Diffusometry in polyelectrolyte membranes IPFDD2003

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

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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.