Ch t i ti f Characterisation of mesopores - ortho...

Ch t i ti f Characterisation of mesopores -ortho-Positronium lifetime m f m

measurement on controlled pore glass controlled pore glass

S Thraenert1 D Enke2 S. Thraenert , D. Enke , R. Krause-Rehberg1

Martin-Luther-Universität Halle-Wittenbergg

Naturwissenschaftliche Fakultät II1Institut für Physik

2Institut für Chemie

OutlinePorous glass - CPG

synthesisyproperties

Principles of PALS d

0.014

0.016

0.018

0.020

1.8 nm

positron and positroniumlifetime measurementthe spectrum

0.006

0.008

0.010

0.012

6 2 nm

4.5 nm

2.5 nm

pdf n

(d)From τ4 to pore size d

the model

E i t l lt100000

1000000

0 5 10 150.000

0.002

0.0046.2 nm

d(nm)

Experimental resultscalibration curvepore size distribution 1000

10000

8 nm

N

d(nm)p

Summary0 100 200 300 400 500 600 700 800 900

10

100

40 nm

o-Ps lifetime measurement on CPG 2

t (ns)

Controlled pore glass - CPGVYCOR-Process

alkali borosilicate

ExtractionTl

HCl/NaOH530 – 710°Cglass

ddPP 1 to 110 nm1 to 110 nmspinodal phase separationspinodal phase separationdecomposition is initiated by heat treatmentalkali rich borate phase pure silicaalkali phase soluble in acid -> silica networkalkali phase soluble in acid -> silica networkpore size depends on basic materialporosity 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.

Controlled pore glass - CPG

different geometries possiblep

homogenous microstructure

controlled pore sizemicrostructure

uniform pore sizewe can choose d (!)


D. Enke, F. Janowski, W. Schwieger, Microporous and Mesoporous Materials 2003, 60, 19-30.




0.014

0.016

0.018

0.020

1.8 nm

positron and positroniumlifetime measurementthe spectrum

0.006

0.008

0.010

0.012

6 2 nm

4.5 nm

2.5 nm

pdf n


the model

E i t l lt100000

1000000

0 5 10 150.000

0.002

0.0046.2 nm

d(nm)


10000

8 nm

N

d(nm)p

Summary0 100 200 300 400 500 600 700 800 900

10

100

40 nm


t (ns)

Principles of PALS: pick-off annihilationPrinciples of PALSpick-off annihilation:

o-Ps captures e- with anti-parallel spinh d i lli i t ll f

positrons from 22Na: thermalize, diffuse, being trapped and annihilate

happens during collisions at walls of porelifetime (τ) decreases rapidlyτ is function of pore size: 1.5 - 142 ns

ppOR: positrons form Ps

palso for closed pore systems25 %

75 %

positronium: p-Ps -> short self annihilation

lifetime of 0.125 nso-Ps -> long self annihilation

lifetime of 142 ns (3γ)-> pick off annihilation (2γ)


> pick off annihilation (2γ)

Principles of PALS

sample preparation: ”sandwich”

positron(ium) lifetime: time between “birth” (1 27 MeV) and “death” (511 keV)positron(ium) lifetime: time between birth” (1,27 MeV) and death” (511 keV)

106

5 nm

104

105

5 nm 26 nm

102

103

0 200 400 600 800101

10

time (ns)


time (ns)

Principles of PALS: typical spectrumtypical lifetime spectrum for CPG (here d = 20 nm):

4 ti l d t4 exponential decay components

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)analysis with LT9 (LifeTime)





0.014

0.016

0.018

0.020

1.8 nm

positron and Positroniumlifetime measurementthe spectrum

0.006

0.008

0.010

0.012

6 2 nm

4.5 nm

2.5 nm

pdf n


the model

E i t l lt100000

1000000

0 5 10 150.000

0.002

0.0046.2 nm

d(nm)


10000

8 nm

N

d(nm)p

Summary0 100 200 300 400 500 600 700 800 900

10

100

40 nm


t (ns)

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 -> δBoltzmann statistics ascribes explicit temperature dependence to the lifetimep p pintegrals of spherical / cylindrical Bessel functionsδ = 0.19 nm mean free path D = 4V/S = dcyl, diameter of cylinder

f th D 4V/S 2/3 d di t f hmean free path D = 4V/S = 2/3 dsphere, diameter of sphere


R. Zaleski, Excited Energy Levels and Various Shapes (EELViS), Institute of Physics, Maria Curie-Sklodowska University, Lublin, Poland




0.014

0.016

0.018

0.020

1.8 nm


0.006

0.008

0.010

0.012

6 2 nm

4.5 nm

2.5 nm

pdf n


the model

E i t l lt100000

1000000

0 5 10 150.000

0.002

0.0046.2 nm

d(nm)


10000

8 nm

N

d(nm)p

Summary0 100 200 300 400 500 600 700 800 900

10

100

40 nm


t (ns)

The experiments at T = 300 K

we measured CPG in a broad pore size rangepore size range

given pore sizes obtained by N2-adsorption or Hg-intrusionN2 adsorption or Hg intrusion

δ = 0.193 nm best fit for our CPG -> calibration curve for calculating pore size

good model for T = 300 K,galso good model for temperature dependence of lifetime?


The T-dependencecalculations: cylindric model with δ = 0.193 nm

although we found good agreement for T > 300 K temperature behavior 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

“ ill power, “capillary condensation”)and o-Ps bonds at the wall

model still too simple but works well for room temperature


temperature

Pore size distribution

D τ4 σ4140

1.8 nm 21.1 ns 14.8 ns2.5 nm 46.9 ns 17.6 ns4 5 nm 65 9 ns 18 9 ns

100

120

(ns) τ4 4.5 nm 65.9 ns 18.9 ns

6.2 nm 80.0 ns 19.3 ns

and its distribution by 60

80

ETE models spheres with δ = 0.19 nm

ill ith δ 0 193)

τ 4

τ4 and its distribution σ4 by analysis of truncated spectra starting from 20 ns

20

40cappillars with δ = 0.193 nm experiment

σ 4 (n

s)

σ4

problem of LT: limit of 142 ns is not taken into account, for large pores unphysically large σ4

1 10 1000

pore size D = 4V/S (nm) from porosimetry

distribution for 4 smaller selected pores


Pore size distribution

distribution of τ4: α4(τ) = α4(λ)λ2, α4(λ) is probability density function (pdf) of 0.012

0.014

0.016

1.8 nm

λ2α4(λ) is probability density function (pdf) of o-Ps annihilation rate, assumed by LT to be a log. Gaussian

0 004

0.006

0.008

0.010

4.5 nm

2.5 nm

df α

4(τ) =

α4(λ

)λ

from distr. α4(τ) it is possible to calc.distribution of diameters of the pore:

⎞⎛

0 20 40 60 80 100 1200.000

0.002

0.004

6.2 nm

4.5 nm

pd

τ(ns)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

cylcyl dd

ddn 44 )()(ττα

τ(ns)

120

140

all we need is a differentiable analytical function τ4 = τ4(dcyl):

60

80

100

ETE Fit

τ 4 (n

s)

⎟⎟⎠

⎞⎜⎜⎝

⎛

+−

+= pcylcyl dd

AAA)/(1 0

2124τ

1 10 1000

20

40


d (nm)

Pore size distributiondistribution norm. to 1

arrows show d directly 0.014

0.016

0.018

0.020

1.8 nm

calculated from mean o-Ps lifetime using cylindric model (1.77 nm, 3.09 nm, 4.38 nm and

0.006

0.008

0.010

0.012

6 2 nm

4.5 nm

2.5 nm

pdf n

(d)

d (n m )

5.80 nm)

this distribution contains the true variation of pore sizes

0 5 10 150.000

0.002

0.0046.2 nm

0 ,0 6

0 ,0 8

0 ,1 0

0 ,1 2

)

( )

g-1 )

true variation of pore sizes but also the effect of irregular not linear character of pores

pore size distribution from BJH method (N2 ads.) for the same 4.5 nm sample

0 ,0 2

0 ,0 4

0 ,0 4

0 ,0 6

V Por

e (c

m3 g

-1

dV/d

r (cm

3 nm

-1 of pores

long tail for larger pores:

overestimation of α4(τ)

volume weighted

0 ,0 00 ,0 0

0 ,0 2

0 5 1 0 1 5d (n m )

f 4( )

nonlinear char. τ4 vs. d


( )

to be published




0.014

0.016

0.018

0.020

1.8 nm


0.006

0.008

0.010

0.012

6 2 nm

4.5 nm

2.5 nm

pdf n


the model

E i t l lt100000

1000000

0 5 10 150.000

0.002

0.0046.2 nm

d(nm)


10000

8 nm

N

d(nm)p

Summary0 100 200 300 400 500 600 700 800 900

10

100

40 nm


t (ns)

Summaryfor T = 300 K we found a calibration curve for CPG

non destructive porosimetry tool for opened and closed pore-systemsmost sensitive for d = 0.5 … 10 nm

for other temperatures the measurements show disagreement to the ETE model -> model still too simplefor pores d < 10 nm we can calculate a pore size distribution

f t near future: 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)

0.014

0.016

0.018

0.020

1.8 nm

0.006

0.008

0.010

0.012

6.2 nm

4.5 nm

2.5 nm

pdf n

(d)

0 5 10 150.000

0.002

0.004

d(nm)


Acknowledgment

Special thanks from our group go to:

R Zaleski and his group R. Zaleski and his group (Lublin/Poland) for EELViS

G. Dlubek (Halle/Germany) for fruitful discussions

all organizers of DZT20


Thanks for your patience!

This talk as pdf?This talk as pdf?

http://positron physik uni halle dehttp://positron.physik.uni-halle.de


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