Dielectric spectroscopy of glass-forming liquids under high pressure

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Dielectric spectroscopy of glass-forming liquids
under high pressure
Marian Paluch Institute of Physics Silesian
University Katowice, POLAND
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Crystallization and vitrification
Enthalpy (H)
Volume
Tga
Tgb
Temperature
Liquid
?p(?lnV / ?T)p
Heat capacity (Cp)
glass
Temperature
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Crystallization and vitrification
?? ?c
1
?c
10-4
??
10-8
Temperature
Tg
Tm
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Liquid glass transiton induced by pressure
Pressure
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Schematic illustration of the high pressure
dielectric set-up
Pressure range up to 1 GPa
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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 (lt5GPA)
Sheets of polystyrene (gt5GPA)
Steel block
Bakelite block
force
G. P. Johari and E. Whalley Faraday Symp. Chem.
Soc.1971
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?-process
?-process
?-process
?-process
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Temperature VFT law
Pressure VFT law
Activation volume
Van der Waals liuid DIBP
H-bonded liquid Xylitol
Polymer PMPS, Mw10k
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Temperature dependence of activation volume
BMMPC
BMPC
PTMPS
PMPS
Tg246 K
Tg261 K
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Sorbitol
Xylitol
Threitol
Glycerol
dTg/dP mp Tg (at 100s)
glycerol 353 57 188.4
threitol 335 79 224
xylitol 342 94 247
sorbitol 405 128 267
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Isobaric fragility
Definitions of fragility
What is the effect of pressure on mp?
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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.
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Effect of pressure on glass transition
temperature
Material dTg/dP (K/GPa)
polystyrene 303 DTA
polymethylphenylsiloxane 290 Dielectric
Polyvinylchloride 189 PVT
Polyvinylacetate 210 DTA
1,2-polybutadiene 240 Dielectric
BMPC 240 Dielectric
o-terphenyl (OTP) 260 DTA
Salol 204 Dielectric
PDE 280 Dielectric
glycerol 35 Dielctric
cyclohexanol 40 DTA
m-fluoroanilina 81 Dielectric
Andersson-Andersson relation
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The ?-relaxation time in P-T plane
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Cohen-Grest model
Doolitle equation
free volume
where
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Tg294 K
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Adam-Gibbs model
at P 0.1MPa
VFT law
Tait equation
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Avramov model
Assumption
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Equation of state model of Avramov
Where
?0 is volume expansion coefficient at ambient
pressure, Cp is specific heat capacity, Vm is the
molar volume and ? is a constant parameter
Predictions of the Avramov model
Non-linear increase of Tg with pressure
Pressure independence of fragilty
with
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Master curve
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The Dynamic Liquid Lattice model of Pakula model
Cooperative rearrangement can be visualized 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
Consequently, the sum of the displacements of
all molecules involved in the process is zero
Unsuccessful attempt because the element in the
center will not be replaced by any of the
neighbors
T. Pakula, J. Mol. Liq. 86, 109 (2000)
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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
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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
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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
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Excess wing
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Silesian University
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Silesian University
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Silesian University
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Silesian University
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R. Richers, et. al. J. Chem. Phys. 2004.
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DHIQ
trans-DHIQ
cis-DHIQ
E?40 KJ/mol
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