Small Angle X-Ray Scattering

Transcription

1 SAXS Small Angle X-Ray Scattering Röntgenkleinwinkelstreuung

2 Intensions Determination of the particle size and the morphology of solid materials:

3 Intensions Determination of the particle size and the morphology of solid materials: Semicrystalline polymers

4 Intensions Determination of the particle size and the morphology of solid materials: Semicrystalline polymers Microphase separated block copolymers

5 Intensions Determination of the particle size and the morphology of solid materials: Semicrystalline polymers Microphase separated block copolymers Polymer blends

6 Basics λ X-rays =01 0,1-05nm 0,5 Measured angles: Θ < 5

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

8 Basics

9 Basics r k 0 : Wave vektor of the primary beam r k : Wave vektor of the secondarybeam r q : Scattering vektor r : Connection vektor between scattering center P 1and P2 θ : Scattering angle

10 Basics r r r q=k-k 0

11 Basics r r r q=k-k 0 Elastic scattering: r r 2π k = k 0 = λ

12 Basics r r r q=k-k 0 Elastic scattering: r r 2π k = k 0 = λ q=q= r 4π λ sinθ

13 Basics

14 Basics Bragg s Law: nλ =2d sinθ hkl

15 Basics Bragg s Law: nλ =2d sinθ hkl insertion of q 2nπ d hkl = q

16 Basics Bragg s Law: nλ =2d sinθ hkl insertion of q 2nπ d hkl = q q is inversely related to the distance in the real space

17 Basics Bragg s Law: nλ =2d sinθ hkl insertion of q 2nπ d hkl = q q is inversely related to the distance in the real space q characterises the reciprocal space

18 Basics Elektrons behave as if they were free

19 Basics Elektrons behave as if they were free All secondary waves are of the same intensity

20 Basics Elektrons behave as if they were free All secondary waves are of the same intensity Thompson equation: I(Θ)=I e 1 1+cos (2Θ) 4πε mc a e e classical electron radius polarisation factor 1

21 Basics Guinier area: Determination of the gyration radius I(q) 4 r r q r exp(- π RS) g mit S = I 3 4π 0

22 Basics Guinier area: Determination of fthe gyration radius I(q) 4 r r q r exp(- π RS) g mit S = I 3 4π 0 Porod area: Determination of the entire surface area of all particles in the sample I(q) I 0 NAQ -4

23 Experimental Technique X-ray source: Copper anode (λ(cuk) α = 0,154 nm)

24 Experimental Technique X-ray source: Copper anode (λ(cuk) α = 0,154 nm) Synchrotrons

25 Experimental Technique X-ray source: Copper anode (λ(cuk) α = 0,154 nm) Synchrotrons Cameras

26 Experimental Technique X-ray source: Copper anode (λ(cuk) α = 0,154 nm) Synchrotrons Cameras Slit Cameras

27 Experimental Technique X-ray source: Copper anode (λ(cuk) α = 0,154 nm) Synchrotrons Cameras Slit Cameras Block Cameras

28 Experimental Technique X-ray source: Copper anode (λ(cuk) α = 0,154 nm) Synchrotrons Cameras Slit Cameras Block Cameras Bonse-Hart Camera

29 Experimental Technique Schematic illustration of a slit camera

30 Experimental Technique Schematic illustration of a slit camera Schematic illustration of a Bonse - Hart Camera

31 Experimental Technique Kratky - camera : Example for a Block Camera

32 Experimental Technique Schematic illustration of a Kratky - camera with block collimation system

33 Experimental Technique h min : First position of measurement R :Plane of registration CG : Center of gravity B1,B2 : Blocks E : Entrance slit P: Sample F: Focus Schematic illustration of the course of beam in a Kratky - camera with block collimation system

34 Measurement and Analysis I(q) = I (q) - (1- φ)i (q) - φi S m Cap (q) I S(q) : Scattering intensity of the sample I m(q) : Scattering intensity of the capillary filled with solvent I (q) : Scattering intensity of the empty capillary Cap φ : Volume fraction of the sample

35 Measurement and Analysis Comparison of the scattering intensities of the solvent, the capillary and the sample

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

37 Measurement and Analysis Comparison of the scattering intensities before and after the desmearing

38 Measurement and Analysis 1000 m -1 ] I(q q) [c q [nm -1 ]

39 Measurement and Analysis Typical pattern for candle wax

40 Measurement and Analysis Typical pattern for a mouse bone

41 Thank you!

42 Literature Glatter, O; Kratky, O:Small Angle X-ray Scattering, Academic Press, Skript des Prakikums Instrumentelle Analytik PC/MC: X-ray scattering of polymers