Post on 24-Jun-2020
P. Levitz CNRS_UPMC Janv 2014 1
MULTI SCALE POROUS AND COLLOIDAL MATERIALS
TEXTURE AND TRANSPORT PROPERTIES
P. E. LEVITZ
pierre.levitz@upmc.fr
1
Part III:
(Diffusive) Transport and invasion properties:
A statistical physics approach
2
DISORDERED
POROUS
MATERIALS
SEE AND/OR GET RELIABLE STRUCTURAL INFORMATION
GEOMETRY ANALYSIS
FUNCTIONALPROPERTIES:TRANSPORT
P. Levitz CNRS_UPMC Janv 2014
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I/ Introduction
- Unconfined diffusion; Diffusion propagator- The model of Langevin- diffusion coefficient and the Kubo’s Equation- Interfacial media and confinement; short and long range exploration of the matrix
II/ Dynamical range and experimental tools
II-1/ / Scattering and the structural dynamics- Elastic, static, dynamical.- Quasi Elastic Neutron Scattering (QUENS) - Correlation photon spectroscopy (Visible light and X ray):
an example of confined diffusion of a colloid in a pore matrix.
II-2/ Pulsed gradient NMR and the self-diffusion PropagatorII-3/ “Road Map” of G(q,t) in confinement and some experimental resutsII-4/ The tortuosity concept
P. Levitz CNRS_UPMC Janv 2014
),( trG : Self-Diffusion Propagator 0,0 tr tr ,
3).exp(),(),(~ drrqitrGtqG dttitqGqG )exp(),(~),(~~
q/1
Diffusive transport at defined space scale .
- Forced Rayleigh- FRAPP- NMR Pulse gradient- QUENS
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)4
exp()4(
1),(2
2/ tDr
tDtrG d
),( trG
Self-Diffusion Propagator
tr ,0,0 tr
0)),((),(
trGD
ttrG
)()0,( rrG
UNCONFINED BROWNIAN DYNAMICS
RTkD B
self 6
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I/ INTERMITTENT BROWNIAN MOTION AND BRIDGE STATISTICSdn
AB
BA
II/ BROWNIAN DYNAMICS ON LONG RANGE
+
++
++ +
+ ++ +
+ + + + ++
++
+
(t=0, r =0)
( t, r)
DIFFUSION IN CONFINEMENT
P. Levitz CNRS_UPMC Janv 2014
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I/ Introduction
- Unconfined diffusion; Diffusion propagator- The model of Langevin- diffusion coefficient and the Kubo’s Equation- Interfacial media and confinement; short and long range exploration of the matrix
II/ Dynamical range and experimental tools
II-1/ / Scattering and the structural dynamics- Elastic, static, dynamical.- Quasi Elastic Neutron Scattering (QUENS) - Correlation photon spectroscopy (Visible light and X ray):
an example of confined diffusion of a colloid in a pore matrix.
II-2/ Pulsed gradient NMR and the self-diffusion PropagatorII-3/ “Road Map” of G(q,t) in confinement and some experimental resutsII-4/ The tortuosity concept
P. Levitz CNRS_UPMC Janv 2014
M
r
(r)
M
PP
II-1/ STATIC SCATTERING
3000 rrrrr d))(
V1)(V
V
r
0r
322 exp))(()( drrqirqI Vstatic
1/q
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II_1/ DYNAMIC AND/OR STATIC SCATTERING
)(0 S
Monochromator
dk
0k
Monochromaticbeam
Noisybeam
),( qS
0
)exp(),(),()(
tmonowithout dtiqSdqSqI
IqImonowithout )( Over all configurations at the same
statistical timeStatic Scattering:
Structure+dynamics
13P. Levitz CNRS_UPMC Janv 2014)()0,( qIqS static
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DYNAMIC SCATTERING:
Quasi Elastic Scattering
Monochromator
dk
0k
Monochromaticbeam
Noisybeam
),( qS
P. Levitz CNRS_UPMC Janv 2014
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0)),((),(
rDr
)exp(~),(~ 2 Dqq q
0),(~),(~2
qDqq
)exp()0,(~),(~),( 2 DqqqqS
Space dependent self motion (dilute case)
)exp()0,(~),(~),( iqqdqS
222
2
)(1),(
DqDqqS
P. Levitz CNRS_UPMC Janv 2014
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DYNAMIC DIFFUSION:
X Photon Correlation Spectroscopy
),( tqI
tdk
0k
Monochromaticbeam
Noisybeam
))(),(1)((),(),(
22
qIqSqItqItqI
staticstatict
diqSqS )exp(),(),(
Siegert ‘s theorem
P. Levitz CNRS_UPMC Janv 2014
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diqSqS )exp(),(),(
)exp()(),( 2 DqqIqS static
Probing Self Diffusion of Diluted Colloids
P. Levitz CNRS_UPMC Janv 2014
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I/ Introduction
- Unconfined diffusion; Diffusion propagator- The model of Langevin- diffusion coefficient and the Kubo’s Equation- Interfacial media and confinement; short and long range exploration of the matrix
II/ Dynamical range and experimental tools
II-1/ / Scattering and the structural dynamics- Elastic, static, dynamical.- Quasi Elastic Neutron Scattering (QUENS) - Correlation photon spectroscopy (Visible light and X ray):
an example of confined diffusion of a colloid in a pore matrix.
II-2/ Pulsed gradient NMR and the self-diffusion PropagatorII-3/ “Road Map” of G(q,t) in confinement and some experimental resutsII-4/ The tortuosity concept
P. Levitz CNRS_UPMC Janv 2014
Diffusive Processes as probed by field gradient NMR
Field Gradient
t=0 t
G G
Gq
tt=0
q/2
0B )).()(( krGrBz +
),( tqM
Echo
2/ ),( tqM
),().exp(),(),( 3 tqGdrrqitrGtqM
tr ,),( trG : Self-Diffusion Propagator
0,0 tr
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“Road Map” of G(q,t) in confinement.( S. Rodts, P.L., 2002,2005)
Short timesexponential form
3 DMacro,Tortuosity
q
t
),( tqG1
0.1
Pseudo nonconfinement
Porod regimes(Interfaces)Algebraic form
- dimensional effects- diffraction effects
Long Times
x
x x
x x
x
x x
xx
x
x
xx
xx xx
x
x x
x x
x
x x
xx
x
x
xx
xx xx
/D
+
++
++
+ ++ +
+ + ++
++
+
(t=0, r =0)23
P. Levitz CNRS_UPMC Janv 2014
D
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Macroscopic comportment; the tortuosity concept
The tortuosity depends on
-Minimal path (geodesic) between two distant points
-Connection between these two points
- Local factor: throats versus molecular size
/DDp
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1.4
1.3
1.2
1.1
1.0
x10-9
10008006004002000
(ms)
2.10
2.00
1.90
x10-9
Dp =1.0710 -9 m2/s
Tortuosité RMN = 1.9
Moelcular Self-Diffusion in Control CPG glassH. Chemmi, V. Tariel, M. Bérard, D. Petit, P. Levitz
D = 0.7 µm 500x500x500TOMCAT-SLS:
V. Tariel, A Stampanoni, E. Gallucciand P. Levitz (May 2008)
Tortuosité DB = 1.85
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Multi-scale Dynamics and some experimental tools….
Moleculardynamics
QENS
~ ps
Moleculardistances
Intermediatedynamics
Spin-echo
~ ns
Nanometricdistances
Intermediatedynamics
Field-cyclingNMRrelaxometry
1 ns 20 s
Diffusioncoefficient
- Pulsed FieldGradientNMR
1 ms 100 ms
1 m to 100 m
Macroscopicconductivity
tracers
~ s
Sample size
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