Fournet & Bomhard - The Indo-European Elements in Hurrian (2010)
Characterization of complex fluids or materials using ...Thank you and see the attached references...
Transcript of Characterization of complex fluids or materials using ...Thank you and see the attached references...
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Characterization of complex fluids or materials using small angles scattering techniques
O. Diat
UMR 5257 (CEA/CNRS/UM2/ENSCM)
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OutlineBrief and classical introduction to scattering methods
•Form and Structure factors •Porous materials, specific surface •Examples
references
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Detector
Incident beam(planar wave)
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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
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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
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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
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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
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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
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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
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« 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
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« 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
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« 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)
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The scattering intensity is the FT of pair-correlation function p(R)
j
k
Rik=50
FT
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« 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
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Latex sphere, O. Spalla
Polydispersity effect
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)(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
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salt = 0.15 M
(O. Spalla, S. Lyonnard Langmuir 02)
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Relationship between Imes and Iabs-mat
44** )()()( qqqIqIqI absabs
Corrabs −=
/es
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SAXS from CeO2 obtained by a slow evaporation of a colloidal suspension and then calcination at different temperature
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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
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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
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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…
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Geopolymerization followed by SAXS
(P. Steins PhD program, CEA/DTCD – Macromolecules 2012 )
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•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
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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• …….