra taken at different

positions indistribution

M. Niederberger

Concept of turbidimetric immunoassayConceptConcept of of turbidimetricturbidimetric immunoassayimmunoassay

Antibody(low reactivity)

221 nm

Antibody(high reactivity)

Latex particle

127 nmLatex particle

Antigen

Concept of turbidimetric immunoassayConceptConcept of of turbidimetricturbidimetric immunoassayimmunoassay

Big Big particlesparticlesaggregateaggregate firstfirst, , then thethen the small small

onesones

TEM of ImmunoassayTEM ofTEM of ImmunoassayImmunoassay

0 mg/L CRP 4.28 mg/L CRP

25 mg/L CRP 156 mg/L CRP

Scale bars 500 nm

StatisticsStatistics,, drying artifactsdrying artifacts ??

0.1 1 100

20

40

60

80

100

50 mg/L CRP

0 min 2 min 5 min 7 min 11 min 15 min

G(d

H)

dH [μm]

0.1 1 100

20

40

60

80

100

171 mg/L CRP

0 min 2 min 4 min 7 min 11 min 15 min

G(d

H)

dH [μm]

SLS of ImmunoassaySLS ofSLS of ImmunoassayImmunoassay• Fast measurement

without equilibration needs

• Kinetic measurements possible

• Ambient conditions without any pressure effects

• Low resolution in particle size

• Low statistical resolution(No fractionation)

92 92 wtwt--%% small laticessmall latices

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

25 °C

Latex mixture + 4.28 mg/L CRP + 50 mg/L CRP + 156 mg/L CRP

G(d

H)

dH [μm]

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.20.0

0.2

0.4

0.6

0.8

1.0

37 °C

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

G(d

H)

dH [μm]

AUC of ImmunoassayAUC ofAUC of ImmunoassayImmunoassay

• AUC has equilibration time > 10 min before experiment

• Fractionation enables to determine correct particle quantities and sizes by turbidity detection (MIEcorrection) with speed profile even over decades of s-values

• 92 wt-% small latices inmixture correctly detected

Figure from:H.G. Müller, A. Schmidt, D. Kranz; Progr. Colloid Polym. Sci. 86, 70 (1991)

MicrogelsMicrogelsMicrogels

3η⋅ρ−ρ

⋅⋅

=18s

dbQ sP2h b = mass ratio of soluble parts

Fringe shift of crosslinked part: 7.90 76%Fringe shift of free chains : 2.37 24%

6.0 6.2 6.4 6.6 6.8 7.0 7.20

2

4

6

8

10

Fr

inge

shi

ft

r [cm]

7,50

PNIPAM MicrogelsPNIPAMPNIPAM MicrogelsMicrogels

Crosslinked 10000 rpm

6.3 6.6 6.90

1

2

3

4

Fr

inge

shi

ft

r [cm]

2,37

Not crosslinked60000 rpm

D. Kuckling

0 5 10 15 20 25 30 35 400.0

0.2

0.4

0.6

0.8

1.0

low crosslinking degree high crosslinking degree

G(Q

)Q

Swelling degree distributionSwelling degree distributionSwelling degree distribution

0 200 400 600 800 1000 12000.0

0.2

0.4

0.6

0.8

1.0

Deswollen (40 °C) Swollen (25 °C)

G(s

)

s [Svedberg]

3

swollen

unswollen

ssQ ⎟⎟

⎠

⎞⎜⎜⎝

⎛=

η⋅ρ−ρ

⋅⋅

=18s

dbQ sP2h

In principle also possible with soluble fraction b

D. Kuckling

Solvent density variationSolvent Solvent density variationdensity variationPS123-P4VP145 in toluene resp. d-toluene

•• DensityDensity in good agreement in good agreement withwith valuesvalues fromfrom densitydensity metermeter•• Particle size Particle size in agreementin agreement with results from with results from DLS DLS or viscosity measurementsor viscosity measurements•• Same Same resultresult forfor corecore crosslinked crosslinked micellesmicelles

40 60 80 1000,0

0,2

0,4

0,6

0,8

1,0

dH [nm]In

tegr

aldi

strib

utio

n

0,0

0,5

1,0

1,5

2,0

ρ[g

/cm

³]

0 100 200 300 400 5000.0

0.2

0.4

0.6

0.8

1.0ρTdT for the following data:==============================low density:PS-P4VP in toluenehigh density:PS-P4VP in tol/tol-d8

lower densityhigher density

inte

gral

dist

ribut

ion

sedimentation coefficient [S]

LMP

s18dρ−ρη

=

CombinationCombination of 2 sof 2 s--distributions distributions in 2 in 2 chemically identical chemically identical solvents yields solvents yields particle sizeparticle size and and density distributiondensity distribution

K. Schilling

s22s11

s1s22s2s11ηη

ρηρηρ ss

ssp −

−=

s2s1

s11s22 )(18ρρ

ηη−−

=ss

d

0 50 100 150 200 250 300 350 400 4500,0

0,2

0,4

0,6

0,8

1,0

ρP = 1.054 g/mlnP = 1.6b = 38.5%

ρP = 1.188 g/mlnP= 1.460b = 61.5%

integral psddifferential psd

PS-PMAA Latex mixture 40 : 60PSPS--PMAA Latex PMAA Latex mixture mixture 40 : 6040 : 60

A. Völkel

A: StarA: Star like crystalslike crystals//whiskerwhisker, d = 17 nm, l = 184 nm, d = 17 nm, l = 184 nmB: Transversal growth,B: Transversal growth, destabilizationdestabilization ofof filamentsfilaments,, further further

densificationdensification ofof corecoreC: CompactC: Compact aggregates with periodicityaggregates with periodicity („(„ChrysanthemunChrysanthemun““ structurestructure))

100 nm200 nm

200 nmA B CSynthetic hybrid colloidsSyntheticSynthetic hybridhybrid colloidscolloids Brushite CaHPO4 * 2H2O

TG 18% Mineral

M. Breulmann

0 10 20 30 40 50 60 700

100

200300

400

0.0

0.2

0.4

0.6

0.8

1.0

g(s*

)

time [

h]

s* [S]

Synthetic hybrid colloidsSyntheticSynthetic hybridhybrid colloidscolloidswhiskerwhisker

dense structuredense structure

• Superposition of particle sizeand density distribution

• Densities can exceed 2 g/ml

Synthetic hybrid colloidsSynthetic Synthetic hybrid hybrid colloidscolloids

0 5 10 15 20 25 30 35 400.0

0.2

0.4

0.6

0.8

1.0 PEG-PMAA-C12

PEG-PMAA-C12 + Ca2+

"Chrysanthemum" 1 week

g(s*

)

s* [Svedberg]

density increasedensity increase

polydispersitypolydispersityincreaseincrease

Combination Combination of AUC of AUC with with DLS DLS or better or better FlFl--FFF FFF is highly is highly desirabledesirable

Diameter(DLS) = 150 nmDiameter(DLS) = 150 nm

•• Clear monitoringClear monitoringof of density density increase uponincrease uponCaCa2+2+ complexationcomplexation

•• Global AnalysisGlobal Analysiscould reveal could reveal densitydensity andand molar molar massmass

1 10

0,00

0,01

0,02

0,03

r*d(

r) [a

.u.]

2 r [nm]200 250 300 350 400 450

01234

I [a.

u.]

λAbs [nm]

Particle size and densityParticle size and densityUV : d = 1.65 nmDLS : d = 1.6 nmAUC: „ d = 1.25 nm“ (s = 3.6 S)calculated with ρCdS = 4.83 g/cm3

dtotal = 1.6 nmdcore = 1.1 nmdshell = 0.5 nm(Lit.: dshell = 0.4 nm)

ρρparticleparticle = 3.2 g/cm= 3.2 g/cm33

ddparticleparticle = 1.6 nm= 1.6 nm

UVUV DLSDLS

s2p

p ds18

ρ+η

=ρ Density core andshell are known

WithWith independentindependent size measurementsize measurement,,hybrid hybrid particle is fully characterizedparticle is fully characterized

CdS

Hybrid ColloidsHybrid Hybrid ColloidsColloids

Ferrihydrite Fe2O3

. x H2O

• Iron storage protein Ferritin forms robust hollow sphere from 24 dimeric subunits

• Ferritin oligomerizes• Different amounts of

ferrihydrite inside the core (up to 4500 Fe)

•• Simultaneous particle sizeSimultaneous particle size andanddensity distributiondensity distribution

•• SizeSize andand amountamount ofof oligomers oligomers ??

•• AmountAmount ofof ferrihydrite inside ferrihydrite inside the corethe core for the for the different different oligomersoligomers ??

FerritinFerritinFerritin

0 20 40 60 80 100 120 140 1600,0

0,2

0,4

0,6

0,8

1,0

Diffusion corrected g(s*) Sum of Gauss Fits Individual Gauss Fits

g(s*

)

s* [S]0 2 4 6 8 10 12 14 16 18 20 22

2.29x10-7cm2s-1

2.93x10-7cm2s-1

4.35x10-7cm2s-1

t0 = 0.455minSign

al [a

.u.]

tret

[min]

Fl-FFF AUCMonomer

Dimer

Trimer

FlFl--FFF separates FFF separates only according only according to to particle sizeparticle size, AUC , AUC according according to to particle sizeparticle size andand densitydensity

AUC noAUC no baseline separationbaseline separation ofof oligomersoligomers ((density distributiondensity distribution))

A. Völkel

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

Global Global analysisanalysis

0 20 40 60 80 100 120 140 1600,0

0,2

0,4

0,6

0,8

1,0

Diffusion corrected g(s*) Sum of Gauss Fits Individual Gauss Fits

g(s*

)

s* [S]0 100 200 300 400 500 600 700 800

0.0

0.2

0.4

0.6

0.8

1.0

g (s

)

s (S)

Ferritin low Fe3+ content

Ferritin high Fe3+ content

Ferritin with higher

Ferritin with higher FeFe 3+3+

content

content has different

has different

sedimentation behaviour

sedimentation behaviour

First direct observation of near critical size clusters by AFM

First direct observation of near critical size clusters by AFM

Molecules that are missing in the next frame

Molecules that appeared after captureof the previous frame

S.T. S.T. YauYau, P.G. , P.G. Vekilov Vekilov „Quasi„Quasi--planar nucleus structure planar nucleus structure in in apoferritin crystallizationapoferritin crystallization“, Nature “, Nature 406406, 494 , 494 -- 497; 3 August 2000497; 3 August 2000

CrystallizationCrystallization

DissolutionDissolution

D.W. D.W. OxtobyOxtoby „„CatchingCatching crystalscrystals at at birthbirth“, Nature “, Nature 406406, 464 , 464 -- 465; 3 August 2000:465; 3 August 2000:

„„Although the first small crystallites involved Although the first small crystallites involved in in nucleationnucleation form in form in the bulkthe bulk ofof the the solutionsolution, , YauYau andand Vekilov Vekilov can observe them only once they have can observe them only once they have fallen to fallen to the bottomthe bottomofof the vesselthe vessel andand attached themselves attached themselves to to the surface therethe surface there. . How can the authors be How can the authors be sure that they are observing the critical early stagessure that they are observing the critical early stages ofof crystallization described by crystallization described by nucleation nucleation ?“?“

σ = 1.1

Capillaries

Reservoir

Reactant ( ) containing solution is layered onto thesecond reactant via the capillary ( )

Formation of a sharp reaction boundary

Synthetic boundary cell of the Vinograd TypeSynthetic boundary cellSynthetic boundary cell ofof the Vinogradthe Vinograd TypeType

L. Börger

Particle formation in a synthetic boundary cellParticle formation in a synthetic boundary cell

2 Generation

N-th Generation

1 Generation

Rea

ctio

n zo

ne1) 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

Sedimentation of Sedimentation of particlesparticlesaccordingaccording to to sizesize, Determination , Determination of of particleparticle sizesize distributiondistributionpossiblepossible

Transformation of a Transformation of a timetime distribution intodistribution into a a radialradial distributiondistribution

0.4 0.8 1.2 1.6 2.00.0

0.2

0.4

0.6

0.8

1.0 8 exptl. Scans Sum Gauss Fit Individual Gauss Fits

g(d H

)

dH [nm]

Synthetic boundary crystallization Synthetic boundary crystallization ultracentrifugationultracentrifugation

All All known stable CdSknown stable CdS growthgrowth species simultaneously accessiblespecies simultaneously accessible in in one one experimentexperiment. Even. Even subcritical clusters detectable subcritical clusters detectable in in solutionsolution

[CdSR[CdSR44]]22--

0.3 nm0.3 nm

[Cd[Cd44SRSR1010]]22--

0.5 nm0.5 nm

[Cd[Cd1010SS44SRSR1616]]44--

1.0 nm1.0 nmStructure unknownStructure unknown

literatureliterature 1.3 nm1.3 nmCdCd1717SS44SRSR2626

1.4 nm1.4 nm

CdCd3232SS1414SRSR36361.8 nm1.8 nm

Structure unknownStructure unknownliteratureliterature 1.6 nm1.6 nm

CdSCdS+ + thiothio--glyceringlycerin

• 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

ConclusionConclusionConclusion

BUT: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 PerspectivesFutureFuture PerspectivesPerspectives• Fast speed profiles and detectors to suppress

diffusion broadening • Multi-detection systems (RI, UV-Vis, SLS and others)• Global Analysis (promising with SEDVEL &

SEDEQUIL + DLS & Fl-FFF) to obtain s, M, D & VBAR distributions

• New ultracentrifugation methods could allow to access new quantities 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 growthinvestigations or chemical reactions in the AUC, etc.

Recommended readingRecommended readingRecommended 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 verygood overview about methods & techniques of analytical ultracentrifugation and avaluable source of modern applications.