3. THE GLASS STATE AND THE GLASS TRANSITION: THERMODYNAMIC and KINETIC ASPECTS.
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Transcript of 3. THE GLASS STATE AND THE GLASS TRANSITION: THERMODYNAMIC and KINETIC ASPECTS.
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3. THE GLASS STATE AND THE GLASS TRANSITION:THERMODYNAMIC and KINETIC ASPECTS
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Differential Scanning Calorimetry
Differential Thermal Analysis
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“The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of the glass and the glass transition.”
[ P. W. Anderson, SCIENCE 267 (1995) pp. 1615-1616. ]
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• Is the glass transition a true thermodynamic phase transition ?
Tg depends on the
cooling rate
Tg depends on the
thermal history
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Ehrenfest relations
p
Tg
CTV
dP
dTdSdS
21
T
Tg
dP
dTdVdV
21
12
T
pT
TV
CR
Prigogine-Defay ratio
must be = 1 if it were a phase transition with a single order parameter
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sub-Tg aging and annealing
Tanneal.
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using Differential Scanning Calorimetry (DSC, TMDSC…)
[J. M. Hutchinson, Thermochimica Acta 324 (1998) 165-174
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using Differential Scanning Calorimetry
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the fictive temperature Tf
B2O3
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the fictive temperature Tf
80 85 90 95 100 105-3,5
-3,0
-2,5
-2,0
-1,5
-1,0
-0,5
0,0
0,5
Heating rate = 1,3 K/min.
Q* (coolin rate)0,04 K/min0,08 K/min0,42 K/min1,3 K/min4,5 K/min15 K/min
HC
on
fig (
J)
T (K)
Tf
93,994,294,695,896,497,2
Glass / SCL
Ethanol
80 85 90 95 100 105 110
50
100
150
200
250
300
350
Glass phase
CP (
J/K
.mo
l)
T (K)
Glass / SCL
CP (J/K.mol)
43,242,6342,3641,8339,639,38
Tg (K)
97,8197,0596,8196,7897,0797,22
Q* (coolin rate)0,04 K/min0,08 K/min0,42 K/min1,3 K/min4,5 K/min15 K/min
heating rate = 1,3 K/min.
SCL phase
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the fictive temperature Tf
phenomenological Tool-Narayanaswamy-Moynihan (TNM) approach
feq T
x
T
x
R
hA
1exp
*
[ Tool, J. Am. Ceram. Soc. 29 (1946) 240.Narayanaswamy, J. Am. Ceram. Soc. 54 (1971) 491.Moynihan et al., J. Am. Ceram. Soc. 59 (1976) 12. ]
curve fitting method:
[I. M. Hodge, J. Non-Cryst. Solids 169 (1994) 211]
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THE KAUZMANN PARADOX
)(lnTdCSSmT
T
pF
EXCESS OF ENTROPY:
crystalglassliquid SSS /
0)( KTTSTK
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W. Kauzmann, Chem. Rev. 43, 219 (1948)
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THE KAUZMANN PARADOXNN
1.0
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STRONG AND FRAGILE GLASS-FORMING LIQUIDS
0 1
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Vogel-Tamman-Fulcher equation:
0
0expTT
TD
(D: strength)
gTTg TTm
)/(
log10fragility index m:
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STRONG AND FRAGILE GLASS-FORMING LIQUIDS
C. A. Angell, J. Non-Cryst. Solids 102, 205 (1988)
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[I. Chang and H. Sillescu]
Ecuación de Stokes-Einstein:
r
TkD B
6
[A. Einstein, Annalen der Physik 17, 549 (1905)]
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