Neutron Scattering in Soft Matter Research:From Biology to Chemistry

Henrich Frielinghaus

Jülich Centre for Neutron ScienceForschungszentrum Jülich GmbHLichtenbergstrasse 185747 Garching (München)

h.frielinghaus@fz-juelich.de

Locations…

– Instruments

NSE

KWS-1, -2

KWS-3

SPHERESDNS

(TREFF)NOSPEC

MARIATOPAS

Apply for beam-time: www.jcns.info !!!

ORNL: NSEILL : IN12-TAS

Scattering TheoryScattering ModelsConcepts

CytologyModel SystemsConcepts

Materials (Polymers…)Model SystemsConcepts

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)

Neutron Sources:

(a)Reactors

235U absobs thermalneutron. Decayto medium heavy nuclei+ 2.5 fast neutrons.Moderation needed (1n).Surplus of 1.5 neutrons.

(b) Spallation Sources

High energy protons hita heavy nucleus (Hg…).Excitation leads to evaporation of 20-25nwith 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…)

New reactor

Old reactor

Reactors

0.8e151990 - 2000FRM-2 Munich

1.5e151970 - 1980HFR Grenoble

2.0e141960 - 1970FRJ-2 Jülich

~1.0e131950 - 1960FRM-1 Munich

Flux [cm-2s-1]PeriodReactor

Spallation Sources

SNS – Oak Ridge, USAJ-PARC – Tokai, JapanECNS – Sweden, Spain…???

Neutron History

1932: Chadwick discovered neutron (2He4 + 4Be96C12 + 0n1). 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 neutronscattering 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 MnO2 was resolved (Nobel prize 1994)

Neutron History

1940s and 1950s : further nuclear reactors were built.

1954: Canadian reactor in Chalk River: Strongest neutron source (3e14 cm-2s-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 thefluxes 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-2s-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.

Instrument Development in Germany

Backscattering Spectrometer ( )Neutron Small Angle Scattering (SANS) diffractometerInstruments 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, USAJ-PARC – Tokai, JapanECNS – Sweden, Spain…???

Neutron Particle Properties

mn = 1.675 10-27 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 µn = -1.913 µN (µN is the nuclear magneton)

The kinetic energy is non-relativistic (Newton, de Broglie…). Units are:

1 meV = 1.602 10-22J 9.044 Å (de Broglie wavelength)

437.4 m/s

(E = hν) 0.2418 1012 Hz (used less frequently)

(E = kBT) 11.60 K

nnnnn

Em

h

vm

h

2==λ

Neutron Particle Properties

De Broglie wavelengthwith mn mass

vn velocityEn energy = ½ mn vn

2

Hot: ~2000KThermal: ambient TCold: ~30K (liquid hydrogen / deuterium)

−

Tk

vvv

B

23

2

1exp~)(φ

Velocity distribution in a thermal source

Comparison neutron – photon (x-ray)

vn = (2En/mn)½ = 2187 m/sc = 3.00⋅108 m/sVelocity

λn= h /(2mnEn)½ = 1.81 Åλx= ch/E = 1.24 ÅWavelength

25 meV10 keVTypical energy

µn = –1.91304275(45) µN0Magnetic moment

½1Spin

00Charge

mn = 1.6749286(10) ⋅10–27 kg mphot = 0Mass

neutron= particle wave

X-rays= transversal wave

particle:

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.

Typical Scattering Experiment:

source

monochromator

slits

preparation

sample

Θ

analyzer

slits

analysis

detector

fk

fE

vmh

ph

ki

ππ 22 ==

2

2

1mvEi =

Typical Scattering Experiment:

source

monochromator

slits

preparation

sample

Θ

analyzer

slits

analysis

detector

fk

fE

vmh

ph

ki

ππ 22 ==

2

2

1mvEi = In

tens

ityif kkQ

−=

if EEE −=∆

Triple Axis Spectrometer:

Bragg´s Scattering Law:

d

Θ

Θ= sin2dnλ

Θ==

sin

2

d

nk

πλπ

For preparing/analyzing the beam:

``Selective Mirror´´

retardation

Bragg´s Scattering Law:

d

Θ

ik

As a sample:

fk

Q

Θ= sin2dnλ

Θ==

sin

2

d

nk

πλπ

d

nkQ

kkQ if

π2sin2 =Θ=

−=

reciprocal space !!

Bragg´s Scattering Law: (different planes)

d All possible Qof constructive interferenceform also a lattice.

(reciprocal lattice)

The priciples of neutron scattering (Born Approximation…)

neutronsincomingofFlux

inneutronsscatteredofFlux Ω=Ωd

dσΩ

⋅=ΩΣ

d

d

Vd

d σ1

Only 10% of neutrons are scattered (coherently). single scattering event

The nuclei appear as pointlike particles (nuclear physics Fermi pseudo potential)

The priciples of neutron scattering (Born Approximation…)

)exp( jj

j rQibA

=

2A

d

d =Ωσ

= )exp()(3 rQirrdAρ

pointlike particles

continuous density

intensity

Isotopes: different b

H – D exchange

The priciples of neutron scattering (Born Approximation…)

randomly distributed nuclear spins

n

2)( bb −

b new coherent scattering length

incoherent cross section

structure of a pointlike particle

)()(

)exp()(3

QsQf

rQirrdA

⋅=

= ρ

Problems of x-ray scattering

formfactor of single atoms f(Q)

structure factor of idealpointlike particles s(Q)

At larger angles intensity reduced.

What model of electron distribution ???

Comparison: neutron and x-ray scattering

Chemical modificationsNon-destructive

Thin samples (0.1 – 0.5mm)Penetration: thick samples 1-5mm, and even more (10cm)

(huge effort)Energy transfers comparable to kineticenergy.

(magnetic dichroism)Spin density directly detectable (µn)

Scattering length ~ Z

Resonances prepare certain nuclei

Heavier atoms scatter more ( res.)

Non-systematic scattering lengthIsotope labelling

Each atom can be highlighted

Formfactor of atomHydrogen electron cloud distorted

Pointlike particles (easy modelling)Hydrogen-nucleus easily detectable

X-raysNeutrons

Scales of Plots:

0

1

2

3

4

5

6

7

8

9

10

Linear Scale

length 2

length 2

length 2

length 2

1

10

Logarithmic Scale

factor 2

factor 2

factor 2

factor 28

4

2

positive values only,huge numbers can bedisplayed !!!

1 10 10010-10

10-9

10-8

10-7

10-6

1x10-5

1x10-4

10-3

10-2

10-1

100

-4

-2

-1

x-4

x-2

x-1

Scales of Plots: (power laws)

Small Angle Neutron Scattering (SANS)

Small Angle Neutron Scattering (SANS)

Small Angle Neutron Scattering (SANS)

δ

0k

1k Q

δ

λπ /210 == kk

4sin( /2)Q

π δλ

=

0 5 10 15 20 2510-7

10-6

10-5

10-4

10-3

10-2

10-1

100

form factor of sphere with radius R

P(Q

R)

Q R

QQ now

Remark on vectors:

elastic

Q-range of Small Angle Scattering Techniques

2 – 15 Å

~ 6000 Å

Wave Length

10Å – 20µm

0.5 – 20µm

Length Scale

Neutron

Light

Probe

According to D = 2 /Q one can explore particles of size:

10-3 Å-1 < Q < 2·10-5 Å-1Double Crystal Diffractometer

5·10-3 Å-1 < Q < 10-4 Å-1Focusing SANS

0.2Å-1 < Q < 10-3 Å-1Pin - Hole SANS

Three different SANS instrumentsallow to measure a particle size in a range of four orders of magnitude:

∆k/k

∆Ω

∆Ω D

, ∆λ/λ

, ∆λ/λ

∆ΩD

∆Ω,

F

Sample

Θ

Qk1

k0

Θ

2( / )4( )2

Tk kU

T

k kL e

k kπ−Φ ∆=

0 UI L F∆ = ⋅ ⋅ ∆ΩIntensity at sample:

Luminosity of the source:

0( ; ) ( ; )D D

dI Q I D T Q

dδ δΣ∆ = ∆ ⋅ ⋅ ⋅ ⋅ ∆Ω

ΩIntensity at detector:

22

2 T Bk k Tm

=

Intensitiesof a SANS exp.and resolution

Resolution:2

2 2 2 2 2 2 21 1[ ( ) ( ) ( ) ( ) ]

12D E

SD C C D

k d dQ d

L L L L

δλδ δλ

< > = + + + +< >6

Θ2

Optimization: D CL L= SDE d2dd ==

. ( / 3) /opt E CQ k d Lδ = ⋅

and

leads to:

Resolutionof a SANS exp.and intensity

LD as large as possible!One limit: C4γ=∆Ω

.2 4 20 2

( )optU D U D

D

QFI L L L L

L k

δ∆ = ∆Ω ∝

2( / )E Cd L

1 10105

106

107

KWS1: Flux on Sample

λ=7; ∆λ/λ=0.2

Entrance Aperture 3*3 cm2

Reactor Power 20MW

L1.68±0.04

Inte

nsity

[n/

cm2 s]

Collimation [m]

-20 -15 -10 -5 0 5 10 15 20

10-6

10-5

10-4

10-3

10-2

10-1

100

2Γ1/22Γ1/2

No

rmal

ized

Int

ensi

tyPosition [cm]

Primary beam:

Characteristics of SANS

Intensity at sample position:

2 2 2 20 2

(4 ) ( )U D U C DD

F QI L L L L

L k

δγ∆ = ∆Ω ∝

Primary beam:

Focusing SANS

Layout of focusing-mirror SANS

toroidal mirror:•size:20x120 cm2

• 1000Å thick layer of Cu65

Example from focusing-mirror SANS

10-4 10-3102

103

104

105

106

107

108

U-SANS Lightscattering

R=(7140±14)Å

(dΣ/

dΩ)[

cm-1]

Q [Å-1]

Latex Spheres: USANS and light scattering

>−−

≤=

− 1y)y1(1

1y1)y(R

5.02

-3 -2 -1 0 1 2 30.0

0.2

0.4

0.6

0.8

1.0

3x1xR

efle

ktiv

ität

y

-5 -4 -3 -2 -1 0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

t-t mode

s-s mode

Si111; λ=4.48Å

Inte

nsity

δ[∆δ]

2

4 sin 2

WC

B

b e F N λδ

π δ

−

∆ =

exp(-W) Debye-Waller factorF geometrical structure factor

Darwin curve

Double crystal diffractometer (DCD)

Layout of the old “Jülich” instrument

“Agamalian” cut

Resolution of DCD

-90 -60 -30 0 30 60 9010-5

10-4

10-3

10-2

10-1

100

2∆δ(t-t)

∆δ(s-s)=30.5µrad∆δ(t-t)=20.5µrad

t-t mode

Theoretical Resolution: Si111

; λ=4.48Å

s-s mode

Inte

nsity

I(δ)

/I(0)

Scattering Angle δ[µrad]

-90 -60 -30 0 30 60 9010-5

10-4

10-3

10-2

10-1

100

2 ∆δ(t-t)

Experim. Resolution: Si111

; λ=4.48Å

s-s mode

t-t mode

∆δ(s-s)=54.2µrad ∆δ(t-t)=25.8µrad

Inte

sity

I(δ)

/I(0)

Scattering Angle δ [µrad]

0 10 20 30 40 505.5

6.0

6.5

7.0

7.5

8.0

ca.4% Latex in Water

Rg=(0.72±0.03)µm

D=(1.87±0.08)µm

Rg=(0.314±0.004)µm

D=(0.82±0.01)µm

Lnd

Σ* /dΩ

[cm

-1]

Q2 [10-8Å-2]-100 0 100 200 300 400 500

10-6

10-5

10-4

10-3

10-2

10-1

100

2∆δ

4% Latex Dispersion in Water

empty beam latex dispersion

(d=0.796µm)

Nor

mal

ized

Inte

nsity

Scattering Angle δ [µrad]

[ ]D mµ 0.82±0.01

1 3 31 0V c m− 2.89±0.04

21 0− Φ 3.4±0.09

Model System: Latex spheres in solution

Given parameters: D=0.796µm; Φ=3.98 10-2

( ) ( )0 H

I QdQ

d I T A D δ

∗ ∆Σ =Ω ⋅ ⋅ ⋅ ⋅ ∆

Lamella Al-Al 2Cu alloy

Lamella structure shownby optical micrograph

Bragg-Reflectionλ=1.8ÅQm=(45±2.7) 10-5 ÅD=(1.4 ± 0.09)µm

Crystallization of syndio-Polypropylene in d-22 solution -large scale view

(Scale bar 2 µm)

Spherulitic morphologyDKD, Focusing SANS, Pin - Hole SANS

10-5 10-4 10-3 10-2 10-110-3

10-1

101

103

105

107

109

Q-4Q-4

dΣ/d

Ω [c

m-1]

Q [Å-1]

Q-2

0.5% s-PP in d-22room temp.

Rg=3.3µm

Large-scale aggregates formed by the sPP-P(E-co-P) diblocks

Scale bar 2 µm

Multi-level structure:

• small scale: 2-d morphology

• intermediate scale: 1-d morphology

• large scale: mass-fractal features

Columnar morphology

MW=38.4k/106.6k

10-5 10-4 10-3 10-2 10-110-2

100

102

104

106

108

Q-1

Q-3

dΣ/d

Ω [c

m-1]

Q [Å-1]

0.5% sPP-P(E-co-P) in d22room temp.

R=2.75µm

Important design elements of SANS

- Monochromator- Position Sensitive Detector- Neutron Lenses

Velocity selector

0 5 10 15500

1000

1500

2000

2500

3000

λ=7.94Å

f=16000 rpm<λ>=8.01Å

∆λ/λ=0.2

Inte

nsitä

t [a

.u.]

λ [Å]

0.00 0.50 1.00 1.50 2.00 2.500.0

0.5

1.0

1.5

2.0

2.5

3.0

Dornier Selector

λ = 2127 / fTheor

λf=2011+0.456f[f]=1/s

theory

λ*f [

103 Å

/s]

f [104min-1]

Example of sample with oriented anisotropic “particles”:

Isoprene rubber stretched

Position sensitive detector

Gas detector

3 3 1 0.77He n H H MeV+ → + +2D-lattice of wires:

Resolution ~1cmTime per count ~10s

Scintillation detector

6 4 3 4.79Li n He H MeV+ → + +

Ce activated 6Li glass

One neutron gives about 4000 photons of 0.4 m wave length

Lenses for SANS

Focal length=(L1+L2)/4

• Refractive index: n2 = 1 - ξξξξ (n is less than 1, i.e. vacuum is the “optically” more dense region → concave lens is focusing!)

• Parameter: ξξξξ = λλλλ2ρρρρ/ππππ = 1.64⋅ 10-6 λ2 [Å] = 8.05 ⋅ 10-5cm for λ= 7Å neutrons of lenses consisting ofMgF2 with scattering length density: ρ = 5.16 ⋅ 1010 cm-2

• Focal length: f = r / ξξξξ = 248.5m for 7Å neutrons

• Several lenses: fN = f / N = 9.94m for N=25 lenses at 7Å(fine tuning by wave length!)

Typical parameters for “SANS” lenses

-30 -20 -10 0 10 20 30-30

-20

-10

0

10

20

30

s [m

m]

w [mm]

R=20mm

ΦΦΦΦ=52mm

Sample measurement with 7 lenses

4 µm

10-5 10-4 10-3 10-2 10-110-1

100

101

102

103

104

105

106

107

108

dΣ/d

Ω [c

m-1]

Scattering vector Q [Å-1]

Sample measurement with lenses

Jülich measurements:— KWS-2— KWS-3 (focussed)— DKD

JAEA measurements:DKDwith 7 MgF2-lenses(19Å, 10m, small detector)

with 70 MgF2-lenses(6.5Å, 10m, small detector)

with 70 MgF2-lenses(6.5Å, 10m, large detector)

conventional 2m SANS(incoherentbgrnotsubtracted)

Neutron Spin Echo (NSE) Spectrometer

• Small energies detectable (soft matter)• Signal in time domain

Summary of technical part:

if kkQ

−=

if EEE −=∆2

Ad

d =Ωσ

= )exp()(3 rQirrdAρ

10-3 Å-1 < Q < 2·10-5 Å-1Double Crystal Diffractometer

5·10-3 Å-1 < Q < 10-4 Å-1Focusing SANS

0.2Å-1 < Q < 10-3 Å-1Pin - Hole SANS

Length scale given by: D = 2 /Q