Characterization of Free volumes in Nano-scale Polymeric and Composite Membrane  Systems Using Positron

Annihilation Spectroscopy*

Y.C. Jean1,2

1Department of Chemistry, University of Missouri-Kansas City

2R&D Center for Membrane Technology and Department of Chemical Engineering, Chung-Yuan Christian

University, Taiwan Collaborators: NIST:T. Nguyen, X. Gu; AIST: R. Suzuki, T. Ohdaira; CMT: J.I.Lai, Y.M. Sun, R. Lee, C.C. Hu*Supports: NSF and NIST, Ministry of Education (Taiwan)

Outline

• Positron and Positronium Annihilation

• I. Positrons in Polymeric Nano-Scale Films

(1) Multi-Layer Structures

(2) Tg-depth dependence

• II. Polymeric Composite Membranes

(1) Surface layer structures

(2) Permeability and selectivity

The Positron

1930: Anti-electron (Positron) predicted by P.A.M. Dirac, Quantum Electrodynamics Theory.

1932: The Positron (positive electron), detected by C.D. Anderson in the cloud chamber from cosmic radiation.

1946: The Positronium atom (positron and electron bound state) detected by M. Deutch from positron annihilation in gases.

1960: Solid state physics: positron is localized in defects; positron is delocalized in lattices-Fermi surface.

1970: Nuclear medicine: positron emission tomography (PET)1975: Surface science: positron has a negative work function.1980-presence: Positron chemistry, material defect and surface tools.

Positron Annihilation Processes

1. When positron and electron meet, they can form Positronium (Ps). Positronium exists in two states, p-Ps (spins anti-aligned) and o-Ps (spins aligned): 2 photons (for p-Ps with 125 ps, or a few ns for pick-off with electrons with molecules) or 3 photon (for o-Ps 142 ns) produced by annihilation.

2. Positrons can freely annihilate with electrons without forming Ps with lifetime ~10-9 s to ∞ (in UHV 10-11 torr, live one hour).

3. The Feynman diagram shows that the annihilation distance starts 10-12.5 m (Δx~ħ/mc) and the time 10-21 s (t~ħ/mc2)-delta function and sudden approximation.

4. Annihilation characteristics depend on electron properties of matter.

Positron Annihilation Spectroscopy (PAS)

PAS monitors annihilation γ-rays properties, which are related to materials and electronic properties of systems studied. Four experimental techniques are currently used in PAS:

1. Positron annihilation lifetime spectroscopy (PAL): atomic and molecular free volumes and holes in polymers, solids.

2. Doppler broadening of annihilation energy spectroscopy (DBES): atomic defects in semiconductors, polymers.

3. Angular correlation of annihilation radiation (ACAR): Anisotropy structures of free volumes, defects, Fermi surface.

4. Variable mono-energetic positron beam: surface and interfaces.

PAS contains the most fundamental properties of molecules (chemistry):

wave function and electron density

• PAL measure positron annihilation lifetime τ:

τ= n |xyz n(x,y,z)* +(x,y,z) dxdydz |2

• DBES measures electrons’ momentum distributions at the longitudinal direction (z):

N(pz)=n pxpy |xy zn(r)* +(r) e-iP•r d r|2 dpxdpy

• 2D-ACAR measures electrons’ momentum distribution at the transverse directions (x,y):

N(px, py)=n pz|xy zn(r)* +(r) e-iP•r d r|2 dpz

Localization of positron and Ps

The Decay Scheme of 22Na

10Ne22

3 ps

0+

2+

E2

1.2746 EC 10%

+ 0.05%

+ 90%

+, EC

3+ 2.60 y

11Na22

0.511 MeV0.511 MeV

180 o

(e-e+)

-

Two-photon Annihilation of a Positron-Electron Annihilation Pair

Calibrated defect radius(Å)

0 i

EE i

)E(N

)E(NS

2

1

N(E

)

E( keV)

Low momentum (S-parameter)

E2E

1 511

S is a measure of defect property:

(1) Large hole Large Sp•x /2

(2) Large defect concentration large S

Doppler broadening S parameter

Positron Annihilation Lifetime

0 5 10 15 20 25

10

100

1000

10000

100000

ç3=1.8 ns

ç2=0.45 ns

ç1=0.125 ns

Cou

nts

Time (ns)

)BAI(Vf

)R

R2sin

2

1

R

R1(

2

1

3fv

1

003

tλii ieλIN(t)

Res

olve

d D

efec

t Siz

e

1 cm

1000

100

10

1

1000

100

10

1Å

OM

TEM X-ray Scattering

Positron Spectroscopy

1 Å 10 100 1000 1 10 100 1000

Depth

Mech

Def

ect C

once

ntra

tion

(pp

m)

10

OM TEM

X-ray Scattering

Positron Spectroscopy

1Å 10 100 1000 1 10 100 1000

Depth

Mech1%

1000

100

1 ppm

STM/AFM

STM/AFM

PAS can resolve size, concentration and distribution of atomic

scale defects

Comparison of PAS and other techniques

A sow positron beam (0- 30 keV) for depth profile (0-10 µm) of free volume

22Na e+ source 50mCi

Moderator

ExB e+ filter

Lifetime detector attachment

Sample chamber

S.S. Detector

Data acquisition system

Accelerator 0- 30kV

Magnetic coils 75G

Depth and dispersion of depth

6.10

400)( EEZ

Free-volume Concept in Macromolecules (polymers)

Free volume is the free moving (very fast, ps-ns) open space (very small, sub-nm) inside a molecule or system.

A simple expression of the free volume (Vf) can be written as the total volume (Vt) minus the “occupied volume” (V0):

Vf = Vt – V0

The existence of free volume (1-10%) makes polymers as the most widely used materials in our human life today.

Polymer film

Substrate

Diagram Of Nano-scale Polymeric Film On Substrate

1. Free-volume S-parameter for different thickness of polystyrene films on Si

0 5 10 15 20 25 300.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.50

S P

ara

me

ter

Positron Incident Energy (keV)

silicon 5 nm 12 nm 20 nm 30 nm 42 nm 55 nm thick film

8796459815175000

Thickness (nm)

S parameter spectrum and profilometry measurement on 80 nm PS film

Thickness (nm)

Density

(g/cm3)

e+ Diffusion length

(nm)

I and II 80 8 1.10 40 5

III 21 3 0.4 0.3 4 2

VEPFIT fitting result from S parameter spectrum

20 40 60 80 100 120 140 160 1801.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.8

2.9

3.0

3.1

3.2

3.3o

-Ps

life

time

(n

s

Temperature (°C)

Tg = 972 C

Ho

le R

ad

ius

(Å)

2. Tg of thick polystyrene film measured by conventional PAL spectroscopy

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.0

0.5

1.0

1.5

2.0

PD

F

Lifetime (ns)

30C 50C 80 C 90 C 110 C 130 C 150 C

3.50 3.64 3.773.353.203.032.86

Free Volume radius (Å)

Free volume distribution of thick PS film at different temperature, Spectchim Acta A,

61,1681, 2005

20 40 60 80 100 120 140 160

0.15

0.20

0.25

0.30

0.35

F

WH

M (Å

)

Temperature (ºC)

FWHM of free volume distribution of thick PS film as a function of temperature

200 400 600 800 1000100

101

102

103

104

105

C

ou

nts

Channel

0.3 keV 0.5 keV 0.7 keV 1.0 keV 1.5 keV 2.0 keV 3.0 keV 5.0 keV 10.0 keV

Raw PAL spectrum measured on thin 80 nm PS film on Si

0 2 4 6 8 101.5

2.0

2.5

3.0

0

10

20

30

40 3 (

ns)

Energy (keV)

o-PsLifetime

I 3 (%

)

0 210 640 1223Mean Depth (nm)

o-Ps intensity

o-Ps lifetime and intensity as a function of depth in 80 nm PS film

Depth profile of Free-volume distribution

A larger hole size and broader free-volume distribution near the surface are observed.

J. Phys. Cond. Matt. 10, 10429 (1998)—a lower Tg near the polymer surface.

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

P

DF

Lifetime (ns)

0.3 keV, surface (mean depth 5 nm) 0.5 keV, (mean depth 12 nm) 1 keV, center (mean depth 36 nm) 1.5 keV, interface (mean depth 70 nm) Bulk thick film

2.86 3.03 3.20 3.35 3.50 3.64 3.77

Free volume radius (Å)

Hole size distribution of 80 nm supported PS film at room temperature

20 40 60 80 100 120 140

2.0

2.2

2.4

2.6

2.8

3.0

3.2

5 nm, Tg =80 5C

36 nm, Tg =98 3 C

70 nm, Tg = 86 2 C

o-P

s lif

etim

e (

ns)

3.03

3.20

3.50

3.64

3.77

Fre

e V

olu

me

ra

diu

s (Å

)

Temperature (C)

2.86

3.35

Glass transition temperature determined from o-Ps lifetime result at different depth of the supported PS film

1.8 2.0 2.2 2.4 2.6 2.8 3.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P

DF

Lifetime (ns)

30 C 50 C 80 C 100C 115 C 130 C

2.67 2.86 3.03 3.20 3.35 3.50 3.64

Free volume radius (Å)

Free volume distribution of 80nm PS film at different temperature

3. FWHM of Free volume distribution of 80nm PS film as a function of temperature

Locations Tg (PAL)Vf/VfT

( below Tg), K-1

Vf/VfT

( above Tg), K-1

FWHM (Å)of free-volume

radiusdistribution

Surface (5 nm)of 80-nm film

80 ± 5ºCβg = 2.3 ± 0.3

×10-3

βr = 5.6 ± 0.4

×10-30.263 0.010

Center (36 nm)of 80-nm film

98 ± 3ºCβg = 1.6 ± 0.3 ×

10-3

r = 7.0 ± 0.4 ×10-

30.159 0.006

Interface (70 nm) of 80-nm film

86 ± 2ºCβg = 1.3 ± 0.2

×10-4

r = 6.7 ± 0.4 × 0-

30.167 0.008

Bulk of thick film 97 ± 2ºCβg = 2.0 ± 0.2 ×

10-3

βr= 6.2 ± 0.3 ×10-

30.156 0.005

Free-volume thermal expansion coefficients and FWHM of distribution in

an 80-nm polystyrene film.

Interpretation: Tg-depth dependence (suppression) in nano-

scale polymeric films:

• Free-volume is distributed at a different degree as a function of the depth

• Near the surface, the free-volume is distributed widest, therefore the Tg is the lowest

• At interface, the free-volume is distributed next widest, Tg is also suppressed.

• Loosely packing, end chains, incomplete entangling of chains, etc. lead to broad distribution.

I. PAS for polymers and nano-films

• PAS is a novel spectroscopic method in determining free-volume physical properties of polymers.

• PAS could provide sub-nano and nano-scopic free-volume size, fraction, distribution and structures.

• PAS is monitoring glass transition of polymer film as a function of depth from surface, films and interfaces.

• Tg is found to be 17 K lower near the surface and 11 K lower in interface than the center of the film.

• Tg suppression can be interpreted as the broadening of free-volume distribution in the surface and interfaces.

P: Permeability

S: Solubility

D: Diffusivity Coefficient

D=A exp(-B/FFV)

FFV: Fractional Free Volume

P’s unit is Barrer=1.0{10 -10 cm3 (STP) cm}/{cm Hg cm2 s}

II. Membrane Composites:

Permselectivity (A/B) of a polymer film is a ratio of permeability PA/PB

DSPB

A

B

A

B

A

DD

SS

pP

BA

)()(/

oMolecule A

Molecule B

Polymer

o

o

oo

o

o

oo

Polyamide Composite membrane: Pervaporation

polyamide composite membranes Interfacial polymerization

2 wt% aqueous TETA solution

Doping temperature: 50 oC

Doping time: 1, 5,10, 30 min

1 wt% TMC/ toluene solution

R. T. and 3 min(dried at R. T.)

Hydrolyzed PAN Polyamide thin-film

Free-volume distributions of base polymers

0.5 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

0.0

0.1

0.2

0.3

0.4

Dry PAN

Drym-PAN

Dry PA

3.32 Å

3.13 Å2.84 Å

3.88

P

DF

o-Ps lifetime (ns)

PAN Polyamide m-PAN

1.2 Å (water)

2.9 Å (isopropanol)

3.62

Free-volume radius (Å)3.343.022.662.221.66

Doppler Broadening Free-volume S (free-volume) and R (pore) parameters in PA and m-PAN membranes

0 5 10 15 20 25 300.450

0.455

0.460

0.465

0.470

0.475

0.480

S p

aram

eter

Positron Energy (keV)

PA m-PAN

0 0.53 1.59 4.35 6.90 9.86 13.2

Mean Depth (m)

Porous m-PANTransition from

dense skin to

porous m-PAN

dense skin

m-PAN

0 5 10 15 20 25 300.30

0.32

0.34

0.36

0.38

0.40

Transition layer from dense skin to porous m-PAN

2 annihilation dense skin in m-PAN

3 annilhilation: Large pores in m-PAN

PA m-PAN

R p

aram

eter

Positron Energy (keV)

0 0.53 1.59

Mean Depth (m)

4.35 6.90 9.86

3-Layer structure of m-PAN from PAS

0.45

0.46

0.47

0.48

0.49

Porous m-PAN layer

Dense

skin

m-PAN

Transition layerfrom dense skin to porous m-PAN

10.03.00.3

S p

ara

me

ter

Mean depth (m)

SEM Cross-section image of m-PAN

402 ± 70 nm

S free volume parameters for interfacial polymerized polyamide on m-PAN at different TETA doping time

0 5 10 15 20 25 30

0.450

0.455

0.460

0.465

0.470

0.475

0.480

0.485

S p

ara

me

ter

Positron Energy (keV)

doped 1min doped 5min doped 10min doped 30min

0 0.44 1.33 3.39 5.36 7.67 10.3

Mean Depth (m)

m-PAN

PA

dense skin to porousm-PAN

R (Pore) parameter of PA/m-PAN at different TETA doping time

0 5 10 15 20 25 300.28

0.30

0.32

0.34

0.36

0.38

PA Porous m-PANTransition layer from dense skin to porous m-PAN

7.365.123.221.660.54

Mean depth (m)

0

Doped 50oC

PA/m-PAN 30 min PA/m-PAN 10 min PA/m-PAN 5 min PA/m-PAN 1 min

R

par

amet

er

Positron incident energy (keV)

SEM skin thickness 100-500 µm249 ± 16 nm PA

326 ± 10 nm

203 ± 29 nm

186 ± 10 nm

402 ± 16 nm m-PAN skin

1 min

5 min

10 min

30 min

TETA doping time deceases PA film thickness: Both PAS and SEM data

0 5 10 15 20 25 30

0

50

100

150

200

250

300

350

400

PAS SEM

Doping time of TETA (min)

PA

th

ick

ne

ss

, PA

S (

nm

)

150

200

250

300

350

400

450

500

PA

th

ick

ne

ss

, SE

M (

nm

)

Three-layer structure of PA/m-PAN;1:PA (50-300 nm); 2:Transition skin to porous PAN (.5-4 µm); 3: porous PAN

0.45

0.46

0.47

0.48

0.49

Polyamidetop layer

3.0

Transition layer from dense skin toporous m-PAN

Porous m-PAN

10.00.2

S p

ara

met

er

Mean depth (m)

Polyamide top layer

Pervaporation performance of polyamide/PAN membranes

Polyamide skin layer of composite membranes reduced the permeation rate, but enhanced the selectivity of water effectively.

PA layer (1): Correlations

0 50 100 150 200 250 3001000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

Flux Water concentration

Thickness of the first layer, L1 (nm)

Flu

x (

g/m

2h

)

95

96

97

98

99

100

Wa

ter

co

nc

en

tra

tio

n in

pe

rme

ate

(w

t%)

0.460 0.462 0.464 0.466 0.4681000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

Flux Water concentration

S parameter in the first layer, S1

Flu

x (

g/m

2 h)

95

96

97

98

99

100

Wa

ter

co

nc

en

tra

tio

n in

pe

rme

ate

(w

t%)

1. PA thickness increases selectivity

2. Free-volume S decreases selectivity

PA layer (2): Correlations

1. Transition layer thickness increases selectivity

2. Less relationship between S (transition) and selectivity

0 1000 2000 3000 4000 5000 6000 70001000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

Flux Water concentration

Thickness of the second layer (nm)

Flu

x (

g/m

2h

)

95

96

97

98

99

100

Wa

ter

co

nc

en

tra

tio

n in

pe

rme

ate

(w

t%)

0.477 0.478 0.479 0.480 0.4811000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

Flux Water concentration

S parameter in the second layer, S2

Flu

x (g

/m2

h)

95

96

97

98

99

100

Wat

er c

on

cen

trat

ion

in p

erm

eate

(w

t%)

Temperature of TETA doping (25, 50, 70 o)Temperature increases PA thickness

0 5 10 15 20 25 300.44

0.45

0.46

0.47

0.48

0.49

7.365.123.221.660.54

Mean depth (m)

0

Doped 10 min:

PATFC021 : 25oC

PATFC025 : 50oC

PATFC003 : 70oC

S p

aram

eter

Positron incident energy (keV)

20 25 30 35 40 45 50 55 60 65 70 75

0.46

0.47

0.48

0.49

0.50

0.51

0.52

0

50

100

150

200

250

300

350

400

S parameter

S p

aram

eter

Temperature (oC)

Thi

ckne

ss (

nm)

Layer 1

Thickness

20 25 30 35 40 45 50 55 60 65 70 750.475

0.476

0.477

0.478

0.479

0.480

0.481

0.482

0

500

1000

1500

2000

2500

3000

3500

4000

S parameter

S p

ara

me

ter

Temperature (oC)

Th

ickn

ess

(n

m)

Layer 2

Thickness

Temp increases both layer 1 and layer 2 thickness but decreases free-volume S parameters

PA layer (1) correlations

0.46 0.47 0.48 0.49 0.50 0.51 0.52600

800

1000

1200

1400

1600

1800

2000

40

60

80

100

Flux

Flu

x (g

/m2 hr

)

S parameter (Layer 1)

Wa

ter

Co

ncen

trat

ion

(wt%

)

Water concentration

0 100 200 300 400500

1000

1500

2000

40

60

80

100

Flu

x (g

/m2 h

r)

Thickness L1 (nm)

Wa

ter

Co

nce

ntr

atio

n in

pe

rme

ate

(w

t%)

Flux

Water concentration

1. Flux (permeability) and S1 free-volume parameter follows D=A exp(-B/ffv)

2. Selectivity decreases as S1 and PA thickness increases

Transition layer (2) correlations

1. Flux (permeability) and S2 free-volume parameter follows D=A exp(-B/ffv)

2. Selectivity decreases as S2 and PA thickness increases

0.476 0.477 0.478 0.479 0.480600

800

1000

1200

1400

1600

1800

2000

40

60

80

100

Flux

Flu

x (g

/m2h

r)

S parameter (Layer 1)

Wa

ter

Co

nce

ntr

atio

n in

pe

rme

ate

(wt%

)

Water concentration

1. A 3-layer structure of the PAN membranes is determined: (1) Skin m-PAN (300-400 nm); (2) Transition larer from dense to porous PAN (2 µm)(3) Porous m-PAN

2. A 3-layer polyamide thin-film composite PAN membrane is(1) polyamide layer: a very near surface layer (50-300 nm)(2) Transition layer from dense to porous m-PAN (0.5-4 µm)(3) Porous m-PAN layer

3. Correlation between free volume S parameter and flux in the free-volume theory: Flux=A(-B/S)

4. Selectivity is mainly controlled by thickness of skin polyamide layer, and secondary affected by the transition layer.

5. Effect of free volume size and selectivity can be investigated using PAS

6. Future applications of PAS to membrane technology for RO and NF are promising.

II. Conclusions based on PA/m-PAN of pervaporation of membrane separation

Summary

I. Nano-scale polymeric films:(1) Depth and interfacial structures for layers and nano-

composite systems.(2) Tg-depth dependence of polymeric systems on

different substrates with different interfacial interactions and UV irradiations.

II. Membranes and coatings:(1) Free-volume depth profile of membranes and

coatings(2) Early detection of polymeric degradations.(3) Effects of free volume size and struture on

membrane performances (permeselectivities)

Jack Liu, Lakshmi Chakka, Dr. Jean, Dr.Hongmin Chen, Wassen