1

Lecture 12Lecture 12

The cooperative relaxation of water at the pore surface of silica glasses The cooperative relaxation of water at the pore surface of silica glasses

2

Complex systems? Complex systems? Complex systems involve the appearance of a new Complex systems involve the appearance of a new ("mesoscopic") length scale, intermediate between ("mesoscopic") length scale, intermediate between

molecular and macroscopic.molecular and macroscopic.

Complex systems? Complex systems? Complex systems involve the appearance of a new Complex systems involve the appearance of a new ("mesoscopic") length scale, intermediate between ("mesoscopic") length scale, intermediate between

molecular and macroscopic.molecular and macroscopic.

Complex liquids (microemulsions, Complex liquids (microemulsions, emulsions, organic particulate systems )emulsions, organic particulate systems )

Glass forming liquids and polymers.Glass forming liquids and polymers.

Porous materials (sol-gel glasses, porous Porous materials (sol-gel glasses, porous glasses, porous silicon, etc.)glasses, porous silicon, etc.)

Biological systems ( protein solutions, Biological systems ( protein solutions, membranes and cell suspensions)membranes and cell suspensions)

Complex liquids (microemulsions, Complex liquids (microemulsions, emulsions, organic particulate systems )emulsions, organic particulate systems )

Glass forming liquids and polymers.Glass forming liquids and polymers.

Porous materials (sol-gel glasses, porous Porous materials (sol-gel glasses, porous glasses, porous silicon, etc.)glasses, porous silicon, etc.)

Biological systems ( protein solutions, Biological systems ( protein solutions, membranes and cell suspensions)membranes and cell suspensions)

3

Initial sodium borosilicate glass of the following composition (% by weight): 62.6% SiO2, 30.4% B2O3, 7%Na2O

Initial sodium borosilicate glass of the following composition (% by weight): 62.6% SiO2, 30.4% B2O3, 7%Na2O

heat treatment at 650heat treatment at 65000C for 100hC for 100hheat treatment at 490heat treatment at 49000C for 165hC for 165himmersion in deionised waterimmersion in deionised water

0.5N HCL0.5N HCL

drying at 200drying at 20000CCrinsing in deionized waterrinsing in deionized water

additional treatment in 0.5N KOHadditional treatment in 0.5N KOH

drdryying at 200ing at 20000CCrinsing in deionized waterrinsing in deionized water

Porous borosilicate glass samplesPorous borosilicate glass samplesPorous borosilicate glass samplesPorous borosilicate glass samples

4

additional treatment in 0.5M KOHadditional treatment in 0.5M KOH

dryingdryingrinsing in deionized waterrinsing in deionized water

dryingdrying

bithermal heat treatment bithermal heat treatment treatment at 650 treatment at 650 00C and at C and at 5530 30 00CCthermal treatment at 530thermal treatment at 53000CC

immersion in deionised waterimmersion in deionised water3M HCL3M HCL

rinsing in deionized waterrinsing in deionized water

Commercial alkali borosilicate glass DV1 of the following composition (mol.%):

7% Na2O, 23% B2O3, 70% SiO2

Commercial alkali borosilicate glass DV1 of the following composition (mol.%):

7% Na2O, 23% B2O3, 70% SiO2

5

SamplesPorosity ,

%Pore diameter,

nmPresence of

silica-gelHumidity h,

%

A 38 40-70 With 1.2

B 48 40-70 Very Small 1.4

C 38 280-400 Small 3.2

D 50 300 Very Small 1.6

I 26.5 5.4 With 3.6

II 42.5 88 No 0.63

III 25.5 11 With 3.39

SamplesPorosity ,

%Pore diameter,

nmPresence of

silica-gelHumidity h,

%

A 38 40-70 With 1.2

B 48 40-70 Very Small 1.4

C 38 280-400 Small 3.2

D 50 300 Very Small 1.6

I 26.5 5.4 With 3.6

II 42.5 88 No 0.63

III 25.5 11 With 3.39

Structure parameters and water contentStructure parameters and water content

10-4

10-2

100

102

Per

mitt

ivity

'' []

10-4

10-2

100

102

Per

mitt

ivity

'' []

Sample CSample C Sample CSample C Sample C after heating Sample C after heating Sample C after heating Sample C after heating

Dielectric response of the porous glass materials Dielectric response of the porous glass materials

7

10-4

10-3

10-2

10-1

100

101

102

Perm

ittivi

ty'' [

]

10-4

10-2

100

102

Pe

rmitt

ivity

'' []

3-D PLOTS OF THE DIELECTRIC LOSSES 3-D PLOTS OF THE DIELECTRIC LOSSES FOR THE POROUS GLASS MATERIALSFOR THE POROUS GLASS MATERIALS

Sample CSample C

Sample IISample II

8

-100 0 100 200 300

0

20

40

60

80

100

'

Temperature ( 0C )

-100 0 100 200 300

0

20

40

60

80

100

'

Temperature ( 0C )

-100 0 100 200 300

0

10

20

30

40

50

''

Temperature ( 0C )

-100 0 100 200 300

0

10

20

30

40

50

''

Temperature ( 0C )

Low frequency behaviour ~20 Hz

-100 0 100 200 300

6

5

4

3

2

'

Temperature ( 0C )

-100 0 100 200 300

6

5

4

3

2

'

Temperature ( 0C )

-100 0 100 200 30010

-3

10-2

10-1

100

101

''

Temperature ( 0C )

-100 0 100 200 30010

-3

10-2

10-1

100

101

''

Temperature ( 0C )

High frequency behaviour ~ 100 kHz

CC

CC

9

10-1

100

101

102

103

104

105

106

100

101

102

' ''

', '

'Frequency (Hz)

12

*( ) = B* n-1, >> 1 *( ) = B* n-1, >> 1

*( ) = -i0/0*( ) = -i0/0

1)

Jonscher

Conductivity

*( ) = / [1 + ( i ) ] + *( ) = / [1 + ( i ) ] +

2) Havriliak-Negami

The fitting modelThe fitting model

10

4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8

10-7

10-6

10-5

10-4

10-33.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7

Sample I II III Ice

, [s

]

1000/T, [K-1]

4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8

10-7

10-6

10-5

10-4

10-33.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7

Sample I II III Ice

, [s

]

1000/T, [K-1]

A - 50 kJ/mol B - 42 kJ/mol

C - 67 kJ/mol D - 19 kJ/mol

Ice - 60 kJ/mol

A - 50 kJ/mol B - 42 kJ/mol

C - 67 kJ/mol D - 19 kJ/mol

Ice - 60 kJ/mol

I - 64 kJ/mol II - 36 kJ/mol

III - 61 kJ/mol

Ice - 60 kJ/mol

I - 64 kJ/mol II - 36 kJ/mol

III - 61 kJ/mol

Ice - 60 kJ/mol

11stst Process Process11stst Process Process

4.6 4.8 5.0 5.2 5.4 5.6 5.8

10-7

10 -6

10 -5

10 -4

10 -33.5 3.7 3.9 4.1 4.3 4.5 4.7

Sample

A

B

C

D

Ice, [s

]

1000/T, [K-1

]

4.6 4.8 5.0 5.2 5.4 5.6 5.8

10-7

10 -6

10 -5

10 -4

10 -33.5 3.7 3.9 4.1 4.3 4.5 4.7

Sample

A

B

C

D

Ice, [s

]

1000/T, [K-1

]

11

-17 -16 -15 -14 -13 -12 -11 -10 -9 -8

0.36

0.39

0.42

0.45

0.48

0.51

0.54

0.57

0.60

0.63

A

B

C

D

I

II

III

ln()-17 -16 -15 -14 -13 -12 -11 -10 -9 -8

0.36

0.39

0.42

0.45

0.48

0.51

0.54

0.57

0.60

0.63

A

B

C

D

I

II

III

ln()

SamplesHumidity h,

%

II 0.63

A 1.2

B 1.4

D 1.6

C 3.2

III 3.39

I 3.6

Dependence of the Cole-Cole parameter Dependence of the Cole-Cole parameter from ln( from ln())

12

170 180 190 200 210 2200.01

0.1

1

A

B

C

D

Temperature, [K]

170 180 190 200 210 2200.01

0.1

1

A

B

C

D

Temperature, [K]

170 180 190 200 210 220

0.1

1

I

II

III

Temperature, [K]

170 180 190 200 210 220

0.1

1

I

II

III

Temperature, [K]

235 240 245 250 255 260 265 270

60

63

66

69

72

75

Ice

Temperature, [K]

235 240 245 250 255 260 265 270

60

63

66

69

72

75

Ice

Temperature, [K]

Temperature dependence of the dielectric strengthTemperature dependence of the dielectric strength

13

170 180 190 200 210 220 230

101

102

(A)

(B)

(D)

(II)

B(T

)

Temperature, [K]

170 180 190 200 210 220 230

101

102

(A)

(B)

(D)

(II)

B(T

)

Temperature, [K]

)()32(

11

111 TBT

)()32(

11

111 TBT

Parallel and anti-parallel Parallel and anti-parallel orientationorientation

170 180 190 200 210 220

6

8

10

12

14

16 B(T)C

B(T)I

B(T)III

B(T

)*1

02

Temperature, [K]

170 180 190 200 210 220

6

8

10

12

14

16 B(T)C

B(T)I

B(T)III

B(T

)*1

02

Temperature, [K]

B(T

)

anti-parallelanti-parallel

Temperature

Orientation of the relaxing dipole units

parallelparallel non-non-correlated correlated

systemsystem

14

010

2030

Perm

ittiv

ity'' [

]

Ewa C1 97-06-01 moisture=3.21%

010

2030

Perm

ittiv

ity'' [

]

Ewa C1 97-06-01 moisture=3.21%

22

220 240 260 280 300 320 340 360 380 40015

20

25

30

35

40

45

50

55

A

B

C

Temperature, [oK]

220 240 260 280 300 320 340 360 380 40015

20

25

30

35

40

45

50

55

A

B

C

Temperature, [oK]

200 250 300 350 400 450 500 5500

10

20

30

40

50

60

70

80

I

III1

III2

Temperature, [oK]

200 250 300 350 400 450 500 5500

10

20

30

40

50

60

70

80

I

III1

III2

Temperature, [oK]

Second ProcessSecond Process

15

L -defectL -defect

V* is the defect effective volume

Vf is the mean free volume for one defect

N is the number of defects in the volume of system V

0 exp

HkT C ea

HkT

d

0 exp

HkT C ea

HkT

d

pV

Vff

~ exp*

p

V

Vff

~ exp*

V V Nf for VV

*

f1V V Nf for

VV

*

f1

N T NHkT

d( ) exp

0N T N

HkT

d( ) exp

0

, where, where, where, where ~1

p por f ~

1p por f

kT

Hp a

or exp~

kT

Hp a

or exp~

SiSi

OO

SiSi

OOOO

SiSi

Orientation DefectOrientation Defect Orientation DefectOrientation Defect

D-defectD-defect

0

*1N

V

VC

0

*1N

V

VC

16

Ha is the activation energy of the reorientationHd is the activation energy of the defect formationo is the reorientation (libration) time of the restricted water molecule in the hydrated cluster is the maximum possible defect concentration

Ha is the activation energy of the reorientationHd is the activation energy of the defect formationo is the reorientation (libration) time of the restricted water molecule in the hydrated cluster is the maximum possible defect concentration

2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6

10-5

10-4

10-3

10-2

A

B

C

, [s

]

1000/T, [K-1]

2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6

10-5

10-4

10-3

10-2

A

B

C

, [s

]

1000/T, [K-1]

2.0 2.5 3.0 3.5 4.0 4.510

-7

10-6

10-5

10-4

10-3

10-2

I

III1

III2

, [s

]

1000/T, [K-1]

2.0 2.5 3.0 3.5 4.0 4.510

-7

10-6

10-5

10-4

10-3

10-2

I

III1

III2

, [s

]

1000/T, [K-1]

Sample Ha

[kJ/mol]

Hd

[kJ/mol]

0

[s]

A 55 39 310-14 910-7

B 54 31 310-15 810-6

C 42 30 910-13 210-5

I 41 29 810-13 510-5

III1 45 33 410-14 110-5

III2 39 22 410-12 210-4

Sample Ha

[kJ/mol]

Hd

[kJ/mol]

0

[s]

A 55 39 310-14 910-7

B 54 31 310-15 810-6

C 42 30 910-13 210-5

I 41 29 810-13 510-5

III1 45 33 410-14 110-5

III2 39 22 410-12 210-4

The fitting results for the second process

17

( t /) ~ et / , Df = 3, where Df is a fractal dimension

Percolation:Percolation: Transfer of electric excitation through the developed system of open pores

*

s

dd t tF

*

s

dd t tF

-100 -50 0 50 100 150 200

Temperature [°C]

020

4060

Perm

ittivit

y' []

Freq. [Hz]=5.10e+03 Freq. [Hz]=1.13e+04 Freq. [Hz]=3.24e+04

-100 -50 0 50 100 150 200

Temperature [°C]

020

4060

Perm

ittivit

y' []

Freq. [Hz]=5.10e+03 Freq. [Hz]=1.13e+04 Freq. [Hz]=3.24e+04

Dielectric relaxation in percolationDielectric relaxation in percolation

10-3 10-2 10-1 100

0.0

0.2

0.4

0.6

0.8

Sample A

Sample B

Sample C

Cor

rela

tion

func

tion

time ( s )10-3 10-2 10-1 100

0.0

0.2

0.4

0.6

0.8

Sample A

Sample B

Sample C

Cor

rela

tion

func

tion

time ( s )

18

The Fractal Dimension of Percolation PassThe Fractal Dimension of Percolation Pass

Sample AA BB CC DD II IIII IIIIII

Fractal dimension Df 00..9999 11..8899 11..3311 22..55 11..9966 22..44 22..22

Sample AA BB CC DD II IIII IIIIII

Fractal dimension Df 00..9999 11..8899 11..3311 22..55 11..9966 22..44 22..22

19

d D

d D

w A a exp w A a exp

w w : size distribution function

, , , A, A: empirical parameters

w w : size distribution function

, , , A, A: empirical parameters

V

Vp

V

Vp : porosity of two phase solid-pore system

Vp : volume of the whole empty space

V : whole volume of the sample

: porosity of two phase solid-pore system

Vp : volume of the whole empty space

V : whole volume of the sample

, , : upper and lower limits of self-similarity

DD : regular fractal dimension of the system

, , : upper and lower limits of self-similarity

DD : regular fractal dimension of the system

,D w d1

,D w d1

= /

: scale parameter [,1]

= /

: scale parameter [,1]

Porous medium in terms of regular and random fractalsPorous medium in terms of regular and random fractals

20

,

when a << 1, << 1

1

11

1

1

1

d D

d D

,

when a << 1, << 1

1

11

1

1

1

d D

d D

1

4 D

1

4 D

10

<< 1d=3, << 1

, 10

<< 1d=3, << 1

,

Sample

Fractal

dimension

Df

Porosity (%)

( obtained from relative

mass

decrement measurements )

Porosity (%)

( obtained from

dielectric

measurements )

A 0.99 38 33

B 1.89 48 47

C 1.31 38 37

D 2.5 50 68

I 1.96 26.5 49

II 2.4 42.5 63

III 2.2 25.5 56

Sample

Fractal

dimension

Df

Porosity (%)

( obtained from relative

mass

decrement measurements )

Porosity (%)

( obtained from

dielectric

measurements )

A 0.99 38 33

B 1.89 48 47

C 1.31 38 37

D 2.5 50 68

I 1.96 26.5 49

II 2.4 42.5 63

III 2.2 25.5 56

Porosity DeterminationPorosity DeterminationPorosity DeterminationPorosity Determination (A.Puzenko,et al., Phys. Rev. ((A.Puzenko,et al., Phys. Rev. (BB), ), 6060, 14348, 1999), 14348, 1999)