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Dielectric spectroscopy of glass-forming liquids under high pressure. M arian Paluch Institute of Physics Silesian University Katowice , POLAND. 10 10 s. 10 2 s. 10 -12 s. :. liquid. liquid-glass transition. crystallization. Volume. glass. crystal. T m. T g. Temperature.
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Dielectric spectroscopy of glass-forming liquidsunder high pressure MarianPaluch Institute of Physics Silesian University Katowice, POLAND
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
Crystallization and vitrification ; c 1 c 10-4 10-8 Temperature Tg Tm Marian Paluch Silesian University
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
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
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
Relaxation dynamics of supercooled liquids di-ethyl phthalate -process -process -process -process Marian Paluch Silesian University
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
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
Sorbitol Xylitol Threitol Glycerol Marian Paluch Silesian University
Isobaric fragility Definitions of fragility: What is the effect of pressure on mp? Marian Paluch Silesian University
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
Effect of pressure on glass transition temperature Andersson-Andersson relation: Marian Paluch Silesian University
The -relaxation time in P-T plane Marian Paluch Silesian University
A A’ B Cohen-Grest model Doolitle equation: free volume: where: Marian Paluch Silesian University
Tg=294 K Marian Paluch Silesian University
Adam-Gibbs model at P =0.1MPa VFT law: Tait equation: Marian Paluch Silesian University
Marian Paluch Silesian University
Marian Paluch Silesian University
Avramov model Assumption: Marian Paluch Silesian University
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
Master curve Marian Paluch Silesian University
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
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
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
Marian Paluch Silesian University
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
”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
Tg=311 K ”Excess wing” KDE Log fJG Marian Paluch Silesian University
Effect of pressure on „excess wing” Marian Paluch Silesian University
Two secondary relaxation processes eugenol Iso-eugenol Marian Paluch Silesian University
Relaxation map Behavior of excess wing below Tg Iso-eugenol Marian Paluch Silesian University
Behavior of the JG process during physical aging (t) dependence Marian Paluch Silesian University
Primary and secondary relaxation in DBP and DOP DBP DOP Marian Paluch Silesian University
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
The relaxation map in di-octyl phthalate Marian Paluch Silesian University
Effect of pressure on secondary relaxation processes di-ethyl phthalate di-butyl phthalate Marian Paluch Silesian University
Relaxation dynamics in DHIQ at ambient and elevated pressure DHIQ R. Richers, et. al. J. Chem. Phys. 2004. Marian Paluch Silesian University
Two secondary modes in DHIQ: which one is the JG process Marian Paluch Silesian University
DHIQ trans-DHIQ cis-DHIQ E=~40 KJ/mol Marian Paluch Silesian University