Dielectric spectroscopy of glass-forming liquids under high pressure Marian Paluch Institute of Physics Silesian University Katowice, POLAND

Marian PaluchSilesian University Crystallization and vitrification glass crystal liquid-glass transition TgTg TmTm Temperature liquid Volume :: s10 2 s s crystallization T ga T gb Temperature Volume Liquid glass  p =(  lnV /  T) p Enthalpy (H) Heat capacity (C p )

Marian PaluchSilesian University Crystallization and vitrification TgTg TmTm  cc Temperature   ;  c

PgPg Pressure Volume glass supercooled liquid Marian PaluchSilesian University Pressure  T =(  lnV /  p) T Liquid – glass transiton induced by pressure P3P3 P2P2 Temperature P 1 < P 2 < P 3 < P 4 TgTg P1P1 P4P4 Volume

F[Hz], C[pF], R[  ] Impedance Analyzer Thermal bath T[°C] P[bar] Pressure meter Hydraulic press High pressure chamber Tensometric sensor Valve Hz – 10 7 Hz Schematic illustration of the high pressure dielectric set-up Pressure range: up to 1 GPa Marian PaluchSilesian University

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

Relaxation dynamics of supercooled liquids di-ethyl phthalate  -process  -process  -process  -process Marian PaluchSilesian University

Marian PaluchSilesian University Van der Waals liuid DIBP H-bonded liquid Xylitol Polymer PMPS, M w =10k Temperature VFT law:Pressure VFT law: Activation volume:

Marian PaluchSilesian University Temperature dependence of activation volume Si CH 3 O n CH 3 Si CH 3 O n T g =246 K PTMPSPMPS T g =261 K BMMPC T g =261 K BMPC T g =240 K

Marian PaluchSilesian University SorbitolXylitol ThreitolGlycerol dT g /dPmpmp T g (at 100s) glycerol35± threitol33± xylitol34± sorbitol40±

Marian PaluchSilesian University Isobaric fragility Definitions of fragility: What is the effect of pressure on m p ?

Marian PaluchSilesian 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 PaluchSilesian University Effect of pressure on glass transition temperature MaterialdT g /dP (K/GPa) polystyrene303 [DTA] polymethylphenylsiloxane290 [Dielectric] Polyvinylchloride189 [PVT] Polyvinylacetate210 [DTA] 1,2-polybutadiene240 [Dielectric] BMPC240 [Dielectric] o-terphenyl (OTP)260 [DTA] Salol204 [Dielectric] PDE280 [Dielectric] glycerol35 [Dielctric] cyclohexanol40 [DTA] m-fluoroanilina81 [Dielectric] Andersson-Andersson relation:

Marian PaluchSilesian University The  -relaxation time in P-T plane

Doolitle equation: A A’ B Cohen-Grest model free volume: where: Marian PaluchSilesian University

Marian PaluchSilesian University T g =294 K

Adam-Gibbs model at P =0.1MPa VFT law: Tait equation: Marian PaluchSilesian University

Marian PaluchSilesian University

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Avramov model Assumption: Marian PaluchSilesian University

Marian PaluchSilesian University Equation of state: model of Avramov Where:  0 is volume expansion coefficient at ambient pressure, C p is specific heat capacity, V m is the molar volume and  is a constant parameter Predictions of the Avramov model Non-linear increase of T g with pressurePressure independence of fragilty with

Marian PaluchSilesian University Master curve

Cooperative rearrangement can be visualized as a collective displacement, involving more than two molecules, along the trajectory to form a closed loop Consequently, the sum of the displacements of all molecules involved in the process is zero T. Pakula, J. Mol. Liq. 86, 109 (2000) 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 The Dynamic Liquid Lattice model of Pakula model Marian PaluchSilesian University

Marian PaluchSilesian University 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: A local volume v is assigned to each molecule. This volume can fluctuate, assuming values not smaller than a minimum volume v 0. The excess volume has an exponential distribution: Molecular transport is driven by a thermally activated process with potential energy barriers E(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:

Marian PaluchSilesian University Herein we consider a linear decrease of the activation energy from E a1 to E a2 in the range between v 0 and v c, as depicted schematically in Figure E a1 E a2 VV0V0 VCVC

Marian PaluchSilesian University

Marian PaluchSilesian University The secondary relaxation process The molecular mechanism underlying the secondary relaxation in various glass formers can be very different. 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 Johari-Goldstein process A prediction concerning the JG relaxation time  JG comes from the coupling model of Ngai

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

Marian PaluchSilesian University KDE T g =311 K ”Excess wing” Log f JG

Marian PaluchSilesian University Effect of pressure on „excess wing”

Marian PaluchSilesian University Iso-eugenol Two secondary relaxation processes eugenol

Marian PaluchSilesian University Iso-eugenol Behavior of excess wing below T g Relaxation map

Marian PaluchSilesian University Behavior of the JG process during physical aging   (t) dependence

Marian PaluchSilesian University Primary and secondary relaxation in DBP and DOP DBP DOP

Marian PaluchSilesian University Aging at T=-96 o C The excess wing in DOP is the JG process Two secondary relaxation processes in DBP and DOP

Marian PaluchSilesian University The relaxation map in di-octyl phthalate

Marian PaluchSilesian University di-ethyl phthalate di-butyl phthalate Effect of pressure on secondary relaxation processes

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

Marian PaluchSilesian University Two secondary modes in DHIQ: which one is the JG process

DHIQ E  =~40 KJ/mol trans-DHIQcis-DHIQ Marian PaluchSilesian University