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

Investigation of Free Volume in Polymers by Positron Annihilation Lifetime Spectroscopy (PALS) Master Thesis by M. Qasim Shaikh Under supervision of Prof. Reinhard Krause-Rehberg Martin-Luther-Universität Halle-Wittenberg Fachbereich Physik

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 Page 02 of 25 Schematic representaion of a single Poly (Propylene) microstructure (X=76) (Simulation, Theodoru et al. 1985)

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 <v h > and mean dispersion σ h ) Pressure-Volume-Temperature-Experiments (PVT) Analysis by Simha-Somcynsky lattice-hole model EOS Fraction of vacancies h, specific hole free. = hv, and occupied volumes, V occ = (1-h)V Correlation of PALS and PVT allows estimation of PALS hole density = N h <v h > All parameters of the structure of hole free volume can be obtained from PALS and PVT Page 03 of 25

Basics of PALS Thermalization Diffusion Annihilation Page 04 of 25

Basic Principles and Theories of Positron Annihilation in Polymers Page 05 of 25

Ps Formation in Polymers β + source e + - - - - - - - - - Ps - - Page 06 of 25

Pick-Off Annihilation 0.5 nm Ps τ= 2-4 ns Ps localization in a hole of the (excess) free volume Ps τ = 1 ns Page 07 of 25 Ps localization in interstitial free volume gives the packing coefficient C of the crystals

Theory of Tau-Eldrup (TE) Model τ The height of the potential is infinity, and δr empirical parameter o Ps pickoff = 1 r Sources of Positron δr = 0.166 nm h rh + δ r o-ps lifetime τ po (ns) 0.5ns 1 2π r h + Sin 2π rh + δ r Page 08 of 25 10 9 8 Tao-Eldrup Standard Model 7 6 5 4 3 2 threshold 1 0 0 1 2 3 4 5 6 7 hole radius r h (Å) mean hole volume v h (τ 3 ) = (4/3)πr h3 (τ 3 )

The Positron Lifetime Measurement Page 09 of 25

Positron Laboratory at MLU Sources of Positron Page 10 of 25

Typical PALS Spectrum 1 2 3 PC Sources of Positron p-ps... τ 1 = 0,125 ns Free Annihilation τ 2 = 0,4 ns o-ps (Pick-off annihilation) τ 3 0,5 ns n(t) = I 1 exp(-t/τ 1 ) + I 2 exp(-t/τ 2 )+ I 3 exp(-t/τ 3 )

Typical Lifetimes in Holes of: Sources of Positron Page 12 of 25

Analysis of COC and PC Cyclo Olefin Copolymer (COC) Poly Carbonate (PC) Un-treated, Pressure Densified, and Gas Exposed. Page 13 of 25

V and V occ vs T (K) [PVT] V occ (cm 3 /g) V (cm 3 /g) 1.10 1.05 1.00 0.95 0.90 0.85 COC 0.1 V 40 80 (0) 120 160 200 (P) V occ 0.1 300 350 400 450 500 550 600 T (K) 200 V occ (cm 3 /g) V (cm 3 /g) 0.95 0.90 0.85 0.80 0.75 PC (0) (P) 300 350 400 450 500 550 600 T (K) V V occ 0.1 40 80 120 160 200 0.1 200 The specific total, V, (black open symbols), and occupied, V occ = (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 14 of 25

vs T(K) (cm 3 /g) 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 COC T 0 (0) (P) 0.00 250 300 350 400 450 500 550 600 T (K) 0.1 40 80 120 160 200 (cm 3 /g) 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 T 0 PC (0) (P) 0.00 250 300 350 400 450 500 550 600 T (K) 0.1 40 80 120 160 200 The specific hole free volume = hv as a function of temperature T and as selection of isobars (P in MPa) for COC and PC. Page 15 of 25

τ 3 and σ 3 vs T (K) [PALS] τ 3 (ns) 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 untreated gas-exposed densified τ 3 COC σ 3 300 350 400 450 500 T (K) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 σ 3 (ns) τ 3 (ns) 300 350 400 450 500 The mean, τ 3, and the mean dispersion, σ 3, 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. 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 untreated gas-exposed densified τ 3 T (K) PC σ 3 T k 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 σ 3 (ns) Page 16 of 25

Probability density function (pdf) [COC] hole radius pdf n(r h ) COC hole volume pdf g n (v h ) COC 2.0 2.5 3.0 3.5 4.0 4.5 r h (Å) 0 100 200 300 v h (Å 3 ) Probability density function (pdf) of the hole radius, n(r h ), and hole volume, g n (v h ), for COC. Blue: densified, red: gas-exposed, black: untreated samples at 300 K (lower curve) and 480 K (upper curve). Page 17 of 25

V h and σ h vs T(K) <v h > (Å 3 ) 160 140 120 100 80 60 40 COC <v h > 300 350 400 450 500 T (K) σ h 90 80 70 60 50 40 30 20 σ h (Å 3 ) <v h > (Å 3 ) 300 350 400 450 500 The mean, <v h >, and the mean dispersion, σ h, 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. 180 160 140 120 100 80 60 PC <v h > T (K) σ h 90 80 70 60 50 40 30 20 σ h (Å 3 ) Page 18 of 25

Hole density N h 0.11 0.10 COC 0.11 0.10 PC = <v h >N h ' (cm 3 /g) 0.09 0.08 0.07 0.06 0.05 = <v h >N h ' (cm 3 /g) 0.09 0.08 0.07 0.06 0.05 0.04 300 350 400 450 500 T (K) 300 350 400 450 500 T (K) The specific free volume = <v h >N h 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, = hv. 0.04 Page 19 of 25

( and V) vs V h (cm 3 /g) 0.14 0.13 0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04 COC 80 100 120 140 160 <v h > (Å 3 ) V = free volume V = total volume 1.06 1.04 1.02 1.00 0.98 V (cm 3 /g) Plots of the specific free, (T) (red), and total, V(T) (blue) volume vs. the mean hole volume <v h (T)> for COC and PC. Data from above are shown by filled symbols, those from below by empty symbols. (cm 3 /g) Page 20 of 25 0.12 0.10 0.08 0.06 0.04 = hv = N h <v h > V = V occ + N h <v h > PC 0.92 0.90 0.88 0.86 0.84 0.02 = free volume 0.82 V = total volume 0.00 80 100 120 140 160 0.80 180 <v h > (Å 3 ) V V (cm 3 /g)

Epoxy Resin (DGEBA) H 2 C O HC H 2 C O CH 3 OH CH 3 O C O CH 2 CH CH 2 O C O CH 2 CH CH 2 CH 3 n CH 3 Resin of diglycidyl ether of bisphenol-a (DGEBA) = free volume V = total volume Page 21 of 25

Epoxy Resin (DGEBA) σ h (Å 3 ) <v h > (Å 3 ) 160 140 120 100 80 60 40 20 DGEBA <v h > σ h T 0 ' ER1 0 50 100 150 200 250 300 350 400 T (K) The mean hole volume, <v h >, and the mean hole volume dispersion, σ h, as a function of the temperature T for ER6 (filled symbols) and ER1 (empty symbols). ER6 Page 22 of 25 ER1 - monomer of DGEBA (n 0.18 = 1 unit) ER6 - oligomer of DGEBA (n 5 = 6 units)

Polymethylphenylsiloxane (PMPS) σ h (Å 3 ) <v h > (Å 3 ) 160 140 120 100 80 60 40 20 0 <v h > σ h T k 100 150 200 250 300 350 T (K) The mean, <v h >, and the mean dispersion, σ h as a function of the temperature T for PMPS. Page 23 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 Kansy Institute of Physics and Chemistry of Metals, Silesian University, Katowice, Poland. Page 24 of 25