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Static - PPT Presentation

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

length fractal linear dynamics fractal length dynamics linear sls time dimension small structure region scales power law large probes diffusion objects volume

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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…