calorimetric glass...

Calorimetric Glass Transition

Yuanzheng Yue

Wuhan University of Technology, China

Aalborg University, Denmark

Joint ICTP-IAEA Workshop, Trieste, Italy, Nov. 6-10, 2017

Outline• Background and motivation• Case 1: Borosilicate and phosphate glasses

– Dulong Petit Law – The Cp m relation– Pressure effect on fictive temperature– Structural source of the Cp change– Prediction of Tg by topological model

• Case 2: Hyperquenched (HQ) glasses– Relaxation in multi-component oxide systems– Relaxation in metallic glasses– Tg of SiO2

– Relaxation in HQ strong glass formers (SiO2 and GeO2)

• Case 3: Mechanically vitrified glasses• Case 4: Metal-organic framework glasses

– Evidence for polyamorprphism in ZIF-4– Melting and glass transition of ZIFs– Ultrahigh glass-forming ability of ZIF-62

2







3

One of the 125 big questions in science (till 2030):

What is the nature of the glass transition? Science, 2005

Numerous models about glass transition are emerging:Macroscopic models (entropy, energy, free volume), Mode-coupling theory, Frustration-based model, Elastic model (harmonic), Local expansion model, Shoving model, Liquid fragility theory, Topological model….

Angell, Science 1995

Debenedetti & Stillinger, Nature 2001

Ediger, Harrowell, J. Chem. Phys. 2012

…..

Here I focus on the calorimetric glass transition.

Calorimetric glass transition is reflected by a sudden change in heat capacity

400 500 600 700 800 9000.8

1.0

1.2

1.4

1.6

1.8

qh=qc=10 K/min

upscan

downscan

Tg

Cp (

Jg

-1K

-1)

T (K)

Cp = (dH/dT)p Cv

• Glass transition temperature (Tg) is a dynamic temperature, measured as the onset temperature of glass-liquid transition.

• Melting temperature (Tm) is a thermodynamic temperature.

Key values for glass transition:Heat capacity (Cpg) and its jump at Tg (Cp)

for a normally cooled glass

400 500 600 700 800 9000.8

1.0

1.2

1.4

1.6

1.8

Cpl

Cpg

qh=qc=10 K/min

Tg

Cp (

Jg

-1K

-1)

T (K)

Cp

Cp(PO3)2 glass

d

Heat capacity for a hyperquenched glass

(rockwool glass at ~106 K/s)

400 600 800 1000

0.6

0.8

1.0

1.2

1.4

1.6

64 J/g

Tg

Tc

The hatched area:

energy released from 1g fiber

upscan 1

upscan 2

T (K)

Cp (

Jg

-1K

-1)

Determination of the glass transition (Tg)

and the fictive temperatures (Tf)

Basic equation:

Y. Z. Yue, et al., Chem. Phys. Lett. 2002; J. Chem. Phys. 2004

f

g

eq

c

T

Tpgplp

T

Tp dTCCdTCC )()( 12

400 600 800 1000 1200

0.8

1.0

1.2

1.4

1.6

1.8

BA

B

A

Cpg

Cpl

Cp2

Cp1

=

Tg=941 K Tf=1141 K

T (K)

Cp (

Jg

-1K

-1)

Cpg = a + bT + c/T2 + d/T0.5

900 950 1000 1050 1100 1150

=Tg=941 K Tf=1141 K

T (K)

Glass transition

Influenced by

• Chemical composition and liquid fragility

• Thermal and mechanical history

• Types and strength of chemical bonds

• Network connectivity

• Topological degree of atomic freedom

• Atomic packing

• Microscopic heterogeneity

• Cluster structure







10

Dulong Petit Law applies when the unit of Cp is converted to J/mol of atoms?

400 500 600 700 800 900

15

20

25

30

35

40

45

Cp (

J m

ol-1

K-1)*

T (K)

*Jouls per mole of atoms, not per mole of molecules

B2O3 increases

3R

0 20 40 60 80

23

24

25

Cp

g a

t T

g (

Jm

ol-1

K-1)*

B2O3 (mol%)

Dulong Petit Lawworks at Tg

Cp≈3R law works for oxide glasses at Tg

400 600 800 1000 1200 1400 1600

15

20

25

30

35

40

45

50

Cp (

J m

ol-1

K-1)*

T (K)

*Jouls per mole of atoms

3R

NaPoLi

CMP

borosilicate

basaltic

Diopsite

SiO2

35Al2O365SiO2

Cp as a function of composition

100 200 300 400 500 60050

80

110

140

170

Cp (

J m

ol-1

K-1)

T (oC)

75B

63B-12Si

51B-24Si

37B-37Si

24B-51Si

12B-63Si

6B-69Si

75Si400 450 500 550 600

75

100

125

150

175

Tg

Cpg

Cpl

0 20 40 60 8010

20

30

40

50

60

1.2

1.3

1.4

1.5

1.6

Experiment (Cp)

Model (Cp)

C

p (

J m

ol-1

K-1)

[B2O3] (mol%)

Experiment (Cp,l/Cp,g)

Cp

,l/C

p,g (

-)

Smedskjaer et al. J. Phys. Chem. B. 115 (2011) 12930

Configurational heat capacity (Cp) increases with increasing the B2O3/SiO2

Relation between Cp and kinetic fragility

20 30 40 50 600

10

20

30

40

50

60

C

p (

J m

ol-1

K-1)

m (-)

Implication: There is a link between Cp to the kinetic fragility for the same series of glasses.

)1(0

mm

TA

pg

C

The network connectivity increases with increasing B2O3, but the fragility increases.

0 20 40 60 80

0.0

0.2

0.4

0.6

0.8

NB

O/T

B2O3 (mol%)

Implication: The network connectivity is not the main controlling factor for liquid fragility.

0 20 40 60 8010

20

30

40

50

60

1.2

1.3

1.4

1.5

1.6

Experiment (Cp)

Model (Cp)

C

p (

J m

ol-1

K-1)

[B2O3] (mol%)

Experiment (Cp,l/Cp,g)

Cp

,l/C

p,g (

-)

B2O3 mol% increase

IRO B3SiO4-O-

q=1.0

q=0.08400 600 800 1000 1200 1400 1600

Rela

tive I

nte

nsity (

A.U

.)

Wavenumber (cm-1)

The IRO band is greatly enhanced by increasing B2O3 content

Raman on 75q B2O3 - 75(1-q) SiO2 - 15Na2O - 10CaOq = [B2O3]/([B2O3]+[SiO2])

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

40

44

48

52

56

fragili

ty m

Total Area of IRO bands0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

20

30

40

50

Cp

,co

nf (

J m

ol-1

K-1)

Total Area of IRO Bands

IRO units increase Cp,conf and m

Link between Cp,conf and IRO units

The content of IRO units has a dominant contribution to the evolution of Cp,conf with composition in borate-silicate glasses.

H. Liu, et al., PCCP, 18 (2016) 10887

Topological model and temperature dependent constraint theory

Phillips & Thorpe:

• Atomic structure of a glass- a network of bond constraints

• Each atom has 3 degrees of freedom, but they are removed by:

Two - body Linear constraints

Three – body angular constraints

Gupta & Mauro:

• Temperature dependent constraint theory

• network constraints vs. composition

Predicting glass properties, e.g.,Tg , m, Hv

Phillips & Thorpe, Sol .State Commun. (1985)

Gupta & Mauro, J. Chem. Phys. (2009) SeSe

SeSe

SeSe

(a)

(b)

(c)

GeGe

GeGe GeGe

SeSeSeSe

SeSe

SeSeSeSe

(a)

(b)

(c)

GeGe

GeGe GeGe

Type and counting of Constraints

• type: B-O and MNB-O linear constraintsTwo constraints at each oxygen

• Β type: O-B-O angular constraints− Five β constraints at each Q4 unit.− Three at each Q3 unit.

• γ type: B-O-B and B-O-M(NB) angular constraints− One g constraint at each bridging oxygen

• μ type: modifier rigidity (due to clustering)− Two μ constraints per NBO-forming Na atom

Ranking of Constraints

Each type of constraint has its onset temperatures, which is the temperature where constraints become rigid as temperature is lowered.

T T T Tg

0 10 20 30 40

0

1

2

3

O-

Na+ Na

+

Na+

O

T > T

T < T < T

T < T < T

Tg < T < T

Ato

mic

degre

es o

f fr

eedom

[Na2O] (mol%)

T < Tg

Co

olin

g

B-O

MNB

-O

O

B

B B

O

O- O

-

Predicting Tg by using temperature dependent constraint theory

Good prediction, but challenge for complex systems

Smedskjaer, Mauro, Sen, Yue, Chem. Mater. 22 (2010) 5358Smedskjaer, Mauro, Youngman, Hogue, Potuzak, Yue, J. Phys. Chem. B 115 (2011) 12930.

Pressure induced enhancement of the Cp overshoot for CaP2O6 glass

500 600 700 800 90080

100

120

140

160

180

200

2nd DSC upscan

Cp (

Jm

ol-1

K-1)

T (K)

1st DSC upscan after

500 MPa compression

780 790 800 810 820 830

120

140

160

180

200

220

Cp (

Jm

ol-1

K-1

)

T (K)

P (MPa)

a: 500

b: 300

c: 200

d: 100

e: 20

0.1

a

b

cd

e

Why? Pressure drives glass deep in the potential energy landscape. When being heated, glass absorb energy from the surrounding, and hence enhances Cp’.

Thermodynamic consequences of compression and relaxation for CMP

300

400

500

600

700

800

0 100 200 300 400 500 600 700

0.5

0.6

0.7

0.8

0.9 b)

a)

780 800 820 840100

120

140

160

180

Cpl

Cp(T)

T2T1

Hover

Cp (

Jm

ol-1

K-1

)

T (K)

H

over (J

mol-1

)

S

over (J

mol-1

)

P (MPa)

dTCTCHT

T plpover 2

1

))((

dTST

T T

CTC

overplp

2

1

))((

Potential energy decreases during compression.

Entropy change decreases during compression.

Yue, et al. J. Chem. Phys. 2007

Fictive temperature (Tf) decreases with pressure for CMP

0 100 200 300 400 500 600764

768

772

776

700 750 800 850100

120

140

160

180

A

B

BA =

Tf

Cp (

Jm

ol-1

K-1

)

T (K)

TfA

(K

)

P (MPa)

Moynihan, et al. J. Am. Ceram. Soc. 1976Yue, et al. Chem. Phys. Lett. 2002; J. Chem. Phys. 2007

To determine Tf correctly we should apply the correct method:Enthalpy-matching method

Structural relaxation in compressed borate glasses

Smedskjaer et al, Sci. Rep. (2014)







26

Approaches we used

NMRHRTEM

DSC

HyperquenchingBall milling

Sub-Tg annealing(at T<Tg)

Charaterizations

Stone Wool

Milled powder

Metallic glass

DSC output reflects the change of potential energy during heating or annealing

400 600 800 1000

0.8

1.0

1.2

1.4

1.6 Stone wool

Cp1

Cp2

T (K)

Cp (

Jg

-1K

-1)

DSC is a sensitive tool for detecting the

energetic and structural evolution of glass

Tm Tf Tg

Supercooled liquid

standard

glass

HQG

Enth

alp

y

Temperature

H

annealing

Tf2

high Tf glass

(e.g. stone wool)

Tg

Tf1

Tm

Collective configuration coordinate

Crystal

low Tf glass

(e.g. ultrastable film)

Pote

ntial energ

y

Z*

Yue, et al. APL 2002Angell, et al. JPCM 2003Hu, et al. JPC-C 2009Qiao, et al. JACerS 2016

Hyperquenching-Annealing-Calorimetry Hyperquenched (HQ) basalt glass

400 600 800 1000

0.6

0.8

1.0

1.2

1.4

1.6

Cp1

Teq

Cp2

T (K)

Cp (

Jg

-1K

-1)

Tc

Cp overshoot

400 600 800 10000.8

1.0

1.2

1.4

1.6

1.8ta=90 min

gf

Ta (K)

a: 573

b: 623

c: 673

d: 723

e: 773

f: 798

g: 823

edcba

T (K)

Cp (

Jg

-1K

-1)

An approach – for understanding the glass transition and relaxation

Excess enthalpy of fresh HQ fibers Excess enthalpy of annealed HQ fibers

eq

c

T

T ppexcess dTCCH )( 12

Yue and Angell, Nature 2004

Energy ‘bird’

Yue, et al., Appl. Phys. Lett. 2002;

Yue, et al. Chem. Phys. Lett. 2002

Basalt (relatively fragile)

400 600 800 1000

0.55

0.60

0.65

0.70

0.75

0.80

T (K)

d

ta

a: 0 min

b: 30 min

c: 2 hrs

d: 11 hrs

e: 19 hrs

f : 27 hrs

g: standard

g

f

ec

b a

Cp (

Jg

-1K

-1)

Ta = 565 K (0.71Tg)

400 500 600 700 800 900 10000.8

1.0

1.2

1.4

1.6

1.8

IGFEDC

AB

Cp (

Jg

-1K

-1)

T (K)

H

ta

A: non-annealed

B: 1 min

C: 4 min

D: 15 min

E: 50 min

F: 3.5 h

G: 12 h

H: 2 days

I: 8 days

Onset of pre-endotherm

Ta=723 K (0.77Tg)

GeO2 (strong)

Differences in sub-Tg relaxation between a

fragile and a strong system

More heterogeneous

More non-exponential

Less cooperative

Pre-endotherm

Less heterogeneous

Less non-exponential

more cooperative

No pre-endotherm

Hu and Yue, JPC-B (2008)Yue and Angell, Nature (2004)

Double “glass transition” upon 55 days aging

400 500 600 700 800 900 1000

1.0

1.2

1.4

1.6

1.8 upscan 1

upscan 2

cooled at 106 K/s

aged at 773 K for 55 days

Cp (

Jg

-1K

-1)

T (K)

400 500 600 700 800 900 1000 1100

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Energy release exotherm

pre-endotherm

Cp

,exc (

Jg

-1K

-1)

T (K)

It shows that the relaxation is highly exponential, and hence, highly energetically heterogeneous

‘Shadow glass’ transition

Yue and Angell, Nature 2004

0 20 40 60 80 100 120 140 1600.00

0.01

0.02

0.03

0.04

0.05

0.06

hyperquenched annealed super-annealed crystallized

Z(

)

(cm-1)

Vibrational density of state (VDOS) of HQ glasses

• VDOS peak at ~35 cm−1 in the HQ state

• The peak is suppressed by annealing.

• The peak disappears in crystallized state.

• Source: topologically diverse defects

Implication: vibrational structure changes with the state of configurational excitation of the liquid.

Angell, Yue, et al. J. Phys: Cond. Mat. (2003)

Relaxation in hyperquenched 20MgO-20CaO-60SiO2 glasses – detecting structural heterogeneity

400 600 800 1000 1200

0.9

1.2

1.5

Cp (

Jg

-1K

-1)

T (K)

Remarkable!

two sub-Tg energy

release peaks

Tg=999 K

400 600 800 1000

0.9

1.2

1.5

2nd upscan

Cp (

Jg

-1K

-1)

T (K)

1st upscan

2 sub-Tg relaxation peaks 2 kinds of structural domains?

400 600 800 1000

0.6

0.8

1.0

1.2

1.4

1.6T

g

Tc

upscan 1

upscan 2

T (K)

Cp (

Jg

-1K

-1)

Each has its own structural heterogeneity.

Two structural domains in the liquid state are frozen-in at high Tf.

Yue and Angell, Nature 2004, Yue, et al., Zhang, et al, JACerS 2013, 2017

Effect of sub-Tg annealing time on the Cp pattern and hence on the

energetic elvolution of the two structural domains

Peak dimishes vertically

(like strong systems)

Peak diminshes horizontally

(like fragile systems)

Two structural domains (strong and fragile ones)?

400 600 800 1000

0.55

0.60

0.65

0.70

0.75

0.80

T (K)

d

a: 0 minb: 30 minc: 2 hrsd: 11 hrse: 19 hrsf : 27 hrsg: standard g

f

ec

b a

Cp (

Jg

-1K

-1)

400 600 800 10000.8

1.0

1.2

1.4

1.6

Cp (

Jg

-1K

-1)

T (K)

Ta=823 K

Fresh

Standard

1 h

6 h

24 h

4 d

(a)

400 500 600 700 800 900 10000.8

1.0

1.2

1.4

1.6

1.8

101 102 103 104 105 106

0.4

0.6

0.8

1.0

E

rem

/E

tot

ta (s)

IGFEDC

AB

Cp (

Jg

-1K

-1)

T (K)

H

ta

A: non-annealedB: 1 minC: 4 min D: 15 minE: 50 minF: 3.5 hG: 12 hH: 2 daysI: 8 days

Ta=723 K

Onset of pre-endotherm

Tg of SiO2 drastically drops with increasing

water content

200 400 600 800 1000 1200 1400 1600 18000.7

0.8

0.9

1.0

1.1

1.2

1.3

1336 K

water content

~1 ppm

~1021 ppm

1434 K

Cp (

Jg

-1K

-1)

T (K)

Y. Z. Yue, Front. Mater. 2 (2015) 1

Comparison between the measured Cp and the calculated Cp

400 800 1200 1600

40

50

60

70

80

data

Einstein Equation

SiO2 glass (<1 ppm water)

qh=10 K/min

Cp (

Jm

ol-1

K-1

)

T (K)

Cv = 3REi(Xi)

E(x) = x2ex/(ex-1)2

x = h/kT = /T

where = Einstein temperature

s = 1100 K (Si vibrations)

T = 370 K (transverse oxygen

vibrations)

L = 1220 K (longitudinal

oxygen oscillations)

Tg of silica decreases with repeating the DSC scans

400 800 1200 16000.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

SiO2 glass (~1 ppm OH)

qh=10 K/min

upscan 11

upscan 1

Cp (

Jg

-1K

-1)

T (K)0 2 4 6 8 10 12

1300

1350

1400

1450

Tg (

K)

Number of DSC scans

Cristobalite formation and weakening of bonds by repeating reheating?

Enthalpy relaxation of a hyperquenched (HQ) normal glass and a HQ Silica

400 600 800 1000 1200 1400 16000.7

0.8

0.9

1.0

1.1

1.2

Upscan 2

Upscan 1

Tg=1356 K (1083 ºC)

SiO2 fiber

T (K)C

p (

Jg

-1K

-1)

HQ vitreous silica

HQ normal glass

300 400 500 600 700 800 900

0.8

1.0

1.2

1.4

1.6

Upscan 1

Ca(PO3)2 fibers

qh=qc=20 K/min

T (K)

Cp (

Jg

-1K

-1)

Upscan 2

Effect of the annealing temperature Ta on the Cp,exc

0.0

0.1

0.2

0.3

d)

c)

b)

ta=12 hrs Ta (K)

A not annealed

B 523

C 623

D 723

E 823

G

E

EF

D

D

C

CC

BB

B

A

A

A C ED

B

A

HQGeO2

HQBas HQSiO2

Cp,e

xc (

Jg

-1K

-1)

a)

ta=24 hrs Ta (K)

A not annealed

B 873

C 923

D 948

E 1073

0.5 0.6 0.7 0.8 0.9 1.0 1.1

0.0

0.1

0.2

0.3

T/Tg (K/K)

ta=3 hrs Ta (K)

A no-annealed

B 603

C 643

D 683

E 723

F 743

G 763

HQCmP

T/Tg (K/K)

0.5 0.6 0.7 0.8 0.9 1.0 1.1

ta=3 hrs Ta (K)

A not annealed

B 650

C 700

Effect of annealing time (ta) on Cp,exc of HQ glasses

0.0

0.1

0.2

0.3

b)

A

ta (hrs)

A 0

B 0.017

C 0.25

D 3.5

E 12

F 192

Cp

,exc (

Jg

-1K

-1)

a)

d)

B

C

A

HQGeO2

HQSiO2

c)

0.5 0.6 0.7 0.8 0.9 1.0 1.1

0.0

0.1

0.2

0.3

T/Tg (K/K)

FEDC

B

B CD CA

ta (hrs)

A 0

B 0.25

C 3.5

ta (hrs)

A 0

B 3

C 24

HQCmP ta (hrs)

A 0

B 0.11

C 1

D 9

E 27

T/Tg (K/K)

0.5 0.6 0.7 0.8 0.9 1.0 1.1

BC

A

HQBas

Y. Z. Yue, Front. Mater. 2 (2015) 1

(49m/s)

(35m/s) (25m/s) (17m/s)

Cu46Zr46Al8

monotonic

Non-montonic structural response to sub-Tg

annealing measured by x-ray scattering

Annealing dependence of the structural unit size

Annealing dependence of the correlation length

Critical temperature for the dramatic decreases in Rc: Tc ~ around 1.3Tg

Total structural factors PDF

Schematic scenario of the structural evolution during fragile-to-strong transition

Zhou, et al. J. Chem. Phys. (2015)







44

Potential energy landscape

Two paths towards the glass state far from equilibirum:• Thermally hyperquench liquids• Mechanically hyper-mill crystals

Fiber spinner

Ball mill

hyperquenching

Tg

Tf

Crystal

Ultrastable glass

Tm

Pote

nti

al

En

ergy

Z collective configuration coordinate

mechanical milling

Sub-Tg relaxation

Higher Tf

Contrasr in relaxation between hyperquenched and

milling-derived glasses

900700500300T (K)

Cp

(JK

-1g-1

)

0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

Main peak

S2

B

HQBas

C

p (

JK

-1g

-1)

T/Tg (K/K)

As-milled Ag3PS

4A

S1Shoulder

Qiao, et al, J. Am. Ceram. 100 (2017) 968

360 400 440 480 520 560

-1.5

-1.0

-0.5

0.0

0.5

1.0T

g

S1

Cp2

C

p (

JK

-1g

-1)

T (K)

Cp1

S2

(a)

As-milled Ag3PS4

As-quenched basalt glass

As-milled Ag3PS4 glass is highly structurally heterogeneous.

The two peaks originate from - and –relaxations.

Cp(sub-Tg)=Cp2-Cp1

Contrast in relaxation behavior between the two glasses

400 420 440 460 480 500

0.00

0.05

0.10

0.15

GFEDCB

Cp (

JK

-1g

-1)

T (K)

Tmax

(K)

A As-milled

B 400

C 413

D 423

E 440

F 459

G 471

A

Energy release of both the as-milled Ag3PS4 glass (curve A) and the dynamically heated Ag3PS4 (curves B to G)

Y. Z. Yue, et al, Appl. Phys. Lett. 81 (2002) 2983

A. Qiao, et al. J. Am. Ceram. Soc. 100 (2017) 968-974

The milling-derived Ag3PS4 glass has similar relaxation feature to that of HQ glasses. But the former is structurally more heterogeneous.

Energy release of basalt glass wool after annealing at various Ta







48

MOF glass family has emerged…

• Concerning chemical bonds, melt-quenched glasses have

3 families：

– Inorganic non-metallic glasses (e.g. oxide,

chalcogenide glasses, fluride…)

– Organic glasses (polymer, molecular glasses…)

– Metallic glasses

• A new family: Organic-inorganic hybrid glasses:

– ZIF glass, coordination polymers

49

Bennett, Tan, Yue, et al., Nature Com. 6 (2015) 8079Bennett, Yue, Li, et al., J. Am. Chem. Soc. 138 (2106) 3484Tao, Bennett, Yue, et al. Adv. Mater. 29 (2017) 1601705Umeyama, et al. J. Am. Chem. Soc. 137 (2015) 864.Zhao, et al. J. Am. Chem. Soc. 138 (2016) 10818

We have succeeded in vitrifyingseveral Zeolitic imidazolate frameworks (ZIFs)

- ZIF is a subset of MOFse.g., ZIF-4, structurally analogous to SiO2

Zeolitic topology

Bondingunit for SiO2

Bonding unit for ZIF-4

SiO2 network

But their properties differ significantly.

Zn(C3H3N2)2

50

Coordinating bonds!Covalent+ionic mixed bonds!

Observe fascinating transitions in ZIF-4 by DSC

400 500 600 700 800 900 1000 1100-4

-2

0

2

4

6

Cp (

Jg

-1K

-1)

T (K)

20 K/min upscan

crystallization

melting

foaming

onset of gas release

lattice collapse

amorphisation

LDA to HDL

solvent release

80

85

90

95

100

Ma

ss (

%)

51

350 400 450 500 550 600 650

1.0

1.2

1.4

1.6

Cp (

Jg

-1K

-1)

T (K)

ZIF-42nd upscan at 20 K/min

Tg=570 K

Crystal ZIFdesolvation-LDA HDAHDL phasecrystal ZIF-zni MeltBulk glass Foam glass!

LDA: Low density amorphous phase HAD: High density amorphous phase

Crystal ZIF-4 Amorphisation Crystal ZIF-zni

a) b) c)

350 400 450 500 550 600 650 7000.8

1.0

1.2

1.4

1.6

350 400 450 500 550 600 650 700

1.0

1.2

1.4

1.6

Cp

Tg of HDA

Cpl

Cp (

Jg

-1K

-1)

T (K)

Cpg

Upscan 2

LDL-HDL

liquid transition

Cp (

Jg

-1K

-1)

T (K)

123

Tg of HDA=563 K

Cp=0.14 Jg-1K

-1

Cpl/Cpg=1.1

release of

solvent

collapse into LDA

Glass transition of HDA

upscan rate:

10 K/min

400 500 600 700 800 900 1000 1100-4

-2

0

2

4

6

Cp (

Jg

-1K

-1)

T (K)

20 K/min upscan

crystallization

melting

foaming

onset of gas release

lattice collapse

amorphisation

solvent release

80

85

90

95

100

Ma

ss (

%)

Calorimetric evidence for polyamorphic transitionsand glass formation

52

Potential energy landscape of ZIF-4

ZI

ZIF-4

LDA

HDA/MQG

ZIF-zni

kBTm

kBTgLDA

kBTgHDA/MQG

Pote

nti

al E

ner

gy

Configurational Coordinate

exo endo

HmAmorphization

Quench-vitrifying

53

Co-existence of LDA and HDA phases!

480 520 560 600 640 680

LDA

300 400 500 600 7001.0

1.2

1.4

1.6 HG

F

E

D

CB

Cp (

Jg

-1K

-1)

T (K)

A

A: 529 K

B: 563 K

C: 578 K

D: 588 K

E: 601 K

F: 608 K

G: 613 K

H: 673 K

G

H

FEDCB

Heat flow

(A

U)

T (K)

A

Rescans of ZIF-4 after the sample

was scanned to different T

Scan rate: 10 K/min

HDA

Polyamphic transition in ZIF-4 54

Fragilities of LDA and HDA phases

LDA phase is superstrong!

It is stronger than HDA phase and melt-quenched glass!

0.90 0.92 0.94 0.96 0.98 1.00 1.02

9

10

11

12

13

HDA: m=41

LDA: m=18

log

(

in

Pa

s)

Tg/T

ZIF-4DSC data to viscosity datalog = 11.35 – logqh (Tf)

Yue, von der Ohe, Jensen, JCP (2004)

Dashed line: MYEGA fit

Mauro, Yue, Ellison, Gupta, Allan,PNAS (2009)

11

15exp153log

T

Tm

T

T gg

Compare with other systems

0.4 0.5 0.6 0.7 0.8 0.9 1.0

-4

-2

0

2

4

6

8

10

12

log (

Pa

s)

Tg/T (K/K)

SiO 2 (m

=20)

Anorthite

(m=53)

ZIF-4 LDA (SAXS) (m=14)

ZIF-4 LDA (DSC) (m=18)

ZIF-4 HDA (D

SC) (m=41)

Triphe

nyle

thylen

e (m

=101

)

56

Summary

Glass transition is an fascinating complex problem. Investigation of

glass transition is continuing…..

I thank

all my co-authors and collaborators.

Thank you for your attention!

calorimetric glass...

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