3. THE GLASS STATE AND THE GLASS TRANSITION : THERMODYNAMIC and KINETIC ASPECTS

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

sub-Tg aging and annealing

Tanneal.

Phase transitions of 1st and 2nd order(Ehrenfest classification)

vTl

dTdP

·

Clausius-Clapeyron

PCvTdT

dP 1

Ehrenfest

TdTdP

Phase transitions of 1st and 2nd order(Ehrenfest classification)

1st-order, 2nd-order and Lambda-type transitions

v1 v2

s1 s2

cp, , T

v1 = v2

s1 = s2

cp, , T

v1 = v2

s1 = s2

cp1 cp2

1 2

T1 T2

[ T1 = T2 ; P1 = P2 ; g1 = g2 ]

Ehrenfest relations

p

Tg

CTV

dPdT

dSdS

21

T

Tg

dPdT

dVdV

21

12

T

pT

TVC

R

Prigogine-Defay ratio

must be = 1 if it were a phase transition with a single order parameter

using Differential Scanning Calorimetry (DSC, TMDSC…)

[J. M. Hutchinson, Thermochimica Acta 324 (1998) 165-174

using Differential Scanning Calorimetry

the fictive temperature Tf

B2O3

[M. A. R. et al., J. Non-Cryst. Solids 221 (1997) 170]

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

onfig

(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.m

ol)

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

[B. Kabtoul and M. A. R., Phys. Status Solidi A 208, 2249–2253 (2011)]

the fictive temperature Tf

phenomenological Tool-Narayanaswamy-Moynihan (TNM) approach

feq T

xTx

RhA 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

TpF

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]

Stokes-Einstein equation:

rTkD B

6

[A. Einstein, Annalen der Physik 17, 549 (1905)]

B2O3

o-terphenyl

v

H