Master Thesis

by M. Qasim Shaikh

Under supervision of

Prof. Reinhard Krause-Rehberg

Investigation of Free Volume in Polymers by Positron Annihilation Lifetime Spectroscopy (PALS)

Martin-Luther-Universität

Halle-Wittenberg

Fachbereich Physik

Page 02 of 25

Structure of the free volume

• free volume due to structural, static or dynamic, disorder

• important for several macroscopic properties of these materials,

• viscosity, molecular transport, structural relaxation, and physical aging

Schematic representaion of a single Poly (Propylene) microstructure (X=76)

(Simulation, Theodoru et al. 1985)

Page 03 of 25

Experimental Ways to determine Free Volume in Polymers

• Positron Annihilation Lifetime Spectroscopy (PALS)– Detection of subnanometric local free volumes (holes):

Size distribution (mean hole volume <vh> and mean dispersion σh)

• Pressure-Volume-Temperature-Experiments (PVT)Analysis by Simha-Somcynsky lattice-hole model EOS

– Fraction of vacancies h, specific hole free. Vf = hV, and occupiedvolumes, Vocc = (1-h)V

• Correlation of PALS and PVT– allows estimation of PALS hole density Vf = Nh´<vh>

→ All parameters of the structure of hole freevolume can be obtained from PALS and PVT

Page 04 of 25

Basics of PALS

•Thermalization

•Diffusion

•Annihilation

Page 05 of 25

Basic Principles and Theories of Positron Annihilation in Polymers

Page 06 of 25

Ps

Ps Formation in Polymers

-

--

-

----

---

e+

β+ source

Page 07 of 25

Pick-Off Annihilation

Ps

= 2 - 4 ns

τ = 1 ns

τ

Ps

0.5 nm

Ps localization in a hole of the (excess) freevolume

Ps localization in interstitial free volumegives the packing co-efficient ´C´ of thecrystals

Page 08 of 25

Theory of Tau-Eldrup (TE) Model

Sources of Positron

The height of the potential is infinity, and δr – empirical parameter δr = 0.166 nm

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+

++

−

=−

rrrSin

rrr

ns

h

h

h

hpickoffPso

δπ

πδ

τ2

211

5.00 1 2 3 4 5 6 7

0123456789

10

o-Ps

life

time τ p

o (ns

)hole radius rh (Å)

Tao-Eldrup Standard Model

threshold

mean hole volume

vh(τ3) = (4/3)πrh3(τ3)

Page 09 of 25

The Positron Lifetime Measurement

Page 10 of 25

Positron Laboratory at MLU

Sources of Positron

.......

Typical PALS Spectrum

Sources of Positron2

3

1

n(t) = I1 exp(-t/τ1) + I2 exp(-t/τ2)+ I3 exp(-t/τ3)

p-Ps

τ1 = 0,125 ns

Free Annihilation

τ2 = 0,4 ns

o-Ps (Pick-offannihilation)

τ3 › 0,5 ns

PC

Page 12 of 25

Typical Lifetimes in Holes of:

Sources of PositronSources of Positron

Page 13 of 25

Analysis of COC and PC

Cyclo Olefin Copolymer (COC) Poly Carbonate (PC)

• Un-treated,

• Pressure Densified, and

• Gas Exposed.

Page 14 of 25

V and Vocc vs T (K) [PVT]

300 350 400 450 500 550 6000.85

0.90

0.95

1.00

1.05

1.10

Tg(P)

Voc

c (cm

3 /g)

V

(cm

3 /g)

T (K)

COC 0.14080

120160200

0.1

200

V

Vocc

Tg(0)

300 350 400 450 500 550 600

0.75

0.80

0.85

0.90

0.95

Tg(P)

Voc

c (cm

3 /g)

V (c

m3 /g

)

T (K)

PC

Vocc

V0.14080

120160200

0.1

200

Tg(0)

The specific total, V, (black open symbols), and occupied, Vocc = (1 – h)V(blue symbols) volume as a function of temperature T and as selection of isobars (P in MPa) for COC and PC.

Page 15 of 25

Vf vs T(K)

The specific hole free volume Vf = hV as a function of temperature T and as selection of isobars (P in MPa) for COC and PC.

250 300 350 400 450 500 550 6000.000.020.040.060.080.100.120.140.160.18

Tg(P)

Tg(0)

Vf (c

m3 /g

)

T (K)

COC

T0

Vf0.14080

120160200

250 300 350 400 450 500 550 6000.000.020.040.060.080.100.120.140.16

Tg(P)

Tg(0)

Vf (c

m3 /g

)T (K)

T0

PCVf

0.14080

120160200

Page 16 of 25

τ3 and σ3 vs T (K) [PALS]

The mean, τ3, and the mean dispersion, σ3, of o-Ps lifetimes as a function of temperature T for densified at 200 MPa (blue), gas-exposed (read) and untreated (black) COC and PC.

300 350 400 450 5001.4

1.6

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

σ3

σ3 (n

s)

τ3 (n

s)

T (K)

τ3

Tg

untreated gas-exposeddensified

COC

300 350 400 450 5001.41.61.82.02.22.42.62.83.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Tk

untreated gas-exposeddensified

σ 3 (ns)

τ3 (n

s)

T (K)

PC

Tg

τ3

σ3

Page 17 of 25

Probability density function (pdf) [COC]

Probability density function (pdf) of the hole radius, n(rh), and hole volume, gn(vh), for COC. Blue: densified, red: gas-exposed, black: untreated samples at 300 K (lower curve) and 480 K (upper curve).

2.0 2.5 3.0 3.5 4.0 4.5

hole

radi

us p

df n

(r h)

rh (Å)

COC

0 100 200 300

hole

vol

ume

pdf g

n(vh)

vh (Å3)

COC

Probability density function (pdf) [COC]

Page 18 of 25

Vh and σh vs T(K)

The mean, <vh>, and the mean dispersion, σh, of the hole volume as a function of temperature T for densified at 200 MPa (blue), gas-exposed (red) and untreated (black) COC and PC.

300 350 400 450 50040

60

80

100

120

140

160

20

304050

607080

90

σ h (Å3 )

<vh>

(Å3 )

T (K)

σh

<vh>

COC

Tg

300 350 400 450 500

60

80

100

120

140

160

180

20

30

40

50

60

70

80

90

σ h (Å3 )

<vh>

(Å3 )

T (K)

PC

Tg

<vh>

σh

Page 19 of 25

Hole density Nh’

The specific free volume Vf = <vh>Nh’ from PALS at 10-5 Pa as a function of temperature for untreated (black filled circles), densified at 200 MPa (blue squares), and gas-exposed (read diamonds) COC and PC. The black empty circles show 0.1 MPa isobars from PVT experiments for the untreated polymers, Vf = hV.

300 350 400 450 5000.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

Vf =

<v h>N

h' (cm

3 /g)

T (K)

COC

300 350 400 450 5000.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

V f = <

v h>Nh' (

cm3 /g

)T (K)

PC

Page 20 of 25

(Vf and V) vs Vh

Plots of the specific free, Vf(T) (red), and total, V(T) (blue) volume vs. the mean hole volume <vh(T)> for COC and PC. Data from above Tg are shown by filled symbols, those from below by empty symbols.

80 100 120 140 1600.040.050.060.070.080.090.100.110.120.130.14

0.98

1.00

1.02

1.04

1.06

V (c

m3 /g

)

Vf (c

m3 /g

)

<vh> (Å3)

V

COC

Vf

80 100 120 140 160 1800.00

0.02

0.04

0.06

0.08

0.10

0.12

0.80

0.82

0.84

0.86

0.88

0.90

0.92

V

V (c

m3 /g

)Vf (c

m3 /g

)

<vh> (Å3)

PC

Vf

(Vf and V) vs Vh

Vf = hV = Nh’<vh>

V = Vocc + Nh’<vh>

Vf = free volumeV = total volume

Vf = free volumeV = total volume

Page 21 of 25

Epoxy Resin (DGEBA)Epoxy Resin (DGEBA)

O CH2 CH CH2

OH

OH2CHCH2C

O

CCH3

CH3

O CH2 CH CH2

O

O CCH3

CH3

n

Resin of diglycidyl ether of bisphenol-A (DGEBA)

Vf = free volumeV = total volume

Page 22 of 25

Epoxy Resin (DGEBA)

The mean hole volume, <vh>, and the mean hole volume dispersion, σh, as a function of the temperature T for ER6 (filled symbols) and ER1 (empty symbols).

50 100 150 200 250 300 350 4000

20

40

60

80

100

120

140

160

ER1

T0'

σ h (Å3 )

<vh>

(Å3 )

T (K)

DGEBA

<vh>

σh

Tg

ER6

Epoxy Resin (DGEBA)

ER1 - monomer of DGEBA (n ≈ 0.18 = 1 unit)

ER6 - oligomer of DGEBA (n ≈ 5 = 6 units)

Page 23 of 25

Polymethylphenylsiloxane (PMPS)

The mean, <vh>, and the mean dispersion, σh as a function of the temperature T for PMPS.

100 150 200 250 300 3500

20406080

100120140160

Tk

σ h (Å3 )

<

v h> (Å

3 )

T (K)

Tg

<vh>

σh

Polymethylphenylsiloxane (PMPS)

Page 24 of 25

Acknowledgement

Emeritus Prof. Günter Dlubek,ITA Institut für innovative Technologien GmbH, Halle, Germany.

Prof. Reinhard Krause-Rehberg,Fachbereich Physik, Martin-Luther University, Halle, Germany.

Dr. Jürgen Pionteck, Leibniz Institut für Polymerforschung, e.V., Dresden, Germany.

Dr. Doz. Dr. habil. Marian Paluch, Institute of Physics, Silesian University, Katowice, Poland,

Dr. Jerzy KansyInstitute of Physics and Chemistry of Metals, Silesian University, Katowice, Poland.

Acknowledgement