Light Scattering Part 1 Aggregate Structure amp Internal Dynamics 786 Understanding SLS static data I q control parameter q units 1Length Large q probes small length scales ID: 558477
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Slide1
Static Light Scattering Part 1: Aggregate Structure & Internal Dynamics
786Slide2
Understanding SLS ‘static’ dataI
(
q
): control parameter q [units 1/Length] Large q probes small length scales Small q probes large length scales Shape of I vs q reveals particle structureSlide3
What can light scattering measure?
Molar mass,
M
Size, rg
Second
virial
coefficient, A2 Translational diffusion coefficient, DT - Can be used to calculate rh
For a solute
in solution
, light scattering can determine:Slide4
Understanding SLS ‘static’ dataVery
small particles scatter
isotropically
I(q) ~ constantLarger aggregates can be assessed for their fractal dimension Df, in region where I ~ q-
Df
rusnauka.comSlide5
Dimensionality
From linear dimension to areal dimension, non-fractal linear objects are squared to give area
From linear dimension to volume dimension, non-fractal linear objects are cubed to give volume
Fractal objects: can’t obtain area simply by squaring linear portion, nor volume simply by cubing linear segmentSlide6
Fractal Dimensions1 dimensional object
2 dimensional object
3 dimensional object
D
f
> 1 Df approaching 2 Df > 1 Df approaching 2Slide7
Example: CNT dispersionsCNT dispersions reveal fractal aggregates
Fractal region may not extend over entire q range
Remember:
Large
q
probes small length
scales; Small q probes large length scales Slide8
Example: Fullerene NP aggregationAggregate growth extends range of q in the power law regionSlide9
Df ~ 1? …
C
orrection to Stokes for
RodsDLS measures Diffusion constant D
Spheres:
Rods with length
L
diameter
d
:
van
Bruggen
,
Lekkerkerker
,
Dhont
,
Physical Review E
(1997)
56
4394
.
Brancaa, Magazu
,
Mangione.
Diamond & Related Materials
(2005)
14
846.Slide10
Dependence on Aspect Ratio
p
=
D/L;
Legend indicates values of
L
(nm)
Both bundling & length increase diffusion time
τ
as a function of aspect ratio
pSlide11
Also: dynamics as a function of angle
SLS
can simultaneously
measure angular dependence of dynamics in the systemDiffusive dynamics are defined by 2 quantities: control parameter wave vector q [units 1/Length] measured time scale τ Diffusion has units [L2/T] D = 1/q
2
τ
We can measure τ vs q. If D is constant, we expect…Slide12
Typical diffusive behavior should exhibit a power law with slope -2
Fluctuation time
-scale
τ vs. q
-2
If D is a constant, then
D
= 1/
q
2
τ
a
nd so
τ
=
(1/
D) q
-2Slide13
Dynamics
in Combo evolve over time.
The
‘kinks’ in the dynamics at higher q, beginning at 1/q ~ 75 nm, are robust!
Typical diffusive behavior should exhibit a power law with slope -2
Fluctuation time
-scale τ vs. q
-2Slide14
Investigating Morphology
Transition at 1/q ~ 75 nm in both structure and dynamics
m
ay suggests spherical ‘primary particles’ at sizes <75 nm.
DYNAMICS
STRUCTURE
Power law region indicates fractal structure,
D
f
< 3.Slide15
Lab tasksSLS on CNT samplesSLS on protein/polymer/gel samples
More to come on SLS…