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Dielectric spectroscopy of glass-forming liquids under high pressure

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  1. Dielectric spectroscopy of glass-forming liquidsunder high pressure MarianPaluch Institute of Physics Silesian University Katowice, POLAND

  2. 1010s 102s 10-12s : liquid liquid-glass transition crystallization Volume glass crystal Tm Tg Temperature Crystallization and vitrification Enthalpy (H) Volume Tga Tgb Temperature Liquid p=(lnV / T)p Heat capacity (Cp) glass Temperature Marian Paluch Silesian University

  3. Crystallization and vitrification ; c 1 c 10-4  10-8 Temperature Tg Tm Marian Paluch Silesian University

  4. supercooled liquid Volume T=(lnV / p)T glass P1 < P2 < P3 < P4 Pg P1 Pressure P2 Tg P3 P4 Volume Temperature Liquid – glass transiton induced by pressure Pressure Marian Paluch Silesian University

  5. Impedance Analyzer Pressure meter Hydraulic press F[Hz], C[pF], R[] P[bar] 10-2Hz – 107 Hz High pressure chamber T[°C] Tensometric sensor Thermal bath Valve Schematic illustration of the high pressure dielectric set-up Pressure range: up to 1 GPa Marian Paluch Silesian University

  6. Pressure range: up to 10GPa Pressure range: up to 2GPa Force The sample is confined between the carbidge anvils by gasket made of plastic force Bakelite block Steel block tungsten carbide anvil The gaskets were: Epoxy-fiber laminates (<5GPA) Sheets of polystyrene (>5GPA) Steel block Bakelite block G. P. Johari and E. Whalley Faraday Symp. Chem. Soc.1971 force Marian Paluch Silesian University

  7. Relaxation dynamics of supercooled liquids di-ethyl phthalate -process -process -process -process Marian Paluch Silesian University

  8. Temperature VFT law: Pressure VFT law: Activation volume: Van der Waals liuid DIBP H-bonded liquid Xylitol Polymer PMPS, Mw=10k Marian Paluch Silesian University

  9. C H C C H H 3 3 3 S i O S i O n n Tg=261 K Tg=240 K Temperature dependence of activation volume BMMPC BMPC PMPS PTMPS Tg=246 K Tg=261 K Marian Paluch Silesian University

  10. Sorbitol Xylitol Threitol Glycerol Marian Paluch Silesian University

  11. Isobaric fragility Definitions of fragility: What is the effect of pressure on mp? Marian Paluch Silesian University

  12. Effect of pressure on fragility It is usually observed that fragility decreases with increasing pressure in the case of Van der Waals liquids. Van der Waals liquids Effect of pressure on fragilty is often much more complex for H-bonded than for Van der Waals liquids. Marian Paluch Silesian University

  13. Effect of pressure on glass transition temperature Andersson-Andersson relation: Marian Paluch Silesian University

  14. The -relaxation time in P-T plane Marian Paluch Silesian University

  15. A A’ B Cohen-Grest model Doolitle equation: free volume: where: Marian Paluch Silesian University

  16. Tg=294 K Marian Paluch Silesian University

  17. Adam-Gibbs model at P =0.1MPa VFT law: Tait equation: Marian Paluch Silesian University

  18. Marian Paluch Silesian University

  19. Marian Paluch Silesian University

  20. Avramov model Assumption: Marian Paluch Silesian University

  21. Equation of state: model of Avramov Where: 0is volume expansion coefficient at ambient pressure, Cpis specific heat capacity, Vmis the molar volume and is a constant parameter Predictions of the Avramov model Pressure independence of fragilty Non-linear increase of Tg with pressure with Marian Paluch Silesian University

  22. Master curve Marian Paluch Silesian University

  23. The Dynamic Liquid Lattice model of Pakula model Cooperative rearrangement can bevisualized as a collective displacement, involving more than two molecules, along the trajectory to form a closed loop Unsuccessful attemt when neighboring elements try to move in opposite dire- ction Unsuccessful attempt because the element in the center will not be replaced by any of the neighbors Consequently, the sum of the displacements of all molecules involved in the process is zero T. Pakula, J. Mol. Liq. 86, 109 (2000) Marian Paluch Silesian University

  24. Molecular transport is driven by a thermally activated process with potential energy barriersE(v) dependent on the local density of the system. The probability for a molecule to take part in a local rearrangement is given by the Boltzman factor: A local volume v is assigned to each molecule. This volume can fluctuate, assuming values not smaller than a minimum volume v0. The excess volume has an exponential distribution: The probability that a given molecule participates in the collective displacement determines  In order to obtain an explicit temperature dependence of the relaxation times, Pakula assumed: Marian Paluch Silesian University

  25. Ea1 Ea2 V0 VC V Herein we consider a linear decrease of the activation energy from Ea1 to Ea2in the range between v0 and vc, as depicted schematically in Figure Marian Paluch Silesian University

  26. Marian Paluch Silesian University

  27. The secondary relaxation process Intermolecular origin (motion of the entire molecule as a whole) Trivial intramolecular origin (rotational motion of a small isolated group of the entire molecule) The molecular mechanism underlying the secondary relaxation in various glass formers can be very different. The Johari-Goldstein process A prediction concerning the JG relaxation time JG comes from the coupling model of Ngai Marian Paluch Silesian University

  28. ”Excess wing” Type A – „excess wing” • KDE • PDE • BMMPC • Salol • Glycerol • Propylen carbonate, PC Two types of glasses: Type B – well resolved  peak • Sorbitol • Xylitol • Di-butyl phthlate • Di-ethyl phthalate • BMPC PC Tg=159 K Aging Lunkenheimer, et. al., PRL Excess wing Marian Paluch Silesian University

  29. Tg=311 K ”Excess wing” KDE Log fJG Marian Paluch Silesian University

  30. Effect of pressure on „excess wing” Marian Paluch Silesian University

  31. Two secondary relaxation processes eugenol Iso-eugenol Marian Paluch Silesian University

  32. Relaxation map Behavior of excess wing below Tg Iso-eugenol Marian Paluch Silesian University

  33. Behavior of the JG process during physical aging (t) dependence Marian Paluch Silesian University

  34. Primary and secondary relaxation in DBP and DOP DBP DOP Marian Paluch Silesian University

  35. Two secondary relaxation processes in DBP and DOP The excess wing in DOP is the JG process Aging at T=-96 oC Marian Paluch Silesian University

  36. The relaxation map in di-octyl phthalate Marian Paluch Silesian University

  37. Effect of pressure on secondary relaxation processes di-ethyl phthalate di-butyl phthalate Marian Paluch Silesian University

  38. Relaxation dynamics in DHIQ at ambient and elevated pressure DHIQ R. Richers, et. al. J. Chem. Phys. 2004. Marian Paluch Silesian University

  39. Two secondary modes in DHIQ: which one is the JG process Marian Paluch Silesian University

  40. DHIQ trans-DHIQ cis-DHIQ E=~40 KJ/mol Marian Paluch Silesian University