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Novel Far-Infrared Application to
Spectroscopic Techniques and Their the^Stu&y-of- Zeolite
Chemistry
Simon Robert Gibbon
A Thesis submitted for the degree of Doctor of Philosophy of the
University of London and for the Diploma of
Imperial College
Department of Electrical Engineering, Imperial College of
Science and Technology, South Kensington,London SW7
November 1987
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To Kate
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Abstract
The use of untuned resonators has been developed so as to allow
absorptions of zeolites to be studied below 100cm“l.
Computer simulations of the radiation density within various
geometries of untuned resonator were used to determine the best
design for untuned resonators to study solid samples. Several
different resonators were used in order to test the predictions of
the simulations.
An untuned resonator was used to study the absorptions of sodium
exchanged zeolites X, Y, A and L.No sharp absorptions were observed
below 100cm“ .̂ Silicalite, a high silica zeolite, was also studied
and found to have weak absorptions below 40cm"l when dehydrated.
These absorptions were seen to disappear on rehydration of the
zeolite.
The vibrational spectra below 400cm~l of a series of zeolites
were obtained, in order to gain insight into the interactions of
adsorbates with cations within the zeolites.
Monovalent cation forms of hydrated zeolite X were studied both
at 303K and 108K. Spectra at low temperatures show localisation of
cations about the most energetically favourable site. This has
revealed information on the mobility of different cations and their
degree of solvation within the zeolites.
A series of monovalent-divalent mixed cation exchanged zeolite A
have been investigated and their spectral properties related to
ion-exchange properties.
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The spectra of a large number of cation exchanged zeolite L
samples have been determined and related to the results obtained
from Szilard-Chalmers recoil studies.
These results have been used to obtain a clearer picture of the
environment of cations, both solvated and dehydrated, within
zeolites.
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Acknowledgements 5
I am greatly indebted to Professors J.C. Anderson,H.A. Gebbie
and L.V.C. Rees for their friendly supervision and guidance.
I would like to thank all my friends in both the Electrical
Engineering and Chemistry Departments for many fruitful
discussions, encouragement and generosity.
Financial support was provided by the Science and Engineering
Research Council in the form of a Research Studentship during the
course of this work.
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CONTENTS1 Introduction ................................... 141.1
Zeolites ..................................... 141.2 Major Uses of
Zeolites ....................... 141.2.1 Sorption
................................... 151.2.2 Molecular Sieving
.......................... 151.2.3 Ion Exchange
............................... 161.2.4 Catalysis
.................................. 161.2.5 Curious Uses
............................... 171.2.6 Future Uses
................................ 181.3 Zeolite Structure
............................ 181.3.1 Zeolite L
.................................. 191.3.2 Zeolite X
.................................. 211.3.3 Zeolite A
.................................. 221.3.4 Mordenite
.................................. 231.3.5 Silicalite-1
............................... 251.4 Infrared Spectroscopy for the
Study of ZeoliteStructure .............. 261.5 Magic Angle-Spinning
Solid State NuclearMagnetic Resonance
............................... 291.6 Far-Infrared Spectroscopy
.................... 301.7 Far-Infrared Spectroscopy of Zeolites
........ 311.8 The Untuned Resonator Technique .............. 391.9
Objectives of the Work ....................... 402 Fourier
Transform Spectroscopy................. 422.1 The Mathematics of
Fourier Transform Spectroscopy
......................................... 433 The Theory of Untuned
Resonators ............... 533.1 The Theory of Homogeneous Cavity
Sample Cellsfor Gaseous Absorbers ............................
533.2 Solids in Homogeneous Cavities ............... 633.3
Absorption of Parallel Sided Sheets .......... 673.3.1 Calculation
of Absorption .................. 673.3.2 Interferometer
Transmission ................ 713.3.3 Reflection from Vacuum Cavity
Window....... 743.3.4 Absorption of Parallel Sided Sheet within
anUntuned Resonator ................................ 773.4
Inhomogeneity ............................... 794 Cation Vibrations
within Zeolites ............... 805 Experimental Techniques and
Equipment.......... 865.1 Characterisation of Zeolites
................. 865.1.1 Supplied Zeolites
.......................... 865.1.2 Preparation of Ion Exchange
Samples ........ 875.1.2.1 Zeolite L
................................ 875.1.2.2 Zeolite X
................................ 875.1.2.3 Zeolite A
................................ 885.1.2.4 Silicalite-1
............................. 885.1.2.5 Mordenites
............................... 885.1.3 Hydration
.................................. 885.1.4 Dehydration
................................ 885.1.5 Polythene Pellets
.......................... 895.1.6 Analysis of Zeolites
....................... 90
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5.1.6.1 Wet Chemistry :- Analysis for Silicon andAluminium
........................................ 905.1.6.2 Electron
Spectroscopy for Chemical Analysis(E.S.C.A.)
....................................... 905.1.6.3 Thermogravimetric
Analysis ............... 915.1.6.4 Mid-Infrared Analysis
.................... 915.2 Far-Infrared Spectroscopy
.................... 925.2.1 Instrumental
............................... 925.2.2 Computation
................................ 955.3 Untuned Resonator
Far-Infrared Work .......... 975.3.1 Common Experimental Technique
.............. 975.3.2 The Original Cavity System.................
995.3.3 The Novel Cavity System .................... 1016 The
Far-Infrared Spectra of Zeolites ........... 1056.1 The Effect of
Hydration on Cations withinZeolite X
........................................ 1056.1.1 Sodium Zeolite X
........................... 1086.1.2 Potassium Zeolite X
........................ 1096.1.3 Ammonium Zeolite X
......................... 1136.1.4 Lithium Zeolite X
.......................... 1146.1.5 Common Themes From Zeolite X
............... 1156.2 Hydration of Zeolite A
....................... 1166.2.1 Sodium Zeolite A
........................... 1186.2.2 Divalent Cation Zeolite A
.................. 1206.2.3 Themes From Zeolite A
...................... 1246.3 Cations in Zeolite L
........................ 1256.3.1 Cation Site Identification in
Zeolite L .... 1276.3.2 Effect of Hydration On Zeolite L
........... 1346.3.3 Varying Degree of Exchange in Zeolite L ....
1376.3.4 Themes From Zeolite L ...................... 1416.4
Natural Clinoptilolite ...................... 1426.5 Zeolon 700 -
Natural Ferrierite .............. 1466.6 Mordenites
................................... 1496.6.1 Themes From Mordenite
...................... 1587 Computer Simulation of Untuned
Resonators ....... 1607.1 Objective
................................... 1607.2 Background
................................... 1607.2.1 Simplifications
............................ 1617.3 The Components of the
System................. 1637.3.1 The Source
................................. 1637.3.2 The Cavity
................................. 1647.3.3 Absorber
................................... 1647.3.4 Detector
................................... 1657.3.5 Radiation
.................................. 1657.4 Mathematics of the
Simulation ................ 1657.4.1 Ray Bouncing
Program....................... 1657.4.2 Absorber Interaction
Program ............... 1757.4.3 Cavity Radiation
Program................... 1757.4.4 Cavity Hole Calibration
.................... 1788 Results of Computer Simulations of An
UntunedResonator ............ 1798.1 Background
................................... 1798.2 Results
...................................... 1828.2.1 The Effect of
Varying the Plug Size ........ 182
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8.2.2 The Effect of Varying the Entrance and ExitHole Sizes
....................................... 1858.2.3 The Effect of
Varying the Exit Hole Size .... 1888.2.4 The Effect of Varying Exit
Height .......... 1918.3 Design Considerations for an Untuned
Resonator 1948.4 Lessons Learnt ...............................
1959 Untuned Resonator Results ...................... 1979.1
Determination of the Cavity Q ................ 1979.2 Polymers
..................................... 1999.2.1 Synthetic Polymers
......................... 1999.2.2 Natural Polymers
........................... 2019.2.2.1
Cellulose................................. 2019.2.2.2
Lignin.................................... 2059.3 The State of
Water within Zeolitic Cavities ... 2069.4 Determination of
Effective Pathlength In theNovel Cavity
..................................... 2119.5 Uniformity of
Radiation Field within the NovelCavity
........................................... 2159.6 The Effect of
Hydration on the VeryFar-Infrared Spectrum of Silicalite
.............. 21710 Conclusions ...............................
22210.1 Far-Infrared Spectroscopy of Zeolites ....... 22210.2
Untuned Resonator Studies ................... 223
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FIGURES1.1a Building Units of Zeolite L Structure ....... 201.1b
Atomic Structure of Zeolite L perpendicular tothe C-Axis
....................................... 201.1c Bond Network of
Zeolite L perpendicular to theC-Axis
........................................... 201.Id Atomic Structure
of Zeolite L parallel to theC-Axis
........................................... 21l.le Bond Network of
Zeolite L parallel to theC-Axis
........................................... 211.2a Structure of
Sodalite Cage in Zeolite X ..... 221.2b bond Network of Zeolite X
................... 221.3a Atomic Structure of Zeolite A
............... 231.3b Bond Network of Zeolite A
................... 231.4a Atomic Structure of Potassium Mordenite
..... 241.4b Bond Network of Potassium Mordenite ......... 241.4c
Atomic Structure of Calcium Mordenite ....... 251.4d Bond Network
of Calcium Mordenite ........... 251.5a Secondary Building Unit of
Silicalite ...... 251.5b Atomic Structure of Silicalite-1
............ 261.5c Bond Network of Silicalite-1 ................
262.1 Fourier Spectrometer ......................... 432.2
Interferogram of Single Frequency Source ..... 462.3 Interferogram
of Broad Band Source .......... 493.1 Untuned Resonator
............................ 533.2 Photons Through Cavity Hole
.................. 583.3 Screening Effect
............................. 663.4 Parallel Sided Sheet Geometry
................ 683.5 Interferometer Interference
.................. 723.6 Transmission of 6 Micron Beamsplitter
........ 733.7 Transmission of 35 Micron Beamsplitter ....... 733.8
Transmission of 100 Micron Beamsplitter ...... 733.9 Transmission
of 135 Micron Beamsplitter ...... 733.10 Variation of Transmission
of llOum CavityWindow with Wavenumber ...........................
753.11 Variation of Window Transmission withAbsorption Coefficient
........................... 763.12 Variation of Window Transmission
withRefractive Index ................................. 763.13
Variation of Window Transmission withThickness
........................................ 763.14 Variation of Window
Transmission withWavenumber .......................................
763.15 Variation of Absorption Integral withAbsorption Coefficient
........................... 773.16 Variation of Absorption Integral
withRefractive Index ................................. 773.17
Variation of Absorption Integral withThickness
........................................ 783.18 Variation of
Absorption Integral Transmissionwith Wavenumber
.................................. 785.1 RIIC FS-720 Fourier
Spectrophotometer ........ 935.2 Construction of a Golay Cell
................. 945.3 Original Cavity Set-Up
....................... 1005.4 Original Cavity Signal Flow
.................. 1015.5 Novel Cavity Set-Up
.......................... 103
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5.6 Novel Cavity Signal F l o w .................... 1046.1a
Cation Site I' in Zeolite X ................. 1066.1b Cation Site I
in Zeolite X .................. 1066.1c Cation Site II' in Zeolite
X ................ 1076 . Id Cation Site II in Zeolite X
................ 1076.2 Far-Infrared Spectra of Sodium Zeolite X
..... 1086.3 Far-Infrared Spectra of Potassium Zeolite X ... 1106.4
Far-Infrared Spectrum of Ammonium Zeolite X. .. 1136.5 Far-Infrared
Spectrum of Lithium Zeolite X .... 1146 .6a Cation Site I in
Zeolite A .................. 1166 .6b Cation Site II in Zeolite A
................. 1176 .6c Cation Site III in Zeolite A
................ 1176 . 8 Far-Infrared Spectrum of Sodium Zeolite A
.... 1196 . 8 Far-Infrared Spectrum of Magnesium Zeolite A ..
1216.9 Far-Infrared Spectrum of Calcium Zeolite A .... 1226.11
Far-Infrared Spectrum of Magnesium CalciumZeolite A
........................................ 1236.11a Cation Site A in
Zeolite L ............. 1256.11b Cation Site A in Zeolite L
............. 1266.11c Cation Site C in Zeolite L .................
1266 . lid Cation Site D in Zeolite L ................. 1266.12
Far-Infrared Spectra of Dehydrated PotassiumZeolite L
........................................ 1296.13 Far-Infrared
Spectra of Dehydrated CaesiumZeolite L
........................................ 1296.14 Far-Infrared
Spectra of Dehydrated RubidiumZeolite L
........................................ 1316.15 Far-Infrared
Spectra of Dehydrated AmmoniumZeolite L
........................................ 1316.16 Far-Infrared
Spectra of Dehydrated SodiumZeolite L
........................................ 1336.17 Far-Infrared
Spectra of Dehydrated LithiumZeolite L
........................................ 1336.18 Far-Infrared
Spectra of Hydrated PotassiumZeolite L
........................................ 1356.19 Far-Infrared
Spectra of Hydrated SodiumZeolite L
........................................ 1356.20 Far-Infrared
Spectra of Hydrated LithiumZeolite L
........................................ 1376.21 Far-Infrared
Spectra of Hydrated RubidiumZeolite L
........................................ 1376.22 Far-Infrared
Spectra of Potassium/AmmoniumZeolite L at 108K
................................. 1386.23 Far-Infrared Spectra of
Potassium/AmmoniumZeolite L at 303K
................................. 1386.24 Far-Infrared Spectra of
Potassium/SodiumZeolite L at 108K .................................
1396.25 Far-Infrared Spectra of Potassium/SodiumZeolite L at 303K
................................. 1396.26 Far-Infrared Spectra of
Potassium/LithiumZeolite L at 108K
................................. 1406.27 Far-Infrared Spectra of
Potassium/LithiumZeolite L at 303K
................................. 1406.28 Far-Infrared Spectra of
Potassium Zeolite L at108K
............................................. 1416.29 Far-Infrared
Spectra of Potassium Zeolite L at303K
............................................. 141
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6.30b Bond Network of Clinoptilolite ............. 1436.30a
Atomic Structure of Clinoptilolite ......... 1436.31a
Clinoptilolite Cation Site A ............... 1436.31b
Clinoptilolite Cation Site B ............... 1446.32 Far-Infrared
Spectra of Natural
Clinoptilolite..................................................
1456.33a Atomic Structure of Ferrierite ............. 1476.33b Bond
Network of Ferrierite ................. 1476.33c Magnesium Cation
Site in Ferrierite ........ 1476.33d Sodium Cation Site in
Ferrierite ........... 1486.34 Far-Infrared Spectra of Natural
Ferrierite -Zeolon 700 .......................................
1496.35a Potassium in Mordenite Cation Site II ..... 1506.35b
Potassium in Mordenite Cation Site I V ..... 1506.35c Potassium in
Mordenite Cation Site VI ..... 1516.36 Far-Infrared Spectrum of
Dehydrated HydrogenMordenite
........................................ 1526.37 Far-Infrared
Spectrum of Dehydrated SodiumMordenite
........................................ 1526.38 Far-Infrared
Spectrum of Dehydrated LithiumMordenite
........................................ 1536.39 Far-Infrared
Spectrum of Dehydrated PotassiumMordenite
........................................ 1536.40 Far-Infrared
Spectrum of Dehydrated RubidiumMordenite
........................................ 1546.41 Far-Infrared
Spectrum of Dehydrated CaesiumMordenite
........................................ 1546.42a Calcium in
Mordenite Cation Site I .......... 1546.42b Calcium in Mordenite
Cation Site III ....... 1556.42c Calcium in Mordenite Cation Site I
V ......... 1556.42d Calcium in Mordenite Cation Site VI ........
1556.43 Far-Infrared Spectrum of Dehydrated MagnesiumMordenite
........................................ 1566.44 Far-Infrared
Spectrum of Dehydrated BariumMordenite
........................................ 1566 .45 Far-Infrared
Spectrum of Dehydrated CobaltMordenite
........................................ 1576.46 Far-Infrared
Spectrum of Dehydrated NickelMordenite
........................................ 1576.47 Far-Infrared
Spectrum of Dehydrated CopperMordenite
........................................ 1577.1 Two Dimensional
Cavity Replicas .............. 1617.2 Plan Views of Cavity
......................... 1627.3 Orientation of Axes
.......................... 1667.4 2-D Horizontal Reflection
.................... 1677.5 Off-Axis 2-D Horizontal Reflection
........... 1697.6 Infinite Cavity ..............................
1707.7 Reflections of Plug .......................... 1728.1 Source
Rays .................................. 1798.2 Radial Positions
............................. 1808.3 Vertical Positions
........................... 1818.4 Fraction of Rays Detected vs.
Plug Size ...... 1838.5 Detected Energy vs. Plug Size
................ 1838.7 Inhomogeneity vs. Plug Size
.................. 1848 . 6 Detected Pathlength vs. Plug Size
............ 1848 . 8 Q vs. Plug Size
.............................. 1858.10 Detected Energy vs. Hole
Size ............... 186
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8.9 Fraction of Rays Detected vs. Hole Size ..... 1868.12
Inhomogeneity vs. Hole Size ................. 1878.11 Detected
Pathlength vs. Hole Size ........... 1878.13 Q vs. Hole Size
............................. 1888.15 Detected Energy vs. Exit Hole
Size .......... 1898.14 Fraction of Rays Detected vs. Exit Hole
Size . 1898.17 Inhomogeneity vs. Exit Hole Size ............
1908.16 Detected Pathlength vs. Exit Hole Size ...... 1908.18 Q vs.
Exit Hole Size ........................ 1918.20 Detected Energy vs.
Exit Height ............. 1928.19 Fraction of Rays Detected vs.
Exit Height .... 1928.21 Detected Pathlength vs. Exit Height
......... 1938.22 Inhomogeneity vs. Exit Height ...............
1938.23 Q vs. Exit Height ........................... 1949.1
Far-Infrared Spectrum of Cavity with Calibration Hole
........................................ 1989.2 Far-Infrared
Variation of Cavity Q ........... 1999.3 Far-Infrared Absorption
Coefficient of PVC .... 2009.4 Far-Infrared Absorption Coefficient
of PVDF ... 2009.5 Far-Infrared Absorption Coefficient of PTFE ...
2019.6 Structure of Cellobiose ...................... 2029.7
Structure of Cellulose ....................... 2029 . 8
Far-Infrared Spectrum of Qualitative FilterPaper
............................................ 2039.9 Far-Infrared
Spectrum of Hardened Filter Paper 2039.10 Far-Infrared Spectrum of
Wiper Paper ........ 2049.11 Far-Infrared Spectrum of Paper
Computer Tape . 2049.12 Far-Infrared Spectrum of Cartridge Paper
.... 2059.13 Far-Infrared Spectrum of Lignin ............. 2069.14
Far-Infrared Absorption Coefficient of SodiumZeolite A
........................................ 2099.15 Far-Infrared
Absorption Coefficient of SodiumZeolite X
........................................ 2109.16 Far-Infrared
Spectrum of Interferometer Systemwith Water Vapour
................................ 2129.17 Far-Infrared Spectrum of
Cavity ContainingWater Vapour .....................................
2129.18 Far-Infrared Dependence of Cavity Pathlength . 2149.19
Vertical Cavity Homogeneity Tests .......... 2169.20 Horizontal
Cavity Homogeneity Tests ......... 2179.21 Far-Infrared Absorption
Coefficient of DriedSilicalite
....................................... 2199.22 Far-Infrared
Absorption Coefficient of WetSilicalite
....................................... 220
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TABLES1.2 Cation Vibrations for Zeolites X and Y afterButler et
al ..................................... 331.2 Cation Vibrations
for Zeolites X, Y and E afterBrodskii and Zhdanov
............................. 351.3 Cation Vibrations for Zeolites
X, Y and US-EXafter Peuker and Kunath ..........................
361.4 Cation Vibrations for Zeolite A after Kosslicket al
............................................ 375.1 Golay Cell
Parameters ........................ 986.1 Calculated Vibrational
Band Assignments forCations in Zeolite L Based on Bands Observed in
Potassium Zeolite L .............................. 1306.2
Vibrational Band Assignments for Cations inZeolite L
........................................ 134
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Corrigenda
Pages 8 6 , 130-141 : The formula used for zeolite L is based on
eight cations per unit cell in the original material. It is more
normal to state the formula in terms of 36 tetrahedral atoms per
unit cell. The original zeolite L formula stated in this form
isNa0.2k 7.6 C (a 1 0 2 ) 8 (s i -02) 28 3 • (H2° )24 -
Page 122 : The excess form used in figure 6.9 is a non-washed
calcium exchanged zeolite A containing the calcium exchange salt,
calcium chloride.
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1 Introduction
1.1 Zeolites
Zeolites are tectosilicates; crystalline, three dimensional
frameworks of silica tetrahedra in which some of the silicons are
replaced by aluminium^/2 ,3, The replacement of silicon by
aluminium gives rise to a framework negative charge which is
balanced by cations located at energetically favourable sites about
the framework. Zeolites have the general formula :
M V [ { A l 0 2)x{ Si 02)y] . z H 20
where M is a cation of charge n+ and x, y and z are numbers of
atoms.
The three dimensional framework is an open structure in which
large void volumes, cavities and channels, are present. In these
cavities and channels it is possible to adsorb gases or liquids or
build-up metal clusters^.These pores allow the cations present to
be exchanged under mild conditions. Sites on the framework or the
exchangeable cations or metal clusters present can act as catalytic
centres for reactant species which enter the channel structure^. in
normal atmospheric conditions most zeolites absorb water vapour
from the atmosphere to fill their cavities.
1.2 Major Uses of Zeolites
The uses of zeolites are many and varied, ranging from catalysis
to meat production. The main uses and the unique characteristics
which command their use over other materials are outlined
below.
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1.2.1 Sorption
One of the first commercial uses of zeolites was as a desiccant;
several zeolites both natural and synthetic have a very high
capacity for water uptake and gases dried through zeolites have a
very low residual water content^. Sodium zeolite A produced by
Union Carbide? as Linde Molecular Sieve 4A has a water uptake of
29% by weight and pellets can be produced with a capacity of 22%.
Zeolites are used as moisture scavengers in polyurethane
formulations to stop break-up of the pore system causing blistering
and as hydrogen absorbers in high zinc paints8 . Some paper
coatings now incorporate zeolites which scavenge water to stop
adhesion failure between the coating and the paper, roughen the
surface and give heat and light resistance^.
A p a r t f r o m t h e i r a b i l i t y t o s e l e c t i v e
l y r e m o v e w a t e r
d u e t o t h e i r p o l a r n a t u r e , t h e y a r e a b l
e t o r e m o v e a w i d e
v a r i e t y o f p o l a r m o l e c u l e s f r o m g a s e s
a n d l i q u i d s ^ .
Z e o l i t e s a r e u s e d f o r t h e r e m o v a l o f w a
t e r , c a r b o n
d i o x i d e a n d s u l p h u r c o m p o u n d s f r o m o i
l r e l a t e d g a s e s ;
p o l l u t i o n c o n t r o l i n e x h a u s t g a s ; f o r
t h e r e m o v a l o f
m e r c u r y v a p o u r a n d o x i d e s o f n i t r o g e n
f r o m f a c t o r y w a s t e
g a s e s ^ .
1.2.2 Molecular Sieving
Z e o l i t e s h a v e l o n g b e e n u s e d a s m o l e c u
l a r s i e v e s , i n
t h a t t h e y s e l e c t i v e l y a b s o r b m o l e c u l
e s o n t h e b a s i s o f
t h e s i z e o f t h e molecules^. Z e o l i t e s , b e i n g
c r y s t a l l i n e , h a v e a p r e c i s e l y d e f i n e d p
o r e d i a m e t e r i n t o t h e
t h r e e d i m e n s i o n a l c h a n n e l a n d c a v i t y
s t r u c t u r e .
M o l e c u l e s w h i c h p o s s e s s a V a n d e r W a a l
' s d i a m e t e r g r e a t e r
t h a n t h i s c r i t i c a l p o r e d i a m e t e r a r e u
n a b l e t o e n t e r t h e
c h a n n e l s t r u c t u r e a n d a r e t h u s n o t a d s
o r b e d ; w h e r e a s
m o l e c u l e s w h i c h p o s s e s s V a n d e r W a a l '
s d i a m e t e r l e s s t h v n
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the critical pore diameter can enter and be adsorbed. Linde
Molecular Sieve 5A, calcium zeolite A is used for the separation of
n-type paraffins from petroleum fractions. It works by admitting
the n-type paraffins and excluding iso-type paraffins and aromatics
due to the size of its pores^ (0.5nm).
1.2.3 Ion Exchange
Many zeolites behave as ion exchangers, in that ions from the
zeolite exchange with ions in a solution in which the zeolite is
placed. The ultimate degree of exchange is controlled by the
thermodynamics of the exchange and the relative size of the ions
and the controlling apertures to the cation sites. Some zeolites
are selective for specific cations. The naturally occurring zeolite
clinoptilolite has been used for waste water purification to
selectively remove ammonium ions^. A major development in the use
of zeolites for ion exchange is the gradual replacement of
phosphate water softeners by sodium zeolite A in detergents, due
largely to the serious ecological problems caused by phosphate
ions. Sodium zeolite A selectively exchanges sodium ions for the
calcium and magnesium ions^5/ which cause hard water.
1.2.4 Catalysis
The primary advantage of zeolites for use as catalysts in
various petrochemical processes is their shape selectivity. This is
due to the fixed size of the cavities near catalytically active
siteŝ -G. The primary catalytic sites within zeolites are the
Bronsted and Lewis acid sites, similar to those in amorphous
aluminosilicates, but due to the molecular shape selectivity the
product distribution obtained is far more favourable and can be
controlled by the choice of zeolite
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catalyst. The acid sites, present within the zeolites, catalyse
cracking and isomerization reactions of alkanes and alkylation of
aromatic hydrocarbons1?. Hydrocracking can be accomplished by the
incorporation of metals normally used for homogeneous type
catalysis, i.e. lanthanides and platinum^.
The largest step change in zeolite technology occurred with the
discovery of Mobil's zeolite ZSM-5 (Zeolite Socony M o b i l Z S M
- 5 is able to catalyse the conversion of methanol to high octane
petrol at low temperatures and pressures. The largest use for ZSM-5
is in the isomerization of xylenes, in which it produces large
excess quantities of para-xylene over the other isomer because of
the diffusion controlled reaction.ZSM-5 has very low contents of
both cations and aluminium. It also possesses a pore structure
devoid of cavities and therefore its catalytic life is extended due
to lack of coke build-up which needs cavities to
occurrapidly^O.
1.2.5 Curious Uses
Some of the most unconventional uses of zeolites have been in
agriculture and horticulture. Zeolite addition to soil in Japan has
been carried out throughout recorded history^l. The scientific
basis for its use is now understood to be the inhibition of
ammonium ion leaching, as well as the concentration and retention
of heavy metal ions, stopping their introduction into food crops22.
The use of zeolites as feed supplements for pigs23 and chickens24
has been shown to give rise to weight rises and increased egg
yields.
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In the future the most spectacular advances are likely to be
made in the field of zeolite catalysis following in the footsteps
of ZSM-5 rather than in novel agricultural uses. Work is already
being undertaken to fully understand the total nature of shape
selectivity in catalysis within the complex three dimensional
cavities of zeolites2 .̂ Detailed crystallographic work to
precisely locate positions of c a t i o n s 2 **/27 has been going
on for some time and now this is being complemented by computer
graphics2** which allow true visualisation of the processes
involved. This increased understanding, given by energy calculation
programs2**, should allow predictions to be made as to the most
advantageous geometries and compositions for the optimal
catalyst.
1 . 2 . 6 F u tu r e U se s
1.3 Zeolite Structure
Zeolites are hydrated aluminosilicates with uniquely defined
crystal structures. They possess a pore structure within which are
sited cations. The cation sites are uniquely defined forming a set
of sites of differing energies, in which the cations are
distributed according to their type and statistics. It is possible
to say only that a particular cation site has a fractional
occupancy, meaning that only a particular fraction of the total
number of sites of that type are occupied by cations. The occupancy
fraction of a particular set of sites will vary with the type of
cation due to size and charge differences, as well as with
differences in aluminium to silicon ratio and degree of hydration.
Certain cations are not able to fit into certain sites and only
half the number of divalent cations compared to monovalent cations
are needed to balance a given framework charge.
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19
The framework is composed of silicon surrounded by oxygen in a
tetrahedral arrangement. The central silicon atom can be replaced
by an aluminium atom giving a tetrahedron with a negative charge.
The various tetrahedra are then joined, so that each oxygen is
shared by two tetrahedra. The linking of groups of tetrahedra give
rise to the so-called secondary building units of zeolite
structure. The eight secondary building units are capable of
building all the zeolitic frameworks. The similarities between the
different zeolite structures can be used to divide them into
families according to the secondary building units used.
Hydrophillic zeolites, both natural and synthetic, contain water
adsorbed within the channels and cavities of the crystals. The
volume of water adsorbed by a zeolite is used as a measure of the
total intracrystalline pore volume. This assumes that the water
molecule is small enough to penetrate all intracrystalline pores
and that the density of water within zeolites is the same as normal
water. The second assumption is a good approximation, but is flawed
as the density will be affected by both the cation charge and
framework silicon to aluminium ratio.
1.3.1 Zeolite L
Barrer and Villager used X-ray crystallography^ to obtain the
correct crystal structure of zeolite L. Zeolite L is based on the
double six ring (hexagonal prism) and the eighteen tetrahedra unit
(cancrinite cage). These are shown in figure 1.1a.
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20
Figure 1.la
Cago Prism
The double six ring joins the eighteen tetrahedra units so that
they are symmetrically arranged (see figures 1 .1b and c).
Figure 1.lb Figure 1.lc
® S i l i c o n Q> S o d i u m
The columns of eighteen tetrahedra units are joined by single
oxygen bridges giving rise to twelve membered rings which produce
wide channels parallel to the C-axis, as shown in figures 1 .Id and
e.
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21
Figure l.d Figure 1.le
® Oxygen • Silicon
0 Potassium O Sodium
The cation environments in zeolite L are described in section
6.3.
1.3.2 Zeolite X
Zeolite X is isostructural with zeolite Y having the structure
of the natural zeolite Faujasite. Zeolites X and Y are both
synthetic with zeolite Y (48-76 Al atoms) having a lower aluminium
content than that of zeolite X (77-96 Al atoms). It is constructed
from sodalite cages (see figure 1 .2a) which are joined via oxygen
bridges through four of the eight six faces, forming hexagonal
prisms (see figure 1 .1a), in a tetrahedral array^l. in this way
the sodalite cages are arranged tetrahedrally with respect to one
another, giving rise to four, six and twelve faces (see figure
1.2b). The supercage formed between the sodalite units controls the
channel system with a free diameter of 0.78nm.
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22
Figure 1.2a Figure 1.2b
The cation environments in zeolite X are described in section 6
.1 .
1.3.3 Zeolite A
Zeolite A is constructed from sodalite cages (see figure 1 .2a)
which are in a cubic array and joined by oxygen bridges between the
six four faces of the cages32. The restricting aperture in the
channel system of Zeolite A is the eight ring which has an aperture
of 0.5nm. The aperture of the cavity is further restricted by the
type of cation which is present as one cation site is within the
eight ring window. Figure 1.3a shows a single unit cell of zeolite
A, while figure 1.3b shows four unit cells joined.
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23
Figure 1.3a Figure 1.3b
O x y g e n @ S o d i u m
0 S i l i c o n
The cation environments in zeolite A are described in section 6
.2 .
1.3.4 Mordenite
Mordenite is a complex structure to visualise. It is made up of
linked five ring units in a series of chains which are joined in
such a way as to give two channels, one an eight ring and the other
a twelve ring33f as shown in figures 1.4a and b. Eight water and
cation sites can be identified, the major cation sites being in the
centre of the eight rings of one channel, close by the five rings
lining the large channel and coordinated to the four oxygen atoms
in adjacent rings.
Figures 1.4a and b show the structure of potassiummordenite34
#
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24
Figure 1.4a Figure 1.4b
The structure of calcium mordenite^S shows the occupation of
different cation sites from potassium mordenite.
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25
Figure 1.4c Figure 1.4d
® Silicon Site I ^ Calcium
The cation positions in Mordenite are described in section
6.4.
1.3.5 Silicalite-1
Silicalite-l36 is isostructural with ZSM-5. They are members of
the pentasil series of zeolites, with silicalite- 1 being the very
low aluminium end member oft h i s s e r i e s ^ O ,
The ZSM-5 structure is made by the stacking of the units shown
in figure 1.5a.
Figure 1.5a
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26
The structure of silicalite is shown in figure 1.5b and c.
Figure 1.5b Figure 1.5c
° Silicon
Intergrowths of other pentasil members are reported to be a
common occurrence caused by stacking faults giving rise to small
amounts of ZSM-11 type structure. The primary difference between
the pentasil zeolites and most other zeolites is their lack of
cavities, having only a constant diameter pore system, only
slightly enlarged at intersections. This is an important advantage
for catalysis as the tendency for coke formation is much
decreased.
1.4 Infrared Spectroscopy for the Study of Zeolite Structure
Initially all structural work on zeolites was carried out using
X-ray diffraction techniques. Neutron and X-ray diffraction are the
only techniques readily available for entire structure elucidation
using single
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27
crystal studies, but once the structure has been elucidated it
is not as well suited to small changes in structure as are infrared
studies.
Vibrational bands within the infrared spectrum of zeolites are
specifically related to certain structural features. Study of these
bands allows a crude picture of an unknown zeolite to be built up,
or alternatively and more appropriately, variations with different
treatments of a known zeolite can be used to understand slight
changes.
Flanigen et al^7 systematically studied a wide range of
different types of zeolites. From this study some principal
correlations emerged:
i) each zeolite structural unit has a typical infrared
pattern.ii) there are strong similarities between zeolites of the
same structural type and in the same group.
They also found they could classify the vibrations between
1300cm”1 and 200cm” 1 into 2 classes:
i) internal vibrations of TO4 tetrahedra, not distinguishable
between Si04 and AIO4 . These are insensitive to change in the
framework.ii) vibrations related to external linkages between
tetrahedra, which are sensitive to changes in the framework. These
vibrations show up the presence of secondary building units and
building block polyhe- dra.
The bands over which these vibrations occur and the structural
features to which they are assigned are listed below^?:
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28
TO4 Vibrations.
Asymmetric Stretch Symmetric Stretch T-0 Bend
1250-950cm-1720-650cm-1500-420cm“l
External Linkage Vibrations.
Asymmetric Stretch Symmetric Stretch Double Rings Pore
Opening
1 1 5 0 -1 0 5 0 c m - 1
8 2 0 - 7 5 0 c n r 1
650-500CIH-14 2 0 -3 0 0 cm - 1
Several other general observations can be made on the factors
effecting the infrared spectrum:
the frequency of any band shifts with changes in the silicon to
aluminium ratio;the position of bands is also related to the type
and class of zeolite e.g. for the Faujasite zeolite group the
double six-ring vibration is always symmetric and between
540-585cm~l;zeolites devoid of double-rings or larger polyhedra
show only weak bands in the 540-630cm“l range; "breathing" motion
of isolated rings forming pore openings in zeolites between
300-420cm”l is seen as a distinct band;the cation composition
affects both the frequency and intensity of the infrared
bands38/39.
The use of infrared spectroscopy for checking structural changes
caused by a variety of treatments is thus highly effective.
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29
1.5 Magic Angle-Spinning Solid State Nuclear Magnetic
Resonance
Nuclear magnetic resonance spectroscopy studies atomic nuclei
which have magnetic moments arising from nuclear spin, in the
presence of an applied magnetic field. The different chemical
environments of atomic nuclei give rise to different frequency
chemical shifts, which are expressed as parts per million
(ppm):
c h e m i c a l s h i f t ( p p m ) =C h e m i c a l S h i f t {
H z ) x 106
O b s e r v a t i o n F r e q u e n c y (// z )
this is then independent of the field strength of the magnetic
field.
Magic angle-spinning solid state nuclear magnetic resonance
(MAS-NMR) has enabled high resolution spectra to be obtained. The
sample is spun at the "magic angle" of 54°44' (with respect to the
axis of the magnetic field) to remove the line broadening shift of
the anisotropy caused by the solid state of the sample giving
different nuclear orientations. This is combined with high power
decoupling and cross-polarisation in order to enhance the signal
from nuclei present at low concentrations.
The use of silicon and aluminium MAS-NMR has given increased
information about the environment experienced by cations and
adsorbed molecules within zeolites. The exact arrangement of
silicon and aluminium tetrahedra relates precisely to the
electrostatic field experienced by cations within the structure.
The most fundamental result obtained from MAS-NMR is the
confirmation of the validity of Lowenstein's rule, this is that two
aluminium atoms will not occupy adjacent tetrahedral sites.
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30
The work of Lippmaa et al^, as repeated and extended by Thomas
et al^l, has been neatly correlated considering geometrical as well
as chemical considerations by Smith and Blackwell^. They have shown
a semi-quantitative relationship between mean interatomic distances
and angles determined by X-ray diffraction and the NMR chemical
shift for silicons bonded to silicon tetrahedra only.
MAS-NMR allows one to determine the ratio of the various
different types of silicon or aluminium tetrahedra,i.e. the number
of aluminium atoms surrounding a silicon tetrahedron or vice versa.
The maximum shift seen with different atomic environments is 40ppm
as compared to a maximum geometrical shift of 12ppm. The large size
of the geometrical shift as compared to the more fundamental
chemical shift means that any interpretations of MAS-NMR spectra
must be based, at least in part, on comparisons with spectra of
similar zeolites with different silicon to aluminium ratios to show
a trend.
1.6 Far-Infrared Spectroscopy
The far-infrared is considered to be from 0.05mm to 1mm
wavelength or 2 0 0cm“l to 1 0cm“*l, above this is the infrared
region and below this is the sub-millimetre region. Over the entire
region very few effective laboratory radiation sources exist. For
this reason the development of spectrometers was many years behind
that of the infrared, where energetic sources are plentiful. The
only effective laboratory sources in the far-infrared are blackbody
sources and these need to be filtered in order to protect sensitive
detectors from the shorter wavelength radiation. It was not until
effective room temperature detectors were invented that commercial
spectrometers were made possible.
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31
The study of the far-infrared was begun by Rubens and his
co-workers between 1892-1922^3, it was continued after 1922 by
others using grating instruments^. it was in the late 1960's and
early 70's that prolific growth occurred in the use of far-infrared
spectroscopy^. This is well demonstrated by the growth in
publishing on the subject. Only 100 papers on far-infrared
spectroscopy were published in 1964 but by 1968 this had grown to
nearly 200 per year. Even though the rate of growth appeared to
have slowed, in 1985 in excess of 700 papers were published.
Several factors have combined to produce this effect:
i) the development of interferometric spectrometers, providing
signal to noise levels previously unobtainable with the low power
radiation sources available.ii) the increased interest in liquid
and solid state chemistry and physics about which the far-infrared
is an abundant source of information.
1.7 Far-Infrared Spectroscopy of Zeolites
Brodskii, Zhdanov and Stanevich^^ were the first people to apply
far-infrared spectroscopy to the study of zeolites. They carried
out a study of zeolite X substituted with monovalent cations and
found a systematic variation of the vibrational bands with the
cation mass. They thus assigned the observed vibrational bands to
the vibrations of cations with respect to the framework. They found
that the vibrational frequency of cations in particular sites was
proportional to the inverse of the square root of the product of
the mass and the cube of the cation radius. This would be the type
of relationship suggested by a simple harmonic oscillation in which
the framework is considered to have infinite mass and the cation is
able to vibrate at a frequency determined by its mass and the force
constant. They were able by selective ion exchange to assign the
cation
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32
dependent bands to particular cation localisation sites within
the zeolite framework. They also showed how the vibrational bands
were affected by the dehydration of the zeolite causing the cation
to be more firmly bound to the framework.
Brodskii, Zhdanov and Stanevich^ consolidated their previous
work by studying a range of both cation compositions and silicon to
aluminium ratio zeolites with the Faujasite structure(i.e. the
synthetic zeolites X and Y). They observed the effect of decreasing
aluminium content on the occupancy of various cation sites and
hence the disappearance of certain bands. They saw the technique as
being a way of understanding the energy inequivalence between
various sites within the zeolite framework.
Dyrikheev, Kiselev, Lygin and Tul'chinskii^ studied the effect
of dehydration on the far-infrared spectrum of calcium X. They
showed how the cation is highly solvated in the hydrated state as
is shown by the lack of well resolved bands. On dehydration,
localisation of the cation occurs and well resolved bands are then
visible in the far-infrared spectrum.
In 1977 Brodskii, Zhdanov, Krasaavttseve and S a m u l e v i c h
4 9 published a paper on a synthetic chabazite zeolite exchanged
with monovalent and divalent cations. This zeolite has only two
crystallographic cation positions, but several bands can be found
in the far-infrared spectra which vary depending on the cationic
form of the zeolite. They suggest that this shows a greater
inequivalence in cation site energies than suggested by
crystallographic studies. They were also able to observe a large
change in the spectra on prolonged extreme heat treatment, showing
the effect of cation migration.
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33
An extensive study of dehydrated and solvated, mono- and
divalent cationic zeolites was carried out by Butler, Angell,
McAllister and Risen^O. They partially repeated the work of
Brodskii, Zhdanov and Samulevich but without reaching all the same
conclusions. They extended the previous work by studying the
effects of a variety of different solvents on the far-infrared
spectra. They were able to explain the spectral effects in terms of
the geometry that could be expected for the solvated ions. They
tried to interpret the vibrational frequencies in terms of cationic
conduction by several possible mechanisms. They reached the
conclusion that cationic conduction was likely to be a co-operative
phenomena and therefore did not lend itself well to modelling by
simple models of the single jump kind.
Table 1.1 summaries the assignments made by Butler etal.
Table 1.1 Cation Vibrations (cm-1) for Dehydrated Zeolites X and
Y after Butler et al.
Site I II IIICation X Y X Y X YLi+ 380Na+ 160 167 190 180 67K+
107 156 133 58Rb+ 108 48Cs+ 86 62 39 30Ag+ 50 82Ca2+ 287 256 273
227Sr2+ 189 150Ba2+ 137 107
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34
In 1979, Peuker and K u n a t h ^ l studied a variety of
previously unstudied zeolites. Ultra-stable zeolite X was found to
have a weak band which could be associated with sodium cations in
zeolites X and Y at Site I, presumably due to residual cations in
this site (110cm~l). They also showed the non-conforming nature of
lithium cationic vibration bands due to the high charge to radius
ratio of the lithium cation producing a distortion of the simple
harmonic model. The study of chloromethane adsorbed on lithium X
showed the direct effect of the adsorbate on the cations within the
super-cage.
At the Fifth International Zeolite Conference in Naples in 1980
Brodskii and Zhdanov52 presented a paper which reviewed both their
own work and that of others in the field of far-infrared
spectroscopy of zeolites. They presented improved spectra
showing:
i) dependence of vibrational bands on the mass and charge of a
cation;ii) change in cation vibration frequencies with changes in
silicon to aluminium ratios;iii) changes in cation vibrational
bands with adsorption into the zeolites.
Brodskii and Zhdanov summarised their own work on cation
vibrations of faujasite (X and Y) and chabazite(E) zeolites, this
is reproduced in the table below:
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35
Table 1.2 Cation Vibrations (cm”*) for DehydratedZeolites X, Y
and E after Brodskii and Zhdanov.
Table 1.2 when compared to Table 1.1 shows a high degree of
agreement over the assignment of cations in sites II and III, but
no agreement over the assignment of cations in site I.
Peuker and Kunath^3 presented results of their further studies
on monovalent cation containing zeolite X, showing the effect of
different adsorbates and the deviation of lithium from the mass
dependence relationship, which they explained in terms of a
reduction of the force constant. They published the definitive
assignment of cation bands to monovalent cations.
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36
Table 1.3 Cation Vibrations (cm“l) for DehydratedZeolites X, Y
and US-EX after Peuker and Kunath.
Site I I r II IIICation X Y US X Y X Y XLi+ 153 119 202Na+ 156
156 151 110 113 189 185 67K+ 106 73 156 56
A paper presented at a workshop in Hungary in 1982 by Kosslick,
Walther, Roethe and Roethe54 developed a relationship for the
vibrational frequency based on the mass of the cation and the
cation-oxygen distance. This effectively takes into account the
force constant problem the necessity for which was widely realised.
They obtained very good agreement between vibrational frequencies
predicted from their model and experimentally observed vibrational
frequencies. This model appears to accurately predict the
vibrational frequency of lithium cations, for which no previous
model had been able to account.
Also in this paper, Kosslick et al presented, for the first
time, assignments for a variety of alkali and alkaline earth metal
cations in zeolite A. These are shown in table 1.4.
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37
Table 1.4 Cation Vibrations (cm"l) for DehydratedZeolite A after
Kosslick et a l .
Cation I II IIILi+ 320 170Na+ 210 100 87K+ 130 75 55Rb+ 55-60 46
20Mg2+ 315Ca2+ 270Sr2+ 160Ba2+ 106
Loeffler, Peuker and Kunath55 at the same workshop presented
observations on the interaction between cations and adsorbed
benzene molecules. These showed the modification of certain cation
bands by their association with benzene. Peuker, Moeller and
Kunath^G also presented a paper specifically on the interactions of
a series of zeolite Xs.
Pechar57/58,59f between 1981 and the present time, has been
publishing papers on the study of a wide range of natural zeolites'
far-infrared spectra. He has been able to assign vibrational bands
to cations by correspondence with similar sites in previously
studied zeolites.
A review by F r i p i a t ^ O in 1982 provides an excellent
comparison of the similarities of cationic environments in clays
and zeolites, by reviewing some of the work done on the
far-infrared spectra of both.
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38
Tabourier, Carru and Wacrenier^l studied both the dielectric and
far-infrared properties of cations in X type zeolites. They used
the existence of independent cationic vibration modes to suggest
that cation-cation repulsion effects, as well as cation-framework
repulsion effects, should be responsible for the dielectric
properties. The dielectric response measured suggested that the
cation-cation repulsions are very weak compared to cation-framework
repulsions.
Ozin, Baker and Parins62 used far-infrared spectroscopy to study
the auto-reduction and clustering of silver cations in Y type
zeolites induced by heat treatment. They were able to make
tentative assignments of vibrational bands to modes of silver ions,
atoms and clusters. This is the first study where bands due to
uncharged non-molecular species have been postulated.The extension
of this technique to the study of iron containing zeolites may well
be relevant to the study of Fischer-Tropsch type catalysts.
Stock, Dombrowski, Fruwert and Ratajczak^3 studied ammonium and
hydrogen forms of zeolites X and Y. In order to correctly interpret
their spectra they re-examined the data presented in tables 1.1,
1.2 and1.3. They concluded that four regions in the spectrum could
be assigned to sodium cation bands in faujasite type zeolites, site
II : 182-196cm“l, site I : 156-161cm"l, site I' : 110cm“ ̂and site
III : 63-66cm”l. They discovered bands due to ammonium cations but
no bands due to hydrogen ions or hydrogen bridged hydroxyl groups,
only the disappearance of sodium cation vibrations.
Ozin et al^4,65,66,67,68 have used far-infrared spectroscopy as
their primary tool in further studies of silver clustering in
zeolites A and Y. They have
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39
extended their work to consider assignments of bands and their
intensities by GF-Matrix methods on simplified cation sites with
increased symmetry to make the problem tractable. Their work
studying Faujasite type zeolites largely agrees with the
assignments of Peuker and KunathS^ (c.f. table 1.3), with the
addition of identifying some previously unassigned bands, broadly
in agreement with Stock et al^3.
No et al69 have carried out similar calculation work to Ozin et
al but on zeolite A structure, using assumed net atomic charges and
force constants in order to be able to carry out a normal mode
analysis for sodium zeolite A.
1.8 The Untuned Resonator Technique
The commonest long pathlength cell is the white cell. This type
of cell is only suitable for gases, as scattering by solid samples
will destroy the desired effect.
An untuned resonator is a vessel in which a sample and radiation
interact. It has three apertures, one for radiation entrance, one
for radiation detection and one providing a known loss to calibrate
the cavity. The cavity is designed in such a way as to have
multiple reflection paths, minimum reflection losses and resonant
modes widely spaced to give an isotropic radiation field within the
cavity.
The true origin of this technique is from the measurement of
acoustic properties of r o o m s ’7^ 71 which was extended and used
as an analogy by Lamb72 to develop the theory for electromagnetic
radiation. In 1946, Becker and A u t l e r 7 3 built a 2.5m cube
spectrometer to
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40
study a water vapour rotation line at 0.833cm"^ which interfered
with radar. The technique was not revived for another 30 years
until at the Appleton Laboratories^4,75 a smaller resonator was
constructed to study anomalous absorption of water vapour in the
sub-millimetre region which was affecting remote sensing and
sub-millimetre wave astronomy. These untuned resonators were also
used to study polytetraf luoroethylene solid samples?*^??.
The untuned resonator technique has several advantages for study
in the sub-millimetre region:
a) radiation is collected over large solid angles, hence weak
radiation sources can be used.b) no diffraction problems exist, as
no images are formed.c) the long photon path in the cavity is
either fully interacting with gaseous samples or partially with
solid samples, but non-interacting photons are recirculated.d) the
isotropic radiation field allows solid samples in any form to be
used and complex dielectric properties to be determined?9,80.
The technique has been used to study polymers^l, biological
materials*^ and materials with potential electronic
applications^^/84.
1.9 Objectives of the Work
The primary aim of this work was to investigate the state of
various extra-framework species within zeolites using far-infrared
spectroscopy.
One major area of interest was the state of water within
zeolites. The state of water within zeolites is of interest as many
of the commercially useful processes
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41
involve hydrated zeolites. The state of water will affect the
ion exchange of radioactive cations into the cavities. It also
presents a unique environment in which to study the properties of
water itself. In order to enable this study to be conducted, it was
necessary to further develop the untuned resonator technique. The
further development of untuned resonators was seen to be necessary
to allow the study of zeolite powders below lOOcm-l wavenumbers.
This further development was also seen to open up hew possibilities
for the examination of previously inaccessible systems, e.g. cement
and biological materials.
The other area of interest was the study of the environment of
cations within zeolites. Multiple cation exchanges of zeolites
could be carried out and the resulting cation forms investigated by
the use of far-infrared spectroscopy. It was intended to use
conventional transmission spectroscopy but a flexible method of
sample preparation was necessary in order to allow many samples to
be studied.
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42
2 Fourier Transform Spectroscopy
Fourier Transform Spectrometers are based on the interference
between two coherent light beams of differing pathlength and first
became widely used in the far-infrared where the inherent advantage
of improved signal to noise ratio was necessary to overcome low
energy output of available radiation sources. This improved signal
to noise ratio comes from two advantageous effects, which are
described below.
The main advantage of Fourier Transform Spectroscopy results
from the fact that every element of the interferogram contains
information about all the elements in the final spectrum: this is
the Fellgett advantage^. If one considers a spectrum containing N
elements then in a Fourier Transform Spectrometer each element is
observed for the total observation time of T. Whereas in a
monochromating spectrometer each element is only observed for T/N.
If one observes a spectrum with both instruments for the same
length of time the sig- nal-to-noise ratio of the Fourier Transform
Spectrometer is square root of N times that of the monochromated
instrument. This is a multiplexing advantage which is gained by
astronomers using grating spectrometers which spread the entire
spectrum over a photographic plate thereby getting the same
advantage as by using a Fourier transform instrument. The computer
used by Fourier Transform Spectrometry and the photographic plate
used in monochromating spectrometry allow one to multiplex.
The second major advantage of a Fourier Transform Spectrometer
is the throughput advantage first noted by Jacquinot86. The
circular symmetry of a Fourier Transform Spectrometer means that
compared to a monochromating instrument of the same resolving power
the Fourier Transform Spectrometer will always have higher energy
throughput.
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43
2.1 The Mathematics of Fourier Transform Spectroscopy
This section outlines the mathematics of Fourier Transform
Spectroscopy and is drawn from many sources, the main ones being
Chamberlain's^7 and chantry's** 8 excellent books.
A diagrammatic Fourier spectrometer is shown in figure 2.1.
Figure 2.1 F o u r i e r S p e c t r o m e t e r .
S o u r c e
Radiation from the lamp is split at the beam splitter, half is
transmitted to the moving mirror and half is reflected to the fixed
mirror. The radiation is reflected from the two mirrors and
recombines with interference at the beam splitter. The radiation is
again split with half going to the detector and half returning to
the source. The type of interference which occurs on recombination
at the beam splitter will depend on the distance of the two mirrors
from the beam
-
44
The difference between the distance travelled by the radiation
from the two mirrors to the beam splitter is called the path
difference. When both mirrors are the same distance from the beam
splitter then constructive interference will occur no matter what
the wavelength of the radiation, this is called zero path
difference. If one considers a single frequency source, then the
intensity of the signal detected will vary as a function of the
path difference. When the path difference, p, is an integral number
of wavelengths then constructive interference will result in
maximum intensity.
s p l i t t e r . I f t h e m ovin g m ir r o r i s sc a n n e d
to w a r d s andaway from t h e beam s p l i t t e r th e n t h e i
n t e r f e r e n c e w h ic ho c c u r s on r e c o m b in a t io
n c o n t i n u a l l y c h a n g e s .
In expressing the mathematical analysis of Fourier spectroscopy
it is convenient to use wavenumber, defined by:
1
whereA., is the wavelength andv 0 is the frequency in
wavenumbers.
( 2 .2 . 1)
The interference maxima and minima will occur at path
differences, p, given by
p = n \ 0 /t = 0 ,+ 1 ........oo for maximum,
n = 0, + 1 ........ oo for minimum.
-
45
The actual intensity of radiation detected if the moving mirror
is scanned across a range of pathlengths is given by:
where IQ is the intensity of the single frequency source.
For a hypothetical source emitting N single frequency lines the
intensity would vary as the sum of the individual
contributions:
where 1^ is the intensity of the kth line of wavenumber vfc.
In the case of a single frequency line it would be possible to
calculate the frequency of the line from the interferogram by
simple mathematics and knowing the separation between the maxima
(figure 2.2). For more than two lines this simple approach becomes
impossible.
/(p) = 2/0(l +cos(27rv0p)} ( 2 .2 .2 )
(2.2.3)
-
46
F i g u r e 2 . 2
I n t e r f o r o g r a m o f S i n g l e F r e q u e n c y S o
u r c e
W a v e l c n g t h / 2
The method of extracting the spectral information from the
interferogram of a source comprising a band of frequencies becomes
one of applying a Fourier transformation. The Fourier transform is
outlined below.
If one considers the single frequency source and only the
oscillatory part of the interferogram:
Now, multiplying this by a function due to a single frequency
which varies between 0 and infinity, the integrated intensity is
given by:
U p ) = / ( p ) - 2 / 0
( 2 . 2 . 4 )
= 2/ ol cos (2 /ri'0p ) c o s ( 2 / r v p ) d p ( 2 . 2 . 5
)
-
47
Now:/(v) = 0 i f v £ v 0
* 0 i f v = v 0
/(v) is the Fourier transformation of I(p) (and a representation
of the spectrum that would be obtained with a dispersive
spectrometer).
In the case of N single frequencies, v* :
r + »7 ( v ) = J 7 ( p ) c o s ( 2 7 r v p ) d p ( 2 . 2 . 6
)
¥= I k i f v = v^then/c = 1 , N
= 0 i f v ¥= v k t hen k = 1 , N
In practise the interferogram is not obtained from minus
infinity to plus infinity and hence can not be carried out over
this range, but only over a finite range (”Pmax
-
48
a r e t h e i n s t r u m e n t a l l i n e s h a p e f u n c t
i o n s c a u s e d b y
t h e t r u n c a t i o n o f t h e i n t e r f e r o g r a m ,
r e s u l t i n g i n a
f i n i t e h a l f - w i d t h a t t h e c e n t r a l m a x i
m u m , w h i c h l i m i t s
r e s o l u t i o n . T h e o t h e r e f f e c t s o f t h e i
n s t r u m e n t a l l i n e
s h a p e f u n c t i o n , t h e s i d e - l o b e s , c a n b
e m i n i m i s e d a t t h e
e x p e n s e o f d e c r e a s e d r e s o l u t i o n , b y c
a u s i n g t h e
i n t e r f e r o g r a m t o a p p r o a c h z e r o s m o o t
h l y r a t h e r t h a n
a b r u p t l y b y i m m e d i a t e t r u n c a t i o n . T h
e m i n i m i s a t i o n i s
a c h i e v e d b y m u l t i p l y i n g t h e i n t e r f e r
o g r a m b y a f u n c t i o n
w h i c h i s u n i t y a t z e r o p a t h d i f f e r e n c e
a n d d e c r e a s e s
t o w a r d s z e r o a t t h e t r u n c a t i o n . S e v e r
a l f u n c t i o n s c a n b e
u s e d f o r t h i s p r o c e s s w h i c h r e d u c e s t h
e i n t e n s i t y o f t h e
s e c o n d a r y m a x i m a , b u t i t a l s o d e c r e a s
e s t h e r e s o l u t i o n -
i n t h e c a s e o f t r i a n g u l a r a p o d i s a t i o n
b y a p p r o x i m a t e l y a
f a c t o r o f t w o .
T h e r e s o l v i n g p o w e r i s o f t h e f o r m :
C o n s i d e r i n g t h e d i a g r a m m a t i c s p e c t r
o m e t e r , t h e s o u r c e
e m i t s a c o n t i n u o u s r a d i a t i o n s p e c t r u
m . T h i s w i l l g i v e
r i s e t o a n i n t e r f e r o g r a m c o m p o s e d o f c
o n t r i b u t i o n s f r o m
e a c h i n f i n i t e s i m a l f r e q u e n c y e l e m e n
t , t h u s :
^ V P max ( 2 .2 .8 )
( 2 . 2 . 9 )
-
49
F i g u r e 2 . 3
Intcrferogram of Broad Band Source
2
Ji
-
50
7(p) = / ( p ) - ^ / ( 0)
- / ( p ) - / ( ~ )
- 2 o / (v) cos ( 2 n v p ) d p ( 2 . 2 . 1 2 )
The choice of apodisation function determines the spectral
window of the spectrometer as in practice the interferogram, I(p)
is multiplied by the apodisation function, A(p) which relates to
the line shape function A(v) hence:
I ca IcO)* P max
A ( p ) I (p) cos (2/rv p ) d pP min
I ( v ) { A ( v - v ' ) + A ( v + v ' ) } d v ( 2 . 2 . 1 3
)
7colcO ) =+ 00
f ( v ' ) { A ( v - v ' } d v 'CO
( 2 . 2 . 1 4 )
wherev* is the dummy variable.
Thus the spectrum which is obtained is a convolution of the
spectrum with the line shape function. This is equivalent to the
convolution of a dispersion spectrometers spectral window(slit
size) with the spectrum.
The calculation of the interferogram is normally carried out
using a digital computer, the use of which is not discussed here.
It is however necessary to consider the effects on the resulting
spectrum of taking a finite number of sam p l e s .
-
51
When an interferogram is recorded for computationa finite number
of points on it are digitised at a set interval over the travel of
the mirror. It is hence possible that an actual sample was not
taken at the exact zero path difference, but a point near to it.
This will result in the whole interferogram being shifted, thus a
constant error. This error in zero path difference will manifest
itself as a frequency dependent phase error in the spectrum
-
52
^ c C l ' W U L e C ' O l M / ^ C v ) ) 2 (2.2.18)
It is not always convenient or sensible to record an entire
double sided interferogram, and hence a single sided interferogram
is recorded, from slightly before zero path difference to pmax* In
this case the distortions introduced by the cosine transform are
entirely intolerable. Since the phase error can be considered to be
a slowly varying function it can be obtained with sufficient
accuracy from a small double sided portion of the interferogram
around zero path difference, p=0, i.e.:
These few values of the phase error obtained can either be used
as points for further interpolation, or the function can be
convoluted with the full single sided inter ferogram from 0
-
53
3 The Theory of Untuned Resonators
3.1 The Theory of Homogeneous Cavity Sample Cells for Gaseous
Absorbers
The derivation of useful quantities from cavity measurements
will be described in terms of the ideal cavity shown in figure
3.1.
Figure 3.1Untuned Resonator
Detector
The rotating mode scrambler is necessary when either the
radiation source is monochromatic or high resolution spectra are
required. The mode scrambler ensures uniform energy density and
that all the normal modes of the cavity are excited.
The simplest method of derivation is that first used by Lamb72r
the rate theory explanation of photon absorption.
In the evacuated cavity shown, the rate of photon increase is
given by:
-
54
d N k
dt M *(0 CLkS N K (3.1.1)
whereN]̂ is the number of photons of type k in the cavity.S is
the surface area of the cavity walls. M]̂ (t) is the rate of
creation of photons. a k is the constant of proportionality for
absorption.
The equation 3.1.1 is purely for one single excited mode, k,
within the cavity. Once equilibrium has been reached within the
cavity,
d N k dt = 0 (3.1.2)
i.e. rate of creation = rate of absorption.
On the introduction of an absorbing gas into the cavity equation
3.1.1 is changed to:
d N k
d tM k( t ) - a k S N k - p k V N k (3.1.3)
whereV is the volume of the cavity and hence of the gas.p k is
the constant of proportionality for the gaseous absorption.
Once again at equilibrium, d N kd t
-
55
The process can then be considered in terms of the Q of the
cavity and its individual processes, where Q is defined by:
1 rate of loss of photons .— = ----------- ;------------ ( o . 1
. ■Q (jo x no of photons
and to is the resonant angular frequency.
The total Q of the cavity is made up of the Q's of the
individual absorption processes i.e.
_J_______ 1 ( 1Q W Qi/(A:) + QC(A:) (3.1.5)
whereQw is the Q due to the walls.Q q is the Q due to the
gas.
from the definition of Q (equation 3.1.4):
a, 5 =Qur(k)
(3.1.6)
PkV QgW
where to* is the resonant frequency of mode k.
Now representing 3.1.3 in terms of Q:
d N k t a ) kN k | a) kN k d t +Qt/(A:) + QC(A:) ( 3 . 1 . 7
)
-
56
or in terms of the total Q of the cavity:
d N k | aj kN k cit + Q(fc) M * ( 0 ( 3 . 1 . 8 )
The average, over a number, of pulses of equation3.1.8 gives the
average number of pho t o n s :
N = Q(fc)CUjfc < M fc(0>„u (3.1.9)
In order to generalise the expression to all excited modes, the
average is taken over all excited modes:
n k- 1
_ _1 y' Q(fc)7i7A; n k.\\ w k
(3.1.10)
where n is the number of excited modes, and the time average ĵ
v for the kth mode is ~Mk.
If all modes are equally excited and photons in all modes are
equally likely to be absorbed 3.1.10 becomes:
W = ( 3 .1 .1(JO
Now, if one once again considers an evacuated cavity i.e. with
no absorbing gas, then Q = Qg and the number of photons is given
by:
A7, QvMCO
( 3 . 1 . 1 2 )
-
57
If the cavity is refilled with enough gas to halve the number of
photons then:
yv2 60 2 1 ( 3 . 1 . 1 3 )
From this Q = Q„/2 and hence QU = QC (3.1.14)
The attenuation coefficient of the radiation in the gas can then
be determined from Q. If all other losses in the system were
negligible, then the radiation would decay as exp-cut/Q. As in t
seconds a photon travels x = ct, this becomes exp-cux/cQc. Thus the
mean free path in the absorbing medium is expressed by cQc/a)r so
that the absorption coefficient is given by:
“ = ̂ (3.1.15)
It is not possible to derive a simple expression for Qw as the
cavity is not ideal as described above.
Qw can be obtained from experiment by introducing a hole into
the wall of the cavity for which the loss of radiation can be
calculated, as Qjj. The total Q of the evacuated cavity with a hole
in it is given by:
I = _ L 4. J _Q Q w Qh (3.1.16)
If the hole is of sufficient size so as to halve the number of
photons in the cavity then as before, QH = Qw . Qpĵ for a given
hole size, is calculated giving QWt Then Q q can be determined by a
further experiment with the cavity filled with gas.
-
58
An expression for Q jj can be obtained relatively simply from
the kinetic theory of ideal gases. Figure 3.2 shows a hole in a
cavity wall.
Figure 3.2 Photons Through Cavity Hole
td>
Wall
The number of photons which will hit the area A of the hole in a
short time will be:
AccosOdt (3.1.17)
where c is the speed of light.
Assuming a uniform density and angular distribution of
velocities throughout the cavity, then the number of photons per
unit volume moving between 0 and e+de is:
^ £ s i n 0 d 0 ( 3 . 1 . 1 8 )4/r V
where V is the volume of the cavity.
Thus combining 3.1.17 and 3.1.18 the number of photons escaping
through an area A of the wall per second i s :
N Acn2
cosf ls in OdQ2V 0( 3 . 1 . 1 9 )
-
59
N A c 4 1 /
H en ce from 3 . 1 . 1 1
_ o ) NQ " ~ N A c
= 8 l t V XA
( 3 . 1 . 2 0 )
It is then possible to calculate the absorption coefficient of
the gas by measuring the photon density of the evacuated cavity,
the evacuated cavity with a hole in the wall and the cavity
containing an absorbing gas.
The above derivation makes the following assumptions about the
radiation within the cavity:
i) the radiation density within the cavity is homogeneous
throughout the entire volume;ii) absorption of radiation by the
source and detector are negligible, whe n compared to the walls of
the cavity;iii) all cavity modes are equally excited;iv) detector
responsivity is linear.Condition i) is not true near to the
calibration
hole, source or detector, but the effect of the inhomogeneity is
minimal as the cavity is filled by the absorbing gas. The mode
stirrer ensures that all modes are nearly equally excited.
A n y radiation detection devices must have a linear
relationship between energy measured and output. In order to avoid
having to calculate this relationship ratios of detector outputs
can be used in calculations.
-
60
IfDw is the detector output from the evacuated cavity. Dfj is
the detector output from the evacuated cavity with a hole in it.Dq
is the detector output from the cavity filled with absorbing
gas.
Then:
D h = Q H D \/ Q h + Q w
( 3 . 1 . 2 1 )
R GWD c _ Q c D w Qc + Q w
( 3 . 1 . 2 2 )
Now as Q jj can be calculated as shown above, Qw can be derived
in terms of Q jj and R h w *
Q w ~ Q h(1 - R hv)
R„ w
From 3.1.22 Qq can be derived:
( 3 . 1 . 2 3 )
QcQ w R o w 1 ~ R gw
( 3 . 1 . 2 4 )
Then substituting for from 3.1.23 into 3.1.24:
QcR hw (1 - Rc w)
( 3 . 1 . 2 5 )
Then to obtain the absorption coefficient from equation 3.1.15,
substitution of Qq gives:
-
61
(3.1 .26)- ̂ ̂ }lw ( ̂ ^ci/) 1c Row (1 “ R h\ / )Qh
The alternative method of carrying out the experiment is to
introduce a gas of known absorption coefficient instead of a hole
and calibrate in this manner.
If D c is the detector output from the cavity containing the
calibration gas,then:
RcwD c _ Q cD \/ Qc + Qw
( 3 . 1 . 2 7 )
Then by similar derivation as in the hole calibration:
_ to Rct/{ 1 Rev) 1 c R c i / ( 1 ~ R ci/)Qc
( 3 . 1 . 2 8 )
Then substituting for the known absorption coefficient of the
calibration gas:
otc Rcurjl R g / ) R c v ( l - R c v ) ac
( 3 . 1 . 2 9 )
One thus has two alternative procedures for obtaining the
absorption coefficient of a gas.
The single frequency derivation above can be used for any
frequency of source. However, the advantage of using a cavity is
limited in frequency range, as shown below.
-
62
In an evacuated cavity Q is related solely to the losses in the
cavity walls, i.e. absorption and transmission. The frequency
dependence of the reflectivity of a metal was derived empirically
by Hagen and Rubens89 and can be expressed as:
R~ 1 - 22 go e 0
a( 3 . 1 . 30 )
whereco is the angular frequency of the radiation, e0 is the
permittivity of a vacuum and a is the d.c. conductivity of the
metal.
Now considering the losses in the cavity wall, the cavity wall
absorption coefficient is given by:
y « ( l - / 0
oc(Joe0
a( 3 . 1 . 3 1 )
If the radiation is over a relatively narrow band, thus allowing
conductivity to be considered as constant, then:
( 3 . 1 . 3 2 )
From this it can be seen that the Q of the evacuated cavity is
related to the frequency of the radiation by:
( 3 . 1 . 33 )
-
63
The Q of the cavity relates to the average time spent by a
photon in the cavity and hence the average photon path length
i.e.
( 3 . 1 . 3 4 )
Hence the effective pathlength of radiation within the cavity
decreases with increasing frequency.
The decreasing reflectivity of the metal results in two
effects:
i) losses in the cavity walls become greater.ii) sensitivity of
the cavity becomes less, as it has less effective pathlength.
These two factors result in an upper limit on the frequency at
which a cavity is a useful cell for studying gaseous a b s o r b e
r s .
The lower frequency limit is defined by the need to be able to
obtain a homogeneous radiation field of equally stimulated modes.
The normal criteria used for this is that the minimum dimension of
the cavity should be at least one hundred times greater than the
wavelength of the minimum frequency being studied76.
3.2 Solids in Homogeneous Cavities
When solids are placed within an evacuated cavity the effect is
considerably different from that produced by gases. The solid, in
whatever form, has now introduced a new set of boundaries into the
cavity. These boundaries are where the refractive index changes and
hence reflection can occur.
-
64
The effect of reflection is not the same as in plane wave
transmission spectroscopy where the energy will be reflected to the
source and is effectively lost. Inside the cavity any reflected
radiation is recycled. The effect is more subtle as now one has to
consider the results of interference of both reflected and
transmitted r a d i a t i o n .
An effect seen for solid samples, which should be avoided if
possible, is the shielding of the interior of the samples when they
have a high absorbance and/or a large volume. A fundamental
relationship of the cavity as derived earlier showed an inverse
linear relationship between the Q of a sample and its linear
absorption coefficient and volume (equation 3.1.15).
The loss of detected signal when a solid is placed inside the
cavity is proportional to the absorption cross-section of the
sample i.e. its equivalent Black Body area. The absorption
cross-section can be calculated by ignoring interference effects
as:
wherea, is the linear absorption coefficient, d is a measure of
the thickness of the sample and 6s is an element of the
surface.
When a,d«i then this simplifies as now, exp(-a,d) ~ i-a,d
hence:
(3.2.1)
(3.2.2)
-
65
where V is the volume of the sample.
The method for determining the linear absorption coefficient
once the Q of the sample, Q s , has been calculated from equation
3.1.25 is outlined below based on the derivation of Llewllyn-Jones
et al76.
Q s can be related to the Black Body area, A, by equation
3.1.20:
Qs8 i t V c
A.A(3.2.3)
whereV c is the volume of the cavity.
Now integrating equation 3.2.2 in isotropic radiation and
neglecting effects of reflection due to differences in refractive
index between the sample and the cavity volume:
o-0 = 4a,I/s (3.2.4)
whereV s is the volume of the sample.
In order to correct for the effects of differences in refractive
index Llewllyn-Jones et al?6, calculated a correction factor by a
ray tracing method. So that the equivalent Black Body area is 1.6
times the value calculated in equation 3.2.4. Hence substituting
the corrected equation 3.2.4 into equation 3.2.3 one obtains the
linear absorption coefficient of the sample:
-
66
-
67
i) Llewllyn-Jones et who considered theeffect of the real
coefficient of refraction on the imaginary and derived a shape
correction factor by a "ray-tracing" approach. They found the shape
correction factor was constant over a large range of shapes and
sizes of solid samp l e s .ii) Kremer et a l 7 9 , 8 0 f who worked
out a method for the solution of both the real and imaginary parts
of the refractive index using a series of very high accuracy single
frequency measurements.
The major approach in this work has been to use samples of known
optical properties and of the same geometry and volume as the
experimental specimens to calibrate the cavity, allowing similar
samples of materials of unknown optical properties to be studied.
This approach is most effective when the materials have similar
optical properties, e.g. silica and silicates.
3.3 Absorption of Parallel Sided Sheets
There have been several instances in the course of this work
where it has been necessary to know the absorption properties of
parallel sided sheets. These have arisen for:
a) beam splitter transmission of interferometers;b) calibration
hole transmission from evacuatedcavit i e s ;c) absorption of
samples within a cavity.
3.3.1 Calculation of Absorption
A Pascal computer program was written which allows one to obtain
information on the absorption of samples in the above three
situations. Specifically, the program can calculate the following
quantities:
-
6 8
a) reflection, transmission and absorption versus angle of
incidence.b) fixed angle of incidence reflection, transmission and
absorption versus wavenumber.c) integrated angle of incidence
reflection, transmission and absorption versus wavenumber.d)
integrated angle of incidence reflection, transmission and
absorption versus thickness.e) integrated angle of incidence
reflection, transmission and absorption versus imaginary part of
the complex refractive index.f) integrated angle of incidence
reflection, transmission and absorption versus real part of the
complex refractive index.g) iteration of experimentally determined
cavity absorption to determine the range of possible complex
refractive index, both real and imaginary.
Figure 3.4
whereI is the incident radiation power.R is the fraction of
radiation reflected. T is the fraction of radiation reflected.
-
69
d is the thickness of the sheet.n,k are the real and imaginary
parts of the complex refractive index.
The method of calculation of the coefficients is outlined
below.
Hadley and Dennison^l solved the Maxwell equation boundary-value
problem for a parallel sided sheet of absorbing material in an
infinite lossless dielectric medium. Kremer et a l 7^ reduced these
equations to a simpler form where the dielectric was air or vacuum.
The interaction of electromagnetic radiation with parallel sided
samples is determined by the real (n) and imaginary (k) complex
refractive indices, the wavelength (A.), the thickness of the sheet
(d) and the angle of incidence (0).
The formula for the reflection (R), transmission (T) and
absorption (A) coefficients of a parallel sided sheet as shown in
figure 3.1 are elucidated below, the formula are highly algebraic
and very little physical significance exists in any of the
intermediate values. The subscript "s" signifies the sample and the
subscript "o" signifies the medium surrounding the sample.
For radiation polarised perpendicular to the plane of
incidence:(Values specific to perpendicular polarisation are
signified by use of the subscript a . )
f coshy- tcosa ~Da
(3.3.1.1)
T a
-
70
/!„= 1 - T „ - R „
D a = ^ c o s h y + x s i n l v y + ^ c o s a + c o s i n a
y =4- i tqsad
k
a = 4 / r p sgdk
q sa = ^ \ ] J ^ f [ { n 2- k 2- s i n 2 0)2 + 4 n 2fc2] - ( r i
2- k 2~ s i n 2 9)}
p sa “ ( V U ^ 2- ̂ 2" sin20)2 + 4rt2A;2] + (ft2 - A:2 -
sin20)j
_ 2 _ 2 , _ 2PsO P SO P SO
p 0 = n Q cos 0
£-(p L + 2^2 4 p L p 2o
P 4o
T =(p L - P » ) 2 + 4 c?2 2 so P o
p 40
0 = (P2s o
2^2 4 p L p ;Po
x = 4 p sg(pLPo
p = 4 q 2saPo-{Pso2
P 40
-
71
4
-
72
F ig u r e 3 .5
Interferometer Radiation Intensities
RIT
TI
Source
2RT1
Detector
Each beam encounters one reflection from and one transmission
through the beam splitter. The detected portion of the incoming
radiation is given by the expression below:
where R a and T a are the polarisation averaged reflection and
transmission coefficients of the beamsplitter at 45°.
The computer program was used to calculate the transmission of
the interferometer over a range of wavenumbers for the thicknesses
of beam splitters used in the present work (figures 3.6, 3.7, 3.8
and 3.9). The beam splitter was made of Melinex polyester film. The
values of the complex index of refraction of biaxially orientated
polyester film have been taken from the work of Igoshin et al ^ 2
.
(3.3.2.1)
-
Frac
tion
al C
oeff
icie
nts
Frac
tion
al C
oeff
icie
nts
73
F i g u r e 3 . 6 F i g u r e 3 . 7
6u Me l in ex B e a m s p l i t t e r n 1.69, k 0.06
35u Melinex Beamsplitter n 1.69 k 0.06
Figure 3 . 8 Figure 3.9lOOu M el in ex B e a m s p l i t t e
r
n 1.69, k 0.06135u Melinex Beamsplitter
n 1.69 k 0.06
-
74
3.3.3 Reflection from Vacuum Cavity Window
Most of the present work was carried out under vacuum in order
to avoid interference from the spectrum of water vapour. In order
to keep the vacuum it was necessary to use a Melinex (polyester)
window over the calibration hole. The hole was therefore not acting
as a true black body due to reflection from the polyester film.
The radiation passing through the cavity window is incident from
all angles. The correction to the derivation of Lamb for a hole in
an untuned resonator involves the integration of the coefficient of
transmission over all angles of incidence from 0 to n / 2 .
The transmission coefficient of the window is :
T w=s 2 ) T a(
-
75
z r - ° -—77 f 3( T a ( 8 , n , k , c l , A . ) + A a ( 6 , n ,
k , d , \ . ) } (3.3.3.3)Q u 4 Tt V J o
The corrected value Q of the calibration hole was used in the
present work.
The variation of the integrated sum of absorption and
transmission is shown below for llOum polyester film used as window
material for calibration.
Figure 3.10A p p a r e n t W i n d o w T r a n s m i s s i o
n
k 0 .0 6 , n l . 6 9 , l l O u m
The variation of transmission with various parameters, as
calculated by the computer program, are shown below:
-
Fra
ctio
nal
Coe
ffic
ient
s F
ract
iona
l C
oeff
icie
nts
76
Variation of Absorption w ith k
F i g u r e 3 . 1 1
n l .6 9 , l lO u m , 1 0 0 c m - l
k
Figure 3.13Variat io n of A b sorp t i on
w i t h T h i c k n e s s n l . 6 9 , k0.06, 1 0 0 c m - l
Thickness(mm)
Varia t ion of Absorp t i on w i t h n
F i g u r e 3 . 1 2
k0.06, l lOum, 1 0 0 cm - l
Figure 3.14Varia t ion of Absorp t i on
w i t h W avenum ber n l . 6 9 , k0.06, l lOum
-
77
3.3.4 Absorption of Parallel Sided Sheet within an Untuned
Resonator
A parallel sided sample placed within the cavity is equivalent
to a two sided hole as modelled by Lamb and outlined in section
2.3. Photons will strike the sample with equal probability from
either side and at any angle, the number of photons will be twice
the value calculated from Lamb's derivation, as 0 now varies from 0
to 4/r not 2n as in the case of the calibration hole. The Q of the
parallel sided sample is thus given by:
1 K a r 2— = - — — A a( 0 , n , k , d , A.)sin0cos0d0 ( 3 . 3 .
4 . 1 )Q s ZJT V Jo
Graphs are shown of the variation of the absorption integral
with wavenumber, thickness, imaginary and real parts of the complex
refractive index.
Figure 3.15Var ia t io n of A b sorp t i on w i t h k
n3.88, 1mm, 1 0 0 c m - l
k
Figure 3.16Variat ion of Absorp t i on w i t h n
k0 .0226, 1mm, 1 0 0 c m - l
-
Fra
ctio
na
l C
oef
fici
ents
78
V a r ia t io n of A b s o r p t i o n
F i g u r e 3 . 1 7
w i t h T h i c k n e s s k 0 .0 2 2 6 , n 3 .8 8 , 1 0 0 c m -
l
Var ia t io n of Absorpt io n
F i