“Light Scattering from Polymer Solutions and Nanoparticle Dispersions”

By: PD Dr. Wolfgang SchaertlInstitut für Physikalische Chemie, Universität Mainz, Welderweg 11, 55099 Mainz, Germanyschaertl@uni-mainz.de

Parts from the new book of the same title, published by Springer in July 2007

Slides are found at: http://www.uni-mainz.de/FB/Chemie/wschaertl/105.php

02 2, cos x tE x t E

c

1. Light Scattering – Theoretical Background

1.1. Introduction

Light-wave interacts with the charges constituting a given molecule in remodelling the spatial charge distribution:

Molecule constitutes the emitter of an electromagnetic wave of the same wavelength as the incident one (“elastic scattering”)

E

m

sE

Note: usually vertical polarization of both incident and scattered light (vv-geometry)

Particles larger than 20 nm: - several oscillating dipoles created simultaneously within one given particle- interference leads to a non-isotropic angular dependence of the scattered light intensity - particle form factor, characteristic for size and shape of the scattering particle- scattered intensity I ~ NiMi

2Pi(q) (scattering vector q, see below!)

Particles smaller than /20: - scattered intensity independent of scattering angle, I ~ NiMi

2

Particles in solution show Brownian motion (D = kT/(6hR), and <Dr(t)2>=6Dt)=> Interference pattern and resulting scattered intensity fluctuate with time

2 22

02 2 2

41 exp 2 DsD D

EmE i t krt r c r c

1.2. Static Light Scattering

Detector (photomultiplier, photodiode): scattered intensity only! 2

s s s sI E E E

detector

rDI

sampleI0

Scattered light wave emitted by one oscillating dipole

Light source I0 = laser: focussed, monochromatic, coherent

Sample cell: cylindrical quartz cuvette, embedded in toluene bath (T, nD)

Standard Light Scattering Setup of the Schmidt Group, Phys.Chem., Mainz:

lasersample,bath

detector ongoniometer arm

Standard Light Scattering Setup of the Schmidt Group, Phys.Chem., Mainz:

Standard Light Scattering Setup of the Schmidt Group, Phys.Chem., Mainz:

Scattering volume: defined by intersection of incident beam and optical aperture of the detection optics

Important: scattered intensity has to be normalized

.

Scattering from dilute solutions of very small particles (“point scatterers”)(e.g. nanoparticles or polymer chains smaller than /20)

2

,( )T N

cI b kT

c

:

kTc M

21 2 ...( )kT A c

c M

222 2

,040

4 ( )DDL

nb n KcN

in cm2g-2Mol

40I

2222 2

,040

4 ( )( )D DD solution solvent

L

n rR b c M n c M I Ic VN

,std abs

solution solventstd

IR I I

I

Fluctuation theory:

contrast factor

Ideal solutions, van’t Hoff:

Real solutions, enthalpic interactions solvent-solute:

Absolute scattered intensity of ideal solutions, Rayleigh ratio ([cm-1]):

and

Scattering standard Istd: Toluene( Iabs = 1.4 e-5 cm-1 )

Reason of “Sky Blue”! (scattering from gas molecules of atmosphere)

1KcR M

21 2 ...Kc A c

R M

Scattering from dilute solutions of larger particles

- scattered intensity dependent on scattering angle (interference)

The scattering vector q (in [cm-1]) , length scale of the light scattering experiment:

q

0k

k

4 sin( )2Dnq

Real solutions, enthalpic interactions solvent-solute expressed by 2nd Virial coeff.:

q

q = inverse observational length scale of the light scattering experiment:

q-scale resolution information comment

qR << 1 whole coil mass, radius of gyration e.g. Zimm plot

qR < 1 topology cylinder, sphere, …

qR ≈ 1 topology quantitative size of cylinder, ...

qR > 1 chain conformation helical, stretched, ...

qR >> 1 chain segments chain segment density

Scattering from 2 scattering centers – interference of scattered waves

2 2

1 1

1 exp 1 exp exp ijs sI i i I iqr D D

0k

k

0k

k

ijr

A B

C

???AB BC

cosijAB r 02 cosij ijr k r

0 2ijAB r k

cosijBC r 2 cos 180ij ijr k r

2ijBC r k

0 2 2ij ijAB BC r k k r q

leads to phase difference: ijr qD

2 interfering waves with phase difference D:

2 2

( ) exp( ) exp exp( ) 1 exps s sI q E ikr E i kr E ikr i D D

orientational average and normalization lead to:

22 21 1

222 2

1 1 1 1

1 1( ) exp

sin1 1 11 ...6

Z Z

iji j

Z Z Z Zij

iji j i jij

P q I q iqrZNZ b

qrq rZ Zqr

.

22 2

1 1 1 1

2Z Z Z Z

j i i jij ji j i j

r s s s s s

2 2 2

1 1

2Z Z

ii j

s Z s

2 21( ) 1 ...3P q s q

21 2 ...( )

Kc A cR MP q

Zimm equation:

2 22

1 11 23( )Kc s q A cR M

2 2

1 1 1 1

( ) exp expZ Z Z Z

i j iji j i j

I q Nb iq r r Nb iqr

Scattered intensity due to Z pair-wise intraparticular interferences, N particles:

replacing Cartesian coordinates ri by center-of-mass coordinates si we get:

regarding the reciprocal scattered intensity, and including solute-solvent interactions finally yields the well-known Zimm-Equation (series expansion of P(q), valid for small R):

s2, Rg2 = squared radius of gyration

The Zimm-Plot, leading to M, s (= Rg) and A2:

0,0 5,0 10,0 15,0 20,01,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

6,0

Kc/R

/ 10

-7m

ol/g

(q2+kc) / 1010cm-2

2 22

1 11 23( )Kc s q A cR M

q = 0

c = 0example: 5 c, 25 q

Zimm analysis of polydisperse samples yields the following averages:

1

1

K

k k kk

w K

k kk

N M MM

N M

The z-average squared radius of gyration:

2 2

22 1

2

1

K

k k kk

z g Kz

k kk

N M ss R

N M

The weight average molar mass

Reason: for given species k, Ik ~ NkMk2

Fractal Dimensions

( ) fdM R R: 1gq R

:

( ) 22 fdI q M q-: :

log 2 logfI q d q

topology df

cylinder, rod 1thin disk 2

homogeneous sphere 3

ideal Gaussian coil 2Gaussian coil with excluded volume 5/3

branched Gaussian chain 16/7

if

log log logfP q I q cM d q

0 2 4 6 8 10 1210-5

10-4

10-3

10-2

10-1

100

P(q

)

qR

Particle form factor for “large” particles

for homogeneous spherical particles of radius R:

26

9( ) sin cosP q qR qR qRqR

first minimum at qR = 4.49

2 22 2

1 1 1 1

sin1 1 1( ) expZ Z Z Z

ijij

i j i j ij

qrP q I q iqr

Z ZNZ b qr

Zimm!

1.3. Dynamic Light ScatteringBrownian motion of the solute particles leads to fluctuations of the scattered intensity

,( , ) (0, ) ( , ) ( , ) ( , ) exp( )s V T s sG r n t n r t F q G r iqr dr

isotropic diffusive particle motion232 2

2

3 ( )2( , ) ( ) exp3 2 ( )[ ] ( )s

rG r RR

D D

mean-squared displacement of the scattering particle:

2 6 sR D D 6s

H

kT kTDf Rh

change of particle position with time is expressed by van Hove selfcorrelation function,DLS-signal is the corresponding Fourier transform (dynamic structure factor)

Stokes-Einstein, Fluctuation - Dissipation

2

2

( , ) ( , )( , ) exp( ) ( , ) *( , ) 1,

s s s sI q t I q tF q D q E q t E q t

I q t

<I(t)

I(t+

)>T

I(t

)

t

1

2

The Dynamic Light Scattering Experiment - photon correlation spectroscopy

Siegert relation:

2

exp 2 ,

s

I t I t

D q

note: usually the “coherence factor” fc is smaller than 1, i.e.:

2

2

( , ) ( , ) 1 ( , ),

c sI q t I q t f F q

I q t

fc increases with decreasing pinhole diameter, but photon count rate decreases!

log

F s(q,)

F s(q,)

log

DLS from polydisperse (bimodal) samples

2

0

, exps s s sF q P D q D dD

2 21 1 2 2, exp exps s sF q A q D A q D

”Cumulant method“, series expansion, only valid for small size polydispersities < 50 %

2 31 2 3

1 1ln , ...2! 3!sF q

first Cumulant 1 ²sD q yields inverse average hydrodynamic radius 1HR

second Cumulant 22 42 s sD D q yields polydispersity

22

221

s s

Ds

D D

D

for samples with average particle size larger than 10 nm:

2

2i i i i

appi i i

n M P q DD q

n M P q

2 21app s gz zD q D K R q

Data analysis for polydisperse (monomodal) samples

note: 2i i i iI q n M P q

Cumulant analysis – graphic explanation:monodisperse sample polydisperse sample

linear slope yields diffusion coefficient slope at =0 yields apparent diffusioncoefficient, which is an average weightedwith niMi

2Pi(q)

log(

F s(q,)

Dy/Dx=-Dsq2

log(

F s(q,)

Dy/Dx=-Dsq2

large, slowparticles

small, fastparticles

Dapp vs. q2:

0 1x1010 2x1010 3x1010 4x1010

0,0

5,0x10-15

1,0x10-14

1,5x10-14

2,0x10-14

D/m

2 s-1

q2/cm-2

s zD

0,00 0,01 0,02 0,03 0,0410-5

10-4

10-3

10-2

10-1

100

R = 60 nm R = 80 nm R = 100 nm

P(q

)

q [nm-1]

1q 2q

Explanation for Dapp(q):

2

2i i i i

appi i i

n M P q DD q

n M P q

for larger particle fraction i, P(q) drops first,leading to an increase of the average Dapp(q)

27

0 5 10 15 200

10

20

30

40

50

Ni

P(R

i)

Ri/nm0 5 10 15 20

0

5

10

15

20

Ni

P(R

i)

Ri/nm

0,00000 0,00002-0,2

0,0

Data: Data2_lng1Model: cumulantChi^2 = 3.7224E-8P1 0.00882 ±0.00003P2 -10790.57918 ±0.23957P3 896471.16145 ±926.09523

Dapp(90°)=2.04e-11 m2/s, entspr. R = 10.5 nmPI = 0.09, DR/R=10% (Normalvert.)

lng1

ln g

1(90

°,)

/s

0,000000 0,000004 0,000008 0,000012 0,000016 0,000020-0,20

-0,18

-0,16

-0,14

-0,12

-0,10

-0,08

-0,06

-0,04

-0,02

0,00Data: Data2_lng1Model: cumulantChi^2 = 3.3258E-10P1 0.0079 ±5.5823E-6P2 -8423.55623 ±0.25513P3 2723184.05649±4894.69843

Dapp(90°)=1.59e-11 m2/s, entspr. R = 13.5 nmPI = 0.20, DR/R=30% (Normalvert.)

lng1

ln g

1(90

°,)

/s

ln(g1())=P1+P2*+P3/2 *^2PI = SQRT(P3/P2^2)

28

0 5 10 15 20 25 30 35 400

20

40

60

80

100

Ni

P(R

i)

Ri/nm

0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,00084,00E-012

6,00E-012

8,00E-012

1,00E-011

1,20E-011

Dap

p/m2 s-1

q2/nm-2 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,00082,60E-008

2,62E-008

2,64E-008

2,66E-008

2,68E-008

2,70E-008

2,72E-008

2,74E-008

2,76E-008

2,78E-008

2,80E-008

q2/nm-2

RH/m

29

0 50 100 150 200 250 3000

20

40

60

80

100

Ni

P(R

i)

Ri/nm

0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,00085,00E-013

1,00E-012

1,50E-012

2,00E-012

Dap

p/m2 s-1

q2/nm-2 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,00081,00E-007

1,20E-007

1,40E-007

1,60E-007

1,80E-007

2,00E-007

q2/nm-2

RH/m

30

0 200 400 600 800 10000

5

10

15

20

NiP

(Ri)

Ri/nm

0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,0008

3,60E-013

3,80E-013

4,00E-013

4,20E-013

4,40E-013

Dap

p/m2 s-1

q2/nm-2 0,0001 0,0002 0,0003 0,0004 0,0005 0,0006 0,0007 0,00085,20E-007

5,25E-007

5,30E-007

5,35E-007

5,40E-007

5,45E-007

5,50E-007

5,55E-007

5,60E-007

5,65E-007

5,70E-007

q2/nm-2

RH/m

1 ln 0.53

lD

topology r-ratiohomogeneous sphere 0.775

hollow sphere 1ellipsoid 0.775 - 4

random polymer coil 1.505cylinder of length l,

diameter D

Combining static and dynamic light scattering, the r-ratio:

g

H

RR

r

for polydisperse samples: 2 1g HZ ZR Rr

Sample topology (sphere, coil, etc…) is known

yes no

Dynamic light scatteringsufficient (“particle sizing“)

Static light scattering necessary

Time intensity correlation function decays single-exponentially

yes no

Only one scattering angle needed, determine particle size (RH) from Stokes-Einstein-Eq.(in case there are no particle interactions (polyelectrolytes!)

Sample is polydisperse or shows non-diffusive relaxation processes!- to determine “true” average particle size, extrapolation q -> 0- to analyze polydispersity, various methods

Strategy for particle characterization by light scattering - A

Applicability of commercial particle sizers!

wM

Sample topology is unknown,static light scattering necessary

yes no

Particle radius larger than 50 nm and/or very polydisperse sample:use more sophisticated methods to evaluate particle form factor

Plot of vs. is linearKcR

2q

Dynamic light scattering to determine 11

H H zR R

Estimate (!) particle topology from g

H

RR

r

Strategy for particle characterization by light scattering - B

Particle radius between 10 and 50 nm:analyze data following Zimm-eq. to get:

g zR 2AWM

1. Galinsky, G.;Burchard, W. Macromolecules 1997, 30, 4445-4453

Samples:Several starch fractions prepared by controlled acid degradation of potatoe starch,dissolved in 0.5M NaOH

Sample characteristics obtained for very dilute solutions by Zimm analysis:

sample 10-6 Mw

(g/mol)Rg

(nm)104 A2

[(mol cm3)/g2]

LD11 0.92 36 1.00LD16 1.87 48 0.60LD12 5.20 70 0.28

LD19 14.5 113 0.13LD18 43 180 0.082LD17 64 190 0.060LD13 97 233 0.025

2. Static Light Scattering – Selected Examples

Normalized particle form factorsuniversal up to values of qRg = 2

Details at higher q (smaller length scales) – Kratky Plot:

C

form factor fits:

2

22

1 311 6

g

g

C qRP q

C qR

C related to branching probability, increases with molar mass

Are the starch samples, although not self-similar, fractal objects?

log logfdfP q q P q d q

- minimum slope reached at qRg ≈ 10 (maximum q-range covered by SLS experiment !) - at higher q values (simulations or X-ray scattering) slope approaches -2.0 - characteristic for a linear polymer chain (C = 1). - at very small length scale only linear chain sections visible (non-branched outer chains)

2. Pencer, J.;Hallett, F. R. Langmuir 2003, 19, 7488-7497

Samples:uni-lamellar vesicles of lipid molecules 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine (SOPC) by extrusion

monodisperse vesicles 2 23 31 1

3 3

3 o io i

o io i

j qR j qRP q R R

qR qRR R

2oR R t

2iR R t 1 2

sin cosx xj xx x

Data Analysis:

thin-shell approximation 2sin qR

P qqR

small values of qR, Guinier approximation 22exp 3gP q q R

52 2

3

135 1

i og o

i o

R RR R

R R

typical q-range of light scattering experiments: 0.002 nm-1 to 0.03 nm-1

vesicles prepared by extrusion: radii 20 to 100 nm => first minimum of the particle form factor not visible in static light scattering

particle form factor of thin shell ellipsoidal vesicles, two symmetry axes (a,b,b)

21

0

sin, ,

quP q a b dx

qu

2 2 2 21u a x b x

cosx

0k k

prolate vesicles, surface area 4 (60 nm)2 oblate vesicles, surface area 4 (60 nm)2

anisotropy vs. polydispersity:

static light scattering from monodisperse ellipsoidal vesicles can formally be expressed in terms of scattering from polydisperse spherical vesicles !

=> impossible to de-convolute contributions from vesicle shape and size polydispersity using SLS data alone !

2sin

, ,b

a

qRP q a b G R dR

qR

2 2 2 2

1 RG Ra b R b

monodisperse ellipsoidal vesicles

2

0

2

0

,R

R

M P q R G R dRP q

M G R dR

2

sin,

qRP q R

qR

polydisperse spherical vesicles

combination of SLS and DLS:DLS: intensity-weighted size distribution => number-weighted size distribution (fit a,b) => SLS: particle form factor

input for a,b – fits to SLS data

,

result:polydisperse (DR = 10%) oblate vesicles,a : b < 1 : 2.5

3. Fuetterer, T.;Nordskog, A.;Hellweg, T.;Findenegg, G. H.;Foerster, S.; Dewhurst, C. D. Physical Review E 2004, 70, 1-11

Samples:worm-like micelles in aqueous solution, by association of the amphiphilic diblock copolymer poly-butadiene(125)-b-poly(ethylenoxide)(155)

monodisperse stiff rods 2

0

sin sin 22 4qL ql qL

P q dqlqL ql qL

asymmetric Schulz-Zimm distribution

11 exp 1

1

k kw wk L L k L L

p Lk

1 1w nk M M

polydisperse stiff rods

0

0

L p L P q dLP q

L p L dL

Koyama, flexible wormlike chains

22

0

sin '1 1exp '3 '

Kl

KK

q xg xP q l x q xf x dx

q xg xl

Analysis of SLS-results:

Holtzer-plot of SLS-data :

plateau value = mass per length of a rod-like scattering particle

.Rq q I q vs qKc

389 , 1.2w w nL nm M M

380 , 2.0, 410w w n KL nm M M l nm

fit results:(i) polydisperse stiff rods:

(ii) polydisperse wormlike chains:

Analysis of DLS-results:

3

21

0

, 2 , exp 2 2 1n T Rn

g q S n qL D q n n D

2

9ln ,3

TT R

kT L DD DL d Lh

amplitudes depend on the length scale of the DLS experiment:

- long diffusion distances (qL < 4): only pure translational diffusion S0

- intermediate length scales (4 < qL < 15): all modes (n = 0, 1, 2) present

according to Kirkwood and Riseman:

polydispersity leads to an average amplitude correlation function!

DLS relaxation rates :

linear fit over the whole q-range: significant deviation from zero intercept, additional relaxation processes or “higher modes” at higher q

2 2 14.0 0.4 10z

D nm s 60 6HR nm 2g HR R results:

Rg from Zimm-analysis and calculations!

4. Wang, X. H.;Wu, C. Macromolecules 1999, 32, 4299-4301

samples:high molar mass PNIPAM chains in (deuterated) water

reversibility of the coil-globule transition:

molten globule ? surface of the sphere has a lower density than its center

Selected Examples – Static Light Scattering:sample problem solution

branched polymeric nanoparticles

self-similarity (fractals) ?; details at qR > 2 by Kratky plot (P(q) q2 vs. q), fitting parameters for branched polymers, simulation of P(q) at qR > 10 (SLS: qR < 10) => not fractal !

vesicles (nanocapsules)

distinguish size polydispersity and shape anisotropy in P(q) ?

combine DLS (only size polydispersity !) and SLS to simulate expt. P(q)

worm-like micelles characterization: length, Rg/RH (RH: no rotation-translation-coupling if qL < 4)

details at higher q by Holtzer plot (I(q) q vs. q), fit P(q), Rg from Zimm-analysis at small q values

PNIPAM chains in water at different T

coil – globule - transition Rg from Zimm-analysis, RH by DLS, decrease in R and Rg / RH

3. Dynamic Light Scattering – Selected Examples

1. Vanhoudt, J.;Clauwaert, J. Langmuir 1999, 15, 44-57

sample: spherical latex particles in dilute dispersions

sample s2 s3 s4 s5 s6 s7nominal diameter/nm 19 54 91 19, 91 19, 54 54, 91

diameter ratio - - - 4.8 2.8 1.7

Data analysis of polydisperse samples:

1. Cumulant method (CUM), polynomial series expansion:

2

0.5 0.5 21ln ln

2f g f 2

0appB d D q

22

0

B d

polydispersity index 2

2PI

particle diameter is a so-called harmonic z-average:

6

5

i ii

i ii

n dd

n d

(only for homogeneous spheres) 2 6i iM d

2. non-negatively least squares method (NNLS):

2

21

1 1

expN M

j i i jj i

g b

M exponentials considered for the exponential series, yielding a set of coefficients bi defining the particle size distribution for decay rates equally distributed on a log scale.

3. Exponential sampling (ES):

1 1max

expnn

See 2., decay rates chosen according to:

4. Provencher’s CONTIN algorithm:

22

22 1

1i

i i

Bg e d LB

Numerical procedure to calculate a continuous decay rate distribution B(), also calledInverse Laplace Transformation, enclosed in most commercial DLS setups.

5. double-exponential method (DE):

1 21 1 2g b e b e

Results:

sample s2 s3 s4 s5 s6 s7

nominal diameter 19 ± 1.5 54 ± 2.7 91 ± 3 19, 91 19, 54 54, 91diameter ratio - - - 4.8 2.8 1.7

<d> - CUM (1.) 20.3 55.0 87.0 36.9 29.5 69.0

PI – CUM (1.) 0.029 0.009 0.008 0.248 0.191 0.069d1,d2 – NNLS (2.) - - - 18, 81 16, 50 -

d1,d2 – ES (3.) - - - - 19, 54 -d1,d2 – DE (5.) - - - - 18, 54 -

Bimodal samples s5, s6, s7: I1(q=0) = I2(q=0)

Note: bimodal samples with d2/d1 < 2 (s7) beyond resolution of DLS !

2. van der Zande, B. M. I.;Dhont, J. K. G.;Bohmer, M. R.;Philipse, A. P. Langmuir 2000, 16, 459-464

sample (TEM-results): colloidal gold nanoparticles stabilized with poly(vinylpyrrolidone) (M = 40000 g/Mol)

system length L[nm]

DL[nm]

diameter d[nm]

Dd[nm]

aspect ratio L/d

Sphere18 18 5 - - -

Sphere15 15 3 - - -

Rod2.6a 47 17 18 3 2.6

Rod2.6b 39 10 15 3 2.6

Rod8.9 146 37 17 3 8.9

Rod12.6 189 24 15 3 12.6

Rod14 283 22 20 3 14.0

Rod17.2 259 60 15 3 17.2

Rod17.4 279 68 16 3 17.4

Rod39 660 20 17 3 39.0

Rod49 729 - 15 3 49.0

DLS setup and data analysis:

Kr ion laser (647.1 nm far from the absorption peak of the gold particles (500 nm))

Measurements in vv-mode and vh-mode (depolarized dynamic light scattering DDLS)(v = vertical, h = horizontal polarization)

intensity autocorrelation functions were fitted to single exponential decays, including a second Cumulant to account for particle size polydispersity

22 , expg q y b q c q

vv-mode (only translation is detected):

depolarized dynamic light scattering (vh-mode) (translation and rotation are detected, no coupling in case qL < 5)

22 Tb q D q

22 12T Rb q D q D

translational diffusion coefficient DT determined from the slope, rotational diffusion coefficient DR from the intercept of the data measured in vh –geometry.

Results:

q2 / 1014 m-2

q2 / 1014 m-2

qmaxL > 5 (≈ 9) !

qL < 5

diffusion coefficients according to Tirado and de la Torre,using as input parameters length and diameter from TEM

2

2

3

ln 0.312 0.565 0.1003

3 ln 0.662 0.917 0.050

T

R

kT L d dDL d L L

kT L d dDL d L L

h

h

system 10-12 DT, exp[m2s-1]

10-12 DT, calc[m2s-1]

DR, exp[s-1]

DR, calc[s-1]

Rod8.9 6.0 8.4 306 2238Rod12.6 4.9 7.4 281 1258Rod14 2.9 5.2 66 396

Rod17.2 4.0 6.0 177 563Rod17.4 3.5 5.6 175 452Rod39 1.2 2.9 14 46Rod49 0.7 2.8 30

values determined by DDLS systematically too small, because PVP-layer (thickness 10 – 15 nm) not visible in TEM !

Selected Examples – Dynamic Light Scattering:

sample problem solution

bimodal spheres size resolution - double exponential fits- size distribution fits- CONTIN ; only if R1/R2 > 2

stiff gold nanorods length and diameter in solution =?;deviation TEM – DLS ?

depolarized DLS (vh) => Drot standard DLS (vv) => Dtrans;deviation TEM-DLS due to PVP stabilization layer