...E.,re.:.4r_v . 1:3
.9; .3}. 9].... El:
. .

I I!

inn-L‘s. are. at .5.
.- Lr {quXsiIBZQlirS
:36! . 21'...

3.1 .5 .2!!! .1

viz... 7.23.! .lztiile

. .aflflHnWIQV .Chue-vhru
t 21...... . 1.35.5.
i .v. Nu.» . .dwwutitn
1:... A. Elana:
.-

.!u v!”

A

.3...

33.5.71» . 1:: rinitwc

 

1733007001

ICHI IIIIIIIIIIIIIIIIIIIIIIIIIII

MHHIBHIIHIIIJUIHHHIIHIIHHUllllllIUUIIIHHIHHI

1293 00563 3254

I llBRARY

Michigan State
I University

 

This is to certify that the

dissertation entitled

ALKALI METAL NMR, RELAXATION TIMES
AND MAGNETIC SUSCEPTIBILITIES OF SOME
ALKALIDES AND ELECTRIDES

presented by

Lauren Elizabeth Hill McMiIIs

has been accepted towards fulfillment
of the requirements for

Ph . D. _degree in Chemistry

 

 

DateJarch 13, 1989

MS U is an Affirmative Action/Equal Opportunity Institution

 

MSU

LIBRARIES
.-,—.

 

 

 

RETURNING MATERIALS:
Piece in book drop to
remove this checkout from
your record. FINES wiII
be charged if book is
returned after the date
stamped below.

 

 

 

ALKALI METAL NMR, RELAXATION TIMES AND MAGNETIC
SUSCEI’TIBILI'I'IES OF SOME ALKALIDES AND ELECTRIDES

By

Lauren Elizabeth Hill McMills

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1989

!"

ABSTRACT
ALKALI METAL NMR, RELAXATION TIMES AND MAGNETIC
SUSCEPTIBILITIES OF SOME ALKALIDES AND ELECT RIDES
By
Lauren Elizabeth Hill McMills

Solid-state alkalide and electride spin-lattice relaxation times were obtained
for the first time. The dominant means of relaxation in these compounds
was shown to arise from a quadrupolar mechanism. The 23N a NMR results
showed that the Na” ion is extremely resistant to relaxation at low
temperatures in Cs+(18C6)2-Na‘ where the T1 value at 173 K is 107 sec., the
longest spin-lattice relaxation time for sodium known to date. The 87Rb
NMR results for Cs+(18C6)2-Rb', Cs+(15C5)2-Rb’ and Rb+(15C5)2-Rb' suggest
that the relaxation processes in the latter two compounds are more efficient
than in Cs+(18C6)2'Rb'. Structural and symmetry differences in the 18C6 and
15C5 complexes are probably responsible for the differences in the observed
relaxation behavior in both the 23N a and 87Rb NMR studies. The 133Cs NMR
spectra of Cs+(18C6)2-e‘ consisted of two peaks each having distinct
temperature-dependent relaxation times.

The use of a modified NMR spin echo method allowed the first
observation of 16* and Rb+ cations in alkalides and electrides in the solid state.
This technique can be used to probe the local environments and symmetries
of these compounds.

A study of methylamine-assisted solubilization of lithium by NMR and
optical spectroscopy demonstrated that the species Li+(CH3NH2)4 dissolves in
a variety of solvents, both by itself and with sodium. Extensive 23Na and 7Li

NMR measurements of Li+(CH3NH2)x-Na’ and Li+(CH3CH2NH2)x-Na’ with

Th4
ind
Li‘
cm
ter

ex‘

x=4, 6, 8, 12 and 16 showed that Li+ and Na' are present in these solutions.
The 23Na NMR chemical shift of Na' in Li+(CH3CH2NH2)x-Na‘ is
independent of both temperature and the amount of ethylamine, whereas in
Li+(CH3NH2)x~Na‘ the Na‘ peak position is both temperature and
concentration dependent. The paramagnetic shift with increasing
temperature of the Na' peak in the Li+(CH3NH2)4-Na‘ solution is due to an
exchange process as evidenced by a 23Na NMR spectrum of a frozen sample,
which consisted of a peak at -55 ppm as expected for the Na' ion. NMR and
optical studies proved that Na' does not exist in the solutions that contain
lithium, sodium and ammonia. Thus, the compound Li+(NH3)4°Na' does
not form.

The magnetic susceptibilities of K+(15C5)2-e‘ and Rb+(15C5)2~e' nearly
follow Curie law. DSC and magnetic susceptibility studies showed that
mixtures of the electrides and their corresponding alkalides are often obtained
in attempted syntheses of electrides. The two electrides have susceptibilities
that are relatively field independent before and after annealing. Loading the
samples in zero field has no effect on the magnetic susceptibility behavior of
either compound. The compound K+(15C5)2-e' has the largest Weiss
constant, 9 ~ -19 K in the series Cs+(18C6)2-e', Cs+(15C5)2-e', Rb+(15CS)2-e‘ and
K+(15C5)2-e'. No antiferromagnetic transition was observed for either

compound.

TO MY FATHER, DEREK L. HILL,
FOR HIS LOVE, COURAGE AND UNDERSTANDING

iv

ACKNOWLEDGEMENTS

I would like to express my deep appreciation to Professor James L. Dye for
his support during this work. I will always admire him for his never ending
thirst for knowledge. A special acknowledgement goes to my collaborators in
the "NMR group": Ahmed Ellaboudy, Jineun Kim and Judy Eglin for the
long hours and arctic temperatures endured at the Clinical Center, Illinois
and Cambridge.

I would also like to thank those past and present in the Dye group who
provided both support and friendship: Rui Huang, Kevin Moeggenborg,
Evelyn Jackson, Kuo Lih Tsai, Francoise Tientaga, Mark Kuchenmeister,
Joseph Skowyra, Marc DeBacker, Mary Tinkham, Odette Fussa-Rydel, Steven
Dawes and Margaret Faber.

Other members of the chemistry department deserve special recognition
for their excellent work: Keki Mistry, Manfred Langer, Scott Bankroff, Dort
Boettger, Kermit Johnson and Marty Rabb.

A special thank you to my parents for their love and encouragement, to
Kathleen for her listening ear and especially to Mark who was always there
for me.

Financial support from Michigan Sate University and the National Science
Foundation (N SF-84-14154, NSF-87-14751 and NSF INT-86-19636) are
gratefully acknowledged and appreciated.

IV.

TABLE OF CONTENTS

{Egg
LIST OF TABLES ....................................................................................... viii
LIST OF FIGURES ........................................................................................ xi
Introduction .................................................................................................... I
Spin-lattice Relaxation Studies of Alkalides and Electrides ............... 20
II. A. Introduction .......................................................................................... 20
II. B. Theory of Quadrupolar Relaxation .................................................. 25
II. C. Experimental ......................................................................................... 32
II. D. Results .................................................................................................... 43
II. D. 1. Simple and Model Salts ............................................................ 43
II. D. 2. Alkalide and Electride Samples .............................................. 51
II. D. 2. a. 23Na NMR ......................................................................... 51
II. D. 2. b. 37Rb NMR .......................................................................... 66
II. D. 2. c. 133Cs NMR ......................................................................... 75
II. D. 2. d. 39K NMR ............................................................................ 80
II. E. Conclusions ............................................................................................ 82
39K and 87Rb NMR of Alkalides and Electrides Using the
Spin-Echo Technique .................................................................................. 85
III. A. Introduction ......................................................................................... 85
III. B. Theory .................................................................................................... 86
III. C. Experimental ........................................................................................ 87
III. D. Results and Discussion ...................................................................... 89
III. D. 1. Model Salts ................................................................................. 89
III. D. 2. Alkalides and Electrides .......................................................... 96
III. E. Conclusions ........................................................................................ 104
23Na and 7Li Solution NMR Studies of Li+(CH3NH2)x-Na',
Li+(CH3CH2NH2)x°Na' and Li+(NH3)4-Na' .......................................... 106
IV. A. Introduction ...................................................................................... 106
IV. B. Methylamine-Assisted Solubilization of Lithium .................... 108

vi

VI.

IV. C. Results With Li+(CH3NH2)x-Na' and

Li+(CH3CH2NH2)x°N a" ................................................................... 118
N. D. Li+(NH3)4-Na' Results .................................................................... 125
IV. E. Conclusions ...................................................................................... 132

Magnetic Properties of Two Electrides: K+(15C5)2-e' and

Rb+(15C5)2°e' ............................................................................................... 134
Summary and Suggestions for Future Work ...................................... 153
LIST OF REFERENCES ............................................................................. 157

vii

Ia‘

Ta‘

Ta

Ta

I;

LIST OF TABLES

Page

Table 1. 23N a NMR Results at 52.94 MHz.38 ....................................................... 7
Table 2. 39K MAS-NMR Results.103 .................................................................... 17
Table 3. 87Rb MAS-NMR Results.103 .................................................................. 18
Table 4. A Comparison of Measured (T10b5) and Literature

(Tllit) Spin-Lattice Relaxation Times for some

Alkali Halides at Room Temperature ................................................ 43
Table 5. Spin-Lattice Relaxation Values for the Alkali Halides

and the Quadrupole Moments and Sternheimer

Antishielding Factors for the Alkali Metal Nuclei .......................... 45
Table 6. The Gyromagnetic Ratios, Nuclear Spins and the

Interatomic Distances for the Alkali Halide Samples ..................... 47
Table 7. Scaled Spin-Lattice Relaxation Times ................................................. 48
Table 8. The Room Temperature T1 values for Three Model

Salts (23N a NMR) .................................................................................... 49
Table 9. 23N a NMR Spin-Lattice Relaxation Data for

Cs+(18C6)2-Na' .......................................................................................... 52
Table 10. Estimated Dipolar Spin-Spin Relaxation Rates

and Correlation Times for Cs+(18C6)2-Na' ....................................... 57
Table 11. 23N a NMR Spin-Lattice Relaxation Results of
Cs+(15C5)2-Na' .............. ' .......................................................................... 63

viii

Tab

Tat

Tat

Ta'

Ta

Ta

Table 12.

Table 13.

Table 14.

Table 15.

Table 16.

Table 17.

Table 18.

Table 19.

Table 20.

Table 21.

Table 22.

Table 23.

Table 24.

87Rb NMR Spin-Lattice Relaxation Results of
Cs+(18C6)2-Rb" ......................................................................................... 67

87Rb NMR Spin-Lattice Relaxation Results of
Cs+(15C5)2°Rb' ......................................................................................... 70

37Rb NMR Spin-Lattice Relaxation Results of

Rb+(15C5)2-Rb' ........................................................................................ 72
133C5 NMR Spin-Lattice Relaxation Results of
Cs+(18C6)2-e' ............................................................................................ 78

39K NMR Spin-Lattice Relaxation Results of
Cs+(15C5)2-K‘ .......................................... - ................................................. 8 2

Comparison of N MR Parameters of K+(18C6)-SCN'
and Rb+(18C6)'SCN' .............................................................................. 93

7Li and 23N a N MR Results of Lithium and Sodium

in Excess CH3NH2 ................................................................................ 112
7Li and 23Na NMR Results of Li+(CH3NH2)4 and
Sodium in 2-aminopropane .............................................................. 112

7Li and 23Na NMR Results of Li+(CH3NH2)4 and
Sodium in a Mixture of CH3CH2NH2, DEE and

Pentane ................................................................................................... 113
7Li NMR Results of Li+(CH3NH2)4 in MeZO ................................. 117
7Li NMR Results of Li+(CH3NH2)4 ............................... ' ................... 1 17
7Li and 23N a NMR Results of Li+(CH3CH2NH2)x~Na' ................ 121
7Li and 23N a NMR Results of Li+(CH3NH2)x°Na' ........................ 121

ix

Tat

Tat

Tat

Table 25. 7Li NMR Results for Li+(NH3)4-Na' ................................................ 126

Table 26. 23Na NMR Results for the Li+(NH3)4-Na' system ........................ 131

Table 27. A Summary of K+(15C5)2-e" and Rb+(15C5)2-e’
Susceptibility Results. ......................................................................... 151

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

LIST OF FIGURES

Representative complexants ...................................................

23N a NMR spectra of N a+(C222)-N a", both static and

spinning at 52.94 MHz.38 ..........................................................

23N a MAS-NMR spectra of N a+(C222)-N a’ as a
function of frequency. The proton decoupled peak
of N a+(C222) (solid line) and its simulated lineshape

(dashed line) are shown in the insert.39 ...............................

Chemical shift vs 1/ T for Cs+(18C6)2-e'. The
temperatures of points marked with an x were

calibrated using methanol.52 ...................................................

133Cs NMR spectra of Cs+(18C6)2-Na’x°e’1.x

where a) x=0.2 and b) x=0.8 ......................................................

Inversion Recovery pulse sequence (a) and

Schematic (b) ...............................................................................

Example of an Inversion Recovery sequence (a)
and a computer determination (b) of the T1 value

for Cs+(18C6)2-Rb‘ at 233 K .......................................................

Saturation Recovery pulse sequence (a) and

Schematic (b) ...............................................................................

Example of a Saturation Recovery pulse sequence

for Cs+(15C5)2-Rb' at 213 K .......................................................

xi

Page

.......... 2

.......... 6

.......... 8

........ 13

........ 15

........ 34

........ 36

........ 37

........ 38

Figi

Fig

Fig

Fig

Fig

Fig

F1!

F1.

Fl

Pi

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

An example of a 90° pulse length determination

for CsCl at room temperature ......................................................... 42
Representative structures of a) N a+(C222)-SCN',

b) N a+(12C4)2-Cl' and c) N a+(18C6)-SCN' ..................................... 50
Ln T1 versus Temperature (a) and In Tz" versus

Temperature (b) for Cs+(18C6)2-Na' ............................................... 53
23Na NMR static spectrum of Cs+(18C6)2-Na' at 269 K .............. 55
Ln Tz" (dipolar) versus Temperature for

Cs+(18C6)2°Na' .................................................................................... 58

Plot of In Tc vs 1 / T for Cs+(18C6)2-Na' .......................................... 60

23N a NMR spectrum of Cs+(HMHCY)°Na' showing
both the N a' peak and the folded over 27A1 peak ...................... 62

Ln T1 versus Temperature (a) and In Tz“ versus

Temperature (b) for Cs+(15C5)2-Na' ............................................... 64
Ln T1 versus Temperature (a) and In Tz" versus
Temperature (b) for Cs+(18C6)2-Rb' ............................................... 68

Ln T1 versus Temperature (a) and In Tz" versus
Temperature (b) for Cs+(15C5)2-Rb' ............................................... 71

Ln T1 versus Temperature (a) and In Tz" versus
Temperature (b) for Rb+(15C5)2-Rb' ............................................... 73

A comparison of the spin-lattice relaxation times
of a) Cs+(18C6)2°Rb', b) Cs+(15C5)2-Rb' and
c) Rb+(15C5)2-Rb' ................................................................................ 74

133C5 NMR static spectra of Cs+(18C6)2-e' at

xii

 

 

Fl}
Fig

Fig

Pie

Figure 23.

Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28..

Figure 29.

Figure 30.

Figure 31.
Figure 32.

Figure 33.

Figure 34.

a) 208 K and b) 243 K .......................................................................... 76

Ln T1 versus Temperature for peak 1 (a) and
peak 2 (b) in Cs+(18C6)2-e" ................................................................ 79

l33Cs NMR static spectra of Cs+(18C6)2-C5' at
various temperature ......................................................................... 81

39K NMR spectra of KCl using a single pulse

experiment (a) and a spin-echo experiment in

which two different time intervals were used

(b and c) ................................................................................................ 90

Observed (a) and simulated (b) 39K NMR lineshapes
of K+(18C6)-SCN' ............................................................................... 91

Observed (a) and simulated (b) 87Rb NMR lineshapes
of Rb+(18C6)°SCN‘ ............................................................................. 92

39K NMR static spectra of a) K+(15C5)2-I' and
b) K+(12C4)2-I' ..................................................................................... 94

39K NMR static spectra of a) K+(C222)-I' and
b) K+(C222)-SCN' ................................................................................ 95

39K NMR static spectra of a) K+(C222)-e' and

b) K+(C222)-K‘ .................................................................................... 97
39K NW static spectrum of K+(15C5)2.e' ..................................... 99
39K NMR static spectrum of K+(15C5)2°K' .................................... 99

87Rb NMR static spectrum of a) Rb+(18C6)-Na'
and b) Rb+(C222)°Rb' ....................................................................... 100

87Rb N MR static spectrum of Rb+(15C5)2-Rb' ............................ 101

xiii

 

Fig

Fig

Fig

Figure 35.
Figure 36.

Figure 37.

Figure 38.

Figure 39.

Figure 40.

Figure 41.

Figure 42.

Figure 43.

Figure 44.

Figure 45.

87Rb NMR static 'spectrum of Rb+(18C6)-Rb' ............................. 102
87Rb NMR static spectrum of Rb+(15C5)2-e' ............................... 103

23Na NMR spectrum (a) and 7Li NMR
spectrum (b) of a solution of lithium,
sodium and excess methylamine ................................................. 109

23Na NMR spectrum (a) and 7Li NMR
spectrum (b) of a solution of Li+(CH3NH2)4,
sodium and 2—aminopropane ....................................................... 110

23N a NMR spectrum (a) and 7Li NMR

spectrum (b) of a solution of Li+(CH3NH2)4,

sodium and a mixture of ethylamine,

diethylether and pentane ............................................................... 111

7Li NMR spectra of Li+(CH3NH2)4 in MezO at
-60° C. Spectrum (b) was obtained four and a
half hours after spectrum (a) ......................................................... 115

Representative 23N a and 7Li NMR spectra of
Li+(CH3NH2)4-Na' ........................................................................... 12

Representative 23N a and 7Li NMR spectra of
Li" (CH3NH2)4°Na' ........................................................................... I 23

23N a NMR spectrum of a frozen sample of
Li+(CH3NH2)4'Na' ........................................................................... 124

7Li NMR spectrum of Li+(NH3)4-Na‘ at -73 ° C ......................... 128

23Na NMR spectrum of Li+(NH3)4-Na'
at -70° C .............................................................................................. 129

xiv

Figure 46.

Figure 47.
Figure 48.
Figure 49.
Figure 50.

Figure 51.

Figure 52.

23N a NMR spectra of Li+(NH3)4-Na’ at several

temperatures ..................................................................................... 130
DSC Traces of a) K+(15C5)2-e' and b) K+(15C5)2'K'- .................. 136
DSC Traces of a) Rb+(15C5)2-e' and b) Rb+(15C5)2-Rb' .............. 137
DSC Trace of a pure sample of Rb+(15C5)2-e' ............................. 138
Plot of 1/XM vs Temperature for Rb+(15C5)2-e' ......................... 146

Plot of 1/ XM vs Temperature for Rb+(15C5)2-e’
at several fields ................................................................................. 148

Plot of 1 /XM vs Temperature for K+(15C5)2'e' ........................... 150

XV

at
St
w:

5F

99

I. Introduction

Since Weyl discovered in 1864 that alkali metals dissolve in liquid
ammonia, metal amine solutions have been and continue to be widely
studied.1 Dilute alkali metal solutions exhibit a characteristic blue color
whereas concentrated solutions have a metallic bronze color. The major
species present in dilute solution (conc < 10'3 M) are the solvated electron, e‘

(solv), and the metal cation, M+(SOIV), which are formed according to the

equation:
MIS) J53" M+solv + e'solv (1-1)

Optical absorption studies have shown the presence of a strong absorption
in the near infrared region, having a peak maximum at 6800 cm'1.2'5 The
absorption peaks have an asymmetrical shape with a high energy tail in the
visible region which accounts for the characteristic blue color of these
solutions. The spectral shape and position of the peaks are independent of
the metal used and are similar to those produced by pulse radiolysis of the
pure solvent.5r7 The EPR spectrum of a metal-ammonia solution consists of a
narrow line having a linewidth of 0.5 Gauss, which indicates that the electron
does not interact for long times with either cation or solvent3l9, but must
exchange sites rapidly.

The investigation of metal-ammonia solutions led to the present study by
Dye and coworkers of solvated metals in amine and ether solvents. From

these studies, two new classes of compounds, alkalides and electrides have

1

be

Cl'

fo

se
ar
ar
ar
ce
50
ad

011

C05

2

been synthesized. Alkalides consist of an alkali metal cation, alkali metal
anion, and a complexant. Electrides are composed of an alkali metal cation as
in the alkalides, but the anion is a trapped electron. The complexants can be a
crown ether1 0, cryptand11 or an aza crown complex.12 The structural
' formulas of 15-crown-5, cryptand (2,2,2) and hexamethylhexacyclen are shown

in Figure 1.

N
(\o/\ ”0,... 0’» <— .CH3 Hag—y
O o N o o H30—N N—CH3
to 0—7 (jg—10$ <_ .CHe HaC. >

\__l N

a) 15-crown-5 (1505) b) Cryptand 222 (C222) c) Hexamethyl Hexacyclen
(HMHCY)

Figure 1. Representative Complexants

Alkalides and electrides are extremely temperature, moisture, and air
sensitive and therefore must be handled under inert atmosphere or vacuum
and must be kept cold at all times (T<-20° 0,13,14,15 Syntheses of alkalides
and electrides consist of introducing stoichiometric amounts of complexant
and alkali metal(s) into a reaction vessel in a helium-filled glove box. The
cell is then attached to a vacuum line, evacuated and the metal distilled.16 A
solvent such as methylamine (CH3NH2) or dimethylether (MezO) is then
added to dissolve both metal and complexant. This process is usually carried
out at temperatures of -20°C or below. The alkalide or electride powder is
then obtained either by the removal of solvent or by the addition of a

cosolvent such as trimethylamine or diethylether. A washing solvent is then

adde
filtr;

incl?
spe
eva

mel

obs

res
ett
sto
sir.

I0

as

50

C.
in

in

SI

5(

3

added to remove any excess complexant through a series of washings and
filtrations.17'19 '

These compounds have been characterized by numerous methods
including pressed powder dc conductivity“,20 ,magnetic susceptibility21, EPR
spectroscopy22 and absorption spectra of their films by rapid solvent
evaporation23'25 or vapor deposition25:27. The identification of the alkali
metal anion in the alkalides was based upon absorption spectra since it had
been shown that the peak position in M+(C222)-M' corresponds closely to that
observed for the corresponding anion in solution.23 N a“, K“, Rb‘ and Cs" in
M+(C222)-M‘ have absorption peaks at 15,400, 11,900, 11,600 and 10,500 cm'1
respectively compared to the values of 15,400, 12,000, 11,200 and 9800 an1 in
ethylenediamine solutions.28 The identification of a heteronuclear film of
stoichiometry M+LoNa', for example, will show a single absorption maximum
similar to that in Na+(C222)-N a". Due to the sensitivity of the peak position
to the surroundings it was determined that the assignments could not always
give a conclusive identification and therefore this method could not be used
as an absolute test of the stoichiometry of the compound in question. A
solution to this problem was solid state NMR spectroscopy which gives a peak
characteristic of the complexed cation and that of the alkali metal anion.
Consequently, solid state NMR spectroscopy has become an instrumental tool
in the characterization of alkalides and electrides. This chapter will show
how NMR spectroscopy of alkalides and electrides has evolved from a means
of identification to a probe of the interactions within these compounds.

Alkali metal NMR spectroscopy has been widely studied in the solution
state.29 For example, 23Na N MR confirmed the existence of N a+ and N a' in
solutions of sodium and C222 in various solvents by the observation of two

peaks.30:31 The chemical shift of Na', ~61 ppm, is the same as that calculated

4

for the gaseous anion.5"2 This indicates that the 2p electrons of N a" are well
shielded by the two 35 electrons from interaction with the solvent. The
chemical shift of N a“ is insensitive to the host structure and the Na“ peak is
extremely symmetrical lending further credence to the effective shielding of
the N a' anion from its surroundings by the 3s electrons. In contrast, the
NMR peaks of Na+ in solutions are shifted paramagnetically from that
expected for N a+(g). These peaks tend to be broader and less symmetrical than
that of N a‘ and the differences in chemical shifts are due to interactions by
solvent or by anion electron density with the p orbitals of Na+.33v34 This
showed the potential use of alkali metal NMR as a diagnostic tool. However,
as mentioned previously, the drawback to optical spectroscopy as an
identification tool was that it required solutions or films. Since solution state
NMR appeared to be highly successful as an identification technique, solid
state NMR was turned to in the hope that it would be a definitive diagnostic
tool.

The main difficulty in obtaining high resolution solid state spectra is the
substantial broadening of the NMR lines relative to those in fluids due to the
absence of sufficient nuclear motion in crystalline solids. The line
broadening results from a distribution of crystalline orientations and is due to
magnetic dipolar and quadrupolar interactions as well as chemical shift
anisotropy. In 1959, Andrew and Lowe showed that in some cases one could
obtain solid state spectra which rivaled that of solution spectra by using a
technique called magic angle sample spinning (MAS-NMR) nuclear magnetic
resonance.35'37 This is achieved by rapidly rotating a sample about an axis
inclined at the "magic angle" of 54°44' (cos1 (1 /3)1/2) to the Zeeman field
direction. Theoretically, by spinning at the magic angle, first order

quadrupolar, dipolar and chemical shift interactions can be removed from the

dei

id
se
fr.
e)

N

5

center of the spectrum and appear as spinning sidebands. Figure 2
demonstrates the difference in linewidth between a static and spinning 23N a
NMR spectrum of Na+(C222)-Na' taken at 200 MI-Iz.38 The static spectrum of
N a+(C222)-Na' consists of a broad Na' peak having a linewidth of
approximately 2600 Hz centered at ~ -60 ppm relative to Na+(aq). A very
broad shoulder attributed to N a+ occurs on the low field side of the peak.
Upon spinning of the sample one sees a dramatic change in the appearance of
the spectrum. The linewidth of N a' is reduced from 2600 Hz down to 290 Hz
while its chemical shift remained constant at -61.3 ppm. The broad N a+ peak
is quite discernible having a chemical shift of -23.7 ppm and linewidth of 1200
Hz. Table 1 shows the results of the 23Na MAS and static studies illustrating
the importance of solid state NMR in the studies of these compounds.

The use of solid state. NMR spectroscopy goes beyond that of an
identification tool. The sources of line broadening can be determined in
several ways including combining of static and MAS results at several
frequencies, lineshape analysis of the static spectra, and proton decoupling
experiments. In addition, through lineshape analysis it is possible to extract
NMR parameters such as the quadrupole coupling constant, QCC, the
asymmetry parameter, n, and the chemical shift anisotropy tensor.

Figure 3 shows the 23Na MAS NMR spectrum of Na+(C222)°Na’ as a
function of frequency.39v40 The insert shows the proton-decoupled peak of
N a+(C222)-N a' (solid line) and the simulated lineshape of Na+(C222)-Na'
(dashed line). A quadrupolar coupling constant of 1.2 :t: 0.1 MHz and
asymmetry parameter of 0.1 were used to give the best agreement between the
observed and simulated lineshapes.4O It should be noted that the asymmetry
parameter must be zero due to 3-fold symmetry in the molecule. The second

moment can be calculated with the Van Vleck expression:41

 

 

 

 

 

 

 

 

bio+0222 - No-1
r—NO-
(NON-SPINNING)
NO+ l0222
(SPINNING)
4 l l I l L I l 1
+|OO O -|OO -200

8 [ppm FROM No+(oq.)]

Figure 2. 23N a NMR spectra of N a+C222-N a" , both static and spinning at
52.94 NIHZ. 38

Table 1. 23Na NMR Results at 52.94 MHz.38

Commund E (i 1 ppm)a A2112 (Hz)b
_1\_T_a.+(C222)'Na’ -24 1 200
N a+(C222)°_l\la_’ -61 290
(2800)
K+ (C222)-Na' '61 I 70
(2200)
Rb+(C222)-Na' -61 360
Li+(C211)'Na’ -63 850
K"'(18C6)°Na' -56 120
Rb+(18C6)°Na' -60 90
CS+(18C6)2°Na‘ —62 75
(1200)
K+(15C5)2'Na' -61 90
(I 000)
Rb+(I5C5)2-Na' -61 90
CS"’(15C5)2-Na' ~61
flg+(12C4)2'Na‘ -14
N a+(12C4)2'_I\£' -62
K+(12C4)2°N a“ -61 51

a Chemical shifts are referenced to N a+(aq) at infinite dilution.
b Linewidths in parentheses refer to the static spectra.

 

 

 

Figure 3.

 

 

52.94 MHz -'H-coupled

52.35 MHz - 'H-coupied

 

92.29 MHz r'H -coupled

52.94 MHz-'H-decoupied

k

'20 ' 4O '60
ppm

1

20 O

'80 ‘100 'I20 'I4O

23Na MAS-NMR spectra of N a+C222-N a‘ as a function of
frequency. The proton decoupled peak of N a+C222 (solid line)
and its simulated lineshape (dashed line) are shown in the
insert.39

wh:
dis‘

The
Stru
the
calc

COII'.

Whei
fquL

is £01

em’in

9
(Av2)=— @211 3 (5+1) 2% (1.2)

where 71 and 75 are the magnetogyric ratios of the I and S nuclei and rk is the
distance of the kth nucleus of spin S from the nucleus being studied.

Assuming a Gaussian lineshape, the full width at half height is given by:

L
2
(Av1 ) = 2.35 [(13%)] Hz (1.3)
‘2-

Therefore it is possible to calculate the dipolar linewidth if the crystal
structure is known. From the above equations, the dipolar contribution to
the static linewidth of Na+(C222) was calculated to be 3340 Hz. The total
calculated linewidth is then 3670 Hz when the predicted quadrupolar
contribution of 330 Hz is taken into account. This value is in excellent
agreement with the measured linewidth of 3700 :t 300 Hz. The isotropic
chemical shift of Na+(C222) was calculated to be -6.5 i 0.5 ppm using the
following expression for the shift of the center of gravity (CG):42

NIH -—| ILI
L ( ) JK1+ (1.4)

where v1, is the isotropic Larmor frequency, vQ is the nuclear quadrupole
frequency and I is the nuclear spin. This value of the isotropic chemical shift
is consistent with that found for Na+(C222) in solution.13

As mentioned previously, the Na' chemical shift is insensitive to its

environment. This is emphasized by the absence of a frequency dependent

che
qua

Fro
can

all

Frox

heig

10

chemical shift as seen in Figure 3 and the narrowness of N a“. The nuclear
quadrupole frequency, vQ is related to the quadrupole coupling constant,

eZqQ/ h by the relation:

36qu
=21 (21—1)h (15)

From this equation it can be seen that the upper limit to the quadrupole
coupling constant for N a' is 2vq. The center of gravity of a powder pattern for

a MAS spectrum is shifted from the Larmor frequency by:

:3;
AV="‘1E(ZI’1)(ZI+3)VL (1.6)

From this equation 2vQ s 0.26 MHz for the Na‘ peak. The full width at half-
height for a MAS lineshape is given by“:

I' I 2
_f_4"<22 a 3_
Av 4T|LI(I+1) 4JI 1+ 3 ] (1.7)

From this equation it follows that 2vQ s 0.23 MHz. This value is much larger
than that of the spinning rate and therefore only the central transition would
be expected to contribute to the observed spectrum.

Therefore, the N a' anion is in a much more symmetric environment than
the N at cation as seen from the values of the quadrupolar coupling constants,
the field dependency of the peaks and the lineshapes of the peaks. This is but
one example of how solid state NMR can be used as a means of identification

and as a probe of the interactions within a system.

sa

sh

CO.

str

of
cor
de;
lo I
ani<
the
para
CS'
Ran
bellt
T.
PPm.

11

Whereas quadrupolar and dipolar interactions dominate in the 23N a NMR
spectra of alkalides, chemical shift anisotropy and dipolar interactions tend to
dominate the central transition in 133Cs NMR spectra of alkalides and
electrides. The 133Cs nucleus possesses a small quadrupole moment which
permits detection of the complexed cation and the chemical shift of Cs+ is
extremely sensitive to the electron density at the nucleus which can be used
to determine the percent atomic character of the complexed cesium cation in
electrides.

The chemical shifts of the complexed cations in both the 18C6 and 15C5
sandwiched systems are nearly independent of the anion.45 The chemical
shift of Cs+(18C6)2~X' compounds, where X is an alkali metal anion, is at ~60 :t
2 ppm for all of the alkalide salts with the exception of the ceside. The
consistency of the chemical shift indicates that the complexed cation
structures in these compounds do not change significantly in the sodide,
potasside and rubidide salts. The Cs+(18C6)2'Cs" 133Cs NMR spectrum consists
of two peaks both of which are paramagnetically shifted from those of the
corresponding gaseous ions. In addition, both peaks are temperature
dependent. The temperature dependence of the cationic chemical shift is due
to the existence of two different environments for the cation, and that of the
anionic chemical shift is due to the sensitivity of the excited state character in
the Cs’ ground state to the local environment. The Cs’ peak is significantly
paramagnetically shifted from that of the calculated chemical shift for Cs‘(g).46
Cs’ has low lying d and f orbitals and therefore would exhibit significant
Ramsey shifts, which are inversely proportional to the energy difference
between the ground and excited states.47

The 133"Cs NMR spectrum of Cs+(18C6)2oe" consists of a single peak at +81

ppm. The reason for the significant paramagnetic shift relative to that of

Whe
the ;
simp
Shift
Vern
that

Whic}

12

other Cs+(18C6)2 compounds could either be due to tighter coordination of
the Cs+ by the crown ethers, or to contact with the paramagnetic electron. The
structure of Cs+(18C6)2~e' consists of a cavity at each anionic site in the
lattice.48 The electride structure is isostructural with that of the
Cs+(18C6)2-Na' structure where the mean Cs-O distance is 3.35A in both
compounds.49 The use of solid state NMR in conjunction with the known
crystal structure aids in the study of the interactions between the trapped
electron and the complexed cation. Cs+(18C6)2~e‘ is a Curie-Weiss paramagnet
showing no magnetic ordering or spin-pairing over the temperature range of
1.8 to 250 K.22 The paramagnetic or Knight shift in this compound is due to
the strong local magnetic field generated at the nucleus by paramagnetic
electron density. The Cs+ cation is sensitive to overlap with the trapped
electron as the lowest energy unoccupied orbital in the Cs+ cation is the 6s
orbital which has a non-zero electron density at the nucleus. The Knight shift

is given by50:
81:
K(T) = [3N0] <I‘P(O)l2> X (T) (1-3)

where N o is Avogadro's Number, <| W(0)l2> is the average electron density at
the nucleus and x(T) is the molar magnetic susceptibility. In general, for a
simple paramagnet, K(T) is proportional to 1/ T. The Cs+(18C6)2 e" chemical
shift was studied as a function of temperature. A graph of chemical shift
versus 1/ T shows a straight line as expected.45 ( Figure 4 ). The graph shows
that the value of the chemical shift at infinite temperature is ~61 i 10 ppm
which agrees with the chemical shifts of Cs+(18C6)2 in alkalides.

Figr

13

240
220
200
100
ISO

 

(( J.

l 2 V 3.0 3.5 4.0 4.5 5.0 5.5 5.0
l/T (x103)

 

 

Figure 4. Chemical shift vs 1/ T for Cs+(18C6)2'e'. The temperatures of
points marked with an x were calibrated using methanol.52

elei
Fig

wh
frac
ind

eth

red
ani
inte
stoi
con
The
thre
elec
of t
Shit
Sun
The
Whit

14

It is possible to calculate the percent atomic character of the trapped
electron from the known magnetic susceptibility and the slope of the graph in
Figure 4. The fractional atomic character is defined as:

F___ (its?) (1.9)

where < l \yo I 2>atom has been estimated to be 2.645 x 1024 e'cm'3.51 The
fractional atomic character for Cs+(18C6)2-e' is calculated to be 3.3 x 104. This
indicates that the cation is well screened by its interaction with the crown
ether oxygen lone pairs.

A 133Cs NMR study of mixed alkalide-electride salts was done to see if a
reduction of trapped electron density through the substitution of diamagnetic
anions for the trapped electrons would change the electron-electron
interactions. Figure 5 shows the 133Cs NMR spectra of samples with
stoichiometry Cs+(18C6)2-Na',‘-e'1.x in which x = 0.2 and 0.8.45 The spectra
consist of five lines with chemical shifts of ~61, +26, +42, +57 and +73 ppm.
The peak at ~61 ppm is due to Cs+(18C6)2 in the pure electride. The center
three peaks are spaced approximately 1/ 8th the distance between the pure
electride and pure sodide cationic peaks. From the known crystal structures
of the sodide and electride it was determined that the four paramagnetically
shifted peaks in the system were due to the complexed cation being
surrounded by eight, seven, six and five electrons in order of decreasing shift.
The NMR spectra can therefore be accounted for by a regular superlattice in

which electrons are substituted by Na' ions.52

15

 

 

Figure 5. 133Cs NMR spectra of Cs+(18C6)2°N a‘x.e'1-x where a) x=0.2 and b)
x=0.8.

16

Whereas 23N a and 133Cs NMR have been used extensively to identify and
probe the nature of these compounds, 39K and 87Rb NMR have not been as
successful. Until recently, only K‘ and Rb“ had been observed in solid
alkalides and electrides. The potassium and rubidium cations were
unobservable using the typical one pulse experiment due to the extreme line
broadening of the N MR peak. Tinkham and Dye reported the first
observation of K' in both solution and crystalline potassides.53 A 39K NMR
spectrum of a solution of K+(15C5)2-K’ in MezO consisted of two peaks at ~9.9
and ~99.3 ppm which were assigned to K+(15C5)2 and K’ respectively. The
measured chemical shift of the gaseous potassium atom is ~101 i 5 ppm54 and
the anion is expected to be 2 ppm more diamagnetic at ~103 :l: 5 ppm55. As in
the analogous case with the 23Na NMR spectrum of Na+(C222)-Na', the K'
peak is narrower than that of the K+(15C5)2 peak reflecting the more
spherically symmetric environment of K" compared with K+(15C5)2. In
general, the chemical shifts observed for potassides are within experimental
error of that expected for K'(g). Table 2 shows a summary of the chemical
shifts and linewidths of potassides. The linewidths tend to increase with
cation size in the M+(15C5)2-K' series indicating an increase in the cation~
anion interactions.

A similar situation was found in 87Rb NMR. The rubidium was readily
observed in solution.31r56 The complexed rubidium cation however was not
observable due to extreme quadrupolar line broadening57 until Dye and
coworkers observed two peaks in the 87Rb NMR spectrum of a 0.68 M
solution of Rb+(15C5)2°Rb" in MeZO. The chemical shifts of the two peaks, 33
ppm and ~192 ppm were assigned to Rb+(15C5)2 and Rh” respectively.53 The
linewidth of Rb+(15C5)2 is on the order of 5000 Hz and that of Rb’ is 170 Hz

again showing the lower symmetry of the cation environment relative to that

17

Table 2. 39K MAS-NMR Results.103

 

Commund ma A2112 IE)
K+(15C5)2~1(_‘ ~105(1) 70
Rb+(15C5)2-K'b 405(2) 120
Cs+(15C5)2°K' ~105(5) 220
I<Rb(18C6)b no signal

Cs+(18C6)2°K' -115(10) 150
K+(C222)-Rb' no signal

aChemical shifts are referenced to K+(aq) at infinite dilution.
Uncertainty of last digit given in parentheses.

bProbably contain both K' and Rb' as indicated by rubidium XANES.

18

of the anion. Table 3 shows a summary of the chemical shifts and linewidths
of rubidides. The Rb' signal varies between ~189 and ~199 ppm depending on
the frequency. In several cases, the expected signal of Rb” was not observed.
For example, the 87Rb NMR spectra of Rb+(C222)°Rb' and K+(C222)-Rb' did not
show Rb" signals even though optical and x~ray absorption studies indicated
that these compounds are both true rubidides.59‘61 Therefore the absence of a
Rb' NMR peak cannot be used as conclusive proof that the compound is not a

rubidide.

Table 3. 87Rb MAS-NMR Results.103

Commund m a 1 2 Hz
KRb(15C5)2 4910) 370(30)

Rb+(15C5)2-R_b' 4910) 460(30)

CS+(15C5)2'Rb’ 489(2) 490(30)

Cs+(18C6)2'Rb' 4940) 650(30)

KRb(18C6) no signal

aChemical shifts are referenced to Rb+(aq) at infinite dilution.
Uncertainty of last digit given parentheses.

Recently, Oldfield and coworkers published the first observation of K+ in
compounds other than simple salts through the use of a spin echo technique
to be more fully described in a later chapter.62 Through the use of this
modified spin echo technique it has been possible to detect potassium and
rubidium cation signals in alkalides and electrides.63 These results will be
discussed in Chapter 3.

In conclusion, solid state NMR has proven to be an invaluable tool in the
investigation of alkalides and electrides. 23Na and 133Cs NMR have been

used extensively to probe the cation-anion interactions in these compounds

19

through lineshape analysis, frequency studies and decoupling experiments.
37Rb and 39K N MR had not been as thoroughly studied. However, through
the use of the modified Hahn spin echo technique important NMR
parameters have been extracted. It is obvious that solid state NMR
spectroscopy will continue to reveal information about the interactions in

these compounds.

IE:

cor
hih
inte
ha.
asy
ten
inv
of

fun

latt

Shie
hox
nec
89m
rela
fieh
teas
alka

tim6

II. Spin-Lattice Relaxation Studies of Alkalides and Electrides.

II. A. Introduction.

Chapter One showed that NMR lines in solids are broad due to a
combination of dipolar, chemical shift anisotropy and quadrupolar
interactions. In order to understand the local structure of the compound(s) of
interest one can probe these interactions through the use of solid state NMR.
In addition, through computer lineshape simulation, parameters such as the
asymmetry parameter, quadrupolar coupling constant and chemical shift
tensors can be deduced. While these parameters are important in the
investigation of the static interactions within a solid, there is another branch
of NMR spectroscopy which deals with the dynamic processes, and is
fundamental in the investigation of solids. This process is known as spin-
lattice relaxation.

The study of spin-lattice relaxation has been very important in NMR
studies for two reasons. The spin-lattice relaxation time of a solid determines
how fast one can pulse the sample and therefore controls the total time
necessary for data accumulation. This point is of great importance since in
general, solids have long spin-lattice relaxation times. The spin-lattice
relaxation time also provides information about the fluctuating internal
fields present at a given nuclear site. This chapter will focus on the second
reason, as the purpose of this project was to probe the interactions within the
alkalides and an electride through the determination of spin-lattice relaxation

times.

20

in

5)’

thl

foi

eq
rat

OCt

eqi

rel.

Spi

tirr

inte

Spi:

per-

the

21

There are two relaxation times. The spin-lattice relaxation time, T1, is the
time necessary for the nuclear spin system to transfer energy from the spins to
the lattice. The spin-spin relaxation time, T2, is the measure of the rate at
which energy is distributed within the spin system.

In considering spin-lattice relaxation one can take a thermodynamic view,
in which the spins are considered to be in an isolated thermodynamic
system.64 It is assumed that the coupling between nuclei is much stronger
than the coupling between the nuclei and the lattice. The establishment of
thermal equilibrium between the spins and the lattice can occur in the
following manner. First, the spin system attains internal thermal
equilibrium with a "spin temperature" which is defined by the population
ratios of two energy levels, given by the Boltzmann distribution law. This
occurs in a time T2. Secondly, the "spin temperature" will come into
equilibrium with the "lattice temperature" with a time constant T1>>T2. The
relaxation mechanism can then be considered to be a transfer of heat from the
spins to the lattice "bath" as shown below.

Relaxation can be understood by a quantum mechanical description of the
time-dependent terms of the Hamiltonian, H1(t) which represent the
interactions involved between the spin system and the lattice.‘55 Consider a
spin system 5 having levels la), ..., IB), etc. with energies n.3,... If a
perturbation, such as a coupling with a lattice, is applied to this system, then

the system can be represented by the equation:

IC) = 2 can) e'i‘” la) (2.1)
a

eqi

The

Fou

Whe
the ;
ma g
Sque
for

Char.-

22

IC) is the state of the system and the coefficients Ca obey the Schrtiedinger

equation:

iii-(i = 2 [a EH10) E [3 Jcimaflt C (2-2)
I3

in which (0043 = 01—8. If H1 (t) can be written as a single product then H1(t) =
AF(t) where A is an operator acting on the variables of the system and F(t) is a
random function. Therefore the transition probability or relaxation rate can

begivenby:
' IAI '2
ww=Ka B): 1(a)”) (2.3)

The term J(co) is called the spectral density function and is given by the

Fourier transforms of the correlation function G(1):

J (co) = J 6(1) e'i‘mdr = J- F(t) F(t+1) 6“" (11 (2.4)

where in dealing with quadrupolar systems F(t) is the electric field gradient at
the nucleus of interest at time t. The bar indicates an ensemble average. The
magnitude of the expression in Eqn. (2.4) is dependent on both the mean
square electric field gradient at the nucleus and the characteristic time scale
for the fluctuations present in the field gradient. This time scale is
characterized by the term 1c, the correlation time which describes the motion

represented by the correlation function 6(1):

2 3
6(1) = 6(0) c(~hl/TC) (2.5)

The correlation time corresponds to the average time between molecular
collisions for translational motion or the average time for a molecule to
rotate one radian in the case of reorientational motion. Therefore a more
mobile solution will have a shorter correlation time. The correlation time is
dependent on molecular size, symmetry and the viscosity of the solution. In
the case where waflzrcz << 1, known as the extreme narrowing condition,
T1=T2 for solutions, with a few exceptions. This is not true in the case of
solids as the spin-spin interaction is so strong in the solid state and therefore
the spin-spin interaction rate will be much faster than the spin-lattice
relaxation rate which means that T1 >> T2. The spectral density can then be

described in terms of the correlation time and the resulting equation is:

to

J =26 O ——
(03) ( ) “(”8572

(2.6)

Therefore the transition probability can be written in the following form:

= 20(0) l<oc IAI B>|2 —_°_T

(2.7)
+310) “3 12

This leads to an expression for the rate of change of the populations Pa:

 

Pa = (2.8)

2 4
where N is equal to the total number of spins and N + and N_ are the number

of nuclei in the two spin states. Therefore

=W... <P..- P3) (2.9)

where Pa” is the polarization at thermal equilibrium and is given by the

 

 

equation:
hmI ho)I
°° —i _l

Therefore it has been shown that spin-lattice relaxation is the process by
which the temperature of the spins and the temperature of the lattice come
into equilibrium.

As mentioned, information about the fluctuating internal fields present at
the nuclear site can be determined from the nuclear spin-lattice relaxation
time. These fluctuating fields can be either magnetic or electric in nature. If
the electric quadrupole moment is zero or negligibly small, the internal
motion of the atoms in the solid such as hindered rotation or diffusion, for
example, can provide the dominant relaxation mechanism.66 The presence
of paramagnetic impurities can also be the cause for the fluctuating fields in
both the solid and liquid state. If a nucleus possesses an electric quadrupole
moment then the induced quadrupole interaction via lattice vibrations can

provide the dominant relaxation mechanism.

 

 

 

IF:l

2 5
II. B. Theogg of Quadrupolar Relaxation.

It was Pound who first demonstrated experimentally that for nuclei with I
> 1/2, the dominant relaxation mechanism in ionic crystals was quadrupolar
in nature.57‘69 He determined that "at not too low" temperatures (T~ 100 K)
quadrupolar relaxation may be more important than impurity relaxation in
pure crystals, whereas "at low" temperatures (TS ~ 6 K) impurity relaxation is
dominant over quadrupolar relaxation. It should be noted that quadrupolar
relaxation is strongly dependent on temperature and is ineffective at lower
temperatures while impurity relaxation is relatively temperature
independent and therefore becomes dominant at low temperatures.

Before the theory of quadrupolar relaxation can be discussed, it is necessary
to first look at a description of lattice vibrations which occur by means of
lattice phonons. This description has been used in the theory of the physical
properties of crystals such as shielding, antishielding and covalent effects
which are difficult to estimate and therefore hinder accurate calculations of
relaxation times.

In a phonon spectrum, the low-frequency portion can be described by a
simple Debye spectrum. The high-frequency portion of the spectrum which
differs for different crystals, usually exhibits maxima which are associated
with acoustic and optical vibrational branches. An approximation of the
dependence of the frequency on the phase vector and the polarization index is
given by Debye's approximation of a propagation velocity, v, which is both
independent of the direction of the polarization of the wave and the
propagation of the wave.65 The number of modes of oscillation which have

frequencies between a) and (0 + do: is:

26

_3N “f2 _ 3N a3 2
o(m)dco-—4 df-—-41:—co dco (2.11)
811:3 8113 v3

where a is the lattice spacing, N is the total number of atoms, v is the
propagation velocity of the wave and f is the phase vector. Therefore the

spectrum is given by:

2
0(a))=-312-‘°—3 since Na3=v (2.12)

The spectrum must have a high-frequency cutoff Q as the total number of

modes is restricted to the 3N degrees of freedom of the lattice. Therefore

11
Iowa) do) = 3N (2.13)
o

where

2
0(w)=9—:§°— and £2=§(61:2)”2 (2.14)

Finally the Debye temperature 6 of the crystal is defined by the equation:

RD :27; (2.15)

An effective temperature T" can then be defined as T"=T/9. The Debye
temperature is on the order of 200 K to 300 K for many compoundsfi5 This

means that the definition of "low" temperature means 56 K whereas " high"

27

temperature is on the order of >100K if the Debye temperature for the
compound(s) in question is between 200 K and 300 K.

Quadrupolar relaxation is caused by the induced fluctuations in the
electrical field gradient at a given nucleus due to the displacement of the
lattice site via lattice vibrations. The local distortion of the lattice is described

by the relative displacements of two lattice sites which is given by 70:

,~[;’i-3—]q (2.16)

where r is the relative displacement, R is the interatomic distance, it is the
wavelength of the vibrational mode and q is the amplitude of the vibration.
At high temperatures the amplitude of vibration can be approximated by a
classical oscillator with energy E given by the equation below:

1 2 2 1
13:— =—kT 2.1
2Mcoq 2 ( 7)

where M is the molecular mass of the crystal. Therefore the displacement is

expressed in the following manner:

 

1/2
-kT
[M012 J (2.18)

The quadrupolar Hamiltonian can be written in the expanded form65:

0 1 2
H agar”. U.

Q Q (2.19)

28

where HQW is the static quadrupolar interaction which perturbs the equally
spaced Zeeman levels of the nucleus in the presence of an external magnetic
field. This term is time independent and will lead to a pure quadrupole
spectrum and is therefore taken to be zero. The Hamiltonian can then be

written as:

HQu) = (1’ + ‘2’ (2.20)

where

 

 

"of—2?: 8:2 "62¢er .1215}ng (2.21)
R R 3r2 R5
The term g is a multiplication factor which accounts for Sternheimer
antishielding effects, covalent effects etc. In the presence of a nuclear
quadrupole moment, the valence electrons polarize the originally spherically
symmetrical inner "core" electrons thereby causing a distortion from
spherical symmetry and a contribution to the external field gradient at the
nucleus. This amplification of the overall field gradient is denoted by the
Sternheimer antishielding factor, [3.71 The crystalline field will interact with
the nuclear quadrupole moment and with the quadrupole and higher
moments induced by the quadrupole moment in the charge cloud
surrounding the the nucleus. This induced quadrupole moment can be
considerably larger (factor of 10 to 100) than the quadrupole moment itself.
The first order term in HQm in Eqn. (2.20) gives rise to the "direct
processes" in which the nuclear spin can make either an upward or

downward transition while one of the lattice oscillators is de-excited or

29

excited respectively. The contribution of the direct processes to the relaxation
is essentially zero as the probability of the direct process is equal to the
resonance frequency which is in the radiofrequency region.65 The second
order term of HQU) and the higher order terms of HQQ) are assumed to be
negligible as they give rise to Raman processes which are not important to the
relaxation mechanism. It is the first order term of HQQ) which gives rise to
the relevent Raman processes which involves the absorption of one phonon
and the emission of another phonon. In this case the frequencies to and (0' of
the phonons satisfy the relation 0) ~ (0' = (no where (no is the nuclear resonance
frequency and (u can take all the values inside the phonon spectrum. The two
Raman process in which either two phonons are absorbed or two phonons
are emitted is neglected because the relation 01 + co' = (no restricts this process
to a very small portion of the phonon spectrum.
The transition probability W, for the relevent Raman process is given by

(“in

1w—§_3. _ 2
TI" " 1‘26”. P((0i) 13((1)j)5(coi mjimL) IHI dcoidu)j (2.22)

The integral takes into account all of the combinations by which a phonon of
lattice mode i can be absorbed while a phonon of lattice mode j can be
emitted. The integral is taken over all the possible lattice frequencies where
com is the maximum allowed frequency for a Debye spectrum. The delta
function ensures that the energy difference between the initial and final states
is the energy exchanged between the lattice and spin systems. The density of
lattice modes per unit frequency interval is denoted by Mao). It is assumed

that p(coi) = Mon) since the Larmor frequency (0L is small compared to the

latt
Del

Wht

whe
spin

mun

was

ham
Vanl
Cryst
quad
thit .-
time

MEX;
mode
a$um

30

lattice frequencies (by a factor of 105-107) and therefore p(co) is defined as for a
Debye distribution:

 

= 3Vao2 2 23
ptw) 2W, (. )

where V is the molecular volume of the crystal. The integration of Equation

(2.22) gives an expression for the spin-lattice relaxation rate:

2 2
1 9 ezyQ kT]
Tel R3) [mv’ ”'2‘”

 

where the mass density m=M/ V. From this equation it is apparent that the
spin-lattice relaxation time is inversely proportional to the square of the
temperature.

A general theory of quadrupolar spin-lattice relaxation in crystalline solids
was first developed by J. VanKranendonk.72 A general expression for the
transition probability and its temperature dependence was derived by
VanKranendonk to explain the nature of nuclear spin-lattice relaxation in
crystalline solids which occur from the interaction of the nuclear electric
quadrupole moment with the crystalline electric field. This derivation shows
that at low temperatures (T*< 0.02) the quadrupolar spin-lattice relaxation
time is inversely proportional to T7 and at high temperatures (T? 0.5) the
relaxation time is inversely proportional to T2 A simple one parameter
model was also developed in which the crystalline field at a nucleus is
assumed to consist of equal point charges placed on the nearest neighboring

lattice sites. These charges possess a magnitude which is a measure of the

31

quadrupolar spin-lattice coupling. VanKranendonk was then able to perform
detailed calculations on N aCl-type crystals using this point charge model.
These calculations have been used successfully on other compounds which
do not have the N aCl structure; however, this could be due in part to the fact
that the measurements were performed at temperatures greater than or equal
to 9/2. In this region the temperature dependence of the relaxation process is
independent of both the spin-lattice coupling and the vibrational spectrum.73
Although the VanKranendonk theory correctly accounts for the total number
of vibrational modes and the relaxation caused by acoustic phonons it does
not specifically look at the optic vibrations.73 The overall temperature
dependence of the spin-lattice relaxation due to the optic vibrations should
differ slightly from that of the acoustic vibrations. In both cases, one expects
that the spin-lattice relaxation would be inversely proportional to the square
of the temperature at high temperatures. However a difference between the
two types of vibrations would be noted as the optic branches, occurring in the
higher frequency range, would depopulate faster with decreasing temperature
and therefore show a greater rate of change in the spin-lattice relaxation time.
If a crystal relaxes by a Raman process containing both optic and acoustic
mode vibrations, an initial deviation from T1 ac T'2 behavior with decreasing
temperature would be caused by the depopulation of the optic modes. As the
probability for optic mode relaxation decreased, relaxation via acoustic mode
vibration would dominate and follow the expected behavior derived by
VanKranendonk. Although the theory derived by VanKranendonk does not
give a definitive explanation of the quadrupolar spin-lattice relaxation
process in crystalline solids, it has been used as a model in both theoretical

and experimental investigations of quadrupolar relaxation.

Va
str
cm
011
are
wil
vit
vil:
flu
Vai
sys
the
of I
reqi
thet
pho
quai

shm

£21

I.

meas
whet

them:

32

Alkalides and Electrides are very complicated systems. The
VanKranendonk theory was tested on simple alkali halide salts in which the
structures have been elucidated. In general, the alkalide and electride
compounds are not made up of rigid lattices, rather the lattices are "soft".
One can picture these compounds as consisting of a cation and anion which
are surrounded by a "sea" of protons due to the complexants. These protons
will continuously vibrate and as the temperature increases the rate of
vibration will increase as the complexants become more flexible. These
vibrations will cause time-dependent electric field gradients due to the
fluctuating field and can therefore lead to relaxation processes. The
VanKranendonk theory assumes one Debye temperature will describe the
system of interest, however due to the nature of alkalides and electrides and
the various time-dependent perturbations that occur due to the "soft" nature
of the lattices, it is expected that a series of Debye temperatures would be
required to describe these systems. In order to use the VanKranendonk
theory in a quantitative manner it would be necessary to determine the
phonon spectrum for these compounds. The VanKranendonk theory of
quadrupolar relaxation can still be used in a qualitative manner as it will be
shown that quadrupolar relaxation processes are the main mode of relaxation

in the alkalide and electride compounds.

11. C. Experimental Section.

Two methods, Inversion Recovery and Saturation Recovery, were used to
measure the spin-lattice relaxation times of the alkalides and an electride.
When a sample is placed in a magnetic field, the spins will tend to align

themselves with the magnetic field, which shall be denoted the z' direction.

or
be
re-
ac<
wi

CaI

wh.
the
give

inte

At 5
dela
irite]

used

33

The Inversion Recovery pulse sequence and schematic are shown in Figure 6.
First, a 180° pulse is applied which causes the spins to invert. A variable delay
time 1, allows the spins to begin to relax back to their original positions before
a detecting 90° pulse is applied which brings the spins into the y' direction

and allows the signal to be measured. This sequence is repeated N times in
order to obtain a satisfactory signal-to ~noise ratio. A delay time, Td, is used
between each sequence in order to allow the Boltzmann population (Mo) to be
re—established. This means that Td must be on the order of 5T1. The
accumulated FID is then Fourier Transformed and the sequence is repeated
with another delay time 1. The value of the spin-lattice relaxation time, T1,

can be obtained from the equation:
M.=M0[1-2cxp<-r/r,)1 (2.25)

where Mt is the magnetization or intensity of the signal at time t and M0 is
the magnetization at infinite time. The total nuclear magnetization at a
given delay can be measured by either the calculated signal intensity or the
integrated signal. When the delay times are much longer than the value of
T1 the measured signal intensity is equal to the equilibrium magnetization.
At short delay times, (1 < T11n2) the signal will be negative, whereas at long
delay times, full recovery will be obtained where Mo = Mt, At some
intermediate time, the signal will be zero and this time, denoted 1mm, can be

used to obtain an estimate of the T1 value where

tnull
T = (2.26)

 

34

Inversion Recovery

Pulse Sequence : 180° - 1 - 90°

2'

 

 

 

 

 

[180°- ‘C-90°Ta-len Td 2 5T1
180° 0°
., J7 . l l
AQ

Figure 6. Inversion Recovery Pulse Sequence (a) and Schematic (b).

35

An example of an Inversion Recovery sequence is shown in Figure 7. In
general, the Inversion recovery sequence is not a practical method in the case
of solids because of time constraints since the T1 values of solids can be on the
order of seconds or longer. Due to the long delay times needed between each
pulse sequence, the Inversion Recovery method is most often used in the
relaxation studies of solutions where the spin-lattice relaxation times tend to
be very short.

The second method, Saturation Recovery, is the general method used in
the spin-lattice relaxation studies of solids. The advantage of this method is
that there is no need to wait 5T1 between each sequence. The pulse sequence
and schematic are shown in Figure 8. Since the spins align themselves with
the magnetic field a train of 90° pulses, also called a homogeneity spoiling
pulse, are applied to cause a random distribution of spins in the y' direction.
After a wait time, 1, another 90 ° pulse is applied and an FID is obtained. This
sequence is repeated until a satisfactory signal-to-noise ratio is obtained.
There is no need to wait between each sequence as the process begins with
zero net magnetization of the spins. As in the Inversion Recovery method
the resultant FID is Fourier Transformed and a series of 1 values are used. An
example of a Saturation Recovery sequence is shown in Figure 9. The T1

value is obtained from the equation:

M1 = M0 [l-cxp(-T/rl)] (2.27)

The data were analyzed by KINFIT analysis,74 a nonlinear curve fitting
program and/ or by an analysis program called SIMFIT. A temperature study

was also done for all of the compounds studied in order to determine the

36

.Mmmu “a thGUwCEU how 029, C. 05 “0 3v sozmfifihzmv
839:8 a can A3 00:033.... Egan.“ 62835 an Co 83:35

as so. n F ..ll.

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

c. enema

 

:2:

 

37

Saturation Recovery

Pulse Sequence : 90° , HSP - 1 - 90° - Ta

 

 

 

 

 

[90°, HSP - 1 - 90°- Ta. HSP] n

F

., JUIHJI

' Train of 90°

 

 

I

n

. N

90° AQ

Figure 8. Saturation Recovery Pulse Sequence (3) and Schematic (b).

i ll l

l

l

lduut Jdddluwt

1(usec) —-)

Figure 9. Exampleo ofa Saturati Reco vueryseq ence forCs+(15C5)2-Rb' at

213K.

39

temperature dependence of the spin-lattice relaxation times of the
compounds.

The spin-spin relaxation times (T2) were measured directly from the
linewidth (full-width-at-half-height) of the nearly Gaussian alkali metal
anion NMR lineshape. There are two types of lineshapes which are found in
NMR spectroscopy; homogeneous and inhomogeneous lineshapes. A
homogeneous lineshape consists of a sum of individual lines which possess
the same lifetime broadening and do not shift relative to each other.65 In this

case the spin-spin relaxation time for a Gaussian lineshape is given by

_ __1__
2 - "Mi/2 (2.28)

where Av1/2 is the full width at half height. This equation can be used in the
case in which the dipole-dipole interactions within the solid cause the spins
to be indistinguishable in the frequency domain so that the flip-flop process of
the spins cause the spins to relax equally. An inhomogeneous lineshape is
made up of sum of non-overlapping individual lines. In this case the lines
are shifted relative to each other and the distribution of these shifts
determines the lineshape. Individual lifetime broadening may occur within
each spectral packet; however, coupling between the spectral packets does not
exist. In the case of an inhomogeneous lineshape, the measured linewidth
gives a time constant which is related to the strength of the interaction.

In the case of alkali metal NMR, as mentioned previously, there are three
sources of linebroadening: dipolar, quadrupolar and chemical shift
anisotropy. Whereas dipolar broadening can cause either a homogeneous or

inhomogeneous lineshape, the other two sources lead to inhomogeneous

40

broadening. If the lineshape is due to pure homogeneous effects then the
spin-spin relaxation time obtained from the linewidth of the NMR peak is an
accurate measurement. If inhomogeneous broadening plays a role in the
lineshape of these compounds then the T2 value obtained from the lineshape
is a lower limit to the actual value. The values of the spin-spin relaxation
time will be reported as Tz" where the " indicates that the value may include
some inhomogeneous interaction. In order to obtain an accurate value of T2
one must use a spin echo technique which is the most common method of
measurement for the spin-spin relaxation time.

The studies were carried out on a Bruker 400 MSL spectrometer at
Cambridge University in England and on Bruker 400 AM and Bruker 180
WH spectrometers at Michigan State University. Saturation recovery and
Inversion recovery methods were used to obtain the spin-lattice relaxation
times. Upfield (diamagnetic) shifts are negative. The resonance frequencies
in a 400 MHz instrument for 23Na, 39K, 87Rb and 133Cs are 105.8, 18.67, 130.9
and 52.48 MHz respectively. An external standard was used to determine the
chemical shift relative to the value of the reference in aqueous solution at
infinite dilution. Variable temperature experiments in the range of 170 to
300K were performed by using a Bruker variable temperature control unit in
the Bruker 400 MSL spectrometer and through regulation of the air flow from
a high pressure liquid nitrogen dewar on the 400 AM spectrometer. Static
spectra were obtained for all of the samples except for the compound
Cs+(15C5)2-K', for which the magic angle sample spinning (MAS) technique
was used on the Bruker 400 AM spectrometer. It was necessary to spin the
Cs+(15C5)2-K" sample due to the poor sensitivity of the 39K nucleus.

An important parameter in the spin-lattice relaxation experiment is the

determination of the 90° pulse. The method used to determine the 90° pulse

41

consists of obtaining a series of spectra having differing pulse lengths. The
180° pulse is defined as the pulse length used to obtain a null signal and the
90° pulse is determined to be half the 180° pulse length value. An example of
a 90° pulse length determination is shown in Figure 10. In order to obtain
accurate results, the 90° pulse must be measured for each sample as different

probes as well as the samples themselves can cause the 90° pulse to be slightly
different. The values of the 90° pulses used in the experiments are as follows.
The 90° pulse values used on the Bruker 400 MSL for 23Na, 39K, 87Rb and
133Cs were 5.85, 27.5, 7.9 and 7.5 usec respectively. The Bruker 400 AM 90°
pulse values were 4.7, 12.0, 3.9, and 14.8 usec for 23Na, 39K, 37Rb and 133Cs
respectively. The 90° pulse used for 23N a on the Bruker WH 180 was 4.5 usec.

The alkalide and electride samples were prepared as previously described
in Chapter One of this thesis.13'15 The model salts were prepared by
combining stoichiometric amounts of conventional alkali metal salts and
complexant which were dissolved in either hot methanol or 2-propanol as
described by Pedersen.75'76 The solutions were cooled to allow crystal
formation and then filtered and washed. The crystals were either allowed to
dry at room temperature in air or under vacuum.

The crystalline alkalide and electride compounds were loaded into either
cylindrical A1203 rotors with Kel-F caps or homemade Delrin cylindrical
rotors with screw-on caps. The A1203 rotors were equipped with Kel-F caps
which had holes in the centers to allow a Kel-F bolt and nut to be used in
order to prevent the caps from coming apart at low temperatures. The rotors
were packed with powdered samples while under a cooled dry nitrogen
atmosphere. The samples were transferred to the spectrometer while in

liquid nitrogen and loaded into the precooled NMR probe.

42

.ohzfimafimh

800% “a _UmU .8» cougar—flab .5wa 83m com a Co 29:58 :< .3 0.53m

nun

 

Dun

 

 

 

 

 

 

 

43

H. D. RESULTS.
II. D. 1. Simple and Model Sa_1_t_§_:

Spin-lattice relaxation measurements on a series of alkali metal halides
were made at room temperature on the Bruker 400 MSL for the purpose of
testing the automation programs and the reliability of the measurements. A

summary of these results is shown in Table 4.

Table 4. A Comparison of Measured (T101353) and Literature (T1111) Spin-lattice
Relaxation Times for some Alkali Halides at Room Temperature.

Compound THEM 11mm
NaCl 14.3 i 1 12a
KCl 12911 szab
RbCl 0.342 i 0.1 0.250a
C50 188. :l: 20 190 C

aSee Reference 77. Accuracy reported to be within 10%.
bEstimated value. See Reference 77.
CSee Reference 78. Error reported to be i20 sec.

The observed spin-lattice relaxation times of the powdered samples are in
good agreement with the literature values, with the exception of KCl which is
a factor of two different from the estimated literature value. The spin-lattice
relaxation time, T11“, for KCl was determined by Wikner, Blumberg and
Hahn using the known 35C] KCl T1 value. By using the assumption that the
size of the ions were nearly the same and taking advantage of the fact that the
nuclear spins for K and C1 are both 3/2 a crude value for 39KCl was

obtained.77

vvi
val
at

5a:
the
spi
nta
the

011

rel.-
fltt
the

qua
hat
res<
110‘
gfiv(
Era
qua
h€a(
tem
qual

Squa

44

In addition to these results, relaxation measurements were made on N aCl
with the Bruker WH 180 spectrometer. It is interesting to note that the T1
value for static N aCl at 47.62 MHz was the same, 14.4 $4 sec, as that obtained
at 105.8 MHz and furthermore, the T1 value was the same for the spinning
sample, 13.7 2!: .4 sec at 47.62 MHz. These spin-lattice relaxation results show
that T1 for NaCl is not affected by rotation of the sample. In principal, the
spin-lattice relaxation time of a sample should not be affected by the
macroscopic spinning of the compound unless the spinning frequency is on
the order of the Larmor frequency.79 Therefore since the spinning rate was
on the order of 1-2 KHz and the Larmor frequency is on the order of MHz, the
T1 value is not changed upon spinning of the NaCl sample. The spin-spin
relaxation time however, is dependent on sample rotation. In the case of
fluids, in the extreme narrowing region where motion causes decoupling of
the spins, T2 approaches T1. However, to date there have been no reports that
T2 has approached the value of T1 as a result of sample rotation.

The main mode of relaxation for these alkali metal salts is through
quadrupolar relaxation. This fact might seem surprising since these salts
have cubic structures. Cubic symmetry means a zero field gradient at the
resonant nucleus which in turn leads to a zero static quadrupolar interaction.
However, induced field gradients which are caused by lattice vibrations will
give rise to a time dependent quadrupolar interaction via a fluctuating field
gradient. Experimental studies have shown that these salts undergo
quadrupolar relaxation. For example, the spin-lattice relaxation times for
NaCl were determined to be inversely proportional to the square of the
temperature.77 In the case of nuclear lattice-phonon interactions which are
quadrupolar in nature the relaxation times are inversely proportional to the

square of the quadrupole moments of two isotopes in the same crystal. The

4 5
thermal relaxation time ratio T1(37Rb)/T1(35Rb) of the two isotopes of
rubidium is 1.231: 0.40 whereas the calculated ratio of the inverse square of
their quadrupole moments is 1.027.70 In addition there is a trend between the
T1 value of the alkali metal salts and the respective quadrupole moments as

seen in Table 5.

Table 5. Spin-lattice Relaxation Values for the Alkali Halides and the
Quadrupole Moments and Sternheimer Antishielding Factors for

 

the Alkali Metal Nuclei.
Compound Nucleus ng10'28m2)a Jib T1 sec
NaCl 23N a 0.10 ~5.07 14.3 :l: 0 1
KCl 39K 0.049 ~18.2 12.9 i 0 1
RbCl 87Rb 0.13 ~51 0.342 :l: 0.1
CsCl 133Cs -0.003 ~102.5 188. :l: 20
aSee Reference 80.
bSee Reference 81.

From Table 5 it can be seen that as the quadrupole moment increases the
spin-lattice relaxation time decreases. CsCl has the largest T1 value and the
smallest quadrupole moment, whereas RbCl, with the largest quadrupole
moment, has the shortest spin-lattice relaxation time. This trend indicates
that the quadrupolar relaxation mechanism is more efficient for those
compounds with nuclei that have large quadrupole moments. Although the
results shown in Table 5 reflect the dependence of the quadrupolar relaxation
rate on the nuclear electric quadrupole moment, a 1:1 correspondence of the

T1 values and quadrupole moments does not occur even though the

4 6
structures of NaCl, KCl and RbCl are similar. This is due to the difference in

the Sternheimer antishielding factor for the nuclei, which describes the
amplification of the electric field gradient at the nuclear site because of the
distortion of the core electrons from spherical symmetry. The antishielding
factor increases with increasing atomic number. Therefore from Table 5, it
can be seen that the values of T1 for 23NaCl and 39KC1 are very close even
though the nuclear quadrupole moment for the 39K nucleus is half that of the
23Na nucleus. The same is true for 37Rb, where the nuclear quadrupole
moment is close to that of the 23Na nuclues but the relaxation rate is much
faster for 87Rb. Other factors such as the internuclear distance and the type of
vibrational modes are also important when a comparison of the T1 values
involves similar structures.

Since the main source of line broadening in the powdered samples of the
alkali halides is due to dipolar interactions, one may wonder about the effect
this has on the spin-lattice relaxation times of these compounds. The dipolar

relaxation rate can be expressed by:

(4)188 (2.29)
IS

where 71 and 75 are the gyromagnetic ratios and r155 is the interatomic
distance. The expected quadrupolar relaxation rate can be estimated from the

expression below:

)0 )2
{Tl—I .. 21+3 {542' (1 +13)2 (230)

K 1) 12(21-1)K h I

47

where I is the nuclear spin, Q is the quadrupole moment and B is the
Sternheimer antishielding factor. Since eq o»: 1/ r3 the above expression can be

modified to:

 

Q
l-l—l .. 21+3 i—lzlnplz
(T1) I’m-ml?)k ’ (2'31)

Table 6 gives the relevant data needed to make the comparison between the
expected dipolar and quadrupolar relaxation times and Table 7 shows the

scaled spin-lattice relaxation times.

Table 6. The Gyromagnetic Ratios, Nuclear Spins and the Interatomic
Distances for the Alkali Halide Samples.

Nucleus y_x_1_0_7 (£14 _s_‘1L I_ Compound X-CISA)
23Na 7.09 3/ 2 NaCl 2.361
39K 1.25 3/ 2 KC] 2.667
85Rb 259 5/ 2

87Rb 8.78 3 /2 RbCl 2.787
133Cs 3 53 7/2 CsCl 2 906

" See Reference 82.

 

48

Table 7. Scaled Spin-lattice Relaxation Times.

 

Compound Dipolar Quadrupolar Measured
N aCl 1.0 1.0 1.0
KCl 0.016 0.4845 1.1
RbCl (87Rb) 0.61 94.27 42
CsCl 0.071 0.0164 0.076

————--_———-——-——_————-_———~-—-—-_—_--‘_—_—-~‘—“—-—--_.

The comparison was made by dividing the expected dipolar relaxation time,
the expected quadrupolar relaxation times and the actual relaxation times by
the respective values calculated for N aCl, therefore all of the N aCl values are
equal to one. A comparison of the results show that the estimated
quadrupolar ratios are overwhelmingly close to those of the measured ratios.
Therefore both this calculation and the experimental results obtained by
Wikner, Blumberg and Hahn overwhelmingly support quadrupolar spin-
lattice relaxation as being the dominant relaxation mechanism in these alkali
halide salts.

In addition, the spin-lattice relaxation times for several model salts were
measured at room temperature. The results are shown in Table 8. The
purpose of this brief study was to probe the spin-lattice relaxlion times of the
N a+ cation and compare the results with the Na‘ anion. This goal was most
easily accomplished by investigating several model salts even though there
have been two homonuclear sodides, Na+(C222)-Na' and Na+(C221)-Na',
synthesized to date. Figure 2 in Chapter 1 showed both the static and
spinning 23Na NMR spectra of N a+(C222)-N a'. From these spectra it can be

seen that the Na+ and Na’ peaks are close enough that overlapping of the

49

peaks would interfere with an accurate determination of the T1 values for the

two species.

Table 8. The Room Temperature T1 Values for three Model Salts.(23N a

NIVIR)
Compound T1Obs (sec)
N a+(C222)'SCN' 0.012 :1: 0.004
N a+(12C4)2-C1' 0.2 :l: 0.1
N a+(18C6)°SCN' 0.05 :t 0.01

The difference in the relaxation times can be most easily understood if one
considers the structures of the complexed cations in the three compounds
shown in Figure 11. It can be assumed from the structure of N a+(C222)-I' that
the Na+(C222)-SCN' structure consists of a cation which is located at the
center of the molecule cavity of the bicyclic complexant and surrounded by all
eight heteroatoms of the ligand.83 The local structure of the Na+ in
N a+(12C4)2-Cl'05H20 has D4 symmetry where the oxygen atoms of the two
crown ether rings occupy the vertices of a square antiprism which is centered
around the N a+ cation.84 The staggered arrangement of the cation complex
allows easy movement of the sodium ions from sandwich to sandwich. The
structure of the complex cation in the Na+(18C6)-SCN'~H20 monoclinic
structure is highly unusual. The N a+ cation is surrounded by five essentially
coplanar oxygen atoms and the sixth oxygen atom which forms a distorted
pentagonal bipyramidal coordination of the cation.85 It can be inferred from
the structures and their description that the most symmetrical compound is
N a+(1 2C4)2-Cl'. As can be seen from Table 8, Na+(12C4)2-Cl' has the longest T1
value of the three model salts and Na+(C222)-SCN" has the shortest T1 value.

50

 

 

Figure 11. Representative structures of a) N a*(C222)'SCN', b) N a*(12C4)2'Cl'
and c) Na+(18C6)'SCN'.

51

The spin-lattice relaxation is the most efficient in the least symmetrical
compound which must then be the cryptand salt. The spin-lattice relaxation
time is short in these compounds because of the strong quadrupolar
interactions produced by the fluctuation of the electric field gradient. This
fluctuation is caused by vibrations of the counter ion and ether oxygens in the

crown or cryptand.

II. D. 2. Alkalide and Electride Samples.
II. D. 2. a. 23Na NMR.

Spin-lattice relaxation measurements were performed on several sodides;
however, the results for only two sodides, Cs+(18C6)2-N a" and Cs+(15C5)2-Na'
will be reported here for reasons to be explained later in this section. The
Cs+(18C6)2-Na' results were obtained on the Bruker 400 AM at Michigan State
University. The results are shown in Table 9, while Figure 12 shows the
temperature dependence of both the spin-lattice relaxation times and the
apparent spin-spin relaxation times. As can be seen from the figure, the spin-
lattice relaxation times decrease rapidly with increasing temperature. At 173
K the spin-lattice relaxation time is extremely long, 107 sec, indicating that the
quadrupolar mechanism is extremely inefficient due to the highly
symmetrical nature of the N a' ion as a result of its outer electron
configuration. This is the longest T1 value known to date for sodium. As the
temperature is raised, molecular motion within the compound increases,
providing a means of relaxation and therefore decreasing the time needed for
relaxation. This is confirmed by the spin-spin relaxation times, determined
from the linewidth of the spectra, which indicate that as the temperature is

raised, the line narrows considerably due to the increased molecular motion

5 2
Table 9. 23Na NMR Spin-Lattice Relaxation Data for Cs+(18C6)2-Na'.

Temperature (i_2 K) T1(sec) 12" x10“‘.(s§g).a
173 107.4 :1: 11.3 1.50
191 64.6 :1: 5.4 1.49
195 38.1 :I: 2.3 1.45
211 13.4 :1: 1.8 . . 1.48
222 8.5 :1: 0.8 1.68
237 6.9 :1: 0.3 2.12

2.52 0.96 :l: 0.22 —-
269 0.99 i 0.33 2.12
273 0.94 i 0.08 2.36
293 0.39 i 0.11 4.80

a Uncertainty to i 0.09 x 10—4 sec.

53

 

a) .

In T1
to
l

I

 

 

 

 

 

 

 

5 1 5 2 5 3 5.4 5 5 5 6 5 7
In T(K)
-7.6 u
b) ‘
-7.8 -
-8.0 -
. -8.2 -
f! .
E.
-8.4 -
I
at
-8.6 -
q
-88 - Ia
~90 r r ‘ I ' i ' ' ' ' '
5.1 5.2 5.3 5.4 5.5 5.6 5.7
In T(K)

Figure 12. LnT1 versus Temperature (a) and In Tz" versus Temperature (b)
for Cs+(18C6)2-Na'.

54

within the sample. It should be noted that the chemical shift does not change
at all throughout the entire temperature range. In addition there was no sign
of decomposition during the experiment demonstrating the thermal stability
of the compound.

Figure 13 shows the 23N a NMR spectrum of Cs+(18C6)2-Na‘ at 269 K. This
spectrum is extremely interesting as the satellite peaks for the spin 3/2
nucleus can be observed. This is the first time such satellites have been
observed in the 23N a NMR static spectrum of a powdered sodide. From this
spectrum it is possible to accurately determine the quadrupolar frequency, dig),
and the quadrupolar contibution to the linewidth of the central transition.
The distance between the two satellite peaks is equal to 2(0Q65 The
quadrupolar frequency obtained from the Cs+(18C6)2-Na' spectrum is .045
MHz. The relationship between the quadrupolar frequency and the

quadrupolar coupling constant, eZqQ/ h, is given by:

- 36qu

Since I=3/ 2 for sodium, the quadrupolar coupling constant is equal to 20m,
which is equal to 9.0 x 10'2 MHz for Cs+(18C6)2-Na'. The linewidth due to the
quadrupolar interaction can be estimated by using the equation shown below

which relates the linewidth and the second moment 36:

Atom = 2J1n 4 %§b—%L— (104-1) - 3/4) (2.33)

55

 

 

Valli/c,

r

 

f ' I ' i v 1 . x
20000 0 -20000 -40000
HER?!

Figure 13. 23N a NMR static spectrum of Cs+(18C6)2°Na‘ at 269K.

5 6
where (”L is the Larmor frequency. The value for the quadrupolar
contribution to the linewidth is then determined to be 39 Hz, which is
extremely small considering the overall linewidth of the peak (1500 Hz). This
value is comparable to those observed in solutions of sodium and crown
ethers such as 15-crown-5 and 12—crown4.37 Therefore it appears that dipolar
broadening is the main source of line broadening of the sodium anion NMR
signal. This result is not surprising as this compound as well as all alkalides
and electrides can be considered to be made of up point charges which are
embedded in a "sea of protons". The dipolar contribution to the overall spin-
spin relaxation in the Cs+(18C6)2-Na' system can be estimated by the following

equation:

(2.34)

If one assumes that the static quadrupolar interaction is temperature
independent then the spin-spin relaxation time due to the dipolar coupling of
the sodide anion with the surrounding protons can be calculated. Table 10
shows the estimated dipolar spin-spin relaxation times for Cs+(18C6)2-Na'
calculated from Eqn. (2.34) and Figure 14 represents the behavior of the
dipolar spin-spin relaxation times with temperature. It is interesting to note

that while dipolar interactions are the main source of line broadening in this

57

Table 10. Estimated Dipolar Spin-Spin Relaxation Rates and Correlation

 

Times for Cs+(18C6)2-Na'.
Temperature (52 Tz‘x 10'4 (sec) 1c x 10+12_(sic)_
173 1.51 1.88
191 1.50 1.92
195 1.46 2.12
211 1.49 1.97
222 1.49 1.97
237 2.14 0.950
273 2.38 0.849

293 4.89 0.568

58

 

 

 

 

-7.5
I

-8.0 '-
1'.‘
5
i
'2.
E a
5

-8.5 '-

I .
'90 I T ' I r T r l '
5 1 5 2 5.3 5.4 5 5 5 6 5 7
In T(K)

Figure 14. Ln Tz" (dipolar) versus Temperature for Cs+(18C6)2-Na'.

59

system, the main mechanism for spin-lattice relaxation is quadrupolar
relaxation due to phonon-lattice interactions as shown by the temperature
dependence of the relaxation times.

The dipolar linewidth was calculated for Cs+(18C6)2°Na’ using the
VanVleck formula shown in Eqn. (1.2). The summation term 2(1/rij)5 was
calculated from the known N a-H distances.88 Only protons within a 10 A
radius were considered. The calculated linewidth is 2741 Hz. This is a
reasonable value as the measured linewidth at 173 K is 2122 Hz. This
calculated linewidth represents the linewidth expected if the Cs+(18C6)2-Na"
system could be considered to be a rigid lattice. The temperature dependence
of the correlation time Tc, was then estimated by using the equation for a

nucleus I being relaxed by a nucleus 5:65

6
1 1
[film =§ylz y; 112 S(S+1) x, 201?) (2.35)

where the spinéspin relaxation times (1/T2)DD used were estimated by
subtracting the dipolar 1/T2 values which had been corrected for the
quadrupolar interaction from the 1/T2 value asssociated from the VanVleck
calculation. The results for the temperature dependence of the estimated
correlation times are shown in Table 10 and a graph of In re vs 1/ T is shown
in Figure 15. The graph shows that there are apparently two regions of
motion in the Cs+(18C6)2-Na'. At low temperatures the correlation time
remains relatively constant indicating that motion in the crown ethers are
mainly due to the protons exchanging equilibrium positions. As the
temperature increases, the motion within the molecule increases. In this

higher temperature region it appears that the crown ether rings have become

In to

60

 

 

 

 

~26
'27“ l . I
4
.28-
B
‘29 ' l ‘ r f
0.003 0.004 0.005 0.006

111'

Figure 15. Plot of In Tc vs 1/ T for Cs+(18C6)2-Na'.

mc

wl‘

61

more flexible and vibrate freely, leading to a "decoupling" of the protons
which is shown by the narrowing of the linewidth.

There is no evidence for impurity relaxation due to the presence of trapped
electrons as the relaxation does not appear to level off at low temperatures. It
is possible that such a phenomena would be observed if lower temperatures
were probed since alkalides always contain a small amount of trapped
electrons as shown by magnetic susceptibility and EPR results.15

Several other spin-relaxation studies of sodides were performed on the
Bruker 400 MSL spectrometer at Cambridge University. Unfortunately these
results were clouded by the presence of a second unknown peak which
overlapped the Na' peak in all of the sodide samples an example of which is
shown in Figure 16. Spin-lattice relaxation times could not be accurately
determined as the overlapping of the two peaks interfered with the intensity
of the sodide peak. Initially, this peak was thought to be due to
decomposition of the compound, however, it was later attributed to a 27A1
signal due to the presence of aluminum in the stator which caused a folding
over of the signal into the spectrum window. If this peak had been identified
earlier, the problem could have been corrected by changing the offset of the
spectrum to avoid the interference. Although much of the data must be
repeated in order to obtain accurate results, the spin-lattice results of
Cs+(15C5)2-Na' will be presented here. The Na' peak of Cs+(15C5)2-Na' was
narrow enough above 238 K that it was not affected by the aluminum peak.
Unfortunately, the temperature range is not as extensive as the
Cs+(18C6)2-Na' study, however it is still possible to draw some conclusions.
The Cs+(15C5)2-Na' data are presented in Table 11 and the temperature
dependence of the spin-lattice relaxation times is shown in Figure 17. In the

temperature range of 238 K to 273 K the spin-lattice time of Na' decreases

62

 

Figure 16. 23Na NMR spectrum of Cs+(HMHCY)-Na' showing both the N a'
peak and the folded over 27A1 peak.

63

Table 11. 23Na NMR Spin-lattice Relaxation Results of Cs+(15C5)2-Na'.

Igmpgrature (i 2 E) T sec ' Tz‘x 10‘5(§_e_c1 § 1 :I: 322m)
238 0 .516 :1: 0.046 7.14 i 0.09 -61.3
243 0 .475 i 0.046 7.43 i 0.09 -60.3
248 0 .436 i 0.044 8.44 i 0.09 -58.9
253 0 .414 :1: 0.036 8.44 i 0.09 ‘59 .8

273 0 .223 2': 0.011 11.6 :t 0.09 -55.2

64

 

a) I

InT1

 

 

 

5.4 5.5 5.6 5.7
lnT

 

b)

~9.1 n

-9.2 -

-9.3 -

In 12*

~9.4 -

 

 

 

-9.6 . . . 1 -
5.4 5.5 5.6 5.7
lnT

Figure 17. Ln T1 versus Temperature (a) and In T2* versus Temperature (b)
for Cs+(15CS)2-Na'.

65

steadily. It is difficult to compare the temperature dependences of the spin-
lattice relaxation times for the two sodides due to the restricted temperature
range of the Cs+(15C5)2-Na' study. However, it appears that the T1 values
become more comparable as the temperature increases. A more in depth
relaxation study of of Cs+(15C5)2-Na’ is needed to accurately compare the two
sodides.

The apparent spin-spin relaxation times in Cs+(15C5)2-Na' increase with
increasing temperature, again indicating the effect of molecular motion on
the spin-spin relaxation times. The resonance position of N a' in
Cs+(15C5)2-Na' shifted diamagnetically by 6.2 ppm over the temperature range
studied as shown in Table 11. Although the chemical shift was not as
resistant to change in Cs+(15C5)2-Na‘ as it was for Cs+(18C6)2-Na', the
tendency for the chemical shift to remain constant indicates the absence of
any induced orbital angular momentum in the N a' ion. There was no sign of
decomposition of the Cs+(15C5)2-Na' sample during the experiment.

The dominant mechanism in the spin-lattice relaxation of Cs+(15C5)2-Na'
is quadrupolar as can be seen from the temperature dependence. The reason
why quadrupolar relaxation appears to be more efficient in Cs+(15C5)2-Na'
than in Cs+(18C6)2-Na' could be due to differences in the crystal structures of
the two complexes, the presence of trapped electrons, or increased motion of
the crown ether rings. The structure of Cs+(15C5)2-Na' has not been yet been
determined. The Cs+(18C6)2~Na' crystal structure is monoclinic and each N a‘
is coordinated by eight complexed cations.88 The crown ether molecules
assume a conformation where the oxygen atoms are directed towards the Cs+
ion allowing complexation of the cation. The anions and cations lie in

alternating planes which are perpendicular to the c-axis. Differences in the

66

two structures could lead to differences in the quadrupolar relaxation

behavior.
II. D. 2. b. 87Rb NMR.

The spin-lattice relaxation results for three rubidides, Cs+(18C6)2-Rb',
Cs+(15C5)2-Rb" and Rb+(15C5)2~Rb‘ will be presented here. The results for
Cs+(18C6)2~Rb‘ were obtained with a Bruker 400 AM spectrometer while the
Cs+(15C5)2~Rb' and Rb+(15C5)2-Rb‘ data were acquired on the Bruker 400 MSL
spectrometer. In all cases the compounds were sufficiently stable to allow the
study of a broad temperature range without apparent decomposition.

The results for Cs+(18C6)2-Rb' are presented in Table 12. Figure 18 shows
the temperature dependence of both the spin-lattice relaxation and the spin-
spin relaxation times of Cs+(18C6)2-Rb’. The spin-lattice relaxation times are
short in this compound, meaning that T1 is no longer much greater than T2.
Because of this, the Inversion Recovery method had to be used in to obtain
the spin-lattice values for temperatures above 193 K. As for the sodides, the
T1 values decrease sharply with increasing temperature and level off at
approximately 283 K. The T2" values increase rapidly with increasing
temperature and become nearly temperature independent above 233 K where
molecular motion apparently becomes very important. There is a sharp break
at 233 K in the temperature dependence of both T1 and T2“ for Cs+(18C6)2-Rb'.
It is possible that this abrupt change in behavior is due to a phase transition,
such as a softening transition in the crown ether, but DSC studies have not
been made on this compound to confirm this supposition. The curvature of
the T1 data at low temperatures suggest that at lower temperatures the

relaxation might become temperature independent due to relaxation by

""1

67

Table 12. 87Rb NMR Spin-lattice Relaxation Results of Cs+(18C6)2-Rb‘.

Temperature (i 2 K)

175
183
193
198
204
214

243
2.53
263
273

293
303

T sec

123 5: 0.09
1.14 :1: 0.01
1.04 :1: 0.02
0.39 i 0.01
0.83 :I: 0.01
059 :1: 0.02
0.32 a: 0.02
0.052 a: 0.01
0.035 :I: 0.02
0.025 2|: 0.01
0.018 i 0.01
0.014 t 0.01
0.011 i 0.01
0.007 t 0.002
0.006 :1: 0.002

IZ‘zLO‘Slaesl

5.35 :1: 0.05
5.61 :I: 0.05
6.76 i 0.05
5.95 :I: 0.05
6.93 :1: 0.05
7.18 :I: 0.05
7.24 :1: 0.05
11.7 :I: 0.05
12.7 :1: 0.05
12.9 i 0.05
12.8 :t 0.05
12.8 :t 0.05
12.6 :I: 0.05
12.4 :I: 0.05
12.8 i 0.05

68

 

a) ‘

In'l'1

 

 

 

 

In'I'

 

b) ‘

fluII.I
nI

In T2‘
ob
A

l

 

 

 

InT

Figure 18. Ln T1 versus Temperature (a) and T24 versus Temperature (b)
for Cs+(18C6)2~Rb‘.

69

trapped electrons which are always present in alkalide samples. This
phenomenon was observed in 23N a NMR spin-lattice relaxation studies of
N aF, at temperatures below ~ 130 K, where the T1 values tended towards a
temperature independent value characteristic of paramagnetic impurities.73

The results for Cs+(15C5)2-Rb' are shown in Table 13. At low temperatures,
it appears that impurity relaxation, due to the presence of trapped electrons,
begins to be the dominant mechanism for relaxation as seen in Figure 19. As
in the other compounds, the relaxation times drop off rapidly with increasing
temperature until approximately 240 K where the relaxation appears to level
off. The spin-spin relaxation behavior follows the typical pattern by
increasing with increasing temperature and reaching a plateau at higher
temperatures where the Rb‘ has narrowed due to molecular motions. There
is no appreciable change in the chemical shift throughout the temperature
range as seen in Table 13.

The Rb+(15C5)2:Rb' results presented in Table 14 show no indication of
impurity relaxation at lower temperatures as would be expected if there were
a high concentration of trapped electrons. The T1 values drop off rapidly
until approximately 260 K where the relaxation begins to level off as seen in
Figure 20. The T2* values show a gradual narrowing of the line until 253 K
where the Tz" values become nearly constant. As for Cs+(15C5)2-Rb‘, the
chemical shift remains relatively constant throughout the entire temperature
range. Again, due to the temperature dependence of the spin-lattice
relaxation values it is apparent that quadrupolar relaxation is dominant in
this system.

A comparison of the relaxation times for the three rubidides is shown in
Figure 21. It appears that the quadrupolar relaxation mechanism is most
efficient in the Rb+(15C5)2°Rb' and Cs+(15C5)2-Rb' compounds and least

7 0
Table 13. 87Rb NMR Spin-lattice Relaxation Results of Cs+(15C5)2-Rb'.

Temperature (i 2 _Ig) ' T1(sec2 T2" x 10*5 §e_c) 5 I :I: lppm)
203 0.244 :1: 0.027 9.28 :1: 0.05 -193.4
213 0.20 i 0.035 9.64 i 0.05 -193.9
223 0.090 i 0.003 9.90 :1: 0.05 -193.7
233 0.036 :1: 0.001 11.3 :t 0.1 -193.0
2.38 0.014 t 0.001 11.9 :1: 0.1 -193.3
243 0.019 :1: 0.001 12.0 :1: 0.1 -192.9
248 0.015 :1: 0.001 11.9 :1: 0.1 -193.0
263 0.0078 :1: 0.0002 12.3 :1: 0.1 -193.2
268 0.0090 :1: 0.0001 12.0 :1: 0.1 -193.3
273 0.0070 i 0.0004 12.0 i 0.1 -192.0

278 0.0072 i 0.0004 12.3 i 0.1 -191.1

71

 

 

 

 

 

 

 

 

-1
a)
.
.2-
.
fl -
E -3
I
-4- I
I
'5 ' r ' I #fl—nfi—q
5 3 5 4 5.5 5.6 5.7
In'l'
-9.0
b) a I I
-9.1 -
in
'—
.5
-9.2 -
I
I
~93 - u 4 u . r -
5.3 5.4 5.5 5.6 5.7
InT

Figure 19. Ln T1 versus Temperature (a) and In Tz‘ versus Temperature for
Cs+(18C6)2-Rb‘.

7 2
Table 14. 87Rb NMR Spin-lattice Relaxation Results of Rb+(15C5)2-Rb'.

Temp (i 2 K) T1(sec) 1211:4934 (fl) 5 (:1: 1 ppm)
208 018540.02 0.934005 4193.4
213 : 0.081 4002 1.054005 -194.7
23 003940006 1.204005 -194.2
233 001840.002 1.294005 -l93.6
238 001340001 1.294005 -1942
243 00093400009 1.344005 -193.5
248 000754 0.0006 1.344005 -194.2
253 00059400005 1.404005 -193.9
258 00048400005 1.404005 493.3
263 0.0031 40.0005 1.404005 -193.1

273 0.0027 i 0.0005 1.40 :I: 0.05 -192.7

73

 

In T1

 

 

 

5.3 5.4 5.5 5.6 5.7

 

-8.8

-8.9 H

-9.0 -

In T2‘

 

 

 

5.3 5.4 5.5 5.6 5.7
InT

Figure 20. Ln T1 versus Temperature (a) and In Tz" versus Temperature (b)
for Rb+(15C5)2-Rb'.

Figure 21.

In T1

74

 

 

 

2
III
0-1 In.
I
° 0
.2. ' Cs+(1806)2.Rb-
. o Cs+(1505)2.Rb-
- I Rb+(1505)2.Rb-
. I
I.“
I
-4-- I0 I
I. '
0
II... III
I
I
'6 l ' l f r r F* r '

 

. 1 .
5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

InT

A comparison of the spin-lattice relaxation times of
Cs+(18C6)2-Rb', Cs+(ISCS)2-Rb' and Rb+(15C5)2-Rb‘.

‘J

I- =.'. _
1' —!-—_

75

efficient in Cs+(18C6)2-Rb‘. Relaxation studies of Cs+(15CS)2-Rb" and
Rb+(15C5)2-Rb' at lower temperatures will allow a better comparison of the
spin-lattice relaxation for the three rubidides.

One way to strengthen the hypothesis that quadrupolar relaxation is the
dominant form of relaxation in these rubidides would be to compare the
relaxation times at a specific temperature of the two isotopes of rubidium as
was done for RbCl. This experiment is not trivial as the quadrupole moment
of 85Rb is twice that of 87Rb so that quadrupolar broadening of the line could
prohibit the observation of the spectrum. Nevertheless, this experiment
should be attempted in order to verify the means of relaxation in these

rubidides.

II. D. 2. c. 133Cs NMR

Cs+(18C6)2-e' spin-lattice relaxation measurements were performed at
Cambridge University. The spectra consisted of two peaks, a peak at ~ +81
ppm as expected and a second more paramagnetic peak. At 203 K the
paramagnetic peak was dominant with the diamagnetic peak appearing as a
shoulder. However, at 243K the spectrum consisted of two full peaks with the
more paramagnetic peak the dominant of the two. Figure 22 shows the
Cs+(18C6)2-e' spectra at 203 K and 248 K. Two peaks in the 133Cs NMR
spectrum of Cs+(18C6)2:e' were also observed by Dawes during a careful
temperature study of the chemical shift in the Cs+(18C6)2-e' system in which
the more paramagnetic peak was actually a shoulder on the diamagnetic peak,
increasing in intensity as the temperature increased.52 The two peaks were
reported by Dawes to be separated by approximately 20 ppm and showed a

parallel temperature dependence.

76

2061(

 

 

 

2431<

 

 

TrVfiWTfifiTvi'Vfi

1000 500

Vifi‘iv Vfivrfj—

. .1
-500

9'1

PHI

Figure 22. 133Cs NMR static spectra of Cs+(18C6)2-e' at a) 208K and b) 243K.

7 7
Analysis was performed on both peaks and the results are tabulated in

Table 15. Figure 23 shows the temperature dependence of the T1 relaxation
time for both peaks. The paramagnetic peak is labeled as peak #1 and the
more diamagnetic peak is denoted as peak #2. Figure 23 shows that at low
temperatures the T1 values for peak #1 and peak #2 remain relatively
constant until ~250 K, where the values decrease with increasing
temperature. It appears that the relaxation mechanism for the two peaks is
due to the trapped electron at lower temperatures; however, as the
temperature is increased quadrupolar relaxation becomes dominant.

The structure of Cs+(18C6)2-e" is monoclinic with four molecules per unit
cell. It is essentially isostructural with the Cs+(18C6)2-Na' structure, but there
is only noise level density at the anionic site in the electride.48 In addition,
magnetic susceptibility studies show that Cs+(18C6)2°e" is a localized electride
as it obeys Curie-Weiss behavior.22 The structure of Cs+(18C6)2°e' shows that
the Cs+ ion is well shielded from the trapped electron. The quadrupolar
relaxation of the cation appears to be efficient, however, even greater than
that observed for Na' in Cs+(18C6)2‘Na'. This is due to the fact that the Na“
ion is extremely symmetrical and resistant to relaxation whereas the Cs+
environment is not as symmetrical and therefore more conducive to
relaxation.

Attempts were made to obtain spin-lattice relaxation results for
Cs+(18C6)2-Cs’ on both the Bruker 400 MSL at Cambridge University and on
the Bruker 400 AM at Michigan State University. In both cases the compound
used was not a pure ceside. The spectra contained three peaks; two peaks due
to Cs+(18C6)2 and Cs‘ as expected for Cs+(18C6)2°C5' and a third peak due to
Cs+(18C6)2 from the compound Cs+(18C6)2-e'. These three peaks tended to

78

Table 15. 133Cs NMR Spin-Lattice Relaxation Results of Cs+(18C6)2-e'.

Temperature (1 2 K)

218
223
238
243

T1 (sec) peak 1

0.726 :I: 0.040
0.699 :I: 0.054
0.704 :I: 0.026
0.653 :I: 0.030
0.694 :I: 0.015
0.652 :I: 0.021
0.566 i 0.009
0.426 i 0.034
0.371 i 0.026
0.342 :I: 0.022
0.322 :I: 0.010
0.265 :I: 0.014

T1 (sec) peak 2

1.03 :1: 0.09

0.929 :I: 0.100
0.848 :I: 0.098
0.646 :I: 0.081
0.564 :I: 0.037
0.546 :I: 0.014
0.503 :I: 0.013
0.383 :I: 0.018
0.321 i 0.011
0.293 :I: 0.009
0.294 1 0.012
0.272 t 0.010

In T1

In T1

Figure 23.

79

 

 

 

 

 

 

 

 

-0.2
' I
-0.4 "‘ . .
I
1
-0.6 I
J
-0.8 -
‘
-1.o - n
‘ I
-1.2 -
‘
-1.4 f u . u u 4
5.3 5.4 5.5 5.6 5.7
InT
1
b) 4
° ' I
‘ I
-1 -
l "a
'2 I I T I
5.3 5.4 5.5 5.6 5.7
InT
Ln T1 versus Temperature for peak 1 (a) and peak 2 (b) in

Cs+(18C6)2-e'.

«I

80

overlap which made accurate determinations of the spin-lattice relaxation
times difficult so that an accurate temperature dependence of the spin-lattice
relaxation for Cs+(18C6)2-CS' could not be obtained. Only one value for the
spin-lattice relaxation was determined. At a temperature of 197 K, T1 = 4.4 :t
0.1 sec for Cs’ in Cs+(18C6)2-CS'. It was extremely difficult to phase the Cs‘
peak due to the presence of the two other peaks. A spin-lattice relaxation
value for the cation of Cs+(18C6)2-CS' was not obtained for this reason. The
spectra of Cs+(18C6)2°Cs’ at several temperatures shown in Figure 24 are
extremely interesting in that the Cs’ peak is not as symmetrical as expected.
The shape of the Cs‘ peak shows the typical powder pattern expected for
chemical shift anisotropy. In order to obtain accurate spin-lattice relaxation
values for both Cs+ and Cs’ in Cs+(18C6)2-Cs‘z measurements should be
performed while spinning at the magic angle in order to prevent overlap of

the peaks.

II. D. 2. d. 39KNMR.

Attempts were made to obtain 39K NMR relaxation times for Cs+(15C5)2-K'
on both the Bruker 400 MSL and Bruker 400 AM spectrometers. An in-depth
temperature study of the spin-lattice relaxation of K‘ in this compound could
not be obtained due the poor sensitivity of the 39K nucleus. The total amount
of time needed to obtain spectra with sufficient signal-to noise ratio was
prohibitive even though MAS was used instead of static methods on the
Bruker 400 AM spectrometer.. Spin-lattice relaxation times were obtained at
three temperatures. However, KINFIT analysis of the data showed that the
error of the calculated relaxation times was too large to be acceptable for two

of the three temperatures. The results are shown below in Table 16.

81

253K

243 K

10%
m M
”'3‘ M

203K

 

Figure 24. 133Cs NMR static spectra of Cs+(18C6)2-Cs’ at various temperatures.

8 2
Table 16. 39K MASS NMR Spin-lattice Relaxation Results for Cs+(15C5)2-K'.

Tem erature K T1 sec
212 :I: 2 0.039 :I: 0.03
230 :I: 2 0.011 :I: 0.005
250 :I: 4 0.029 :I: 0.02

With the exception of the results at 230 K, the results are very poor and
therefore very few conclusions can be made. It is apparent however, from
these results, that the relaxation in Cs+(15C5)2-K' is extremely efficient. In
order to understand the relaxation in this compound as well as other
potassides it will be necessary to repeat these results in order to obtain an
accurate temperature study of the spin-lattice relaxation values. This will be a
lengthy process as approximately six hours was needed at each temperature to

obtain appropriate signal-to—noise ratios.

11. E. Conclusions.

This study was the first investigation of spin-lattice relaxation times of
alkalides and electrides in the solid state. Although this study is by no means
complete, we have shown that the determination of spin-lattice relaxation
times in these compounds is feasible and provides a useful probe of the
interactions in these unique species. Continuation of this study can provide
further information about the nature of relaxation processes in alkalides and

electrides.

8 3
The 23N a NMR results showed that the spherically symmetric N a' ion is

extremely resistant to relaxation at low temperatures (<225 K) in the
Cs+(18C6)2-Na' case where the T1 value at 173 K is 107 sec, the longest spin-
lattice relaxation value for sodium known to date. The Cs+(15C5)2-Na' results
should be repeated in order to obtain a broader temperature range which
would allow a better understanding of the T1 temperature dependence of this
compound and verify the large difference in the T1 values for the two
compounds. An analogous situation is seen in the 87Rb results of
Cs+(18C6)2-Rb', Cs+(15C5)2-Rb' and Rb+(15C5)2-Rb' where relaxation processes
in Cs+(15C5)2-Rb' and Rb+(15C5)2-Rb' are more efficient than the
Cs+(18C6)2-Rb'. Again the reason for this is probably due to structural
differences between the 18C6 complex and the two ISCS complexes. A
comparison of the 23N a and 87Rb results reveal that the anionic relaxation is
much more efficient in the three rubidides than in the two sodides. This
could be due to the fact that although the Rb‘ ion is spherically symmetrical it
may be more prone to distortion as evidenced by the value of the
Sternheimer antishielding factor and therefore less resistant to relaxation
than the Na“ ion.

The 1”CS and 39K experiments were not successful, but it should be
possible to obtain reasonable data for these two nuclei. It may be necessary to
use MAS in the 133Cs case in order to eliminate the overlapping of peaks. In
addition, it is imperative to synthesize a pure sample of Cs+(18C6)2-Cs‘, which
is extremely difficult, in order to obtain accurate T1 values for the C5" ion.
Figure 24 showing the static Cs’ peak in Cs+(18C6)2-C5' is intriguing as it is the
first time a deviation from a symmetric peak has been observed in an anion
of an alkalide. The Cs+(18C6)2-e‘ experiments need to be rerun to further

understand the nature of the two peaks and their relaxation behavior. 39K

84

NMR will be more difficult due to the time needed to obtain a satisfactory
signal-to- noise ratio because of the low sensitivity of the nucleus.

Except for Cs+(18C6)2-e" this study only considered the relaxation of the
alkali metal anions. A study of the nature of the relaxation of the alkali metal
cations should also be done. This will be more difficult as 23N a, 7Li and 133Cs
will be the only promising candidates. 87Rb and 39K spin-lattice relaxation
studies of the cations will most likely be impossible due to the fact that Rb+
and K+ can not be observed without the use of a modified spin echo
technique to be discussed in Chapter 3. A further impediment to the study of
relaxation of the complexed cations will be the added time required to obtain
adequate spectra. However, this should be attempted in order to further
understand these compounds.

Although the "effective Debye temperatures" have not been determined
for any of the alkalides and electrides, from the temperature dependence and
nucleus dependence of the spin-lattice relaxation times it is clear that the
quadrupolar relaxation mechanism is responsible for relaxation in these
compounds. The VanKranendonk theory is able to describe the quadrupolar
relaxation processes of simple alkali halide salts but is not readily extended to
complicated systems such as alkalides and electrides due to limitations in the
knowledge of parameters such as the nature of the phonon spectrum in these
compounds. It is hoped that a relaxation theory which can accurately account
for the properties of alkalides and electrides will be developed in order to

further understand these compounds.

111. 39K and 87Rb NMR of Alkalides and Electrides Using the Spin-Echo
Technique.

III. A. Introduction.

Solid state NMR spectroscopy has been used successfully as a tool in the
identification of the alkali metal anions, N a’, K‘, Rb‘, and Cs‘. In all cases the
diamagnetically shifted alkali metal anion peaks are relatively sharp and
symmetrical as expected for these anions. In addition 23Na and 133C5 NMR
spectroscopy has been used extensively, as shown in Chapter 1, to probe the
local environments of the respective cations in various alkalides and
electrides. Unfortunately previous studies of 39K and 37Rb NMR were
unsuccesful in obtaining either K+ or Rb+ cation peaks in the solid state due
to the low sensitivity of the 39K nucleus and the large quadrupole moment of
the 87Rb nucleus. The 39K nucleus also has a low gyromagnetic ratio which
gives rise to probe "ringing" and either a distortion of the line or a severe
broadening of the line.

Recently, Oldfield and coworkers reported that a two pulse spin-echo
sequence with appropriate phase cycling could be used to obtain an
undistorted second order powder pattern for compounds using 39K NMR.62
Therefore a study was undertaken to use this technique to obtain 39K and

37Rb spectra of alkalides and electrides containing either K+ or Rb+.

85

Wh
8M

86

III. B. Theory.

Nuclei with I> 1/2 possess a magnetic moment, )1, and an electric
quadrupole moment, Q, which is caused by the non-spherical charge
distribution of the nucleus. The interaction of the quadrupole moment with
the electrical field gradient, perturbs the equally spaced 21 + 1 nuclear energy
levels which causes the 21 resonance lines to shift and broaden. The
Hamiltonian can be written as the sum of the Zeeman Hamiltonian, Hz, and
the quadrupolar Hamiltonian, HQ where the quadrupolar Hamiltonian can

be treated as a small perturbation on the purely Zeeman terms:65

H=HZ+HQ (3.1)

where

112 = -yh (1-0) H01 (3.2)

where y is the gyromagnetic ratio and o is the chemical shift anisotropy tensor

and H0 is the static Hamiltonian. The quadrupolar Hamiltonian is given by:

1
2 2 2
312-1 +11 (Ix-1Mt (3.3)

0.)
_ Q
“0‘75“

where mQ is the quadrupolar frequency and 11 is the asymmetry parameter

given by:

n =——— where 0<r|<l (3.4)

The
for z

1850

whe

the

wh.
spi:
ext)
ovc

des

a5)

[5

PM
I 1.
Un

87

The asymmetry parameter is a measure of the deviation from axial symmetry
for a given molecule. The first and second order frequency shifts for the 21

resonance lines of an axially symmetric system, in which 11:0, are:

(1)
00:2) = —29 (m— 1/2) (3cos20 -1) (3.5)

where 0 is the angle between the principal axis of the electic field gradient and
the laboratory axis, and:
(2) “’0
=__II+1-3/4 - 2 2-

mm 16ml} ( > }(1 cos 0)(9cos0 1) (3.6)
where there is no first order shift for the central transition of the half-integer
spin (m=1 / 2). The second order effects are inversely proportional to the
external magnetic field and normally the satellites are broad and spread out
over the entire spectral width and are therefore not observable. In order to
describe and compare the local environments around the K+ and Rb+ cations

in alkalides and electrides it will be necessary to discuss the values of the

asymmetry parameter and the quadrupole coupling constant.

III. C. Experimental.

Static 87Rb and 39K NMR spectra were obtained on a 9.39 Tesla (400 MHz
proton frequency) Bruker AM system at Michigan State University and an
11.7 Tesla (500 MHz proton frequency) homebuilt spectrometer at the

University of Illinois. A dewared NMR probe head was used to acheive

88

temperatures from ~60 °C to room temperature. The compounds were kept in
a cold stream of nitrogen gas without cooling the inner side of the magnet.
Due to strong quadrupolar interactions and/ or low nuclear sensitivities, the
signals have a very short free-induction decay (FID) and are therefore
overwhelmed by "ringing" of the transmitter circuits, probe circuits and
receiver recovery. The following quadrupole spin echo pulse sequence with
16 pusle phase cycling was used to average out this ringing.62 The basic Hahn
echo is given by:

(91) 4’1 - 1:1 "' (62)¢2 42 - (AQ)¢3 (3-7)

where AQ is the time needed for acquisition and the 16-step phase cycling

process for the phases of the pulses and the receiver were:

4,1 = xxxx YYYY xxxx YYYY
()2 = XYXY XYXY XYXY XYXY (3.8)
()3 = YYYY xxxx YYYY xxxx

where X, Y, X, and Y represent 0°, 90°, 180° and 270° phase shifts-respectively.
The intervals 1:1 and 1:2 are the spacings between the two pulses and the time
for echo formation after the second pulse, respectively. The purpose of this
sequence was to cause destructive interference at the FID tails and to remove
baseline artifacts from the spectra. The pulse widths, 01 and 02 used were
either a 45° or 90° solid pulse with 01 = 202. Spectra were obtained using both
a 45°-90° pulse sequence and a 90°-90° pulse sequence. Although little
difference was seen between the two pulse sequences used it was decided that

the 45°-90° pulse sequence was the preferred method. Figure 25 illustrates the

 

89

difference between a single pulse experiment and a spin echo experiment for
39K NMR. Figure 25a illustrates a normal one pulse experiment for KCl. In
general this leads to a spectrum in which the KC] peak is lost in the baseline
distortion due to the ringing of the probe. Figures 25b and c show the result

of the spin echo experiment when two different time intervals are used. In
Figure 25b, the time intervals are not sufficient to remove all of the ringing
and therefore some baseline distortion is visible, however, in Figure 25c a
spectrum, free of distortion, is obtained when the time intervals are long
enough to remove any ringing due to the probe. The NMR lineshapes were
simulated using the program VMASS which accounts for chemical shift
anisotropy and quadrupolar interactions and can be used for either static or

spinning spectra.39

111. D. Results and Discussion.

III. D. 1. Model Salts.

In general, the K1“ and Rb+ cations form 1:1 complexes with ligands such as
C222 and 18C6, and 1:2 complexes with ligands such as 15C5 and 12C4.
Although these cations tend to form similar complexes, the cations have a
definite effect on the 39K and 87Rb NMR lineshapes of similar compounds.
For example, Figure 26 shows the observed and simulated 39K NMR
lineshape for K+(18C6)-SCN' whereas Figure 27 shows the observed and
simulated 37Rb NMR lineshape for Rb+(18C6)-SCN‘. Table 17 shows the
differences in the values of the asymmetry parameters, quadrupole coupling

constants and chemical shift values for the two compounds.

-A£‘_:

90

.§ c5 5 2829:. as; .8845 2E
9%: Eoszoaxm 20m 5% new 3 Bostoaxm $.20 29% 8 48.8an0 .mm 2:90

:2. 1 1

51;}. o< _Iluv||1_~c_lll_p III—3311'.

l

I t u _ A0

 

 

 

 

 

 

I

 

COP _I I.

.3 2 leliaTlalLaTll
>4 1 . ...

q a
. .
. .
. .
. .
. .
. .
. .

.

 

 

 

 

 

 

. 4
CV l I

2 _I.._4 _I.|

 

 

 

 

 

r ..2... L

 

91

 

 

 

 

a)
:1.
If I 1 ‘
2000 0 -3000
W“
b)
I'— I I
2000 0 4%
W!“

Figure 26. Observed (a) and simulated (h) 39K NMR lineshapes of
K.+(18C6)°SCN'.

92

 

 

 

a)
I I I
2:!) 0 -2(I)
m
b)
1* l I fi
300 100 -100 .300
ppm

Figure 27. Observed (a) and simulated (b) 87Rb NMR lineshapes of
Rb+(18C6)°SCN'.

9 3
Table 17. Comparison of NMR Parameters for K+(18C6)-SCN' and

Rb+(18C6)'SCN'.
Commund 5 (ppm) _n_ _engZ h (MHZ)
K+(18C6)°SCN' 47 0.6 2.0
Rb+(18C6)°SCN' 100 1 .0 4.5

The asymmetry parameter values indicate that the K+(18C6)-SCN' is more
symmetric than the Rb+(18C6)-SCN’ and therefore the change in the cation
alters the structure of the compound even though there is only a slight
difference in the sizes of the Rb“ and K+ cations. In addition the quadrupole
coupling constant for Rb+(18C6)-SCN' is 2.25 times greater than that of
K+(18C6):SCN'. These results are not surprising due to the fact that by simply
replacing the K+ cation by a Rb+ cation with no other changes would increase
the quadrupolar interaction by a factor of ~ 7 due to differences in the
quadrupole moments and antishielding factors of the two cations. (Table 5
Chapter 2.)

A comparison of model salts that contain K+ shows that the 1:1 and 2:1
complexes tend to have different NMR lineshapes. Figure 28 shows the 39K
NMR spectra for K+(15C5)2:I' and K+(12C4)2-I'. Both spectra consist of a single
symmetrical peak indicating that the K+ is in a symmetrical environment in
both cases. In contrast, Figure 29 shows the 39K NMR lineshapes for
K+(C222)-I' and K+(C222)-SCN‘. In this case the lineshapes are extremely

similar, consisting of very broad lines suggesting a cationic environment

94

a)

 

 

2000 ' 0 I 4090

b)

 

 

Figure 28. 39K NMR static spectra of a) K+(15C5)2-l' and b) K+(12C4)2-I‘.

95

 

 

 

a)
4000 ' 2000 V 0 '2000
. ppm
b)
7 2000 0 .2000
pp“

Figure 29. 39K NMR static spectra of a) K+(C222)-I’ and b) K+(C222)-SCN'.

9 6
which deviates from axial symmetry. Figure 29 also shows that the NMR

lineshape is independent of the anion in the C222 model compounds.
However a comparison of Figure 26 and Figure 29 shows that the 39K N MR
lineshapes can be dependent on the choice of complexant. It appears that the
C222 encapsulates the K+ cation and therefore protects it from the
surrounding anion, whereas the planar 18C6 allows ion pair formation and

therefore the choice of anion can have an effect on the lineshape.
111. D. 2. Alkalides and Electrides.

The alkalide and electride 39K and 87Rb spin echo NMR spectra are similar
to those of the model salts. Figure 30 shows the 39K NMR spectra for
K+(C222):K‘ and K+(C222)-e’. It can be seen that the K+(C222) lineshape is the
same for the two compounds, consisting of broad peaks similar to the
lineshapes of K+(C222)-I' and K+(C222):SCN‘. These spectra a're characteristic
quadrupolar powder patterns. The spectrum of K+(C222)-K‘ is quite
interesting in that although the K' peak position is at ~ -100 ppm as expected
for the anion, it is centered in the middle of the cation peak. The similarities
of the K+(C222) NMR peaks for the two compounds indicate that the local
environment of the K+ cation does not change significantly with the change
in anion. The structures of K+(C222)-K- and K+(C222)-e' confirm the 39K
NMR results.90:91 The structure of K+(C222)-K' shows that there are contact
pairs of potassium anions in this compound allowing for the formation of
the "di-potasside" ion, K2“. The structure of K+(C222):e' is similar to that of
the potasside as electron pair formation is present. In contrast to the
quadrupolar lineshapes of the K+(C222)-e’ and K+(C222)-K' compounds, the

spectrum of K+(15C5)2-e' consists of a relatively sharp and narrow line as

”ME-J”; "' ‘1

97

a)

 

 

 

 

 

I I r I r I r I
1500 0 2000
PPM

Figure 30. 39K NMR static spectra of a) K+(C222)°e' and b) K+(C222)-K'.

98

shown in Figure 31. The structure of K+(15C5)2-e' has not yet been elucidated.
However the shape of the NMR peak suggests that the K+ cation is in a
symmetric enivironment. The spectrum of K+(15C5)2-K', shown in Figure 32,
shows only the K' peak. The K+(15C5)2 peak was not observed even though
several attempts were made. It is possible that the strong K’ signal
overwhelmed the weaker and probably broader K+ cation signal. The 39K
NMR results have overwhelmingly showed the utility of the Spin echo pulse
sequence in the study of alkalides and electrides.

The 37Rb NMR spin echo results of the alkalide and electride compounds
were in general much broader than the 39K NMR spectra. This is due to the
large quadrupole moment, gyromagnetic ratio and Sternheimer antishielding
factor of the 87Rb nucleus which result in a further broadening of the line in
comparison to the 39K NMR results. Figure 33 shows a comparison of the
87Rb NMR spectra of Rb+(18C6)~Na' and Rb+(C222)-Rb'. The lineshape of
Rb+(18C6)-Na' shows a characteristic quadrupolar powder pattern whereas the
Rb+(C222)-Rb' cationic peak is more symmetrical indicating a difference in the
structures of the two compounds. The structure of Rb+(C222)-Rb" is similar to
that of K+(C222)-K' where a dimeric sz" exists.91 It is interesting to note that
the Rb“ signal was not observed. The opposite is observed in the 87Rb N MR
spectrum of Rb+(15C5)2°Rb‘ where only the Rb" peak is observed as seen in
Figure 34. The spectrum of Rb+(18C6)-Rb' consists of both the Rb+ and Rb’
peaks as seen in Figure 35. The Rb“ peak is sharp and symmetrical as expected
for the symmetrical anion and the lineshape of the Rb+ cation peak is typical
of a quadrupolar pattern. The spectrum of Rb+(15C5)2-e' shown in Figure 36,
consists of a broad noisy peak even after 40,000 scans. This peak, although
broadened by quadrupolar interactions is relatively symmetrical indicting that

the Rb+ cation is in a symmetric environment. Magnetic susceptibility

”3'”:

.99

 

1500 ' 0 ' -1500

Figure 31. 39K NMR static spectrum of K+(15C5)2-e'.

 

LM

 

Figure 32. 39K NMR static spectrum of K+(15C5)2~K'.

 

100

 

 

 

 

a)
F'f‘IlllllT'IllvfiA
000.0 400.0 0.0
PPH
b)
Tali—II-IIIIIT
90°00 40°00 0'0
PPH

Figure 33. 87Rb NMR static spectra of a) Rb+(18C6)'N a' and b) Rb+(C222)-Rb’.

101

 

 

 

 

r—
400.0

1 1 1 *1 5r r55 r
300.3 200.0 100.0 0.0 -100.0 -200.0 -300.0
PPH

Figure 34. 87Rb NMR static spectrum of Rb+(15C5)2-Rb‘.

1
”‘00. 0

102

 

 

ppm

Figure 35. 87Rb NMR static spectrum of Rb+(18C6)-Rb'.

"’_'—".h‘

103

 

 

 

 

 

Figure 36. 37Rb NMR static spectrum of Rb+(15C5)2-e‘.

 

l 0 4
results, which are presented in Chapter 5 strengthen the argument that the
electride is localized. It is obvious from the 87Rb NMR results that while the
spin echo pulse sequence is advantageous in the probe of the local
environment of the rubidium cation or anion, the absence of either a Rb+ or

Rb’ peak is not proof that they are absent in the compound.

III. E. Conclusions.

The spin-echo technique with phase cycling has proven to be a powerful
tool in the 39K and 87Rb NMR study of alkalides and electrides. This is the
first time that K+ and Rb+ have been observed in the solid states for these
compounds. By using this technique it is possible to use solid state 39K and
87Rb NMR as a probe of the local environments of the cations in various
compounds. The observed lineshapes emphasize the differences in
symmetry around these species. Correlation between the observed lineshapes
and structures can yield much information about the properties of these
compounds. Although a great deal of information has been gleaned from
this study it is necessary to use a larger sweepwidth, which means a fast
digitizer, in order to study some of the compounds which have linewidths
greater than 150 kHz. In particular, a fast digitizer would be extremely helpful
in the case of 87Rb NMR where the linewidths for Rb+ are extremely broad
and difficult to phase correctly. Further studies need to be made to assure that
the correct delay times are being used and that the lineshapes are not being
distorted. Additional studies at other fields could yield futher information
and temperature studies should be performed, especially on the electrides to

see what changes occur with differences in temperature. Overall, however

105

the spin echo technique has proven to be an extremely useful tool in the

study of the magnetic properties of alkalides and electrides.

 

IV. 23N a and 71.1 Solution NMR Studies of Li+(CH3NH2)x-Na',
U+(CH3CH2NH2)x-Na'and Li"'(NH3)4-Na’.

IV. A. Introduction.

Although approximately forty alkalides and electrides have been
synthesized and characterized, it is generally assumed that these compounds
are very difficult to prepare. In fact, the synthesis procedure for these
compounds is rather straightforward if the metals, complexants and solvents
are rigorously purified and the glassware is stringently cleaned.14:15 The
successful preparation of these compounds is also very dependent on the
choice of solvent(s) used, as alkali metal solutions are prone to autocatalytic
decomposition.

It was recently discovered that solvents that contain neither acidic nor [3
hydrogen atoms are more resistent to autocatalytic decomposition.” On this
basis, and from general experience, dimethyl ether (Me20), diethyl ether
(DEE), methylamine (CH3N H2) and trimethylamine (TMA) have emerged as
routinely used solvents. Prior to the use of these solvents, it was found that
the addition of lithium metal to a solution of starting materials in CH3NH2
inhibited the decomposition process. These solutions appeared to be more
stable than those solutions which did not contain lithium metal.93r94 The
end product was not appreciably contaminated with lithium metal since at
the end of the synthesis the lithium, which stayed in solution as the
methylamine complex was simply washed away from the crystals.

In addition to enhancing the stability of solutions, the presence of

dissolved lithium metal in a solution of starting materials aids in the

106

 

107

synthesis of compounds which cannot be made by other methods. For
example, when lithium metal is used in the synthesis of Cs+(18C6)2-Cs‘ a pure
compound is obtained; whereas, if the compound is synthesized without the
presence of dissolved lithium in the solution a mixture of Cs+(18C6)2-e' and
Cs+(18C6)2°C5' is almost always obtainedfi’5 M. Faber also found that
methylamine enhances the solubility of lithium in certain solvents.96 For
instance, lithium metal is insoluble in 2-aminopropane; however, a solution
of Li+(CH3NH2)4 is soluble in 2-aminopropane.

This initial work by Faber was continued by O. Fussé who found that the
presence of lithium in solutions that contain starting materials appeared to
produce stabilization of other alkali metals present in solution, even in the
absence of complexing agents.97 Sodium metal is known to be only slightly
soluble in methylamine in the absence of a complexing agent.98 However,
Fussé found that equimolar amounts of lithium and sodium will dissolve in
methylamine to form a solution that is at least 0.1M in both sodium and
lithium. Similar results were observed when rubidium was used instead of
sodium. It was presumed that the solutions had the stoichiometry
Li+(CH3NH2)4-M' where M" is N a' or Rb'. Optical spectroscopy was used to
study the nature of the species in these solutions. First, an absorption
spectrum of a thin film of lithium in methylamine showed a plasma edge
absorption peak indicating the presence of delocalized electrons. This
solution was then poured over a sodium mirror and Fussé observed an
optical absorption peak at 660 nm as expected for the presence of Na‘.
Attempts by Fussé to obtain Li+(CH3NH2)4-Na‘ in crystalline form were
unsuccessful. The work of Faber and Fussa showed that Li+(CH3NH2)4-e'
could serve as a powerful reducing agent in various solvents as well as a

species which can solubilize alkali metals by forming alkali metal anions.

108

IV. B. Methylamine—Assisted Solubilization of Lithium.

The purpose of the present project was to continue the work of Faber and

Fussé and to identify the species present in these solutions. The initial .

samples were prepared by I. Skowyra and the nature of these samples was
investigated by 7Li and 23N a solution NMR. The samples were prepared by
adding lithium and sodium metals and an excess amount of CH3NH2 to a
cell. The CH3NH2 was removed until a thick blue film remained and then
the appopriate solvent was added. This procedure was carried out at ~ -70 °C.
The samples were run on a Bruker WH 180 spectrometer. The resonance
frequencies for 7Li and 23N a are 69.95 MHz and 47.62 MHz respectively. The
chemical shifts, corrected to be relative to Na+(aq) or Li+(aq) at infinite
dilution, were determined directly from the peak positions by comparison
with a 0.1M solution of NaCl or a 0.1M solution of LiClO4. Upfield
(diamagnetic) shifts are negative.

A solution of lithium, sodium and an excess amount of methylamine
yielded a sharp 7Li NMR peak and a sharp 23N a NMR peak. The temperature
study of these peaks indicated that the chemical shifts of both peaks are
independent of temperature as shown in Table 18. The 23N a NMR peak is at -
60 ppm as expected for Na". Representative spectra are shown in Figure 37. A
solution of Li+(CH3NH2)4, sodium and 2—aminopropane also consisted of a
sharp 7Li peak and a broad 23'N a peak. The chemical shift of both the 7Li and
23N a N MR peaks were temperature dependent. The results are shown in
Table 19 and Figure 38. A final solution of Li+(CH3NH2)4 and sodium in a
mixture of ethylamine, diethylether and pentane of unknown proportions

yielded similar results which are summarized in Table 20 and Figure 39.

 

109

a)

 

 

I -..A Jl I I l
--ALIL .A—AJ‘A~-‘~ ‘ v ' ..-yv—‘v-
“f ‘I ' "'

.A A A _
“W'- V
V fi' 'qu

 

AAIALIIIIlllllllllLllllLLLLlLLJilllllllLlLlLllllLlllllLllllllLlllllllllllllllllldL
zoo 200 100 a -100 -200 400 «00

pp!“

b)

 

_4 41.L JL-_.

—1 r “T ‘1 ‘ ‘

 

 

 

[AALLLLLLLIALLAIAA11111IIIJLLJILILLLILLLLILALIlLLLLlLllllLl

300 200 I 00 0 - 1 CO -230

ppm

Figure 37. 23N a NMR spectrum (a) and 7Li NMR spectrum (b) of a solution
of lithium, sodium and excess methylamine.

110

   

b)

 

 

Figure 38. 23Na NMR spectrum (a) and 7Li NMR spectrum (b) of a solution
of Li+(CH3NH2)4, sodium and 2-arninopropane.

111

a)

 

b)

 

+1411; széon 1k OILIWLLLL 1

P131“

Figure 39. 23Na NMR spectrum (a) and 7Li NMR spectrum (b) of a solution
of Li+(CH3NH2)4, sodium and a mixture of ethylamine,
diethylether and pentane.

 

112

Table 18. 7Li and 23N a NMR results of lithium and Sodium in excess

 

CH3NH2_
Nucleus Temperature (:I: 2°C) 5 (i 0.2 ppm)

7L1 -87 2.6
-61 2.5
~42 2.6
23'Na ~86 -60.4
~58 -60.5
-41 -60.4

Table 19. 7Li and 23Na NMR results of Lithium and Sodium in 2-

 

aminopropane.
Nu eus Temperature (i 2 °C) 5 (i 0.2 ppm)
7Li -89 1.9
~60 1.8
-40 2.0
23Na -90 -64.6
~57 —62.4

113

Table 20. 7Li and 23N a NMR results of Lithium and Sodium in a mixture of

 

 

CH3CH2NH2, DEE and pentane.
Nucleus Temperature (i 2°C) i 0.2 m

71.1 -90 1.8
~57 . 1.9
-38 2.7
23"Na -90 -63.6
-57 -63.4
~39 ~63.0

These results show that in all three solutions the Li+ cation is well-
shielded from its surroundings as the chemical shifts are relatively
temperature independent. It is also evident that Na‘ is present in solution
and the chemical shift values in all three solutions confirm that the ion is in
a symmetric environment, as the chemical shift is the same as that expected
for N a'(g) 32.

Additional support for the presence of N a" in these solutions is given by
the optical spectra for several of these solutions”. Optical specta of a solution
with stoichiometry Li+(CH3NH2)4-Na' showed an absorption peak at 660 nm
at ~55 °C diagnostic for Na’. A solution of Li+(CH3NH2)4 and sodium in
isopropylamine also consisted of an absorption peak at 660 nm.

Since Li metal is insoluble in dimethyl ether we were curious to see if
Li+(CH3NH2)4 was soluble in dimethyl ether. The samples were first

prepared by adding an excess amount of methylamine to an apparatus

114

containing lithium metal. A bronze solution was formed and then the
methylamine was slowly distilled off until a blue-gold film remained. A
small amount of Mezo was then added. This method was tried several times
with no success as lithium metal would precipitate out of solution upon the
addition of MezO. The solution also had a tendency to bump when the MezO
was added therefore making the preparation of a stoichiometric solution
difficult. Due to the problems with sample preparation it was initially
thought that the solution was unstable. Therefore a different strategy was
used. Stoichiometric amounts of lithium metal and methylamine were
added to the NMR apparatus to form a bronze solution. The Li+(CH3NH2)4
solution was then frozen in liquid nitrogen and a small amount of Me20 was
distilled into the apparatus. This solution was then kept frozen in liquid
nitrogen until just prior to use. The sample was thawed in a ~70 °C bath just
before being loaded into the Bruker WH 180 spectrometer.

A time study of the solution at ~60 °C was performed to see if the sample
decomposed with time. The 7Li NMR results were quite interesting. Initially
the spectrum consisted of two peaks having chemical shifts of ~22.8 and ~19.9
ppm. Gradually, over a period of approximately four and a half hours, the
diamagnetic peak became smaller and there was a slight diamagnetic shift in
both peaks. Figure 40 shows two of the spectra and the relative sizes of the
two peaks after an elapsed time of four and a half hours.

After the sample was removed from the magnet, a small amount of
lithium metal was observed at the top of the NMR tube. The sample was
stored in liquid nitrogen overnight. The next morning, the sample was
placed in a ~70 °C bath and a phase separation was observed. The top phase
was bronze in color indicative of Li+(CH3NH2)4 while the blue-black phase of
Li+(CH3NH2)4 / MezO was on the bottom. The 7Li NMR study was repeated

115

a)

 

 

 

 

 

 

100 0 ‘100
PP!“

b)
4-1!...11....l.1.1‘....|....
100 0 -100
ppm

Figure 40. 7Li NMR spectra of Li+(CH3NH2)4 in MeZO at ~60 °C. Spectrum
(b) was obtained four and a half hours after spectrum (a).

 

116

on this sample. Again two peaks were observed. As the temperature was
raised, both peaks shifted paramagnetically, with the chemical shifts
returning to the original values upon cooling, as seen in Table 21.

There was no significant change in the relative amplitudes of the two
peaks with temperature. A stoichiometric solution of Li+(CH3NH2)4 was
prepared and a 7Li NMR study was done in order to assign the two NMR
peaks. At ~50 °C the chemical shift of the Li+(CH3NH2)4 peak was at ~20.4
ppm. The peak shifted paramagnetically with increasing temperature as
shown in Table 22.

This result indicates that the smaller, more diamagnetic peak is due to the
presence of Li+(CH3NH2)4, This result is not surprising as the NMR time
study showed that as time passed the Li+(CH3NH2)4 became more soluble in
MezO. An experiment was carried out to see if there was a limit to the
amount of MezO which can be added to a solution of Li+(CH3NH2)4. Again a
solution of Li+(CH3NH2)4 was prepared and dimethylether was slowly added.
Upon the addition of a small amount of MezO, a small ring of lithium metal
would form on the top of the solution which would disappear after several
minutes. This occurred after each addition of MezO. A phase separation was
again observed. MezO was added until the vessel was full. The phase
separation did not disappear with the addition of MezO and all the lithium
metal appeared to remain in solution. The conclusion of this qualitative
experiment is that Li+(CH3NH2)4 is slightly soluble in MezO and the resulting

solution is quite stable.

l l 7
Table 21. 7Li NMR results of Li"'(CH3NH2)4 in MezO.

 

Temperature (:1: 2°C) 51 (:I: 0.2 ppm) i 0.2 m
~60 21.7 19.2
~50 23.0 20.4
~40 24.3 21.6
~60 21.6 19.1

 

Table 22. 7Li NMR results of Li+(CH3NH2)4.

 

 

Temperature (i 2°C) i 0.2 m
~50 20.4
~40 22.1

~20 25.1

 

l l 8
IV. C. Results withLi+SCH3N H2)x-_I\i§' and Li+(CH3CH2NH2)x:_lS§.

At about the time these experiments were being carried out, R. Concepcion
synthesized and characterized the simplest sodide prepared to date,
Li+(HzNCH2CH2NH2)2~Na'.100 This gold-bronze crystalline powder melts at ~
23 °C to form a gold-colored liquid. At 0 °C the liquid forms a dark blue
solution containing precipitated metal. Raising the temperature further to 30
°C causes irreversible decomposition. These melting, decomplexation and
decomposition processes have been confirmed by DSC studies. Solid state 7Li
and 23N a NMR spectra of the solid compound at T5 ~70 °C consisted of single
broad lines with chemical shifts of 0.1 ppm and ~59 ppm for
Li+(H2NCH2CH2NH2)2 and N a' respectively. The successful synthesis of this
compound was a significant breakthrough as it was hoped that it would lead
to additional inexpensive and easily prepared alkalides and electrides for use
as reductants in organic syntheses.

The synthesis of Li+(H2NCH2CH2NH2)2-Na' and the preliminary results of
Fussa on Li+(CH3NH2)4-M' formed the basis for this study of the series
Li+(CH3NH2)x~Na', Li+(CH3CH2NH2)x-Na' and Li+(NH3)4°Na' via solution
NMR. This portion of the project was done in collaboration with I. Kim.

The solutions were made by one of two methods. Stoichiometric amounts
of lithium metal and sodium metal were loaded into the NMR apparatus,
while in a helium-filled dry box. The cell was then removed to a vacuum
line and evacuated to 10‘5 torr. The cell was cooled to liquid nitrogen
temperature and a stoichiometric amount of solvent was added. This
precaution to cool the apparatus was taken as the solution will tend to bump
and cause small amounts of metal to line the sides of the cell. These particles

of metal are extremely difficult to wash back down into the solution and

119

therefore an error in the stoichiometry of the solution is introduced. The
NMR tube was then sealed off from the apparatus and the solution was
allowed to form while in a ~40 to ~70 °C bath. The second method is different
in that the sodium metal was added first and NH3 was condensed into the cell
to dissolve the metal. The NH3(qu) was then completely removed to leave a
sodium metal mirror. Then the lithium metal and solvent were added as in
the first method. The advantage of the sodium mirror is that it facilitates the
dissolution of sodium metal in the solvent. The samples were stored in a ~40
°C bath prior to use.

The NMR results for the Li+(CH3NH2)x-Na’ and Li+(CH3CH2NH2)x-N a"
will be discussed first. Solutions were made for each solvent series where
x=4, 6, 8, 12 and 16. The NMR spectra were taken on a Bruker WH 180
spectrometer with the same parameters as previously described.

The Li+(CH3CH2N H2)x-N a" solutions are blue-gold in color as compared to
the Li+(CH3NH2)x-Na' solutions which are gold in color. All of the solutions
were stable up to at least 0 °C; however, they decomposed over a period of
approximately two months at ~40 °C. The Li+(CH3NH2)x-Na' solutions do not
freeze at dry ice temperatures and show no signs of phase separation. The
Li+(CH3CH2NH2)x°Na‘ solutions do freeze at ~ ~75 °C for the case where x=4;
however none of the solutions show any signs of phase separation. In
general, the 7Li NMR spectra for the Li+(CH3CH2NH2)x-Na' series consisted of
one symmetric peak with a chemical shift of 2 i 1 ppm. The peak is both
concentration and temperature independent. The 23N a NMR spectra for this
series also consist of one symmetric peak which is also temperature and
concentration independent with a vchemical shift of ~58 :I: 4 ppm which is
diagnostic for Na“. The linewidth of the 23Na NMR peak is ~100 Hz above ~75

°C. Below ~75 °C, the solutions freeze to form the solid sodide with a

W551 n 1
. '3“..-—
C

1 2 0
linewidth of ~530 :I: 50 Hz. A very small peak for Na(s) that could have been

due to a slight excess of sodium over lithium was observed in the two most
concentrated solutions. The 7Li NMR spectra for the Li+(CH3NH2)x-Na'
series showed only one peak that depended on both temperature and
concentration. The peak shifted paramagnetically with decreasing
methylamine concentration as well as with increasing temperature. The
same type of behavior was observed for the 23N a spectra. While the three
more dilute solutions had chemical shifts of ~~59 :I: 2 ppm as expected for N a',
the sodium peaks for Li+(CH3NH2)4-Na' and Li+(CH3NH2)5oNa' were
significantly shifted paramagnetically from the typical N a' position. The Na’
peaks of the two most concentrated solutions are surprisingly temperature
dependent; they shift paramagnetically with increasing temperature. In
several instances when the Li+(CH3NH2)x°Na' solutions were freshly made
without using NH3(liq) to dissolve sodium metal, several peaks were
observed in both the 7Li and 23N a spectra. These peaks would sometimes
disappear with increasing temperaure but always disappeared over a short
period of time. This indicates that more than one species of Na is present in
the sample initially. This may be indicative of incomplete lithium
solubilization. A summary of the 7Li and 23N a results are shown in Tables 23
and 24. Representative spectra are shown in Figures 41 and 42.

A sample of Li(CH3NH2)4-Na' was frozen in liquid nitrogen and then
loaded into the spectrometer which had been cooled to the lowest possible
temperature (~175K) As the aquisition time was on the order of a minute
there was enough time to obtain a spectrum before the sample thawed. The
resulting 23N a NMR spectrum consisted of a broad peak centered at ~54.8 ppm
(:1: 5) as seen in Figure 43. The fact that the frozen spectrum has a chemical

shift value as expected for N a' whereas the chemical shift values for the

 

l 2 1
Table 23. 7Li and 23N a NMR Results for Li+(CH3CH2NH2)x-Na".*

Nucleus Temp (°C) 5(x=4) 5(x=8) 6(x=12) 5(x=16)

7Li ~20 2.1 2.1 2.9 1.4
~40 2.1 1.7 3.1 1.2
~60 2.0 1.2 2.9 1.6

23N a ~20 ~58.1 ~58.8 ~54.7 ~58.2
~40 ~58.3 -60.1 ~54.4 ~59.2
~60 ~58.5 -60.0 ~54.3 -60.1
~80 ~59.2 ~54.5 ~60.2

"Chemical shift values have an uncertainty of ilppm and temperatures are
accurate to :I: 2° C.

Table 24. 7Li and 23N a NMR Results for Li+(CH3NH2)x-Na‘.*

Nucleus T(°C) 8(x=4) 5(x=6) 6(x=8) 8(x=12) 5(x=16)

7Li ~20 9.0 6.0 3.2 2.3 2.5
~40 7.4 4.8 2.7 2.0 2.2
~60 5.6 4.0 2.3 2.1 2.1
~70 3.7 2.2 2.1 2.1

23N a ~20 1 .9 ~26.7 ~50.7 ~58.9 ~58.0
~40 ~10.4 ~33.9 ~53.5 ~59.5 ~59.0
~60 ~21.8 ~41.3 ~55.8 ~59.9 ~59.6
~80 ~43.0 ~56.2 ~60.1 ~59.8

"Chemical shift values have an uncertaintly of :I:1 ppm and temperatures are
accurate to 1 2° C.

122

a)

 

 

 

 

 

 

1000 0 ~1000
PPm
b)
-1.1111.114..11....L.14.11.116..U1LLLLIILL.11..11.212141,
200 100 -100 200
1’1”“

Figure 41. Representative 23Na and 7Li NMR spectra of
I..i"’(CH3CHzNH2)4-Na'.

123

 

 

 

 

 

 

a)
111...]..1111111411111.4241.41141..1144
200 o ~2oo 400
ppm
b)
IPILI 11.1.114101 111
zoo 0 ~20!)

Figure 42. Representative 23N a and 7Li NMR spectra of Li+(CH3N H2)4-N a’.

124

d

 

.-aZ.£~$ZmEUV+5 «o 2958 58¢ a 40 55.56on M22 «Zmu .9. 0.59m

Ema
o8 . - o

q '1 1— 1¢: 11 11 11 1‘ Id 1d 41 d I“ In 11 1d d 1— JI J J a —

 

 

125

solution at higher temperatures are significantly shifted confirms that this
paramagnetic shift in solution is due to an exchange process. If a Knight shift
were responsible for the temperature dependence of the peak position then
one would observe a diamagnetic shift with increasing temperature which is
not the case in this system. An additional cause of the paramagnetic shift
with temperature could be due to an increased concentration of electrons at
higher temperatures.

The temperature and concentration independence of both the 7Li and 23N a
NMR spectra in the Li+(CH3CH2NH2)x-Na’ series indicate that the Li+ ion is
well-shielded by the ethylamine molecules, preventing the N a‘ ions from
communicating with the Li+ cation. It is apparent from the N MR results for
the Li+(CH3NH2)x-Na' series that the smaller methylamine molecules can
not screen the Li+ as well from the surrounding N a' ions and solvated
electrons, so that a paramagnetic shift is observed in both the 7Li and 23Na
spectra with increasing temperature. The paramagnetic shift is largest for the
Li+(CH3NH2)4-Na‘ solution as the Li+ is the least shielded in this solution.
The shift becomes smaller with increasing concentration of methylamine as
the methylamine is able to shield the Li+ cation from the surrounding Na'

ions and electrons.

IV. D. Li+(NH3)4-_l\_l_g' Results.

In addition to studying the systems Li+(C H3N H 2)x-N a and
Li+(CH3CH2NH2)x~Na', an additional system with stoichiometry
Li+(NH3)4-Na' was investigated. As N a“ had not been previously detected in
solutions containing ammonia we were particularly interested to see if 23N a

solution NMR would enable us to detect the presence of N a' in this solution.

126

The compound Li+(NH3)4 has been thoroughly characterized.101 This
compound has the lowest melting point, 89K, of any known metal and has
two known solid phases.102 There is a cubic phase between 82 and 88K and
another cubic phase below 82K. Susceptibility measurements indicate that the
sample is paramagnetic in the liquid state, followed by a slight decrease in
susceptibility on freezing, and a 25 percent decrease at the phase transition.
Curie-Weiss behavior is observed in the low temperature phase down to 15K
with a leveling off below that temperature.

The Li+(NH3)4-Na‘ samples were prepared and studied in the same
manner as described previously for the samples of Li+(CH3NH2)x~Na' and
Li+(CH3CH2NH2)x-Na'. Samples with the overall composition Li+(NH3)4-N a‘
are viscous gold liquids which are stable indefinitely at ~40 °C. It is important
to dissolve N a(s) first in NH3(qu) and form a mirror as otherwise the
ammonia will preferentially dissolve Li(s) first.

The 7Li NMR spectra for this sample consist of a sharp narrow peak which
shifts slightly paramagnetically with increasing temperature as shown in

Table 25 below.

Table 25. 7Li NMR results for Li+(NH3)4-Na‘.

 

 

Temperature (1' 2°C) 5 (i 0.2 ppm) A2112 (i0.2ppm)
~73 19.9 1.4
~60 20.3 1.4
~40 20.8 1.5

~70 20.0 1.7

127

The value of the chemical shift is 20.0 ppm :I:1 ppm with a linewidth of ~1.4
ppm 10.3 ppm. A representative spectrum is shown in Figure 44. This 20.0
ppm chemical shift value is considerable when compared to the 7Li NMR
chemical shift values for Li+(CH3NH2)x-Na' and Li+(CH3CH2NH2)x-Na". It is
obvious that the presence of ammonia results in a high concentration of
electrons, which cause a paramagnetic shift.

The 23Na NMR spectra for the Li+(NH3)4-Na' solution were both
provocative and misleading. A one day old sample of Li+(NH3)4-Na’ showed
two 23Na solution NMR peaks. The first peak at ~1200 ppm was due to the
presence of sodium metal. The second peak, which was extemely broad,
having a linewidth of ~162 ppm (:I: 15), was centered at ~23.3 ppm at a
temperature of ~93 °C, as seen in Figure 45. Even though the chemical shift
was not at ~61 ppm as expected for Na‘ this peak was assumed to be due to N a'
which had been paramagnetically shifted due to the presence of electrons in
the solution. The width of this peak was not reduced through decoupling.
The "Na'" peak shifted paramagnetically with increasing temperature. The
N a(s) peak grew with increasing temperature, indicating that the solubility of
the sodium metal decreased with increasing temperature.

After the sample was allowed to sit for several days, a third peak appeared
in the 23Na NMR spectrum. This peak was very sharp and symmetrical
having a chemical shift value of ~ 188.0 ppm. Interestingly enough, this peak
also shifted paramagnetically with increasing temperature as did the "Na'"
and Na(s) peaks, and in addition as the temperature increased this peak
decreased while the Na(s) peak increased. This peak was thought to be due to
the presence of Na+ in equilibrium with Na' and Na metal. A summary of
the temperature depedence of the chemical shifts is shown in Table 26 and

the series of spectra are shown in Figure 46.

128

 

 

100 0 -100

Figure 44. 7Li NMR spectrum of Li+(N H3)4-N a" at ~73° C.

 

 

. . 1 . I . 1 1 1 . I 1 1 1 L
1000 0 -IDOD

Figure 45. 23N3 NMR spectrum of Li+(NH3)4-Na' at ~70° C.

130

 

 

 

 

 

 

 

~20
”J W
1 000 0 -1 000
- 4.0
l\
J / "
any. L‘yfiwm '. flaw-“’11:“
1000 0 ~1 000
° 50
..J/ ‘1.
4| .1” r. ".3..- . " Q.
«1L. ”5““. fl “Vic . I”
J 1 I a L
1000 0 -1000
ppm

Figure 46. 23N a NMR spectra of Li+(NH3)4-Na' at various temperatures.

l3 1
Table 26. 23N a NMR results for the Li+(NH3)4-Na' system.

 

Temperature (i 2 °C) 1 2 m A2122 (1 10 ppm)
~73 ~21 199
~60 -8 165
~40 +6 163
~20 +12 180

In order to try to prove that N a' was present in NH3, the sample was
frozen in N2(liq), as in the Li+(CH3NH2)4~Na' case, and loaded into the NMR
spectrometer. However, a reasonable spectrum could not be obtained due to
poor signal to noise. A special quartz dewar was built in order to increase the
acquistion time for this sample as this dewar allowed the sample to remain in
N 2(liq) without cooling the magnet during the NMR acquisition. The signal-
to-noise ratio was still extremely poor with the spectrum consisting of a broad
"bumpy" line. The sample was removed from the dewar and a spectrum was
obtained of the empty dewar. It was a surprise to find that this spectrum was
exactly the same. The dewar was then removed and a spectrum for the empty
dewar was run with the same results. The conclusion was then that the "Na'
" peak was due to the presence of sodium in the Pyrex dewar and in the Pyrex
N MR tubes.

Optical and reflectance spectroscopy results confirmed this conclusion as
the results showed only a plasma edge indicating the presence of conduction
electrons. No sign of an N a' absorption peak was observed.

A solution of lithium, sodium and excess NH3 (ratio 1:1:10 moles) was

added to a cell and allowed to remain overnight at ~70 °C. Due to the viscous

132

nature of the solution it was difficult to tell if all of the sodium metal had
dissolved. The solution was allowed to stay at ~40 ~ ~50 °C for several hours
more and then NH3 was removed until the overall stoichiometry of the
solution was Li(NH3)4Na. Then the solution was poured through a frit into
the other chamber. The NH3(liq) was removed and the metal content was
analyzed. If the solution with stoichiometry Li+(N H3)4-N a" existed then there
would be a 1:1 ratio of Li metal to Na metal in the solution which had been
transferred to the other chamber. However, the analysis showed that there
was a > 50 fold excess of lithium metal over sodium metal indicating that
sodium metal is only slightly soluble in this solution and that the liquid

phase was essentially Li+(NH3)4, a known compound.

IV. E. Conclusions.

This study on the methylamine-assisted solubilization of lithium,
Li+(CH3NH2)x-Na', Li+(CH3CH2NH2)x-Na' and the nonexistent
Li+(NH3)4~Na' has several interesting points. Lithium does not dissolve
easily in solvents by itself, however Li+(CH3NH2)4 dissolves easily in a
variety of solvents. Sodium is only slightly soluble in methylamine
however, solutions with stoichiometry Li+(CH3NH2)4.M' where M’ is Na' or
Rb' can be prepared. Although crystalline compounds have not been
obtained, a search for "simple" alkalides should be continued as these
compounds and solutions have the potential for routine use as reducing
agents.

The search for the presence of N a' in liquid ammonia has been pursued for
many years. Although it was thought at first that this study showed that N a'

does indeed exist in NH3, it is obvious from the series of experiments

133

performed in this work that Na" is definitely not present as a significant

speices in liquid ammonia, even at saturation.

V. Magnetic Properties of Two Electrides: K+(15C5)2-e' and Rb+(15C5)2-e'.

This chapter will discuss the magnetic properties of two electrides,
K+(15C5)2-e' and Rb+(15C5)2~e’, which were first synthesized and characterized
by M. L. Tinkham.103 The purpose of this investigation was to see what effect
if any the cationic packing had on the magnetic properties of these two
electrides. Since the electride Cs+(15C5)2oe‘ is antiferromagnetic 104 it was
thought that these electrides might show similar behavior.

Analysis performed by Tinkham confirmed the stoichiometries of
K+(15C5)2-e' and Rb+(15C5)2-e' for the two electrides.103 The optical spectrum
of each compound consisted of a single peak at ~ 7800 cm'1 which corresponds
to the presence of trapped electrons. The Rb+(15C5)2~e‘ optical spectra also
contained a second peak at 9600 cm'1 indicating the presence of Rb“. The
relative amplitudes of the two peaks dependended on the sample and
preparation, from which it was concluded that Rb+(15C5)2-e' samples tend to
be contaminated with varying amounts of Rb+(15C5)2-Rb'. Pressed powder
conductivity measurements showed that both electrides behave as
semiconductors. The EPR spectrum of each electride consisted of a single
narrow line that showed no sign of hyperfine splitting. In both cases the g
values were very close to the free electron g value. It should be noted that
recent attempts to obtain an EPR spectrum of K+(15C5)2-e' failed due to strong
microwave power absorption by the sample which caused the spectrometer to
lose its lock 105.

Recent spin echo N MR experiments revealed a single sharp peak at ~47
ppm for K+(15C5)2 in K+(15C5)2-e' as discussed in Chapter 3. No peak was
observed for Rb+(15C5)2 in the electride. A peak for K‘ was observed in the

134

135

NMR spectrum of K+(15C5)2-K' 53 and for Rb" in the NMR spectrum of
Rb+(15C5)2~Rb' 53. While the absence of a Rb+ peak in Rb+(15C5)2-e‘ does not
aid in the characterization of the compound, the absence of a Rb‘ peak
indicates that substantial concentrations of rubidide were not present in the
sample.

Differential Scanning Calorimetry experiments were done to investigate
the stability and purity of these compounds105. The K+(15C5)2-e' results
indicated that the electride can be crystallized without detectable
contamination by potasside. When a ramping rate of 5° C/ min is used,
K+(15C5)2-e‘ decomposes at 40 °C, without melting first whereas K+(15C5)2-K‘
decomposes irreversibly at ~55 °C as seen in Figure 47. The DSC results for
Rb+(15C5)2-e" showed contamination of the electride by the rubidide in
virtually all samples. Rb+(15C5)2-Rb’ irreversibly decomposes at 54 °C when
ramped at 5 °C / min. The Rb+(15C5)2~e‘ traces, in general, consisted of peaks at
~34 °C and ~68 °C for Rb+(15C5)2-e" and Rb+(15C5)2~Rb' respectively. The DSC
traces for both Rb+(15C5)2-Rb' and Rb+(15C5)2-e' are shown in Figure 48. In
each case, the samples were prepared with ~10% excess 15C5 which indicates
that a larger excess of 15C5 is required to make the rubidide-free electride.
When a 23% excess of 15C5 was used, the rubide was absent as shown in the
DSC trace in Figure 49. The rubidide-free sample of Rb+(15C5)2-e' melted at 19
°C and irreversibly decomposed at 22 °C when ramped at a rate of 5 °C/ min.
It is evident from the DSC results that K+(15C5)2-e' is more stable than
Rb+(15C5)2~e' as was indicated by visual observations. Although both
electrides are "relatively stable" compounds, they slowly decompose with
time (~ one month) when stored at ~80 °C. As a precaution, therefore these
samples were always stored in liquid nitrogen and were used promptly after

preparation.

136

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a) 6
‘5
E
3 2‘
a
O
:1:
2 4 fl .
0 35 85
Temperature (°C)
b) 4
3 4
’2’ 2 ~
E
E ..
a
O
:1:
- 0
I
4 - . -
‘ 0 40 » 90
Temperature (°C)

Figure 47. DSC Trace of a) K+(15C5)2~e‘ and b) K+(15C5)2-K'.

137

 

a)3.5

Heat Flow (Wig)

 

 

 

0 r
10 60

TerrperanJre (°C)

 

.h
\ _

 

N

Heat Flow (Wig)

 

o « ' L
-2 ' f - r
10 30 50
Temperature (°C)

 

 

 

Figure 48. DSC Trace of a) Rb+(15C5)2-e' and b) Rb+(15C5)2-Rb'.

Heat Flow (N/g)

2.5

138

 

 

 

 

20 _
Telpereture (’0)

Figure 49. DSC Trace of a pure sample of Rb+(15C5)2-e‘. '

81

 

139

One goal of this project was to obtain crystal structures of K+(15C5)2-e' and
Rb+(15C5)2-e'. Even though crystal growing techniques have been vastly
improved in the last few years through the efforts of several people 52:97,
crystal growth and subsequent isolation of crystals is still not an easy feat.
Many attempts were made to grow single crystals of suitable quality for x-ray
studies; however, problems with decomposition and poor crystal quality
persisted. Saturated solutions which contained a number of seed crystals
were cooled from -45 °C to ~70 °C over a period of 50 hours. The mother
liquor was then removed and the resultant dry, cold crystals were observed
under a microsc0pe while in a copper block at -70 °C. The crystals were
covered with purified octane for protection. In all cases microscopic
examination revealed that the crystals were not suitable for x-ray studies.
Saturated solutions of dimethyl ether-trimethylamine mixtures and dimethyl
ether- diethyl ether were tried. Further attempts are being made by R. Huang
htflfiskflm

With this backgron information about these two electrides, we now
consider the magnetic susceptibility studies. After a short introduction to
magnetism, the magnetic susceptiblity results for K+(15C5)2-e' and
Rb+(15C5)2-e' will be discussed.

The magnetic properties of a material can be classified by its response to an
applied magnetic field. The susceptibility, or response is given by the

equafion

-M.
x- H (5.1)

140

where M is the magnetization or magnetic moment per unit volume and H
is the applied magnetic field. If the material is isotropic, M and H are parallel
and X is a scalar term; otherwise X is a tensor.

Diamagnetic materials, in which all the spins are paired, are characterized
by a small negative temperature-independent susceptibility. The negative
value indicates that the induced moment is opposed to the magnetic field.
All molecules have diamagnetic contributions to their susceptibilities as all
electrons precess in a field and therefore show a weak diamagnetism.
Paramagnetic materials possess permanent magnetic moments and have a
positive magnetic susceptibility. This magnetic behavior is due to the
tendency of the applied field to orient the moments in the direction of the
field while the tendency of thermal agitation is to preserve a random
orientation of magnetic moments. A simple paramagnet can be considered to
consist of N identical atoms each having a total angular momentum I. The

magnetic contribution to the Hemholtz free energy, F, is given by 107:

-_F_
ckT = : e-guBHJz (5.2)

Jz=-J

where “B is the Bohr magneton, g is the free electron g value and 12
represents the 214-1 thermally accessible states. The total magnetization is

given by:

(5.3)

141

where V is the volume of the sample and aF/BH is the magnetic moment and
is calculated from the summation and differentiation of Equation (5.2) and

B](x), the Brillouin function, is defined by:

 

I I I I
=21_+1 I 2J+lI -.1. I I
3100 2] COthL 2] J x 2] COthL 2]] x (5.4)

For the case in which guBH<<kT, the small-x expansion of the Brillouin

function yields the following expression for the molar susceptibility (VX)

_ (gun)2 J(J+1)
XM "NA 3 kB'l‘

 

(5.5)

From Equation (5.5) it can be seen that the susceptibility of a paramagnet will
vary inversely with temperature. This is known as the Curie law. The Curie
constant, C, is defined by:

C=-11(g )2 J(J+1) (5.6)
v ”B k3

 

and therefore

at” = -% (5.7)

For the case I=S=l / 2, the value of the Curie constant is 0.376 which assumes
that the system consists of 100% independent unpaired spins and that orbital

angular momentum is quenched.

142

A modified version of the Curie law is given by the Curie-Weiss law
which takes deviations from pure Curie law behavior due to coupling among
the spins into account. The form of Curie-Weiss law used here also includes
the possibility that not all spins contribute to XM. This expression is given by
fC

XM = 'T—e' (5.8)

where f is the fraction of unpaired spins and 6 is called the Weiss constant,
the value of which can be used to indicate whether a material is purely
paramagnetic (9:0), ferromagnetic (9>0) or antiferromagnetic (6<0) by using
the high temperature susceptibility. While, strictly speaking, the terms
ferromagnetic and antiferromagnetic refer to cooperative effects among the
spins, leading to a magnetic transition as the temperature is decreased, it
should be noted that 9 can be non-zero even when no transition is observed.

A ferromagnet has a nonvanishing magnetic moment even in zero
applied magnetic field. The interactions between the magnetic atoms favor a
parallel alignment with the magnetic moments. At absolute zero, there is
complete alignment with the magnetization at maximum value. As the
temperature is raised, the magnetic moments begin to go towards a random
orientation and consequently the magnetization begins to decrease, slowly at
first, and then more quickly until the spontaneous magnetization becomes
zero at a characteristic temperature, Tc, known as the Curie temperature.
Above the Curie temperature the susceptibility decreases with temperature.
When T >> Tc Equation (5.7) is obeyed.

An antiferromagnetic material consists of a lattice of magnetic atoms

which can be divided into two or more interpenetrating lattices, called a

143

superlattice. The spins are ordered below a temperature known as the N eél
temperature, TN, and are disordered above the Neél temperature. The
susceptibility of an antiferromagnet is characterized by an increase in the
susceptibility with temperature below TN and a decrease, as in paramagnetic
materials, above TN. As with ferromagnetic materials, the susceptibility
follows Equation (5.7) when T >> TN. In contrast to ferromagnetic substances,
however, 6<0.

In general, alkalides are diamagnetic compounds due to the fact that all
spins are paired. At low temperatures (T< 20 K) there is a deviation from the
temperature independent susceptibility characteristic of diamagnetic
materials. This deviation is known as a "Curie tail" in which the
susceptibility drops very rapidly with increasing temperature before settling
into the typical temperature-independent pattern. The variation of the
magnitude of the Curie tail from one sample to another indicates that it is
caused by varying concentrations of trapped electrons.

One might have thought that all electrides would have the same magnetic
behavior. However, this is not the case. Cs+(18C6)2-e‘ is a localized electride
that follows Curie-Weiss behavior with a Weiss constant of -1.5 K 22.
Cs+(15C5)2-e' is an antiferromagnetic compound having a Neél temperature
of 4.3 K 104. Li+C211-e' shows spin pairing as the temperature is decreased.108

The striking difference in the magnetic behavior of Cs+(18C6)2'e' and
Cs+(15C5)z~e' is intriguing. The structures of Cs+(18C6)2-e' 43 and Cs+(lSC5)2:e'
109 are both known. The Cs+(18C6)2-e‘ structure is essentially’analogous to the
structure of Cs+(18C6)2Na' with the exception that there is only noise level
density at the anionic site in the electride, consistent with the assumption
that the trapped electron is the anion. The ions pack in alternate planes of

cations and anionic holes perpendicular to the c-axis. Since the structure of

144

Cs+(15C5)2-e' has just been recently solved it is not yet clear what features of
the structure give rise to the antiferromagnetic behavior. Although the two
electrides are somewhat similar in their packing, Cs+(18C6)2-e‘ is monoclinic
with four molecules per unit cell, whereas Cs+(15C5)2°e' is triclinic with one
molecule per unit cell. It is apparent that the Cs+ cation fits snugly between
the two 18C6 rings and is therefore well-shielded from the electrons, whereas
the 15C5 rings are slightly smaller and are not able to completely shield the
cation from its surroundings. A major purpose of the present investigation
was to see if the magnetic behavior of K+(15C5)2-e' and Rb+(15C5)2-e' is the
same as that observed for the cesium compound.

Magnetic susceptibility studies were performed on an S.H.E. Variable
Temperature Susceptometer equipped with a Superconducting Quantum
Interference Device (SQUID). The samples were loaded into Kel-F buckets
with snap on lids while in a nitrogen-filled glove bag. As an extra precaution,
the lid and bottom of the SQUID buckets were tied together through two pairs
of holes to prevent the loss of sample. The temperature range of the study
was from 1.8 K to 225 K. The samples were loaded into the SQUID both in the
presence of a field and in zero field. To ensure that the field was essentially
zero and that the residual fields were mimimal (~ 5-10 Gauss) the field was
cycled before the start of the experiment. The electronic contribution to the
molar susceptibility was calculated by the following equation:

xsample + bucket ' xdecomposed sample + bucket

X = moles of sample (59)

 

in which the terms in the numerator are "apparent susceptibilities" given by

145

M

x.pp...n.=——-°"Iff”‘d (5.10)

and do not specifically include the sample size.

The temperature and field dependence of the susceptibility were measured
for both K+(15C5)2-e' and Rb+(15C5)2-e‘. The data were fit by using the general
non-linear curvefitting program KIN FIT.110 A modified version of the

Curie-Weiss equation:

x=§6+3 (5.11)

where B is a temperature independent correction term which was used when
data for the entire temperature range were analyzed. Diamagnetic impurities,
such as M’, and metallic paramagnetic impurities such as precipitated metal
can be accounted for in the B term. The Curie-Weiss equation (5.8) was used
for data at temperatures greater than or equal to 40 K. The method of using
equation 5.8 to analyze the data is more accurate than the modified version of
the Curie-Weiss equation in which the entire temperature range is used,
because the Curie-Weiss equation is a high temperature approximation. It is
expected that deviations will occur at lower temperatures and therefore in the
studies of these two electrides temperatures greater than 40 K followed the
expected Curie law behavior in which the temperature was inversely
proportional to the susceptibility.

A representative plot of 1/ XM vs T for Rb+(15C5)2°e' is shown in Figure 50.
The plot follows Curie law behavior with a slight deviation at low
temperatures. When the entire temperature range is taken into

consideration, the best-fit parameters are f = 0.75 :I: .03, 9 = -2.1 i .6 K and B =

1le

146

 

 

 

 

 

. , .
o 100 200 300
Temp 00

Figure 50. 1/ XM vs Temperature for Rb+(15C5)2-e'.

147

+170 1 43 (x 10'6) mol'1. When temperatures greater than or equal to 40 K
were used, the values were f= 0.80 :l: .01 and 6 = -2.4 i 0.3 K. For a pure
paramagnetic species one would expect 100% unpaired spins (f=1.0); therefore,
the lower value indicates the presence of a diamagnetic impurity such as the
rubidide. It is known from optical and DSC results that rubidide is often
present in electride samples. Another possibility for the low concentration of
unpaired spins could be the presence of decomposition. A SQUID run was
done with the same preparation that showed a pure Rb+(15C5)2-e' DSC trace.
The run was somewhat flawed because during decomposition of the sample a
small amount of the decomposed product oozed out of the sample bucket and
may have been lost. If so, the measured number of moles of sample would be
too small. The fraction of unpaired spins is determined from the slope of the
line, which is directly proportional to the number of moles while the Weiss
constant is calculated from the intercept at 1/ x = 0. Since some of the sample
may have been lost, a reliable determination of the true slope could not be
assured. A smaller than true mass would give a smaller calculated slope
which would lead to a higher value of the percent of unpaired spins. The
Kinfit analysis for this data indicated that there were ~112 :l: 22% unpaired
spins when the entire temperature range was taken into account. For
temperatures greater than or equal to 40 K there were ~108i 1% unpaired
spins. These values are consistent with some sample loss. The value of 0 is,
however, independent of the sample mass. A value of -2.0 :t .4 K was found
in this run. The negative value of the Weiss constant indicates that
Rb+(15C5)2-e" has a slight tendency towards antiferromagnetic interactions,
however an antiferromagnetic transition was not observed. An extensive
field study showed that the susceptibility of Rb+(15C5)2-e' is independent of

field within experimental error (5.4%) as shown in Figure 51. The top line is

148

 

 

 

 

30
20 u
I
E 'I
§ '
II
10 a ' "
fl
0 I I i T I
1 2 3 4
Temp (K)

I 1/Xm

Top: 025 K?

Bottom: 0.5, 1.0,

2.0, 3.0 and 5.0 K:

Figure 51. 1/ XM vs Temperature for Rb+(15C5)2e' at several fields.

149

from the 0.25 kG data whereas the bottom line consists of the data for the
fields 0.5 , 1.0, 2.0, 3.0 and 5.0 kG. The larger value of the susceptibility at
every temperature for the 0.25 kG data is probably due to the effects of
residual fields which are more important at lower fields. The field
independence of the susceptibility was observed whether the sample was
loaded in the presence of a field or in zero field. Attempts to anneal the
sample had no apparent effect on the susceptibility.

The results for K+(15C5)2-e' are quite similar to those of Rb+(15C5)2-e'.
Again the compound follows Curie law behavior, but with a distinct
deviation at low temperatures as seen in a representative plot of l/XM vs T
(Figure 52). The average percent of unpaired spins was 74 d: 7%, 0 = -20.4 i .6
K and B = -200 :t 60 (x 105) mol'1 when the entire temperature range was
used. When only temperatures greater than or equal to 40 K were taken into
account, the sample had an average of 62 :l: 7 % unpaired spins and 9 = -13 :t: 1
K. As with the Rb+(15C5)2-e‘ results, the low value of unpaired spins is
mostly likely due to the presence of potasside or decomposition. As for
Rb+(15C5)2-e', there were two runs that indicated more than 100% unpaired
spins for K+(15C5)2-e' when the entire temperature range was used. The
Weiss values for these cases were determined to be -29 :l: 10 K and —23 :l: 1 K.
When temperatures above 40 K were used the Weiss values were calculated
to be -15.2 :t .6 K (f= 0.86) and -10.60 :t .7 K (f= 0.80). A summary of the results
is given in Table 27. The fact that the percent of spins is not 100% in all cases
is in accord with the hypothesis that the presence of alkalide or
decomposition is the cause of the commonly obtained low value for the
percent of unpaired spins. The larger negative value of the Weiss constant
indicates there is significantly greater antiferromagnetic interactions for

K+(15C5)2-e‘ than for Rb+(l5C5)2-e'. Field studies showed that the

thm

 

150

 

 

 

 

I .
200 300

' I
0 100

Temp 00

Figure 52. 1 /XM vs Temperature for K+(15C5)2-e'.

15 1
Table 27. A Summary of K+(15C5)2.g' and Rb+(15§5)2-g' Susceptibility Results.

 

Sample {1:2 Qfi) B (x 10‘6 mol'l)
K+(15C5)2'e’ (1a) .74 i .07 -20.4 :I: 0.6 -200 :l: 60
(1b) .62 :1: .07 -13 :1: 1
(2a) .8 :l: 0.2 -19 :l: 2 150 :1: 270
(2b) .85 :t .01 -13.9 :I: 0.4
(3a) 1.1 :l: 0.3 ~29 :1: 10 -280 :l: 74
(3b) .86 :l: .01 -15.2 i 0.6
(4a) 1.1 :t 0.1 -23 :l: 1 -402 :1: 76

(4b) .80 i .03 -10.6 :l: 0.7

Rb+(15C5)2-e' (1a) .72 a: .06 -3.2 :I: 0.2 164 :t: 68
(1b) .77 i .02 -3.8 :I: 0.4
(2a) .75 d: .03 -2.1 :l: 0.6 170 :l: 43
(2b) .80 :t .01 :-2.4 :I: 0.3
(3a) .71 a: 0.2 -2.8 :I: 0.1 50 i 30
(3b) .73 1: 0.2 -2.9 :l: 0.4
(4a) .59 i .09 -1.9 :1: 0.3 350 :l: 100
(4b) .71 :l: .03 -5.6 :t 0.6
(5a) 1.1 i 0.1 -2.5 i: 0.1 -150 a: 85

(5b) 1.1 :l: 0.1 -1.7 :t 0.3

1 Eqn. (5.10) was used to obtain parameters for those runs denoted by an "a".
2 Eqn. (5.8 ) was used to obtain parameters for those runs denoted by a "b".

152

susceptibility of the compound is independent of the field, within :1: 3.4%,
whether or not the sample was loaded in the presence of a field. An
antiferromagnetic transition was never observed even after attempts to
anneal the sample.

In conclusion, K+(15C5)2:e' and Rb+(15C5)2-e' are essentially Curie law
paramagnets with deviations at low temperatures indicative of
antiferromagnetic interactions. This indicates that the cations are well-
shielded from their surroundings. The compound K+(15C5)2-e’ shows a
greater deviation from simple Curie law behavior with a larger negative
value of the Weiss constant. The differences in the magnetic behavior of
Cs+(18C6)2-e' and Cs+(15C5)2-e' can be attributed to the differences in the
structures of the two electrides. Although it was assumed that the electron-
electron interactions in K+(15C5)2-e' and Rb+(15C5)2-e' would be even
stronger than in Cs+(15C5)2~e', the differences in the magnetic susceptibility
behavior of these compounds suggest rather marked structural differences.
Apparently the magnetic behavior in electrides is strikingly structure
dependent and not just dependent on the average distance between electron-

trapping sites.

VI. Summary and Suggestions for Future Work.

This study was the first investigation of spin-lattice relaxation times of
alkalides and electrides in the solid state. Although the "effective Debye
temperatures" have not been determined for any of the alkalides and
electrides, from the temperature dependence and nucleus dependence of the
spin-lattice relaxtion times it is clear that the quadrupolar mechanism is
responsible for relaxation in these compounds.

The 23Na NMR results showed that the symmetric Na' ion is extremely
resistant to relaxation at low temperatures in Cs+(18C6)2-Na' where the T1
value at 173 K is 107 sec, which is the longest spin-lattice relaxation time for
sodium known to date. The Cs+(15C5)2°Na' results are analogous to those of
Cs+(18C6)2-Na'. However, further studies on the former compound should
be done in order to obtain a broader temperature range which would allow a
better understanding of its T1 temperature dependence. The 87Rb NMR
results for Cs+(18C6)2-Rb', Cs+(15C5)2-Rb' and Rb+(15C5)2-Rb' were also very
successful showing that the relaxation processes in the Cs+(15C5)2-Rb' and
Rb+(15C5)2-Rb" compounds are more efficient than in Cs+(18C6)2-Rb'.
Structural and symmetry differences between the 18C6 and 15C5 complexes
are probably responsible for the differences in the relaxation behavior in both
the 23N a and 87Rb NMR studies. A comparison of the 23Na and 87Rb results
shows that the anionic relaxation is much more efficient in the rubidides
than in the sodides. This could be due to the fact that the Rb‘ ion may be
more prone to distortion as evidenced by the value of the antishielding factor

and therefore less resistant to relaxation than the N a' ion. Further studies of

153

154

sodides should be done to see whether all of the sodides have the same
relaxtion behavior as the two sodides studied.

The 133Cs and 39K results were not as successful; however, further studies
should be done. It may be necessary to use MAS-NMR to obtain a spectrum
of Cs+(18C6)2-CS' in which the peaks do not overlap. In addition it would be
necessary to use a pure sample of Cs+(18C6)2-CS' in order to obtain accurate T1
values for the Cs‘ and Cs+ ions. The Cs+(18C6)2-e‘ results need to be verified
in order to further understand the nature of the two peaks observed and their
differing relaxation behavior. 39K NMR relaxation studies will be more
difficult due to the time needed to obtain a satisfactory signal-to-noise ratio
because of the low sensitivity of the nucleus.

With the exception of Cs+(18C6)2-e', this study only considered the
relaxation of the alkali metal anions. A study of the nature of the relaxation
of the alkali metal cations could also be done. This will prove to be more
difficult but 23Na, 7Li and 133Cs are the most promising candidates. 87Rb and
39K spin-lattice relaxation studies of the cations will probably be impossible as
Rb+ and K+ can not be observed without the use of a modified spin echo
technique. A further impediment to the relaxation study of the complexed
cations will be the added time required to obtain adequate spectra.

The spin echo technique has proven to be a powerful tool in the study of
alkalides and electrides. This is the first time that K+ and Rb+ have been
observed in the solid state for these compounds. Through the use of this
technique, it will be possible to probe the local environments of the Rb“ and
K+ cations in alkalides and electrides. The observed lineshapes emphasize
the differences in symmetry and the local structures of the species.

Correlation between the observed NMR spectra and the structures can yield

155

information about the temperature-dependent dynamic properties of these
compounds.

Further studies need to be made in order to assure that sufficiently long
delay times are being used and that the lineshapes are not being distorted. It
will be necessary to use a larger sweepwidth (faster digitizer) to study
compounds with broad linewidths. A faster digitizer would be particularly
helpful in the 87Rb NMR studies where the spectra consist of very broad lines.
Additional studies at different fields and temperatures could also yield
further infomation.

The study on the methylamine-assisted solubilization of lithium has
shown that the species Li+(CH3NH2)4 dissolves in a variety of solvents, both
by itself and with sodium as shown by NMR and optical spectroscopy. The
search for "simple" alkalides was extended to the Li+(CH3NH2)x-Na' and
Li+(CH3CH2NH2)x-Na' compounds. Although crystalline compounds have
not been isolated, 23Na NMR meaurements have proven that Na' is indeed
present in these solutions. The 23Na NMR chemical shift of the
Li+(CH3CH2NH2)x-Na' series is independent of both temperature and the
amount of ethylarnine. The 23Na NMR spectra for the Li+(CH3NH2)x-Na'
series showed, however, that the chemical shift depended on both
temperature and the amount of methylamine. It was shown conclusively
that an exchange process is responsible for the paramagnetic shift of
Li+(CH3NH2)4'Na' with increasing temperature, as a 23Na NMR spectrum of
a frozen sample consisted of a peak centered at -55 ppm as expected for the
N a‘ ion. Both 23Na NMR and optical studies of the "Li+(NH3)4:Na'" species
showed definitively that Na“ does not exist in this solution and that in fact

this system contains primarily Li(NH3)4 , N a+ and Na(s).

1 5 6
It has been shown that K+(15C5)2-e" and Rb+(15C5)2-e' are essentially Curie

law paramagnets despite slight deviations at temperatures below ~ 20K. This
indicates that the cations are well shielded from their surroundings. These
compounds are field independent before and after annealing. Loading the
samples in zero field has no effect on the magnetic susceptibility behavior of
either compound. The K+(15C5)2-e' has a much larger Weiss constant.
However, no sign of antiferromagnetic behavior was observed for either
compound. It has also been shown by both magnetic susceptibility studies
and Differential Scanning Calorimetry that mixtures of the electrides and
their corresponding alkalides are often obtained and the synthesis of the
alkalide-free electride is not easy. It would be very useful to obtain the x-ray
crystal structures of both compounds in order to fully compare the magnetic
susceptibilty results of these compounds with those of Cs+(18C6)2-e' and
Cs+(15C5)2°e'.

2.

4.

6.

10.

11.

12.

13.

14.

15.

LIST OF REFERENCES

. W. Weyl, Annalen der Physik und Chemie l9_7, 601 (1864).

H. Blades and ].W. Hodgins, Can. I. Chem. 33, 411 (1955).

G. Rubinstein, T. Tuttle, S. Golden, I. Phys. Chem. 7_7, 2872 (1973).
RC. Douthit and LL. Dye, I. Am. Chem. Soc. 8_2_, 4472 (1960).

RK Quinn and 1.]. Lagowski, I. Phys. Chem. _7_3_, 2326 (1969).

].L. Dye, M.G. DeBacker, I.A. Eyre, and L.M. Dorfrnan, I. Phys. Chem. 26,
839 (1972).

].W. Fletcher and W.A. Seddon, I. Phys. Chem. 7_9, 3055 (1975).
CA. Hutchinson and RC. Pastor, Rev. Mod. Phys. _25, 258 (1953).
CA. Hutchinson and RC. Pastor, I. Chem. Phys. 2_1_, 1959 (1953).
CJ. Pedersen, I. Am. Chem. Soc. 82, 7017 (1967).

B. Dietrich, I.M. Lehn, and JP. Sauvage, Tet. Letters 3_4, 2885 and 2889
(1969).

GP. Pez, LL. Mador, I.E. Calla, R.K. Crissey and CE. Forbes, I. Am. Chem.
Soc. M, 4098 (1985).

I.L. Dye, C.W. Andrews, and SE. Mathews, I. Phys. Chem. _7_9, 3065 (1975)
I.L.Dye, I. Phys. Chem. 84, 1084 (1980).

IL. Dye, I. Phys. Chem. 8_8, 3842 (1984).

157

16.

17.

18.

19.

20.

21.

24.

26.

27.

28.

29.

l 5 8
AL. Wayda and I.L. Dye, I. Chem. Educ. 6_2, 356 (1985)

I.L. Dye, I.M, Ceraso, M.T. Lok, B.L. Barnett and FJ. Tehan, I. Am. Chem.

Soc. %, 608 (1974).

FJ. Tehan, B.L. Barnett and I.L. Dye, I. Am. Chem. Soc. 28, 7203 (1974).
B. VanEck, L.D. Le, D. Issa and I.L Dye, Inorg. Chem. 2_1_, 1966 (1982).

I. Papaioannou, S. Iaenicke and I.L. Dye, I. Solid State Chem. 6_7, 122

(1987).

1.5. Landers, I.L. Dye, A. Stacy and MJ. Sienko, I. Phys. Chem. 8_5, 1096

(1981).

D. Issa, A. Ellaboudy, R. Ianakiraman and I.L. Dye, I. Phys. Chem. 88, 3847
(1984).

I.L. Dye, M.R. Yemen and M.G. DaGue, I. Chem. Phys. 88, 1665 (1978).

M.G. DaGue, I.S. Landers, H.L. Lewis and I.L. Dye, Chem. Phys. Lett. 88,
169 (1979).

I.L. Dye, M.G. DaGue, M.R. Yeman, I.S. Landers and H.L. Lewis, I. Phys.
Chem. 851, 1096 (1982).

L.D. Le, D. Issa, B. VanEck and I.L. Dye, I. Phys. Chem. 88, 7 (1982).

S. Iaenicke, M.K. Faber, I.L. Dye and W.P. Pratt, Ir., I. Solid State Chem. 88,
239 (1987).

RR. Dewald and I.L. Dye, I. Phys. Chem. 88, 121 (1964).

B. Lindman, S. Forsen, "NMR and the Periodic Table", (R.K. Harris and B.
Mann, eds.), Academic Press, New York, 1978.

30.

31.

32.

33.

35.

36.

37.

38.

39.

40.

41.

42.

43.

45.

1 5 9
I.M. Ceraso and I.L. Dye, 1. Chem. Phys. 81, 1585 (1974).

I.L. Dye, C.W. Andrews and I.M. Ceraso, I. Phys. Chem. fl, 3076 (1975).
N .C. Pyper and RP. Edwards, unpublished results.

D. Ikenberry and TR Das, Phys. Rev. A _1_3_8_, 822 (1965).

C. Deverell, Prog. Nucl. Magn. Reson. Spectrosc. _4, 278 (1969).

BR. Andrew, A. Bradbury and RG. Eades, Nature (London) lg, 1802
(1959). '

E.R. Andrew, Arch. Sci. (Geneva) 12, 103 (1959).
1.]. Lowe, Phys. Rev. Lett. 2, 285 (1959).

A. Ellaboudy, M.L. Tinkham, B. VanEck and I. L. Dye, I. Phys. Chem. 88,
3352 (1984).

I.L. Dye and M.G. DeBacker, Ann. Rev. Phys. Chem. _38, 271 (1987).
A. Ellaboudy and I.L. Dye, I. Mag. Res. 88, 491 (1986).

I.H. VanVleck, Phys. Rev. E, 1168 (1948).

H.-I. Behrens and B. Schnabel, Physica B g4, 185 (1982).

E. Kundla, A. Samosan and E. Lippmaa, Chem. Phys. Lett. 88, 229 (1981).

D Freude, I. Haase, I. Klinowski, T.A. Carpenter and G. Roniker, Chem.
Phys. Lett. 112, 365, 1985.

SB. Dawes, A.S. Ellaboudy and I.L. Dye, I. Am. Chem. Soc. 189, 3508
(1987).

47.

49.

50.

51.

52.

53.

55.

56.

57.

58.

59.

60.

l 6 0
N .C. Pyper and RP. Edwards, I. Am. Chem. Soc. 108, 78 (1986).

N .F. Ramsey, Phys. Rev. 7_7, 567 (1950); _7_84 699 (1950); 834 540 (1951); 88,
243 (1952).

SB. Dawes, D.L. Ward, R.H. Huang and I.L. Dye, I. Am. Chem. Soc. 198,
3534 (1986).

SB. Dawes, O. Fussa, D.L. Ward and I.L. Dye, unpublished results.
W.D. Knight, Phys. Rev. 28, 1259 (1944).

RF. Edwards, Adv. Inorg. Chem. Radiochem. g, 135 (1982).

SB. Dawes, Ph.D. Dissertation, Michigan State University, 1986.
M.L. Tinkham and I.L. Dye, I. Am. Chem. Soc. 192‘, 6129 (1985).
A. Beckmann, K.D. Boklen and D2. Elke, Z. Phys. 2_7_(_)_, 173 (1974).
G. Malli and S. Fraga, Theor. Chim. Acta. 8, 275 (1966).

D.M. Holton, P.P. Edwards, D.C. Johnson, C]. Page, W. McFarlane and B.
Wood, I. Chem. Soc. Chem. Commun. 248 (1984).

S. Khazaeli, I.L. Dye, and AI. Popov, Spectrochimica Acta 39A, 19 (1983).

M.L. Tinkham, A. Ellaboudy, I.L. Dye and PB. Smith, I. Phys. Chem. 28,
14 (1986).

I.L. Dye, M.R. Yemen, M.G. DaGue and I.M. Lehn, I. Chem. Phys. 88, 1665
(1978).

O. Fussa, S.M. Kauzlarich, I.L. Dye and BK. Teo, I. Am. Chem. Soc. 182,
3727 (1985).

61.

62.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

76.

1 6 1
Fussa and Dye, unpublished results.

A.C. Kunwar, G.L. Turner and E. Oldfield, |.Mag. Res. 89, 124 (1986).

A. Ellaboudy, L.E.H. McMills, I. Kim. I.L. Eglin and I.L. Dye, unpublished
results.

C.P. Slichter, "Principles of Magnetic Resonance", Harper and Row, New
York, 1963.

A. Abragam, "Principles of Nuclear Magnetism", Clarendon Press, Oxford,
1961.

GE. Pake. Solid State Physics 2, 1 (1956).
R.V. Pound, Phys. Rev. _7_9, 685 (1950).
RV. Pound, I. Phys. Chem. 5_7, 743 (1953).

R.V. Pound, "Progress in Nuclear Physics", vol. 2, Pergamon Press,
London, 1952, p.21.

R.L. Mieher, Phys. Rev. _125, 1537 (1962).

RM. Sternheimer, Phys. Rev. 80, 102 (1950).

I. VanKranendonk, Physica 29, 781 (1954).

MJ. Weber, Phys. Rev. 1_3_Q, 1 (1963).

I.L. Dye and V.A. Nicely, I. Chem. Educ. 888, 443 (1971).
CJ. Pedersen, I. Am. Chem. Soc. _8_9, 7017 (1967).

CJ. Pedersen, I. Am. Chem. Soc. 22, 386 (1970).

78.

79.

80.

81.

82.

83.

85.

87.

89.

90.

91.

l 6 2
EC. Wikner, W.E. Blumberg and EL. Hahn, Phys. Rev. 1_1__8, 631 (1960).

A. Tzalrnona and ER. Andrew, Proc. 18th Ampere Congress, Nottingham
1974, p.241.

A.C. Cunningham and SM. Day, Phys. Rev. 182, 287 (1966).

R.K. Harris, "Nuclear Magnetic Resonance Spectroscopy", Pitman:
London, 1983.

RF. McEachran, AD. Stauffer and S. Grieta, I. Phys. lg, 3119 (1979).

"Powder Diffraction File": Inorganic Phases, International Centre for
Diffraction Data 1983.

D. Moras and R. Weiss, Acta Cryst. 29B, 396 (1973).
RF. Van Remoortere and RP. Boer, Inorg. Chem. 18, 2071 (1974).
M. Dobler, I.D. Dunitz and P. Seiler, Acta Cryst. 30B, 2741 (1974).

I.L. Dye and AS. Ellaboudy, Chapter IV in "Modern NMR Techniques and
Their Application to Chemistry" ed. A.I. Popov, in press.

D.M. Holton, A. Ellaboudy, N .C. Pyper and RP. Edwards, I. Chem. Phys.
84, 1089 (1986).

D.L. Ward, S.B. Dawes, O. Fussa and I.L. Dye, Abstracts, American
Crystallographic Association Proceedings, Series 2, Vol. 13, 1985, p.25.

A.C. Kunwar, G.L. Turner and E. Oldfield, I. Mag. Res. 89, 124 (1986).
Written by J. Kim, this lab.

D.L. Ward, R.H. Huang and I.L. Dye, Acta. Cryst. C44, 1374 (1988).

1 6 3
92. RH. Huang, D.L. Ward and I.L. Dye, submitted to I. Am. Chem. Soc.

93. I.L. Dye, Progress in Inorg. Chem. 82, 327 (1984).

94. D. Issa and I.L. Dye, I. Am. Chem. Soc. L021, 3781 (1982).

95. A. Ellaboudy, Ph.D. Dissertation, Michigan State University, 1984.
96. M.K. Faber, Ph.D. Dissertation, Michigan State University, 1985.
97. O. Fussa, Ph.D. Dissertation, Michigan State University, 1986.

98. RR. Dewald and K.W. Browall, I. Phys. Chem. E, 129 (1970).

99. I.B. Skowyra, unpublished results.

100. R. Concepcion and I.L. Dye, I. Am. Chem. Soc. 192, 7203 (1987).

101. A.M. Stacey, D.C. Iohnson, and M.I. Sienko, I. Chem. Phys. 7_6, 4248
(1982).

102. A.M. Stacey and M.I. Sienko, Inorg. Chem. fl, 2294 (1982).

103. M. L. Tinkham, Ph.D. Dissertation, Michigan State University, 1985.
104. SB. Dawes and I.L. Dye, unpublished results.

105. A. Ellaboudy and L.E.H. McMills, unpublished results.

106. I.L. Eglin, unpublished results.

107. N .W. Ashcroft and N .D. Mermin, "Solid State Physics", Saunders
College, Philadelphia, 1976.

108. 1.5. Landers, I.L. Dye, A. Stacy and M.I. Sienko, I. Phys. Chem. g, 1096
(1981).

164

109. R. Huang, D.L. Ward and I.L. Dye, unpublished results.

110. 1.1. Dye and V.A. Nicely ]. Chem. Ed. g, 43, (1971).

"IIIIIIIIIIIIIIIIT