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

Transcription

1 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

2 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)

3 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

4 Basics of PALS Thermalization Diffusion Annihilation Page 04 of 25

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

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

7 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

8 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 = 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 Tao-Eldrup Standard Model threshold hole radius r h (Å) mean hole volume v h (τ 3 ) = (4/3)πr h3 (τ 3 )

9 The Positron Lifetime Measurement Page 09 of 25

10 Positron Laboratory at MLU Sources of Positron Page 10 of 25

11 Typical PALS Spectrum 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 )

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

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

14 V and V occ vs T (K) [PVT] V occ (cm 3 /g) V (cm 3 /g) COC 0.1 V (0) (P) V occ T (K) 200 V occ (cm 3 /g) V (cm 3 /g) PC (0) (P) T (K) V V occ 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

15 vs T(K) (cm 3 /g) COC T 0 (0) (P) T (K) (cm 3 /g) T 0 PC (0) (P) T (K) 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

16 τ 3 and σ 3 vs T (K) [PALS] τ 3 (ns) untreated gas-exposed densified τ 3 COC σ T (K) σ 3 (ns) τ 3 (ns) 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 untreated gas-exposed densified τ 3 T (K) PC σ 3 T k σ 3 (ns) Page 16 of 25

17 Probability density function (pdf) [COC] hole radius pdf n(r h ) COC hole volume pdf g n (v h ) COC r h (Å) 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

18 V h and σ h vs T(K) <v h > (Å 3 ) COC <v h > T (K) σ h σ h (Å 3 ) <v h > (Å 3 ) 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 PC <v h > T (K) σ h σ h (Å 3 ) Page 18 of 25

19 Hole density N h COC PC = <v h >N h ' (cm 3 /g) = <v h >N h ' (cm 3 /g) T (K) 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 Page 19 of 25

20 ( and V) vs V h (cm 3 /g) COC <v h > (Å 3 ) V = free volume V = total volume 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 = hv = N h <v h > V = V occ + N h <v h > PC = free volume 0.82 V = total volume <v h > (Å 3 ) V V (cm 3 /g)

21 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

22 Epoxy Resin (DGEBA) σ h (Å 3 ) <v h > (Å 3 ) DGEBA <v h > σ h T 0 ' ER 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)

23 Polymethylphenylsiloxane (PMPS) σ h (Å 3 ) <v h > (Å 3 ) <v h > σ h T k 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

24 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