multi scale porous and colloidal materials texture …mathieu.bauchy.com/umi/levitz2014c.pdf ·...

P. Levitz CNRS_UPMC Janv 2014 1

MULTI SCALE POROUS AND COLLOIDAL MATERIALS

TEXTURE AND TRANSPORT PROPERTIES

P. E. LEVITZ

[email protected]

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

3P. Levitz CNRS_UPMC Janv 2014

4

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


),( 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



)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

(1907)8P. Levitz CNRS_UPMC Janv 2014

10

I/ INTERMITTENT BROWNIAN MOTION AND BRIDGE STATISTICSdn

AB

BA

II/ BROWNIAN DYNAMICS ON LONG RANGE

+

++

++ +

+ ++ +

+ + + + ++

++

+

(t=0, r =0)

( t, r)

DIFFUSION IN CONFINEMENT


11

I/ Introduction







M

r

(r)

M

PP

II-1/ STATIC SCATTERING

3000 rrrrr d))(

V1)(V

V

r

0r

322 exp))(()( drrqirqI Vstatic

1/q


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

14

DYNAMIC SCATTERING:

Quasi Elastic Scattering

Monochromator

dk

0k

Monochromaticbeam

Noisybeam

),( qS


15

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


19

DYNAMIC DIFFUSION:

X Photon Correlation Spectroscopy

),( tqI

tdk

0k

Monochromaticbeam

Noisybeam

))(),(1)((),(),(

22

qIqSqItqItqI

staticstatict

diqSqS )exp(),(),(

Siegert ‘s theorem


20

diqSqS )exp(),(),(

)exp()(),( 2 DqqIqS static

Probing Self Diffusion of Diluted Colloids


21

I/ Introduction







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


“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


D

24

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


25

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


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


multi scale porous and colloidal materials texture …mathieu.bauchy.com/umi/levitz2014c.pdf ·...

Documents