investigation of free volume in polymers by positron annihilation...
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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
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