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This is to certify that the

thesis entitled

EPR StUJiGS Of CS+(188U/\15CJ)8-
And Li+(C211)e-

presented by

Kerry Ann Reidy

has been accepted towards fulfillment
of the requirements for

Masters degree in Chemistry

 

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EPR STUDIES OF Cs+(18C6)(15C5)e'
AND Li+(c211)e'

By

Kerry Ann Reidy

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Chemistry

1992

A» ‘ ‘
(r J/\ ’3

.-

ABSTRACT

EPR STUDIES OF Cs+(18C6)(15C5)e‘
* AND Li+(C211)e-

By

Kerry Ann Reidy

The similarities between Cs+(l8C6)2e', Cs+(15C5)2e', and
Cs+(18C6)(15C5)e', have been explored via electron paramagnetic
resonance techniques. It was found that the mixed sandwich compound
yielded different EPR results than the two “parent” compounds. The
number of paramagnetic centers changed throughout the temperature range
of about 100-200 K in the mixed sandwich compound, thus disobeying the
Curie Law in that temperature range. The number of unpaired spins
remained the same in the two “parent” compounds within that same
temperature range, thus they followed the Curie Law. This finding
suggests that the mixed sandwich compound does not behave merely as a
mixture of the two “parent” compounds, but as a unique compound.

Similar EPR studies of Li+(C211)e- revealed very inconsistent
results. This compound has traditionally been the most difficult to handle,

which contributes to the inconsistencies observed from the EPR results.

ACKNOWLEDGMENTS

I would first like to thank the two research advisors who have
supervised me and guided me over the last two years, Dr. John McCracken
and Dr. James Dye. Their ultimate wisdom and enthusiasm was the driving
force for this research and I am grateful to the both of them. I only hope
that I can live up to their expectations over the next three years. I thank
the two research groups with whom I have worked, in particular Hong-In
Lee for the many helpful quantum mechanical discussions and especially to
Michelle Mac for experiencing this ordeal with me and always lending a
helping hand.

I thank my family and friends for being patient with me and for
being understanding. Without them, I may not have made it this far.

Lastly, I thank Robert Cedergren for the many sleepless nights
helping me with this document, for listening to me, for putting up with me
during the crucial last minute, and for all of his love and support over the

past two years.

K.A.R.

TABLE OF CONTENTS

Page
LIST OF TABLES .............................................................................. iv
LIST OF FIGURES ............................................................................. v
CHAPTER 1.
Historical Background of Alkalides and electrides .......................... 1
CHAPTER 2.
Experimental Procedures for the Synthesis of
Cs+(18C6)(15C5)e' ................................................................... 18
CHAPTER 3.
Theoretical Approach to Electron Paramagnetic
Resonance ................................................................................ 27
CHAPTER 4.
EPR Results and Discussion of Cs+(18C6)(15C5)e'
and Li+(C211)e' ....................................................................... 39
CHAPTER 5.
In the Future
1. Advanced EPR Studies of some HMHCY Sodides ........... 53
II. EPR Studies of the Photoexcited Triplet State of
K+(C222)e' and K+(C222)K' ....................................... 62
IH. Synthesis and Characterization of New Alkalides
and Electrides ........................................................... 64

ii

iii
REFERENCES .................................................................................. 66
APPENDIX ....................................................................................... 69

LIST OF TABLES

Page

1. Structural data for alkalides and electrides ....................................... 6

2. EPR results for one of three samples of Cs+(18C6)(15C5)e’ ............. 42
3. Comparison of Cs+(18C6)2e', Cs+(15C5)2e' and

Cs+(18C6)(15C5)e' ....................................................................... 48

iv

LIST OF FIGURES

Page

. Typical complexants used to synthesize alkalides and

electrides ...................................................................................... 3

. F-center, a negative ion vacancy with one excess electron bound at

the vacancy ................................................................................... 7
Interstitial ion or Fraenkel defect .................................................... 8

. Representation of the ion packing in Cs+(18C6)2Na‘ (top) and

CS+(HMHCY)Na' (bottom) ............................................................ 11
. Magnetic susceptibility data [llxcm vs. T(K)] for Cs+(15C5)2e' ......... 14

. Common organic solvents. The 1° and 2° amines are not as

resistive to reduction as the ethers or the 3° amines due to the

ionizable protons on the former amines .......................................... 19

. K-cell used in the synthesis of alkalides and electrides ...................... 21

. Precession of electron spin angular momentum and magnetic

moment in a magnetic field ............................................................ 28

. Electron spin levels in a magnetic field. Resonance is achieved

when the frequency of the incident radiation matches the frequency

corresponding to the energy level separation ................................... 30

10. Energy level diagram describing the effect of nuclear hyperfine

interaction .................................................................................. 36

. Schematic diagram of a CW-EPR spectrometer .............................. 38

V

12.

13.

14.
15.

16.
17.

18.
19.
20.
21.

22.
23.

v i
CW-EPR Spectra of Cs+(l8C6)(15C5)e' at temperatures of 91K

(top spectrum) and 221K (bottom spectrum) .................................. 40

Relative intensity vs. reciprocal temperature (UK) for

Cs+(18C6)(15C5)e' ..................................................................... 43
Asymmetry of lineshape with respect to inverse lineshape ............... 46
CW-EPR spectra of Li+(C211)e' at temperatures of 90K

(top spectrum) and 220K (bottom spectrum) ................................. 50
Intensity vs. 1/1‘ from EPR results of Li+(C211)e' ......................... 51
Individual spin packets which are homogeneously broadened
enveloped by an inhomogeneously broadened line .......................... 55
Evolution of the magnetization during a single 1t/2 pulse ................. 56
2-pulse echo sequence and evolution of the magnetization ................ 58
Allowed and semi-forbidden transitions in an EPR spectrum ........... 59

Echo diagram describing echo nuclear modulation a) after n/2
pulse, b) after 1: pulse, c) at the time of the echo ............................. 61
CW-EPR Spectrum of K+(C222)K' at 130 K .................................. 63
Two aromatic complexants used to produce potential alkalides

and electrides .............................................................................. 65

CHAPTER 1

HISTORICAL BACKGROUND OF
ALKALIDES AND ELECTRIDES

The group IA elements, or alkali metals, most commonly take on the
plus one oxidation state. In fact, they are so reactive in their metallic form
that this form does not exist in nature. It has traditionally been taught in
freshman chemistry classes that these metals will eagerly give up an
electron to form a stable salt, such as sodium chloride. This occurs in part
due to the fact that both sodium and chloride now take on a more stable
inert gas electron configuration. Adding an electron to an alkali metal fills
the S-orbital but in a less strongly favored configuration then the inert gas
configuration, so it was deemed highly unlikely. In the year 1974, it was
found that alkali metals, under very specific conditions, could form stable
salts where the alkali metal maintains both a plus one oxidation state as well
as the peculiar minus one oxidation statela'd. The research group of Dr.
James L. Dye discovered these crystalline salts and the research Still
continues today.

These crystalline compounds consist of an alkali metal cation
encapsulated by some complexant along with some anion, either an alkali
metal anion or an electron. These materials represent new classes of
compounds coined alkalides and electrides. The main difference between

the two compounds is the anion. In alkalides, an alkali metal is the anion
1

2
while in electrides, an electron is the anion. Electrides originate from

solvated electrons and alkalides from solvated alkali metal anions. Solvated
electrons are thought of as electrons in solution that do not belong
specifically to one single molecule or even to a collection of molecules
which maintain a well defined geometry. They are not trapped as in
organic glasses. Because of the light mass of the electrons, they are
considerably more mobile than other anions in salts thus they are fairly
free to travel throughout the solution which contributes to their unique
properties. These properties of solvated electrons have been studied by
several different research groups in a time period of over eighty yearsz. It
was observed many years ago that if a chunk of sodium was reacted with
pure anhydrous ammonia, a deep blue solution formed. This blue solution
was thought to indicate the solvated electron. When preparing the stable
solutions that contain solvated electrons or alkali metal anions, solvent
choice is of high importance. The solvent needs to be resistant to reduction
and to be a strong solvator of the cation but the process of solvating the
electron or anion is of lower importance. However, alkali metals only
dissolve in a few solvents other than ammonia, such as
hexamethylphosphoramide (HMPA), a few primary amines, and a few
polyethers.

By making use of the discovery of crown ethers by Pederson3 in
1967, and of cryptands (Figure l) by Jean-Marie Lehn4 in 1969, the Dye
group showed that the solubility of the alkali metals could be greatly
increased. It follows then- that an important aspect of synthesizing alkalides
or electrides is the complexing ability of the species that complexes the

cation. The particular complexant must be resistant to reduction as well as

O I
VO\°)
18- crown -6
(18C6)
(CH3 CH3 /\ 0’ ‘O/w
H C'N N 'CH N N
3 CH 1) 3 Qbo
N 3 CINJ 0l 0
\__/
Hexamethyl Hexacyclen Cryptand [22.2]

(HMHCY) (C222)

Figure 1: Typical complexants used to
synthesize alkalides and electrides

4
be a strong enough complexant such that it will win the battle for solvating

the cation over any strongly polar solvent. These cyclic and bicyclic
complexants are nearly resistant to reduction and deprotonation and have
been quite useful in the development of alkalide and electride synthesis.
The role of the complexant is to encapsulate the alkali metal cation so that
the electron that the metaI ejects will go into solution, or attach to an alkali
metal to form the metal anion in solution.

After proper work-up procedures, eventually the electron will either
remain as itself in the solid structure, or add to some remaining unreacted
alkali metal to form the alkali metal anion in solution and/or in the solid.
To be more specific, 18-crown—6 is a very common complexant used in this
research and when the alkali metal, the solvent and the complexant come
into contact with one another, the complexant encapsulates the alkali metal
cation on the hole formed by the ring. The lone pairs of electrons on the
oxygen atoms in the ether unit of the crown, are oriented towards the
positive ion, thus providing stability of the complex. The complexants play
other roles in the synthesis of alkalides and electrides. For example they
play an inteng part in aiding in the solvation of the alkali metal in certain
solvents that cannot dissolve the metal alone. This increases the list of only
a handful of solvents available for use to several more and greatly enhances

the solubility. The equilibria of the reactions are shifted:

 

Mt.) .— = M+ + e301. (1-1)

 

M+ + C " M“C (1-2)

 

5
where C represents the complexant. These equilibria, together with

equation I-3,

 

MG) + 5,0,, = = M (1-3)

 

allow us to synthesize concentrated alkali metal solutions in solvents such as
tetrahydrofuran (THF) or dimethyl ether (MezO) that contain M+C with the
counterion as either M' or the solvated electron, or perhaps a mixture of
the two. It is possible to adjust the concentration of the relative anionic
species by changing the ratio of complexant to metal. However, some
solutions will contain both M' and solvated electrons in addition to some
unreacted complexants, even if it is a stoichiometric solution. In the
absence of complexant, the solubility of the metal is often very small.
When this is true and the cation complexation constant is very large, these
two equilibria can be used to describe the behavior, (Eqs. I-4, I-S).

 

Mts) + C < > M+C + C'sorv (1-4)

 

2M(,) + C: r M+C + M' (1-5)

In preparing the alkalides or electrides, a second solvent that is less
polar than the first is added so that the polycrystalline material falls out of
solution. If the crystals are of appropriate shapes and sizes, the crystal
structure can be attempted. Up to now, the crystal structures have been
solved for 30 alkalides and four electrides, (Table l).

Table 1

Structural Data for Alkalides and Electrides

 

Compound

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Space Group Compound Space Group
Cs+(18C6)2e' Monoclinic Rb+(18C6)Rb' Monoclinic
Cs+(15C5)2e' Triclinic Cs+(C222)CS' Monoclinic
Li+(C211)Na' Orthorhombic K+(HMHCY)Na' Orthorhombic
Na+(C222)Na' Rhombohedral Rb+(HMHCY)Na' Orthorhombic
Na+(C221)Na’ Monoclinic Cs+(HMHCY)Na' Orthorhombic
K+(C222)Na' Orthorhombic Rb+(18C6)Na'MeNI§ Orthorhombic

K+(12C4)2Na' Monoclinic K+(18C6)(12C4)Na' Orthorhombic

Rb+(15C5)2Na' Monoclinic K+(18C6)(12C4)K' Orthorhombic

Cs+(18C6)2Na' Monoclinic K+(18C6)(12C4)K'.(18C6) Monoclinic

Cs+(15C5)2Na' Triclinic Li+2(TMTCY)2(MeNH)Na' Orthorhombic

Cs+(15C5)2K' Triclinic Li+2(TMTCY)2(MeNH)Na' Orthorhombic

Rb+(15C5)2Rb' Monoclinic Li+2('I'M'I‘CY) Orthorhombic

(DMTCY)'MeNH2Na'

Cs+(18C6)2CS‘ Orth. Pbca Li+(18C6)Na'(MeNH2)2 Monoclinic
Li+(C21 1)e' Orth. Pbcn Li+(18C6)Na'(MeNH2)2.(l8C6)3 Rhombohedral
K+(C222)e- Monoclinic Cs+(18C6)(15C5)Na- P21 /m
K+(C222)K' Triclinic K+(18C6)Na°(MeNH2)2.(18C6) Rhombohedral

Rb+(C222)Rb- Triclinic Li+(MlCH)Na')2(MeNH2) Monoclinic

 

 

. 7
A pure alkalide would consist of an alkali metal with an ns° electron

configuration (M+) and ns2 electron configuration (M') (where the metals
need not be the same) thus they are expected to be diamagnetic. However,
magnetic susCeptibility and EPR studies have shown that some
paramagnetic species do exist in these polycrystalline materials. The
reason for this is due to the presence of trapped electrons in anionic
vacancies in the crystals. These defect electrons occupy holes, and such

electron-occupied holes are called F-centers (Figure 2).

 

Figure 2: An F-center is a negative ion vacancy with
one excess electron bound at the vacancy.

The electron of an F-center can generally be thennally excited to a
conduction band5, thus giving rise to an n-type semi-conductor. Another
type of defect electron that possibly exists in these systems is an interstitial

defect or Fraenkel defect (Figure 3). The fact that the electrons are weakly

8
bound has been taken advantage of in that photoelectron emission and

thermionic emission have been demonstrated from alkalides and electrides.

Because of the wide range of behavior of the magnetic properties of
electrides and alkalides, as well as the optical and electronic properties,
these compounds can act as a probe for determining the interactions of
weakly bound electrons with each other and with surrounding ions and
molecules.

Electron spin echo envelope modulation (ESEEM) is a pulsed EPR
technique that can take on the challenge of mapping these electrons and

their interactions. This topic will be addressed in a later chapter.

Figure 3: Interstitial IQn (Fraenkel defect)

a distortion in a point because there is an
atom in a position where it does not belong.

9
The most extensively studied alkalide to date is Na+(C222)Na-1b.c,

mainly because of its remarkable stability relative to the other alkalides and
electrides. Even though most of these ionic salts are sensitive to air,
moisture, and to other reducing agents as well as to temperature,
Na+(C222)Na' is stable under vacuum for several days at room
temperature and indefinitely at low temperature. However it is
thermodynamically unstable towards decomposition. Crystalline alkalides
and electrides are subject to an irreversible decomposition process as the
temperature is raised. The decomposition usually accelerates at around 0°C
although this is dependent upon the system. The crystal structure of
Na+(C222)Na- has been found to‘be rhombohedral with a space group in
the hexagonal setting. '

The Na+(C222)Na' crystal is a very brilliant gold-copper color and
one might think that it is a metal. However, it is not a metal and instead is
an intrinsic semi-conductor with an apparent band gap of 2.4 eVlb. EPR
studies as well as magnetic susceptibility studies Show that the pure
N a+(C222)Na' material is only weakly paramagnetic, whether in the form
of a powder, thin film or microcrystal. The effect of light was studied by
recording the EPR spectrum while the sample was illuminated in the
cavitylb. Illumination of the sample was provided by a 150W tungsten
lamp which was focused directly on the grid of the EPR cavity. Unfiltered
visible light (UV excluded) or 630 nm light, produced an increase in the
EPR signal. The results from the EPR measurements showed only the
photoproduction of a low concentration of paramagnetic species. The g-
value was found to be 2.005 which is close to that of trapped electrons in
solids of this type. No other paramagnetic species were observed. The

lifetime at room temperature of the paramagnetic species was long, with a

1 0
half-life of about 30 seconds. The addition of EPR active material was

thought to be due to the dissociation of defect electron pairs which were
present before illumination of the Na+(C222)Na'.

Other alkalides and electrides were studied via EPR yielding quite
interesting results. In one study6, various EPR measurements of sodides
were compared. Three of the sodides were sandwich compounds, in which
two complexant molecules encapsulate the cation, and three sodides
involved the complexant hexamethyl hexacyclen (HMHCY) (see Figure 1).
In the sandwich compounds, [Cs+(l8C6)2Na-, Cs+(15C5)2Na-,
Cs+(12C4)2Na-], each Cs+ ion is sandwiched between pairs of the respective
crown ether, while the Na‘ ion is surrounded by eight such complexed
cations, at roughly equal distances. In the other compounds, each HMHCY
complexed Cs+, Rb+ or K+ is nearly in contact with Na' at much larger
distance from other anionic sites (Figure 4).

The HMHCY sodides provided atypical EPR spectra in that resolved
hyperfine splitting existed following the 2nI + 1 rule for a number of EPR
lines (where n = the number of identical nuclei involved and I = the
nuclear spin). For example, Cs has a spin of I = 7/2 so if the trapped
electrons in the anionic site were close enough to the Cs ion to interact, one
would expect [2(1)(7/2)+1 = 8] an eight line pattern. This is in fact what is
observed. The same pattern is observed for Rb (I = 5/2), a six line pattern
and K (I = 3/2) a four line pattern. A direct measurement of the isotropic
part of the hyperfine coupling constant was made from each spectrum.

The behavior of the EPR intensities was also measured as a function
of temperature. In general, these systems follow Curie Law behavior. A
plot of intensity versus 1/'[‘ (K) yielding a straight line follows Curie's

Law. Thus the concentration of unpaired spins is constant during that

11

 

Figure 4: Representation of the

ion packing in Cs+(18C6)2Na- (top)
and Cs+(HMHCY)Na-' (bottom).

l 2
particular temperature range. Furthermore, the trapped electrons do not

strongly interact with each other. Interestingly, K+(HMHCY)Na' showed
no temperature dependence of the signal intensity during the temperature
change of 190 - 240 K. A possible explanation of this is spin pairing or
antiferromagnetic coupling between electrons with different temperature
dependences in the two sites.

The EPR measurements revealed only a single line for the two
sandwich compounds, Cs+(15C5)2Na- and Cs+(12C4)2Na- with g-values of
2.0020 and 2.0025, respectively. These are close to the free electron g-
value which implies that little spin-orbit coupling exists. The peak to peak
line widths were 2.21 and 4.40 G respectively. These spectra provided
very little information.

In contrast, the sandwich compound Cs+(18C6)2Na- showed a broad
line with a sharp central narrow line. Each synthesis was slightly different
so the relative intensities of the two peaks also varied. The spectrum
showed no resolved hyperfine coupling and the line broadening was
thought to come from superhyperfme interactions with several surrounding
nuclei rather than a shifting of the g-values. The differences in the
structures of these two families of compounds clearly agrees with the fact
that hyperfine interactions are observed for the contact HMHCY
complexes, while none is seen for the sandwich compounds.

What happens when two different types of crown ethers are forced
to react under the proper conditions, with an alkali metal? In this case, a
mixed sandwich was formed and the properties of these types of

compounds are presently being studied. Here I would like to discuss the
comparison between Cs+(18C6)2e', Cs+(15C5)2e', and later, compare these

l 3
results with those found in this study of the most recent mixed sandwich

compound, Cs+(1 8C6)(15C5)e‘.

The crystal structure of Cs+(15C5)2e' belongs to the triclinic space
group in which the electride contains only complexed cations, Cs+(15C5)2,
and trapped electrons that were undetectable by x-ray diffraction7. The
Cs+-O distances have an average value of 3.154 A. The apparent band gap
of this compound was at least 1.0 eV and it was thought to be an insulator.
This system involved localized electrons with a ground state energy at least
1.0 eV below the conduction band, as indicated by the the fact that no
detectable intrinsic electronic conductivity was observed below 190K3. It
was later found that this system was an ionic conductor rather than an
electronic conductor with an activation energy of 0.6 eV9. These results
were sample dependent however.

The magnetic susceptibility of Cs+(1SCS)2e- showed Curie-Weiss
behavior8 down to 2K after being quenched from room temperature to 5K
(Figure 5). However, different behavior was observed when the
Cs+(15C5)2e* was gradually cooled from 250 K. An antiferromagnetic
transition occurs with a Neel temperature of 4.2 K. However, at
temperatures well above the Neel temperature, the susceptibility followed
the Curie-Weiss law. Several NMR experiments were carried out on this
electride3. Initially, two peaks were observed with chemical shifts at 490
ppm and 290 ppm from a temperature range of 265-280 K. Above 280 K,
only one peak was observed at 290 ppm, most likely due to a phase
transition at that temperature. EPR measurements10 revealed a Single
narrow line for three samples at 200 K. The peak to peak linewidth was
0.6 G with a g-value of 2.0022ilx10‘4. The samples subject for EPR
analysis were always quenched from 270K - 2.5K. and followed the NF

m on N or
I l l l

(emu‘moi) x 10"
U ‘
l 1

1112‘
N
l

l

14

 

 

0

I J I

lift illrrfi
020406080100120140160180200220240260

70‘)

Figure 5: Magnetic susceptibility data
(l/Xem versus temperature) for
Cs+(15C5)2e-.

l 5
dependence expected for Curie-Weiss paramagnets. There was no

Significant shift in the g-value with temperature, but it was found that the
peak to peak linewidth increased with decreasing temperature.
Cs+(18C6)2e' was the first electride to have its crystal structure
determined, which was foundto be monoclinic1 1. The crystal structure, as
well as optical, electrical, and magnetic properties, Show that Cs+(18C6)2e'
has each electron trapped in an elliptically-shaped empty cavity of a radius
about 2.4 A. In addition, each electron was found to be surrounded by
eight sandwich-complexed cesium cations. Initial conductivity studies
showed that this compound had an apparent band gap of 0.9 eV. which
implied that this electride was a semi-conductorl 2. However, later it was
shown that this compound indicated the presence of ionic conductivity
which is in disagreement with the previous results3. 133Cs NMR had been
shown to be a primary technique for the characterization of Cs+(18C6)2e'
and it was used as a probe to understand the interactions of the trapped
electron with the encapsulated cation . The electrons appeared to be
localized and were found to interact With each other and the cation only
weakly. The NMR results showed only one peak with a chemical shift of
+8lppm13. This chemical shift describes a paramagnetic shift from that of
other Cs(18C6)2 compounds which could be due to contact with the
electron, or perhaps a tighter coordination of the Cs with thecrown ethers.
The paramagnetic shift in the Cs+(18C6)2e' is the contact shift (or Knight
shift). The paramagnetic electron density produces a strong magnetic field
at the nucleus which results in the Knight shift. The fact that there was
only one N MR peak present in the 133Cs NMR (due only to Cs+ and no
CS'), and that the peak was shifted paramagnetically, was consistent with

this compound being an electride.

16

dependence expected for Curie-Weiss paramagnets. There was no
significant shift in the g-value with temperature, but it was found that the
peak to peak linewidth increased with decreasing temperature.
Cs+(18C6)2e' was the first electride to have its crystal structure
determined, which was found to be monoclinicl 1. The crystal structure, as
well as optical, electrical, and magnetic properties, show that Cs+(18C6)2e'
has each electron trapped in an elliptically-shaped empty cavity of a radius
about 2.4 A. In addition, each electron was found to be surrounded by
eight sandwich-complexed cesium cations. Initial conductivity studies
showed that this compound had an apparent band gap of 0.9 eV. which
implied that this electride was a semi-conductor”. However, later it was
shown that this compound indicated the presence of ionic conductivity
which is in disagreement with the previous results3. 133Cs NMR had been
shown to be a primary technique for the characterization of Cs+(l8C6)2e'
and it was used as a probe to understand the interactions of the trapped
electron with the encapsulated cation . The electrons appeared to be
localized and were found to interact with each other and the cation only
weakly. The NMR results Showed only one peak with a chemical shift of
+81ppm13. This chemical shift describes a paramagnetic shift from that of
other Cs(18C6)2 compounds which could be due to contact with the
electron, or perhaps a tighter coordination of the Cs with the crown ethers.
The paramagnetic shift in the Cs+(18C6)2e' is the contact shift (or Knight
shift). The paramagnetic electron density produces a strong magnetic field
at the nucleus which results in the Knight shift. The fact that there was
only one NMR peak present in the 133Cs NMR (due only to Cs+ and no
CS'), and that the peak was Shifted paramagnetically, was consistent with

this compound being an electride.

1 7
were locally trapped and that they exhibited spin pairing as the temperature

was decreased. Finally, crystalline material was synthesized and
characterized, and the space group symmetry of the Li+(C211)e' was found
to be orthorhombic. Once the crystalline material could be produced, it
was found via magnetic susceptibility, that the electride might be
independent of the ratio, Li/complexant. In addition, the magnetic
susceptibility results showed an anti-ferromagnetic behavior, thus the data
could not be fit by the Curie-Weiss equation. EPR results of the new and
improved crystalline material should help clear up some of the mysteries of
this electride.

EPR studies of the type discussed here are continued in this research,
focussing on Cs+(15C5)(18C6)e' and Li+(C211)e'. Clarification of some
of the uncertainties with the Li+(C211)e' characteristics as well as a
comparison between the mixed sandwich electride, Cs+(18C6)(15C5)e', and
the other two similar electrides, Cs+(l8C6)2e' and Cs+(15C5)2e‘ were
attempted. It is worthwhile to proceed in the next chapter with a detailed

explanation of the experimental procedures.

CHAPTER 2

EXPERIMENTAL PROCEDURES FOR THE
SYNTHESIS OF C's+(18C6)(15CS)e'

Preparation of alkali metal solutions, alkalides and electrides would
not be as tedious if the highly reactive nature of the solvated or trapped
electron and alkali metal anions did not exist. Oxygen, water, alcohols and
other reducible substances must be kept out of the reaction vessel.
Furthermore, the reaction vessel must be immersed in a cold bath at
temperatures around -40°C during synthesis and kept cold during use and
storage of the alkalides and electrides. Presumably, the reason for this is
that the complexants and solvents are themselves reducible substances“.
This ultimately leads to decomposition of the solid or solution. A solvent
such as dimethyl ether is a preferred solvent because of its resistance to
reduction. Since dimethyl ether (MezO) does not have ionizable protons,
or protons that are beta to the oxygen, this leads to resistance to reduction,
so that it is a very robust solvent. Primary and secondary amines have
ionizable protons, thus making them less desirable. Trimethylamine
(TMA) and, to some extent, diethyl ether (Et20) also maintain a resistance
towards reduction, although Et20 has beta hydrogens, and these two

solvents serve as suitable co-solvents (Figure 6). The combination of

MezO and TMA provides the greatest resistance to reduction.

18

19

 

 

 

' N'Ix "7
/-'O H4 l '////R R( ///R
H H
H3C \CH3
Dirnethyl ether Primary Amine Secondary Amine
N: . .,
4 ”’/// '0
H C CH
3 CH3 3 H3CH2C / \CH2CH3
Trimethylamine Diethyl ether

Figure 6: Common organic solvents. The 1° and 2° amines are
not as resistive to reduction as the ethers or 3° amine,
due to the ionizable protons on the former amines.

- 20
Preparation of Cs+(15CS)(18C6)e-.

The preparation of an electrideoften requires the use of a K-oell
(Figure 7) that is made mostly of quartz (especially when lithium metal is
used). This prevents accidental contamination with a sodide when a metal
other than Cs is used in the synthesis, due to exchange of the natural Na+ in
the borosillicate glass of Pyrex with another alkali metal cation in the
presence of an electron or M'. The synthesis of alkalides does not require
a quartz K-cell, except for the case of lithium, because lithium is the most
likely alkali metal to exchange with the sodium in glass. Initially, the K-
cell was cleaned rigorously to inhibit solution decomposition. The
apparatus was partially filled with an aqua regia solution which was
composed of three parts HCl and one part HNO3. This was allowed to
stand for one day. The following day, the solution was poured out and
washed six times with distilled water, followed by six rinses with
conductance water. The conductance water was distilled water that had
been deionized and redistilled through a high reflux ratio column so that
less than 1 ppm of impurity remained. The K-cell was then placed in an
oven at around 275°C to completely dry. Sometimes the K-oell apparatus
was placed on the vacuum line overnight, with the proper 9 mm Ultra-
Torr attachments at points 1 and 2, and evacuated so as to check for any
faults in the glass as well as to distill out any water that remained in the K-
cell. As is evident from this description, the cleaning process is very
important and takes time and patience, so planning an experiment ahead of
time is always advantageous.

Once the K-cell had been cleaned and it was determined that it could
sustain a vacuum of 10‘5 torr, the K-cell, the appropriate length of a Cs

metal ampoule, a spatula and a thistle tube were all placed in the Vacuum

21

Fingers
Stopcock K

To Vacuumé—flIZ;E I

    

 

Point 2

 

Tube Y

 

 

 

Point 1

Point 3 Point 4

Bulb A Bulb 8

Figure 7: K-cell used in the synthesis
of alkalides and electrides.

2 2
Atmosphere Company (VAC) Glove Box outer chamber to be evacuated to

about 10 mtorr. Once the outer chamber had been evacuated, the
equipment could be accessed through the port and brought into the glove
box. A metal ampoule of the appropriate length was scored with a knife
stored in the glove box and cracked. The portion of the cracked ampoule
containing the metal was placed into tube Y so that the sealed part of the
ampoule was facing towards the inside of the apparatus (this was done so as
to help prevent any bumping of the metal when it was distilled). If the
ampoule was cracked in the middle of the Cs metal portion, both parts
were placed in the side tube. The Ultra-Torr attachment was then placed
securely on the end of the side tube at point 1. Next the complexant was
added through point 2 and into bulb B. The thistle tube (15 cm long,

4 mm OD Pyrex tubing with a funnel at the top) was very handy at this
point because it helped prevent any of the complexant from adhering to the
sides of the tube X. Approximately the same molar amounts of the two
complexants were added to the apparatus. When synthesizing an electride,
a slight excess of complexant is preferred. The opposite is true in an
alkalide synthesis. Once the two complexants had been added to the bulb,
the ultra-torr attachment was attached to point 2, and the apparatus was
ready to come out of the glove box. It was important to check that the
stopcock was closed and that both Ultra-Torr attachments were tightly
secured.

Once the apparatus was taken out of the glove box, it was imperative
that no oxygen was allowed into the K-cell. At this point, the K-cell
apparatus, which contained a He atmosphere, was directly attached to the
vacuum line and evacuated. When the pressure had reached 10-5 torr, the

apparatus was sealed with a torch at points 1 and 4. Since 15C5 is a

2 3
somewhat volatile liquid, a dry ice/isopropanol bath was used to keep the

15C5 cold in order to prevent it from distilling into the cold trap under
vaCuum. When the two side-arms had been sealed-off, a freshly distilled
Cs mirror was deposited into bulb A by using a light flame. A nice gold-
colored mirror always formed rather quickly. It was important not to
distill the Cs too rapidly or else largeballs of metal would form and
deposit on the bottom of the bulb. This was not disastrous, but the thinner
the film was, the faster the metal could be used in the reaction. It was also
important to prevent the metal from depositing too high on the neck of the
vessel so as to approach the stopcock. Applying heat near a stopcock is not
a good idea anyway, when the importance of a good vacuum is at stake.
After the metal had been completely distilled, the stem of the tube was
sealed at the narrowed portion of the glass, point 3.

About 10-15 mL. of solvent (Me20) was then introduced into bulb
B, which contained the two crown ether complexants, through an extended-
tee, at about -35°C. In addition to the MezO, about 1-2 mL. of
methylamine was added to bulb B to aid in dissolving the crown ethers.
This process is not customary in general electride synthesis, but was helpful
in this particular procedure. It was crucial that the crown ethers were
dissolved as completely as possible before allowing the solution to contact
the metal mirror. This actually is a rather difficult process because the
dimethyl ether has a low boiling point (-24.8°C) so the temperature of the
bath cannot be raised too high, but high enough to dissolve the crowns.
About -35°C appeared to be a good temperature for this process. Once the
complexants had dissolved, the solution was exposed to the mirror (bulb A)
and the deep blue color, indicative of solvated electrons was formed

immediately. It was important to let the metal react completely with the

2 4
complexants so that no metal mirror remained. The amount of Cs that had

been added to the reaction vessel was insufficient to react with all of the
crown present, in order to prevent the formation of a ceside. A deficient
amount of alkali metal was always added during an electride synthesis, so
that reaction of all of the alkali metal with complexant was an indication
that electride had been formed. This process usually took about a day and
a half. Once all of the metal had been dissolved, about 3—5 mL. of TMA
was added to bulb A at -7 8°C. TMA acts as the cosolvent for
crystallization of the product. All of the solution was poured through the
frit to bulb B and the remaining deep blue mirror was washed very well by
using a cotton swab dipped in liquid nitrogen to distill over some clean
solvent which was then used to dissolve the mirror. This sometimes took
several hours. At this point, the solution was brought to saturation by
evaporation of MezO. Crystal growth was effected by slow evaporation of
the solvents through three additional frits, at ‘78°C over a period of about a
week. It was important to keep the two bulbs and the frit in a dry
ice/isopropanol bath throughout the entire procedure since electrides are
very sensitive to higher temperatures. Several syntheses yielded only
decomposition products because the temperature of the apparatus was not
kept extremely cold. During this waiting time, the solution was carefully
checked to monitor the progress of crystal formation. When about 5 mL.
remained in the bulb and crystals were present, (usually, a polycrystalline
material was produced) the remaining solvent was poured through the
fritted glass to bulb A and distilled out of the apparatus. The black
material that had formed was not necessarily clean material, so it was
important to wash it carefully with a cosolvent such as TMA or Et20. This
entailed adding about 10 mL. of cosolvent to the flask containing the

2 5
crystals and decanting through the frit anything that dissolved in the

solvent, such as any unused crown. The solvent was then distilled back into
bulb B and the procedure was repeated several times until one was
confident that the material was free of complexant. Finally, the crystalline
material was left to dry on the vacuum line overnight by pumping at about
10'6 torr while the K-cell was kept in. a dry ice/rsopropanol bath.

It is important to note that the cleaning ritual described earlier, was
especially important in that it helped eliminate impurities. In addition, by
avoiding a faSt precipitation of the product, good polycrystalline material is
usually produced. By going through this extra trouble, we were allowed to
produce crystalline material more consistently.

When the crystals were dry, the entire K-cell was taken off the
vacuum line and prepared for flipping of the apparatus so that the crystals
would fall nicely into the fingers, which would subsequently be sealed from
the apparatus. This preparation entailed placing the K-cell in a large
storage container for the dry ice, so that the fingers and bulb B, which
contained the electride crystals, were in contact with the cold cubes of dry
ice. This was done so that when the crystals came in contact with the
fingers, they would not be exposed immediately to a warm surface.
Instead, there was no temperature change since both parts of the apparatus
were in the same environment. Following this procedure, the fingers were
immediately placed in a large dewar containing liquid nitrogen and sealed
from the apparatus with a hot flame.

When the time came to transfer the material into an EPR tube, this
was performed in a glove bag equipped with a flow of nitrogen gas. A tall
dewar containing the samples, a glass cutting knife, the EPR tube (4 mm

0D quartz tube attached with a graded seal to a stopcock and vacuum line

2 6
joint) , a few melting point capillary tubes, and a mortar and pestle, were

all placed inside the glove bag through the opening. Typically, about four
liters of liquid nitrogen were poured into a large Styrofoam dewar in the
glove bag to create a large positive pressure of the inert gas in the glove
bag which would in turn drive out any air that got in the bag during
loading of the appropriate equipment. This process was repeated several
times so that all of the air had escaped and the glove bag was then kept cold
until the procedure was completed. The mortar was then filled with liquid
nitrogen and the sample tube was scored with a glassblower's knife and
broken. The contents were poured immediately into the very cold mortar.
The crystals were then crushed with the pre-cooled pestle to a very fine
powder. A very small amount of the powder was then placed in the
capillary tube and the entire capillary tube was then placed into the large
EPR tube and kept cold in liquid nitrogen. The reason for using the
capillary tubes was that it had been found in previous experiments that
when the powder was loaded directly into the EPR tube, a light film would
coat the sides of the tube and it was often difficult to collect all of the
sample at the bottom of the tube. By using the capillary tubes this problem
was eliminated and no further complications were observed. The EPR tube
was then placed on the vacuum line, and the quartz tube was immersed in
liquid nitrogen and sealed by using a very hot flame, after which it could

be used for EPR measurements.

CHAPTER 3
THEORETICAL APPROACH TO
ELECTRON PARAMAGNETIC RESONANCE

Electron Paramagnetic Resonance, or EPR, is a sensitive technique
for the detection of paramagnetic speciesl7atb. The presence of unpaired
electrons in atoms or molecules gives rise to a magnetic dipole moment.
Classically, the energy of a magnetic dipoles, u, in a static magnetic field,

H, is given by Eq. III-l,

u = magnetic moment
or H = field strength (111-1)

0 = angle between it & H
E = -u Hcos0

When 0 = 0°and u > 0, the minimum energy is obtained resulting in a
parallel configuration of the dipole for a given value of the magnetic field
strength. When 0 = 180°, the maximum energy is obtained and an anti-
parallel configuration of the dipole is obtained with respect to the magnetic
field strength.

The static picture presented in Figure 8, is perturbed by the presence
of electron spin angular momentum, which causes the moments to precess

2 7

28

about the direction of the applied magnetic field at an angle, 9, determined
by the value of the spin angular momentum and in a direction given by: it
x H. Because spin angular momentum is quantized, only certain discrete
angles, and therefore, discrete interaction energies for the electron spin
with the applied field are allowed. For a system with a single unpaired

electron spin, the allowed values for the electron spin angular momentum

A“ M

Figure 8: Precession of electronic Spin
angular momentum and magnetic
moment in a magnetic field.

 

are given by, MJ, where Ms is the electron spin quantum number and can
take on the values of i 1/2. The energies of these two states are given by

Eq. III-2,

E = MsgBH (III-2)

29

where, g is the Lande’ g-factor, [3 is the Bohr magneton and H is the
magnetic field in Gauss. In EPR spectroscopy, the energy difference
between these two states (Eq. III-3),

AB = ng (III-3)

is probed, (see Appendix A for a complete derivation). For a typical
laboratory magnetic field of 3400 G, AB is on the order of 10'24 J thus the
frequency of the electromagnetic radiation used for this spectroscopy is on
the order of 10 GHz, corresponding to the microwave region (Figure 9).

Thus, the interaction of a magnetic dipole with electromagnetic
radiation can induce transitions between two Zeeman levels if the photon
(hv) equals the separation gBH.

Since this system has discrete energy levels which are

described by well defined quantum numbers, necessarily, an eigenvalue

equation can be written. Consider a system where Xi represents an

eigenvalue of a state and (bi represents an eigenfunction or basis set for that

eigenvalue. An eigenvalue equation can be written as follows (Eq. III-4)
A
0¢i = Ki¢i (III-4)

where 6 is the necessary operator for the system. Since EPR deals with
spin angular momentum, a Spin operator is appropriate here. This spin
operator will operate on a function specifically defining a spin state.
Consider the system with one unpaired electron, S = 1/2, resulting in two

quantum numbers, MS = i 1/2. The components Msh, of angular

momentum along the magnetic field direction are measured by the quantum

30

 

 

E=gBH

= (2.00232)(9.27402E-28J/G)(3400G)
= 6.314E-24 J

 

 

 

H (G)

7

 

Figure 9: Electron spin levels in a magnetic field.
Resonance is achieved when the frequency
of the incident radiation matches the

frequency corresponding to the energy
level separation.

3 l
A
numbers, Ms. Thus if S'h is the angular momentum operator, Eqs. III-5,
III-6a and III-6b:

§¢i = Ms¢i (III-5)
or

g, (Ms = 1/2) = 1/2¢(Ms = 1/2) (III-6a)
So (M8 = -1/2) = -1/2¢(M, = -1/2) (III-6b)

Using the more common notation, Dirac notation and designating the
axes of quantization of the angular momentum to be the z-direction, Eqs
III-7a and III-7b,

gz I1/2> = 1/2 I1/2> (III-7a)

SIM/2) = -1/2 I-l/2) (III-7b)

If we let on be equivalent to M5 = 1/2 and [3 to M5 = -1/2, these expressions

can be Simplified even more, Eqs. 111-83 and III-8b,

|1/2> = |ot) = in, (III-8a)
|-1/2> = “3) = on (III-8b)
Ms is a precise measure of the spin angular momentum components, and

the energies associated with such systems are obtained from the

Schrodinger equation (Eq. III-9),

32
91in = Ei¢i (III-9)

where H is the spin Hamiltonian operator. Eqs III-10a,b then follow,
94a) = Ea lot) (III-10a)

911B) = Eu IB) (III-10b)

It is important to note that operators having the same set of eigenfunctions

have a useful property in that they must commute.

It was shown in the Appendix, that #2 = -yMsTI thus it may be
A

expected that “2 (the magnetic moment operator) should be proportional to
A
$2. This results in Eq. III-ll,

A A A
u, = -y 8211 = -gBSz (III-11)

Now combine Eqs. III-l and III-ll resulting in the spin Hamiltonian,

Eq. 111-12,

A
at = gBHSz (III-12)

An expansion of this can be written as, Eq. III-13a and III-13b,
A
Ma) = gBHSzIa> (IH-13a)

= l/2gBHIor)

3 3
94B) = gBH’ézIB) (III-13b)

= -1/2gBHII3)

For a transition between or and B , Eq. III-l4 expresses the energy

difference,

AB = Ea - E5 = gBH = hv. (III-14)

thus complying with Figure 9 and the energy level splittings.

The interactions discussed thus far have been between an electron f
and a magnetic field. If this were the only effect measured by the EPR, all
spectra would be relatively indistinguishable as they would only consist of
one line. The only useful feature would be the g-value. However, the
electron spin magnetic dipole can interact with with nuclei in its vicinity, as
some nuclei possess an intrinsic spin angular moment and a magnetic
moment associated with it. Magnetic nuclei can produce a local magnetic
field, and the interactions between the electron and the magnetic nucleus is
the known as the nuclear hyperfine interaction. This interaction can be
either orientation dependent (anisotropic), or independent of the
orientation of the field (isotropic).

Consider a nucleus which has an intrinsic spin, I=l/2. The nuclear
hyperfine interaction splits each of the Zeeman levels into two levels
(Figure 10). The observed transitions are those obeying the EPR selection
rules, Ms = i l and M1 = 0.

3 4
The Hamiltonian describing the hyperfine interaction follows
Eq. III-15.
A A
Hiso = hAoSzIz (III-15)

. A .
where A0 is the isotropic hyperfine coupling constant, I2 is the nuclear spin
operator and the measurement of the interaction between an electron and a

nucleus is hAo. Thus the total Hamiltonian is given by, Eq. III-l6.

A A A
at = ngSz + hAOSzIz (III-16)

A A
Since the energy values of S2 are Ms = il/2 and for 12, M1 = i1/2, four

possible spin states are obtained (Eq. III-17),

lac, an) “369 an)
lac, in) use, Bu) (111-17)
and can be further related (Eqs. III-18a, III-18b),
A
Szlae. Bn) = 1/2|ae, Bn) (III-18a)
(III-18b)

A
Izlae, Bu) : *1/2laet Bn)

Thus the energies for these States can be obtained, Eq. III-19

Basin = (one, BanIae. Bn) (III-19)

A A A
= (ac, BulgBHSz + hAOSzIzlaea Bn)

3 5
= 1/2gBH - 1/4hAo

and the energies for the other states are obtained similarly (Eq. III-20),

Bacon = 1/2gBH +1/4hAo
Efieun = -1/2gBH -1/4hAo (III-20)
EBeBn = -1/2g|3H +1/4hAo

This same procedure is followed for a system where I = 1. In this case,

there are six spin states (Eq. IH-21),

|1/2, i) Hm. I)
|1/2, 0) Ha, 0) (111-21)
ha. -1) Ha, -1)

Similarly to Eq. III-19, the energies can be obtained. The interactions
between an electron and a nucleus (1 = 1/2), are easiest viewed in an energy
level diagram (Figure 10).

Now that a general background of EPR theory has been discussed, it
is worthwhile to mention the instrumentation. A typical EPR spectrometer
(Figure 11) consists of the following components: a magnet,a cavity
(which contains a set of Helmholtz coils) to contain the sample, a source of
microwave radiation, a detection system, and signal processing and Signal
enhancement electronics. When the resonance condition is satisfied,
microwave power is absorbed by the sample. Because the experiment is
carried out with a fixed source frequency, the spectrum is generated by

measuring the microwave power absorbed by the sample as a function of

36

 

 

 

 

 

 

-1/2 __I_
_h_A°_
2
-< 1/2
H(G) I

 

 

__> transitions which
obey selection rules

""""" * transitions which
disobey selection rules

Figure 10: Energy level diagram describing the
effect of nuclear hyperfine interactions.

37

the the magnetic field strength. Monochromatic radiation is derived from
a klystron. The frequency of this radiation is adjusted so that standing
waves are set up in the sample cavity. The sample is placed into a region
of the cavity where the microwave magnetic field is at a maximum. The
sensitivity of the experiment is determined, in part, by the quality factor,

or Q, of the cavity. An expression for Q is given in Eq. III-22.

Q = 27C (Estored/Edissipated/cycle) (III-22)

Essentially, microwave radiation in the cavity makes "Q" passes through
the sample before it exits to the detector. Microwave energy is physically
coupled into and out of the sample cavity by a small hole called the iris.
The signal is then deflected to the crystal detector and eventually, the signal
can be viewed on the oscilloscope or recorded. The phase sensitive
detection technique utilizes small amplitude magnetic field modulation to
"package" the EPR signals with a specific carrier frequency and then
amplifies and detects only signals occurring at that frequency. Because
noise occurs at random frequencies, this procedure enhances the signal-to-
noise ratio of the measurements by eliminating much of the noise. The
advantage of phase sensitive detection is the increase in sensitivity, but as a

result, the signal will appear as a first derivative.

38

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f a CW-EPR Spectrometer.

mg 0

Schematic Draw'

Figure 11

CHAPTER 4

EPR Results and Discussion of

Cs+(l8C6)(15C5)e‘ and Li+(C211)e-

Cs+(15C5)(18C6)e'

EPR studies were performed on Cs+(18C6)(15C5)e' to obtain
additional information regarding the electronic interactions of this system.
A Bruker ER-200D spectrometer operating at X-band was used for these
experiments. The temperature was controlled by using a cold stream of
nitrogen gas through a transfer line connected indirectly to the TEloz
rectangular cavity, and the temperature was calibrated with a copper-
constantan thermocouple with an Omega model 199 digital readout system.
An ER350 NMR gaussmeter was used to measure the magnetic field with l
mG resolution. The g-value was measured directly from magnetic field
and frequency measurements. The data were collected with an IBM-AT
computer.

The Cs+(l8C6)(15C5)e' sample was transferred into an EPR tube as
previously described. The temperature in the EPR cavity,was changed
about every 8 degrees from roughly 90K to 200K, depending on the
particular experiment. The sample was never moved once inside of the
cavity, so as to prevent any inconsistencies in the positioning of the tube
with respect to the microwave radiation. The resulting spectrum (Figure
12), was a narrow line with a g-value of 2.0019. No resolved hyperfine

splitting was observed and the peak to peak linewidths varied from 1.34 G
3 9

40

 

 

 

lG'

 

Figure 12: CW-EPR spectra of Cs+(18C6)(15C5)e' at
temperatures of 91K (top spectrum) and
221K (bottom spectrum).

41
at 91 K to 0.965 G at 221 K.

The instrumental settings were kept constant throughout the
temperature changes, except for the gain because the intensity of the line
became weaker as temperature was increased. Relative intensities were
obtained to account for the differences in this factor. Table 2 shows the
parameters obtained from the EPR data.

The most accurate way to determine the intensity of an EPR line is to
integrate the first derivative spectrum twice. This can be a very tedious
procedure however, without the proper computer software. If the
linewidths of two components are equal, then peak-to-peak amplitudes of
the derivative lines will be proportional to their intensities. However, if
the linewidths are different, a modification is needed to obtain the

approximate relative intensities from this expression173 (Eq. IV-l)

1 °C Ymax (Apr)2 (IV‘I)

1 represents the intensity of the line, 2Ymax is the peak to peak derivative

amplitude and Apr is the peak to peak width, thus the peak to peak

derivative amplitude is inversely proportional to the linewidth squared for
a given intensity. For more precise determinations of the EPR line
intensities, a double integration of the first derivative EPR signal was
performed using the program Spectra Calc. A plot of Intensity vs. 1/1‘
revealed a nearly Straight line but the intercept at UT = 00, is negative.
Thus the compound has behavior similar to the Curie Law (Figure 13) in
the temperature range of 91K - 221K but not the expected intercept. If the
Curie Law were exactly followed, the concentration of unpaired spins

would be constant within this temperature range. The EPR results suggest

42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE 2
EPR Results for One of Three Samples of
Cs+(18C6)(15C5)e'

Rel Intensity T(K) 1/1‘ (K) A/B
185428 91 1.10E-02 1.51
140624 101 9.90E-03 1.49
118461 121 8.26E-03 1.57
100755 131 7.63E-03 1.69
83656 141 7.09E-03 1.75
68019 151 6.62E-03 1.82
51834 161 6.21E-03 1.74
38441 171 5.85E-03 1.50
25793 181 5.52E-03 1.32
23432 191 5.24E-03 1.12
17634 201 4.98E-03 1.01
15105 211 4.74E-03 1.09
10002 221 4.52E-03 1.15
10244 231 4.33E-03 1.01
16197 241 4.15E-03 0.90
18026 222 4.50E-03 1.08

 

 

 

 

 

Intensity
(arbitrary units)

43

 

 

200000 '-
: a
150000 "
. a
‘ a
100000 ‘ El
' a
‘ a
50000 ‘ a
1 a
l a“
- a
0 V I I U ‘l I U I U U I I U I Y I
0.004 0.006 0.008 0.010 0.012
l/T (l/K)

Figure 13: Relative Intensity vs. Reciprocal

Temperature (UK) for
Cs+(18C6)(15C5)e'

44

a decrease in the number of spins as the temperature is increased.
Interestingly, however, when the temperature was raised to 241 K, the
relative intensity increased, in contrast to the previous recordings. In
addition, when the temperature was lowered back to 221 K, the relative
intensity of the EPR line had greatly increased relative to the intensity of
the line recorded at the same temperature, only moments before (refer to
Table 2). This observation was noted with two of the three samples, (it
was not attempted with the third). This effect could be due to thermally
induced electron-pair dissociation above 221K, with slow recombination.
It could also result from thermally induced decomposition. It should be
noted that similar strange time effects were seen in the susceptibility
studies.

The magnetic susceptibility results show that this compound has a
very small fraction of unpaired spins. When l/x vs. T (K) is plotted, the
results do not exhibit a straight line over the same temperature range that
the EPR results were obtained. Thus these results do not obey the Curie
Law. However, at very low temperatures, magnetic susceptibility obeys
the Curie Law. The susceptibility also depended on sample preparation but
the results in any case did not point towards the Curie Law in the higher
temperature range. Thus both susceptibility and EPR indicate deviation
from a constant number of spins. It should be noted that spin susceptibility
is measured in EPR whereas bulk susceptibility is measured in magnetic
susceptibility experiments, so it is possible that the EPR results do not
convey the major contributions to the susceptibility. These other
contributions could have been broadened out, or perhaps they arise from a

triplet state which was not observed in the EPR spectrum.

4 5
The analysis of the N MR results did not follow Curie's Law either.

A plot of the chemical shift versus T, over the temperature range
comparable to that of the EPR measurements, yielded a relatively straight
line with a positive slope. This indicated that as the temperature is raised,
the number of spins increases, which once again does not agree with the
EPR results, except those at the higheSt temperature.

The A/B ratios (Table 2) from the EPR spectra were measured for
these electrides and the results are plotted vs. inverse temperature (Figure
14). This plot did not show a monotonic pattern in the A/B ratios with
respect to the temperature. The increase in this ratio with increase in
temperature could be due to an increase in the microwave conductivity.
The abrupt decrease at 160K - 190K could be indicative of a phase
transition or "softening" mode that also affects the spin susceptibility. The
lineshapes that were observed in these spectra, were not purely Gaussian or
purely Lorentzian, or even a combination of the two lineshapes. It appears
that the lineshapes have some Dysonian character. The Dysonian
lineshapelg, which is a characteristic EPR lineshape in metals, depends on
several parameters. These parameters are: T9, the time it takes for an
electron to diffuse through the skin depth (5), TT, the time it takes for an
electron to traverse the sample, T1, the electron spin lattice relaxation time,
and T2, the electron spin-spin relaxation time. The Dysonian line has a
characteristic about it in that the lower portion of the line and the upper
portion of the line are not symmetric, in fact, the upper portion amplitude
(low field) is at least 2.6 times that of the lower portion for a metallic
sheet. This is referred to as the A/B ratio. However, Webb extended this
theory for use with spherical particles in the region of the normal skin

effect19. Webb concluded that metallic particles whose radii, r, are large

A/B

[Cs+(18C6)(15C5)e-]

46

2.0:
1.8“
1.6;
1.4-

1.2-

 

 

1.0J4I I I u v I l I 1 v I fi It 1 I
0.004 0.006 0.008 0.010 0.012

l/T (K)

Figure 14: Asymmetry of Lineshape with
Respect to Inverse Temperature (l/K)

4 7
compared to 5, will still have a nearly symmetric EPR signal where A/B z
1, if TD>> T1. Therefore, even though the sample may be metallic, if the
sample particle size is small compared to the skin depth, or the relaxation
time is very short, the EPR signal will be nearly symmetric.

The fact that this electride was found to have a conductivity band gap
of only 0.06 eV, suggests that it is posSibly a low band gap semi-conductor,
or a metal. Due to the small band gap, there may be an accessible triplet
State; however there is no direct evidence for this.

The mixed sandwich electride has now been characterized by a
variety of methods and a summary and comparison can now be made to
two other similar electrides, namely, Cs+(18C6)2e', and Cs+(15C5)2e‘.
This is most easily understood by means of a summary table (Table 3).

In addition, both the Cs+(18C6)2e‘ and the Cs+(15C5)2e', were found
to be the first cases of ionic conductors, rather than electronic conductors,
whereas the band gap of the mixed sandwich, Cs+(l8C6)(15C5)e-, was very
small, indicative of a small-gap semi-conductor, or possibly even a metal
with grain boundary resistance. The NMR chemical shift of the mixed
sandwich was intermediate between the two other sandwich compounds
discussed here. Magnetic susceptibility results at low temperatures (below
60K) showed Curie Law behavior for earlier samples of Cs+(18C6)2e- and
for quenched samples of Cs+(18C6)(15C5)e', but the results for
Cs+(15C5)2e- were dependent on whether or not the system was quenched
or annealed. Recently, the earlier results on CS+(18C6)2e' have been called
into question and appear to have resulted from the inclusion of small
amounts of CS' or solvent. This phenomenon is still under study. The
results from the EPR measurements showed that the two "parent"

compounds followed Curie's Law. In other words, there was no change in

48

 

 

 

 

 

TABLE 3
COMPARISONS OF Cs+(l8C6)2e', Cs+(15C5)ze', and
Cs+(18C6)(15C5)e'
Sample Magnetic EPR NMR I Apparent Crystal
Susceptibility band gap Symmetry
1 congtivity
Cs+(18C6)2c' C-W Follows Below >1.0 eV monoclinic
paramagnet Curie's Law 250K 5 is
“’1"! “0 Spin linear’with
pamng* 1/1‘
Cs+(15C5)2c' C-W down C—W Below at least 1.0 triclinic
to 2K after paramagnet 240K 5 is eV
quenching. . ’ .
After anneal, 111??” With
antiferromag
behavior
Cs+(18C6)(15 Follows Follows Susceptibility 0.06 eV monoclinic
C - Curie's Law Curie's Law increases
below 60K. except at with
Above 60K, higher increasing T.
the temperatures
susceptibility
increases.

 

 

 

 

 

 

*Recently, M. Wagner has shown that an antiferromagnetic transition occurs at = 50K for

carefully crystallized samples.

 

49

the number of active paramagnetic centers within the temperature range
studied. These results correspond well with the susceptibility studies of
Cs+(18C6)2e' and Cs+(15C5)2e’ (if the sample was quenched), however, the
results are not so clear-cut with the mixed sandwich. This has already been
attributed to the fact that some of the contributions to the susceptibility may
be EPR silent. This is apparently not the case with the other electrides in
this study. '

Finally, the biggest difference among these three compounds is the
powder conductivity results. The apparent band gaps of Cs+(15C5)2e' and
Cs+(18C6)2e- are at least 1.0 eV, which is drastically different from that of
Cs+(18C6)(15C5)e- which has a very small band gap of 0.06 eV. Overall,
this mixed sandwich electride is primarily spin-paired and the defect

electrons may obey the Curie Law at low temperatures, but with deviations

markedly at higher temperatures.

Li +( C21 1) e-

The EPR measurement methods were the same as described above.
Previous studies have indicated that below 200K, spin pairing occurred and
above this temperature, Curie-Weiss behavior was obeyed. The EPR
spectrum obtained in this study, was a narrow line with a linewidth of 0.48
G at 91K and 0.35 G at 219K (Figure 15). The intensities of the spectra
were found to very scattered over the temperature range from 91K to
219K as shown in Figure 16. At 219K, the EPR spectrum was recorded
twice and yielded different results. The first spectrum was measured as a
continuation of the previously increasing set of temperatures, where the
temperature initially was brought down to 91K quickly. After the

measurement at 219K, the temperature was increased again up to 239K

50

-u
-—_

 

 

 

 

 

lI

1G

 

Figure 15: CW—EPR spectra of Li+(C211)e‘ at
temperatures of 90K (top spectrum) and

220K (bottom spectrum).

Relative Intensity

(arbitrary units)

51

d
1
q

 

 

0 WVVII'T'Ui'Iivt'j'V“'I'1"""l

0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.011 0.012

l/T(K)

Figure 16: Intensity vs. l/T (UK) from EPR

Results of Li+(C211)e'

52

(this high of a temperature often results in decomposition of electrides).
The intensity increased at this temperature and as the temperature was
lowered back down to 219K, the intensity was not the same as previously
recorded. Once again, (this same effect was observed in the
Cs+(18C6)(15C5)e' sample) the intensity was larger, so perhaps partial
decomposition had occurred at around this temperature.

The crystal structure data revealed a large cavity with an estimated
diameter of 4.3A15b. These cavities form open channels along the y-axis
of the crystal with a distance between cavities of about SA. Smaller
channels are exhibited along the z-axis. It is possible that these electrons
are more strongly coupled than those in Cs+(15C5)2e°, which shows
electron localization and Curie-Weiss behavior above 4.5K, but weaker
than those in K+(C222)e- which shows complete electron pairing. The
optical absorption spectra and magnetic susceptibility data, are in
agreement with this proposed behavior. The EPR results described here
indicate the serious problems with stability and will have to be repeated.
Experience has shown that Li+(C211)e' is the most thermally unstable
compound we have ever handled. It appears that another sample-loading

technique will be required to avoid decomposition.

CHAPTER 5

IN THE FUTURE...

IAv EPR i f meHMHY i

Although electron trapping at anionic sites is assumed in alkalides
and electrides, the only direct experimental evidence supporting this
assertion for electrons trapped in alkalides has come from the cw-EPR and
ENDOR experiments, mentioned in Chapter One, for the alkalide series:
Cs+(HMHCY)Na', Rb+(HMHCY)Na', and K+(HMHCY)Na'. Further
characterization of the electron-trapping sites of these three alkalides is
proposed. The specific aims of this research are to better define the site at
which electrons are trapped in these materials, to gain a detailed
understanding of how the unpaired electron spin density is delocalized over
their molecular framework and how this delocalization depends on alkalide
structure. These studies will be addressed by using the ESEEM
techniquezoaab to measure weak, superhyperfine couplings between the
paramagnetic center and nearby magnetically-coupled nuclei that are
unresolved in the cw-EPR experiment due to inhomogeneous broadening of
the resonance lineshape. This research will focus on the complete
characterization of the magnetic couplings between the various group 1A
metals and magnetic nuclei in the complexant molecules that are coupled to
trapped electrons in these materials. The HMHCY sodides have been

chosen for this study because of their enhanced thermal stability as
5 3

54

compared to that of other alkalides and electrides and because of their
extensive characterization by x-ray crystallography, cw-EPR6 and ENDOR
techniquesZMab. Furthermore, cw-EPR studies done on the series,
Cs+(HMHCY)Na‘, Rb+(HMHCY)Na', K+(HMHCY)Na', show that the
couplings between the paramagnetic center and the closest alkali metal
cation in these materials is dependent on the alkalide structure.

ESEEM studies will be performed at different microwave
frequencies from 6-18 GHz. The superhyperfine interactions will also be
measured, between the trapped electrons and the magnetic nuclei of the
surrounding complexant molecules focusing initially on the 14N couplings.
These initial studies will be followed by experiments on HMHCY sodides
where the complexant is labeled with 13C and /or 2H. Together, the results
of these experiments should provide the most accurate information

regarding the "structure" of the electron trapping site obtained to date.

ESEEM

Different local fields surrounded by unpaired electrons in a sample
give rise to inhomogeneous broadening. A cause of this type of broadening
is from dipolar interactions between spins with different Larrnor
frequencies, or from magnetic anisotropy. A spin packet is a group of
spins that see the same local field in the sample and can be visualized in
Figure 17.

Each spin packet has a Lorentzian lineshape but the overall envelope
has a gaussian lineshape. Figure 17 represents the inhomogeneously
broadened line. A homogeneous system would consist of only one spin
packet of Lorentzian lineshape and this type of broadening can be caused

from spin lattice relaxation, dipole-dipole interactions between like spins,

55

and spin interactions with the microwave field. Inhomogeneously
broadened lines can mask the hyperfine structure in an EPR spectrum, so
this type of broadening often results in a loss of resolution in the spectrum,

and to unresolved hyperfine structure.

 

 

 

 

 

 

 

 

\\\\‘\\\\\\\\\\\\\\\\\\\\\\\\\\“u .

 

 

i 11L

(”0

.9

Figure 17: Individual spin packets which are
homogeneously broadened, enveloped by
an inhomogeneously broadened line.

Inhomogeneous broadening can be reversed by performing a Spin-
echo experiment. As was noted in the discussion on cw-EPR, electrons can
assume either a parallel or anti-parallel configuration when in an external
magnetic field. A Boltzmann distribution describes the populations of the
[3 state (lower in energy) and the or state. The resulting magnetization, M2,
is established in the direction parallel to the magnetic field, Ho. The

magnetization changes upon application of a pulse, and this is best

56

described by a vector diagram, using a coordinate system which rotates

with a frequency (omw (Figure 18).

   

Figure 18:Evolution of the magnetization
during a single 1t/2 pulse

The result of applying a 1t/2 pulse, the duration of which is dependent on
the strength of the microwave magnetic field, is a rotation of the
magnetization through a flip angle, [3, in the plane perpendicular to the x-
axis, where B = YeH1tp where Ye is the gyromagnetic ratio (or
magnetogyric ratio), H1 is the field intensity of the microwave pulse and tp
is the duration time of the pulse. In this case, the flip angle, [3, is 1t/2, but
this is only the simplest case. Virtually any sequence can be used. The
single 1t/2 pulse transforms the original longitudinal magnetization, Mz,
into a transverse y-magnetization. It is worth noting that the flip angle is
most commonly specified with respect to the on-resonance magnetization.
This means that the 1t/2 pulse tums Mz into the y-direction exactly 90°. If
there were off-resonance components as well, there would be x-

components and z-components following the n/2 pulse. These components

5 7
are said to be unimportant for basic pulsed EPR spectroscopy. Therefore,
if we assume that the resonance condition, (omw = ycHo, is true, after the
1t/2 pulse, all of the magnetization remains in the y-direction. A precession
will occur about the z-axis if the Larmor frequency (yeHo) does not equal
the microwave frequency. The precessional frequency, 0, will be equal to
m-comw. Since the detector is aligned in the direction of the y-axis, the
difference frequency is directly measured.

In an ESEEM experiment, a 1t/2 pulse yields a magnetization in the
y-direction. Immediately after this pulse, the transverse magnetization
vectors, or spin packets, begin to precess with their frequencies (21 The
signal that is observed in the time domain, is a sinusoidal oscillating signal
known as a free induction decay, or simply an FID, so the precession
results in an FID which decays rapidly. After a certain amount of time, the
FID will disappear completely and there is no detectable signal. A time T,
is taken before the second microwave pulse turns the spin packets 180°
about the x-axis. At this point, the directions of precession of the
individual spin packets will remain the same, so at an additional time T, the
spin packets refocus in the -y direction. The resulting -y magnetization
will build up and decay again within a short time and is referred to as the
spin echo. This is also called the backfolded FID (Figure 19). This two-
pulse scheme has an echo amplitude associated with it which is a function of
the pulse interval, 1:. The decay of the spin echo amplitude is modulated by
anisotropy in the hyperfine coupling and is characterized by TM, the phase
memory time or the time it takes for the echo amplitude to decay to l/e of
its initial value.

EPR spectra are often poorly resolved. Consequently, the spin echo

shows little structure. As a result, the echo amplitude is used as the main

5 8
source of information in ESEEM experiments. The static field strength,
Ho, and the time interval between each microwave pulse are variables upon
which the amplitude depends. Modulation effects on the amplitudes of the

echoes will now be treated.

‘7‘.
Vfli’

 

 

Figure 19: 2-pulse echo sequence and
evolution of the magnetization.

Nuclear Modulation Effect

As just described, the couplings between the nuclear spin and the
electron spin can cause a modulation of the echo intensity. .It is useful to
revert back to a cw-EPR experiment with I = 1/2 and S = 1/2, via
anisotropic hyperfine interactions. If. the hyperfine interactions were only
isotropic, only the usual EPR transitions would be allowed (Figure 20).

The nature of the anisotropic interactions of the nuclear spin states are

 

59

 

 

 

 

 

 

 

 

Ms M:
llz 1’2
112 -1l2
----- semi-forbidden transitions

allowed transitions

 

-1(2 -1I2
-1l2 1l2

Figure 20: Allowed and semi-forbidden
transitions in EPR spectrum.

60

mixed, and therefore the transitions 1,3 and 2,4 are only "semi-forbidden".
Echo modulation is best understood by using a vector diagram (Figure 21).
Pay close attention to the pairs of transitions that originate from the same
energy level (e.g. (01,3 and (01,4). Assume that the resonant frequency of
the allowed transition, (01.4 is equivalent to that of the microwave
frequency (i.e. 031,4 = (me ). Upon application of short microwave pulses
(a large frequency spread), all transitions are excited simultaneously. The
microwaves can induce transitions at one level but end at a different level.
This is called branching of transitions, and is essential for the nuclear
modulation effect.

During the first evolution period following the 1t/2 pulse, the
orientation of vector 1 remains unaffected, (Figure 21a) whereas vector 2
precesses with a frequency 032 = (01,4 - (013. After the time interval, 13, the
1: pulse turns vector 1 into the —y direction as well as giving rise to a new
component 2' due to nuclear state mixing and branching of the transitions,
(Figure 21b). The same behavior is observed for vector 2, resulting in a
new vector 1'. During the second evolution period, vectors 1 and 1'
remain unaltered, while vectors 2 and 2' precess with the frequency (1)2
(Figure 21c). As a result of this effect, vectors 1' and 2' are no longer
oriented along the -y direction thus the intensity of the echo is reduced.

The orientation of the vector depends on I, therefore, the maximum
contribution is obtained only if during the refocussing process in time “c,
precesses an integral number of times, where 21m = ((01 - (02):. The decay
time in the 2-pulse experiment is determined by TM (or T2) which is often
short, thus the echo and the modulations will decay quickly, resulting in

broad lines in the frequency domain.

61

 

 

 

 

 

 

 

 

Figure 21: Echo diagram describing echo nuclear
modulation a) after 1t/2 pulse, b) after
1t pulse and evolution c) at the time of the echo.

62

I EPR ie f Ph oex i e Tri 1e e f K+(Q;2_2)_e;a_n_d_
3+(Q2221K‘

For over one hundred years, it has been known that many organic
compounds could be photoexcited to exhibit a strong phosphorescence or
afterglow. However, it was not until the year 1958 that these photoexcited
molecules were observed via EPR methods”. The electrons in an S = 1
state (triplet) interact with one another to produce markedly different
spectra from typical doublet spectra. Here I propose to photoexcite the
compounds K+(C222)e' and K+(C222)K- into their triplet states, and study
their EPR properties.

Many properties of alkalides and electrides have been studied, but
there has never been direct evidence of the triplet state. Optical spectra of
thin films of K+(C222)e‘, showed dramatically different spectra than
typical electrides23. A continually rising absorbance in the near IR region
was observed, which is similar to the spectra of metallic solutions of alkali
metals in liquid ammonia23. These results showed that either shallow traps
existed, or electron delocalization. Direct current powder conductivity
measurements showed an activation energy of about 0.02 eV23 over a
temperature range of 103K - 153K. This result suggested that the
compound is not metallic, but instead, that weakly bound electrons exist.

The magnetic susceptibility results showed that this compound
consisted mainly of paired electrons as the temperature approached 0 K.
As the temperature was increased, the susceptibility increased, suggesting
that there was electron pair dissociation, which was thermally induced, or
that a triplet state was being populated. This observation will be
contemplated by EPR studies.

63

 

 

 

 

5G

 

 

Figure 22: CW-EPR spectrum of K+(C222)K- at 130K

64

Preliminary EPR results show that the K+(C222)K' compound has
axial symmetry (Figure 22). Thus far, attempts have been made to
photoexcite these samples with an 800 W projection lamp as well as a UV
lamp, but no spectrum indicative of a triplet state has been observed. Both
of these compounds have singlet ground states, but it is predicted that they
have low lying triplet states, thus different light sources will be used to

attempt to observe the triplet state via EPR.

III hesi nd Characterization f New Alkalides an Ele tride

With such diversities of the properties of the class of compounds
discussed thus far, we are anxious to prepare new electrides and alkalides.
One of the goals, is to prepare compounds in which the complexant has
attached to it, an aromatic molecule, such as benzene or naphthalene
(Figure 23). It is of interest to know where the electron will reside in a
situation where there is an excess of electrons. Will the electron delocalize
into the aromatic molecule or will it remain outside of the complexant
completely? Recently, attempts were made to reduce the dibenzo-18C6
(DBC) complexant with both K metal and Na metal. The synthesis was
virtually the same as previously described. Solution EPR studies revealed
no signal at all, probably due to the fact that benzene is difficult to reduce.
In fact, Na is not a strong enough reducing agent to reduce benzene, even
in the presence of a complexant. Naphthalene is however much easier to
reduce, and we recently acquired some of the dinaphtho-18C6 complexant.
This compound will probably serve as a much better model for these types
of studies. We plan to focus on the synthesis and study of alkalides and

electrides that are expected to exhibit new types of behavior.

65

(\0/07
3061
Dibenzo- 1 8-Crown-6
(\0/07
L2/0\0)
Dinaphtho- 1 8-Crown-6

Figure 23 : Two aromatic complexants
used to produce potential
electrides and alkalides.

REFERENCES

a. Dye, J. L.,DeBacker, M. G.,Annu. Rev. Phys. Chem. 1987, 38,
271. ‘

b. DeBacker, M. G., Sauvage, F. X., Dye, J. L.,Chem. Phys Lett.,
1990, 73, 291.

c. Dye, J.L., Science, 1990, 247, 663.

d. Tehan, F. J., Barnett, B. L., Dye, J. L., J. Am. Chem. Soc. 1974,
96, 7203.

Kraus, C. A., . Am. Chem. Soc. 1974, 96, 7203; Thompson, J. C.,
Electrons in Liquid Ammonia (Oxford Univ. Press, Oxford, 1976).
Pederson, C. J., J. Am. Chem. Soc. 1967, 89, 2495, J. Am. Chem.
Soc. 1967, 89, 7017, J. Am. Chem. Soc. 1970, 92, 386.

Lehn, J-M., Sauvage, J. P., Dietrich, B., Tett. Letters, 1969, 1969,
2885; Tett. Letters, 1969, 1969, 2889; Lehn, J-M., Acc. Chem. Res.
1978, I 1, 49; Lehn, J-M, Angew. Chem. Int. Ed. Engl. 1988, 27,
89.

Kittel, C., Introduction to Solid State Physics, John Wiley and Sons,
New York, 1986.

Shin, D-H, Ellaboudy, A. S., Dye, J. L., DeBacker, M. G., J. Phys.
Chem. 1991, 95, 7085.

Ward, D. L., Huang, R. 11., Kuchenmeister, M. E., Dye, J. L., Acta.
Cryst. 1990, C46, 1831.

Dawes, S. B., Eglin, J. L., Moeggenborg, K. J., Kim, J., Dye, J. L., J.

Am. Chem. Soc. 1991, 113, 1605.
66

10.
11.

12.

13.

14.

15

16.

17.

18.
19.
20.

67

Moeggenborg, K. J ., Papaioannou, J ., Dye, J. L., Chem. OfMat.
1991, 3, 514.

Dawes, S. B., Ph.D. Dissertation, Michigan State University, 198 6.
Ward, D. L., Huang, R. H., Dawes, S. B., Dye, J. L., J. Am. Chem.
Soc. 1986, 108, 3534.

Issa, D., Ellaboudy, A. S., Janakiraman, R., Dye, J. L., J. Phys,
Chem.

Dawes, S. B., Ellaboudy, A. S., Dye, J. L., J. Am. Chem. Soc. 1987,
109, 3508. f

Shin, D-H., Ph.D. Dissertation, Michigan State University, 1896.
a.Landers, J. S., Dye, J. L., Stacy, A., Sienko, M. J ., J. Phys. Chem.
1981, 85, 1096. b. Huang, R. H., Faber, M. K., Ward, D. L., Dye,
J. L., unpublished results from this laboratory.

Cauliez, R, Jackson, J. E., Dye, J. L., Tett. Letters, 1991, 32, 38,
5039.

For a general treatment of EPR theory, see: a. Wertz, J. B., Bolton,
J. R., Electron Spin Resonance Elementary Theory and Practical
Applications, McGraw-Hill, New York, 1972. b. Davis, J. C.,
Advanced Physical Chemistry, The Ronald Press Co., New York,
1965.

Dyson, F. J ., Phys. Rev., 1955, 98, 2, 349.

Webb, R. H., Phys. Rev., 1967, 158, 2, 225.

For a general treatment of pulsed EPR methods, see: a. Schweiger,
A., Angew. Chem. Int. Ed. Engl., 1991, 30, 265. b. Keijers, C. P.,
Reijerse, E. J ., Schmidt, J., Pulsed EPR: A New Field of
Applications. New York, 1989.

21.

22.
23.

6 8
a. Ellaboudy, A. S., Bender, C. J ., Kim, J ., Shin, D-H,.,
Kuchenmeister, M. E., Babcock, G. T., Dye, J. L., J. Am. Chem. Soc.
1991, 113, 2347. b. Kuchenmeister, M. B., Dye, J. L., J. Am.
Chem. Soc. 1989, 111, 935.
Hutchinson, C. A., Mangum, B. W., J. Chem. Phys., 1961, 34, 908.
Huang, R. H., Faber, M. K., Moeggenborg, K. J., Ward, D. L., Dye,
J. L., Nature, 1988, 331, 599.

Anmdix
Quantization of Angular Momenmm

Imagine a particle with mass, m, and a linear momentum described by Eq.

1, with a velocity, v.
p = mv (1)

If it is assumed that the particle is a quantum mechanical particle, it will

have De Broglie wavelength associated with it, as described by Eq. 2,
k = M) (2)

The probability of finding a particle at any point in a line, box, ring, etc. is
the square of the amplitude of this wave, 1». For the probability to be
independent of time, the wave function must maintain a single value.
Therefore, there should be no interferences of the wave with itself while
traveling around the line, ring, etc. A ring for example, is required to
have a circumference which is an integral number of De Broglie
wavelengths, M, thus rearranging Eq. 2, and subsequent substitutions
results in Eqs. 3-5,

2m = M1 (3)

2m = Mh/p (4)

69

7 0

pr = Mil/21: = M11 = Po (5)
The magnitude of angular momentum of the particle is pq,, and should be
an integral multiple of TI where M will also be an integer 0,1,2,....M = 0
represents an electron in an orbital with no nodes, such as a 0' orbital, and
M = 1 is the case of an electron in a 1: orbital. This basic model can be
directly applied to the angular momentum of an electron. It is also
important to note that the particle in the box, ring etc. represents

quantization of angular momentum.

Relating Angular Momenmm with Magnetic Moment

Consider the same particle with with mass m, velocity v, charge q, in a
circle with radius r. Associated with the current i, is a magnetic field.

Associated with that magnetic field is a point dipole with a magnetic

moment , Hz-
112 = iA (6)

where A is the area of a circle, m2 and i = qv/c27tr. Substituting the
values for A and i, Eq. 7,

112 = qvan/c27tr =qu/2c (7)
but recall that p = mv from Eq. 1. Substitute this into Eq. 7,

Hz = qmvr/2mc (8)

7 1
Now substitute p¢ for mvr to obtain Eq. 9,

uz=qp¢12mc (9)
Now let 7 = q/2mc and substitute this into Eq. 9,
“z = Wm (10)

and finally, use Eq. 5 to substitute for p4,,

112 = W11 (11)
To convert angular momentum to the magnetic moment, use Eq. 12,

q = -e/2mc (12)
but in general,

7 = -ge/2mc (13)

where g is a factor that must be included for all cases, except a system with
purely orbital angular momentum. For every multiple of orbital angular
momentum, there is an orbital magnetic moment of eh/41tmc. In the case
of an electron, this whole expression is simplified as B or the Bohr
magneton (B = 9.2741 x 10'21 erg/G). For electron spin, the value of g is

2.00232 (for a free electron, g6). So uz can now be written with respect to

the magnetic field, H, as (Eq. 14)

7 2
112 = YMsTI (14)

where Ms is the spin quantum number. Re-writing this expression while

substituting Bg/Ti for 7 yields Eq. 15,
Hz = gBMS (15)

Quantization of spin angular momentum leads to quantization of energy

levels. From before, E = -qu and substituting Eq. 15 for 112,

Many transitions can be drawn in an energy level diagram and comparison

with the observed spectrum shows that not all transitions occur. Thus there
is a notion of "allowed" and "forbidden" transitions. "Allowed" transitions
require a knowledge of the EPR selection rules. When the energy of a

quantum (monochromatic incident radiation) matches the energy level

separation, absorption occurs. The selection rule, AMS = :1 leads to

possible values of Ms i 1/2. This leads to values of energy (Eq. 17),
E = i 1/2gBH (17)

and these energies are referred to as the Zeeman energies.

MICHIan STATE UNIV. LIBRARIES
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