IN POROUS MATERIALS Yuri Feldman Tutorial lecture 5 in Kazan Federal University 2 Initial sodium borosilicate glass of the following composition by weight 626 SiO 2 304 B 2 ID: 391516
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1
DIELECTRIC RELAXATION IN POROUS MATERIALS
Yuri Feldman
Tutorial
lecture 5 in
Kazan Federal University Slide2
2
Initial sodium borosilicate glass of the following composition
(% by weight): 62.6% SiO2
, 30.4% B2
O
3
, 7%Na2O
heat treatment at 650
0
C for 100h
heat treatment at 490
0
C for 165h
immersion in deionised water
0.5N HCL
drying at 200
0
C
rinsing in deionized water
Sample C
Sample A
additional treatment in 0.5N KOH
dr
y
ing at 200
0
C
rinsing in deionized water
Sample B
Sample D
Porous borosilicate glass samplesSlide3
3
Sample II
additional treatment in 0.5M KOH
drying
rinsing in deionized water
drying
bithermal heat treatment
treatment at
650
0
C and at
5
30
0
C
thermal treatment at 530
0
C
immersion in deionised water
3M HCL
rinsing in deionized water
Sample III
Sample I
Commercial alkali borosilicate glass DV1
of the following composition
(mol.%): 7% Na
2
O, 23% B
2
O
3
, 70% SiO
2Slide4
4
Structure parameters and water contentSlide5
1
Sample C
3
Sample C after heating
Dielectric response of the porous glass materials Slide6
6
3-D PLOTS OF THE DIELECTRIC LOSSES FOR THE POROUS GLASS MATERIALS
Sample C
Sample IISlide7
7
Low frequency behaviour ~20 Hz
High frequency behaviour ~ 100 kHz
A
B
C
A
B
CSlide8
8
1
2
*
( ) =
B
*
n-1
,
>> 1
*
( ) = -i
0
/
0
1)
Jonscher
Conductivity
*
( ) = / [1 + ( i )
]
+
2)
Havriliak-Negami
The fitting modelSlide9
9
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/mol1st
ProcessSlide10
10
Samples
Humidity
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
from ln()Slide11
11
Temperature dependence of the dielectric strengthSlide12
12
Parallel and anti-parallel
orientation
B(T)
anti-parallel
Temperature
Orientation of the relaxing dipole units
parallel
non-correlated systemSlide13
13
The symmetric broadening of dielectric spectra
The Empirical
Cole-Cole law
(1941 )
(1-
)
/ 2
Character of
interaction
Temperature
Structure
etc
is a phenomenological parameter
is the relaxation time
?
is the
dielectric strength
?
13Slide14
N.
Shinyashiki, S. Yagihara
, I. Arita, S.
Mashimo, JPCB,
102
(1998) p. 3249
What is behind the relationship
()?
How can we use experimental knowledge about
and ?For instance does their temperature or concentration dependencies explain the nature of dipole matrix interactions in complex systems
?
14Slide15
The Traditional Theoretical Models
Fractional Cole-Cole equation
for relaxation function
f(t)
Anomalous Diffusion
Dipole-Matrix interactions
Fractal set
Due to space averaging both space and time fractal properties are incorporated in parameters
.
Continuous time random walk (CTRW) model.
The random Energy Landscape
r
Levy flights
R.Metzler
, J.
Klafter
, Physics Reports, 339 (2000) 1-77
W.T. Coffey, J. Mol. Liq. 114 (2004) 5-25
R.Hilfer
,
Phisica
A, 329 (2003) 35-40
15Slide16
16
Dipole-matrix interaction
The symmetric broadening of dielectric spectra
Ryabov et al
J. Chem. Phys.
116 (2002) 8611.
Fractal set Slide17
All dependences
for
different CS can be described
by Universal function
N
is the average number of
relaxation
acts
in the time interval t=
is the macroscopic relaxation time
0 is the
cutoff relaxation time
- fractal dimension of the relaxation
acts in time
<
0
>
0
A
is the asymptotic value of fractal dimension not dependent on temperature
,
and
N depends on temperature, concentration, etc
is
a minimum number of relaxation acts
If
is a monotonic function
Scaling relationsSlide18
18
Sample C
A
0.19
is the fractal dimension of
the time
set of interactions
Sample
Porous
Size, nmSpecific porous area, m2/gPorosity%H,%
C
280-4009.88038
3.2Rich water content
The total number of
the relaxation
acts during
the time
>
0
t
0
0
During the
time of 1
ps
, 70
relaxation acts occurs.
The
density of the
relaxation
acts on the time interval
Slide19
Sample D
Poor water content
<
0
A=0.495
t
0
0
<
0
Sample
Porous
Size, nm
Specific porous area, m
2
/g
Porosity%
H,%
D
300
8.74
50
1.2
t
0
0
19Slide20
20
How can we link the numbers
of the relaxation acts in time and the molecular
structure, in which they
occurred ?
Additional
parameters
should be considered :
which can be
incorporated by using the Kirkwood-Froehlich approach
Kirkwood-Froehlich approach
Temperature
B
Orientation of the relaxing dipole units
anti-parallel
parallel
non-correlated system
is
the average dipole moment
of the
i
-
th
cell
<…> indicate
a
statistical averaging
over all possible configurations.
Θ
is
the angle between the dipole moment of a given
cell and neighboring ones,
N
n
is the number of the nearest
cell dipoles.Slide21
21
For water molecules in porous
glasses
The effective number
of the correlated water
molecules is
Sample C
T
m
195 K
θ
is the angle between the dipole moment
of a given cell and neighboring ones,
Nn
is the number of the nearest cell dipoles.
reflect the system state with
balanced parallel and anti parallel dipole orientations . The corresponding values of parameters are :
The
maximum conditions: Slide22
Sample C:
l
The kinetic and structural properties
The CC relaxation process is associated with the
anomalous sub-diffusion.
R. Metzler and J.
Klafter
, Phys. Rep., 339,1(2000
).
R. Hilfer, Applications of Fractional Calculus in Physics,
Ed. By R
. Hilfer
,(World Scientific, Singapore,2000).The time-space scaling relationship
A
nomalous sub-diffusion
Arrhenius temperature dependence
is a monotonically
decreasing function
of
temperature throughout the temperature range
An anti parallel orientation of the cell dipoles, m, is stipulated by the influence of the porous matrix interface
Two main scales of cluster in the Ice-like layer on the matrix interface
L
l
L
2
is the
macroscopic scale
of the matrix interface area
l
2
is
the area of the
mesoscopic scale
of the Kirkwood-Froehlich elementary unit
with an average dipole moment
m
At T<<T
m
Slide23
Sample C:
Coupling the kinetic and structural properties
The parallel orientation of the cell dipoles,
m
, is stipulated by the influence of the external layers of the water molecules
At T >> T
m
Slide24
T
m
= 195K
L
R
R
L
The
Kirqwood
-Froehlich cell
- F
1
- F
2
- HSlide25
25
2
Second ProcessSlide26
26
L -defect
V
*
is the defect effective volume
V
f
is the mean free volume for one defect
N is the number of defects in the volume of system V
, where
Si
O
Si
O
O
Si
Orientation Defect
D-defectSlide27
27
H
a
is the activation energy of the reorientation
H
d
is the activation energy of the defect formation
o is the reorientation (libration) time of the restricted water molecule in the hydrated cluster is the maximum possible defect concentration
The fitting results for the second processSlide28
28
( t /
) ~ e(
t /
, Df = 3, where D
f is a fractal dimension
Percolation:
Transfer of electric excitation through the developed system of open pores
Dielectric relaxation in percolationSlide29
29
The Fractal Dimension of Percolation PassSlide30
30
w
: size distribution function
, , A
: empirical parameters
: porosity of two phase solid-pore system
V
p
: volume of the whole empty space
V
: whole volume of the sample
,
: upper and lower limits of self-similarity
D
: regular fractal dimension of the system
= /
: scale parameter [,1]
Porous medium in terms of regular and random fractalsSlide31
31
Porosity Determination
(
A.Puzenko,et
al., Phys. Rev. (
B
),
60
, 14348, 1999)Slide32
32
O
Percolation
The transition associated with the formation of a continuous path spanning an arbitrarily large ("infinite") range.
The percolation cluster is a self-similar fractal.
y
z
B
C
E
D
Q
A
x
O
Static condition of
renormalization