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2. Static Light Scattering Selected Examples
1. Wu, C.Woo, K. F.Luo, X.Ma, D.-Z.
Macromolecules 1994, 27, 6055-6060
samples segmented copolymer poly(ethyleneterephta
late-co-caprolactone) (PET-PCL) (polydispersity
of chain length and composition !)
Bushuk and Benoit at least three independent SLS
experiments in different solvents necessary to
determine both molar mass distribution and
composition profile of a polydisperse
heterogeneous copolymer sample consisting of
monomer species A, B
Zimm-approach
apparent weight distribution
2
weight fractions for the whole copolymer sample
known from synthesis
refractive index increments for pure
homopolymers of type A , B
homogeneous copolymer composition and therefore
refractive index increment independent of molar
mass
Apparent molar mass from Zimm analysis for a
given solvent-copolymer-pair
Equation with 3 unknowns
3
Experimental quantities from 1 SLS and
refractometry
To solve the mathematical problem, 3 equations
( 3 SLS experiments in different solvents)
needed !
3 solvents must satisfy the following conditions
- average refractive index increments of
corresponding copolymer-solvent pairs different -
copolymer has to be soluble - copolymer
solutions should be transparent - feasible to
purify all copolymer solutions from dust
new procedure by Wu et al. replace the 3 SLS
experiments by a combination of SLS and DLS
affording only 2 different solvents, based on
4
DLS from polydisperse samples the dynamic Zimm
equation
molar mass dependence of M expressed by a scaling
law
For a given set of scaling parameters, the
diffusion coefficient distribution can be
converted into the apparent molar mass
distribution. DLS experiments in 2 different
solvents lead to
From these DLS-results in combination with
refractometry, wA(M) is calculated !
, leading to
5
Experimental results
SLS measurements for copolymer samples dissolved
in chloroform Zimm plot
6
Apparent sample characteristics (of two copolymer
fractions) from SLS and DLS
Refractive index increments (all in mL/g)
7
diffusion coefficient distribution, obtained by
Laplace inversion of the DLS results
low-M and high-M copolymer in THF
8
scaling parameters
low-M and high-M copolymer in THF
9
high-M
low-M
Heterogeneous copolymer !
10
2. 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
11
Normalized particle form factors universal up to
values of qRg 2
12
Details at higher q (smaller length scales)
Kratky Plot

form factor fits
C related to branching probability, increases
with molar mass
13
Are the starch samples, although not
self-similar, fractal objects?

• - 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)

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Application of the Zimm approach to the
semi-dilute concentration regime
correlation length
dilute regime
Zimm equation !
semi-dilute regime
c overlap concentration, Rg,app mesh
size scaling laws analogous to linear chains (m
-0.75), here m -1
15

• at c gt c ( 2.8 g/l) universal scaling Rg,app
  c-1
• - at higher c cluster formation (particle
  aggregation)

16
The dimensionless apparent particle form factor
all data superimpose, yielding particle form
factor measured in dilute solutions !
17
Concluding remarks - shape of branched starch
macromolecules not changed by particle
interactions ! I.) if the two limiting
scattering curves at c 0 and q 0 are
determined, the whole data set of scattered
intensities detected for finite sample
concentrations and finite scattering vectors
can be reconstructed from the parameters Rg,
M, A2, c, m. II.) intercept and initial slope
for SLS data set obtained at any concentration,
yielding Rg,app and S(q0), allow to
construct particle form factor!
18
3. 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-phosphocholi
ne (SOPC) by extrusion
Data Analysis
19
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 gt first minimum
of the particle form factor not visible in static
light scattering
20
effect of vesicle polydispersity on measured
particle form factors
Gamma function for the size distribution
size polydispersity
monodisp.!
21
polydispersity and angular dependence of RH,app
(DLS)
22
particle form factor of thin shell ellipsoidal
vesicles, two symmetry axes (a,b,b)
oblate vesicles, surface area 4 p (60 nm)2
prolate vesicles, surface area 4 p (60 nm)2
23
anisotropy vs. polydispersity
static light scattering from monodisperse
ellipsoidal vesicles can formally be expressed
in terms of scattering from polydisperse
spherical vesicles ! gt impossible to
de-convolute contributions from vesicle shape and
size polydispersity using SLS data alone !
combination of SLS and DLS DLS
intensity-weighted size distribution gt
number-weighted size distribution (fit a,b) gt
SLS particle form factor
24
input for a,b fits to SLS data
,
result polydisperse (DR 10) oblate
vesicles, a b lt 1 2.5
25
4. 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)
Analysis of SLS-results
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Analysis of DLS-results
amplitudes depend on the length scale of the DLS
experiment - long diffusion distances (qL lt 4)
only pure translational diffusion S0 -
intermediate length scales (4 lt qL lt 15) all
modes (n 0, 1, 2) present
according to Kirkwood and Riseman
polydispersity leads to a weight average
amplitude correlation function
27
Holtzer-plot of SLS-data
plateau value mass per length of a rod-like
scattering particle
28
DLS relaxation rates
linear fit over the whole q-range significant
deviation from zero intercept, additional
relaxation processes or higher modes at higher
q
Rg from Zimm-analysis and calculations!
29
5. Wang, X. H.Wu, C. Macromolecules 1999, 32,
4299-4301
samples high molar mass PNIPAM chains in
(deuterated) water
30
reversibility of the coil-globule transition
molten globule ? surface of the sphere has a
lower density than its center