Characterization of complex fluids or materials using ...Thank you and see the attached references...

30
Characterization of complex fluids or materials using small angles scattering techniques O. Diat UMR 5257 (CEA/CNRS/UM2/ENSCM)

Transcript of Characterization of complex fluids or materials using ...Thank you and see the attached references...

Page 1: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Characterization of complex fluids or materials using small angles scattering techniques

O. Diat

UMR 5257 (CEA/CNRS/UM2/ENSCM)

Page 2: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

OutlineBrief and classical introduction to scattering methods

•Form and Structure factors •Porous materials, specific surface •Examples

references

Page 3: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Detector

Incident beam(planar wave)

Page 4: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering
Page 5: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering
Page 6: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

rdtreeR

EtRdE rkkitRkiS

issrrr rrrrr

),(1

4

1),( ).().(

0 ρπ

ω −−−−=

Hyp Born approx : far field detection, weak scattering (s index for scattering, i for incident)

0r

θ

R

)(rrρ rd

r

ikr

skr

jj btrtr ),(),(rr

∑= ρρ ρρρ −=∆

=−=2

sin4

q and θ

λπ

is kkqrrr

Scattering vectorScatters densityScattering length

Classic:10-1<q(nm-1)<4

Special: 6.10-3<q(nm-1)<20

Page 7: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Fundamental equation of the instantaneous scattering amplitude :the FT of small heterogeneities ( of the dielectrique cte or electronic or nuclear) depending on the radiation, light, x-ray or neutron

∫−−− ∆==

V

rqitRkiSS rdetre

REtqEtRE s

rrrr rrrr.).(

0 ),(1

4

1),(),( ρ

πω

ρρρ −=∆

0r

θ

R

)(rrρ rd

r

ikr

skr

Integral over the irradiated volume

Page 8: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

cmcm

eb

eTh

132

0

10.83,24

−==πε

3cm/cmin Thmolecular

rayX bV

Z=−ρ

FEDORS table, polymer engineering, 14 (2), 1974, 147-154

scattering length density for X-ray radiation

Page 9: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Do not work with too much hydrogenated compound in performing SANS!Incoherent scattering depends on energy!

(fm)

scattering length density for neutron radiation

3cm/cmin cohA

molecular

cohneutron b

M

dN

V

b ==ρ

Page 10: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

ρH2O = -0.56 1010 cm-2

ρD2O = 6.38 1010 cm-2

ρpolystyrene = 1.41 1010 cm-2

ρD-PS = 6.47 1010 cm-2

Contrast enhanced in neutron scattering if possibility of deuteration!

scattering length density for neutron radiation

3cm/cmin cohA

molecular

cohneutron b

M

dN

V

b ==ρ

Page 11: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

For an assembly of discrete particles:

[ ] rdrrRrrdr j

N

jjj

rrrr)()()(

1

ρδρ ∆+−=∆ ∑=

j

j

j Rqi

qG

jrqi

j

Vj

N

jS erderqE

rrrr

444 3444 21

rrr .

)(

).(

1

])([)( ρ∆∝ ∫∑=

∫−−− ∆=

V

rqitRkiS rdetre

REqE s

rrr rrrr.).(

0 ),(1

4

1)( ρ

πω

drjr j

Rj+1Rj

∑j

Page 12: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

« Scattering intensity »or differential scattering cross-section

∑∑−−==

Ω j k

RRqikj

kjeqGqGEEd

d

V).(** )()(.

),(1 rrrrrλθσ

j

j

j Rqi

qG

jrqi

j

Vj

N

jS erdertqE

rrrr

444 3444 21

rrr .

)(

).(

1

])([),( ρ∆∝ ∫∑=

Ωd

d

V

),(1 λθσ

Page 13: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

« Scattering intensity »or differential scattering cross-section

∑∑−−==

Ω j k

RRqikj

kjeqGqGEEd

d

V).(** )()(.

),(1 rrrrrλθσ

−∆

∆∝

=−∆∆=∆

RdeR

RqI

RrdRrrR

Rqi

S

V j

rr

rr

rrrrvr

rr.2

2

2

)(

)( of ansformFourier tr)( and

)()()()(

ρ

ρ

γρρρ

444 3444 21

rrr rr

jrqi

j

Vj

j rderqG j ).()()( ρ∆= ∫

When j=k

Page 14: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

« Scattering intensity »or differential scattering cross-section

∑∑−−==

Ω j k

RRqikj

kjeqGqGEEd

d

V).(** )()(.

),(1 rrrrrλθσ

444 3444 21

rrr rr

jrqi

j

Vj

j rderqG j ).()()( ρ∆= ∫

When j=k

dRqR

qRRR

)sin()(~4

nsorientatio allaver averagean with

functionon distributidistancepair p(R)

22

043421

=

∆∝ ∫ ρπ

j

k

Rik=50

R50 100

p(R)

Page 15: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

The scattering intensity is the FT of pair-correlation function p(R)

j

k

Rik=50

FT

Page 16: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

« Scattering intensity »or differential scattering cross-section

For diluted system (uncorrelated scatterers and identical)

)(...),(1

)( 2 qPVd

d

VqI partS ρλθσ ∆Φ=

Ω=

For concentred system (identical scatterers) and centrosymmetric

[ ] ∞→→−+=

∆Φ=+=

∫∞

qasdRqR

qRRRg

V

NqS

qSqPVqIV

NqG

V

NqI

S

partSS

s

1sin

1)(41)(factor structure

)()(...)()()(

2

0

2'2

π

ρr

10-2 cm-1

1cm-1

Page 17: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering
Page 18: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering
Page 19: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Latex sphere, O. Spalla

Polydispersity effect

Page 20: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

)(cm ...).(

),(1 1exp −

∆Ω=

Ω=

sacqabs etT

I

d

d

VI

λψλθσ

22

0

2 )).(1(2. ρϕϕπ ∆−== ∫∞

ssabs dqqIQ

( )2

4

)(2

lim

ρπ ∆

=Σ ∞→qabsqI

Porod law

Invariant (for 2-phase system)

Specific surface

Page 21: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

salt = 0.15 M

(O. Spalla, S. Lyonnard Langmuir 02)

Page 22: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering
Page 23: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Relationship between Imes and Iabs-mat

44** )()()( qqqIqIqI absabs

Corrabs −=

/es

Page 24: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

SAXS from CeO2 obtained by a slow evaporation of a colloidal suspension and then calcination at different temperature

Page 25: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

50 nm

X-ray scattering

0.01 0.1 1

0.01

0.1

1

10

100

Inte

nsity

(cm

-1)

q (Å-1)

q-4

Mesoporous materials, MCM or SBA type

J. Cambedouzou et al, JAC 2012

Page 26: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Modèle pour le calcul du diagramme de poudre de mésoporeux hexagonaux

w arp

Rg

Rn,m

Rr

rh

n,mpore

uv

q

z

x φ

qh

ψx

u

∑−=Np

pg qAqAqA )()()(

+−= ∑ ∑

i jiijppippgggg

b qRJqRJRqRJqRJRqRJRqRJRqL

qI

,0

21

2011

21

23

23

)()()()()(2)(4)( ρπ

Page 27: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Autre exemple : MCM-41

0.1 0.2 0.3 0.4 0.5 0.6

0.01

0.1

1

10

100

Inte

nsity

(cm

-1)

q (Å-1)

Rp=16.5 ÅRp=15 Å

expRp=18 Å

Caractérisation structurale :

-a = 44.2 Å

-Rp = 16.5 Å

-Désordre 20% paracristal

Estimation surface spécifique

0.1 0.2 0.3 0.4 0.5 0.6

1E28

1E29

1E30

Iq4 (c

m-5)

q (Å-1)

Σ = 8.74e5 cm-1

pour la poudre

Soit:

S=400 m²/g

À comparer avec S BET = 1100 m2/g…

Page 28: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Geopolymerization followed by SAXS

(P. Steins PhD program, CEA/DTCD – Macromolecules 2012 )

Page 29: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

•To use always refererence sample and empty cellin similar conditions

•To known the sample thickness and otherscattering parameters

• To get data in absolute units

• to the largest (suitable) q-range as possible (whennecessary)

•If possible to do SAXS and SANS (differentcontrast with same scale!)

To perform scattering experiments

Page 30: Characterization of complex fluids or materials using ...Thank you and see the attached references for more details • 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering

Thank you and see the attachedreferences for more details

• 1. Guinier, A. and Fournet, G. (1955) Small-Angle Scattering of X-rays, Wiley, New York.

• 2. Glatter, O. and Kratky, O., Eds., (1982), Small-Angle X-ray Scattering, AcademicPress, London.

• 3. Feigin, L.A. and Svergun, D.I. (1987) Structure Analysis by Small-Angle X-ray and Neutron Scattering, Plenum Press, New York.

• 4. Brumberger, H., Ed., (1995) Modern Aspects of Small-Angle Scattering, Kluwer Academic, Dordrecht.

• 5. Lindner, P. and Zemb, T., Eds., (2002) Neutrons, X-rays and Light : Scatteringmethods applied to soft condensed matter, Elsevier, Amsterdam.

• 6. Schmidt, P.W. (1995) in Modern Aspects of Small-Angle Scattering, Brumberger, H., Ed., p. 1, Kluwer Academic, Dordrecht.

• 7. « Soft matter characterization: scattering, imaging and manipulation », Pecora, Borsali edited by Springer,

• 8. X-ray data booklet LBL, California• 9. Neutron Data Booklet, ILL/ITU• 10. SASfit software package, PS Institure• 11. O. Spalla et al, JAC 36 (2003) 338 + présentation Bombannes, école d’été• 12. J. Teixeira, JAC 21 (1988), 781• …….