SAXSSAXS

Small Angle X-Ray Scattering

RöntgenkleinwinkelstreuungRöntgenkleinwinkelstreuung

Intensions

• Determination of the particle size and the morphology of solid materials:

Intensions

• Determination of the particle size and the morphology of solid materials:

– Semicrystalline polymers

Intensions

• Determination of the particle size and the morphology of solid materials:

– Semicrystalline polymers

– Microphase separated block copolymers

Intensions

• Determination of the particle size and the morphology of solid materials:

– Semicrystalline polymers

– Microphase separated block copolymers

– Polymer blendsPolymer blends

Basics

= 0 1 0 5 nmλX-rays = 0,1 - 0,5 nmMeasured angles: < 5 °λ

Θ

Basics

• Reason for the scattering:densitiy fluctuations (differences in the electron density)electron density)Measurement of the excess electron density

Basics

Basics

0k :Wave vektor of the primary beam

k :Wave vektor of the secondarybeam

r

rk : Wave vektor of the secondary beamq :Scattering vektorr : Connection vektor between

r

r

1 2 scattering center P and Pθ :Scattering angle

Basics0q = k - k

r rr

Basics0q = k - k

r rr

Elastic scattering:2πk k

r r0k = k =

λ

Basics0q = k - k

r rr

Elastic scattering:2πk k

r r0k = k =

λ

4π4π q = q = sinθλ

→r

Basics

Basics• Bragg‘s Law:

hklnλ = 2d sinθhkl

Basics• Bragg‘s Law:

hklnλ = 2d sinθ• insertion of q

hkl

2nπhkl

2nπd =q

Basics• Bragg‘s Law:

hklnλ = 2d sinθ• insertion of q

hkl

2nπhkl

2nπd =q

• q is inversely related to the distance in the real space

Basics• Bragg‘s Law:

hklnλ = 2d sinθ• insertion of q

hkl

2nπhkl

2nπd =q

• q is inversely related to the distance in the real space

• q characterises the qreciprocal space

Basics

• Elektrons behave as if they were free

Basics

• Elektrons behave as if they were freeAll secondary waves are of the same intensityintensity

Basics

• Elektrons behave as if they were freeAll secondary waves are of the same intensityintensity Thompson equation:

22 2

e 0 2 20 e

e 1 1+ cos (2Θ)I (Θ) = I4πε m c a 2

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠polarisation factor 1classical electron radius

0 e

≈

⎝ ⎠⎝ ⎠ 14424431442443

Basics

Guinier area: Determination f h i diof the gyration radius

2 2 2g

I(q) 4 q exp(- π R S ) mit S =I 3 4

∝rr r

g0

( )I 3 4π

Basics

Guinier area: Determination f th ti diof the gyration radius

2 2 2g

I(q) 4 q exp(- π R S ) mit S =I 3 4

∝rr r

g0

( )I 3 4π

Porod area: Determination of the entire surface area of all particles in the sampleall particles in the sample

-4

0

I(q) N A QI

∝0

Experimental Technique

• X-ray source: Copper anode (λ(CuK)α = 0,154 nm)

Experimental Technique

• X-ray source: Copper anode (λ(CuK)α = 0,154 nm)SynchrotronsSynchrotrons

Experimental Technique

• X-ray source: Copper anode (λ(CuK)α = 0,154 nm)SynchrotronsSynchrotrons

• Cameras

Experimental Technique

• X-ray source: Copper anode (λ(CuK)α = 0,154 nm)SynchrotronsSynchrotrons

• Cameras– Slit Cameras

Experimental Technique

• X-ray source: Copper anode (λ(CuK)α = 0,154 nm)SynchrotronsSynchrotrons

• Cameras– Slit Cameras– Block CamerasBlock Cameras

Experimental Technique

• X-ray source: Copper anode (λ(CuK)α = 0,154 nm)SynchrotronsSynchrotrons

• Cameras– Slit Cameras– Block CamerasBlock Cameras– Bonse-Hart Camera

Experimental Technique

Schematic illustration of a slit camera

Experimental Technique

Schematic illustration of a slit camera Schematic illustration of a Bonse - Hart Camera

Experimental Technique

Kratky - camera :Example for a Block Camera

Experimental Technique

Schematic illustration of a Kratky - camera with block collimation system

Experimental Technique

minh :First position of measurementR :Plane of registration

B1,B2 : BlocksE : Entrance slit

R :Plane of registrationCG : Center of gravity

P : SampleF : Focus

Schematic illustration of the course of beam in a Kratky - camera with block collimation system

Measurement and Analysis

S m CapI(q) = I (q) - (1- )I (q) - I (q)φ φ

SI (q) : Scattering intensity of the sampleI (q) : Scattering intensity of the capillary filled with solventm

Cap

I (q) : Scattering intensity of the capillary filled with solventI (q) : Scattering intensity of the empty capillary

: Volume fraction of the sampleφ

Measurement and Analysis

Comparison of the scattering intensities of the solvent, the capillary and the sample

Measurement and Analysis

• The geometry of the block collimation system causes an effect called smearing (slit length and slit width effect)g )Scattering intensity has to be desmeared

Measurement and Analysis

Comparison of the scattering intensities before and after the desmearing

Measurement and Analysis1000

100

m-1

]

10

q) [c

1I(q

0.1

0 0.2 0.4 0.6 0.8 1.0

q [nm-1]

Measurement and Analysis

Typical pattern for candle wax

Measurement and Analysis

Typical pattern for a mouse bone

Thank you!

Literature• Glatter, O; Kratky, O:Small Angle X-ray Scattering, Academic Press,

19821982• http://www.phsik.tu-dresden.de/isp/nano/kkk.php• Skript des Prakikums Instrumentelle Analytik PC/MC: X-ray

scattering of polymers• http://www.tu-darmstadt.de/fb/ms/fg/ee/lehre/Methoden/V0712.pdf• http://www tu-• http://www.tu-

darmstadt.de/fb/ms/fg/sf/uebung/SAXS_und_ASAXS.pdf• http://www.tu-berlin.de/~insi/ag_gradzielski/Bglmat4.pdf