Folie 1

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Light Scattering what you learned so far
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Static versus Dynamic Light Scattering
from time-independent intraparticle interferences
you determine average scattered intensity gt
particle form factor P(q), radius of gyration Rg,
molar mass M (, A2)
from time-dependent interparticle interferences
you determine time-intensity correlation
function gt hydrodynamic radius RH
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The scattering vector q (in cm-1) , (inverse)
length scale of light scattering
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The famous Zimm-Equation (series expansion of
P(q), valid for 10 nm lt R lt 50 nm
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Averages determined by SLS (Zimm-Plot) from
polydisperse samples
Particle form factor for large (gt 200 nm)
particles, e.g. spheres
first minimum at qR 4.49
Zimm!
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The concept of fractal dimensions analysis of
P(q) for qR gt 1
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Dynamic Light Scattering time-intensity-correla
tion function, Stokes-Einstein-eq. and RH
DLS from polydisperse samples
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Combining static and dynamic light scattering,
the r-ratio
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Selected Examples Dynamic Light Scattering
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Selected Examples Static Light Scattering
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4. Non-Standard Light Scattering Techniques
4.1. Single Angle Scattering Using Goniometer
Setups
components 1. laser light source (coherent,
focussed, monochromatic, polarized) 2.
goniometer with motor, step-wise adjustment of
scattering angle 3. sample bath
(thermostate, index match) and cylindrical sample
cell 4. detector (photomultiplier or
photodiode) 5. computer with
A/D-converter and hardware correlator
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Goniometer setup of the Schmidt group
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Single Angle Scattering advantages and
disadvantages
accurate adjustment of scattering angles /-
correlation time scale 100 ns - lt 10 s -
scattering angle range 30 - 150 - series
of angular-dependent measurements long time -
DLS for low scattering contrast/slow processes
long time - transparent, purified and highly
dilute samples needed - difficulties in
analyzing polydisperse samples
technical solutions time scale
enhancement simultaneous measurement at multiple
q q-scale enhancement optical lenses area
detectors for q lt 1 ! turbid samples cross
correlation or backscattering polydisperse
samples combine fractionation and SLS
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4.2. Simultaneous Multiangle Scattering (MALS)
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MALS - setup of the Schmidt group
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Simultaneous Multiangle Scattering combined with
GPC or FFF
Laser
GPC
Interface
flow cell
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GPC MALS - setup of the Schmidt group
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Wintermantel, M.Gerle, M.Fischer, K.Schmidt,
M.Wataoka, I.Urakawa, H. Kajiwara,
K.Tsukahara, Y. Macromolecules 1996, 29, 978-983
samples polystyrene polymacromonomers,
synthesized by radical polymerization of
anionic MMA end-functionalized polystyrene
macromonomers (bottle-brushes), MW/MN gt 2 !
GPC-MALS - GPC connected to an on-line Knauer
combined viscometer/RI-detector and an ALV1800
MALS (19 angles plus one monitor channel) -
home-made cylindrical flow cell with 38 µL total
volume - scattering intensity detected at 19
scattering angles over 2 s at DT 4 s during
elution
wormlike chain model
contour length L, Kuhn length Lk
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reduced scattered intensity plotted versus q2 for
three sample fractions
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Rg vs. MW for a homologous series of
bottlebrushes, wormlike chain model
results M(side chains) 2900 g/mol Lk 89
nm M(side chains) 5000 g/mol Lk 208 nm
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4.3. Turbid Samples (A) Fiber-Optic
Quasielastic Light Scattering (FOQELS)
Wiese, H.Horn, D. Journal of Chemical Physics
1991, 94, 6429-6443 (BASF !)
suppresses multiple scattering, defines the
scattering angle as 180
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samples aqueous polymer latex dispersions
(particle size from 41 nm to 326 nm), as
prepared without further purification, particle
concentrations above 1 wt !
data analysis
concentrated dispersions amplitude
autocorrelation function includes contributions
of the static structure factor (interparticle
interferences!)
collective diffusion coefficient
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Dc vs. concentration, different particle sizes
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position of the maximum of the structure factor
compared to q of FOQELS
q lt qm length scale gt particle
dist., interparticle interactions gt collective
diffusion Dc(c) ?
q
q gt qm length scale lt particle dist. gt
selfdiffusion Ds(c) ?
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4.4. Turbid Samples - (B) Crosscorrelation
Techniques - Dual Color and 3d Dynamic Light
Scattering (identical q and scattering volume,
different set of interferences gt no multiple
scattering)
I. 3d DLS (Prof. Schurtenberger, Univ.Fribourg,
CH)
www.lsinstruments.ch/3DDLS.htm
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II. Dual Color Dynamic Light Scattering
Stieber, F.Richtering, W. Langmuir 1995, 11,
4724-4727
sample polystyrene latex spheres 2R 82 nm (q lt
qm)
light scattering setup dual color or two color
crosscorrelation (TCC) setup - 2 light sources
with different wavelengths from 1 argon ion laser
in multiline mode (488 nm and 514.5 nm) -
single-mode optical fibers for the optical
alignment - scattering angles from 15 to 140
(FOQELS 180 only !)
data analysis CONTIN (constrained inverse
Laplace transformation) note q lt qm gt at
higher particle conc. only Dc
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comparison of auto- and crosscorrelation
filled symbols autocorrelation, artefacts and
bad resolution (multiple scattering) open
symbols crosscorrelation, 2 defined relaxation
processes multiple scattering increases with
decreasing q (increasing length scale)
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the origin of Dslow ?
gt slow process Dslow is selfdiffusion (strong
slowing-down with increasing conc.)
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4.5. Dynamic Light Scattering using CCD area
detectors

• concave lens CCD area detector (multiple q at
  once),
• simultaneous light scattering at very small
  scattering angles
• improves measurement time, small-q-scale

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II. CCD area detector at one defined q Dq DLS
replace time averaging by ensemble averaging
improves measurement time, long-t-scale
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Wong, A. P. Y.Wiltzius, P. Rev.Sci.Instrum.
1993, 64, 2547-2549
sample commercial latex particles (diameter 215
nm) in glycerol at T 51C, rectangular cuvette
of thickness 1 mm
setup
detection scheme
digitized image, 500 x 450 pixel, 10 concentric
rings radius 20, 40, ...., 200 pixel no. of
pixels 80, 160, .... , 800 q-range 10 - 60,
simultaneous
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calculation of the intensity correlation function
average speckle intensity of each ring
deviation from the average intensity for each
pixel
from two pictures taken at t 0 and t t (tmin
100 ms)
Note ltgt ensemble-average!
conventional single-angle light scattering ltgt
time-average!
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results
q 29748 cm-1, 20834 cm-1 and 14832 cm-1
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goniometer setup
relaxation time G-1 gt 20 s !
Ds 1.67e-10 cm2s-1 1 e-14 m2s-1
Stokes-Einstein-equation, viscosity of 0.137 Pa
s gt R 107.5 nm
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Kirsch, S.Frenz, V.Schartl, W.Bartsch,
E.Sillescu, H. Journal of Chemical Physics
1996, 104, 1758-1761
multi speckle correlation spectroscopy (MSCS)
sample spherical latex particles (R 350) nm in
glycerol at T 10C !
setup
data acquisition
images of 512x256 pixels digitized, scattered
intensity for 50 random speckles ( 2x2 pixel)
stored at frame rate 0.33 s
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calculation of the intensity correlation function
data represented 50 individual traces of I(q,t)
at (nearly) identical q
1. normalized intensity correlation function for
each speckle calculated by time-averaging
total number of pictures Npic 50.000 - 150.000,
n 0, 1, 2, .., k 0, 1, 2, ..
2. time-averaged correlation functions are
ensemble averaged over all speckles
total number of speckles Nsp 20 - 50
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comparison MSCS conventional DLS (PCS)
MSCS results (symbols) for 20 speckles, 150.000
pictures (texpt 50.000 s) PCS results (lines)
texpt 70.000 s inset, symbols filled 1
speckle correlation, open 20 speckle ensemble
average
improved statistics by combined
time-ensemble-averaging !