PowerPointPrsentation

1
Sub- and superdiffusive displacement laws in
disordered media probed by NMR techniques Rainer
Kimmich, Yujie Li, German Farrher, Nail
Fatkullin, Markus Kehr Sektion
Kernresonanzspektroskopie, Universität Ulm,
Germany
2
R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)
3
Outline

• perspectives of NMR techniques to measure
  ltr2(t)gt
• over many orders of magnitude of time
• Systems showing anomalous transport properties
• (fluids in confining geometries, porous media,
  polymer melts in bulk)
• Examples polymer dynamics,
• hydrodynamic dispersion in porous media

4
NMR diffusometry in the fringe field of a
superconducting magnet
5
B1 gradients (radio frequency field) instead of
B0 gradients
6
Combination of fringe-field with rotating frame
NMR diffusometry (or likewise with the pulsed
gradient spin echo (PGSE) variant)
water in VitraPor (10-6 m pore size)
MAGROFI
FFStE
7
Intermolecular interactions and relative
displacements
8
Spin-lattice relaxation by molecular motions
homonuclear dipole-dipole coupling dominates for
I 1/2 (e.g. protons)
intra reorientations inter relative
translations
9
(No Transcript)
10
Evaluation of the relative intermolecular mean
square displacement from field-cycling NMR
relaxometry data

• spin-lattice relaxation by dipolar coupling of
  protons
• distinction of intra- and inter-molecular
  contributions
• separable by mixtures of deuterated and
  undeuterated molecules

undeuterated species
dilute solution of undeuterated molecules in
deuterated matrix
11
(No Transcript)
12
fringe field NMR diffusometry
field-cycling NMR relaxometry
13
Intramolecular spin-lattice relaxation by chain
modes also reflects the mean squared displacement
behavior
14

• three different model theories for polymer chain
  modes
• ? three different experimental scenarios
• Rouse model
• (chain in a viscous medium no hydrodynamic
  backflow
• no entanglements, i.e. M lt Mc)
• Renormalized Rouse formalism
• (entanglements, i.e. M gt Mc, t ltlt tterminal)
• Tube/reptation concept
• (chains confined in nanoscopic tubes)

15
Rouse model Bead-and-spring chain in a
viscous medium without backflow
(MltMc)
16
I. Laws for NMR measurands predicted by the
Rouse model (polymer melts M lt Mc no
entanglements)
17
II. Laws for NMR measurands predicted by the
renormalized Rouse formalism (polymer melts M
gt Mc entanglements t ltlt tterminal)
relaxation
diffusion
18
III. Tube/reptation concept by Doi and
Edwards (definition of 4 characteristic time
constants)
19
Laws for NMR measurands predicted by the
tube/reptation concept (polymer melts confined
in mesoscopic pores)
mean squared segment displacement
spin-lattice relaxation time
limits
(I)DE
(II)DE
(III)DE
(IV)DE
20
crossover from Rouse to reptation chain
dynamics with decreasing tube diameter
a) harmonic radial potential theory b) and
Monte Carlo simulations of a modified
Stockmayer chain model in a tube with hard
walls )
A.Denissov, M.Kroutieva, N.Fatkullin, R. Ki., J.
Chem. Phys. 116 (2002) 5217
21

• M lt Mc , bulk scen. I
• M gt Mc , bulk scen. II
• M arb., confined scen. III

? experimental juxtaposition of the three model
scenarios
22
Field-cycling NMR relaxometry at 85C
Rouse
bulk PEO 2000, Mwlt Mc
23
Field-cycling NMR relaxometry at 85C
Rouse
bulk PEO 2000, MwltMc
Ren. Rouse
bulk PEO 10 000 MwgtMc
24
polymer melts confined in pores
Linear polyethyleneoxide (PEO Mw6000) in
solid cross-linked polyhydroxyethylmethacrylate
(PHEMA)
E. Fischer et al., Macromolecules 37 (2004) 3277
25
Field-cycling NMR relaxometry at 85C
Rouse
bulk PEO 2000, MwltMc
Ren. Rouse
bulk PEO 10 000 MwgtMc
PEO 2,000 to 10,000 confined in nanopores from 8
to 60 nm
Evaluation of tube diameter effective on time
scale 10-9 ... 10-5 s 0.6 nm
26
(No Transcript)
27
Hydrodynamic dispersion
28
simulation of hydrodynamic dispersion
29
experimental set-up
30
hydrodynamic dispersion measurement of
incoherent displacements while coherent flow
velocity is compensated
31
water flowing through VitraPor (10-4 m pore size)
32
Summary

• NMR variants promise access to mean squared
  displacements
• in the time range 10-10 s 100 s
• (... and beyond magnetic resonance imaging of
  interdiffusion
• of isotopically labeled molecules)
• hydrodynamic dispersion shows cross-over from
  sub-
• to superdiffusive behavior with increasing Pe
• chain dynamics under mesoscopic confinement
• reveals characteristic laws of the
  tube/reptation model

33
recent collaborators Esteban Anoardo Ioan
Ardelean Bogdan Buhai German Farrher Nail
Fatkullin Elmar Fischer Ravinath Kausik Markus
Kehr Elke Kossel Ravinath Kausik Yujie Li Carlos
Mattea
Funding Deutsche Forschungsgemeinschaft Alexande
r-von-Humboldt Foundation Volkswagen Foundation
34
(No Transcript)
35
Low-frequency surface relaxation Reorientation
mediated by translational displacements (RMTD)
reorientation determined by a) translational
diffusion b) surface topology
36
NMR diffusometry and the tube/reptation concept
37
(No Transcript)
38
Renormalized Rouse
spin-lattice relaxation dispersion of
polyisobutylene melts MwgtMc (H.W. Weber, R. K.,
Macromolecules (26 (1993) 2597)
39
spin-lattice relaxation dispersion of
polyethylene oxide melts (R. K., N. Fatkullin,
R.-O. Seitter, K. Gille, J. Chem. Phys. 98 (1998)
2173)
40
R. Ki., N. Fatkullin, R.-O. Seitter, K. Gille,
J. Chem. Phys. 98 (1998) 2173
41
polymers confined in pores
melts in bulk (entangled polymers)
R. Ki., R. O. Seitter, U. Beginn, M. Möller, N.
Fatkullin, Chem. Phys. Letters 307 (1999) 147
42
(No Transcript)
43
The corset effect
rigid crosslinked HEMADMA methacrylate
matrix pore diameters from 8 to 60 nm that
is up to 122 PEO diameters up to 15 PEO
Flory radii
44

• FC-relaxometry and length scales
• polymer dynamics ? the corset effect
• surface relaxation mechanisms ? the
  flow-relaxation effect

Crossover to bulk ?
Does flow influence T1 ?
45

46
(No Transcript)
47

• (mutual) obstruction effect
• Gaussian propagator, DD(t)
• (e.g. single-file diffusion in zeolites,
• Rouse mode based diffusion)
• trapping effect
• non-Gaussian propagator
• waiting time distribution due to traps
• (e.g. random walk on fractals, reptation)

reptation ? trapping effect ? non-Gaussian
propagators ? special evaluation theory for
spin echo attenuation required! ? Elmar Fischer
48
Low-frequency surface relaxation Reorientation
mediated by translational displacements (RMTD)
reorientation determined by a) translational
diffusion b) surface topology
49
NMR diffusometry in the fringe field of a
superconducting magnet
9.4 T, 400 MHz, 10-5 T/m
4.7 T, 200 MHz, 60 T/m
50
typical echo attenuation curves measured in
linear PEO (Mw11,200) confined in PHEMA pores
at 80C (fringe field technique 60 T/m 200 MHz)
1 fitting parameter pore diameter dpore
(8/-1) nm
echo attenuation formalism (N. Fatkullin, R.
Ki., Phys. Rev. E 52 (1995) 3273)
51
Rotating frame imaging
k-space signal recorded as the FID amplitude
immediately after the B1(x) pulse nutation
frequency encoding w1tpkxx
52
Rapid Rotating-Frame Imaging
stroboscopic acquisition
P. Maffei et al., J. Magn. Reson. A 107 (1994)
40 K.R. Metz et al., J. Magn. Reson. B 103 (1994)
152
53
Conventional field-gradient NMR diffusometry
54
(No Transcript)
55
nuclear quadrupole coupling to electric field
gradients for Igt1/2 (e.g. deuterons)
nuclear dipole-dipole coupling dominates for
I1/2 (e.g. protons)
56
2 classes of anomalous diffusion

• Time dependent diffusion coefficient
• DD(t) in a homogeneous medium
• (mutual obstruction)
• Gaussian propagator
• example single-file diffusion in straight
  cylindrical pores,
• Rouse mode based diffusion
• Diffusion under geometrical restrictions
• (waiting time distribution due to traps)
• non-Gaussian propagator
• examples reptation, random walk on fractals

57
experimental findings for different time scales
the corset effect pore walls are sensed over
more than 60 chain diameters or more than 7
Flory radii !
C. Mattea et al., Appl. Magn. Reson. 27 (2004)
371 N. Fatkullin et al., ChemPhysChem 5 (2004)
884 and NJP 6 (2004) 46
58
(No Transcript)
59
flow velocity map of a random-site percolation
model object recorded with a NMR velocity mapping
technique
1
6 cm
0
6 cm
60

• polymer dynamics in general
• local segment (and sidegroup) fluctuations
• chain modes
• 
  global chain displacements
• techniques to probe chain modes
• field-gradient NMR diffusometry
• 
  field-cycling NMR relaxometry

61
chain modes (comp. B)
62
the corset effect - a finite size phenomenon
ltngt small ? segments can only be displaced along
the contour line of the chain
N. Fatkullin, R. Ki., E. Fischer, C. Mattea, U.
Beginn, M. Kroutieva, New J. Phys. 6, 46 (2004)
63
(No Transcript)
64
B1 gradients
strong gradients thin coils high-power
transmitters
65
Larger confinements (i.e. dconf 10 RF
mm) ? crossover to bulk dynamics ?
66
(No Transcript)
67
Field-gradient NMR diffusometry
68
(No Transcript)
69
distinction limits (II)DE lt - - gt (III)DE of
the tube reptation model? t lt tRouse lt - - gt
t gt tRouse
70
(No Transcript)