Neutron Scattering in Soft Matter Research: From Biology to Chemistry. Henrich Frielinghaus

Transcription

1 Neutron Scattering in Soft Matter Research: From Biology to Chemistry Henrich Frielinghaus Jülich Centre for Neutron Science Forschungszentrum Jülich GmbH Lichtenbergstrasse Garching (München) h.frielinghaus@fz-juelich.de

2 Locations

3 Instruments Apply for beam-time: DNS SPHERES KWS-1, -2 MARIA ORNL: NSE ILL: IN12-TAS (TREFF) NOSPEC NSE TOPAS KWS-3

4 Scattering Theory Scattering Models Concepts Materials (Polymers ) Model Systems Concepts Cytology Model Systems Concepts

5 Scope of the Lectures Technical part (what is a neutron? what instruments?) Polymer part (what is a polymer? how does it scatter?) Soft matter part (what is soft matter? how does it scatter?) General part (more general questions) Links to Biology, Chemistry and materials research. Mathematics (sometimes rudimentary, sometimes more precise) Fourier transformation (should become plastic) Power laws (should be interpreted directly)

6 Neutron Sources: (a) Reactors 235 U absobs thermal neutron. Decay to medium heavy nuclei fast neutrons. Moderation needed (1n). Surplus of 1.5 neutrons. (b) Spallation Sources High energy protons hit a heavy nucleus (Hg ). Excitation leads to evaporation of 20-25n with 1 to 100MeV. Decay of nucleus. The spallation source is pulsed. Peak intensity very high (good for instruments: TOF). The medium flux compares well to reactors (not so well for SANS, NSE )

7 New reactor Old reactor

8 Reactors Reactor FRM-1 Munich FRJ-2 Jülich HFR Grenoble FRM-2 Munich Period Flux [cm -2 s -1 ] ~1.0e13 2.0e14 1.5e15 0.8e15 Spallation Sources SNS Oak Ridge, USA J-PARC Tokai, Japan ECNS Sweden, Spain???

9 Neutron History 1932: Chadwick discovered neutron ( 2 He Be 9 6 C n 1 ). No electric charge = neutral particle. Standard theory says: 1 up + 2 down quarks (charge - 2 = 0). 1936: Hahn & Meitner observe fission. Mitchell & Powers conduct first neutron scattering experiment. 1942: Fermi built first nuclear reactor (Chicago pile = first controlled chain reaction) 1943: Oak Ridge Graphite Reactor: 3.5MW for production of fissionable material 1945: Shull s first neutron diffractometer: antiferromagnetic structure of MnO 2 was resolved (Nobel prize 1994)

10 Neutron History 1940s and 1950s: further nuclear reactors were built. 1954: Canadian reactor in Chalk River: Strongest neutron source (3e14 cm -2 s -1 ). Brockhouse developed 3-axis spectrometer for: inelastic scattering of excitations in solid materials (Nobel prize 1994) Important development: Cold Source. In Harwell, England the cold source ran on liquid hydrogen. (Cold, slower) Neutrons with long wavelengths were accessible. 1960s: High flux reactor in Brookhaven, USA came to operation. Since then the fluxes did not increase dramatically anymore. 1972: High flux reactor in Greoble, France at the Institut Laue Langevin, ILL came to operation. Flux 1.5e15 cm -2 s -1 is the highest flux in the world. Germany: 1955: Munich atom egg. 1960s: Jülich FRJ-2 reactor. 2004: High flux reactor in Munich, Germany at the Technical University of Munich came to operation. Germany s best reactor.

11 Instrument Development in Germany Backscattering Spectrometer ( ) Neutron Small Angle Scattering (SANS) diffractometer Instruments for diffuse neutron scattering (DNS) High resolution time-of-flight spectrometers Spallation Source History 1960s: Pioneer work at the Argonne National Laboratory (Chicago, USA). Rutherford laboratory, UK: strongest spallation source with a proton beam of 200 kw. Future: SNS Oak Ridge, USA J-PARC Tokai, Japan ECNS Sweden, Spain???

12 Neutron Particle Properties m n = kg radioactive particle with =889.1 ± 1.8s n p + + e - + ν practically stable, since v = ~1000m/s and length ~100m. Spin ½ particle with µ n = µ N (µ N is the nuclear magneton) The kinetic energy is non-relativistic (Newton, de Broglie ). Units are: 1 mev = J Å (de Broglie wavelength) m/s (E = hν) Hz (used less frequently) (E = k B T) K

13 Neutron Particle Properties λ n = h m v n n = h 2m n E n De Broglie wavelength with m n mass v n velocity E n energy = ½ m n v n 2 Hot: ~2000K Thermal: ambient T Cold: ~30K (liquid hydrogen / deuterium)

14 Velocity distribution in a thermal source φ( v) ~ v 3 exp v k T B

15 Comparison neutron photon (x-ray) particle: Mass Charge Spin Magnetic moment Typical energy Wavelength Velocity X-rays = transversal wave m phot = kev λ x = ch/e = 1.24 Å c = m/s neutron = particle wave m n = (10) kg 0 ½ µ n = (45) µ N 25 mev λ n = h /(2m n E n ) ½ = 1.81 Å v n = (2E n /m n ) ½ = 2187 m/s Both kinds of radiation used to study materials (soft matter, liquids, ) No charge, but strong interaction of photon with electrons. Magnetic moment allows neutrons to study magnetic structures. Energy given here: λ 1Å. (for SANS λ 6 to 15Å) For this wavelength, the large neutron mass leads to small energies. Relative changes of this energy are easily detectable. These energy changes are suitable for soft-matter research. For x-rays one needs larger efforts to detect changes of the energy.

16 Typical Scattering Experiment: slits Θ slits detector source monochromator sample analyzer preparation analysis k i = 2π 2π p = mv h h k f Ei = 1 mv 2 2 E f

17 Typical Scattering Experiment: slits Θ slits detector source monochromator sample analyzer preparation analysis k i 2π 2π = p = mv h h Ei = 1 mv 2 2 Q = k f k i E = E f E i k f E f Intensity

18 Triple Axis Spectrometer:

19 Bragg s Scattering Law: Θ For preparing/analyzing the beam: d nλ = 2d sin Θ retardation k = 2π = λ πn d sin Θ ``Selective Mirror

20 Bragg s Scattering Law: Θ As a sample: d nλ = 2d sin Θ k = 2π = λ πn d sin Θ k i Q k f Q Q = = k f k 2 k sin Θ = i 2πn d reciprocal space!!

21 Bragg s Scattering Law: (different planes) d All possible Q of constructive interference form also a lattice. (reciprocal lattice)

22 The priciples of neutron scattering (Born Approximation ) dσ = dω Flux of scattered neutrons in Ω Flux of incoming neutrons dσ dω 1 = V dσ dω Only 10% of neutrons are scattered (coherently). single scattering event The nuclei appear as pointlike particles (nuclear physics Fermi pseudo potential)

23 The priciples of neutron scattering (Born Approximation ) A = j b j exp( iqr ) j pointlike particles 3 A = d r ρ( r )exp( iqr ) continuous density dσ = dω A 2 intensity Isotopes: different b H D exchange

24 The priciples of neutron scattering (Born Approximation ) n randomly distributed nuclear spins b 2 ( b b ) new coherent scattering length incoherent cross section structure of a pointlike particle

25 Problems of x-ray scattering A = 3 d r ( r )exp( iqr ) f ( Q) s( Q) = ρ structure factor of ideal pointlike particles s(q) formfactor of single atoms f(q) At larger angles intensity reduced. What model of electron distribution???

26 Comparison: neutron and x-ray scattering Neutrons Pointlike particles (easy modelling) Hydrogen-nucleus easily detectable Non-systematic scattering length Isotope labelling Each atom can be highlighted Spin density directly detectable (µ n ) Energy transfers comparable to kinetic energy. Penetration: thick samples 1-5mm, and even more (10cm) Non-destructive X-rays Formfactor of atom Hydrogen electron cloud distorted Scattering length ~ Z Resonances prepare certain nuclei Heavier atoms scatter more ( res.) (magnetic dichroism) (huge effort) Thin samples ( mm) Chemical modifications

27 Scales of Plots: Linear Scale Logarithmic Scale length 2 length 2 length factor 2 factor 2 factor length 2 1 factor 2 0 positive values only, huge numbers can be displayed!!!

28 Scales of Plots: (power laws) x10-4 1x x -4 x -1 x

29 Small Angle Neutron Scattering (SANS)

30 Small Angle Neutron Scattering (SANS)

31 Small Angle Neutron Scattering (SANS) δ δ k1 k 0 Q P(QR) 10 0 form factor of sphere with radius R k 0 = k1 = 2π / λ Q = 4π sin( δ /2) λ elastic Q R Remark on vectors: Q now Q

32 Q-range of Small Angle Scattering Techniques According to D = 2 /Q one can explore particles of size: Probe Light Neutron Wave Length ~ 6000 Å 2 15 Å Length Scale µm 10Å 20µm Three different SANS instruments allow to measure a particle size in a range of four orders of magnitude: Pin - Hole SANS Focusing SANS Double Crystal Diffractometer 0.2Å -1 < Q < 10-3 Å Å -1 < Q < 10-4 Å Å -1 < Q < Å -1

33 Intensities of a SANS exp. and resolution Ω,, λ/λ Sample F Θ k 0 Θ k 1 k/k Q Ω D Ω Ω D, λ/λ Intensity at sample: I0 = LU F Ω Luminosity of the source: L U = Φ 2π k ( ) k T 4 e ( k / k T ) 2 k k kt m = k T B Intensity at detector: dσ I D ( δ ; Q) = I0 D T ( δ ; Q) Ω dω D

34 Resolution of a SANS exp. and intensity Resolution: k d d 1 1 δλ < δq > = [ ( ) + ( ) + ( + ) + ( ) ] 2 2 D 2 E ds Θδ 2 12 LD LC LC LD < λ > 6 Optimization: LD LC and = d E = d D = 2dS leads to: δ Q. = ( k / 3) d / L opt E C F δq I0 = L Ω L L ( ) L 2 2 opt. 4 2 U D U D LD k ( d / L ) E C 2 L D as large as possible! One limit: Ω = 4γ C

35 Characteristics of SANS Intensity at sample position: Primary beam: Intensity [n/cm 2 s] λ=7; λ/λ=0.2 Entrance Aperture 3*3 cm 2 Reactor Power 20MW KWS1: Flux on Sample L 1.68± Collimation [m] Normalized Intensity Γ 1/2 2Γ 1/ Position [cm]

36 Focusing SANS F δq I0 = L Ω L L (4 γ ) ( ) L U D U C D LD k Primary beam:

37 Layout of focusing-mirror SANS toroidal mirror: size:20x120 cm Å thick layer of Cu 65

38 Example from focusing-mirror SANS Latex Spheres: USANS and light scattering (dσ/dω)[cm -1 ] U-SANS Lightscattering R=(7140±14)Å Q [Å -1 ]

39 Double crystal diffractometer (DCD) Darwin curve Reflektivität x 1x 1 1 (1 y R (y) = ) y y 1 > y Intensity Si 111 ; λ=4.48å s-s mode t-t mode δ[ δ] δ = W 2 bc e F N λ 4π sin 2δ exp(-w) Debye-Waller factor F geometrical structure factor B

40 Layout of the old Jülich instrument Agamalian cut

41 Resolution of DCD Experim. Resolution: Si 111 ; λ=4.48å Theoretical Resolution: Si 111 ; λ=4.48å Intesity I(δ)/I(0) δ(t-t) δ(s-s)=54.2µrad δ(t-t)=25.8µrad s-s mode t-t mode Intensity I(δ)/I(0) δ(t-t) δ(s-s)=30.5µrad δ(t-t)=20.5µrad s-s mode t-t mode Scattering Angle δ [µrad] Scattering Angle δ[µrad]

42 Model System: Latex spheres in solution % Latex Dispersion in Water 2 δ empty beam latex dispersion (d=0.796µm) ( ) d Σ I Q ( Q) = dω I T A D δ 0 H 8.0 ca.4% Latex in Water R g =(0.72±0.03)µm D=(1.87±0.08)µm Normalized Intensity Ln{dΣ * /dω[cm -1 ]} R g =(0.314±0.004)µm D=(0.82±0.01)µm Scattering Angle δ [µrad] Q 2 [10-8 Å -2 ] Given parameters: D=0.796µm; Φ= D [ m ] µ 0.82±0.01 V c m 2.89±0.04 Φ ±0.09

43 Lamella Al-Al 2 Cu alloy Lamella structure shown by optical micrograph Bragg-Reflection λ=1.8å Q m =(45±2.7) 10-5 Å D=(1.4 ± 0.09)µm

44 Crystallization of syndio-polypropylene in d-22 solution - large scale view DKD, Focusing SANS, Pin - Hole SANS Spherulitic morphology dσ/dω [cm -1 ] Rg=3.3µm Q % s-pp in d-22 room temp. Q Q [Å -1 ] Q -2 (Scale bar 2 µm)

45 Large-scale aggregates formed by the spp-p(e-co-p) diblocks 10 8 R=2.75µm M W =38.4k/106.6k 10 6 Q -3 dσ/dω [cm -1 ] % spp-p(e-co-p) in d22 room temp Q [Å -1 ] Multi-level structure: small scale: 2-d morphology intermediate scale: 1-d morphology large scale: mass-fractal features Q -1 Columnar morphology Scale bar 2 µm

46 Important design elements of SANS - Monochromator - Position Sensitive Detector - Neutron Lenses

47 Velocity selector λ*f [10 3 Å/s] λf= f [f]=1/s Dornier Selector theory λ = 2127 / f Theor Intensität [a.u.] f=16000 rpm <λ>=8.01å λ/λ=0.2 λ=7.94å f [10 4 min -1 ] λ [Å]

48 Position sensitive detector Example of sample with oriented anisotropic particles : Isoprene rubber stretched

49 Gas detector 2D-lattice of wires: He + n H + H MeV Resolution ~1cm Time per count ~10 s

50 Scintillation detector Ce activated 6 Li glass Li + n He + H MeV One neutron gives about 4000 photons of 0.4 m wave length

51 Lenses for SANS Focal length=(l 1 +L 2 )/4

52 Typical parameters for SANS lenses Φ=52mm s [mm] R=20mm Refractive index: n 2 = 1 - ξ (n is less than 1, i.e. vacuum is the optically more dense region concave lens is focusing!) Parameter: ξ = λ 2 ρ/π = λ 2 [Å] = cm for λ= 7Å neutrons of lenses consisting of MgF 2 with scattering length density: ρ = cm -2 Focal length: f = r / ξ = 248.5m for 7Å neutrons Several lenses: f N = f / N = 9.94m for N=25 lenses at 7Å (fine tuning by wave length!) w [mm]

53 Sample measurement with 7 lenses 4 µm

54 Sample measurement with lenses dσ/dω [cm -1 ] Scattering vector Q [Å -1 ] Jülich measurements: KWS-2 KWS-3 (focussed) DKD JAEA measurements: DKD with 7 MgF 2 -lenses (19Å, 10m, small detector) with 70 MgF 2 -lenses (6.5Å, 10m, small detector) with 70 MgF 2 -lenses (6.5Å, 10m, large detector) conventional 2m SANS (incoherent bgr not subtracted)

55 Neutron Spin Echo (NSE) Spectrometer Small energies detectable (soft matter) Signal in time domain

56 Summary of technical part: Q = k f k i A 3 = d r ρ( r )exp( iqr ) E = E f E i dσ = dω A 2 Pin - Hole SANS Focusing SANS Double Crystal Diffractometer 0.2Å -1 < Q < 10-3 Å Å -1 < Q < 10-4 Å Å -1 < Q < Å -1 Length scale given by: D = 2 /Q