Characterisation
Ch
t i ti of
f mesopores ortho-Positronium
m lifetime
f m
measurement on
controlled pore glass
S Thraenert1, D.
S.
D Enke2,
R. Krause-Rehberg1
Martin-Luther-Universität
Halle-Wittenberg
g
Naturwissenschaftliche Fakultät II
1Institut für Physik
2Institut für Chemie
Outline
Porous glass - CPG
‰
‰
Principles of PALS
‰
‰
‰
„
0.018
0.016
0.012
1000000
the model
‰
calibration curve
pore size distribution
p
Summary
1.8 nm
0.014
100000
E
Experimental
i
t l results
lt
‰
„
0.020
From τ4 to pore size d
‰
„
positron and
d positronium
lifetime measurement
the spectrum
pdf n(d)
„
synthesis
y
properties
2.5 nm
0.010
4.5 nm
0.008
0.006
6 2 nm
6.2
0.004
10000
0.002
N
„
0.000
0
1000
5
10
8 nm
15
d(nm)
100
40 nm
10
0
100
200
300
400
500
600
700
800
900
t (ns)
o-Ps lifetime measurement on CPG
2
Controlled pore glass - CPG
VYCOR-Process
alkali borosilicate
glass
l
Extraction
T
530 – 710°C
HCl/NaOH
dP
„
„
„
„
„
„
1 to 110 nm
spinodal phase separation
decomposition is initiated by heat treatment
alkali rich borate phase <-> pure silica
alkali phase soluble in acid -> silica network
pore size depends on basic material
porosity of 50 %
F. Janowski, D. Enke in F. Schüth, K.S.W. Sing, J. Weitkamp (Eds.), Handbook of Porous Solids, WILEY-VCH, Weinheim, 2002, 1432-1542.
o-Ps lifetime measurement on CPG
3
Controlled pore glass - CPG
„
„
„
different geometries
p
possible
homogenous
microstructure
uniform pore size
„
controlled pore size
„
we can choose d (!)
D. Enke, F. Janowski, W. Schwieger, Microporous and Mesoporous Materials 2003, 60, 19-30.
o-Ps lifetime measurement on CPG
4
Outline
Porous glass - CPG
‰
‰
Principles of PALS
‰
‰
‰
„
0.018
0.016
0.012
1000000
the model
‰
calibration curve
pore size distribution
p
Summary
1.8 nm
0.014
100000
E
Experimental
i
t l results
lt
‰
„
0.020
From τ4 to pore size d
‰
„
positron and
d positronium
lifetime measurement
the spectrum
pdf n(d)
„
synthesis
y
properties
2.5 nm
0.010
4.5 nm
0.008
0.006
6 2 nm
6.2
0.004
10000
0.002
N
„
0.000
0
1000
5
10
8 nm
15
d(nm)
100
40 nm
10
0
100
200
300
400
500
600
700
800
900
t (ns)
o-Ps lifetime measurement on CPG
5
Principles of PALS:
PALS pick-off annihilation
positrons from 22Na:
„
thermalize, diffuse, being
pp and annihilate
trapped
„
OR: positrons form Ps
25 %
pick-off annihilation:
„
o-Ps captures e- with anti-parallel spin
„
h
happens
during
d i collisions
lli i
att walls
ll of
f pore
„
lifetime (τ) decreases rapidly
„
τ is function of p
pore size: 1.5 - 142 ns
„
also for closed pore systems
75 %
positronium:
„ p-Ps -> short self annihilation
lifetime of 0.125 ns
„ o-Ps -> long self annihilation
lifetime of 142 ns (3γ)
->> pick off annihilation (2γ)
o-Ps lifetime measurement on CPG
6
Principles of PALS
„
sample preparation: ”sandwich”
„
positron(ium) lifetime: time between “birth”
birth” (1,27
(1 27 MeV) and “death”
death” (511 keV)
10
6
10
5
10
4
10
3
10
2
10
1
5 nm
26 nm
0
200
400
600
800
time (ns)
o-Ps lifetime measurement on CPG
7
Principles of PALS: typical spectrum
typical lifetime spectrum for CPG (here d = 20 nm):
„
4 exponential
ti l d
decay components
t
„
p-Ps -> 0.125 ns
„
free positrons ~ 0.5 ns
„
o-Ps in disordered structure ~ 1.5 ns
„
o-Ps in pores
„
analysis with LT9 (LifeTime)
o-Ps lifetime measurement on CPG
8
Outline
Porous glass - CPG
‰
‰
Principles of PALS
‰
‰
‰
„
0.018
0.016
0.012
1000000
the model
‰
calibration curve
pore size distribution
p
Summary
1.8 nm
0.014
100000
E
Experimental
i
t l results
lt
‰
„
0.020
From τ4 to pore size d
‰
„
positron and
d Positronium
lifetime measurement
the spectrum
pdf n(d)
„
synthesis
y
properties
2.5 nm
0.010
4.5 nm
0.008
0.006
6 2 nm
6.2
0.004
10000
0.002
N
„
0.000
0
1000
5
10
8 nm
15
d(nm)
100
40 nm
10
0
100
200
300
400
500
600
700
800
900
t (ns)
o-Ps lifetime measurement on CPG
9
Extended Tao Eldrup model
„
extended TE model (calculations by EELViS):
‰
‰
‰
‰
‰
‰
quantum well of infinite height, but: overlap of o-Ps wave function and wall of pore -> δ
Boltzmann statistics ascribes explicit
p
temperature
p
dependence
p
to the lifetime
integrals of spherical / cylindrical Bessel functions
δ = 0.19 nm
mean free path D = 4V/S = dcyl, diameter of cylinder
mean free
f
path
th D = 4V/S = 2/3 dsphere, diameter
di
t of
f sphere
h
R. Zaleski, Excited Energy Levels and Various Shapes (EELViS), Institute of Physics, Maria Curie-Sklodowska University, Lublin, Poland
o-Ps lifetime measurement on CPG
10
Outline
Porous glass - CPG
‰
‰
Principles of PALS
‰
‰
‰
„
0.018
0.016
0.012
1000000
the model
‰
calibration curve
pore size distribution
p
Summary
1.8 nm
0.014
100000
E
Experimental
i
t l results
lt
‰
„
0.020
From τ4 to pore size d
‰
„
positron and
d Positronium
lifetime measurement
the spectrum
pdf n(d)
„
synthesis
y
properties
2.5 nm
0.010
4.5 nm
0.008
0.006
6 2 nm
6.2
0.004
10000
0.002
N
„
0.000
0
1000
5
10
8 nm
15
d(nm)
100
40 nm
10
0
100
200
300
400
500
600
700
800
900
t (ns)
o-Ps lifetime measurement on CPG
11
The experiments at T = 300 K
„
„
„
„
o-Ps lifetime measurement on CPG
we measured CPG in a broad
pore size range
given pore sizes obtained by
N2-adsorption
adsorption or Hg
Hg-intrusion
intrusion
δ = 0.193 nm best fit for
our CPG -> calibration curve
for calculating pore size
g
good
model for T = 300 K,
also good model for
temperature dependence of
lifetime?
12
The T-dependence
„
„
„
„
calculations: cylindric model
with δ = 0.193 nm
although we found good
agreement for T > 300 K
temperature behavior
cannot be explained very
well at low temperatures
for 20 nm a catching effect
of o-Ps at low temperatures
may occur (van-der-waals
power, “capillary
“
ill
condensation”)
and o-Ps bonds at the wall
model still too simple but
works well for room
temperature
o-Ps lifetime measurement on CPG
13
τ4 (ns)
Pore size distribution
140
D
120
1.8 nm
100
τ4
80
ETE models
spheres with δ = 0.19 nm
cappillars
ill
with
ith δ = 0.193
0 193 nm
experiment
σ4 (ns))
60
40
„
σ4
20
0
1
10
100
„
pore size D = 4V/S (nm) from porosimetry
„
o-Ps lifetime measurement on CPG
τ4
σ4
21.1 ns
14.8 ns
2.5 nm
46.9 ns
17.6 ns
4 5 nm
4.5
65 9 ns
65.9
18 9 ns
18.9
6.2 nm
80.0 ns
19.3 ns
τ4 and its distribution σ4 by
analysis of truncated spectra
starting from 20 ns
problem of LT: limit of 142 ns
is not taken into account, for
large pores unphysically large σ4
distribution for 4 smaller
selected pores
14
Pore size distribution
,
α4(λ) is probability density function (pdf) of
o-Ps annihilation rate, assumed by LT to be
a log. Gaussian
from distr. α4(τ) it is possible to calc.
distribution of diameters of the pore:
⎛ dτ 4
n(d cyl ) = α 4 (τ )⎜
⎜ dd
⎝ cyl
„
0.012
0.010
0.006
4.5 nm
0 004
0.004
6.2 nm
0.002
0.000
0
20
40
60
80
100
120
τ(ns)
⎞
⎟
⎟
⎠
all we need is a differentiable analytical
function τ4 = τ4(dcyl):
2.5 nm
0.008
140
120
100
τ4 (ns)
„
1.8 nm
0.014
2
distribution of τ4: α4(τ) = α4(λ)λ2
pd
df α4(τ) = α4(λ)λ
„
0.016
⎛
⎞
A1 − A2
⎜
⎟
τ 4 = A2 + ⎜
p ⎟
⎝ 1 + (d cyl / d cyl 0 ) ⎠
ETE
Fit
80
60
40
20
0
1
10
100
d (nm)
o-Ps lifetime measurement on CPG
15
Pore size distribution
0.020
„
0.018
0.016
1.8 nm
„
0.014
pdf n(d)
0.012
2.5 nm
0.010
4.5 nm
0.008
0.006
6 2 nm
6.2
0.004
0.002
„
0.000
5
0 ,1 2
VPore (cm3g-1)
0 ,1 0
0 ,0 8
0 ,0 6
d ((n m )
10
pore size distribution from
BJH method (N2 ads.) for
the same 4.5 nm sample
volume weighted
15
0 ,0 6
0 ,0 4
0 ,0 4
0 ,0 2
dV/dr (cm3nm-1g-1)
0
„
0 ,0 2
0 ,0 0
0
5
10
distribution norm. to 1
arrows show d directly
calculated from mean o-Ps
lifetime using cylindric model
(1.77 nm, 3.09 nm, 4.38 nm and
5.80 nm)
this distribution contains the
true variation of pore sizes
but also the effect of
irregular not linear character
of pores
long tail for larger pores:
‰
overestimation of
f α4((τ))
‰
nonlinear char. τ4 vs. d
0 ,0 0
15
d ((n m )
to be published
o-Ps lifetime measurement on CPG
16
Outline
Porous glass - CPG
‰
‰
Principles of PALS
‰
‰
‰
„
0.018
0.016
0.012
1000000
the model
‰
calibration curve
pore size distribution
p
Summary
1.8 nm
0.014
100000
E
Experimental
i
t l results
lt
‰
„
0.020
From τ4 to pore size d
‰
„
positron and
d Positronium
lifetime measurement
the spectrum
pdf n(d)
„
synthesis
y
properties
2.5 nm
0.010
4.5 nm
0.008
0.006
6 2 nm
6.2
0.004
10000
0.002
N
„
0.000
0
1000
5
10
8 nm
15
d(nm)
100
40 nm
10
0
100
200
300
400
500
600
700
800
900
t (ns)
o-Ps lifetime measurement on CPG
17
Summary
for T = 300 K we found a calibration curve for CPG
‰
‰
„
„
„
non destructive porosimetry tool for opened and closed pore-systems
most sensitive for d = 0.5 … 10 nm
for other temperatures the measurements show disagreement to the ETE
model -> model still too simple
for pores d < 10 nm we can calculate a pore size distribution
near future:
f t
‰
‰
phase transition of gas in CPG (to be presented @ PPC9 Wuhan / China, May 2008)
SBA-15 (to be presented @ COPS VIII Edinburgh / Scotland, June 2008)
0.020
0.018
0.016
1.8 nm
0.014
0.012
pdf n(d)
„
2.5 nm
0.010
4.5 nm
0.008
0.006
6.2 nm
0.004
0.002
0.000
0
5
10
15
d(nm)
o-Ps lifetime measurement on CPG
18
Acknowledgment
Special thanks from our group go to:
„
„
„
R. Zaleski and his group
R
(Lublin/Poland) for EELViS
G. Dlubek (Halle/Germany)
for fruitful discussions
all organizers of DZT20
o-Ps lifetime measurement on CPG
19
„
Thanks for your patience!
„
„
This talk as pdf?
http://positron physik uni halle de
http://positron.physik.uni-halle.de
o-Ps lifetime measurement on CPG
20