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
Differential Scanning Calorimetry
Differential Thermal Analysis
“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. ]
• Is the glass transition a true thermodynamic phase transition ?
Tg depends on the
cooling rate
Tg depends on the
thermal history
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
sub-Tg aging and annealing
Tanneal.
using Differential Scanning Calorimetry (DSC, TMDSC…)
[J. M. Hutchinson, Thermochimica Acta 324 (1998) 165-174
using Differential Scanning Calorimetry
the fictive temperature Tf
B2O3
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
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]
THE KAUZMANN PARADOX
)(lnTdCSSmT
T
pF
EXCESS OF ENTROPY:
crystalglassliquid SSS /
0)( KTTSTK
W. Kauzmann, Chem. Rev. 43, 219 (1948)
THE KAUZMANN PARADOXNN
1.0
STRONG AND FRAGILE GLASS-FORMING LIQUIDS
0 1
Vogel-Tamman-Fulcher equation:
0
0expTT
TD
(D: strength)
gTTg TTm
)/(
log10fragility index m:
STRONG AND FRAGILE GLASS-FORMING LIQUIDS
C. A. Angell, J. Non-Cryst. Solids 102, 205 (1988)
[I. Chang and H. Sillescu]
Ecuación de Stokes-Einstein:
r
TkD B
6
[A. Einstein, Annalen der Physik 17, 549 (1905)]