1. 1
NMR-Investigation of Structure of
Polymeric Multilayer Membranes and
Fluid Mobility inside Membranes
Results of NMR-diffusometry

2. 2
Aims:
 To show that NMR-diffusometry can
be applied as a microscopic method
for studying some structural
properties of polymeric membranes
 To study features of fluid behavior
imbedded inside membrane

3. 3
Why can NMR-diffusometry be
used as a microscopy?
introduction

4. 4
Methodical basics of microscopy of
solid matrices…
Collection of particles
with well-known
characterizations
Interactions with
solid matrix
Collection of particles
with new
characterizations
SOLID MATRIX

5. 5
Diffusometry as a microscopy
‘Free-moving’ fluid
molecules
(gas, liquid)
Interactions with solid
matrix (restrictions)
Fluid molecules
interacted with wall of
solid matrix
SOLID MATRIX
(porous medium)

6. 6
Free diffusion: Time Dependence of
Mean Square Displacement
0 100 200 300 400 500 600
0
20
40
60
80
100
120
140
Monte-Carlo result
Einstein formula
experimental time
m.s.d.
Results of computer simulation (Monte-Carlo Method)
exp
2
exp
2
...,6 trdsmDtr 
x
z
y
Diffusion coefficient Experimental time

7. 7
Free diffusion: Time Dependence of
Diffusion Coefficient D
exp
2
6Dtr 
0 100 200 300 400 500 600
20
30
40
50
D ( t exp
) = const ( t exp
)
DiffusionCoefficient,D
experimental time
Results of computer simulation (Monte-Carlo Method)
x
z
y

8. 8
Restricted Diffusion: Time Dependence
of Mean Square Displacement
0 100 200 300 400 500 600
0
10
20
30
40
50
60
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600
m.s.d.
experimental time
free diffusion
restricted diffusion
experimental time
m.s.d.
Results of computer simulation (Monte-Carlo Method)
x
z
y
d

9. 9
Restricted Diffusion: Time
Dependence of D
x
Results of computer simulation (Monte-Carlo Method)
10
1
10
2
10
310
0
10
1
10
2
10
2
10
3
10
1
D
(texp
)~
texp
1
DiffusionCoefficient,D
experimental time
Free diffusion
Restricted diffusion
  1
expexpexp
2
exp
2
~,6
6








ttDDtd
dr
Dtr
z
y
d

10. 10
NMR-Diffusometry:
Initial Information Is in Diffusion Decays
0 1 2 3 4 5 6
10
-6
10
-4
10
-2
10
0
SINGLE-exponential
diffusion decay
NormilizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
 
 
 Dtq
qA
DtqA
A
A
exp
2exp
2
0 0
lnln 















0 1 2 3 4 5 6
0.4
0.5
0.6
0.7
0.8
0.9
1
NormalizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
DOUBLE-exp. decay:
D 1
= 2.7 x 10
-9
, D 2
= 7 x 10
-11
THREE-exp. decay:
D 1
= 2.7 x 10
-9
, D 2
= 7 x 10
-11
D 2
= 2 x 10
-13
SINGLE-exp. decay
D = 2.7 x 10
-9
  ii i Dtqp
A
A
exp
2
0
ln 






D

11. 11
NMR-Diffusometry:
Decay for Free Diffusion
Results of computer simulation (Monte-Carlo Method)
x
z
y
0 1 2 3
10
-4
10
-3
10
-2
10
-1
10
0
q
2
t exp
NormalizedAmplitude,A/A0
 Dtq
A
A
exp
2
0
ln 






12. 12
0.0 0.5 1.0 1.5 2.0
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
NormalizedAmplitude,A/A0
q
2
t exp
Free Diffusion
Restricted Diffusion
NMR-Diffusometry:
Decay for Restricted Diffusion
Results of computer simulation (Monte-Carlo Method)
z
y
d
  ii i Dtqp
A
A
exp
2
0
ln 







13. 13
NMR-Diffusometry:
Average Propagator
     
   exp..exp
....exp..exp
,,
2exp,,
trPFTinversetqA
drqritrPtqA
dsm
dsmdsmdsm

  
0.000 0.005 0.010
0.02
0.04
0.06
0.08
0.10
0.12
0.14
DisplacementProbabilityDistribution
Displasement
Free Diffusion
Restricted Diffusion
0.0 0.5 1.0 1.5 2.0
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
NormalizedAmplitude,A/A0
q
2
t exp
Free Diffusion
Restricted Diffusion
FFT
PROPAGATOR

14. 14
NMR-Diffusometry: Remarks
 q = g,
 is gyromagnetic ratio of resonant nuclear;
 and g – duration and amplitude of pulsed field
gradient, respectively;
 it is unnecessary to have a transparent sample (like
for optic methods) or sample with specially prepared
surface, and so on…
 NMR does not produce sufficient changes in sample
(remaining radiation, damaged pore structure…)
 typical limits for application of NMR are
extremely short relaxation times
 NMR experiment may take a few days

15. 15
NMR-Investigation of
Polymeric Porous Materials
experimental

16. 16
Samples:
 Porous PA-6 filled with water
 Porous polyelectrolyte complex
PEI / PAAc (multilayers) filled with
water
 Porous polyelectrolyte complex
PEI / PAAc (multilayers) produced in
NaCl solution, filled with water

17. 17
Equipment
 NMR spectrometer
Bruker AVANCE 500
operating on frequency 1H 500 MHz
 Diffusion probe Diff30
maximum g = 11.6 T/m
 t° = 22°C

18. 18
PA-6: Shape of Diffusion Decays
0 20 40 60 80 100
10
-2
10
-1
10
0
D 1
= 7 x 10
-12
m
2
/ s
p 1
= 0.011
NormalizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
t exp
= 400 ms
  ii i Dtqp
A
A
exp
2
0
ln 






10
-11
10
-10
10
-9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
freewaterD
free water part
relativepopulation,pi
,
takenbycomponentwithDi
Diffusion Coefficient, D i
, m
2
/ s

19. 19
PA-6: Time Dependence of D
0 20 40 60 80 100
10
-2
10
-1
10
0
50 60 70 80 90
0.005
0.006
0.007
0.008
NormalizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
t exp
300 ms
400 ms
500 ms
q
2
t exp
[ x 10
9
, m
2
s ]
A/A0
10
-1
10
02x10
-12
10
-11
d = ( 6 D texp
)
1/2
d = ( 4.2 ± 0.1 ) m
D ~ t exp
1
DiffusionCoefficient,D,m
2
/s
experimental time, t exp
, s

20. 20
PA-6: Molecular Exchange between
Water in Pores and Water outside Pores
0 10 20 30 40
0.01
0.02
0.03
0.04
Propagator,
DisplacementProbabilityDistribution
Displacement, m
t exp
400 ms
750 ms
900 ms
0.0 0.2 0.4 0.6 0.8 1.0
e
-5
e
-4
mean life-time of water inside pores
 = 1.1 s
water in pores
~ 2.5 %
relativepartofparticleslocatedinpores,pi
t exp
, s

21. 21
PEI / PAAc: Shape of Diffusion Decay
0 50 100 150 200 250 300
10
-3
10
-2
10
-1
10
0
NormalizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
PEI / PAA, t exp
= 400 ms
PA-6, t exp
= 400 ms
0 100 200 300
10
-3
10
-2
10
-1
10
0
NormalizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
t exp
400
600
800

22. 22
PEI / PAAc: Time-Dependence of
Diffusion Coefficient
0.1 1
10
-11
d = ( 6 D t exp
)
1/2
d = ( 5.6 ± 0.1 ) m
D ~ t exp
1
DiffusionCoefficient,D[m
2
/s]
Experimental Time, t exp
, s

23. 23
PEI / PAAc: To Question about
Molecular Exchange
0 10 20 30
0.00
0.01
0.02
0.03
0.04
0.05
0.06
Propagator,
DisplacementProbabilityDistribution
Displacement, m
PEI / PAAc, t exp
= 400 ms
PA-6, t exp
= 400 ms
0 10 20 30
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Displacement, m
Propagator,
DisplacementProbabilityDistribution
t exp
400 ms
600 ms
800 ms
Life-time of water molecules in the pore of PEI / PAAc is lager than
that for PA-6, at least, in a few times.

24. 24
PEI / PAAc Produced in Salt Solution:
Diffusion Decays and Dependence D(t)
100 400
1
2
3
4
5
6
7
8
9
10
d = ( 6 D t exp
)
1/2
=
= ( 5.8 ± 0.1 ) m
D ~ t exp
1
DiffusionCoefficient,D,[x10
11
,m
2
/s]
Experimental Time, t exp
, ms
0 10 20 30 40
10
-2
10
-1
10
0
NormalizedAmplitude,A/A0
q
2
t exp
[ x 10
9
, m
2
s ]
t exp
100 ms
150 ms
200 ms

25. 25
PEI / PAAc: To Question about
Molecular Exchange
0 10 20 30 40
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Propagator,
DisplacementProbabilityDistribution
Displacement, m
t exp
100 ms
150 ms
200 ms
0 5 10 15 20
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 5 10 15 20
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Propagator,
DisplacementProbabilityDistribution
Displacement, m
t exp
= 200 ms
PEI / PAAc
PEI / PAAc
in Salt-Solution
NormalizedPropagators
Displacement

26. 26
Conclusions
 NMR-diffusometry permits:
a) to obtain information about pore size;
b) to characterize features of translational
mobility of fluid molecules inside porous
medium and interaction between solid
matrix and fluid trough the study of
molecular exchange.

27. 27
Conclusions:
 polymeric membranes were studied:
a) the pore sizes were measured:
Material
Pore size,
μm
PA-6
PEI / PAAc
PEI / PAAc + NaCl
4.2±0.1
5.6±0.1
5.8±0.1

28. 28
Conclusions:
b) the materials produced on basis of PEI /
PAAc complex are characterized by the
lager relative part of water located in
pores than porous PA-6;
c) for PA-6, the molecular exchange
between water in pores and water
outside pores were found;
for material PEI / PAAc this effect was
not registered, for material PEI / PAAc
produced in salt-solution molecular
exchange may exist.