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THESIS

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This is to certify that the

dissertation entitled

Advanced Electron Paramagnetic
Resonance Studies of Some Sodides
and an Electride.

presented by

Kerry Ann Reidy-Cedergren

has been accepted towards fulfillment
of the requirements for

 

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MSU is an Affirmative Action/Equal Opportunity Institution 0-12771

 

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University

 

 

 

PLACE IN RETURN BOX to remove this checkout from your record.

TO AVOID FINES return on or before date due.

 

 

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MSU Is An Affirmative Action/Equal Opportunity Institution

ewm pins-9.1

ADVANCED EPR STUDIES OF SOME SODIDES AND AN ELECTRIDE
By
Kerry Ann Reidy-Cedergren

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

, DOCTOR OF PHILOSOPHY

Department of Chemistry

1996

 

ABSTRACT

ADVANCED ELECTRON PARAMAGNETIC RESONANCE STUDIES OF
SOME SODIDES AND AN ELECTRIDE

By
Kerry Ann Reidy-Cedergren

Electrides are a class of compounds in which an alkali metal cation
is encapsulated by a complexant, usually a crown ether or a cryptand, and
the unpaired electron occupies the anionic site in a well defined structural
arrangement. The nature of the sites in which these electrons are located
is important to their physical and magnetic properties. Electron
paramagnetic resonance (EPR) is a good tool for studying these trapping
sites. However, since the electrons are so close together, rapid electron
exchange often occurs to yield a single exchange narrowed EPR signal. A
closely related compound to electrides, alkalides, differs in that an alkali
metal now acts as the anion. Trapped electrons are much more isolated
than the electrons in electrides, thus they are present in small
concentrations which avoids the problems of exchange—narrowing of the
EPR Spectrum. Often there are weak, superhyperfine couplings between the
Paramagnetic center and the nearby magnetically-coupled nuclei that are

unresolved in the CW-EPR spectrum due to inhomogeneous broadening of

 

the resonance lineshape, which can mask the hyperfine structure in th
EPR spectrum. Spin-echo experiments can reverse this observation.
Cavity-trapped electrons in the electride Li+(cryptand [2.1.1]e' ca
interact through rather open channels that connect the cavities to forr
essentially 1D linear chain Heisenberg antiferromagnets (LCHAs). I
each case, the EPR spectrum of powdered samples consists of a narrow, (
2 G. p.p.) slightly anisotropic absorption whose integrated intensity vs.
mirrors the static susceptibility. Very strong rf responses in an ENDO
cavity during near-saturation microwave irradiation, at magnetic fiel
offsets on either side of the EPR line, match the EPRlineshape. Th
frequency at a given position on the rf response curve is equal to th
frequency equivalent of the field offset from the corresponding position 0
the EPR curve. The linear power dependence of the intensity shows that th
rf absorption is a one-photon process. This rf-microwave doubl
resonance demonstrates the presence of a high density of energy level
around the Zeeman level, consistent with the presence of 1D, spin 1/

antiferromagnetic spin-waves, with average lengths of about 50 spins.

ACKNOWLEDGMENTS

This can often be the most difficult part of the thesis writing f0]
of leaving someone out! I will try to include everyone. First I would 1i
thank my two advisors, Professors John McCracken and Jim
Working for such different people has been a very stimulating experii
I cannot think of two better mentors for one to have during grad
school. I thank you both for your patience with me over the years an
teaching me how to be an independent thinker. I will miss the stories
Professor McCracken has provided over the years!! There is no substi
I would also like to thank my other committee members, Professors (
Blanchard and Mike Rathke.

I would not have been able to function without the excellent sei
provided by the glass shop. Manfred, Scott and Keki were always wi
to give my job high priority if I needed it badly enough and I thank t
for that. In addition, Russ, Dick and Sam offered excellence in
machine shop that is second to none. Of course, Ron, Scott and Tom i
always there for me when I blew a major fuse and shut down the vac
lines. MSU is very fortunate to have such talented service shops.

No thesis could ever be completed without the help from secrete

There have been four in particular who have helped over the years, Li

Vada, Beth and Lisa and they deserve tremendous thanks ane
appreciation.

Graduate school presents the opportunity to meet new people and
have been very fortunate to meet many friends over the years who at:
more than just friends. In particular, Dr. Michelle Mac has offered 1
friendship that is unsurpassed by any other friendship that I have had.
cannot thank her enough for going through all of the hoops with me, fron
qualifiers to the final defense. She always could make me laugh, ever
when I had already heard the joke before! I know that good friends neve:
fade and distance will not keep us from staying in touch.

There are many other friends who have provided an occasiona
diversion from work. I thank them all (Sara, Jeff, Beth, Paul, Deena, Chris
Tom, Jerry, Per...) and I will miss them all.

I want to thank the group members that I have worked with over the
years. In particular, Rui, Song, Erik, Andrew and Mike, and also the
Hong-In meister (for countless scientific discussions), Professor Kur‘
Warncke, the boys (GyOrgy and Vlad) and all of the new McCracker
students.

My family, Mom, Dad, Michael, Trish, little Garrett, Pam, Keegar
Krysta, Matty (poll's), Sean, Mom, Karen, Tom, Linnea, Mark, Kyle anc
Keith: You have all at some time during my career, been very supportive

and I thank you for that!!

My daughter, Alexandria, has been the light of my life and inspires
me every day. Now that I have her, I can't imagine life without her.
Finally, I wish to thank my husband Rob. You are my hero, always
saving me when I am in a bind, always there for emotional support, and
always there to make me laugh. I cannot imagine how empty my life

would be'without you and I thank you dearly.

 

 

(Z0 R06 and my little Alexandria Emily

LIST OF TABLES

LIST OF FIGURES

CHAPTER 1.

CHAPTER 2.

CHAPTER 3.

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Page
xi
xii
A historical perspective of alkalides and electrides. .......... 1
Introduction 2
Alkali metal solutions 3
Electrides 5
Thermodynamic considerations 8
Complexing agents: Crown ethers ................................. 9
Complexing agents: Cryptands 11
The first electride crystal structure: Cs+(18C6)2e‘ .......... 13
Localized and delocalized electrons ................................ 15
Trapped electrons 22
The first alkalide 25
Important theoretical considerations ............................. 27
An overall message... 32
Bibliography 36
Synthesis of Cesium Hexamethyl Hexacyclen
Sodide: Cs+(HMHCY)Na-. 41
Introduction 42
Preparation of Cs+(HMHCY)Na' 44
Bibliography 53
Theoretical Treatment of Electron Magnetic
Resonance Spectroscopy 54

 

viii

CHAPTER 4.

CHAPTER 5.

Spectroscopy

 

 

Magnetic interactions
The spin operator

 

The spin Hamiltonian

 

 

The EPR experiment
Application of the Hamiltonian

 

Relaxation ' .......
Electron spin echo envelope modulation ......................

 

Nuclear modulation effect

.. I

 

The density matrix formalism

 

EPR instrumentation

 

The Michigan State University ESEEMometer ...............

Bibliography

.. 92

 

Interesting Magnetic Behavior of the Electride:

Li+(C211)e'. Evidence for 1-Dimensional Spin Waves.

Introduction

 

 

Previous Studies
Synthetic considerations

 

Structral facts

 

Properties of newly synthesized Li+(C211)e‘ ................

Brief magnetism primer

 

 

The spin-Peierls transition
Susceptibility data

 

EPR

 

Pulsed- EPR measurements

 

Anamolous rf-effect

 

ENDOR-lnduced EPR (EIE)

 

Analysis of magnetic data

 

Discussion

 

Conclusions

 

Bibliography .........

 

ESEEM Studies of Electron Trapping in

Csz+(21C7)Na2': Mapping the Electron Density. ........

Background information

 

ix

112
113
1 16
121
127
135
136
145

146
149

154
155

CHAPTER 6.

 

Synthesis of Csz+(21C7)Na2'
Structural information

 

Physical properties of Csz+(21C7)2Na2' ..............
Summary of the physical properties ....................

 

Pulsed and CW-EPR experiments
Discussion

 

 

Bibliography

Multifrequency ESEEM Studies of Potassium

Hexamethyl Hexacyclen Sodide. .........................

 

 

 

 

 

 

Background information 15.
Structural information 16
Thermal stability 19
EPR studies 15
ESEEM studies 19
Conclusions 19
Bibliography ..... 20

 

 

Table 1.1:

Table 1.2:

Table 1.3:

Table 5.1:

 

LIST OF TABLES
Alkali metal radii. Page 11.
Hole diameters of some crown ethers. ................... Page 12.

Current structural data of alkalides and electrides. Page 35.

Comparison between the time domain and the frequency
domain. Page 175'.

xi

LIST OF FIGURES

Figure 1.1: Typical complexants used in the synthesis of alkalides and
electrides. ............................................................... Page 14.

Figure 1.2: Ball and stick model of Cs+(18C6)2e'. ..................... Page 16.

 

Figure 1.3: Optical absorption spectra of solvent free electride films.
................................................................................ Page 18.

Figure 1.4: cw-EPR' spectra of K+(C222)e' before and after irradiation.
................................................................................ Page 20.

Figure 1.5: Picture of an F-Center where the electron density occupies

the anionic vacancy. .............................................. Page 24.
Figure 1.6: Drawing of an interstitial ion. ................................ Page 24.

Figure 2.1: Pyrex® K-cell used in the synthesis of alkalides and some
electrides. ................................................................ Page 45.

Figure 2.2: Quartz apparatus for loading alkalide and electride samples
into EPR tubes. ....................................................... Page 51.

Figure 3.1: Classical picture of the energy of a dipole in a magnetic
field ......................................................... Page 57.

_______.—_4

 

Figure 3.2:

Figure 3.3:

Figure 3.4:

Figure 3.5:

Figure 3.6

Figure 3.7:

Figure 3.8:

Figure 3.9:

Figure 3.10:

Figure 3.11:

Figure 3.12:

Figure 3.13:

The interacting dipoles, [.1e and tin in a magnetic field.
Page 63.

 

Radial dependence of 15, 2;? and 3d wavefunctions of the
hydrogen orbital. Page 65.

 

The effect of the H1 field on the laboratory magnetic field.

 

 

Page 66.
Axial g-tensor. Page 68.
Electron spin levels in a magnetic field. .................. Page 70.

Energy level diagram for an S=1/ 2, 1:1 / 2 system. .. Page 74.
Inhomogeneously broadened line. .......................... Page 76.

Illustration of the rotating frame. .......................... Page 76.

Diagram showing the time evolution of the echo decay

envelope. Page 78.

 

Precessional frequencies of the individual spin packets.
Page 79.

 

Vector scheme for the two-pulse ESEEM experiment.
............ Page 80.

 

d three pulse

ESEEM pulse schemes for the two an
Page 82.

 

experiments. ......

xiii

Figure 3.14

Figure 3.15a:

Figure 3.15b:

Figure 3.16:

Figure 3.17:

Figure 4.1:

Figure 4.2:
Figure 4.3:
I:igure 4.4:

Figure 4.5:

Figure 4.6:

 

Nuclear modulation effect for the two-pulse ESEEM scl"
Page

 

Coupling of two electrons with an I=1/2 nuc
Page

 

Transition matrix elements connecting the four 51
Page

 

Transformation rotation. Pag

 

Basic diagram of the microwave bridge components.
. Page

 

Optical spectra of Li+(C211)e‘ from liquid amm
solutions of various ratios. Pag

 

Space filling model of one molecule of Li+(C211)e'. Page

Packing diagram of Li+(C211) complexed cations. Page

Channel and cavity diagram of Li+(C211)e'. ......... Page

Magnetic flux lines. Page

 

Susceptibility as a function of the temperature

antiferromagnetic, paramagnetic and ferromagi

 

material. Page

Figure 4.7:

Figures 4.8:

Figure 4.9:

Figure 4.10:

Figure 4.11:

Figure 4.12:

Figure 4.13:

Figure 4.14:

 

Magnetic susceptibility of A) crushed crystals an

"powder" of Li+(C211)e' as a function of the tempera

 

Page

EPR spectra of Li+(C211)e' at various temperatures.

 

Page

EPR spectra of Li+(C211)e' at various temperatures.

Page

 

EPR spectra of Li+(C211)e‘ at various temperatures.

Page

 

Relative intensity for the EPR resonance as a function 0
temperature for A) crushed crystals and B) "pow

samples. Page

 

ESE-detected EPR spectrum of Li+(C211)e' collected at 9-

GHz; repeition rate 60 Hz; temperature 4.20 K; t=180 ns.

 

Page
Time domain trace of Li+(C211)e' (1 =170 ns). ....... Page
Time domain trace of Li+(C211)e' (I =263 ns) ........ Page

mug . __.. V“. .-_.

Figure 4.15:

Figure 4.16:

Figure 4.17:

Figure 4.18:

Figure 4.19:

Figure 4.20:

Figure 4.21:

Figure 4.22:

FigUre 4.23:

Figure 4.24:

 

Energy level diagram describing the effect of nu

 

hyperfine interactions. Page

Relaxation pathways in a typical ENDOR experiment.

Page

 

Microwave saturation study. ............................... Page

CW-EPR spectrum collected at 25 K. 'ENDOR' spectra coll!

at 3360.0 G and 3358.0 G. Page

 

CW—EPR spectrum collected at 25 K. 'ENDOR' spectra colli

at 3364.0 G and 3367.0 G. Page

 

Plot of the peak position of the 'ENDOR' effect as a fun

of the dc static field offset, converted to MHZ. ....... Page

Start frequency as a function of the separation betwee:

peaks of the ENDOR induced EPR. ............................ Page

ENDOR induced EPR spectra of Li+(C211)e'. ............ Page

Illustration showing the possible spin interactions in the

zag chains of Li+(C211)e‘. Page

 

Antiferromagnetic spin waves on a line of spins. .. Page

xvi

 

Figure 4.25:

Figure 5.1:
Figure 5.2:

Figure 5.3:

Figure 5.4:

Figure 5.5:

Figure 5.6:

Possible energy level diagram describing the anami

 

rf—effect. Page
Ortep diagram of Cs+2(21C7)2Na'2. .................... Page
One View of four unit cells of Cs+2(21C7)2Na'2. .. Page

Alternate View of the packing of Cs+2(21C7)21\

 

Page

A) Optical spectrum of the solvent evaporated fil:
Cs+2(21C7)2Na'2 in MeNT-Iz. B) 23Na static NMR spec
of Cs+2(21C7)2Na‘2 powder. ............................... Page

A) 133Cs static NMR spectrum recorded at 200K. 1
MAS-NMR spectrum recorded at 200K at B) 5 kHz spir
speed and C) 10 kHz spinning speed. .................... Page

A) CW—EPR spectrum collected at 2.08 11W microwave p(
9.4716 GHz microwave frequency, 5.2 Gpp modul;
amplitude, 100 kHz modulation amplitude, 5x105 gain
3.8 K. B) ESE-EPR spectrum collected at 4.2 K, 250 ns t, E
repitition rate, 45.0 dBm microwave power, 10.011

microwave frequency. Page

 

A) 2-pulse ESEEM trace collected at 9.282 GHz micrO‘
frequency, 3324.0 G field strength, 180 ns t, 10 Hz repel

xvii

Figure 5.8:

Figure 6.1:

Figure 6.2:

Figure 6.3:

Figure 6.4:

rate and 4 scans collected. B) fourier transform spectrum of

trace A. Page 171.

 

A) 3-pulse ESEEM trace collected at 9.282 GHz microwave
frequency, 3324.0 G field strength, 180 ns t, 10 Hz repetition
rate and 16 scans collected. B) fourier transform spectrum

of trace A. Page 172.

 

Attempts to "cap" the alkali metal cation complexed by

HMHCY with 12C4, have thus far failed. ............. Page 185.
Structural information for two HMHCY sodide. ..Page 187.
Diagram of K+(HMHCY)Na'. ............................... Page 188.

Perspectives of Cs+(HMHCY)Na' ......................... Page 189.

Figure 6.5: A) 3-pulse ESEEM trace of K+(HMHCY)Na' at 3300 G, where

“t = 288 ns., T242 ns., tinc = 10 ns., repetition rate = 40 Hz. B)

Fourier transform spectrum of A. ......................... Page 193.

Figure 6.6: A) 3-pulse ESEEM trace of K+(HMHCY)Na’ at 3300 G, where

‘C = 324 ns., T=46 ns., time = 10 ns., repetition rate = 40 Hz. B)

Fourier transform spectrum of A. .......................... Page 196.

xviii

‘ ““M/

 

Figure 6.7: A) 3-pulse ESEEM trace of K+(HMHCY)Na' at 4250 G, where
I = 288 ns., T=42 ns., tinc = 10 ns., repetition rate = 40 Hz. B)

Fourier transform spectrum of A. ......................... Page 198.

xix

CHAPTER 1

A HISTORICAL PERSPECTIVE
OF ALKALIDES AND ELECTRIDES

INTRODUCTION

Ionic salts can be defined by two important characteristics: the
packing, which is composed of well defined charged species, and the size
difference of the anions and cations. The -ide ending of sodium chloride,
Which packs in a face-centered cubic lattice, implies that chlorine must be
negatively charged. Chlorine has an electron affinity of —348 kJ/mol"
thereby exhibiting a strong attraction for an electron. It, as well as the
other halogens, most commonly retain the minus one oxidation state since
the extra electron will fill the outer p-orbital giving the more stable inert
gas electron configuration. Since sodium and the other alkali metals are
800d electron donors, they most commonly possess the plus one oxidation
State- These metals will eagerly give up an electron to an acceptor atom or
moIeCule, to form a stable salt. They are so reactive in their metallic state
that this form does not even exist in nature. Alkali metals may be the most

el . . . . .
eCtITDIDOSItive fam11y, but they too can form salts that contaln alkali metal

 

FCOHV

en -

an 1 tlon states that the larger the negative value of electron affinity, the more attraction it will have for
9 EC tI‘Q

3
anions. In fact, alkali metal anions in the gas phase have been known to

exist for almost fifty years (Patterson et al., 1974). Therefore, if the gegenion
were sufficiently resistant to reduction, one might believe that an ionic salt
of an alkali metal anion could be stable. The electron affinity of sodium is
-52.9 kJ/mol indicating that there is still somewhat of an attraction for an
extra electron. After all, adding an electron to an alkali metal fills the outer
s-orbital but in a less strongly favored configuration than the sodium
cation configuration, so it was deemed highly unlikely. In 1974 it was
found that alkali metals, under very specific conditions, could form stable
ionic salts where the alkali metal maintains both a plus one oxidation
state as well as the peculiar minus one oxidation state in a well defined
structural arrangement (Tehan et al., 1974). This class of compounds was
coined alkalides and the structures and properties of these compounds
have been extensively studied for over twenty years (for useful review
articles, see (Dye, 1977, Dye, 1979, Dye, 1987, Dye, 1993, Dye & Ellaboudy,

1984, Wagner & Dye, 1993) and they continue today.
Alkali metal solutions

In 1864 it was reported that alkali metals could dissolve in liquid
ammoma to generate a beautiful blue color, (Weyl, 1864) . Sir Humphrey

D
av), 1"lad made a similar observation in 1808 (Edwards & Sienko, 1982)

as
was drafted in his laboratory notebook. However, the blue color and

4
fine optical spectrum were not assigned to solvated electrons until Kraus

studied the nature of dilute metals in liquid ammonia and established
tlflat these solutions were ionic in nature (Kraus 8: Lucasse, 1921, Kraus 8:
Lucasse, 1922). He also studied extensively the metallic behavior of these
concentrated solutions, and coined the term ”solvated electron” (Kraus,
1907). Kraus did much of the pioneering work in the field of alkali metal
solutions and found in 1907 that lithium was soluble in both
methylamine (MeNHZ) and ethylamine (EtNHz), and that potassium was
soluble in ethylenediarnine, but that the other alkali metals were relatively
insoluble in most higher primary amines (Kraus, 1907). Since that
discovery, there have been widespread studies of solvated electrons in
liquid ammonia solutions by electron magnetic resonance as well as
Optical spectroscopy and many other physical measurements and
theoretical treatments (Thompson, 1976). Such work has revealed many
aspects of the reactivity of solvated electrons in addition to the physical
characterizations. To understand solvated electron structure, it is useful to
consider that solvated electrons are formed kinetically by a two stage
process (Kevan, 1981). First, localization occurs which depends on the
relative energies of the conduction electron level of the medium as well as
the energy of the localized electron state in the medium. Once localization
is accomplished, solvation occurs. In this case, the electron induces

rearrangements in the surrounding shell of solvent molecules which

 

" ""0: mmw‘mm . _ ”A Q‘W

5
creates a geometry between them. As a result, the geometry of the solvated

electron depends on more than just the medium molecules.

The possible reaction in dilute liquid ammonia solutions

M ‘— “ M+ + 2650” (1.1)

where M' is an alkali metal anion, M” is an alkali metal cation and e'solv is
a solvated electron, is shifted far enough to the right that M' has never
been detected in this solvent. Additional complications arise as the
solution becomes more concentrated due to the appearance of metallic
behavior, ion-pair formation and electron spin-pairing. Thus, there is no
direct evidence that alkali metal anions exist in liquid ammonia solvent,

and in fact, their existence has recently been brought into serious doubt by

Studies of concentrated mixed Li-Na solutions (DeBacker et al., 1994).
Electrides

The electron itself is the simplest anion; therefore, if all of the alkali
metal anions were replaced by trapped electrons, the salt would no longer
be an alkalide, but an electride. Electrides are a class of compounds in
Which an alkali metal cation is encapsulated by a crown ether "sandwich"

or a cryptand and stoichiometric amounts of electrons are released to be
trapped in vacancies. Thus, the electron occupies the anionic vacancy and

serves as the anion. The nomenclature does not apply to systems with

‘ “gm “a: 'exyfiiil‘l‘“ '1 r‘ c 4

Wm

r; are: Wm .
V m “In“

6
well defined molecular orbitals that localize the charge to a single

molecular center. Therefore, typical organic anion radicals would not be
defined as electrides since optical and electron paramagnetic resonance
(EPR) measurements have shown that the unpaired electron occupies
specific orbitals on the molecule. If the density of the trapping sites in
electrides is low enough, strong overlap of the wavefunctions of
neighboring electrons to form a metal can be prevented and localization of
electrons to form electrides can occur. Localization of electrons has an
intportant impact on the characteristics of the electride. A measure of this
has been described. Mott (Mott, 1956) stated that at the non-metal to metal

transition,

aH (rial/3 = 0.25 (1.2)

Where nc is the critical electron concentration, and aH is an effective
hydrogen-like radius for the localized electron. Electrides are highly
paramagnetic species with an average electron concentration on the order
Of 1021 cm'3- The packing of the large cations leaves holes which are
Similar in size to the effective radius of the trapped electrons. These
dimensions yield an effective hydrogen-like radius for the localized state
to be about 2.5 A so that the left-hand side of Equation 1.2 is nearly 0.25.
Even a slight change in electron concentration or in the effective radius of

the electron could lead to some delocalization Of the electrons and

7
possibly to a metallic state in the electride. In such a case, the material is

not a true electride but an "expanded metal".
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 that maintain a well defined geometry.
Because of the light mass of the electrons, they are considerably more
mobile than other anions in salts and thus are fairly free to travel
throughout the solution; this ability contributes to their unique properties.
These traits of solvated electrons have been studied by a number of
different research groups in a time period of more than eighty years. To
prepare stable solutions that contain solvated electrons or alkali metal
anions, solvent choice is of utmost importance. The solvent needs to be
reSistant to reduction and to be a strong solvator of the cation but need not
SOlvate the electron or the alkali metal anion strongly. Alkali metals only
dissolve in a few solvents other than ammonia, such as hexamethyl
Phosphoramide (HMPA), a few primary amines, and a few polyethers.
SOrne more considerations regarding solvent choice during the
Preparation of alkalides and electrides will be discussed throughout this

dissertation.

Them

IE'JC

new”.
I

:‘i'
f"
I)

 

:11}

 

.-u. __ Haw‘hQW-n v-W«W.wn m.

Thermodynamic Considerations

Thermodynamically, metals with a low ionization energy and
small lattice energy can dissolve in amines and other previously
mentioned solvents. The equilibria that describe the solubility of alkali

metals in the proper solvents are shown in Eqs. 1.3 8: 1.4,

M(S) M +solv + e-solv (13)

l l

Mes) + M's) M” + M-solv (1-4)

solv

where M and M’ can be the same or different alkali metals. This reaction
is shifted far to the right when an organic complexant is added to the

mixture (Eq. 1.5), where C denotes the polyether complexant.

 

M: + c ‘— M+c (1.5)

Because of the importance of the solvation energy of the cation, the
metal anion and the solvated electron, the presence of the complexant can
Cil‘ive reactions 1.3 and 1.4 to the right. Solvated electrons are the best
reducing agents with the alkali metal anions nearly as powerful. If they
Were not so unstable and if the conditions did not have to be so stringent,
these solutions would be much more common. Empirical results have

Shown that the equilibrium of reaction 1.1 in NHM) lies far to the right

9
while this reaction in other solvents is not as favorable and as a result, the

solution contains both alkali metal anions and solvated electrons.
Complexing agents: Crown Ethers

By making use of the discovery of crown ethersiby Pedersen
(Pedersen, 1967a, Pedersen, 1967b, Pedersen, 1988) and of cryptands by
Lehn (Lehn et al., 1970), the Dye group showed that the solubility of the
alkali metals could be greatly increased (Dye, 1991). In fact, when
potassium metal is allowed to interact with MezO, the colorless solution
shows that the potassium does not dissolve and produce solvated

electrons. This indicates that the equilibrium concentration is less than
10'5 M at saturation (Dye, 1991). However, when 15C5 is added to the
mixture, the solubility is increased by over four orders of magnitude to
03M at 240 K, (Dye, 1991). It follows then that an important aspect of
synthesizing alkalides or electrides is the complexing ability of the species
that encapsulates the cation. The particular complexant must be resistant
to reduction as well as to decomposition and decomplexation. Pedersen
Showed that the macrocyclic polyethers could form stable complexes with
alkali metal cations and that the stability of these complexes was of
enormous importance. He showed that the stability depends on the
geometrical disposition and the number of ether oxygen atoms in the

macrocycle (Pedersen, 1970). Moreover, the size and the shape of the

 

10
coordinating polyhedra relative to the cation size was shown to be of

importance. These results indicate that the stability of the alkali metal
crown-complexed cation does not necessarily follow the conventional
trend that the weak coordinating ability in alkali metal chemistry is due to
the relatively large size and low charge density of the alkali. metal cations
(Greenwood 8: Earnshaw, 1984). Conventional logic predicts that the
strength of the coordinated complexes should decrease in the order
Li>Na>K>Rb>Cs. However, the maximum stability of alkali metals with
crown ethers is often N a+ and sometimes K’“ or Rb+ but not necessarily Li+.
Pedersen found that the formation of complexes can be prevented by steric

hindrance from the polyether ring (Pedersen, 1967a, Pedersen, 1967b)

Complex formation is shown by Eq. 1.6.

 

 

(M+)solvent + C CM+ + solvent (1.6)

Therefore, complex formation of an alkali metal cation will be minimized
01‘ even'prevented if the cation is too strongly solvated. Typically, the
SOlvation energy of alkali metal cations varies as the reciprocal of the ionic
radius (Pedersen, 1967a). Table 1.1 shows the atomic and cationic radii of
the alkali metals. In addition, Pedersen estimated, from two different
mOdels, the hole diameter of some common crown ethers. These data are
catalogued in Table 1.2. Since the complexants play an integral part in

solvating alkali metals, the list of only a few solvents available for the

 

f

11
formation of metal solutions, vital for alkalide/electride synthesis, is

increased by several more.

Table 1.1
Alkali Metal Radii

 

”ass—r;—

Cryptands

Another group of complexants, collectively called cryptands (Lehn
8t al., 1970), was also found to contain effective ligands. Coordination of
alkali metal cations to the macrobicyclic cryptands occurs by a process in
Which the ligand encapsulates the cation, sometimes with a bicapped
t1'igonal prismatic polyhedron. These complexes are finding increased
Use in the stabilization of uncommon oxidation states and they promote
What were formerly considered to be improbable reactions. The first
S0dide was made by the reaction of Na metal with the cryptand [2.2.2],
“(3222), where the numbers indicate the number of ethyl ether oxygens in

each of the linkages to the two tertiary nitrogen atoms in the cryptand].

12
The reaction was carried out in ethylamine (EtNH2)_ followed by

evacuation to high vacuum, to yield the Na+(C222)Na' salt (Tehan et al.,
1974). The crystal structure revealed that the Na' was located 5.55 A away
from the nearest nitrogen atom in the crypt and 5.16 A away from the
nearest oxygen atom. This observation indicated that Na' is indeed a

separate entity in the structure.

Table 1.2
Hole Diameters of Some Crown Ethers

Crown Ether Hole Diameter
14-crown-4 1.2-1.5
15-crown-5 1.7-2.2

18-crown-6 2.6-3.2
21-crown-7 3.4-4.3

 

To summarize, the thermodynamics of the reaction is driven by the
COmplexant which encapsulates the alkali metal cation. The addition of
CrOwn ethers or cryptands markedly increases the solubility of the alkali
metals by shifting the equilibrium given by Eq. 1.4 to the right because of
the strong complexation of the cation according to Eq. 1.5. The result is to
greatly enhance the concentration of M- in the saturated solution. When
there is an excess of alkali metal present, the equilibrium positions of

reactions 1.3, 1.4 and 1.5 determines the relative concentrations of M- and

 

13

(3150“,). When there are stoichiometric amounts of alkali metal and
complexant, the equilibria given by Eqs. 1.3 and 1.5 determine the relative

concentrations of M' and e-. It should be noted, however that the reaction,

—.—‘

M+C + 2e'501V — M'solv + C ' (1.7)

can yield a mixture of e'soiv and M'solv even when the stoichiometry is that
of the electride. Reaction 1.7 is particularly important when M is Na.

The overall requirements for the complexing agents used in alkalide
and electride synthesis are that they are strong enough complexants so
that they will bind the cation better than the strongly polar solvent used in
SYDthesis. In addition, these cyclic and bicyclic complexants should be
kinetically resistant to reduction since their role is to encapsulate the alkali
II‘letal cation so that the electron released by Eq. 1.3 will either go into
SOlution or attach to an alkali metal to form the metal anion in solution.
I:igure 1.1 represents three complexant classes that are commonly used in

alkalide and electride syntheses.
First Electride Crystal Structure: Cs+(18C6)2e'

After proper work-up procedures and depending on the
StQichiometry and the solvent, the unpaired electron will either occupy the

Void spaces in the solid structure to yield an electride, or it may, form the

kaa—E “ ‘

14
H C
H3C\ 3 >
MCI—13 H 3"‘Ci‘v MN
H3C\

Hexamethyl hexacyclen
(HMHCY)

/oo\
.0. <: 0::
$§§> VAR;

Cryptand [2.1.1] 21-Crown-7 ether
C211) (21C7)

Figure 1.1: Typical complexants used
in the synthesis of alkalides and electrides.

15
alkali metal anion in solution and/ or in the solid. In this specific case,

when 18-crown-6 (18C6) is allowed to react with cesium metal in

stoichiometric amounts in a suitable solvent under anaerobic conditions,

two complexant molecules encapsulate the alkali metal cation to form a

sandwich complex with twelve oxygens coordinated to Cs+. This
electride belongs to the monoclinic crystal system (Dawes at £11., 1986) and
tl‘lere are four molecules per unit cell. The Cs+-e' distances range from 7.71
to 9.40 A. 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 Cs+-O distances range from 3.29 to 4.04 A.
The unpaired electron density is presumably centered at the void site
f()I'Ined by close-packing of eight complexed Cs cations. The ball and stick
model (Figure 1.2) shows the structure of the complexed cation in this
electride, Cs+(18C6)2e-. This particular compound, called a sandwich
electride since the alkali metal is completely encapsulated by two 18C6

I7|-'1C)lecules, is important in the EPR studies discussed at length later.

Localized and Delocalized Electrons

As a class, the behavior of the electrons in electrides can represent
extremes, in which the trapped electrons may be localized or delocalized
as evidenced by optical and conductivity studies. The optical spectrum of

InOst electrides reveals a distinct peak in the near IR region, characteristic

..-—'—'—-v-‘ u-

16

 

® Hydrogen . Carbon

. Oxygen . Cesium

Figure 1.2: Ball and stick model of Cs+(18C6)2e'. This

sandwich molecule is comprised of two 18C6 molecules,
one cesium cation and one isolated electron as the anion
(not shown).

17
of electron localization and similar to that of trapped and solvated

electrons (Thompson, 1976). However, solvent-free films formed by
evaporation of liquid ammonia from a 1:1 mixture 'of potassium metal
and cryptand [2.2.2], showed a remarkably different spectrum (Figure 1.3),
(DaGue et al., 1979). A continually rising absorption throughout the
Visible and into the near IR (a so-called "plasma edge") was observed,
which is indicative of near-metallic behavior. This type of spectrum had
been observed by both reflectance (Kuo, 1994) and transmission when
alkali metals alone were dissolved in liquid ammonia at high enough
Concentrations to be metallic. These data suggested that either the
electrons in K’(C222)e— were delocalized or that very shallow traps were
present. Furthermore, optical spectra were collected with thin films that
had different ratios of complexant to metal. By adjusting this ratio, the
Optical data revealed varying amounts of trapped electrons. To confirm
these findings, another experiment was done with K and C222 without the
uSe of a solvent. Thin films of alkali metals and complexant were co-
Cieposited on a sapphire substrate at -40° C , under high vacuum (10'8 torr)
(Hendrickson, 1994). The same ”plasma edge” was observed in the
Optical spectrum. In addition, the conductivity of the electride films
it‘lCIicated that defect electrons or holes might be responsible for the highly
Q0I‘iclucting nature of this compound. Initial microwave power absorption

Sliudies of powdered K+(C222)e' prepared from NH3U), suggested that

18

Alum)
2.0 [.3 IO 0.7 06 03 0.0
[O '7. T I r I I

 

 

 

'—
\
\
\
\
\
1 \
‘\
\
\
. \
\
2 ‘~
\ ‘
‘ \s
\
\
\
\
\
\“
‘o
‘s
‘\
00 l l

 

1
5 lo :5 20 25
itan“)'0°3

Figure 1.3:. Optical aborption spectra of solvent free electride films.
The SOllCl line represents Cs+(18C6)2e‘_ and the dashed line represents
I<+(C222)e-.

 

19
K+(C222)e' is metallic (DaGue et al., 1979). This high microwave

conductivity was confirmed by measuring the power absorbed by the
crystalline samples (Moeggenborg et al., 1991). Most electrides show little
or no difference from an empty quartz tube, but K+(C222)e' behaved as
finely divided metal powders. This highly microwave conducting effect
was also evidenced when high field EPR experiments in the far infrared
region (250 GHz) were attempted". The highly conductive nature of these
samples did not permit a high enough transmission to obtain a signal.
Measurements made with a superconducting quantum interference
device (SQUID) magnetometer, showed a decrease in the susceptibility as
the temperature approached zero K, suggesting that there was either
thermally induced electron pair dissociation or the population of a triplet
State (Huang et al., 1988). If the triplet state were populated, the energy
1eVel difference could be probed by using EPR techniques. EPR studies of
photoexcited or thermally excited K+(C222)e- and K+(C222)K- were
attempted but the results did not indicate any changes in triplet sub-level
populations, if they exist, as no changes in the EPR spectra were observed
after photoexcitation (Figure 1.4)+. In addition, there was no evidence of
the Ams=i 2 transition or half-field line, which is often present in the EPR
SF'ectra of triplets. After some DC powder conductivity experiments

\
1133 ublished results from a collaboration with the Fred lab at Cornell University, Reidy-Cedergren et al.,

1U I'qiublished results in this lab, Reidy-Cedergren et 111., 1992.

.. ~—‘..‘.__

Relative lntensi (a.u.)

Relative Intensity (an)

20

I l l l I I l I I I I l l I I I I I I I I I I I I 1 l l I I l I I l I l

600 — _.
400 — E _

200 — _

 

 

 

 

 

TYTT'IIIIIIIIIIIIIIIIIIIIIIIIIIIITII

3371 3372 3373 3374 3375 3376 3377
Magnetic Field Strength (G)

J I I I I I I I l I I I I I I I I I I I l l l I I l l I I I I I l I I I

600 — _

.00.“ '_

.4

200 — _

 

 

 

 

 

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIWII

3371 3372 3373 3374 3375 3376 3377
Magnetic Field Strength (G)

 

 

Figure 1.4: (A.) cw-EPR spectrum of K+(C222)e' collected at

100 K, 0.04 G/ pp modulation amplitude, 6.3e3 gain, 200 ms. time
constant, 200 s. sweep time, 100 kHz modulation frequency,
9.4562 GHz microwave frequency. (B.) same as (A.) after
photoexcitation with an 800 W projection lamp. The relative
intensities of the two spectra are within experimental error

of each other and no significant lineshape changes exist
indicating no excitation into a triplet sublevel

 

 

21
showed activated conductivity (Moeggenborg et al., 1991), it appeared that

this electride was not, in fact, metallic but instead contained bound
electrons with a very small band gap. The possibility that the barriers to
electron movement were small, was considered.

The most recent optical and conductivity measurements made on
films that were prepared with full stoichiometric and temperature control,
suggested that partial decomposition of the films actually leads to an
ihcrease in conductivity. The conductivity either remains constant or
increases until about one half of the material is decomposed at which
point the electride rapidly becomes insulating (Hendrickson, 1994). These
recent and surprising results coupled with those obtained previously,
Suggest that the conductivity is due to missing electrons or holes.
According to this view, the pure electride is actually an insulator but even
SIr‘tall quantities of defect holes can cause high conductivities. This
lengthy chain of events illustrates the complexity that can be encountered
With both alkalides and electrides.

The chemical and physical properties of alkalides and electrides are
dependent on the nature of the trapping sites. The magnetic behavior can
be probed by using magnetic resonance techniques. Isolated trapped

electrons are paramagnetic, so EPR can be used to probe the charge
CliStribution around the trapping sites. However, little information is

gained just from EPR experiments with pure electrides. Because the

22
electron sites are so close together, rapid electron exchange can occur on

the EPR time scale, resulting in an exchange narrowed line. Therefore,
usually a single featureless line is observed. This is the case for most
electrides; however, the electride Li+(C211)e' exhibits lineshape changes

with temperature that will be discussed at length in a later chapter.
Trapped Electrons

To avoid the dilemma of featureless EPR lineshapes, one turns to the
"cousin" of electrides, alkalides. Magnetic susceptibility and EPR studies
have shown that paramagnetic species almost always are present in these
polycrystalline materials. The reason for this is the presence of defect
trapped electrons in anionic vacancies in the alkalide crystals. Since
alkalides are crystallized from solutions that contain alkali metal anions
but also usually solvated electrons, electron trapping still occurs.
Depending on the metal, solvent and the synthesis method, the
concentration of defect electrons varies from sample to sample. Pure
alkalides are intrinsically diamagnetic since they contain an alkali metal
cation with an nsO electron configuration (M+) and an alkali metal anion
with an ns2 electron configuration (M-). These materials, if pure would be
EPR silent, but since there are trapped defect electrons at the anionic
vacancies, an EPR resonance can nearly always be observed. In these

crystallites, the electrons are much more separated than in pure electrides

 

23
so the problem of exchanged narrowed EPR lines is avoided. What is the

nature of these trapping sites? These defect electrons occupy holes,
(anionic sites) and such electron-occupied holes are called F-centers
(Figure 1.5). The electrons in F-centers can generally be thermally excited
to a conduction band, thus giving rise to an n-type semi-conductor.
Another type of defect electron that could be present in these systems is an
interstitial or Fraenkel defect (Figure 1.6). Initial studies indicated that
both photoelectron emission and thermionic emission from alkalides and
electrides resulted from the presence of weakly bound electrons. It was
thought that the ground state of electrides or of electrons in F-centers in
alkalides might lie very close to the vacuum level (Huang & Dye, 1990).
However, more recent studies have shown that the most likely candidates
for thermionic emission are defect electrons in shallow traps with energies
near the vacuum level, produced by photo—excitation or other processes
(Kuo,-1994).

One of the major aims of this research is to describe the nature of
these trapping sites. Because of the wide range of behavior of the magnetic
properties of electrides and alkalides, as well as their optical and
electronic properties, these compounds can provide a probe to determine
the nature of interactions of weakly bound electrons with each other and
with surrounding ions and molecules. While the use of EPR methods can

provide some insight into the nature of electron trapping sites, double

 

Figure 1.5: Picture of an F-center where the
electron density occupies the anionic vacancy.

Figure 1.6: An Interstitial Ion (Fraenkel defect)
is a distortion ina point because there is an
atom in a position where it does not belong.

25
resonance techniques such as electron spin echo envelope modulation

(ESEEM), and electron nuclear double resonance (ENDOR) can take on the
challenge of mapping the unpaired electron density at various nuclei and
the nature of the inter-electron coupling. These topics will be addressed in

depth in a subsequent chapter.
The First Alkalide

The most extensively studied alkalide to date is Na+(C222)Na_
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, temperature, and to certain reducing agents, Na+(C222)Na- is
stable under vacuum for several days at room temperature and
indefinitely at low temperature. However, as with all alkalides and
electrides, it is thermodynamically unstable towards decomposition.
Crystalline alkalides and electrides are subject to an irreversible
decomposition process that results from cleavage of the C-0 ether bond
(Cauliez et al., 1991) as the temperature is raised. The decomposition
usually accelerates at around 0°C although this is dependent upon the
system. Na+(C222)Na- crystals have a very brilliant gold-copper color
resembling a metal. Surprisingly, it is not a metal but an intrinsic semi-
conductor with an apparent band gap of 2.4 eV. EPR studies (DeBacker et

al., 1990) as well as magnetic susceptibility studies (Jaenicke & Dye, 1984)

 

26
show that the pure Na+(C222)Na_ material is only weakly paramagnetic,

whether in the form of a powder, thin film or rnicrocrystal. The effect of
light was studied by recording the EPR spectrum while the sample was
illuminated in the cavity (DeBacker et al., 1990). Illumination of the
sample was provided by a 150 W 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 measured to
be 2.005 which is close to that of trapped electrons in solids of this’type
and no other paramagnetic species were observed. The lifetime at room
temperature of the paramagnetic species was long, with a half-life of
about 30 seconds. The formation 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-. Optical data have accumulated over
the years and while the system is becoming better understood, a
quantitative description is not yet complete. The optical data show a
typical absorption at 670 nm indicating Nai In addition, the presence of a
shoulder on the high energy side of the Na- peak could be attributed to
excitation of an electron from the ground 352 state of Na' to the broad

conduction band (Hendrickson, 1994, Hendrickson et al., 1996). Upon

 

27
photolysis with high intensity laser pulses, two additional bands are

observed. One possible explanation for these features is that Na- transfers
energy to two unknown bands, one at a low energy and one at a high
energy. It is believed that Na atoms or a sodium film are responsible for
the higher energy peak and trapped electrons give rise to the low energy
peak. If sodium atoms were responsible, it seems likely that the Na atoms
would recombine with the electron to form Na-. Also, if Na atoms are
present, they would have to be immobilized. EPR measurements of
irradiated samples show no evidence for Na atoms. Another possibility is
that a uniform film of Na metal could be forming but this also should
result in the formation of Na+(C222)Na' since this is how it is produced to
begin with! Only if a conformational change occurred upon irradiation
would the recombination be slow. Finally, it is possible that an exotic new
species is being formed that consists of an electron pair trapped for every
Na“ trapped. Current experiments are in progress to help understand the

behavior upon photolysis.
Important Theoretical Considerations

Over the years, because of the unconventional nature of these
compounds, there has been considerable scrutiny of the alkalides and
particularly the electrides from a theoretical point of View. The current

hypotheses stem from the experimental findings; however, theoretical

28
conclusions that agree with these hypotheses have been questioned

(Golden & Tuttle, 1988) but with highly doubtful arguments.

The experimental data suggest that electrides are ionic compounds
with most of the unpaired electron density located outside of the
complexed cation. Various theoretical treatments and models have been
used to describe electrides, particularly Cs+(18C6)2e- and Cs+(15C5)2e-.
Given the knowledge of the crystal structure, and therefore the location of
the atoms, the dimensions of the electron traps can be obtained by
modeling the atoms as van der Waals spheres. Experimental evidence
from nuclear magnetic resonance (NMR) studies revealed that the atomic
character on the Cs atom of the Cs+(18C6)2e- is only 0.033% (Dawes, 1986,
Dawes et al., 1987). This indicates that the 6s electron density originally
centered on the cesium nucleus has a much smaller density at the Cs
nucleus in the electride. These conclusions were based on the magic angle
Spinning (MAS) NMR spectrum, which consists of one peak,
paramagnetically shifted to +81 ppm from that of other Cs+(18C6)2
compounds (Dawes et al., 1987). This effect is more readily explained by
contact with the unpaired electron rather than a tight coordination of Cs+
by the 18C6 molecule. The paramagnetic shift is derived from the Knight
or contact shift that results from strong local magnetic fields, generated
from paramagnetic electron density at the cesium nucleus, and is given

by,

29
KCT) = (87t/3NA)< I “1(0) l 2>XCT) (1-10)

where NA is Avagadro's number, < | w(0) | 2> is the average electron
density at the nucleus, and x(T) is the molar magnetic susceptibility.
From Eq. 1.10 and the measured temperature dependence of the chemical
shift and susceptibility, the contact electron density for Cs+(18C6)2e' was
calculated to be 8.75x1021 cm'3. The 65 orbital has non-zero electron
density at the nucleus, and is the lowest energy occupied orbital in the

atom. The fractional atomic character, F, can thus be calculated from,

1::<Iw(0)|2>/<Iw(0)12>atom (1.11)

where < l w(0) l 2>atom is the electron density at the nucleus for an isolated
gas atom, which is 2.645x1025 e cm'3 (Edwards & Sienko, 1982). Therefore,
8.75x1021 cm3/2.645x1025 cm'3 = 3.3x10'4 or 0.033%. To put this number
into perspective, the percent atomic character of the gaseous cesium atom
is 100%, that of cesium metal is 59%, cesium dissolved in isopropylamine
is 27% and in cesium-ammonia solutions it is 3-8%, depending on
concentration (Dawes et al., 1987, Edwards & Sienko, 1982). The positive
charge on cesium seems to be very well shielded by its interactions with
the lone pairs of electrons on the crown ether oxygens. The low percent
atomic character has been attributed to the location of the electron density,

presumably in or around the anionic vacancy. In addition, a strong

 

30
coulombic attraction to eight nearest neighbor complexed cesium cations

helps to localize the electron charge (Dawes et al., 1987). The overall
electron density in the electride was determined to be 1.1x10?"1 e-cm’3 at
216K. These results triggered theoretical interest from Golden and Tuttle
(Golden & Tuttle, 1992). They disputed Dawes’ interpretation of the
contact density at the Cs nucleus. After further examination of the 133Cs
NMR results and from their hypothesis of electron distributions, they
claimed that this number is consistent with the assumption that the
maximum electride electron density is simply in the very near proximity
of the Cs nucleus.

Allan and co—workers (Allan et al., 1990) tried to reason the stability
of the unconventional situation given by electrides by using self-consistent
tight binding Hartree-Fock calculations. They found that the complexed
Cs cation is repulsive to the excess electron while the holes in the structure
yield an attractive potential. They also found that the calculated trapped
electron wave function was vanishingly small at the Cs site, which agrees
with the very small percent atomic character determined from NMR
results. These results are directly contradictory to the conclusions of
Golden and Tuttle.

Another group of theoreticians (Renscok et al., 1993) also refuted the

arguments described by Golden and Tuttle. Initially, the question of

 

 

31
charge isolation was addressed by this group. Their calculations sought

to answer the conundrum of why the electron density at the cesium cation
is so small when the electronic wave function, presumably centered in the
trap, should be able to penetrate into the complex and have a higher
density at the cation than is observed. They surmised that since the
oxygen atoms are in van der Waals contact with the Cs+, the crowns are
permanently polarized since the oxygens are negative and the hydrogens
are positive. This charge distribution could possibly form a potential
barrier to an electron between the inside of the complexed cation near the
Cs, and the outside. The calculations led the authors to the conclusion
that most of the unpaired electron density was moved outside of the
complexed Cs cation radius. The model presented by Rencsok represents
only the isolated molecule; nevertheless it supports the conclusion derived
from the experimental evidence that the unpaired electron density in the
cavity is separated from the cation. They also provided convincing
evidence to refute the arguments of Golden and Tuttle [Rencsok 1995
#405]. In addition, high level quantum calculations and interesting
results and pictures were reported by these authors on the unpaired
electron density distribution in the smaller (and fictitious) electride
molecule Li+(9C3)2e' (Rencsok et al., 1993).

Another theoretical treatment that is independent of the others

referenced here, consisted of local density approximation (LDA)

32
calculations (Singh et al., 1993). These ab initio self consistent calculations

were carried out on Cs+(15C5)2e'. The behavior of the self consisten1
potential surprisingly revealed that the electron's potential energy at the
center of the cavity was a maximum and not a minimum, but the total
energy, potential plus kinetic, was a minimum. One usually assumes that
the electron seeks a potential energy minimum; thus, according to this
conclusion, electrides are an exception. Interaction with the core electrons
of the cation and the complexant electrons consistent with the Pauli
exclusion principle, along with the space available at the vacancy
combine to trap the electron in the region of the potential energy
maximum. The total energy is minimized by spreading the electron

density throughout the large cavity thereby reducing its kinetic energy.
An Overall Message...

The majOr take-home lesson is that isolated complexed cation
structure stabilizes the solid, preventing recombination with the trapped
electron. We believe that, to a first approximation, the electride electrons
should be treated as if they are distinct from all other electrons in the
electride, just as is usually done with F-center systems, metals and
solvated-electron systems. The motivation behind the research described
in this thesis stems from this notion and from the desire to acquire

experimental evidence to help clarify various explanations of electride

33
behavior. However, because of the extreme difficulty of viewing the

trapped electrons in the electride directly by X-ray diffraction, we can only
put forth our best efforts to lend support to the idea that the unpaired
electron density does move away from the complexed cation and into the
cavity. '

The compilation presented in this chapter touches on only some of
the issues inspired by alkalide and electride research. Professor Dye has
changed the way that scientists think about chemistry, given the chemical
significance of the research. Not only is there a unique situation to learn
and to characterize a new class of compounds, but there are potentially
important uses for these compounds. For example, alkalides and
electrides are exceptional reducing agents and have been used to prepare
nanoscale particles of metals and alloys (Tsai 8r Dye, 1993). They are also
enticing where very strong reducing agents are necessary, as occurs
occasionally in organic synthesis. What has been learned over the years
from alkalide and electride research has been used to develop new
compounds, similar in nature, for potentially important use. For example,
this lab and others have attempted to produce large organic globular
electron acceptors (LOGEAs). Echegoyen and co-workers (Echegoyen et al.,
1991) introduced the prototype of such compounds called cryptatiums.
The lowest unoccupied molecular orbital (LUMO) of these molecules are at

low energies, so that there is a potential for adding extra electrons to the

34
system. The driving force of research on LOGEAs is the possibility of

producing materials that are superconducting. For the last few years,
many of us in the Dye group as well as other collaborative groups, have
tried to synthesize organic superconductors, by using the techniques
developed in alkalide and electride research, but we have so far obtained
only hints of superconductivity that probably results from other causes.
The Dye research group will continue to face more challenges and to learn
more chemistry.

Finally, it is worthwhile to list the current alkalides and electrides
synthesized in the Dye group, together with their crystal systems (Table

1.3).

 

 

35

Table 1.3
Current Structural Data of Alkalides and Electrides

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compound Crystal ref Compound Crystal ref
System System
Cs+(18C6)2e’ Monoclinic a Rb+(18C6)Rb‘ Monoclinic l
Cs+(15C5);e' Triclinic b Cs+(C222)Cs' Monoclinic i
Li+(C211)I;lla' orthorhombic j K+(HMHCY)Na' Orthorhombic p
Na+(C222)Na' Rhombohedral c Rb+(I-IMHCY)Na' —Orthorhombic r
Na+(C221)Na’ Monoclinic d Cs+(HMI-ICY)Na’ Orthorhombic p
K"’(C222)Na- Orthorhombic e Rb+(18C6)Na‘ Orthorhombic j
MeNH;
K+(12C4)2Na' Monoclinic d K+(18C6)(12C4)Na' Orthorhombic o
Rb+(15C5)-2Na‘ Monoclinic f K+(18C6)(1 2C4)K' Orthorhombic o
Cs+(1 8C6);Na’ Monoclinic f K+( 1 8E168)862)C4)K' Monoclinic O
Cs+(15C5)2Na' Triclinic g Li+2(TMTCY)2 Orthorhombic q
(MeNI-DNa'
CS+(15C5)2K- Monocli HIC h Ll+2(TMTCY) orthorhombic S
(DMTCY)’
MeNHzNa‘
Rb+(15C5)2Rb' Monoclinic h Li+(18C6)Na' Monoclinic q
(MeNH2)2
Cs+(18C6)2Cs’ orthorhombic i mascm Rhombohedral q
(MeNH2)2.(18C6)3
Li+(c211)e- Orthorhombic i K+(1§&'6)Na- Rhorfiaohedrai d
(MeNH2)2.(18C6)3
K+(C222)e' Monoclinic k Rb+(52_22)Rb' Triclinic T
K+(C222)K‘ Triclinic l Cs+(21C7)Na- Triclinic t
Cs+(15CS) Rhombohedral m Cs+(C322)Na- Monoclinic d
(18C6)e-
Li2+(TMP AND Monocl inic d Rb+(12C4)(18C6) Monoclinic o
Na’)2(MeNH2) Na-
Li"(C211)Cs' Monoclinic n K2+(21C7)Na2' Monoclinic t
MeNH;
Rb+(12C4)(18C6) Orthorhombic O
Rb-
References corres nd to the following:
a. (Dawes et al., 986) k. (Huang et al., 1988).
b. (Ward et al., 1990b). 1. (Huang et al., 1989)
c. (Tehan et al., 1974). m. (Wagner et al., 1994)
d. (Huang & Dye, 1996a) . (Huang et al., 1996a)
8. (Ward et al., 1990a). . (Huang, 1994a)
f. (Dawes et al., 1989). . (Kuchenmeister 8: e, 1989)

g. (Huang 8: Dye, 1996a)
(Ward et al., 1990a)
i. (Huang et al., 1987).
j. (Huang et al., 1996b)

. (Huang & Dye, 1996 )
(Huang, 1994a)
(Huang et al., 1990)
(Huang, 1994)

T’WF-O'OO’J

36

BIBLIOGRAPHY

Allan, G., DeBacker, M. G., Lannoo, M., 8: Lefebvre, I. (1990) Europhysics
Letters 11, Why Do the Electrons Play the Role of Anions in the
Electrides?, 49-53.

Cauliez, P. M., Jackson, J. E., 8: Dye, J. L. (1991) Tetrahedron Letters 32, An
Unusual Reduction of Ethylene Occurring during the Thermal
Decomposition of Alkalides and Electrides, 5039—5042.

DaGue, M. G., Landers, J. S., Lewis, H. L., 8: Dye, I. L. (1979) Chemical
Physics Letters 66, Alkali Metal Anions and Trapped Electrons Formed by
Evaporating Metal-Ammonia Solutions which Contain Cryptands, 169-
172.

Dawes, S. 8., Structural and Magnetic Properties of the Electrides of
Cesium Complexed by 15-crown-5 and 18-crown-6., 1986.

Dawes, S. B., Ellaboudy, A. S., 8: Dye, I. L. (1987) Journal of the American
Chemical Society 109, Cesium-133 Solid State Nuclear Magnetic
Resonance Spectroscopy of Alkalides and Electrides, 3508-3513.

Dawes, S. 8., Ward, D. L., Fussa-Rydel, 0., Huang, R.-H., 8: Dye, I. L.
(1989) Inorganic Chemistry 28, Crystal Structures and Properties of Two
Sodides and an Electride, 2132—2136.

Dawes, S. 3., Ward, D. L., Huang, R. H., 8: Dye, J. L. (1986) Journal of the
American Chemical Society 108, First Electride Crystal Structure, 3534-3535.

DeBacker, M. G., Mkadmi, E. B., Sauvage, F. X., Lelieur, J. P., McMills, L. E.
H., Eglin, I. L., Kim, J., Guadagnini, R., Wagner, M., Concepcion, R., 8: Dye,
I. L. (1994) journal of the American Chemical Society 116, Lithium-
Ethylamine and Lithium-Sodium-Ethylamine Systems: A Nonmetallic
Liquid Electride and the Lowest Melting Fused Salt, 6570-6576.

37
DeBacker, M. G., Sauvage, F. X., 8: Dye, J. L. (1990) Chemical Physics Letters

7.3, Interaction of Light with Na+C222 Na". A Laser Flash Photolysis and
EPR Investigation, 291-297.

Dye, I. L. (1977) Scientific American 237, Anions of the Alkali Metals, 92-
105.

Dye, ]. L. (1979) Angewandte Chemie International Edition in English 18,
Compounds of Alkali Metal Anions, 587-598.

Dye, J. L. (1987) Scientific American 257, Electrides, 66—75.

Dye, I. L. (1991) in Metals in Solution, Iournal de Physique IV, Colloque C5
(Damay, P., 8: Leclerq, F., Eds.) pp 259-282, Les Editions de Physique, Les
Ulis, France.

Dye, I. L. (1993) Chemtracts-Inorganic Chemistry 5, Alkalides and Electrides,
243-270.

Dye, J. L., 8: Ellaboudy, A. (1984) Chemistry in Britain 20, Crystalline
Alkalides and Electrides, 210-215.

Echegoyen, L., DeCian, A., Fischer, J., 8: Lehn, ].-M. (1991) Angewandte
Chemie International Edition in English 30, Cryptatium: A Species of
Expanded Atom/Radical Ion Pair Type from Electroreductive
Crystallization of the Macrobicyclic Sodium Tris (Bipyridine) Cryptate,
838-840.

Edwards, P. P., 8: Sienko, M. I. (1982) Accounts of Chemical Research 15, The
Transition to the Metallic State, 87—93.

Golden, S., 8: Tuttle, T. R., Jr. (1988) Journal of the Chemical Society Faraday
Transactions 84, Spectral-Moment Constrained Density Matrices of
Maximum Entropy for the Solvated Electron, 1913-1922.

Golden, S., 8: Tuttle, T. R., Jr. (1992) Physical Review B 45, Spectral-Moment
Constraints on Electride-Electron Locations in the Crystalline Electride
[Cs(18-Crown-6)2], 913-918.

Greenwood, N. N., 8: Earnshaw, A. (1984) Chemistry of the Elements, Vol.
75-110, Pergamon Press, New York.

38

Hendrickson, I. E., Optical and Electrical Properties of Vapor-Deposited
Thin Films of a Sodide and an Electride, 1994.

Hendrickson, I. E., Xu, G., Pratt, W. P., In, 8: Dye, I. L. (1996) Manuscript in

preparation, Photolysis of Na+(Cryptand[2.2.2])Na': Photobleaching of
Absorbance and Quenching of Fluorescence, . _

Huang, R. H., 8: Dye, I. L. (1990) Chemical Physics Letters 166, Low

Temperature (-80°C) Thermionic Electron Emission from Alkalides and
Electrides, 133-136.

Huang, R. H., 8: Dye, I. L. (1996a) unpublished results.

Huang, R. H., 8: Dye, I. L. (1996b) Manuscript in preparation, Synthesis and
Structure of Five Compounds that Contain the Sodium Anion, .

Huang, R. H., Faber, M. K., Moeggenborg, K. J., Ward, D. L., 8: Dye, I. L.

(1988) Nature (London) 331, Structure of K"'(Cryptand[2.2.2]) Electride and
Evidence for Trapped Electron Pairs, 599-601.

Huang, R. H., Wagner, M. 1., 8: Dye, J. L. (1996a) unpublished results.

Huang, R. H., Wagner, M. 1., Gilbert, D. J., Reidy-Cedergren, K., Ward, D.
L., Faber, M. K., 8: Dye, J. L. (1996b) Submitted for Publication, Synthesis,
Structure and Properties of the "Spin-Ladder-Like" Electride,

Li+(Cryptand[2.1.1])e', .

Huang, R. H., Ward, D. L., 8: Dye, J. L. (1989) [ournal of the American
Chemical Society 111, Alkali-Metal-Anion Dimers and Chains in Alkalide
Structures, 5707-5708.

Huang, R. H., Ward, D. L., 8: Dye, J. L. (1990) Acta Crystallographica C46,
Structures of Alkalides and Electrides. IV. Structure of

Li+(TMTCY)[Li+(DMTCY') 'CH3NHZINa', 1835-1837.

Huang, R. H., Ward, D. L., Kuchenmeister, M. E., 8: Dye, J. L. (1987) Iournal
of the American Chemical Society 109, The Crystal Structures of TWO

Cesides Show That Cs' is the Largest Monatomic Ion, 5561-5563.

Huang, 5., Single Crystal X-ray Diffraction and Alkali Metal NMR
Studies of Alkalides, Electrides and Model Compounds, 1994.

39

jaenicke, S., 8: Dye, J. L. (1984) journal of Solid State Chemistry 54,
Photoelectron Emission from Solid Sodides, 320-329.

Kaplan, T. A., Rencsok, R., 8: Harrison, 1. F. (1994) Physical Review B 50,
Valence-electron distribution of cesium crown-ether electrides., 8054-
8058.

Kevan, L. (1981) Accounts of Chemical Research 14, Solvated Electron
Structure in Glassy Matrices., 138-145.

Kraus, C. A. (1907) The journal of the American Chemical Society 29, Solutions.
of metals in non-metallic solvents., 1557-1571.

Kraus, C. A., 8: Lucasse, W. W. (1921) The journal of the American Chemical
Society 43, 2529.

Kraus, C. A., 8: Lucasse, W. W. (1922) The journal of the American Chemical
Society 44, 1941.

Kuchenmeister, M. E., 8: Dye, I. L. (1989) journal of the American Chemical
Society 111, Synthesis and Structures of Two Thermally Stable Sodides
with the Macrocyclic Complexant Hexamethyl Hexacyclen, 935-938.
Kuo, C.-T., Optical Studies of Alkalides and Electrides, 1994.

Lehn, j.-M., Sauvage, j. P., 8: Dietrich, B. (1970) journal of the American
Chemical Society 92, Cryptate Cation Exchange Rates, 2916-2918.

Moeggenborg, K. j., Papaioannou, j., 8: Dye, ]. L. (1991) Chemistry of
Materials 3, Powder Conductivities of Three Electrides, 514-520.

Mott, N. F. (1956) Canadian journal of Physics 34, 1356.

Patterson, T. A., Hotop, H., Kasdan, A., Norcross, D. W., 8: Lineberger, W.
C. (1974) Physical Review Letters 32, 189-92.

Pedersen, C. ]. (1967a) journal of the American Chemical Society 89, Cyclic
Polyethers and their Complexes with Metal Salts, 2495-2496.

Pedersen, C. ]. (1967b) journal of the American Chemical Society 92, New
Macrocyclic Polyethers, 391-394.

40

Pedersen, C. I. (1970) journal of the American Chemical Society 92, Crystalline
Salt Complexes of Macrocyclic Polyethers., 386-394.

Pedersen, C. I. (1988) Science 241, The Discovery of Crown Ethers, 536-
539. -

Rencsok, R., Kaplan, T. A., 8: Harrison, 1. F. (1993) journal of Chemical
Physics 98, Electronic Structure of Li(9-crown-3)2: A Molecule with a

Rydberg-type Ground State, 9758-9764.

Singh, D. j., Krakauer, H., Haas, C., 8: Pickett, W. E. (1993) Nature (London)
365, Theoretical Determination that Electrons Act as Anions in the

Electride Cs+(15-crown-5)2e', 39-42.

Tehan, F. j., Barnett, B. L., 8: Dye, I. L. (1974) journal of the American
Chemical Society 96, Alkali Anions. Preparation and Crystal Structure of a
Compound Which Contains the Cryptated Sodium Cation and the
Sodium Anion, 7203-7208.

Thompson, j. C. (1976) Electrons in Liquid Ammonia, Vol. , Oxford Univ.
Press, Oxford.

Tsai, K.-L., 8: Dye, ]. L. (1993) Chemistry of Materials 5, Synthesis,
Properties, and Characterization of N anometer-Size Metal Particles by
Homogeneous Reduction with Alkalides and Electrides in Aprotic
Solvents, 540-546.

Wagner, M. j., 8: Dye, I. L. (1993) Annual Review of Materials Science 23,
Alkalides, Electrides and Expanded Metals, 223-253.

Wagner, M. j., Huang, R. H., Eglin, ]. L., 8: Dye, I. L. (1994) Nature( London)
368, An Electride with a Giant 6-Electron Ring, 726-729.

Ward, D. L., Huang, R. H., 8: Dye, I. L. (1990a) Acta Crystallographica C 46,
Structures of Alkalides and Electrides. V. Structure of Caesium Bis(15-
Crown-S) Kalide and Rubidium Bis(15-Crown-5) Rubidide, 1838-1841.

Ward, D. L., Huang, R. H., Kuchenmeister, M. E., 8: Dye, I. L. (1990b) Acta
Crystallographica C46, Structures of Alkalides and Electrides. 11. Structure
of Cesium Bis(15-Crown-5) Electride, 1831-1833.

Weyl, W. (1864) Annalen der Physik und Chemie 19, 7601.

CHAPTER 2

SYNTHESIS OF CESIUM
HEXAMETHYL HEXACYCLEN SODIDE:

Cs+(HMHCY)Na'

41

42

INTRODUCTION

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 (MezO) is a preferred solvent because of its
resistance to reduction. Since dimethyl ether does not have ionizable
protons or protons that are beta to the oxygen, this leads to resistance to
reduction, resulting in a very robust solvent. Primary and secondary
amines have ionizable protons, thus making them less desirable.
Trimethylamine (TMA) and, to some extent, diethyl ether (EtzO), even
though it has beta hydrogens, also maintain a resistance towards

reduction, and these two solvents serve as suitable co-solvents. In the case

43
where the alkalide dissolves in both of these solvents, n-pentane serves as

a reasonable substitute. The combination of MezO and TMA however,
provides the greatest resistance to reduction.

It was shown from gas phase NMR (Cauliez et al., 1991) of the
decomposed products of crown ether alkalides that the-products are
butane, ethane, ethylene and ring opened complexant minus the ethylene
linkage. The oxygen atoms in the crown ether are highly electronegative
and when there is a cation complexed to the oxygens, they become even
more electronegative and form a strong dipole. This makes them very
susceptible to attack by an electrophilic substance; thus, when the
conditions are not right to stabilize the alkalide, the ring opens and the
decomposition products are formed. In the case of HMHCY , all of the
oxygens are replaced with nitrogens which are fully methylated, so there
is no place for the electrophile to attack. This results in decomplexation
rather than decomposition. When this occurs, the alkali metal cation that
was complexed with the HMHCY recombines with the unpaired electron
to form a fine metallic powder. This is evidenced in the HMHCY synthesis
occasionally and must be avoided as the alkali metal also has an
unpaired electron and will be observed in the EPR. To avoid this, the
synthesis is completed in a speedy fashion, at a low enough temperature

to prevent decomplexation but with enough care to grow crystals.

44
Preparation of Cs+(HMHCY)Na’

The glassware used to synthesize these compounds is very specific
and it cannot be purchased, therefore it is glassblown in our glass shop
The cell, referred to as a K-cell, is shown in Figure 2.1. When synthesizing
an alkalide, a Pyrex K-cell is used since the threat of exchanging the
natural Na+ in the borosillicate glass of Pyrex with cesium cation in the
presence of M' is minimal. Initially, the K-cell is cleaned rigorously te
inhibit solution decomposition. The apparatus is first rinsed with a
carefully prepared HF solution (5% concentrated HF, 35% concentratec’
HNO3, 60% H20 and a small amount of detergent) to remove
contaminants from the walls of the glass. However, the soapy HF solutior
itself often is difficult to rinse away completely so an aqua regia solution
composed of three parts HCl and one part HNO3 is added to the vessel
This is allowed to stand for one day. The following day, the solution is
poured out and washed six times with distilled water, followed by si>
rinses with conductance water, distilled water that had been deionizec
and redistilled through a high reflux ratio column so that less than 1 pprr
of impurity remained. The K-cell is then placed in an oven at arounc
275°C to dry completely. Finally the K-cell apparatus is placed on the
vacuum line overnight, with the proper 9 mm Ultra-Torr attachments a-

points 1 and 2, and evacuated to check for any faults in the glass as well

45

KFmgers

Stopcock

To Vacuum<E-—(I_,—q-’E

Point 2

 

Tube Y L

 

 

Point 1
Point 3

 

Bulb A

Figure 2.1: Pyrex® K-Cell used in the
synthesis of alkalides and some electrides.

46
as to distill out any water that possibly remained in the K-cell. As is

evident from this description, the cleaning ritual is very important and
takes time and patience, so planning an experiment ahead of time is
always advantageous.

Once the K-cell has been cleaned and could sustain-a vacuum on
the order of 10'6 torr, the K-cell, the appropriate length of a Cs metal
ampoulel, a pipette and bulb, and a spatula are all placed in the Vacuum
Atmosphere Company (VAC) Glove Box outer chamber to be evacuated to
about 30 mtorr. Once the outer chamber has been evacuated, the
equipment can be accessed through the port and brought into the glove
box. The cesium ampoule is scored with a knife that is stored in the glove
box and cracked. The portion of the cracked ampoule containing the
metal is placed into tube Y so that the sealed part of the ampoule is facing
towards the inside of the apparatus (this was done to help prevent any
bumping of the cesium metal when it is distilled). If the ampoule is
cracked in the middle of the Cs metal portion, both parts were placed in
the side tube. The sodium metal and a knife to cut it is stored in the
glovebox. A small portion of the metal is cut away to reveal a shiny

unoxidized portion of the metal and some of the shiny metal is cut and

 

1* To determine the appropriate length of cesium metal ampoule for each experiment, the
conversion (85 mg/cm)(length of C5 ampoule in cm)(mmol/132.9mng)= mmol Cs, when the Cs
metal is poured into 4 mm O.D. Pyrex® tubing.

47
weighed. The sodium is then placed in the refrigerator momentarily te

cool the metal so that it will not stick to the walls of the sidearm during
delivery into the K-cell. The Ultra-Torr attachment is then placed securely
on the end of the side tube at point 1. Next the apprOpriate amount 0
complexant is pipetted through point 2 and into bulb B, and the ultra—tor.
attachment is attached to point 2. This sodide recipe calls for a sligh'
excess of both metals to make sure that only sodide is made, with ne
electride. It is important to make sure the stopcock is closed and that botl
Ultra-Torr attachments are tightly secured before removing the K-cell from
the glove box.

Once the apparatus is taken out of the glove box, it is imperative tha‘
no oxygen is allowed into the K-cell. At this point, the K-cell apparatus
which contains a helium atmosphere, is directly attached to the vacuurr
line and evacuated. When the pressure has reached 10'6 torr, the
apparatus is sealed with a torch at points 1 and 4. Since HMHCY is not a
highly volatile complexant, it is not necessary to cool bulb B with a dr)
ice/isopropanol bath. When the two side-arms have been sealed-off, a
freshly distilled Cs/ Na mirror is deposited into bulb A by using a ligh-
flame at first to distill the cesium, then a hotter flame to distill the lest
volatile sodium. A nice gold-colored mirror always forms rather quickly
It is important not to distill the Cs too rapidly or else large balls of meta

will form and deposit on the bottom of the bulb. This is not disastrous, bu

48
the metal could react faster if there is a larger surface area. It is als

important to prevent the metal from depositing too high on the neck of th
vessel, approaching the stopcock. Applying heat near a stopcock is not
good idea anyway, when the importance of a good vacuum is at stake
After the metal has been completely distilled, the stem of the. tube is seale
at the narrowed portion of the glass, point 3.

About 10 mL. of dimethyl ether is distilled first into a flas
containing Na/ K alloy to react with any impurities, particularly watei
then introduced into bulb B, which contains the HMHCY complexant, a
about -35°C. It is crucial to improving the yield that the HMHCY dissolve
completely before allowing the solution to contact the metal mirror. Thi
actually is a rather difficult process because the dimethyl ether has a 10V
' boiling point (-24.8°C) so the temperature of the bath cannot be raised to!
high, but high enough to dissolve the complexant. A constan
temperature bath is used to maintain a temperature of about -35°C , whicl
is a good temperature for this process, which could take as long as tw'
hours. Once the complexant has dissolved, the solution is exposed to th
mirror (bulb A) and the deep blue color, indicative of solvated electrons, i
formed immediately. It is important to let the complexant react with all 0
the metal mirror to increase the yield of the final products. This proces
usually took about a day. When all of the HMHCY has appeared to hav

reacted, the co-solvent is added to bulb A at -78°C. In typical alkalid

49
syntheses, TMA or EtzO is used as the co-solvent for crystallization of the

product. However, this particular sodide nearly fully dissolves in this
solvent system, so neither of these solvents acted as a good co-solvent.
Instead, n-pentane is used. About 5 mL. of n-pentane is added to the
existing solvent at about -40°C. At this point, the solution. is brought to
saturation by evaporation of MezO. This sometimes takes several hours.
The solution is then poured through the frit to bulb A. The solid which
precipitates out of solution when the saturated solution is made, is lost in
the synthesis, but this assures that the impurities are left behind as well.
The metal mirror is washed very well by using a cotton swab dipped in
liquid nitrogen to distill over some clean solvent which is then used to
dissolve any alkalide remaining in contact with the mirror. Crystal
growth is effected by slow evaporation of the solvents through three
additional frits, at “78°C over a period of about two days where every 15
hours an additional frit is opened. During this waiting time, the. solution
is carefully checked to monitor the progress of crystal formation. When a
small amount of n-pentane remains in the bulb and crystals are present,
the remaining solvent is used to wash carefully the crystals. This is
accomplished by decanting the liquid from bulb B to bulb A, then
distilling the solvent back into bulb B and washing the crystals. This is
repeated several times with the hope that any uncomplexed HMHCY or

Other impurities will dissolve in the n-pentane and pass through the frit to

50
bulb A. Finally, the crystalline material is left to dry on the vacuum

overnight by pumping at about 106 torr while the K-cell is kept in a
ice / isopropanol bath.

It is important to note that the cleaning ritual described earlie
especially important in that it helped eliminate impurities. In addition
avoiding a fast precipitation of the product, good crystalline materie
usually produced. By going through this extra trouble, we are allowee
produce crystalline material more consistently.

When the crystals were dry, the entire K-cell is taken off the vacu
line and prepared for collection of the crystals. This is done by gel
placing bulb A and the fingers in a large storage container of dry ice
that this half of the apparatus was kept very cold. When the K-cel
sufficiently cold, it is removed from the dry ice and flipped upside-dc
and bulb B is gently tapped so that all of the crystals fall nicely into
fingers, which are subsequently placed in liquid nitrogen and sealed ft
the K-cell with a hot flame. This is done so that when the crystals com:
contact with the fingers, they will not be exposed immediately to a we
surface. Instead, there is no temperature change since both parts of
apparatus are in the same temperature environment.

When the time comes to transfer the material into an EPR tube,
is performed in a glove bag equipped with a flow of nitrogen gas the

run through a column. A tall dewar containing the samples, a spatul

51
glass cutting knife, the EPR tube (Figure 2.2) and an agate mortar and

pestle, are all placed inside the glove bag through the opening. Typically,

about four liters of liquid nitrogen are poured into a large foam dewar

Stopcock

E

To Vacuum <—-— O:

 

; <—-—— Grated seal
<———— 4 mm quartz tube

 

 

Figure 2.2: Quartz apparatus for loading
electride or alkalide samples into EPR tubes.

in the glove bag to create a large positive pressure of the inert gas in the
glove bag which will in turn drive out any air that remains in the bag
during loading of the appropriate equipment. The glove bag is purged
several times. Once the mortar has equilibrated and the temperature
inside is cold (the temperature was checked with a thermocouple and was
found to be -100°C), the sample tube is scored with a file and broken. The

contents are poured immediately into the very cold mortar. The crystals

52
are then crushed with the pre-cooled pestle to a very fine powder. This can

often take 30-40 minutes since even very small crystals can have
orientational effects in the EPR spectrum when a powder pattern is
desired. Some sample is then scooped with the cold spatula and funneled
into the EPR tube until about 1 cm. of sample is collected atlthe bottom of
the tube. Since the paramagnetism in this sodide originates from defect
electrons, it is important to load a large amount of sample for EPR
analysis. If very pure crystals are grown, there will be very few defect
electrons and thus a small EPR signal, therefore a large amount of sample
is needed to increase the number of paramagnetic centers. The stopcock is
closed and the EPR tube is immersed in liquid nitrogen, removed from the
glovebag and placed on the vacuum line. The quartz tube is evacuated,
then sealed by using a very hot flame, and is subjected to EPR

measurements.

 

53

BIBLIOGRAPHY

Cauliez, P. M., jackson, j. E., 8: Dye, I. L. (1991) Tetrahedron Letters 32, An
Unusual, Reduction of Ethylene Occurring during the Thermal
Decomposition of Alkalides and Electrides, 5039-5042.

CHAPTER 3

 

THEORETICAL TREATMENT OF ELECTRON
MAGNETIC RESONANCE SPECTROSCOPY

54

55

Spectroscopy

When scientists applied the principles of quantum-mechai
describe atoms and molecules, they found that discrete levels existe
with some characteristic energy. Spectroscopy“ involves the
electromagnetic radiation to probe the energy levels of atoms or moi
that arise from a variety of interactions. Knowledge derived frorr
measurements allows an insight into the structure and the dynan
the particular sample under observation. In magnetic resonanc
probes the different energy states that result from the interaction
molecule's or atom's magnetic moment with an applied magnetic
Transitions between the resulting energy states occur upon the applj

of radiofrequency or microwave radiation.

Magnetic Interactions

Magnetic resonance is driven by the occurrence of magnetic d
which implies angular momentum (a charged particle that is mc
Electromagnetic radiation is composed of oscillating electric and ma

fields, perpendicular to one another. In optical spectroscopy, the

 

IFor useful background of electron paramagnetic resonance spectroscopy, see: (Abr
Bleaney, 1970, Carrington 8: McLachlan, 1979, Wertz 8: Bolton, 1986)

56
interaction of light and the electric dipole moment in a molecule

important. In EPR spectroscopy, a molecule with magnetic dipole
interacts with the magnetic component of the radiation. In N MR, tl
nucleus has only spin angular momentum, however in EPR the electrc
possesses both spin and orbital angular momentum that Contribute in
vectorial sum. The magnetic dipole is measured via the magnetic dipoZ
moment, y. The energy of the interaction between the magnetic field an

the electron dipole moment is Shown in this classical equation,
E .-= :iT-H

: "HHCOSG (3.1)

where u is a proportionality constant between the applied field and th
energy and 0 is the angle betWeen the magnetic field and the axis of th
dipole. This can be described pictorially by three arrangements, FiguI
3.1. The dipole-dipole interactions are a direct consequence of direction:
interactions of two electronic dipoles, in optical spectroscopy and magnet;

dipoles in EPR spectroscopy. One can relate the linear momentum for a

electron, '15" , to the magnetic moment, "If , by,

it 2 7P (3.2)

as in a system with angular momentum that possess a magnetic moment

57

 

 

 

 

 

 

 

 

‘ E =-pH A E =+uH A E =-uHcosG
fl ——
H H S H
0',
2 at "
0 = 0° 0 = 180°

 

 

Figure 3.1: Classical picture of the energy of a dipole
in a magnetic field as a function of the angle between
the dipole moment vector and the magnetic field.

colinear with F . The constant 7 is the magnetogyric ratio, e / 2mc, whel

e is the charge of the electron, m is the mass of the electron, and c is tt
Speed of, light.

Since electrons and nuclei obey quantum, not classical mechanic
magnetic moments are always quantized, therefore only a finite number e
discrete energy levels exists. The magnetic moment of an electron arise
from the "Spin" or the intrinsic angular momentum. The energ
associated with the electron spin magnetic moment is also quantized. B
continuing the classical description above, consider the electron Spi

angular momentum, Sh, and ms, the projection of the electron Spi

58
angular momentum. The electron can have the allowed projectic

= i1 / 2. Assuming quantization for an electron along the field dire

P2 = Ifish/27"; (3.3

Relating the dipole moment of the electron to the spin angular
and the quantum number ms, from Equation 3.2,

uz = (-eh/41tmc)mS (3.4

So far, the orbital angular momentum has not been acknowledged
equations. This is done by introducing the factor, 3,

pl = -g(eh/ 41cmc)mS (3.5:

where g is the Landé g-factor and can be described by,

1 + j(j+1) + S(S+1) - L(L+1)
210+1) (3.6:

 

g:

where J is the Spin-orbit coupling, L is the orbital angular momen
S is the spin angular momentum. For a free electron, the 3

2.00000, j=S, L=0. If the quantity (eh /2mc) is designated as a con

”2 = -gl3ms (3-7:

and substituting Eq. 3.7 into 3.1,

E = -gBS° H (3.8

 

 

59
The Spin Operator

The task in quantum mechanics is to rewrite classica
expressions like Eq. 3.1 in terms of operators. Since this sys
discrete energy levels which are described by well defined e
numbers, an eigenvalue equation can be written. Consider a
where hi represents an eigenvalue of an operator and (bi repree
corresponding eigenfunction. An eigenvalue equation can be ve

follows,

O¢i = Mi (3.9
where 6 is the operator for the system. Spin operators are nece
account for the delicate points that the classical description cam
as the analogy for the coupling between the electron Spin and the
spin. Since EPR incorporates spin angular momentum, a spin 0}:
appropriate here. This Spin operator will operate on a
specifically defining a spin state. Spin operators can be used to
energy levels of an electron in a system. Equation 3.7 can be u

relate the electron dipole moment with the spin magnetic momenl

“z : 'gBms (3.1

and by replacing S with g, the use of the spin operator can cha

the energy in the form of a hamiltonian,

60

__ A
at = gB H -S (3.11)
___ A
H '5 can be expanded,
__ A A A A
H .s = SxHx +SyHy +Ssz _ (3.12)

Assuming quantization along the z-axis, the vector components of t

magnetic field (H) are (0,0,H0), therefore Eq. 3.9 can be written as,

56 = sBHogz (3.13)

When the hamiltonian operates on the wavefunction, the eigenvalue
generated when it is an eigenstate of the hamiltonian. This will be appli
later within this chapter to a real system with an electron and

interacting nucleus.

The Spin Hamiltonian

The Electronic Zeeman Interaction

The time independent hamiltonian shown above, Equation 3.:
describes the interaction between an electron with the applied magne
field, and is called the Electronic Zeeman term. The eigenfunctions of t

hamiltonian are,

(Doe = IOL> and (1)5 = |B>

61
With the corresponding eigenvalues being m5 = +1 / 2 and mS = -1

respectively. The lowest energy state corresponds to mS = -1/ 2 or

assuming a positive g—value. The transition energy between the two st

can be described by,
E = i1/2 gBH
AB = gBH (3.14)
hv = gBH (the "resonance" condition)

where hv is the quantum of energy supplied to the system (h is Plan
constant, v is the frequency of electromagnetic radiation). Fur1
consideration of the g-value5 shows that there is hidden informal
within this factor. Orbital angular and spin angular momenta are fol:
into the g-factor. In other words, the electron g-factor describes how
spin angular momentum couples to the magnetic field. In addition,
nature of the g-value gives an idea of which orbital holds the unpai
electron and is a measure of the deviation from the free electron va

which has only spin angular momentum.
The Nuclear Zeeman Interaction

This term in the hamiltonian, once again assuming that the SYS‘

is in a magnetic field that is defined as the z—axis, can be described as,

 

§The g-value is often treated as a scalar, but strictly speaking, it is a tensor.

62
A
flNz = ‘8NBNHIZ (3.15)

A
where 12 is the nuclear spin operator, BN is the nuclear magneton and

is the nuclear g-value. This term describes the interaction of the nucle
moment with a magnetic field. It is opposite in Sign and smaller
magnitude than the electronic Zeeman term. The spin quantum numb.

mI = i- 1/ 2 are defined such that mI 2+ 1 / 2 is of lowest energy (when gh

positive).
The Hyperfine Interaction

The interactions discussed thus far have been between an electr
Or nucleus and a magnetic field. If this were the only effect measured
using EPR, all spectra would be relatively indistinguishable as they wor
consist of only one line. The only useful feature would be the g-value. T
g-value does not however reveal much information about the molecu
structure of the sample. The resonance can be perturbed by the magne
fields within the paramagnetic substance Since the unpaired electron
sensitive to its local surroundings. These fields arise from the magne
nuclei interacting with the electron spin. Some nuclei possess an intrin
spin angular momentum and thus have a magnetic moment associal
with it them. The interaction between the local magnetic field of 1

nucleus and the electron is the known as the nuclear hyperfine interacti-

63
This interaction can be either orientation dependent with respect to the

laboratory field (anisotropic), or independent of the orientation of the field

(isotr0pic).

 

 

Figure 3.2: The interacting dipoles, lie and lln, are connected by the vector r where 0 is
the angle between r and the applied magnetic field. Since pe >> tin, when referring to the
electron-nuclear hyperfine interaction, it is actually the effect of the nuclear field at the
electron that is being considered, since the nucleus has a magnetic moment. The effective
fields that the electron experiences is the lab field plus the induced hyperfine field.

The hyperfine interaction is composed of two parts, the isotropic or
Fermi contact interaction (Eq. 3.19), and the anisotropic or a Special case,
the dipolar interaction (Eq. 3.21). The Hamiltonian describing the
hyperfine interaction follows,

gthfi = y‘iso + y‘dip (3'16)

The Fermi contact interaction is a through bond interaction where

there exists a non-zero probability of the electron being at the nucleus.

64
This only occurs in s-orbitals and can be seen easily by looking at the

wavefunctions of the ls, 2p and 3d orbitals (Figure 3.3). The 2;? and 3d
orbitals have a node at the origin; therefore, the probability of the electron
being located at the nucleus is zero. The isotropic hyperfine interaction

can be described by the equation,

A.=4311I 0I2e
so 3 W) MI“ (317)

where |1p(0) l 2 is the wavefunction evaluated at the nucleus. By replacing

the magnetic moments with their corresponding Operators, Eq. 3.15

becomes,
A
A... = 43% gemgnfinlweowéz I, (318)
A A
Also = hAoSz 1., (3.19)
A
where A0 is the isotropic hyperfine coupling constant, 12 is the nuclear

A
spin operator, 52 is the electron spin. operator and the measurement of the

interaction energy between the electron and the nucleus is hAo. For
example, in an 1:1/2 system, the single EPR absorption is split into two
peaks, 2% H1 (the local magnetic field produced by the nucleus at the
electron), Figure 3.4.

In fixed systems, it is necessary to consider the classical interaction

between an electron dipole and a nuclear dipole,

65

W15

 

 

W2p

 

 

 

 

Figure 3.3: Radial dependence of the Is, 2;? and 3d
wavefunctions of the hydrogen orbital. Note that
the electron density at the Is orbital is non-zero,
unlike the 2p and 3d orbitals, which have a node
at the nucleus.

66

 

 

I I
I J l

k—Hr—HFHT"

Figure 3.4: The H1 field adds to or opposes the laboratory magnetic field,
depending on the alignment of the moment of the nucleus. When H1 adds
to H0, less magnetic field strength is needed from the laboratory field and
therefore the resonant field is lowered by H1. The opposite is true when
H1 opposes the lab field.

 

E 2 art. ,3 mm}?
r3 5

__ A r
where: lie: gB/S

F3: 8131 (3.20)

By making substitutions with the quantum mechanical counterpart,

 

A A A _._ A __
fldipz ‘geBegan {Gil—.3) _ 3 (S‘I'): I. 1') }
r r (3.21)

The dipolar tensor can be seen by expanding the vectors in Eq. 3.21. The
anisotropic or dipolar component results from the two dipoles interacting.

The strength of this interaction can be described, to a first approximation,

67

2
Adip = (1-3C(3)S 9) “e“n
1' (3.22)

The dipolar matrix is traceless; thus the contribution of the observables
the limit of fast motionl, goes to zero. In solutions where all values of
are equally probable, the term (1-3cosZG) vanishes and therefore 0
dipolar part of the hyperfine also vanishes. In solids, all possib
orientations of 0 are observed, but they are observed unequally and t]
more probable the orientation, the more it contributes to the EF

absorption. Thus the total hamiltonian for an isotropic system is given b
A A
H = 36H 5 - gNBNH-l + hs ~ A i (3.23)

where Q = A01 + T, and T is the hyperfine tensor.

The isotropic g-value is a scalar, but a rigid system can I
anisotropic also, where the more probable orientation, perpendicule
contributes largely to the absorption while the parallel orientations do n
contribute as strongly to the EPR absorption, as illustrated in Figure 3.5.
the field in the x-direction has the same effect as the field in the
direction, they both contribute to the perpendicular component of tl
g-tensor. The field in the z-direction is then different from the x and the

is known to have axial symmetry.

 

1‘ Fast motion is the limit of coupling; i.e. Consider a dipole-dipole interaction of 1 Nfl-Iz. F
motion is when the molecule is rotating quickly with respect to 1 MHz. The time scale for f
motion is on the order of the energy of the interaction.

68

 

 

 

Hi HII
Magnetic Field Strength (G)

 

Figure 3.5: A.) A large number of systems with axes nearly
perpendicular to the field direction, Z, results in a larger
contribution to the EPR lineshape. This is in contrast to the

less likely instance of systems aligned nearly parallel to the
field direction. B.) The powder pattern absorption indicating
the two turning points, parallel and perpendicular where the
field values H” and H_Lrepresent field extrema and therefore
the highest probability of observing a line. There is no
hyperfine interaction illustrated here. C.) First derivative

line of B. The inflection in the line represents the perpendicular
turning point where the more probable orientations contribute
the greatest to the lineshape.

 

69
The EPR Experiment

In a system with one unpaired electron, the electron spin can
possess one of two values, m5=i1 / 2. In the absence'of a magnetic field,
these states are degenerate. In a strong magnetic field, the degeneracy of
these states is split as described by the resonance condition Shown above,
and illustrated Figure 3.6. Resonance is achieved when the frequency of
the radiation times h is equal to the energy level separation. Due to
instrumental constraints, (the sample probe is an RLC circuit operated at
its resonant frequency), the frequency is held constant throughout the
experiment thus the technology does not permit one to sweep the
frequency and the magnetic field is swept instead.

The energy separation needed to satisfy the resonance condition in
EPR is very small compared to that same splitting in optical spectroscopy.
A typical value of AB in optical spectroscopy is 1014 Hz while that in EPR
is On the order of 1010 Hz. Therefore, there are four orders of magnitude
difference in frequency units between the two. The quantity kT at room
temperature is 6x1012 Hz so in optical Spectroscopy, the population of the
upper level is small Since the splitting is huge compared to kT. This
results in high sensitivity even with nanomolar concentrations. The
population difference between the levels in EPR is very small Since the
splitting is less than kT; consequently the sensitivity is reduced to umolar

concentrations. For example, at room temperature and at X-band (9-10

 

70

 

 

E = gBH
0 gm = (2.00232)(9.27402x10'28]/G)(3400G)
= 6.314x10'24]
E
y IB>

 

 

 

H (G)

 

Figure 3.6: Electron Spin levels in a magnetic field. The
degeneracy of the two levels is split when a magnetic field

is applied. Resonance is achieved when the frequency of the
incident radiation matches the frequency corresponding to

the energy level separation. For a typical laboratory magnetic

field of 3400 G, AB is on the order of 10'24 I, thus the frequency of
the electromagnetic radiation used for this spectroscopy is

around 9.5 GHz or the microwave region (X-band).

 

71
GHz), the population difference between the CL and [3 states ca

described by a Boltzmann distribution as follows:

n+1(2 = e-AE/kT
11-1/2

e-gflH/kT

= 0.998 (324)

Therefore, only a 0.2% difference in the population exists betweer
states loe> and IB>. A population difference is crucial for the experin
therefore if there is no difference in population between the two state
EPR resonance will be observed. The system is said to be saturated u
such conditions.

Overall, the interaction of a magnetic dipole with electromagi
radiation can induce transitions between two Zeeman levels if the ph
energy (hv) equals the separation gBH, and the magnetic field compo

of the microwaves is directed perpendicular to the laboratory field.
Application of the Hamiltonian

Consider a nucleus that has an intrinsic nuclear Spin, 121/ 2.
nuclear hyperfine interaction splits each of the Zeeman levels into
levels. The observed transitions are those obeying the EPR selection r'
Ms = i 1 and M1 = 0. The complete hamiltonian for such an isotr

system is,

72

.l

1109

A A AA AA
'8 - ganH °I + hAO(SxIX+S Iy+

3:43 y

(3.25)

For first order energies and assuming quantization along the z-axis,
€qu and 3ny vanish. These terms become important if second order
hyperfine interactions are present. To determine the energies provided in
the hamiltonian, a basis set is employed, consisting of four possible
combinations of electron and nuclear Spin functions.
in: lae,ocn> ¢3= IBe,0In> (3.26)
¢2=|0lerl3n> ¢4=|BeIBn>

A A
5; Operates only on the electron spin function and 12 operates only on the

nuclear spin function,

/\
5.. lone, B.» = 1/2Ioce, BI.) (3.27)
/\
Iz lae/ Bn> = ‘1/ZI (Xe, Bn> (3.28)

Thus the energies for these states can be obtained by solving the
hamiltonian matrix, such as the matrix element where the scalars, gBH,

have been pulled out of the equation,

EaeBn = <09 Bn I fl I (1e, Bn> (3.29)

A A A A
= <oee, [in | gBHSz -gN[3NHIz + hAoSz - Iz lore, Bn>

= 1/2gBH + 1/2gNBNH +1/4hAo

 

73
and the energies for the other states are obtained Similarly,
Eaean = +1 /2gBH - 1/2gNBNI-l + 1/4hAo
EBean

EBeBn

-1/2gBH - 1/2gNBNH - 1/4hAo (3.30)

-1/2gBH + 1/2gNBNH + 1/4hA0

The interactions between an electron and a nucleus (1 = 1/ 2), are easiest
viewed in an energy level diagram (Figure 3.7). Other interactions such as
the nuclear quadrupole interaction and the Spin-spin interaction are
important in some systems but are negligible in the systems presented in

this dissertation, so they will not be discussed.
Relaxation

Discussed in this chapter are a few factors that influence the EPR
linewidths.‘ The resonance lineshape can be broadened by the uncertainty
in the lifetime. The Spin-lattice relaxation time, referred to as T1, can occur
from interactions between a paramagnetic center and thermal vibrations
in the lattice. It is the characteristic time for the spins to equilibrate with
the lattice and can be described by a 1 / e time. If T1 is sufficiently long, one
can observe an EPR spectrum at room temperature. Generally, as the
temperature is decreased, T1 is increased. The spin-spin relaxation time,
T2, occurs due to interactions originating from small local magnetic fields

that exist on some paramagnetic nuclei. These local fields cause a Shift in

74

 

 

 

la> . Iaoe> '
, loeB>
',__| Boe>
| 13>
‘~ “33>
electron Zeeman hyperfine interaction

nuclear Zeeman

A

36 = BHog-S - gNBNH-?+ -§

Figure 3.7: Energy level diagram for a 8:1 / 2, 1:1/2 system.

 

75
the total field at the paramagnetic center. The distribution of energies

serves to broaden the line.

Consider the system where the spins in a sample experiences a
heterogeneous magnetic environment made up of the lab field and weak
local fields arising from magnetic nuclei. When the motionlis very rapid,
the spins sample the full gamut of the heterogeneity thus local fields will
add to or subtract from the lab field by inducing a spread in the resonance
frequency, giving rise to a broadening of the resonance lineshape. This is
known as homogeneous broadening. This takes place when rapid motion
occurs with respect to the EPR time scale, such as in liquids.

In solids, a more complicated situation occurs. The motion is slow,
coming mainly from vibrations, and the spins in general will only be
affected by a small portion of the heterogeneity. When the unpaired
electron is subjected to slightly different effective magnetic fields, as any
given time, only a small portion of spins are sampled. This results in a
superposition of individual spin packets, each shifted slightly from one
another. Each individual spin packet has a lorentzian lineshape and is
homogeneously broadened while the envelope of the Spin packets is the
inhomogeneously broadened line. Figure 3.8 illustrates this point.

When the system is at thermal equilibrium, the magnetization is
along the z axis. A vector sum of the individual moments or spins are

precessing at some frequency (00, about the lab field Bo. Relaxation times

 

76

homogeneously broadened spin packet

(00

.8

(0+

 

 

 

 

 

 

\\\\\\\\\\\\\\\\\\\\\\\\\x\““ _

1 II

Figure 3.8: Inhomogeneously broadened line

 

 

 

Figure 3.9: Rotating frame

77
that describe the gain or loss of magnetization can be described by T1 .

Along x or y, T2 describes the loss of coherence (torque the cone when the
B1 field is turned on so that there is some non-zero projection in the xy
plane). As B1 is turned off, there is a loss and the time it takes for the

frequency to randomize is T2.
Electron Spin Echo Envelope Modulation

Often there are weak superhyperfine couplings between the
paramagnetic center and nearby magnetic nuclei that are unresolved due
to inhomogeneous broadening. Modulations, or a periodic variation of
amplitude, can occurwhich are associated with small splittings of the
resonance line. This modulation effect can be used to measure splittings
that are unresolvable in the presence of inhomogeneous broadening. A
method to probe these interactions used today is Electron Spin Echo
Envelope Modulation (ESEEM). The typical two-pulse sequence and the
time evolution of the echo decay trace is outlined in Figure 3.10.

The principles of ESEEM are based on an inhomogeneously
broadened line originating from anisotropic interactions. The unpaired
electron is subjected to slightly different magnetic fields thus only a small
fraction of the spins are sampled. A superposition of the different spin

packets exists which are all slightly shifted from the resonance frequency,

 

 

78

 

 

 

 

 

 

 

 

 

tau increasing

 

 

 

 

 

 

 

 

 

__ Envelope of

Figure 3.10: Diagram showing the time evolution of the
echo decay envelope. The envelope is modulated by the
couplings between the electron spin and the neighboring
nuclei. The two pulse experiment is a function of the

spacings between the pulses (T). In the three pulse
experiment, the spacing between the second and third

pulses, T, is varied while I is set to a fixed value.

 

79
(00. All spin magnetic moments belonging to the same spin packet precess

with a characteristic precessional frequency (Figure 3.11).
When the first 1: / 2 pulse is applied, the Spin packets dephase
immediately. After a certain time t, on the order of nanoseconds, the

second 11: pulse is applied which flips the magnetization 180°. The same

zH0
(0).:
co \‘2 /
(D.

 

 

Figure 3.11: Precessional frequencies of the individual
spin packets. The magnetization is along the z-axis.

time 1? occurs while the precessional frequencies remain unaltered. After
this time 1: is applied a second time, the Spin packets refocus in the -y
direction and this buildup of magnetization is known as the Spin echo,
primary echo or Hahn echo. The vector scheme for the two pulse
experiment is described in Figure 3.12.

The echo decay trace features the integrated intensity of the echo as

a function of the spacing between the pulses. Fourier transformation of

 

80

 

.Eofiiomxo 2mmmm $39N 2: How ofiozum 888/ "mad waswmm

 

 

Soc 2:3
com—amm b.3838

    

 

 

o Eva
a 35508::
E
\ \ /
> \
/ \
/
x
8:: DEW—m
map—:88

 

 

81
the time domain trace allows one to Observe the frequencies easier. The

decay is not monotonic since the decay is modulated by interactions with
nearby magnetic nuclei. The electron spin packets relax via a T2 or TM
(phase memory time) relaxation process, the time it takes for the echo
amplitude to decay to 1 / e of its initial value. If the echo amplitude decays
exponentially, T2=TM. This relaxation time is generally short thus the
echo and modulations decay very rapidly.

In a 3—pulse experiment, the pulse sequence is changed slightly. In
this case a 1: / 2 pulse is followed by a time 15, then another 1t/2 pulse occurs
to flip the magnetization into the -x direction. After a time T, a final 1t/2
_ pulse occurs so that the magnetization vectors are in the xy plane but they
are dephased with frequencies i a). After the same time T the spins refocus
and the magnetization vector is aligned along the -y direction yielding the
Spin echo or stimulated echo. The pulse sequence schemes for the 2—pulse
echo modulation and 3-pulse echo modulation is Shown in Figure 3.13.

The 3-pulse echo decays via a T1 mechanism.
Nuclear Modulation Effect

The inhomogeneous broadening that is required for the spin echo
effect to occur can mask the hyperfine structure in the EPR Spectrum
resulting in a loss of resolution. The decay is not a monotonic decay but

instead is modulated by the hyperfine frequencies. To understand better

 

 

[1 LA ._
AWL».

Figure 3.13: ESEEM pulse schemes for the
A.) 2-pulse and B.) 3—pulse experiments.

the origin of these modulations, we turn to the classical description of
nuclear modulation. Consider a four level system with S=1/2 and I=1 / 2,
Figure 3.14. The states are mixed by anisotropic hyperfine interactions
therefore all four transitions can be induced by a single microwave pulse.
Branching occurs as a result of microwaves inducing transitions
beginning at one energy level but ending at a different energy level. If the
system were isotropic, only the allowed EPR transitions 1-4 8: 2-3 would
occur, but because of the anisotropic nature of the interaction, the nuclear
spin states are mixed and the semi-forbidden transitions a 8: d are
allowed to some extent. Short microwave pulses yield a large frequency
spread, thus all four transitions can be excited coherently. After the first

it / 2 pulse, the magnetization is split into many components with different

83

 

  

 

 

 

Z
after a time T:
/
/
|1> Y \ (no
(eon—(1)1):
(Doe X
l2> Tc
‘t v
(01 0’2
V l3>

 

 

 

 

V l (”B“)

 

E(’c)=a + b cos (0131+...

  

(wz—wl )1:

 

O)2—(1)1=0)B

Figure 3.14: Nuclear modulation effect for the 2-pulse
echo scheme. The evolution of the spin packets is
shown after the first n/ 2 pulse. The first two terms of
the modulation function [E(1:)] are shown.

 

84
resonance frequencies. Assume a precesses at the frequency of the rotating

frame and 17 does not. After the II/ 2 pulse and during a time I, b starts to
dephase with respect to the rotating frame. After the II pulse, a is inverted
to the -y direction but because of branching, a second component is
formed with frequency 002', from a. The original 12 component will refocus
as usual after a time I after the TC pulse. The projection of the
magnetization of the b’ vector onto -y is given by cos(032-(I)1)I thus it will
not contribute fully to the echo. The same is applied for spin [1 and all
other combination of Spin packets formed by branching of transitions.
Therefore all hyperfine frequencies are expected to appear in the echo

envelope.
The Density Matrix Formalism

The goal of this section of the chapter is to understand the
theoretical framework and the use of the density matrix formalism
developed by Mims (Mims, 1972a, Mims, 1972b). This treatment is a
convenient method for computing the modulation function of the ESEEM
pattern. The expressions are obtained by partitioning the matrices which
describe the time evolution of the quantized system. This review is not
meant to be a comprehensive treatment and can be supplemented by

quantum mechanics texts (Cohen-Tannoudji et al., 1977, Slichter, 1990). It

85
is recommended that the reader works through the math as many steps

have been left out for simplicity.
The general expression for the 2-pulse ESEEM modulation function

with a dimensionality of 21 + 1 is derived.
E(t) = mo: M“ P: M Q, Mr P, M) (3.31)
In a system described by a wavefunction, w,

MCI/t) = Ecn(qrt)¢n(q) (3.32)

m can be obtained from the solution to the SchrOedinger equation. The

density matrix, p, is defined by,

an = cncm" = <n | p l m> = <4)n | p I ¢m> (3.33)
where p is the density operator. The physical observables are determined
by,

<M> = Tr{p,M} = Tr{M,p} (3.34)

The density matrix can now be deduced by implementing the equation of

motion.

dp/dt = i/hIp,aeI (3.35)

therefore the density matrix can be rewritten as,

p = e(-i.%t/h) 9(0) edgft/h) (336)

 

86
In ESEEM, the hamiltonian, 56, describes the interaction of the static field

(3(0) and the resonance field (3%),
.96: .760 + $1 (337)

To calculate the echo signal, E, Eq. 3.31 must be integrated to correlate the
final density, pE, with the initial density, p0. Therefore,

E = n Tr(p5£.) (338)

where n is a proportionality constant. All of the matrices in the general
expression of the modulation function of the 2-pulse ESEEM are Shown

below:

elWat 0 iwct 0
PI = . QI = e
0 elwbt 0 e iwdt
- (3.39)

which come from the time dependent SchrOedinger equation. The general

form of a unitary transformation is given by M = MaIMB where,

M = V u M'l' : v* -u
“11* v” u" v
(3.40)

corresponding to the diagram in Figure 3.15. When the matrices are
multiplied and the trace is taken, as described in Eq. 3.31, Eq. 3.41 is

Obtained.

Emod(I)= I v | 4 + l u | 4 + Iv | 2 | u l 4 [ZCOSOJab’C + 2coswch
- cos(eoab— wcdn - cos(wab + comm] (3.41)

87
Ivl and lul are transition probability amplitudes, which also describe

the extent of which branching of transitions is allowed or forbidden. If
In I = 0 or Iv I = 0 , (this will occur if one transition is fully allowed and
the other fully forbidden) no modulations are present, but an echo will still
be present. To determine the values of lvl and Iu I, the transformations
can be described as rotations of the electron-nuclear coordinate system,
(Figure 3.16).

What do the values of IVI and lul represent? To understand
this mathematically, solve the hamiltonian matrix with a rotation of the

nuclear xy axis, which eliminates the Iy term.

sea/h = (0112+ 1/2(AIz) +1/2(BIX) (3.42)

By applying the raising and lowering operators, the hamiltonian matrix is
simplified and can be diagonalized by means of the rotation operators,
e'ilyn and e’ilyg. These rotation operators correspond to the
transformation matrices Ma and MB, and can be used to diagonalize the
hamiltonian matrix. The use of trigonometric identities comes in handy

when solving the matrix. The product of I v I 2 I u I 2 is then given by,

Iv I 2 I u I 2 = 1 /4[sin2(n-§)] (3.43)

 

88

 

 

 

 

 

 

 

la>
o:
Ib>
Ivl IvI Iul lul
V V
|C>
B V I
Id> )

 

la> :2 |C>
Ib> z: Id>

la> 2 |d>
Ib> 2 lo)

} on the order of I v |

} on the order of I u I

Figure 3.15: A.) This scheme describes the two
electron levels OI and [3, split by the coupling
with an I = 1 / 2 nucleus. B.) The transition
matrix elements connecting the states are shown.

89

 

 

 

Y
A /(ry ’x
/
HO e\/
/
/

Figure 3.16: Transformation rotation where 0
describes the relationship between the two axes.

I, ma and (03. More

This equation can then be related to the frequencies (I)
algebraic manipulations and trigonometric substitutions using half angle
formulas result in,

Emod(I)= 1 + 1 / 4 ((1)13 / (00,0392 [2coseoabI + 2COS(DCdI

- cos(eoab— mam - cos(a)ab + (Dcd)’t] (3.44)

where ((013/ mammz is the modulation depth parameter, k. This term B
within k contains in it the dipolar component of the hyperfine interaction.

In addition,

wa = Wab = [(A/2 + wI)2 + B2/2)2]1/2

WB = ch = [(A/Z + WI)2 + 32/2)1]1/2 (3 45)

 

90
This equation is the functional form of the modulation expression. The

expression describing the 3-pulse modulation function,
Emod(I+T)= 1 - (2031232/ mabzmcdzl IsinzwabI/Z [(l-cosmcd(I + D]

+ Sinzmcd‘t/2[(1-COS(I)ab(T+T)]} (3.46)

It can be seen that if the nuclear zeeman interaction, (01, is equal to the

hyperfine interaction, then the maximum modulation depth will occur.
Note also that there are sum (mab + (Bed) and difference (coab— coed)
frequencies that do not appear in the modulation function for the 3-pulse

modulation function (Mims, 1972b).
EPR Instrumentation

cw-EPR

The first detection of an EPR signal was in 1945 by the Russian
scientist, Zavoiskii. The effect was known for many years, but the
technology was not developed until World War II and the development of
radar. Upon the arrival of microwave technology, components became
available to design and build spectrometers. There are three major
components in a spectrometer: the microwave source, the sample cavity
and the detector. The microwave radiation source is the klystron and it is
housed in the microwave bridge. AS opposed to a conventional light

source, the klystron (resonant source) puts out a narrow frequency range

91
only. Gunn-diodes, an alternate microwave source, have an extended

wavelength range and are more tunable, but they are quite noisy. The
sample cavity in general, is a gold plated silver box (which contains a set
of Helmholtz coils) that helps amplify weak signals from the sample. The
microwave diode detector is used to detect the reflected microwaves which
are then converted to an electrical current. A reference arm supplies the
detector with extra microwave power or bias. Some of the power
originating from the source is funneled into the reference arm, where the
attenuator controls the power level and thus consequently the diode
current, for optimal performance. Other components consist of a magnet,
the Signal processing and signal enhancement electronics and an isolator
which keeps back reflections from coming into the klystron, and separates
the source from the rest of the circuit. The laboratory magnetic field is
modulated by coils inside of the cavity to yield a second AC field. 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 the magnetic field strength. When
the sample absorbs the microwave energy, the Q is lowered since the
samples absorb due to an increase in loss and consequently the
impedance of the cavity. Microwaves are then reflected back into the

microwave bridge (Figure 3.17), resulting in an EPR signal.

 

92

 

Signal Out

A . Detector
Diode

 

 

 

 

 

Reference Arm

 

 

 

 

 

 

 

 

 

 

 

 

Circulator
A. 3
Microwave Source Variable
(Klystron) Attenuator
C‘Wity /\/

 

 

 

Figure 3.17: Basic diagram of the microwave bridge components.

The Michigan State University ESEEMometer

The instrument was built in 1990 by john McCracken. Over the
years there have been some modifications made to the instrument by
Professor McCracken as well as by Dr. Hong—In Lee. Explicit details were
published elsewhere (Lee, 1994, McCracken et al., 1992).

The source for the instrument is a Gigatronics model 610
microwave synthesizer which runs at GHZ frequencies. There are two

pulse channels consisting of a high-speed diode switch and phase

93
modulator. A directional coupler divides the source output so that 10% of

the microwave power is directed to the two pulse arms while 90% is
directed to a reference arm. The pulse widths and phases of each channel
are controlled by a logic box, home built by Dr. Lee, with capabilities of up
to six pulses. The instrument is controlled by a Mac 11 microcomputer
with data collection written in the C (Symantec) computer language.
Sophisticated software for data analysis is written in the MATLAB®
language via a SPARC SUN workstation. The spectrometer is currently
being switched over to an Apple Power Computing 150 microcomputer to
run with LABVIEW® software. The computer is interfaced to a SRS model
SR245 I / O module and a model DC 535 delay generator which controls
accurate timing Signals, the pulses and their spacings.

One of the great things about building your own instrument is the
versatility it can have. This ESEEM Spectrometer currently has the
capabilities of performing 2-pulse, 3-pulse, and 4-pulse experiments. It
can perform Hyperfine sublevel ggrelated spectroscopy (HYSCORE), pulsed
ENDOR, both Mims and Davies, single crystal rotation studies, double

electron-electron spectroscopy.

94

BIBLIOGRAPHY

Abragam, A., 8: Bleaney, B. (1970) Electron Paramagnetic Resonance of
Transition Ions, Vol. , Dover, New York.

Carrington, 8: McLachlan (1979) Principles of Magnetic Resonance, Vol. ,
2 ed., Wiley, New York.

Cohen-Tannoudji, C., Diu, B., 8: Laloé, F. (1977) Quantum Mechanics, Vol.
I 8: II, 1 ed., john Wiley 8: Sons, New York.

Lee, H.-I., Electron Spin Echo Envelope Modulation Studies of Some
Transition Metal Model Complexes, 1994.

McCracken, j., Shin, D.-H., 8: Dye, I. L. (1992) Applied Magnetic Resonance 3,
Pulsed EPR Studies of Polycrystalline Cesium Hexamethyl Hexacyclen
Sodide, 305-316.

Mims, W. B. (1972a) Physical Review B 6, Amplitudes of Superhyperfine
Frequencies Displayed in the Electron-Spin Echo Envelope., 3543-3545.

Mims, W. B. (1972b) Physical Review BS, Envelope Modulation in Spin
Echo Experiments, 2409-2419.

Slichter, C. P. (1990) Principles of Magnetic Resonance, Vol. 1, 3 ed.,
Springer-Verlag, New York.

Wertz, j. E., 8: Bolton, J. R. (1986) Electron Spin Resonance: Elementary
Theory and Practical Application., Vol. , 2 ed., Chapman and Hall, New
York. ‘

 

 

Chapter 4

Interesting Magnetic Behavior of the Electride:
Li+(C211)e'

Evidence for 1-Dimensional Spin Waves

95

96

Introduction

The interest in the paramagnetic films or powders left behind after
rapid evaporation of liquid ammonia from solutions of alkali metals and
cryptands, has lead to extensive studies“. Following this observation, the
pursuit for crystalline electrides with well-defined properties has been long
and arduous. The solutions of interest contain lithium cations
encapsulated in a cryptand [2.1.1] cage, C211, with the remaining
unpaired electrons solvated. Many participants of the Dye group have
studied electrides over the years to try to understand better the elusive
electrons in electrides. Li+ has an ionic radius of 0.6 A and the diameter of
C211 is 1.2 A so one might predict good complexation. Li+(C211)e‘ has a
history'of being very thermally unstable and was therefore very difficult to
synthesize without decomposition. It wasn't until Dr. Rui Huang
mastered this synthesis, that crystals were made and the structure was
determined. With the advent of good crystal growth, it was necessary to
repeat the studies, and here we try to obtain an understanding of the
magnetic behavior and see if a correlation can be made with the crystal

structure. It turns out that each of the other four electrides have very

 

1“For a recent review article of alkalides and electrides, see (Wagner 8: Dye, 1996) and the references therein.

97
different properties from one another, so it was thought that this electride

may also have unique properties. Since the nature of the electron density
distribution is important to the magnetic properties of electrides, EPR

results played an important role.
Previous Studies

The electride, Li+(C211)e', was first studied in 1981 as the residue
obtained by evaporating ammonia from solutions with various ratios of
lithium to C211 (Landers et al., 1981) Initially, the magnetic susceptibility,
optical absorption and EPR properties of Li+(C211)e" were performed on
powders of stoichiometry (Li)x(C211), where x ranged from 0.6 to 2. The
samples were made by rapid solvent evaporation from solutions of Li and
C211 in liquid ammonia at 195 K. These data demonstrated the presence
of at least two major electron-trapping sites in various samples. These
sites were distinguished by magnetic susceptibility data that revealed
either a single peak at ~ 20 K, or alternatively, a broad maximum at 50-60
K. The EPR signal intensity showed that the latter samples contained both
the ”20 K site” and the second Site. The difference in behavior was again
attributed to differences in the mole ratio of lithium. It was not clear
however whether or not a single phase had two electron sites, or if two
different phases were responsible. Figure 4.1 shows the difference in

optical spectra with mole ratios at the extrema of 0.60 and 1.57.

98

Mpml

 

 

Kmox
0.5 -

 

 

 

0.0 i J 1 .

'x'i (cm") ' IO"

Figure 4.1: Optical spectra of Li+(C211)e- from liquid ammonia solutions
of LizC211 ratios of A) 0.60 and B) 1.57. When this ratio is up to 1.15, the

optical spectrum was the same as spectrum A.

99
Synthetic Considerations

There are a few fine points that deserve mentioning regarding the
synthesis of this thermally unstable electride. Most alkalide and electride
syntheses are quite similar in nature, except the solvents and starting
materials change accordingly. They all require specialized glassware and
in this synthesis, a three chamber quartz K-cell is used. The quartz
insures that there is little chance for sodium (natural in Pyrex®) to
exchange with the lithium, resulting most likely in a sodide. The third
chamber was used to dissolve the lithium metal. The other alkali metals
can all be distilled with a torch under vacuum to form a nice mirror on the
surface of the bulb, but lithium must be dissolved. A fine quartz frit is
used between the third, metal dissolving chamber, and the reaction
chamber, to filter out any possible impurities such as iron or lithium
nitrides that may have formed in the glove box. The complexant, C211,
was obtained from Aldrich (98%) and was vacuum-distilled prior to use.
A lithium ingot (under argon) from AESAR (99.9%) was kept in a helium-
filled glove box and subsurface samples were used to provide weighed,
Shiny samples of lithium metal. Initially, MeNHz or NH3, was used to
dissolve the lithium (I personnaly preferred MeNHz). If one was feeling
brave, the third chamber was sealed Off and removed from the cell, but this

was not a necessary step. The dissolved metal was then reacted with the

100
complexant in the first bulb and left to react for a few hours. There was a

trade off in this reaction time as the longer the reaction occurs, the better
the yield, but the greater the chance for decomposition. The MeNHz was
removed followed by several rinses with Mezo to ensure that all of the
MeNHz was evaporated. This was important because a number of lithium
sodides have been made with the solvent MeNHz included in the crystal
structure. A final portion of Mezo was added to the vessel to dissolve the
electride. The second solvent, EtZO, was used to make a saturated solution
and the solution was then poured over to the center bulb containing the

collection fingers. Only about 36 hours were needed to evaporate the
solvent through 2-3 frits. One important point is that the whole
experiment should only take about two and a half days. This will help
minimize the chances of decomposition.

The crystals have a shiny appearance and have either a ”blocky” or
needle-like morphology. This procedure usually resulted in the growth of
crystals up to 0.5 mm edge length when the initial solution was poured
through the frit, leaving behind any precipitate. When precipitate was
formed in the crystal growing chamber prior to distillation, an amorphous
powder with no apparent crystallinity was present, along with crystals.
Moreover, when samples were prepared by rapidly evaporating the
saturated solution, the powdered material was usually produced.

Because this electride is extremely subject to irreversible decomposition,

101 .
the temperature was always kept at or below 223 K during synthesis and

handling. In addition, NMR spectra of decomposed material Showed that
this electride also decomplexes.

One question arises with regard to this synthesis. In a traditional
alkalide/electride synthesis, the stoichiometry is very important, but in
this synthesis, one can change the ratio of Li:C211 drastically and still
make only electride. To date, there has never been a lithide synthesized in
the Dye‘group. The reaction,

Li; ‘— ‘ Li+ + 28'501V ' (4.1)

lies far to the right which would minimize the presence‘of Li' in solution,
a requirement for a lithide synthesis . This equilibrium may be due to the
large solvation energy of Li+. In addition, the relative stability of
crystalline lithides compared to electrides, has been extimated to have a

positive AG° (Wagner 8: Dye, 1996).
Structural Facts

Due to the new synthesis methodology, the source of the two kinds
of magnetic behavior recently became clear. It seems that the properties
and magnetic behavior of the two distinct phases of this electride originate
from one form, the crystal structure, and another powder phase of

unknown structure. The data throughout this chapter will support this

102

 

Figure4.2: Space-filling model of one molecule of Li+(C211)e'.

103
assumption. This electride crystallizes in the orthorhombic crystal

system(Huang et al., 1996) with a = 10.060(4), b: 23.134(8), c = 8.380(4) A
and z = 4. A single molecule drawing of Li+(C211)e" is shown in Figure
4.2. The packing diagram of four unit cells is shown in Figure 4.3. A
visualization program (Dye et al., 1996) was written allOwing one to
envision the empty regions within a crystal by constructing a 3-
dimensional cubic grid. The distance to the nearest van der Waals atomic
or molecular surface is given a number (between 0-255) defining a
corresponding distance. The crystal structure is imported directly by
using Biograf® or Biosym® software and some 8-27 unit cells, where the
van der Waals radii of the atoms are used to devise a packing diagram.
Imagine rolling a sphere down the "halls" of the negative space in the
electride. When the sphere just touches the "wall", that corresponding
radius of the Sphere, and many other spheres down many other "halls", is
mapped out. In other words, the location of a Sphere that would just
touch the atomic surface, is charted. An isosurface routine is used to
display the 3-dimensional contour diagram. To find distance parameters,
the distance number is changed until the feature just disappears to
determine the maximum diameter of a sphere that would just pass
through the channel, or just fit inside of the cavity (Figure 4.4). That
parameter is then used to calculate a real width. Interior details can be

obscurred when a smaller distance parameter is chosen, but it is a more

333%.".
fiel:
33”.?”

. Carbon . Nitrogen
. Oxygen . Lithium

 

 

Figure 4.3: Representation of the packing of four unit cells of Li+(C211)e'.

105

Minor Channel

(8.15A)

  
 

Cavity (4.3 A)-

Major
Channel
(7.19 A)

Figure 4.4: Channel and cavity diagram of Li+(C211)e‘.

106
realistic View of the channel and cavity shape. As a compromise, a larger

distance parameter is chosen resulting in some minor distortions in the
cavities and channels, but the interior view is much mOre apparent.

The crystalline phase contains electron-trapping cavities, each of
approximate diameter 4.3 A, connected in zig-zag fashion along the c axis
by rather open channels of minimum diameter 2.4 A (center-to-center
distance 7.9 A). Each cavity is also connected to next-neighbor cavities,
8.2 A away along c, by channels of diameter 1.5 A. Inter-chain channels
are < 1.0 A in diameter so that the cavity-channel structure is well-
described as "ladder-like". The structure Shows that the excess electron
trapping sites (cavities) are interconnected by zig-zag channels to form an
infinite chain. In addition to being connected to the nearest neighbor
cavity, each cavity is connected further by a somewhat smaller channel to
the next nearest neighbor cavity in the chain. This is of great interest since
the structure suggests essentially 1D magnetic coupling between not only
the nearest neighbors in the linear chain, but also to next-nearest

neighbors.
Properties of Newly Synthesized Li+(C211)e'

The packed powder dc conductivity of Li+(C211)e' from 120 K to
230 K followed semiconductor—type behavior with an apparent band gap

of 0.44 eV (Huang et al., 1996, Wagner, 1994). The 7L1 NMR spectra (Huang

107
et al., 1996, Wagner, 1994) of a number of samples confirm the presence of

two types of samples that have different environments for Li+. NMR
studies of finely crushed crystals of Li+(C211)e’ display an inverse
relationship between the chemical shift and the temperature. The
chemical shift varies from +70 ppm at 170 K to +56 ppm at 230 K. The
percent atomic character of 7L1 due to contact density of the unpaired
electron at the lithium nucleus is 0.16%, obtained by using an unpaired
electron density for the gaseous lithium atom of 1.56 x 1024
e-cm'3 (O'Reilly, 1964). The powder phase of Li+(C211)e' has a different
7Li NMR. The chemical shift shows a linear relationship with inverse
temperature with 0.08% atomic character. The optical spectra of thin,
solvent-free films of Li+(C211)e- obtained by slow evaporation of
ammonia and shown in Figure 4.1, have been reproduced but the origin of
the different spectra is understood better. It now appears that the sample
labeled B (R = 1.57) in that work is what we now refer to as the 'powder'
sample. It Shows a single optical absorption peak at 2.0 um and may have
contained both powder and crystalline phases. Films obtained in the
present work by evaporating dimethyl ether from a solution of the
electride Showed a broad peak at 1.5 um and an extended ”tail” through

the visible. The DSC measurements revealed the onset of decomposition at

about 270 K. The decomposition was very exothermic and exhibited

108
”runaway” behavior, typical of autocatalytic decomposition. No thermal

transitions were observed in the electride between 173 and 270 K.

Brief Magnetism Primer

Since the magnetic moment of an electron is three orders of
magnitude greater than a proton, magnetic effects arise mainly from the
electrons. The unpaired electrons of a paramagnetic system can occupy
certain orbital arrangements and the magnetic behavior as a result of this,
can be described by measuring the magnetic polarization. Various
behaviors are illustrated in Figure 4.5. The magnetic induction, B can be

used to describe the behavior of a system in a magnetic field.

 

 

 

 

 

 

 

 

Figure 4.5: Magnetic flux lines in A) a vacuum, B) paramagnetic substance
in a magnetic field, C) diamagnetic substance in a magnetic field.

109

where ITO is the applied magnetic field strength and MT is the

magnetization. Dividing" both Sides by H0,

B = 1 + 41tM'
H H (4.3)

O 0

where M'/HQ is by definition the magnetic susceptibility per unit volume,

xv. Therefore, Xv = M'/HO is a dimensionless unit. Subsitituting the
volume susceptibility in the equation and knowing the mass of the
material, the molar susceptibility X, can be obtained. There are several
different types of magnetism: diamagnetism, paramagnetism,
antiferromagnetism (AF) and ferromagnetism, to name a few. By
convention, X is negative for diamagnetic substances and positive for
paramagnetic substances. The susceptibility behavior is often studied as a
function 'of the temperature (Figure 4.6). Due to small susceptibilities, AF
materials were originally believed to be anomalous paramagnets
(jakubovics, 1987). Some paramagnetic solids do go through a phase
transition as the temperature is lowered, in which large domains of spins

align with parallel or anti-parallel orientations. When the Spins alternate

 

*After the division, only the magnitude appears after the directional properties of the vectors are factored
out.

110
their respective orientation, they are locked in an arrangement of low

magnetization to produce an AF phase. The characteristic temperature at

which the spins lock into that arrangement is known as the Neél

 

temperature.
X I Ferromagnetic
I I Paramagnetic
I I Antiferromagnetic
| I
l l

 

TN TC
T——)

Figure 4.6: Susceptibility as a function of the temperature for antiferromagnetic,
paramagnetic and ferromagnetic materials. TN represents the temperature at

which the maximum occurs in antiferromagnetic material and TC is the
temperature at which the break occurs in ferromagnetic material.

The susceptibility is derived from the force an applied field exerts on
a sample and it measures the degree by which the measuring field tends
to align the spin system with it. When one refers to the dimensionality of
a system, it is not necessarily the Space dimensionality. The spin

dimensionality arises from the interaction of the Spins of several

1 1 1
interacting ions. It can be defined by the expansion of the exchange term

in the spin Hamiltonian,

at = 21125,. S,+1 (4.4)

and can be expanded for an infinite chain of identical Heisenberg spins

with first and second nearest neighbor interactions,

AA A A
3‘ = 'lezsism ' 212251514

(4.5)

where I measures the strength of the interaction between the spins. A
magnetic linear chain is often restricted to adjacent sites and is a
summation over all of the lattice Sites i and j. This Hamiltonian is
expanded to give,

as = '2] S ((13125jo Blsixij + Siysjyl) (4.6)

Ising found that a system considered infinitely long undergoes
long-range order only at absolute zero (Ising, 1925). Likewise, a
Heisenberg (isotropic) system does not order at finite temperatures. All
known 1-dimensional (1D) systems do, in reality, interact and undergo
long-range order, since interchain interactions become more important as
the temperature approaches absolute zero. There are three different
combinations of OI and I3 and each has its own model to describe the

particular arrangement of spins. The model that is considered in this text

112
is the Heisenberg model. The Heisenberg model has no exact or closed-

form solution for a linear chain Heisenberg AF with 8:1 / 2.
Extrapolations however, can be made to fit the expression (Estes et al.,

1978),

x = 138211—32. [ 0.25 + 0.14995y + 0.30094y2 ]
(4.6)

 

kT 1 + 1.9862y + 0.68854y2 + 6.0626y3

where y = ljl /kT. This equation is then modified to correct for

temperature independent paramagnetism and the "Curie tail".

The spin-Peierls Transition

Most magnetic systems enter a phase of long-range order, such as
antiferromagnetism or ferromagnetism at a particular temperature. When
the system is lowered through this temperature, the transition occurs. If
this system follows an ideal one dimensional model where the
interactions are Short range, order can occur but only if the temperature is
equal to zero (Bray et al., 1983). Quasi one-dimensional systems are those
that have non-zero transition temperatures due to weak interchain
interactions. Exchange coupled Spins on a rigid lattice are best described
by the quasi one-dimensional model. If the lattice is somewhat flexible, a
new type of ordering can occur at low temperatures. This more ordered

transition is called a spin-Peierls transition in antiferromagnetic

113
materials. This transition marks the onset of a progressive spin-lattice

dimerization in a system of quasi-1D AF chains. A uniform AF chain has
been shown to be unstable towards dimerization into an alternating
antiferromagnet (de jongh, 1988). When the temperature is greater than
the onset temperature (TSP), the system behaves as an assembly of uniform
AF chains. When the temperature is lowered below the transition
temperature, elastic distortions in the lattice progress leading to an energy

gap which becomes > 0 at TSP. When T = 0, the energy gap is a maximum.
Suseptibility Data

The temperature and field dependence of the susceptibility were
determined by Dr. Deborah Gilbert, with a Quantum Design SQUID
magnetometer. Li+(C211)e' samples, in a dry nitrogen glove bag at about
200 K, were crushed in a cold mortar, then carefully loaded into Specially
assembled Kel-F® covered buckets. The bucket dimensions were chosen
so that it fit within a plastic straw sample holder and threads were
attached to the bucket to hold it in a fixed position. Samples were
maintained in the absence of air at 223 K or below at all times. The SQUID
measurements of Li+(C211)e', clearly Show a drastic downturn in the
susceptibility as the temperature is decreased below about 14K. A

maximum in the Susceptibility of this sample occurs at around 58 K

114

Figure 4.7: Magnetic susceptibility of A) crushed crystals and B)
"powder" of Li+(C211)e" as a function of the temperature. The solid
line represents a fit by Equation 4.6 modified for the TIP and a
"Curie tail". The inset shows an expansion of the low temperature
region.

115

O: 9.2.»..an«5.
c3 om. oo— cw co 9. cm

hr:__:____Z.—:2:—___::_...L:I_:Z?_:—::_::_:~L:..:PC

 

IllllIllllIlLlllllllllllllllllllLLlJlllllllllIlllllllmllllllllllllllILIIIJJJIlllllllll

B

 

S 2 c. n o
_..tt_...._..IL_..._L
. .Io.o
a n
rind
.1;
a m
loan
a - o... B

 

 

 

IIIII[ITIIIIIIIIIIITIIT7IIIIIIIIIIIIIIIIIIIIIIIIII‘IITIIIIIIIIIIlIlIIllIllIIIIIIIIIIIII

 

 

mqfiun—qq-u—u-qqfi-qd—_-u-d—-q—d—-d-—-udu—ddu--_-——-_—-_——-_-—_———u-_u_

9.
0

ed

N.—

V.

we r:

Kingqndaasns .mIow

G: 33235:.
ov— . on. 8. on co ov ow

b:—.—::_pppb—.:._~:p—:_.::._:L_::__::_:_._::—.b:I—tbh_wht

 

1111

l

 

wean

 

 

 

 

~ujud‘dduJ—J-Jqddddauan.dud—nududddud—djdi—dd_u—uuuuuunj:-—-ud-‘-—-d—uuuu

Kiglgqudaasns .chow

116
(Figure 4.7a). This is consistent with some data obtained previously.

Another sample however showed a similar downturn in the susceptibility
at 14 K, but the maximum in the susceptibility occurred at 20 K (Figure
4.7b), (also similar to data formerly obtained). After carefully scrutinizing
the sample and the preparation, it became evident that these data
corresponded to the crystal phase and the powder phase, respectively. In
reality, the data obtained from the four other investigators over the last 15
years was basically the same as that collected recently. Knowing the
crystal structure and realizing that there are two possible phases has lead
us to the correlation of the presence of "powder-type" and/ or "crystal-
type" phases. The crystalline samples were checked by using X-ray
diffraction before grinding them with a mortar and pestle; thus we were
finally able to determine the properties of the form with known crystal
structure. This also permitted determination of the magnetic properties of
the powder phase, although its structure is not known. It is now apparent
that the synthesis can lead to one or both phases of the solid and that very

subtle differences in the synthesis methods are responsible.
EPR

The EPR data were collected with a Bruker ESP-300E series
spectrometer, operating at X-band. The temperature. was controlled to

within i0.1 K with an Oxford 900 series continuous flow cryostat along

117
with an ITC-4 temperature control unit and a GFs-gas-shielded helium

transfer tube. The g-value was determined by direct measurement of the
magnetic field strength and microwave frequency with an ER-O35M NMR
gaussmeter and an HIP-258 counter which operates at 3-12 GHZ. The
Li+(C211)e' was checked with a small amount of crushed crystals, ~ 5 mg.
The small sample size was necessary to prevent overload of the cavity,
making absolute intensity measurements very difficult.

The EPR spectra of Li+(C211)e' crystalline samples that are finely
crushed exhibit line shapes that depend on the temperature at which the
data are collected. At very low temperatures (from 4-‘10 K) the spectra
have broad, weak, featureless line shapes with peak to peak linewidths
that range from 1.3 to 1.6 G centered at g = 2.0021 (Figure 4.8). At ~10 K, a
shoulder appears on the low-field side of the line and this axial lineshape
feature becomes more pronounced as the temperature is increased,
becoming most well defined at about 25 K. As the temperature was raised

above the spin-pairing temperature (14 K) to 25 K, a 100-fold increase in

signal strength was found. At this temperature, g” = 2.00282 and

g 1.: 2.00246. As the temperature is increased, the two features begin to

coalesce until a single asymmetric line is observed at about 55 K. At and
above the susceptibility maximum at 57 K, the signal was exchange
narrowed to yield a simple derivative shape with g = 2.00274 and a peak-

to-peak linewidth of 0.329 G. As the temperature is raised to about 170 K

118

 

 

 

 

 

 

 

 

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3378 3380 3382 3384 3386 3388
field strength (G)
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3376 3378 3380 ’3382 3384 3386 3388 3390
field strength (G)

 

 

 

 

 

 

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.3 -80001

:

h-t

 

 

l I T I T l l l
3376 3378 3380 3382 3384 3386 3388 3390
field strength (G)

 

 

 

Figure 4.8: EPR spectra collected at 0.04 G/ pp MA, 1.56 kHz MF, 0.200 mW
microwave power, 1.2 ms tc, A) 4.2 K, 2x104 gain, B) 10.2 K, 1x103 gain,
C) 20.5 K, 1x103 gain.

119

 

 

 

 

 

 

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g , I
5—
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g 0 "
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m -
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3378 3380 3382 3384 3386 3388
' Field strength (G)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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3378 3380 3382 3384 3386 3388

Field strength (G)

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e o -- ---

3

.8 '5‘

2 -10-

"32’ 15

"‘ ' I I I I I I
3378 3380 3382 3384 3386 3388

Field strength (G)

 

 

Figure 4.9: EPR spectra collected at 0.04 G / pp MA, 1.56 kHz MF, 0.200 mW
microwave power, 1.2 ms tc, A) 26.9 K, 6.3x102 gain, B) 52.3 K, 2.5x102 gain,
C) 63.5 K, 2.5x102 gain.

120

 

 

 

 

 

 

 

 

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5 .-
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:8
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3378 3380 3382 3384 3386 3388
Field strength (G)

 

 

 

* 2000-

1000‘
0—1
-1000‘

 

-20001
-3000-

 

 

Intensity (arbitrary units)

d

I I I I I
3378 3380 3382 3384 3386 3388
Field strength (G)

 

 

 

 

 

 

 

: El
G
3 1000-
t“
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>x
cl-l
'8 -2000‘
c:
33
-3000
'5 l l l l r I
3378 3380 3382 3384 3386 3388

 

 

Field strength (G)

 

Figure 4.10: EPR spectra collected at 0.04 G / pp MA, 1.56 kHz MF, 0.200 mW
microwave power, 1.2 ms tc, A) 50.1 K, 25x102 gain, B) 17.2 K, 2.5x102 gain,
C) 10.4 K, 1x103 gain.

121
(Figure 4.9), the line shape does not change appreciably, but the intensity

slowly decreases. When the temperature is then decreased, the axial
lineshape begins to form again (Figure 4.10) at a temperature of about 50
K, and at ~23 K the parallel and perpendicular components of the g-tensor
become the most pronounced with the same g-values as reported above.
At ~10 K, only a small shoulder remains and this feature is completely
lost below this temperature. The peak-to-peak linewidth is once again
around 1.39 G. These results demonstrate that the changes in the EPR
spectra are reversible.

Double integration of each EPR spectrum and correction for
instrument gain yields the relative spin susceptibility as a function of
temperature. Such data for the crystalline material and for powder
samples are shown in Figure 4.11. These data show that the spin
susceptibilities have the same temperature and sample dependence as the

bulk susceptibilities obtained from the SQUID measurements.

Pulsed-EPR Measurements

Surprisingly, this electride was able to produce a spin echo, unlike
any of the other electrides. For a spin echo to occur, the cw-EPR line must
be sufficiently inhomogeneous, as is true when there is resolvable

g-anisotropy. The ESE-detected EPR spectrumfi revealed a very large

 

+ The electron spin echo (ESE) detected EPR signal is similar to cw-EPR but there is no field modulation.
The amplitude of a 2-pulse spin echo is detected as a function of the magnetic field.

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3K
7; 3.83506" *3! I: I 3" x B
E 25x106— @888 E a a E
:3 18: m a _
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5 f E] Decrease in temperature
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L5 s—
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g r I I I I T I I
20 4O 60 80 100 120 140 160
Temperature (K)
21‘ 24x106 _ % 9K Increase in temperature
5' 22— E 31016 E Decrease in temperature
3‘ E x
g 20 -—
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8 a. a x
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s 10- a
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m 8—
x x
I I I I I I I I I I
20 4O 6O 80 100 120 140 160 180 200
Temperature (K)

 

 

 

Figure 4.11: Relative intensity of the EPR resonance as a function of the
temperature for A) cruched crystals and B) powder samples. These data
are reflective of the spin susceptibility and can be related to the bulk
susceptibility measured inthe SQUID susceptometer.

 

123

 

echo amplitude

13004

1200 --

1100 —

 

1000—

 

900-—

 

800—

700-

600-

 

 

I I I I I I I I I I
3200 3220 3240 3260 3280 3300 3320 3340 3360 3380

field strength (G)

 

 

 

Figure 4.12: ESE-detected EPR of Li+(C211)e' spectrum collected
at 9.2819 GHz; repetition rate 60 Hz; temperature 4.20 K; 1:180 ns;

 

 

124
spectral width relative to that obtained in the cw-EPR spectrum (Figure

4.12). The lineshape is slightly asymmetric with FWHM = 12 G and is ~85 G
wide. There is no resolvable hyperfine interaction exhibited in this
pattern, consistent with the cw-EPR data. However, since ESE-EPR is
collected in the absorption mode, the flat region of the cw-EFR spectrum is
not reflected in the ESE-EPR spectrum. This shows how broad the
resonance actually is.

Three pulse stimulated echo ESEEM data show fairly shallow
modulations, when a 1: value of 220 ns is chosen (Figure 4.13a). When the
I value is changed to a value that suppresses the proton modulations, the
ESEEM modulations become very weak with a modulation depth less than
6 % of the overall spin echo amplitude (Figure 4.14a). The fourier
transform of each time domain trace is shown in Figures 4.13b and 4.14b.
Spectrum 4.13b shows a strong proton matrix line at about 14 MHZ. No
other assignments can be made as no other peaks can confidently be taken
out of the noise. Spectrum 4.14b shows a very weak peak at the larmor
frequency of lithium, 5.6 MHZ when the proton modulations have been
suppressed. These data suggest that there is relatively strong coupling to

the protons in the cryptand, but very little if any, to the lithium.

 

125

 

1300 . . r , q
1200 I
1100
1000
900

800

echo ampl.

700

600

 

500

 

 

 

 

0 500 1000 1500 2000 2500 3000
time (nsec)

(10
O
-1

 

N N
0 0'1
I ._._L
. 0
I i
' I
I I

—L
0"

 

amplitude
25

 

 

 

I i I i
0 2 4 6 8 10 12 14 16 18 20
frequency (MHz) .

 

Figure 4.13: A) Time domain trace collected at 9.601 GHZ microwave
frequency; 3480G field strength; 1:170 ns; T=40 ns; time 1nc.=10 ns;
repetition rate=6OHz. B) Fourier transform spectrum of A.

1000
900
800
'5'.
8
o 700 .. ............................................................................................... --1
.C
O
0
600 _ ............................................................................................... ..
500 ,.. ............................................................................................. L. . . _
400 1 I 1 1 I
0 500 1000 1500 2000 2500 3000
time (nsec)
2 I I I I I I l I I
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0 . . . . . . . . .................................................................................... _.
3 ......
i
E ..................................................
(I! I
8 10 12 14 16 18 20

126

 

 

 

 

 

 

 

 

 

 

 

frequency (MHz)

Figure 4.14: A) Time domain trace collected at 9.601 GHZ microwave
frequency; 3480G field strength; 1:263 ns; T=37 ns; time inc.=10 ns;
repetition rate=60Hz. B) Fourier transform spectrum of A.

127
Anamolous if-Effect

A Bruker ESP 300E EPR spectrometer equipped with an E-36O DS
ENDOR unit and an ENI model 3200L rf amplifier was used to collect the
double resonance data. While trying to obtain ENDOR data, we quickly
realized that the large signals the instrument was recording were not
"normal" ENDOR spectra. It is useful to look at the energy level diagram
for a system with S=1/2 and I=1/ 2 (Figure 4.15). The spin hamiltonian is

the same as in EPR for such a system,

AA

/\
H/h = 0005Z -(0IIZ +aS I (4.7)

22

where (00 = gBHo/ h and 001 = YHO/ h and it is assumed that g and a are

isotropic scalars. The selectron rules have changed in the ENDOR
experiment, such that AmS =0 and Am1=1. In the experiment, an EPR
transition is first irradiated resulting in a perturbation of the thermal
Boltzmann distribution. The population difference as a consequence,
becomes smaller and the transition is said to be saturated. At this point, a
second rf field is applied coincidently resonant with the nuclear
transitions. As a result of relaxation effects, the EPR resonance is
desaturated with an increase in the EPR signal intensity. This change in

EPR signal intensity is what is detected in the ENDOR experiment.

128

 

 

 

 

 

 

 

Ms MI
/—fi1— 1/2
1/2 1 NMRfrequency
\——— -1/2 '
gBH
“ -l/2
-1/2 1L___/

 

 

 

H (G)

Selection Rules:

AMI = i1
AMS = 0

*— NMR frequency

1/2

Figure 4.15: Energy level diagram describing
the effect of nuclear hyperfine interactions.

 

129

 

 

 

 

 

4 locB>
|aa>3 / »
)1 W24
W23
W.. W/ -2180
>
|Ba>1 V

Figure 4.16: Relaxation pathways in a typical ENDOR experiment.

lines of the order <1 G are not usually good candidates for ENDOR
spectroscopy due to the relaxation properties (Figure 4.16). Given the EPR
linewidths of this electride, it is not expected that an ENDOR resonance
would be observed.

Microwave power saturation studies were performed on this
electride and revealed near saturation at power levels of 25 mW at both 25
K and 55 K (Figure 4.17). The initial ENDOR studies were collected at the
'knee" in the saturation curve. The maximum resolution in the EPR
spectra were found at 25 K, thus initial ENDOR experiments were carried
out at this temperature. When a static field was chosen at the maximum
absorption in the EPR spectrum and sweeping the proton larmor
frequency range, the spectrum did not reveal a typical ENDOR powder
pattern, in fact no resonance was observed. However, in the frequency

limits of 1-10 MHz, 8 very large rf absorption was observed that could not

 

130

 

 

 

 

 

 

 

 

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a E ’3'

meat"

w'ITIII—rilillIIIUII'llIllIfi‘l’IIlTTIlll
2 4 6
Sqare root of microwave power (mw1 / 2)

 

Figure 4.17: Microwave saturation study. The square root of the
microwave power used is plotted as a function of the integrated
intensity of the EPR line. The "knee" in the curve indicates near saturation.

be stabilized at power levels above 70W. As little as SW of rf power was
needed to detect the absorption. A significant portion of the absorption
was below the detectable limits of the rf source of 1 MHz. For laboratory
fields near the low field edge of the EPR resonance, a strong powder
pattern lineshape that resembled the EPR resonance is detected.
Progressive steps of the static magnetic field away from the EPR signal on
either side resulted in an rf absorption that reproduced the EPR lineshape

and was centered at an rf frequency that corresponded to the offset of the

 

131
static field from the EPR resonance. As the static field position is moved

further downfield, the peak position of the ’ENDOR' resonance is shifted to
a higher frequency (Figure 4.18). After a certain point off resonance, the if
is not broadcast effectively, resulting in a depletion of the electromagnetic
radiation in the cavity. This results in a weakening of the resonance, and
eventually, its disappearance. When a static field position on the high
field side of the EPR resonance is chosen, an inverted resonance is
observed with the same tracking characteristics as previously noted
(Figure 4.19). As the static field position is moved further away from the
EPR resonance field, the peak position of the ’ENDOR’ resonance is shifted
to higher frequencies (Figure 4.20) until it becomes undetectable above 45
MHz (low field side) or above 29 MHz (high field side) This effect was
also observed at 4 K and 55 K, and in all cases, the rf lineshapes directly
corresponded to the EPR lineshapes.

The intensity of the double resonance peaks was studied as a
function of the rf power and showed a straight line, log-log relationship
(Figure 4.20) consistent with a one rf-photon process. Thus there are two,
one-photon processes governing this phenomenon. Similar, but weaker,
microwave-rf absorption behavior was also observed for the electrides,
Cs+(18C6)2e' and Cs+(15C5)2e' and the powder of unknown structure,
Na+(C222)e‘ (Ichimura et al., 1996). In addition, weaker peaks were also

observed at 1/ 2, 1 / 3 and 1 / 4 of the fundamental rf frequency. Such

 

 

Spectrum B

Intens1ty (arbitrary units)
J;
I .

 

 

 

I I I I I

I I
3360 3362 3364 3366
Magnetic Field strength (G)

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3358

 

 

 

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3; 10 _

(U

3‘ O —l

'8 -10 -

8

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I I I I
4 6 8 10 12 14

Frequency (MHz)

 

 

 

 

Figure 4.18: A) cw-EPR spectrum of Li+(C211)e' collected at 25 K.
'ENDOR' spectra collected at B) 3360.0 G static field and 25 W rf
power and C) 3358.0 G and 25 W rf power.

 

 

 

133

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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'D a:
5 -4 — .
g. _ Spectrum CI
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3358 3360 3362 3364 3366
Magnetic field strenghth (G)
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e -8-

‘6’ 3 1

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5 -I

 

 

I I I I I I I
6 8 10 12 14 16 18

Frequency (MHz)

 

 

 

Figure 4.19: A) cw-EPR spectrum of Li+(C211)e' collected at 25 K.
'ENDOR' spectra collected at B) 3364.0 G static field and 25 W rf
power and C) 3367.0 G and 25 W rf power.

 

 

134

 

 

 

 

 

 

 

 

log rf power
0.4 0.6 0.8 1.0 1.2
I I I I -
a- 8
26 _
® — 8.6
3K
24 —
22 _ 9e
A 8.4
20 J I“
E 8 8*
V 18 —
.5 83*
3:: ®
8 16 — — 8.2
9* 2K
.34 14 8)
g» " ®
12 - ® 9K 316 If power dependence
91$ 6) peak position _ 3,0
10 -1
®
8 _ ®
8 )K
6 - — 7.8
IE
I I I l I I l l I I I I
6 8 10 12 14 16 18 20 22 24 26 28
shift from EPR inflection (MHz)
Figure 4.20: 8 Plot of the peak position of the 'ENDOR' effect

 

as a function of the dc static field offset converted to MHz.
316 The log-log relationship between the rf
power and the integrated intensity of the 'ENDOR' line.

 

 

Kitsueiut 801

 

135
overtones were also observed in Li+(C211)e', only at high rf power

(between ZOO-300 W) and probably result from harmonics in the rf pulses.
A control experiment was done with concentrated DPPH solutions, and

only a proton matrix line was observed.
ENDOR-Induced EPR (EIE)

In organic free radicals, different radical species may be formed in
solution at the same time. The EPR spectrum of such systems, particularly
when the g-values are close, often consist of a superposition of spectra that
can be difficult to analyze. Since there are fewer lines in an ENDOR
spectrum than an EPR spectrum, the ENDOR will probably exhibit
nonoverlapping signals corresponding to the individual species.
Therefore, the individual EPR resonances can be recorded when a
frequency position is chosen in the ENDOR, and the external magnetic
field is swept. This technique, reported first by Hyde (Hyde, 1965), serves
to separate two overlapping resonances. The EIE experiments were
attempted with Li+(C211)e' and the results are shown in Figure 4.21. The
start frequencies (initial frequency position of the ENDOR resonance)
ranged from 1 MHZ to 25 MHZ. Two peaks appeared with a separation that
was directly related to the change in the start frequency (Figure 4.22). The
peaks were weaker as the start frequency was moved further from the

ENDOR resonance, until eventually, no EIE was observed at all.

 

136

 

 

 

 

25:4
E 20%
E :
5‘ 15; A
c: -I
8 I _
8‘ 10:- A
a: - . A
t; 1 A
a I
13 51 A
_. A
I a
WTWWW
O 2 4 6
Apr(G)

 

Figure 4.21: Start frequency as a function of the separation
betWeen the peaks of the ENDOR-induced EPR.

Analysis of the Magnetic Data

As described above, the packing of the complexed cations in
Li+(C211)e' results in cavities that are connected by rather Open channels
in a zig-zag fashion. Careful inspection of the zig-zag configuration
reveals that each cavity is actually nearly equidistant to its two second
nearest neighbors along the chain with connecting channels that are only
about half as wide. Therefore, one expects 11 (the major magnetic coupling
constant) to result from nearest-neighbors in the zig-zag chains, with a
smaller, yet significant coupling constant (12) from second

nearest-neighbor interactions (Figure 4.23). The distance between cavities

 

137

 

 

H
O
w
ill

 

3.00 MHz start frequencyl

 

  

 

doILousoo
1.1.1.1.1

 

 

Intensity (arbitrary ufits)

T I

I T I T w I
3362 3364 3366 3368
Field Strength (G)

I I
3360 3370

 

 

Intensity (arbitrary units)

 

7.00 MHz start frequencyl

 

10x103 -

 

  

U1
I

O

dn
I

 

 

I I I ’ r I I
3360 . 3362 3364 3366 3368 3370

Field strength (G)

 

 

 

Intensity (arbitrary units)

 

 

11.00 MHz start frequencyl

 

 

I T I I I I
3360 3362 3364 3366 3368 3370

Field strength (G)

 

 

 

Figure 4.22: ENDOR-induced EPR spectra of Li+(C211)e'. The start
frequency represents the frequency position of the ENDOR scan at
which to sweep the magnetic field.

 

 

 

138
in neighboring chains is only 4% larger than that of the nearest-neighbors

within each chain which suggests that no significant inter-chain channels
are expected to exist. One can then speculate that the adjacent chains are
probably nearly magnetically independent of one another. A dilemma
arises if both interactions are AF. If the nearest neighbor interactions align
the spins anti-parallel to one another, this sets up a competition because
now the nearest neighbor interactions are opposed by the second nearest
neighbor interactions. We are unaware of any analytical solution for the
magnetic susceptibility of such a system. Numerical solutions have been
obtained for finite chain lengths, (Biichner et al., 1996, Castilla et al., 1995,
Riera 8: Dobry, 1995, Riera & Koval, 1996). Moreover, extrapolations to
infinite length from exact numerical calculations on finite chains fail to
converge, (Anathakrishna et al., 1976). In addition, second nearest
neighbor magnetic interactions can be complicated . When both
interactions are antiferromagnetic and thus "compete", they tend to
display a wide range of magnetic phase behavior (Anathakrishna et al.,
1976, Bonner, 1985, Biichner et al., 1996, Castilla et al., 1995, Chubukov,
1990, Haldane, 1982a, Hatfield, 1981, Riera 87; Dobry, 1995, Riera & Koval,
1996). However, not many materials with structures that suggest such
interactions have been found (Brown et al., 1979, Chiari et al., 1990, Chiari
et al., 1993, Hase et al., 1993). It seems that the coupling between the

electrons occurs through the channels, thus distance is not the only

 

T 12 T 139 I I
VVV\
I I I - %
JI>>Jz
j 12 T I I
h; / VV\
I I I
Ji<<Jz

FIGURE 4.23: Illustration showing the possible spin
interactions in the zig-zag chains of Li+(C211)e-.

 

 

determining factor (Dye, 1993, Dye et al., 1996). Thus, it is reasonable to
assume rather strong 1D antiferromagnetic coupling between electrons in
adjacent cavities along the chain, weaker coupling between next-nearest
neighbors along the chain, and inter-chain coupling can be considered
negligible. Coronado described a similar behavior as a 1D ”ladder-like”
systems where the chain was a "spin frustrated double chain" (Coronado

etaL,1993)

 

140
Keeping in mind the 1D character, consider the bulk and spin

susceptibility data. The magnetic susceptibility has linear chain
Heisenberg antiferromagnetic (LCHA) behavior ‘with spin-pairing
beginning at 14 K that is complete as T approaches zero. The EPR results
also suggest a spin pairing mechanism with a maximum in the Spin
susceptibility of 57 K in the crystalline sample and 20 K in the 'powder'
sample. These data are in good agreement with the bulk susceptibility
obtained from the SQUID measurements.

LCHA with S = 1, have recently been the focus of many studies.
Inelastic neutron scattering (Renard et al., 1987, Rossat-Mignod et al.,
1990) magnetic resonance spectroscopy (Brunel et al., 1992, Date 8: Kindo,
1990, Date & Kindo, 1992, Kindo et al., 1992) and susceptibility
measurements (Katsumata et al., 1989) have been used to verify the
presence of an energy gap above the ground state, as Haldane conjectured
in 1983 (Haldane, 1983), with much subsequent theoretical support.
Haldane also concluded that one-dimensional LCHAS with S = 1 and S =
1/ 2 (Haldane, 1982b) are qualitatively different, with half integer spins
leading to a gapless spectrum. This initially controversial proposal has
been solidly supported by a solvable model (Affleck, 1989) numeric
studies (Sakai & Minoru, 1990) and experimental evidence (Renard et al.,
1987). Haldane argued that spontaneous dimerization would occur in

S = 1/ 2 systems with competing nearest-neighbor (11) and next-nearest

 

141
neighbor (12) interactions for 12 / 11 _>. 1/ 6. Dimerization can also result as

the temperature is reduced as a result of spin-orbit interactions in
antiferromagnetically coupled chains. As mentioned previously in this
chapter, structural distortions occur to accommodate a spin-Peierls
dimerization (Fukuyama, 1987). This dimerized state, which also leads to
zero susceptibility at 0 K, can be distinguished from Haldane
dimerization, as the latter does not require lattice distortion. A number of
S = 1 LCHAS show excitations which are spin wave-like in nature and EPR
has been used as a direct way to probe the spin states of spin wave modes
(Affleck, 1992,“ Brunel et al., 1992). Both ferromagnetic and anti-
ferromagnetic systems can give spin waves (Figure 4.24). A spin flip
occurs, and the energy of the flipped spin can be distributed to the whole
system of spins. The spin waves at the surface cannot move; they are said
to be "pinned".

The anomalous radio frequency-microwave spectroscopy described
above and the known structure of the electrides suggest anti-ferromagnetic
spin waves. At the very least, this study shows that these electrides have a
dense manifold of energy states in the presence of a magnetic field. The
most striking feature of these results is the narrow conventional EPR
spectrum and yet the ability to excite transitions well below and above the
resonance field with rf frequencies that precisely match the field offset.

This implies the presence of selection rules for the EPR transition that

 

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143
prohibit arbitrary transitions between energy levels. It also demands a

very high density of states as a result of inter-electron coupling such that
strong double resonance absorptions can occur at arbitrary fields (within
limits). Furthermore, this effect was observed with very low microwave
powers (as low as 40 dB) which indicats that saturation is not a necessary
requirement. In essence, two types of electromagnetic radiation are
coupled together to induce this two-photon effect.

The most likely source of a high density of energy levels in these
electrides is the formation of 1D spin-waves. If the ”Curie-tail” in the
susceptibility of Li+(C211)e‘ is due to the presence of odd chains, we infer
from the ~10/o contribution, that the average chain length is ~ 50. This,
together with a distribution of chain lengths would insure a high density
of spin-wave levels. A possible energy level diagram to describe the rf-
microwave effect is shown in Figure 4.25.

The notion that spin waves in ferromagnetic materials could be
affected by a uniform rf field, was discussed by Kittel (Kittel, 1958), and in
anti-ferromagnetic materials, by Orbach and Pincus (Orbach & Pincus,
1959). For this to transpire, the surface spins must experience local
anisotropy that is different from the interior spins. This anisotropy serves
to 'pin' the surface spins and quantize spin wave modes perpendicular to
the direction of the applied magnetic field. Because the

antiferromagnetically coupled electrons in electrides form chains of

 

144

mw photon

 

 

 

 

Figure 4.25: Possible energy level diagram describing the anamolous

If effect. At resonance, a photon, hv, matches the energy level separation.
At lower (and higher) field positions, the rf photon may couple to the
microwave photon to allow the transition.

 

145
considerable length, these spin wave states are band-like in nature and

apparently coupled to the a and [3 electron spin states. Their presence
could be masked in the conventional EPR spectrum by exchange
narrowing of the resonance lineshape. The low rf power necessary to
drive these transitions and the magnetic field dependence of the transition
frequency indicate that the transitions being probed concern the magnetic
moment of the unpaired electron spin. To our knowledge, this report is
the first of its kind, where antiferromagnetic spin waves were excited by
using a uniform rf field. Mattis theorized the type of behavior reported
here for 1D LCHA systems (Mattis, 1965). Studies underway include
'ENDOR' measurements on single crystals of Li+(C211)e' to confirm the
theory regarding the origin of the rf absorptions. We are also modifying
the ENDOR coils so that the rf intensity can be measured accurately across

a variety of frequencies.
Discussion

The electride, Li+(C211)e' has been characterized as a 1D LCHA. We
now find that they show very strong rf -microwave two-photon
absorptions consistent with the presence of rather long chain length spin-
waves. To our knowledge, this is the first observation of this kind for an

S = 1/2 LCHA.

 

146
By using the channel and cavity diagrams, one can relate

qualitatively, the magnetic properties of the electride to the width, length
and shape of their anionic cavities and the channels that interconnect
them (Dye et al., 1996, Wagner, 1994). It is not astonishing to expect the
wave function's excess electrons to extend into the void space between the
cavities in order to minimize kinetic energy. This was illustrated
theoretically for Cs+(15C5)2e' (Singh et al., 1993). Currently, there is no
quantitative relationship between the extent of overlap of the
wavefunctions of neighboring electrons, and the width, length and shape

of the channels.
Conclusions

Although the SQUID and EPR measurements suggest evidence of
gradual spin dimerization, the driving force for this dimerization is not
fully understood. It may be due to a spin-Peierls transition caused by
elastic distortions in the lattice or possibly by competing AF intra-chain
interactions which can contribute to electronically-driven spin
dimerization, as Haldane predicted (Haldane, 1982b).

The spin-Peierls and Haldane dimerizations are both characterized
by a non-magnetic singlet ground state with a finite energy gap. However,
the origin of the two states is quite different. It was noted recently that

small impurities in both Haldane and spin-Peierls materials can have a

 

147
remarkable effect on susceptibility measurements (Ajiro, 1995). High field

magnetization and temperature dependence of the susceptibility revealed
that when the Haldane system, NiC204-2DMIZ (dimethyl imidazOle), was
doped with up to 20% of a nonmagnetic impurity, the Haldane state
survives. However, when CuGeO3, a spin Peierls system, was doped with
only 4% impurity, the spin-Peierls state almost disappeared (Ajiro, 1995).
This suggests that the origin of the Li+(C211)e‘ dimerization could be
determined if doping studies were undertaken.

The negative species in electrides that balances the cationic charges
on complexed alkali cations are nearly-free electrons (Dye, 1990, Dye,
1993, Dye & Huang, 1990, Dye et al., 1996). They are trapped in large
cavities and interact with one another through open connecting channels
(Dye et al., 1996). The geometry, length and diameter of these channels
correlate well with the effective magnetic dimensionality and coupling
constant. The susceptibility data and fits to Equation 4.7 shown in Figure
4.6 and the spin susceptibilities from EPR intensities (Figure 4.11) show
that spin-pairing becomes pronounced below about 10 K and that the
susceptibility goes smoothly to zero at 0 K upon removal of a small Curie
tail contribution. The fit of the data by the 1 D Heisenberg model with a
single value of] is excellent above 14 K for both types of sample. The low
temperature drop in the susceptibility is qualitatively like that of a spin-

Peierls transition, which is a manifestation of the intrinsic instability of a

 

148
1D Heisenberg chain toward dimerization. However, competition

between nearest-neighbor and next nearest neighbor interactions may also
contribute to the dimerization. The "frustration" could be relieved by
redistribution of the electron density within the cavity channel framework
to yield stronger pairwise interactions through the major channels, which
would decrease the interaction with next nearest-neighbor trapped
electrons.

The fact that two phases exist is not unprecented (Dawes et al., 1991,
Wagner et al., 1993). The rf effect was extremely weak when the powder
sample was tested. The signal probably originated from a very minor
contribution of crystalline material and this change in packing can
drastically affects the electron-electron coupling (Dye, 1993). The
powdered samples of Li+(C211)e' grow in such a way as to decrease the
effective value of -I 1/ k3 from 50 K to 18 K, probably by altering the size of
the inter-connecting channels. The differences between the two phases is
also reflected by differences in the 7Li NMR chemical shifts. The reason
why spin dimerization occurs at the same temperature for both phases is

puzzhng.

 

149

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Kindo, K., Takeuchi, T., Yosida, T., 8: Date, M. (1992) Physica B 177, High
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153

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Studies of Cs+(18-crown-6)2e', 3982-3984.

 

Chapter 5

ESEEM Studies of Electron Trapping in
Csz+(21C7)2Na-2: Mapping the Electron
Density

154

 

155

Background Information

Until the year 1974, it was thought that alkali metals could only
have the +1 or 0 oxidation state in the solid phase. It is now well
established that alkali metals can in addition have a ’1 oxidation state in
the solid phase. The alkalide reaction is driven thermodynamically by the
encapsulation of the Cs cation in this case, by a crown ether such as 21C7.
When an equimolar amount-of Na metal is added under anaerobic

conditions, the reaction is as follows:

(\Q (\o/V
C5(m)+Na(m)+<: 0? .___ ’Q: CS 07 Na (51)

W6 <43?)

As was addressed earlier in Chapter 1 of this dissertation, there has been

 

some disagreement as to whether the valence electron of the cation resides
near the nucleus, or if the electron is trapped and occupies the anionic
position. Evidence from our group has agreed with the latter of the two, in
particular, the F-center model. However, most experiments have failed to
answer this question definitively. EPR is one way in which one can probe

the location of the electron density in the electride. During the synthesis of

 

156
Cs+(21C7)Na', the alkali metals and complexants are dissolved together

resulting in an equilibrium between the alkali metal anions and the

solvated electrons,

M+ + 2e"

 

M‘ (5.2)

solv

Electrons then become trapped in the alkalide crystal, as in the F-center
model. The degree of "doping" in the sample depends heavily on the
synthetic procedure. The defect electrons that occupy the anionic
positions are present in small concentrations isolated from one another,
avoiding the problem of an exchange narrowed EPR signal. The driving
force behind these experiments is to obtain information regarding the
nature of the trapped electrons, and to determine whether the electrons are
trapped interstitially, or reside at or near the nucleus of the alkali metal.
While trying to synthesize new alkalides and eventually new
electrides, the choice of complexant is of absolute importance. Ideally,
tight binding of the cation in the complexant can lead to a relatively stable
alkalide perhaps eventually at room temperature. Na+(C222)Na' was the
first crystallized alkalide (Tehan et al., 1974) and it is stable at room
temperature for a couple of days making the possibility of synthesizing
room temperature stable alkalides quite promising. However, since then,
there has not been such a stable alkalide or electride synthesized. The

cesium cation fits very snugly between two 18C6 molecules to form either

 

157
an electride (Dawes et al., 1986) sodide (Dawes et al., 1989) or ceside

(Huang et al., 1987), depending on the respective quantities of the starting
materials. The crown ether 18C6 has a hole diameter in the range of 2.6-
3.2 A while the slightly larger crown ether, 21C7, has a hole diameter of
3.4-4.3 A (Pedersen, 1970) Where two different models were used to
calculate these extremes. Since the ionic diameter in a crystal of Cs+ is
3.34 A, (Pedersen 8: Frensdorff, 1972)'it makes sense that it takes two 18C6
molecules to sufficiently encapsulate the cation. The cesium cation
should fit better in the larger 21C7 complexant and in fact it does, but not

in the conventional way.
Synthesis of Cs+(21C7)Na'

The synthesis of alkalides was already explained in great detail in
chapter 2, but there are a few points worth noting for this particular
alkalide. The complexants initially need to be purified and 21C7 is a very
viscous complexant, therefore it requires a temperature of about 200°C
under anaerobic conditions to sublime. Approximately equimolar
portions of Cs and Na metals were deposited into one bulb of a two-
chamber K-cell (Figure 2.2). To increase the yield and to minimize doping
effects, a slight increase in stoichiometric amount of Cs was added to the
other bulb. When doped material is desired, the stoichiometry changes

such that Na is deficient. This allows the extra electron from the Cs cation

 

158
to become trapped in the anionic voids that cannot be filled by the sodide.

This also increases the number of paramagnetic centers in the material.
MeNH2 was purified over NaK alloy, then distilled onto the complexant
and reacted swiftly. When confident that nearly all of the 21 C7 had
dissolved, the solution was poured over to the metal mirror and was
allowed to react for at least ten hours. It was found that changing this
reaction time altered the yield significantly so the reaction was usually left
overnight at -78°C. Freshly purified EtzO was added to the solution as a
co-solvent to make a saturated solution and the mother liquor was then
poured through the frit to the chamber containing the collection fingers.
Other solvent systems were attempted, e.g. MezO and TMA, but this
combination did not allow for good crystal growth. Crystals were grown
in a temperature cycling bath at -50°C initially, and slowly cooled to a
temperature of -70°C over a period of about 2 days. The sharp needle-like
dark red crystals that remained were then washed with fresh EtZO, the
solvent was removed completely and the crystals were collected and

stored in liquid nitrogen until further use.
Structural Information

A crystal of dimensions 0.1x0.2x0.4 mm3 was used to determine the
crystal structure. A crystal system of triclinic was determined (Huang,

1994) with one molecule per unit cell, where a=10.469 A, b=10.032 A,

 

159
c=12.708 A, oc=90.919°, B=73.385° and 7407.453". The volume of the unit

cell and the density of the crystal were found to be 1216.5A and 1.267
g / cm3, respectively. This is the first alkalide without any symmetry
elements, although most of the alkalide structures are of low symmetry.
Strictly speaking, the empirical formula for this compound is
Cs+2(21C7)2Na'2. The ORTEP diagram is shown in Figure 5.1 where the C31-
O distances range from 3.18 to 3.55A, and the Cs2-O distances range from
3.10 to 3.48A. This indicates that the Cs cations are in non-symmetric
positions in the crystal. The Csl-Cs2 distance is 5.28A and the two Cs-Na
distances are 4.48 A and 4.44A. This implies that a contact ion pair is
present, consequently, this molecule is a good candidate for EPR analysis.
Each Cs cation is bonded to seVen O atoms from one of the 21C7
molecules, and one O atom of the other 21C7 molecule, making the Cs
cation eight coordinate and connects the two Cs+(21C7)Na' complexes
together. The O7-Csl(2)-Ol 16 bond angles are around 74° while the CS1-
O7(116)-C52 bond angles are around 105°. These atoms form a nearly
symmetric parallelogram in the crystal structure. Other pertinent
distances within the crystal packing include Cs-Cs, Cs-Na and Na-Na of
8.90, 7.67 and 7.18A, respectively. Two different perspectives of the

packing of this complex are shown in Figures 5.2 and 5.3.

 

160

 

Figure 5.1: Ortep diagram of Cs+2(21C7)2Na'2.

161

 

. Carbon . Oxygen . Cesium

Figure 5.2: One view of four unit cells of Cs+2(21C7)2Na‘2.

162

. Carbon . Oxygen . Cesium

Figure 5.3: Alternate view of the packing of Cs+2(21C7)2Na‘2.

163
Physical Properties of Cs“2(21C7)2Na'2

Since this is the only alkalide to date with two cation-anion contact
ion pairs in one molecule with two closely separated cations, it was
important to determine as much experimental data about this complex as
possible. One might expect the charge to transfer from Na' to the Cs“. The
properties ascertained include optical spectroscopy, NMR and differential
scanning calorimetry (DSC), as well as EPR methods which will be

reported separately in this chapter.
Optical Spectroscopy

The solvent evaporated optical spectrum (Huang, 1994) of this
alkalide revealed a peak at 650 nm typical of Na- (Figure 5.4a) This
indicates that an electron from the 3s2 ground state is excited into the 383p
state. These data also suggests that there is no compelling difference
between the two different Na' atoms found in the crystal structure.
However, the fact that the absorption is broad may indicate that two
sodide peaks have coalesced into one broad feature. The data were found

to be temperature independent in the range of 153 to 253 K.

 

164

1.3

 

1.2—

1.1 -

0.9 ".
0.8 '-
OO7 —

O..-

Absorbance

0.5-1

0.4-

0.3"

0.2-

0.1 -

 

 

 

 

0.3 0.5 0.7 0.9 1.1 1.3 1 .5

(Thousands)
WuvclcngIh(Microns)

7"1—l’"‘t__l 1 I I I r I I I I I I I I ' I I

300 200 100 O ~100 -200

Figure 5.4: A) Optical spectrum of the solvent eva

IIIUjTIrTfirTIIiTI'l-

-300 ppm

porated film of

Cs+2(21C7)2Na'2 in MeNHz. B) 23Na static NMR spectrum of

Cs+2(21C7)2Na'2 powder.

 

 

165
NMR

Both static and MAS-NMR data were collected (Huang, 1994) on
crushed crystals of the alkalide. Two temperature independent peaks
were observed in the 133Cs NMR at -28 and +60 ppm, indicating that the Cs
cations are chemically and magnetically nonequivalent. These data along
with the range of Cs-O distances, render the Cs cations chemically
nonequivalent. The spectra can be found in Figure 5.5. The 23Na NMR
reveals one single peak located at -56.3 ppm (Figure 5.4b). This peak
position is in the usual region for sodides, about -60 ppm. A temperature
dependence of the chemical shifts showed no dependence in the range of
173 to 263 K. The resonance has a full width half maximum (FWHM) of

about 40 ppm which is consistent with the assignment.
DSC

Differential scanning calorimetry (Huang, 1994) gives stability
information about the compound under observation. A temperature ramp
of 5°C/ minute was chosen and displayed the onset of decomposition at
120°C. The AH associated with that transition was calculated to be -168
kJ/mol. There was also a small irreversible endothermic transition at
-68°C with AH=5 kJ/mol. This may have been due to decomplexation,

where the cation and complexant break bonds between them but the

166

 

 

 

'rfiIIYTIYIYITYTYTYYIT‘IYTTYIYY'YTYTITj—TFITTFYITIFTIIYIIITI'TYIIlYIIIIYIT
600 500 400 300 200 100 0 -100 -300 -500 00m
ppm

Figure 5.5: A) 133Cs static NMR spectrum recorded at 200 K. 133Cs MAS-

NMR spectrum recorded at 200 Kat B) 5 kHz spinning speed and
C) 10 kHz spinning speed.

167
molecules remain intact without decomposing. This was evident in

solution to occur at about -49°C. It appears that this compound is pretty
stable in the solid state possibly because of the highly extensive
coordination between the Cs cations and the O atoms of the crown ether.
In addition, the Cs+—Na' ion pair may be responsible for some added

stability to the complex.
Summary of the Physical Properties

The interesting feature of two contact ion pairs on both sides of the
Cs cations, gives intrigue to the Csz+(21C7)2Na2' complex. The large
complexants are usually ’soft’ or flexible and this presents difficulties in
single crystal growth possibly resulting in disorder. Pedersen (Pedersen,
1967, Pedersen, 1968) stated that the cation size and the cavity size of the
complexant are important variables in judging the stability of
complexation. During crystallization, disorder can be caused by a
packing irregularity or by thermal motion. Although the crystals were not
very big, as crystal sizes of alkalides go, the structure was determined and
many of the physical properties resolved. There were no indications of
charge transfer from the 23Na NMR data or from the Na' peak of the optical
Spectrum; thus, it appears that there is no significant difference between

well isolated Na anions and those which are near the cation.

168
Pulsed and cw-EPR experiments

Continuous wave and advanced EPR methods were chosen to probe
the electronic environment and to map the electron density, since the
crystal structure affords a well understood geometry. Moreover, the
question regarding the Vicinity of the electron density is addressed by
using advanced EPR methods. Crushed crystals of Cszl(21C7)2Na2' were
loaded into an EPR tube as described earlier. Since alkalides are
intrinsically diamagnetic, the presence of defect electrons is relied upon.
The concentration of defect electrons cannot be measured directly, but by
changing the stoichiometry of the starting materials, a relative estimate
can be made. The cw-EPR spectrum is shown in Figure 5.6a. The data
were collected on a Bruker ER 200D spectrometer operating at X-band. The
EPR signal has an axial g-tensor with g”: 2.145 and g _L = 1.996. The
perpendicular feature is split into six lines with a coupling constant of
10 G. The microwave power saturation study shows saturation occurs at
relatively low power (.2 mW) at both 4 and 50 K. The ESE-detected EPR
spectrum displays a broad 550 G wide asymmetric eight line pattern,
indicating one cesium nucleus is coupling to the paramagnetic center
(Figure 5.6b). The tau value used was 250 ns, a resonant frequency of
10.011 GHz, repetition rate of 50 Hz and 45.0 dBm microwave power. We

were most interested in determining the distance between the Cs+ and the

169

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50-
'U
o
e o—
O
m
.0
co
5
3
o
o.
-50—
-100-
I —I I I I I
3100 3200 3300 3400 3500 3600
field strength ((9
f I I I I I T I I
1260 I- ..
- B u
0)
U h
j I!
4..)
-H - -I
H
O -
E .—
(O
0 ~
I:
(J " —.
(D
.. f/J "I
J I l I I I J I J
3100.0 4100.

field strength (G)

Figure 5.6: A) CW-EPR spectrum collected at 2.08 uW microwave power,
9.4716 GHz microwave frequency, 5.2 Gpp modulation amplitude, 100
kHz modulation amplitude, 5x105 gain and 3.8 K. B) ESE-EPR spectrum
collected at 4.2 K, 250 ns I, 50 Hz repitition rate, 45.0 dBm microwave
power, 10.011 GHZ microwave frequency.

170
trapped electrons, to see if they do in fact occupy the anionic vacancies.

Often there are weak superhyperfine interactions between the
paramagnetic center and the nearby magnetic nuclei‘that are unresolved
due to inhomogeneous broadening. The 2-pulse ESEEM data reveal a
textbook example of peaks due to the larmor frequency as well as the
combination line at twice the larmor frequency (see modulation function
for a 2-pulse experiment in chapter 3). In Figure 5.7a, the time domain
trace reveals a weak modulation pattern that dampens modestly. The
fourier transform of this trace, 5.7b, shows a sharp peak at 1.87 MHz
assigned to the Cs nucleus, at the field strength of 3324.0 G. In addition,
the negative going peak at 3.56 MHz (twice that of 1.87) is the sum
combination line of cesium . Since there are many protons in the crown
ether, it is expected that a proton matrix line would also be present at the
larmor frequency of protons, 14 MHz. Note also the sum combination line
at 28 MHz. The 3-pulse data collected at several different 1 values yield
the same peak positions, just different intensities of the lines depending on
the 1: value. Figure 5.8a,b shows the 3-pulse data at 9.282 GHZ. The peaks
at 1.830 MHz and 14.217 MHz can once again be assigned to cesium and
protons respectively. These data suggest that both cesium and protons
couple to the unpaired electron, but to make a more definitive assignment,
it is necessary to change the frequency of the resonator. By changing the

resonator and therefore the frequency, the new frequencies of the peaks

 

echo nmpl.

 

 

 

 

 

 

 

 

 

 

 

 

J l 1
00 500 1000 1500 2000 2500 3000
time(nsoc)
5 I I I I I I
.3 - I B
1.873MH2 '_
4... ....................................................................................
3" ..
14.07MH2. ..
. 2... ..... , ..
3
5
O.
E
C 1..
0"
-1I-
'20 5 10 15 20 25 so as
"OQWMYNHII

Figure 5.7: A) 2-pulse ESEEM trace collected at 9.282 GHz microwave frequency,

3324.0 G field strength, 180 ns 1, 10 Hz repetition rate and 4 scans collected. B) fourier
transform spectrum of trace A.

 

 

mm.
3

 

 

 

 

 

 

 

 

      

 

 

   

 

5m .. ....................................................... ........................................ ..
m .. ....................................................... ............................ , ........... a
mo . ....................................................... ........................................ T
o . ........................................................ ................................. Q ..... .
-m 1 1 1 fl 1 L
O 2000 4000 soon moo 1m 12000 «000
mm
3.5 T 1 U 1 _r j 1 I
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2.5 d
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1.5 ‘
I "‘ q
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05 - I
o l 1 1 4 J 1 L L
0 2 4 6 8 10 12 u I. 8.

Warm

Figure 5.8: A) 3-pulse ESEEM trace collected at 9.282 GHz microwave frequency,

3324.0 G field strength, 180 ns 1:, 10 Hz repetition rate and 16 scans collected. B)
fourier transform spectrum of trace A.

173
should lend support to the assignments made. Figure 5.9a,b exhibits the

effects from increasing the frequency to 11.358 GHz. Once again both the
cesium and proton nuclei are represented by positive and negative peaks
at the proper frequency corresponding to the change in field strength and
the line positions in the three pulse experiments were assigned to cesium
and protons again.

It may seem as though no additional information can be gained by
these types of experiments; however, it is the time domain trace that holds
much of the information. Simulation of the time domain 3-pulse trace
should give information regarding the distance between the Cs nucleus
and the paramagnetic center. The simulation program that was used was
developed based on a perturbation method by Shubin and Dikanov
(Shubin 8: Dikanov, 1988) for I>1 / 2 systems. This treatment assumes the
anisotropy and the nuclear quadrupole interaction are much smaller than
the nuclear Zeeman interaction. The perturbation Hamiltonian is
diagonalized and the Eigenvalues are solved. The modulation function
described in chapter 3 can be expressed as, (Eq. 5.3),

Emod(t,T) = l-kIsinzl /2(0)1:(l-cosu)['c-I-T]))} (5.3)

where the modulation depth parameter, k = (B/(n)2 and B is the dipolar
component of the hyperfine interaction. Since the dipolar part has a 1/ r3

dependence within it, the modulation depth then goes as 1 /r6! Because of

 

 

 

 

 

 

 

 

 

 

J 1 I ‘1 A

b

 

0 3 i '5 a 25
mm

Figure 5.9: A) 2-pulse ESEEM trace collected at 11.358 GHZ microwave
frequency, 4068.0 G field strength, 180 ns t, 10 Hz repetition rate. B)
fourier transform spectrum of trace A.

175
this strong dependence, there is a lot of weight put on the internuclear

distance, as the modulation pattern can change drastically as r changes.
This is illustrated in Figure 5.10. Table 5.1 demonstrates the relationship
between the time domain trace and fourier transform spectrum.

Table 5.1
Comparison Between the Time Domain and the Frequency Domain

 

 

 

 

 

 

 

 

TIME DOMAIN FOURIER TRANSFORM
period corresponds to frequency

amplitude of modulation corresponds to amplitude of frequency
damping of modulation corresponds to linewidth of peak I

 

For large values of r, one would expect small anisotropy, modest
damping, and narrow lines while small values of r should lead to broad
lines, deep modulations and fast damping. In addition, the modulation
depth is a function of the nuclear spin and goes as I(I+1). Since Cs has a
nuclear spin equal to 7/ 2, one might expect deep modulations, but since r
is large, the modulation depth is weakened. The modulation depth is
about 10% of the echo amplitude and Figure 5.11 shows the best
simulation, with an internuclear distance of 4.9 A. The fourier transform

(Figure 5.11b) displays a frequency at 1.87 MHZ which is consistent with

176

 

 

 

 

 

100 3CKXUCK23$223CX;SCZICCK;JCLLLII,:
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L‘Al‘LLLlLJLllull.lLLLLleuLLLUlJ‘j‘lu‘AlLLLAIAlllllllljl
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4.1 lJAAAlJALLlJAAA‘ LLLIAAAJJJLAA‘ J 4' l

 

 

 

tau4T(usecl

Figure 5.10: Simulations of the time domain trace from the 3-pulse ESEEM
experiments of Cs+(21C7)Na' at 9.282 GHZ, and an internuclear distance
parameter, r, of A) 6.0 A and-B) 4.0 A.

177

 

 

mv‘fiVVV'Ufo'vvvv'UV'V'VVYVtvvvf‘YV'U'VV'VIVV'V"1' I """"
LL! <
o A
:3 L .
F. 0
j =409A 1
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01234A‘5678910111213

tau+T(usecI

 

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)

> | c

’ " "" I
A A A A A

‘1‘AAAAJJALJIAAAJJLLL‘ALLAJJJJAIJLJ‘ALA

 

 

0

Frequency (MHz)

Figure 5.10: A) Best simulations of the time domain trace from the 3-

pulse ESEEM experiments of Cs+(21C7)Na‘ at 9.282 GHz, with an
internuclear distance parameter, r, of 4.9 A. B) Fourier transform of A.

178
the assignment made from the ESEEM data.

Discussion

It is clear from the EPR results that a cesium nucleus is interacting
with a trapped electron. The Cs-Na distances are 4.44 and 4.48 A as
determined from the crystal structure, which is slightly smaller in
distance than that obtained from the ESEEM studies. However, these data
still lend support to the F-center model and argue against Golden and
Tuttle’s conclusions as described in chapter 1. They claim that in
Cs+(18C6)2e', the valence electron is in the near vicinity of the Cs+° It is not
stretching the imagination to suggest that the electron occupying the
occasional anionic vacancy in Cs+2(21C7)2Na'2 does not remain in one
position but instead is smeared over a large area thus yielding longer
electron nuclear distance. If the electron density were in close proximity to
the Cs nucleus of Cs+2(21C7)2Na'2, the modulation pattern would appear
drastically different. These ESEEM results are thus the most definitive
evidence that the electron does occupy the anionic vacancy of the alkalide.
Although electride samples produce a strong free induction decay (FID)
corresponding to a long value for T2, no spin echo is observed. This is
consistent with the homogeneous line that typical electrides produce.
Currently the electride of this alkalide has not been successfully

crystallized, and there is no guarantee that the geometry would be

179
isostructural to that of Cs+2(21C7)2Na'2. By using the visualization

method (Dye et al., 1996), the channel and cavity diagram for
Cs+2(21C7)2Na'2 is shown in Figure 5.12. Note the large channels in one
direction (2.2A) with a narrow connection (1.2A). This picture is
consistent with a slightly longer simulated distance between the unpaired
electron and the paramagnetic center. The "hypothetical" electride may
not have the same channels and cavity structure. In an effort to synthesize
the "hypOthetical'f electride, attempts were made to reduce the
stoichiometric quantity of Na+, increasing the doping level until crystals
were made with no Na added. Unfortunately, when 'a Idefic'ienCy of > 25%
Na is attempted, .c‘rystal formation does. not occur, so until our
crystallizatipnmethods are improved, this'electride will have to remain

“hypothetical".

 

I It is worth noting that all of the spectroscopy was collected on various samples from different
preparations. Some samples were doped heavily, while others were not. The end result was
the same in all cases except that the signal intensity changed according to the doping level. A
synthesis prepared from the stoichiometric ratio of CszNaz21C7 of 1:1:.75 resulted in a 25%
deficiency of Na available to accept the unpaired electron, therefore results in a highly doped
sample.

180

  
 

Figure 5.12: Cavity and channel diagram of Csz+(21C7)2Na2'
revealing the anionic sites that the trapped electrons most
likely occupy. The channels reveal the pathway that the
electron has to move from anionic site to anionic site.

181

BIBLIOGRAPHY

Dawes, S. B., Ward, D. L., Fussa-Rydel, 0., Huang, R.-H., 8: Dye, J. L.
(1989) Inorganic Chemistry 28, Crystal Structures and Properties of Two
Sodides and an Electride, 2132-2136.

Dawes, S. 3., Ward, D. L., Huang, R. H., 8: Dye, J. L. (1986) Journal of the
American Chemical Society 108, First Electride Crystal Structure, 3534-3535.

Dye, J. L., Wagner, M. J., Overney, G., Huang, R. H., Nagy, T. F., 8:
Tomanek, D. (1996) Journal of the American Chemical Society 118, Cavities
and Channels in Electrides, 7329-7336.

Huang, R. H., Ward, D. L., Kuchenmeister, M. E., 8: Dye, J. L. (1987) Journal
of the American Chemical Society 109, The Crystal Structures of Two

Cesides Show That Cs' is the Largest Monatomic Ion, 5561-5563.

Huang, 8., Single Crystal X-ray Diffraction and Alkali Metal NMR
Studies of Alkalides, Electrides and Model Compounds, 1994.

Pedersen, C. J. (1967) Journal of the American Chemical Society 89, Cyclic
Polyethers and their Complexes with Metal Salts, 2495-2496.

Pedersen, C. J. (1968) Federation Proceedings 27, 1305.

Pedersen, C. J. (1970) Journal of the American Chemical Society 92, Cyclic
Polyethers and Their Complexes with Metal Salts., 386.

Pedersen, C. J., 8: Frensdorff, H. K. (1972) Angewendte Chemie International
Edition 11, Macrocyclic Polyethers and Their Complexes, 16-25.

Shubin, 8: Dikanov. (1988) .

182
Tehan, F. J., Barnett, B. L., 8: Dye, J. L. (1974) Journal of the American
Chemical Society 96, Alkali Anions. Preparation and Crystal Structure of a
Compound Which Contains the Cryptated Sodium Cation and the
Sodium Anion, 7203-7208.

Chapter 6

 

Multifrequency ESEEM Studies of

PotaSsium Hexamethyl Hexacyclen Sodide

183

184

Background Information

Thermodynamic considerations by Golden and Tuttle suggested
that alkali metal anions could exist in liquid ammonia . The Dye group
pursued salts of alkali metal anions based on thermodynamic
considerations. Unfolding new combinations of alkali metals,
complexants and solvents is of primary interest. In principle, the alkaline
earth metals or even lanthanides could be the cation. In practice, this is
not as simple. Such attempts were made but met with little success. For
instance, effort was made to synthesize crystals of Ba2+(C222)Na' but the
synthesis always failed, not even resulting in powder alkalide (Huang,
1994). It seemed reasonable that a more robust complexing agent might
help stabilize other types of alkalides.

The utility of alkalides and electrides has been limited due to their
thermal instability, resulting from reductive attack on the ether oxygen by
either the weakly bound or unbound electrons. The quest for more robust
complexing agents led to the implementation of a type of complexant that
was more resistant to reductive decomposition. This complexant,
hexamethyl hexacyclen (hereafter referred to as HMHCY), was successfully

used to produce a more stable alkalide. This fully methylated aza analog

185
of 18C6, was presumably less reactive due to the replacement of the

oxygen ether atoms with the less reactive nitrogen atoms. Three sodides of
alkali metal cations K, Rb and Cs were crystallized‘with HMHCY as the
complexing agent. In addition, crown ether complexants such as 12C4
were used to try to place a "cap" over the Cs+(HMHCY)Na' complex (Figure
6.1). The Cs cation fits rather well inside of the HMHCY complexant, but

sits about .91 A above the plane of the four nearly planar

 

 

Figure 6.1: Attempts to "cap" the alkali metal cation complexed by
HMHCY with 12C4, have thus far failed. Note the cup formation of
HMI—ICY with four nitrogens in the same plane and the methyl groups
of the other two nitrogens closing off the bottom of the cup.

N atoms. Based on this, it was proposed that perhaps the 12C4 could

”cap” the Cs cation. Every attempt resulted in crystals of Cs+(HMHCY)Na',

 

186
verified with X-ray crystal diffraction, and crystals of 12C4. Attempts

were made to synthesize Ba2+(HMHCY)Na' but only a oily liquid was
present after several different solvent systems were attempted (Huang,
1994). Currently, there has been no success at synthesizing alkaline earth
sodides, or by capping the CS+(HMHCY)Na‘.; however, this very robust
complexant has served to make three very stable sodides that will the

topic of this chapter.
Structural Information

The structure of three HMHCY sodides, have been determined
(Kuchenmeister 8: Dye, 1989, Ward et al., 1989). All three of the HMHCY
sodides crystallize in the orthorhombic crystal system. The four nitrogens
at'positions 4, 7, 13 and 16 are all coplanar to within 0.09A in the
K+(HMHCY)Na‘ and within 0.03A in CS+(HMHCY)Na’. The methyl groups
that are bonded to these nitrogens form a cage around the alkali metal
cation. The other two nitrogens at positions 1 and 10 are below the plane
of the other four nitrogens by 1.62 A and 1.23 A for K+ and Cs+
respectively. The methyl groups associated with these two nitrogens
essentially close off the bottom of the ring, exhibiting a "cup" formation
(Figure 6.1). Both cations are coordinated to all six nitrogens with cation-
nitrogen distances ranging from 2.90 to 3.01 A and 3.17 to 3.35 A for K and

Cs, respectively. The K+ is located 0.29 A above the nitrogen ring and Cs+

 

 

187
is located 0.91 A above the nitrogen ring. The Cs+-Na' distance is 4.28 A

and the K+-Na' distance is 4.26 A. This information, together with the fact
that the cations sit slightly above the plane of the complexant ring, make
interaction with trapped unpaired spins occupying anionic vacancies,
more likely. This structural information renders this a close ion pair,
without destroying the rudimentary character of the ions. All pertinent
distances are shown in Figure 6.2, and cation-anion packing views are

shown (Figure 6.3, and 6.4).

4N \/— \le
H3C—1N10—‘N CH3
CH3 ‘1’.)
RM , C33
16N N13

\_/

K is located 0. 29A above the center of the plane
Cs is located 0. 91A above the center of the plane

K-N distance —> 2. 90-3. 10A
Cs- N distance -———> 3. 17-3. 35A

 

4.28A
4.26A

Na" distance from KJr
Na’ distance from Cs+

 

Figure 6.2: Structural information for two HMHCY sodide.

188

 

 

 

22.53

 

 

 

 

 

II I7

Figure 6.3: Diagram of K+(HMHCY)Na'

189

   

Figure 6.4: Perspectives of Cs+(HMHCY)Na'

190
Thermal Stability

Samples were prepared under an inert nitrogen atmosphere and
hermetically sealed in anodized aluminum sample pans for DSC
measurement. The initial melting point of K+(HMHCY)Na' was measured
to be 42 °C but decomplexation into the metals, probably NaK alloy and
free amine, occurred at 74°C. Temperatures up to 120°C revealed no
additional decomposition, suggesting that even in the presence of alkali
metals, the HMHCY complexant is resistant to reductive attack. This sodide
is stable at room temperature for up to four days, at which point it
decomplexes. In the case of the Cs+(HMHCY)Na', the onset of melting
occurs at about 8°C With decomplexation occurring at 37°C. This sodide
also decomplexes after about four days, rendering a slow melt in both

cases.
EPR Studies

Studying the electronic environment of alkalides and electrides is
the theme of this dissertation and the HMHCY compounds proved to be a
good subject. Due to the exchange narrowing EPR properties of most
electrides, isolation of the trapped electrons in alkalides proved to be more
successful at determining hyperfine interactions. Since the alkalides

sometimes form sandwich complexes as do the electrides, the alkali metal

 

191
cation cannot communicate with the unpaired electron spin of the defect

electrons since the cations are well shielded from the trapped electrons.
This reduces the chances of obtaining hyperfine interactions in the EPR .
For example, an EPR comparison was done between three sandwich sodides
and three HMHCY sodides (Shin et al., 1991). In the sandwich compounds,
[Cs+(18C6)2Na', Cs+(15C5)2Na', Cs+(12C4)2Na'], each Cs+ ion is
encapsulated 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 distances from other
anionic 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, suggesting very little spin-
orbit coupling. The peak to peak line widths were 2.21 and 4.40 G
respectively. 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 originally thought to come from superhyperfine interactions with
several surrounding nuclei rather than a shifting of the g-values. High
field EPR experiments later determined that the two peaks were due to

trapped electrons residing at two magnetically non-equivalent sites.

 

192
The differences in the structures of these two families of compounds

clearly agrees with the fact that hyperfine interactions are observed for the
contact H MH CY complexes, while none is seen" for the sandwich

compounds.
ESEEM Studies

Multifrequency ESEEM experiments were used to study the electron
trapping sites in these thermally stable sodides, with a precise goal to
determine charge distribution. As was mentioned in the previous chapter,
direct evidence of the electron trapping sites has not been shown until the
ESEEM method was used. eseem experiments were used to measure the
weak superhyperfine couplings to trapped electrons in Cs+(HMHCY)Na'
(McCracken et al., 1992). They showed that two magnetically distinct
groups of 133Cs were present.

Three pulse stimulated echo ESEEM data collected at g=1.998 is
shown in Figure 6.5. The tau value was initially taken at 250 ns and the
ESEEM time domain trace exhibited strong proton modulations. These
data, when fourier transformed, show a relatively large peak at 14 MHZ,
and another large peak near the low frequency edge, at 0.65 MHz. In
addition there is a small rather sharp peak located at 3.9 MHz. These
peaks have been assigned to protons, potassium and sodium, respectively,

based on their larmor frequencies at a field strength of 3391 G. Choosing

193

 

ocho ampl.

 

 

 

 

 

 

 

 

 

amplitude

 

 

 

 

 

 

o 5 10 15 20 as
“money (MN!)

Figure 6.5: A) 3-pulse ESEEM trace of K+(HMHCY)Na' at 3300 G, where ’r =
288 ns., T=42 ns., tinc = 10 ns., repetition rate _= 40 Hz. B) Fourier
transform spectrum of A.

194
the tau value is very important and can aid in peak assignments. The

equation for the modulation function reveals that there is a tau
dependence on the stimulated echo frequencies. Therefore, if a certain tau
value is chosen, it can serve to enhance or suppress certain modulations

in the echo. For example,

th = gNBNH (6-1)

where vN is the larmor frequency, gN is the nuclear g-factor and [3N is the

nuclear Bohr magneton. If the echo is collected at a field strength of 3391 G
and a compound with many protons is under study, then the proton
larmor frequency at that field strength is,

vN = (5.5856912)(5.050824x10'27J/T)(.03391 T/6.63x10‘34J-s) (6.2)
= 14.42 MHZ

and therefore, one might expect a peak to be centered at this frequency.
Protons are often the most abundant element in a sample and the large
modulations can then cause the intensity other frequencies to be
diminished. To suppress the undesired contribution of matrix protons to
the spectrum, the reciprocal of the larmor frequency will yield the tau
value (and integral multiples) that should suppress the proton
modulations (Mims, 1972, Mims 8: Peisach, 1989, Wamcke 8: McCracken,
1994). In this case, multiples of 71 ns should be used to suppress the

proton modulations and possibly bring out any other modulations that

195
are present in the echo envelope. Moreover, 1.5 times the reciprocal of the

larmor frequency of the nucleus of interest, should enhance the
modulations. Thus careful consideration must be given when choosing a
tau value.

When a tau value was chosen to suppress the protons, 213 ns, the
echo envelope revealed weak proton modulations as well as another
modulation. The time domain trace and fourier transformed spectrum
can be found in Figure 6.6. The large peak located at a frequency of 0.67
MHZ was assigned again to potassium and the weaker peak at 14 MHZ was
due to protons, and the intensity was weakened significantly due to the
tau suppression effect. Once again, a smaller more broad peak centered
around 3.8 MHZ was present. The initial judgment was to assign this peak
to Na, however upon choosing the tau value that would enhance this
feature, no increase in that frequency region was observed. This indicates
that the peak cannot be assigned to Na.

The spectrometer dead time limits the start of data collection (140
ns). As a result, reconstruction of the dead time is necessary. To do this, a
windowing function is employed where only the peaks that are believed to
be real, are windowed. This often gives the lineshapes a more realistic
appearance and depletes the baseline thus increasing the signal to noise

ratio. When the 3.9 MHZ peak is not windowed, it does not disappear

 

 

 

 

 

 

 

a
5
o 800- ................................................................................................ .—
Z
3
600.. .............................................................................................. _
400.. ............................................................................................... _.
200. ............... ................ ................ g .............. _
o l J I l l b '
O 1000 2000 3000 4000 5000 6000
time(nsec)
B
10.. ................................................................................................ -.
8.. ............................................................................................ —I

 

 

 

 

 

0 5 10 15 20 25
frequency (MHz).

Figure 6.6: A) 3-pulse ESEEM trace of K+(HMHCY)Na' at 3300 G, where I =

324 ns., T=46 ns., tinc = 10 ns., repetition rate = 40 Hz. B) Fourier

transform spectrum of A.

-2

 

197
completely, but the shape is somewhat distorted. Perhaps the peak was

part of the baseline, but generally, baseline features are not such sharp
peaks. Several attempts were made to bring out the sodium modulations,
if they were present. In addition, two other frequencies were used to try to
confidently assign the frequencies, 11.4 GHZ and 12.2 GHZ. The resonance
was located at a higher field strength thus the larmor frequency changed
accordingly. The stimulated echo, collected at 4100 G and a tau value of
324 ns, showed a very weak modulation pattern (Figure 6.7). Only
protons and potassium were present at this frequency, so more than likely,
the initial aSsignment to sodium was incorrect. Experiments recorded at
12.5 GHZ revealed the same modulation pattern as observed at 11.4 GHZ
with only potassium and protons present. Simulations of all of these data

should verify the assignments.
Conclusions

It was not too surprising that the eseem results indicated that the
trapped electrons in K+(HMHCY)Na’ only interacted with the protons and
potassium. Initial experiments showed a peak at the expected frequency
of sodium, but further investigation negated that assignment. Given the
crystal structure of this sodide, the distance between a sodium anion and
a trapped electron ranges from 8.66 to 9.94 A as the sodium anions are

effectively shielded from one another by the large complexed cation. There

 

 

 

 

 

 

2000 I I I I .
1500 -
.1ooo._ ............................................................................................... _
E.
E
us
0
S . . . :
o : . . . .
0 : : : : :
500... ............... ........ ......... ................ , ................ ............ ....
0.. ............................................................................................. g, ..I
0 500 1 000 1500 2000 2500 3000

time (nsec)

 

amplitude

 

 

 

 

 

45 i i . ; i i i . .
0 2 4 6 8 10 12 14 16 18 20
lrequency (MHz)

Figure 6.7: A) 3-pulse ESEEM trace of K+(HMHCY)Na‘ at 4250 G, where

1: = 288 ns., T=42 ns., tinc = 10 ns., repetition rate = 40 Hz. B) Fourier
transform spectrum of A.

199
is relatively strong interaction between the trapped electrons and the

potassium cation; however, there is a reasonable amount of charge

distribution near the potassium cation.

200

BIBLIOGRAPHY

Kuchenmeister, M. E., 8: Dye, J. L. (1989) Journal of the American Chemical
Society 111, Synthesis and» Structures of Two Thermally Stable Sodides
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