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1
NMR-Investigation of Structure of Polymeric Multilayer Membranes and Fluid Mobility inside Membranes
Results of NMR-diffusometry
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
Why can NMR-diffusometry be used as a microscopy?
introduction
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
Measurement of characterization
SOLID MATRIX
5
Diffusometry as a microscopy‘Free-moving’ fluid molecules (gas, liquid)
Interactions with solid matrix (restrictions)
Fluid molecules interacted with wall of
solid matrix
Measurement of diffusion coefficient
SOLID MATRIX (porous medium)
6
Free diffusion: Time Dependence of Mean Square Displacement
0 100 200 300 400 500 6000
20
40
60
80
100
120
140
Monte-Carlo result Einstein formula
experimental time
m. s
. d.
Results of computer simulation (Monte-Carlo Method)
exp2
exp2 ...,6 trdsmDtr
x
zy
Diffusion coefficient Experimental time
7
Free diffusion: Time Dependence of Diffusion Coefficient D
exp2 6Dtr
0 100 200 300 400 500 600
20
30
40
50
D ( t exp ) = const ( t exp )
Diff
usio
n C
oeffi
cien
t, D
experimental time
Results of computer simulation (Monte-Carlo Method)
x
zy
8
Restricted Diffusion: Time Dependence of Mean Square Displacement
0 100 200 300 400 500 6000
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
zy
d
9
Restricted Diffusion: Time Dependence of D
x
Results of computer simulation (Monte-Carlo Method)
101 102 103100
101
102
102 103
101
D ( t exp ) ~ t
exp 1
Diff
usio
n C
oeffi
cien
t, D
experimental time
Free diffusion Restricted diffusion
1expexpexp2
exp2
~,66
ttDDtd
dr
Dtr
zy
d
10
NMR-Diffusometry:Initial Information Is in Diffusion Decays
0 1 2 3 4 5 6
10-6
10-4
10-2
100
SINGLE-exponentialdiffusion decay
Nor
mili
zed
Am
plitu
de, A
/ A
0
q 2 t exp [ x 10 9 , m 2 s ]
DtqqADtqA
AA
exp2exp
2
0 0lnln
0 1 2 3 4 5 60.4
0.5
0.6
0.7
0.8
0.9
1
Nor
mal
ized
Am
plitu
de, A
/ A
0
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 DtqpAA
exp2
0ln
D
11
NMR-Diffusometry:Decay for Free Diffusion
Results of computer simulation (Monte-Carlo Method)
x
zy
0 1 2 3
10-4
10-3
10-2
10-1
100
q 2 t exp
Nor
mal
ized
Am
plitu
de, A
/ A
0
DtqAA
exp2
0ln
12
0.0 0.5 1.0 1.5 2.010-5
10-4
10-3
10-2
10-1
100
Nor
mal
ized
Am
plitu
de, A
/ A
0
q 2 t exp
Free Diffusion Restricted Diffusion
NMR-Diffusometry:Decay for Restricted Diffusion
Results of computer simulation (Monte-Carlo Method)zy
d
ii i DtqpAA
exp2
0ln
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
Dis
plac
emen
t Pro
babi
lity
Dis
tribu
tion
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
100
Nor
mal
ized
Am
plitu
de, A
/ A
0
q 2 t exp
Free Diffusion Restricted Diffusion
FFT
PROPAGATOR
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
NMR-Investigation of Polymeric Porous Materials
experimental
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
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
PA-6: Shape of Diffusion Decays
0 20 40 60 80 100
10-2
10-1
100
D 1 = 7 x 10 -12 m 2 / s
p 1 = 0.011
Nor
mal
ized
Am
plitu
de, A
/ A
0
q 2 t exp [ x 10 9 , m 2 s ]
t exp
= 400 ms
ii i DtqpAA
exp2
0ln
10-11 10-10 10-90.0
0.1
0.2
0.3
0.4
0.5
0.6
free water D
free water part
rela
tive
popu
latio
n, p
i ,
take
n by
com
pone
nt w
ith D
i
Diffusion Coefficient, D i , m 2 / s
19
PA-6: Time Dependence of D
0 20 40 60 80 100
10-2
10-1
100
50 60 70 80 90
0.005
0.006
0.007
0.008
Nor
mal
ized
Am
plitu
de, A
/ A
0
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 /
A 0
10-1 1002x10-12
10-11
d = ( 6 D texp
)1/2 d = ( 4.2 ± 0.1 ) m
D ~ t exp
1
Diff
usio
n C
oeffi
cien
t, D
, m
2 / s
experimental time, t exp , s
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
Pro
paga
tor ,
Dis
plac
emen
t Pro
babi
lity
Dis
tribu
tion
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 %
rela
tive
part
of p
artic
les
loca
ted
in p
ores
, p i
t exp
, s
21
PEI / PAAc: Shape of Diffusion Decay
0 50 100 150 200 250 300
10-3
10-2
10-1
100
Nor
mal
ized
Am
plitu
de, A
/ A
0
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
100
Nor
mal
ized
Am
plitu
de, A
/ A
0
q 2 t exp [ x 10 9 , m 2 s ]
t exp
400 600 800
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
Diff
usio
n C
oeffi
cien
t, D
[ m
2 / s
]
Experimental Time, t exp
, s
23
PEI / PAAc: To Question about Molecular Exchange
0 10 20 300.00
0.01
0.02
0.03
0.04
0.05
0.06
Pro
paga
tor,
Dis
plac
emen
t Pro
babi
lity
Dis
tribu
tion
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
Pro
paga
tor,
Dis
plac
emen
t Pro
babi
lity
Dis
tribu
tion
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
PEI / PAAc Produced in Salt Solution:Diffusion Decays and Dependence D(t)
100 4001
2
3
4
56789
10
d = ( 6 D t exp ) 1/2=
= ( 5.8 ± 0.1 ) m
D ~ t exp1
Diff
usio
n C
oeffi
cien
t, D
, [ x
10
11 ,
m 2 /
s ]
Experimental Time, t exp, ms0 10 20 30 40
10-2
10-1
100
Nor
mal
ized
Am
plitu
de, A
/ A
0
q 2 t exp [ x 10 9 , m 2 s ]
t exp
100 ms 150 ms 200 ms
25
PEI / PAAc: To Question about Molecular Exchange
0 10 20 30 400.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Pro
paga
tor,
Dis
plac
emen
t Pro
babi
lity
Dis
tribu
tion
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
Pro
paga
tor,
Dis
plac
emen
t Pro
babi
lity
Dis
tribu
tion
Displacement, m
t exp = 200 ms PEI / PAAc PEI / PAAc
in Salt-Solution
Nor
mal
ized
Pro
paga
tors
Displacement
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
Conclusions:
polymeric membranes were studied: a) the pore sizes were measured:
Material Pore size,μm
PA-6PEI / PAAc
PEI / PAAc + NaCl
4.2±0.15.6±0.15.8±0.1
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.