ALKALIMETAL‘NMRSTUDIESOFSODIUM,=RUBIDIUM ¥ _ _
AND CESI‘UM, ANIONS AND THE KINETICS 0F SODIUM «_ _ , l '
CRYPTATE EXCHANGE REACTIONS ’

. Dissertation for the Degree of PH, D.’
MICHIGAN STATE UNIVERSITY . I
I N‘JOSEPHIMIICHAELCERASO - 1 .
1975 , ' '

 

 

 

Date

0-7639

 

This is to certify that the

thesis entitled

ALKALI METAL NMR STUDIES OF
SODIUM, RUBIDIUM AND CESIUM ANIONS
AND THE KINETICS OF
SODIUM—CRYPTATE EXCHANGE REACTIONS

presented by

Joseph Michael Ceraso

has been accepted towards fulfillment
of the requirements for

Pho Do dpgfpp in Chemstry

 

Major professor

9-29-75

 

 

ABSTRACT

ALKALI METAL NMR STUDIES OF SODIUM,
RUBIDIUM AND CESIUM ANIONS AND THE KINETICS OF

SODIUM-CRYPTATE EXCHANGE REACTIONS

By
Joseph Michael Ceraso

The solvent influence on the kinetics of the release of
sodium ion from its complex with the macrobicyclic hexaoxa-
diamine N(CH2CH20CH2CH20CH2CH2)3N (2,2,2 cryptand) has been
investigated by using the pulsed 23Na Fourier transform NMR
technique. Each of the four solvents used, water, ethylene-
diamine (EDA), pyridine (PYR), and tetrahydrofuran (THF),
showed two well-defined resonance absorptions below the
corresponding coalescence temperature. In all cases it was
possible to separately measure line widths and chemical
shifts of the free and complexed sodium ion as a function of
temperature in the absence of exchange. Since the spins are
non—interacting, the transient solution of the modified Bloch
equations which describe the response of a spin system under—
going chemical exchange between two nonequivalent sites is

applicable. Exchange times, T, were calculated by fitting

Joseph Michael Ceraso

the modified Bloch equations to the observed 23

Na line shape
by using a weighted non-linear least-squares technique. For
EDA solutions, a mechanism in which the rate limiting step is
release of sodium ion from the cryptate complex was found to
be in agreement with the observed concentration dependence

of exchange times throughout the entire temperature range
examined. The activation energy for sodium cryptate exchange
was found to vary from 12.9 kilocalories for EDA solution to
16.7 kilocalories for H20 solution.

When 2,2,2 cryptand and an excess of sodium, rubidium
or cesium metal are placed into contact with THF, ethylamine
or methylamine, solutions at least as concentrated as 0.1 M
total metal were obtained. Major species in solution are the
complexed cation and the alkali metal anion M-. The NMR
chemical shift and linewidth have been measured for 23Na- in
THF, EA and MA, for 87Rb- in THF and EA and for 133Cs- in THF.
The chemical shift of Na- is, within experimental error, the
same as that calculated for the gaseous anion (based upon the
measured value for the gaseous atom) and is independent of
solvent. Comparison with the solvent-dependent chemical
shift of Na+ provides conclusive evidence that Na- is a
"genuine" anion with two electrons in a §§_orbital which
shield the gp_electrons from the influence of solvent. The
linewidth increases from THF to EA to MA, suggesting either

an increasing exchange rate with the cryptated cation or,

more probably, the influence of an increasing concentration

Joseph Michael Ceraso

of solvated electrons.

In the case of sodium solutions in all solvents both
Na+C222 and Na' are detected by their NMR peaks. However,
probably because of extreme line-broadening, Rb+C222 and
Cs+C222 are not observed, but only the relatively narrow
line of the corresponding anion. The chemical shifts (dia-
magnetic shift in ppm from the infinitely dilute aqueous ion)
are 185 and 197 for Rb_ in BA and THF, respectively, and 292
for Cs‘ in THF compared with 212 and 344, respectively, for
the gaseous Rb and Cs atoms.

A synthesis of the first crystalline salt of the sodium

anion is described. The salt has the stoichiometry Na+C Na-

222'

(where C222 is 2,2,2 cryptand) and is gold in color at low

temperatures.

ALKALI METAL NMR STUDIES OF SODIUM,
RUBIDIUM AND CESIUM ANIONS AND

THE KINETICS OF SODIUM-CRYPTATE EXCHANGE REACTIONS

BY

Joseph Michael Ceraso

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1975

To my Parents

ii

ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation
to Professor James L. Dye for his endless encouragement
and guidence throughout this research program.

Special thanks go to Steve Landers and Patrick Smith
for their collaborative efforts in the exchange studies.
Thanks go to Professor Max T. Rogers for being second
reader and to Drs. Yves Cahen, Mei—Tak Lok and F. J. Tehan
for assistance in synthesizing 2,2,2 cryptand. Additional
thanks go to C. W. Andrews, Dr. M. G. DeBacker, Miss E. Mei,
Dr. L. D. Long, Dr. N. Papadakis and Dr. D. A. Wright for
their help and suggestions.

Financial assistance from the Atomic Energy Commission
and Michigan State University and a summer term of fellow-

ship from the Dow Chemical Company is acknowledged.

iii

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . .
LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . .
I. INTRODUCTION . . . . . . . . . . . . . . . . .
II. HISTORICAL. . . . . . . . . . . . . . . . . . . .
2.1 Metal Ammonia Solutions. . . . . . . . . . .
2.1.1. Species in M-NH3 Solutions . . . . .
2.1.1.1. Evidence for Monomer Species in
M—NH3 Solutions . . . . . . . .
2.1.1.2. Evidence for Diamagnetic Species
in M-NH3 Solutions. . . . . .
2.1.2. Models for Metal Ammonia Solutions . .
2.2 Alkali Metals in Amines and Ethers . . . . . .
2.2.1. General Properties . . . . . . . .
2.2.2. Major Species Involved in Metal—Amine
and Metal-Ether Solutions. . . . . .
2.2.2.1. Solvated Electrons. . . . . . .
2.2.2.2. Monomers. . . . . . . . . . . .
2.2.2.3. Spin-paired Species . . . . . .
2.2.2.4. Alkali Metal Anions . . . . .
2.3 Overall Equilibrium Scheme . . . . . . .
III. GENERAL FEATURES OF ALKALI METAL ION NMR . . . .

3.1 Introduction . . . . . . . . . . . . . . .

3.2 Shielding Constants of Alkali Metal Ions

iv

Page

viii

xi

10
12
15

15

16
l6
18
19
20
26
28

28

31

Chapter Page

3.2.1. Alkali Metal Ions in Crystals. . . . . 32
3.2.2. Alkali Metal Ions in Solution. . . . . 38
3.3 Quadrupole Relaxation of Alkali Metal Ions in
Solution . . . . . . . . . . . . . . . . . . . 42
IV. EXPERIMENTAL. . . . . . . . . . . . . . . . . . . . 47
4.1 General Techniques . . . . . . . . . . . . . . 47
4.1.1. Glassware Cleaning . . . . . . . . . . 47
4.1.2. Vacuum Techniques. . . . . . . . . . . 47
4.2 Metal Purification . . . . . . . . . . . . . . 48
4.2.1. Storage of Alkali Metal in Small
Quantities . . . . . . . . . . . . . . 48
4.2.1.1. Sodium Metal. . . . . . . . . . 48
4.2.1.2. Cesium and Rubidium Metals. . . 48
4.3 Solvent Purification . . . . . . . . . . . . . 50
4.4 Preparation and Purification of 2,2,2
Cryptand . . . . . . . . . . . . . . . . . . . 52
4.4.1. Synthesis of Diethyl Ester of
Triglycolic Acid . . . . . . . . . . . 53
4.4.2. Hydrolysis of the Diester. . . . . . . 54
4.4.3. Purification of 2,2,2 Cryptand . . . . 54
4.5 Synthesis of a Crystalline Salt of the Sodium
Anion. . . . . . . . . . . . . . . . . . . . . 55
4.6 Solution Preparation . . . . . . . . . . . . . 58
4.6.1. Salt Solutions for NMR Exchange

Studies. . . . . . . . . . . . . . . . 58

Chapter Page

4.6.2. Preparation of Metal Solutions . . . . 58

4.7 The NMR Spectrometer . . . . . . . . . . . . . 61

4.8 Temperature Control and Calibration. . . . . . 63

4.9 Data Reduction . . . . . . . . . . . . . . . . 64

V. SODIUM-23 NMR STUDY OF SODIUM ION - SODIUM CRYPTATE

EXCHANGE RATES IN VARIOUS SOLVENTS . . . . . . . . . 66

5.1 Introduction . . . . . . . . . . . . . . . . . 66
5.2 Determination and Interpretation of the Line

Shapes . . . . . . . . . . . . . . . . . . . . 68

5.2.1. Measurements in the Absence of
Exchange . . . . . . . . . . . . . . . 70
5.2.2. Evaluation of Exchange Times . . . . . 88
5.2.2.1. Exchange Times in EDA
Solutions . . . . . . . . . . . 90

5.2.2.2. Exchange Times in THF, H20 and

PYR Solutions . . . . . . . . . 94
5.3 Results and Discussion . . . . . . . . . . . . 106
5.3.1. Some Sources of Systematic Error . . . 106

5.3.2. Mechanism of Exchange. . . . . . . . . 121
VI. ALKALI METAL NMR STUDIES OF SODIUM, RUBIDIUM AND
CESIUM ANIONS . . . . . . . . . . . . . . . . . . . 131
6.1 Introduction . . . . . . . . . . . . . . . . . 131
6.2 Magnetic Shielding Constants of Alkali Metal
Ions . . . . . . . . . . . . . . . . . . . . . 131

6.3 Results. . . . . . . . . . . . . . . . . . . . 133

vi

Chapter Page

6.4 Discussion . . . . . . . . . . . . . . . . . 134
APPENDIX A - MODIFICATION OF RELAX 2 . . . . . . . . . . 143
APPENDIX B - PROGRAM CONVERT . . . . . . . . . . . . . . 145
APPENDIX C - SOLUTION TO MODIFIED BLOCH EQUATIONS. . . 146
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . 153

vii

Table

II

III

IV

VI

VII

VIII

IX

LIST OF TABLES

Page
Values of the average excitation energy A, and
the expectation value <ri_3>p for alkali metals. . . 37
Experimental and calculated chemical shifts for
rubidium and cesium ions in halide crystals and
aqueous solution. . . . . . . . . . . . . . . . . . 39
Chemical shifts of free and cryptated sodium ions
in solution . . . . . . . . . . . . . . . . . . . . 41
Temperature calibration for NMR . . . . . . . . . . 65

Variation of the relaxation rate and chemical shift

of free sodium cation with temperature in
ethylenediamine . . . . . . . . . . . . . . . . . . 75
Variation of the relaxation rate and chemical shift

of bound sodium cation with temperature in
ethylenediamine . . . . . . . . . . . . . . . . . . 76
Variation of relaxation rate and chemical shift of

free sodium cation with temperature in water. . . . 77
Variation of relaxation rate and chemical shift of
bound sodium cation with temperature in water . . . 78
Variation of the relaxation rate (1/T2) and

chemical shift of free sodium cation with temper-

ature in tetrahydrofuran. . . . . . . . . . . . . . 79

viii

Table

XI

XII

XIII

XIV

XV

XVI

XVII

Variation of relaxation rate and chemical shift
of bound sodium cation with temperature in
tetrahydrofuran . . . . . . . . . . . . . . . . .
Variation of relaxation rate and chemical shift
of free sodium cation with temperature in
pyridine. . . . . . . . . . . . . . . . . . . . .
Variation of relaxation rate and chemical shift

of bound sodium cation with temperature in

pyridine. O O O O O O O O O O C O O O O O O O O 0
Activation energy, Er’ for solvent reorganization
in various solvents . . . . . . . . . . . . . . .

Temperature dependence of the exchange time in
EDAl and corresponding relaxation rates in the
absence of exchange . . . . . . . . . . . . . . .
Temperature dependence of the exchange time in
EDA2 and corresponding relaxation rates in the
absence of exchange . . . . . . . . . . . . . . .
Temperature dependence of the exchange time in
EDA3 and corresponding relaxation rates in the
absence of exchange . . . . . . . . . . . . . . .
Temperature dependence of the exchange time in
H20 and corresponding values for relaxation rates

in the absence of exchange. . . . . . . . . . . .

ix

Page

80

81

82

89

101

102

103

111

Table

XVIII

XIX

XX

XXI

XXII

Page
Temperature dependence of the exchange time in
PYR and corresponding relaxation rates in the
absence of exchange . . . . . . . . . . . . . . . 112
Temperature dependence of the exchange time in
THF and corresponding relaxation rates in the
absence of exchange . . . . . . . . . . . . . . . 113
Comparison of exchange times with and without
intensity correction for EDA3 . . . . . . . . . . 120
Exchange rates and thermodynamic parameters of
sodium cryptate exchange in various solvents. . . 129
Selected list of shielding constants and
linewidths. . . . . . . . . . . . . . . . . . . . 136

 

 

LIST OF FIGURES
Figure Page

1 2,2,2 Cryptand and l8-crown—6. . . . . . . . . . . 3

solv (1), Cs_ (2), K‘ (3) and

2 Spectra at 250C of e
Na_ (4) in THF in the presence of cryptand or
crown. . . . . . . . . . . . . . . . . . . . . . . 21
3 The relation between the peak position of Na' and
of K_ in diisopropyl ether (DIPE), diethyl ether
(DE), hexamethyl phosphoric triamide (HMPA),
tetrahydrofuran (THF), dimethoxyethane (DME),
diglyme, ethylamine (EA), 1,2—propanediamine (PDA)

and ethylenediamine (EDA) at 250C. . . . . . . . . 23

4 The relation between the peak position of K‘ and

-— . . O
of esolv in various solvents at 25 C . . . . . . . 24
5 (a) Effect of quadrupole coupling upon nuclear
Zeeman energies in first order. (b) Hypothetical
spectrum corresponding to energy levels of (a) . . 3O

6 Semilog plot of 1/T2 for 23Na vs the reciprocal

absolute temperature for a solution containing

0.15 M NaBr in EDA . . . . . . . . . . . . . . . . 45
7 Apparatus for the preparation of storage tubes

for sodium metal . . . . . . . . . . . . . . . . . 49
8 Apparatus for preparation of small ampoules of

rubidium and cesium metal. . . . . . . . . . . . . 51

9 Vessel for preparation of Na+C - Na- . . . . . . . 56

xi

Figure Page

10 Vessel for preparation of NMR samples. . . . . . . 59
11 Block diagram of the multinuclear magnetic

resonance spectrometer . . . . . . . . . . . . . . 62
12 A typical KINFIT analysis of the 23Na lineshape

for a solution containing 0.60 M NaBr in EDA.

X represents an experimental point, 0, a calculated

point, =, an experimental and calculated point which

are the same within the resolution of the plot . . 74
13 Semilog plots of l/T2 for 23Na vs reciprocal

absolute temperature for solutions containing

0.6 M NaBr (o) and 0.3 M Na+C222 - Br‘ (0) in EDA. 83
14 Semilog plots of l/T2 for 23Na vs reciprocal

absolute temperature for solutions containing

0.2 M NaCl (0) and 0.2 M Na+C222 - c1— (0) in H20. 84
15 Semilog plots of 1/T2 for 23Na vs reciprocal

absolute temperature for solutions containing

0.4 M Na¢4B (o) and 0.2 M Na+C222 - ¢4B‘ (o)

in THF . . . . . . . . . . . . . . . . . . . . . . 85
16 Semilog plots of 1/T2 for 23Na vs reciprocal

absolute temperature for solutions containing

0.2 M Na¢4B (o) and 0.2 M Na+c222 ° ¢4B“ (o)

in PYR . . . . . . . . . . . . . . . . . . . . . . 86
17 Spectra at various temperatures for a solution of

0.15 M C222 and 0.6 M NaBr in EDA (1 ppm 2

15.87 Hz). . . . . . . . . . . . . . . . . . . . . 91

xii

Figure Page

18 Spectra at various temperatures for a solution of

0.30 M C222 and 0.6 M NaBr in EDA (1 ppm =

15.87 Hz). . . . . . . . . . . . . . . . . . . . . 92
19 Spectra at various temperatures for a solution

of 0.45 M C222 and 0.6 M NaBr in EDA (1 ppm =

15.87 Hz). . . . . . . . . . . . . . . . . . . . . 93
20 Computer fit of spectra obtained with 0.15 M

C222 and 0.6 M NaBr in EDA. (a) 42.6OC;

(b) 25.50c. . . . . . . . . . . . . . . . . . . . 95
21 Computer fit of spectra obtained with 0.15 M

C222 and 0.6 M NaBr in EDA. (a) 64.9OC;

(b) 53.90c. . . . . . . . . . . . . . . . . . . . 96
22 Computer fit of spectra obtained with 0.30 M
C222 and 0.6 M NaBr in EDA. (a) 45.00c;

(b) 30.4OC. . . . . . . . . . . . . . . . . . . . 97
23 Computer fit of spectra obtained with 0.30 M

C222 and 0.6 M NaBr in EDA. (a) 76.4OC;

(b) 50.20c. . . . . . . . . . . . . . . . . . . . 98
24 Computer fit of spectra obtained with 0.45 M

c222 and 0.6 M NaBr in EDA. (a) 30.6OC;

(b) 19.3Oc. . . . . . . . . . . . . . . . . . . . 99
25 Computer fit of spectra obtained with 0.45 M

C222 and 0.6 M NaBr in EDA. (a) 41.9OC;

(b) 36.10c. . . . . . . . . . . . . . . . . . . . 100

xiii

Figure

26

27

28

29

30

31

32

Page

Computer fit of spectra obtained with 0.2 M

c222 and 0.4 M NaI in H20. (a) 23.60c;

(b) 3.30c . . . . . . . . . . . . . . . . . . . . 104
Computer fit of spectra obtained with 0.2 M

c222 and 0.4 M NaI in H20. (a) 39.30c;

(b) 26.9OC. . . . . . . . . . . . . . . . . . . . 105
Computer fit of spectra;obtained with 0.2 M

C222 and 0.4 M Na¢4B in PYR. (a) 93.2Oc;

(b) 66.7OC. . . . . . . . . . . . . . . . . . . . 107
Computer fit of spectra obtained with 0.2 M

(2222 and 0.4 M Na¢4B in PYR. (a) 135.400;

(b) 116.4OC . . . . . . . . . . . . . . . . . . . 108
Computer fit of spectra obtained with 0.2 M

C222 and 0.4 M Na¢4B in THF. (a) 49.40C;

(b) 44.10C. . . . . . . . . . . . . . . . . . . . 109
Computer fit of spectra obtained with 0.2 M

c222 and 0.4 M Na¢4B in THF. (a) 56.80C;

(b) 62.80C. . . . . . . . . . . . . . . . . . . . 110
Computer analysis of the 23Na lineshape for a

solution containing 0.15 M C222 and 0.6 M NaBr in

EDA at 25.50C. (a) No first—order phase correction;

(b) first—order phase corrected . . . . . . . . . 115

xiv

Figure Page

+ from

33 Arrhenius plot of k (rate of release of Na

C222) for EDAl solution. (D) No first-order

phase correction; (O) first-order phase

corrected. . . . . . . . . . . . . . . . . . . . . 117
34 Plot of attenuated intensity I/IO XE frequency for

a 5000 Hz 4-Pole Butterworth active filter . . . . 118
35 Plot of the ratios TObS/Tcalc vs temperature (0C)

for EDAl, EDA2 and EDA3 solutions. . . . . . . . . 124
36 Arrhenius plot of k (rate of release of Na+ from

C222) for EDA2 solution. . . . . . . . . . . . . . 125
37 Arrhenius plot of k (rate of release of Na+ from

C222) for EDA3 solution. . . . . . . . . . . . . . 126
38 Arrhenius plots of k (rate of release of Na+ from

C222) for H20, THF and PYR solutions . . . . . . . 127
39 Three possible models for a species of stoichiom-

etry M” (other than an alkali anion). All of

these models permit solvent interaction with the

outer p electrons of the cation. Ammonia is used

to represent any amine or ether solvent. . . . . . 132
40 23Na NMR spectrum of a solution of Na+C222 . Na‘

in EA (20.2 M) at 1.4OC. Reference is saturated

aqueous NaCl; positive shifts are diamagnetic. . . 135
41 23Na NMR spectra of Na+C222 . Na" solutions (20.1 M)

in three solvents. All chemical shifts are refer-

enced to aqueous Na+ at infinite dilution. . . . . 139

XV

I. INTRODUCTION

Sodium and potassium were first observed to be soluble

1

in liquid ammonia by Weyl in 1863. Since that time, the Study

of physical and chemical properties of metal ammonia (M—NH3)
solutions has been given considerable attention. Properties
of these solutions range from electrolytic at infinite dilution

to metallic at high concentrations. A number of models have

2-10

been postulated to describe the species that exist in

solution at low and moderate concentrations (< 0.1 M). Most
everyone agrees that the properties in very dilute solutions
(< lO—3M) can be predicted by a two-species model. These two

species are the solvated cation and the solvated electron

(esolV ). The situation becomes much more complex at con-

centrations above 0.005 M, since cation-electron and electron-

electron interactions become increasingly important. Some

11,12

properties such as conductance and magnetic susceptibil—

13-15 are concentration dependent and imply that new species

ity
are formed, while other properties such as the optical spectrum

16—18 ESR absorption line shape,19—21

9,22,24

and extinction coefficient,
and partial molar volume of the solute change so little
with concentration that formation of distinctly different new

species seems to be ruled out. To this date no one model ap—

pears to describe satisfactorily the behavior of properties

24 25

of M-NH solutions. Dye has pointed out that a "weak—

3
interaction" model qualitatively agrees with the experimental

results, but that the quantitative agreement is poor.

1

In contrast to metal ammonia solutions which show only
a single, metal independent ESR and optical absorption band
(both attributed to the solvated electron), the ESR and optical
properties of metal—amine and metal—ether solutions are much
richer in information about distinguishable species. Some
of the most obvious differences between metal-amine or metal—
ether and M—NH3 solutions are the drastic reduction in solu-

25-28

bility of the former, the identification by ESR of a

monomeric species with stoichiometry M and the appearance of

29’30 attributed to a dia-

metal-dependent absorption bands
magnetic species with stoichiometry M-. This availability of
specific spectroscopic information makes the study of these
solutions particularly attractive. In spite of these advan—
tages, past studies had been severely hampered because of poor
solubility of the metals (in many cases the metal does not even
dissolve). In 1969 a major breakthrough came from the work

31

of Dye, Nicely, and DeBacker They demonstrated that di-

cyclohexyl 18-crown—6 (a member of a class of monocyclic
polyether complexing agents first synethsized by Pedersen,32

Figure l) considerably enhances alkali metal solubility in

30,33

ethers. Further investigations disclosed that the complex-

ing agent 2,2,2 cryptand (C a member of a class of macro-

222'
heterobicyclic complexing agents first synthesized by Lehn

34 Figure l) enhances metal solubilities in amines

2221-.
and ethers even more effectively than dicyclohexyl 18—crown-
6. The use of these synthetic complexing agents extends the

solvent range in addition to increasing the concentration of

2,2,2 C rypta nd

(C222)

(“AI
(3 C)
C. .3
C3.)
18-C row n— 6
08-0-6)

Figure 1. 2,2,2 Cryptand and l8—crown—6.

dissolved metals in solvents which dissolve metal unassisted.
The research efforts described in this thesis are focused

on the nature of the species responsible for the metal—
dependent visible absorption band in metal-amine and metal—
ether solutions. The evidence to date indicates that this
species is diamagnetic and has the stoichiometry M-. On the
basis of optical evidence alone one cannot distinguish among
several species with stoichiometry M“. These are: (1) an

ion-triple between a cation and two spin-paired electrons,

e— ‘ M+ ° e_, (2) an ion-pair between a cation and a di—
electron, M+ ° eg-, (3) a cation with a pair of electrons in

an expanded orbital which includes the first solvation sheath
molecules, and (4) a genuine alkali anion. A method which can
distinguish among the various models is alkali metal NMR.

A genuine anion M_ with two electrons in an outer s orbital
should have considerably different NMR properties than the
corresponding cation M+. Chapter VI includes a summary of

a multinuclear alkali metal NMR study of metal—ether and metal-
amine solutions which contain Na—, Rb— and Cs_. The results
strongly favor the alkali anion model. A detailed descrip—
tion of the first synthesis of a crystalline salt of the

sodium anion is included in the experimental section (Chapter
IV) . This crystalline salt of the sodium anion and the

alkali metal NMR results are the strongest evidence that
genuine alkali metal anions do exist.35_38

The key factor which makes alkali metal NMR studies of

metal solutions feasible is the enhancement of metal solubility

which is provided by cryptands and crowns. Prior to 1970 the
maximum concentrations of sodium in amines and ethers were
less than 0.01M. These concentrations were too low for prac-

tical NMR studies. With the aid of C solutions as con~

222'
centrated as 0.4M in sodium metal can be prepared.
A second goal of this research is focused on the applica—

tion of pulsed 23

Na Fourier transform NMR lineshape analysis
to permit quantitative examination of exchange rates of sodium
cations in the presence of C222. Initially it was felt impor-

tant to examine the effect of sodium cation exchange upon the

observed lineshape of a sample which contained a dissolved

sodium salt and half the stoichiometric amount of C222. The
overall chemical equilibrium is given by reaction 1.
+ * + k * + +
Na C + Na 2 Na C + Na 1.1

222 222

Sodium cations undergo an exchange between bound and solvated
sites which can affect the NMR lineshape. The influence of
exchange was first investigated in order to determine whether
23Na NMR studies of metal-amine and metal-ether solutions
would be feasible. Exchange rates39 have been reported from
PMR studies on D20 solutions which contain Na+C222 cryptate.
It was clear from the results of this study sodium cation
exchange may be slow enough to be observed directly by using
23Na NMR. A preliminary investigation by Ceraso and Dye4O

did indeed show that exchange rates are slow in ethylene-

diamine (EDA) at 25°C. This is the first example of sodium

cation exchange which is slow enough to exhibit clearly de—
fined separate signals for two environments. Since the study
of such cation exchange phenomena was relatively new, we
decided to examine the influence of the solvent on the ex-
change rates. Chapter V describes an in—depth study of the

. . . . + .
kinetics of complexation reactions of Na —C complexes in

222
several solvents. This chapter also includes a discussion
of some of the causes of systematic errors which are common
to pulse Fourier transform NMR techniques.

23Na NMR lineshape analysis was done in

Since some of the
collaboration with Patrick B. Smith, his M. S. thesis should

also be consulted for further details.

II HISTORICAL

2.1 Metal Ammonia Solutions

 

Alkali and alkaline earth metals dissolve in liquid am—
monia to form blue-colored, paramagnetic solutions. A
wide range of concentrations exists due to the high solu—
bility of metals in ammonia. In the very dilute concentra-
tion range the solutions behave as binary electrolytes with
solvated cations and solvated electrons as the ionic species.
Complex association of these species occurs in the inter-

-l

mediate concentration region (10"3 — 10 M). These inter-

actions influence the physical and chemical properties and
complicate our understanding of the solutions. Above 1 M,
a non-metal to metal transition occurs. Solution properties
become metallic and the conductivity of saturated solutions
approaches that of the free metal.

In the description of the properties and existing models

of M—NH solutions, attention will be mainly given to solu-

3

tions with dilute and intermediate concentrations of metal.
It is not the author's intention to give a complete history
of the prOperties of these solutions. A comprehensive

history is contained in the Proceedings of Colloque Weyl

41 42 43 44
I I I

I, II III and IV. The author merely intends to

focus on selected and current tOpics of interest.

2.1.1. Species in M-NH3 Solutions

 

A variety of models have been postulatedz-10 to des-

cribe the species at low and intermediate concentrations.
Species with stoichiometry M+, e—, M, M—, eg— and M2 have
been postulated to exist within these models. To add to
the complexity of these models, the nature of species with
the same stoichiometry may vary according to the model.

The solvated electron as a species is well established and

will not be directly considered in this discussion.

2.1.1.1. Evidence for Monomer Species in M—NH3 Solu-
tions - Certain properties of metal solutions indicate the
presence of cation—electron interactions. The strongest
evidence comes from the electrical conductance of M-NH3

11’12 and transference measurements45

solutions. Conductance
yield the concentration dependence of the cation conduc-
tance. The cationic equivalent conductance decreases with
increasing concentration of metals, similar to ordinary
electrolytes in ammonia. The total equivalent conductance
also decreases with increasing concentration of metal and
shows a pronounced minimum at 0.04 M concentration of metal.

A single equilibrium constant, K suffices to describe the

1’
concentration dependence of the conductance below about

0.005 M. Furthermore, the magnitude of K1 is similar to that
observed for normal 1 to l electrolytes which form ion—pairs
in ammonia.

46-48

Cation NMR spectra also show the effects of

cation-electron interactions. Concentration dependent
paramagnetic (Knight) shifts are observed. The Knight shift
of a nucleus is caused by the hyperfine interaction between
unpaired electrons and the nucleus. This interaction also
contributes to the spin-lattice relaxation time of the metal

11 sec.)48

nucleus. The correlation times are very short (10—
indicating a short lived cation—electron interaction.
A single extremely narrow ESR line (assigned to the

solvated electron, e—

solv.) 18 observed in dilute solu-
19-21

tions. The band is structureless and has a g-value
of 2.0012. No hyperfine interaction with the metal is ob—

served. Metal solutions also exhibit a broad optical

absorption band (assigned to e—

solv ), which peaks at 0.85

e.v. and is independent of solute. The band shape and
molar extinction coefficient are independent of concentra-
tion and the position of the peak maximum is only slightly

16-18 Cation—electron interactions

concentration dependent.
strongly influence the conductance and NMR properties whereas
they have almost no effect upon ESR and optical properties.
Recent pulse radiolysis studies of liquid deuterated

ammonia solutions which contain dissolved sodium and potas—
sium amides show at least two optical absorption bands.49'50
The initial transient (Amax = 1500 nm) is extremely short—
lived (<150 usec.) and is assigned to the solvated electron

at infinite dilution. The residual absorption (Amax = 1640

nm.) is shifted to the red and is interpreted as represent—

ing two or more overlapping bands corresponding to esolv

10

and a metal—electron species. However, from pulse radiolysis
experiments performed on mixed ammonia—amine solutions,
one would expect that ion-pairing effects would shift the

- 50

peak max1mum of esolv. towards the blue.

2.1.1.2. Evidence for Diamagnetic Species in M-NH3
Solutions - Magnetic data offer the most convincing evi—
dence that at least one diamagnetic species is formed in
M—NH3 solutions. Static magnetic susceptibility studies
14

performed by Freed and Sugarman and radio-frequency ESR

15 both show a

studies performed by Hutchison and Pastor
dramatic decrease in molar paramagnetic susceptibility with
increasing metal concentration. At 0.1 M metal concentra-
tion, the electrons are over 90% spin—paired. The molar
paramagnetic susceptibility is strongly temperature de—
pendent with the diamagnetic states preferred at lower

temperatures. Susceptibility data for potassium indicate

a temperature dependent spin—pairing enthalpy, whereas

15 51

data for sodium do not. Studies by DeMortier et a1.
indicate that electrons in sodium—NH3 solutions are much
less spin—paired than those in K-NH3 solutions. However,

52 53 indicate that spin-pairing

studies of Lok and Tehan
is the same for both K-NH3 and Na—NH3 solutions. More
experimental work is needed to determine whether or not
the cation plays an important role in the spin—pairing

reaction.

An extremely narrow ESR line is observed in M-NH3

 

11

solutions up to concentrations where the electrons are 90%
spin—paired. The narrowness of this line requires that

reactions of the type

2 D + S

in which D can be any doublet state (such as e— or M) and

2-
2 I

times longer than a microsecond. Since magnetic inter—

8 any singlet state (such as e M- or M2), have life-
actions resulting from collision complexes or long-range
interactions would not be expected to exist for more than
a few nanoseconds, it seems appropriate to refer to the
presence of a diamagnetic species.

Enthalpy measurements for Na-NH
22

3 solutions performed

by Gunn parallel the change in magnetic susceptibility
Of K-NH3 solutions with both concentration and temperature.
The enthalpy data can be described satisfactorily by the

following reactions:

where K2 comes from potassium magnetic susceptibility data
and K1 is determined from sodium-ammonia conductance data.24
The slight red shift in the optical absorption band with

increasing concentration of metal is the only other property

 

12

which correlates with the concentration dependence of the

magnetic susceptibility.16.l8

Several diamagnetic species
with different stoichiometries have been postulated to
exist in these solutions. The nature of this diamagnetic

species will be considered in a later section.

2.1.2. Models for Metal Ammonia Solutions

 

2-10 to describe

A variety of models have been postulated
the species that exist in M-NH3 solutions. The strength of
any of these models depends on how well they can predict all
of the known properties of these solutions. Dye24 has clas—
sified the models under one or a combination of three gen-
eral categories: (1) metal-based species; (2) double oc-
cupancy of cavities; (3) electrostatic aggregates.

Models classified under metal-based species include those

.2’4’6’7’10 The for—

which form species such as M, M_ and M2
mation of these species results from strong interactions

between cation and electrons (stronger than simple electro-

static interactions between charged ions). Double occupancy
models3’54’55 consider a pair of electrons, e§_, in the same
polarization center (or cavity). A number of calculation556_62

have been done to determine whether or not two solvated
electrons at separate sites would be more or less stable
than two spin—paired electrons trapped at the same site,
but the results tend to oscillate between the stability of

one over the other. In any event, consideration of the ion-

pairing interaction for a normal 1—2 electrolyte in ammonia

 

13

shows that the fraction of free e3- relative to the ion—

+ 2‘ (stoichiometry M”) will be negligibly small

pair, M - e2
even at concentrations where spin—unpairing is complete.
Both metal-based models and double-occupancy models have
a common weakness. They both predict the formation of new
species even though there is no observable change in the
optical spectrum and molar volume of the solute.

The final category considers the formation of ionic

aggregates between M+ and egolv without destroying the basic

8,9

characteristics of the species. Species with stoichiometry

M, M- and M are viewed as ionic clusters formed from the

2

fundamental species M+ and e—

solv.‘ The PrlnC1p1e advantage

of the ion cluster model is that the optical spectrum and
molar volume of the solute are preserved. However, electro—
static considerations alone, do not permit concentrations of
triple ions and ion quadrapoles in high enough concentration
to explain the magnetic susceptibility or enthalpy data.

While not all models claim the same stoichiometry, M+,

e', M, M— and M2 include simpler models as special cases.
Before arguing the merits of one structure over another
with species of the same stoichiometry, let us note that
Dye24 has tested the stoichiometry represented by these
species to determine whether it agrees with the experi-
mental data.

The choice of equations used to describe the equilibria

among all the species for any model is somewhat arbitrary.

The following set is complete and independent:

14

K
_1
(1) M++e :14
-K2_
(2) M + e Z M
K
_ 3
(3) M +M+ZM2

Values for Kl were calculated from Na conductance data and
values for K2 were calculated from potassium magnetic sus—
ceptibility data. Because both are ion—pairing reactions,
K3 was assumed to be equal to K1' With these values of K1'
K2 and K3, activity coefficients and transference numbers
were calculated and compared with measured values. The re-
sults indicate that reaction 1 alone satisfactorily describes
these electrochemical properties. Inclusion of reactions
2 and 3 gave large deviations from measured behavior.24

In conclusion, none of the present models for concentra—
tion dependence of the properties of M—NH3 solutions are
able to describe completely the experimental results. Dye
has suggested that a "weak-interaction" model involving
normal electrostatic interactions between two species M+
and e‘ is attractive.24 The concentration independence
of partial molar volume of M and the optical spectrum of
egolv. will be preserved with this type of model. In ad—
dition, the electrochemical properties will also be described
by normal electrostatic interactions which include ion-
pairing interactions. As for spin-pairing, a long range

electron—electron interaction is assumed and this should

have little or no effect upon the electrochemical properties

 

15

or the optical spectrum. To explain the long lifetime of
the diamagnetic species, the following type of exchange

process can be invoked:

e— + M- + M— + e—

In this case one electron in the singlet state is replaced

by another. This need not lead to ESR line-broadening.

Although qualitatively correct, this model lacks quantita—

tive treatment.

2.2 Alkali Metals in Amines and Ethers

 

2.2.1. General Properties

 

Alkali metals dissolve in amines and ethers to a much
lesser extent than in ammonia (in many cases the metals do
not dissolve). In spite of the low solubility of metals in
amines and ethers, studies of these solutions are rich in
information about distinguishable species.

The optical spectrum consists of two bands, one in the
visible and the other is near the infrared (IR). The posi—
tion and width of the IR band is solvent dependent and
nearly metal independent. In contrast, the visible band
is only slightly influenced by solvent and is strongly
metal dependent. The species responsible for the metal

independent IR band has been identified as the solvated

electron. The identification is based upon a comparison

 

16

of IR bands in metal solutions with those produced by pulse

63-68 The species responsible

radiolysis in pure solvents.
for the metal dependent visible absorption band was not
clearly identified until after 1968. Prior to this date,
there was much discrepancy about the nature of the species
responsible for the visible band. Experimental results in one
laboratory could not be reproduced in another. The chaos

69 demonstrated that

ended after Hurley, Tuttle and Golden
potassium ions in solution could exchange with sodium in
borosilicate glass. It quickly became clear that for a
given metal, at most two optical bands need be considered
and that the visible band could be associated with a
species of stoichiometry M—. The ESR spectrum shows a
narrow singlet (assigned to the solvated electron) with an
additional hyperfine pattern superimposed upon it.25'26
The hyperfine structure comes from a strong interaction of
the electron spin with the nuclear spin of the metal. This
observation gave the first unambiguous identification for

a species with stoichiometry M (referred to as a monomer

or ion pair).

2.2.2. Major Species Involved in Metal-Amine and Metal-

Ether Solutions

 

2.2.2.1. Solvated Electrons — The strongest evidence

 

that solvated electrons exist in metal—amine and metal—
ether solutions comes from the comparison of the IR band

with the spectrum produced by pulse radiolysis of the pure

17

solvent. The band shape and peak position for both ammonia
and ethylenediamine are independent of the method used. With
the discovery that "crown"31 and "cryptand"30'33 can be used
to dissolve metals in a number of solvents and that an excess
of cryptand yielded the IR band, it was possible to compare
the IR band in metal solutions with those produced by pulse

radiolysis and flash photolysis. Extensive comparison of
1.30

_———

this was made by Lok et_ and the agreement between the

two methods was good. However, the agreement is not exact

70 that the metal solution bands are,

and it has been noted
in general, broader and at slightly higher energies than

those found by pulse radiolysis. The variation in width and
peak position is probably due to the higher concentrations

of metal solutions and may be attributed to formation of a
second diamagnetic species (other than M_) or to an ion—
pairing effect. The single narrow ESR line with the same
g-value as that of M—NH solutions also supports the existence

3

in these solutions. Additional evidence comes from

71-73

Of eEolv.
the conductance of cesium—ethylenediamine (EDA) solutions.
When Walden's rule is used to account for viscosity differ-
ences between ammonia and ethylenediamine, the limiting con-
ductance of Cs—EDA and Cs—NH3 solutions is nearly the same.
Cs—EDA solutions do not show any visible absorption band and,

hence, the conducting anions must be the same species which

are responsible for the IR band.

18

2.2.2.2. Monomers - The first evidence of the existence
of a monomeric species, M, was obtained by Vos and Dye25 from
ESR studies of rubidium and cesium methylamine solutions and
independently by Bar-Eli and Tuttle74 from ESR studies of
potassium in ethylamine solutions. A marked increase in
hyperfine Splitting with a decrease in solvent polarity and

75 The intensity of

an increase in temperature is observed.
the hyperfine signal is low and indicates that the monomer
species is only a minor constituent of the metal-solution
(no Optical spectrum is observed for the monomer species in
metal solution under equilibrium conditions).

Other evidence for the existence of monomers comes from
flash photolysis and pulse radiolysis of metal solutions
(in these cases an optical spectrum for the monomer is
detected, but only under transient conditions). A number of
flash-photolysis studies have been performed on metal-ether

74—81 Most of the solutions

and metal-amine solutions.
studied contain M+ and M— as major species. When a solution
is flashed with light at a wavelength corresponding to

Amax M— (band maximum of M-) photo bleaching of this band
occurs with subsequent formation of a broad IR band. This
IR band transforms rapidly to an intermediate absorption

in the visible and then the intermediate band decays slowly
back to the original M“ band. Even though earlier studies

had been done by others, Kloosterboer et 31.81 were the first

to demonstrate that the intermediate absorption band has the

19

stoichiometry M. These results are consistent with the

following reaction sequence

hv M+

M + M+ + 2e“ + 2M+ ' ’ '

e + M + M+.

Pulse radiolysis studies also indicate the existence of

monomers (again under transient conditions). Bockrath and

65 reported the spectrum of the sodium-electron ion

82

Dorfman
pair (Na) in THF. Pulse radiolysis studies of ethylamine-
THF mixtures show only a single monomer band and the peak
position lies at wavelengths intermediate to that observed
in the pure components. A correlation is observed between
the shift in Amax of the monomer and the magnitude of the
hyperfine splitting constant in these solutions.82 As the
percent atomic character increases (increased hyperfine
splitting constant, corresponding to a larger contact density

at the nucleus) the Optical spectrum of the monomer shifts

increasingly toward the blue.

2.2.2.3. Spin-paired Species — The existence of a spin-

 

paired species, other than M", in these solutions has not
been shown. Studies of solutions of K in ethylamine-ammonia
mixtures with spin concentrations of the order of 10"6 M
indicate a total concentration for the IR absorbing species
to be about 10‘4 M.70 If these results are reliable, the IR

absorption must include contributions from both paramagnetic

20

and diamagnetic species other than K“, since the band maximum
of K- would appear in the visible. If other diamagnetic
species besides MI exist in these solutions, then it may be
possible to correlate the magnetic properties of this new
species with the spin—paired species that exists in M-NH3

solutions.

2.2.2.4. Alkali Metal Anions — Chemists may view the

 

existence of alkali metal anions with skepticism (this was
especially true at the beginning of this research, since no
known salts of alkali metal anions existed), but the evidence
for the existence of these species has mushroomed in the past
six years. The assignment of the stoichiometry M“ to the
species responsible for the metal dependent visible band is
based on numerous experimental facts.

That alkali anions exist in the gas phase was shown by

83 Metal solutions which

Russian scientists in the 1960's.
yield a large visible band and no IR band have very weak or
no ESR signals. The optical spectra of these solutions,
unlike M-NH3 solutions, exhibit metal—dependent absorption
bands. Figure 2 shows the spectra of egolvo' Cs“, K‘ and Na—
in tetrahydrofuran at 250C in the presence of either crown
or cryptand. It seems unlikely that normal electrostatic
interactions between cation and electrons can cause such a

large shift and metal dependence of the solvated electron

absorption band. By comparing the temperature and solvent

21

.csouo no pcmummuo mo mocmmoum may SH
nee EH Ass .42 use Ame Is .lmv Imo .AHV >Homm mo 60mm pm muuomem .m masons

aflIO—X—IEUV genus—3:05:92,
ca 2 2 .1 m. o. m e e

 

A _ _ a _ _ I4 _ .
I.~an
Iiexnv
v. m” NV p
uv
.IAVAVmw
W
. D
.Imwnvya

 

 

 

22

dependence of the optical bands in metal-amine solutions with
the charge—transfer-to-solvent bands of I—,84_86 Matalon,
Golden and Ottolenghi29 assigned the metal-dependent band to
the alkali anion. Some of the characteristics of CTTS trans—

itions are:

1. Pronounced dependence of Ama upon solvent.

X

2. Shift of Ama to lower energies with a decrease in

x
temperature.

3. Correlation between the shift of Amax with solvent
and the temperature coefficient of Amax'

4. Correlation between the position of Amax and the
size of the anion, with a shift to lower energies
for larger ions.

All of these characteristics have been observed for M— bands.
Lok, Tehan and Dye30 have made an in-depth study and have
shown excellent correlations between the peak positions of
Na' and K" as shown in Figure 3. CTTS theory, therefore,
strongly suggests that the species responsible for the
visible band is an alkali anion, but it does not prove
this. For example, solvated electrons also have many of
the same CTTS characteristics as the M‘ species. This is
shown in Figure 4 by the excellent correlation of the
solvated electron peak position with the K‘ peak position
in various solvents. Thus, it might be expected that a
species like e_ ' Na+ ' e- (triple—ion) should give rise

to spectra with CTTS characteristics. Additional evidence

Na'PEAK posmon

Figure

23

 

 

EDA6//

I2PDAo
EA'O
ODIGLYME
°DME
OTHF
HMPA
DEE

ONT
0

I l

 

3.

1.1 1.2
( C M_lx |0_3 )
K" PEAK POSITION

The relation between the peak position of Na-

and of K" in diisopropyl ether (DIPE), diethyl
ether (DE), hexamethyl phosphoric triamide (HMPA),
tetrahydrofuran (THF), dimethoxyethane (DME),
diglyme, ethylamine (EA), 1,2-propanediamine (PDA)

1.3

and ethylenediamine (EDA) at 250C.

 

Ea >H0m .oOmN um mucm>H0m mdoflum>

Io mo.ocm Ix mo coeuemom some on» cmmzhmn coeumHmH one .e ousmflm

20:50.. 52: L.
r. 9x753 See.

. S E S

 

24

 

E _ _ 1 a

l
v

)XOWA

[—

 

OlXVVD
c...

I
-o

(

noulsoa )IVJd "“9

<omfl—

(Om

 

 

25

for the stoichiometry of the metal dependent species comes
78-81 63,87

 

from flash photolysis and pulse radiolysis studies.
In pulse radiolysis studies, a solution containing only a
sodium salt was pulsed and the growth of a visible band

was observed. The decay of the initially produced solvated

electron band was found to be second-order in e- and

solv.

is consistent with the following stoichiometry

2e + Na+ + Na-.
solv.

The same general results were obtained from flash photolysis

71,73

studies. The limiting conductances of metal solutions

which show a visible band are much lower than those found
when large concentrations of solvated electrons are present.
The equivalent conductance when only the metal-dependent
band is present is similar to that of normal salts in amines.
Strong evidence for the assignment of stoichiometry M7 was
obtained by measuring the oscillator strength of the visible

88'89 found an oscillator

transition. Dye and DeBacker
strength of 1.9i0.2 for Na- in EDA solution. This requires
that at least two equivalent electrons be involved in the

transition and may be easily satisfied by a species with

90

stoichiometry M7. Finally, the Faraday effect indicates

a magnetic moment of about 1 Bohr magneton for the excited
state responsible for the visible absorption band. This is

consistent with the highly symmetric structure of M_.

26

The most convincing evidence that genuine alkali anions
do exist comes from the isolation of the first crystalline

36'37 The synthesis of this com-

salt of the sodium anion.
pound will be described in the experimental section (Chapter
IV).

Prior to the work described in this thesis it was clear

that species with stoichiometry M- exist in metal solutions.

 

There was not available enough evidence to distinguish be—

tween genuine alkali anions and several alternative struc-

+

tures such as the ion—triple, e_ - M . e—, or an ion-pair
between a cation and a dielectron M+ . e3“. Chapter VI will

offer strong evidence that genuine alkali metal anions are

present rather than other species with stoichiometry M—.

2.3 Overall Equilibrium Scheme

 

A general overall equilibrium scheme for species in

solution may be represented as follows33

2M(s) Z M‘ + M+
tt _
M + e
+¢ solv.
+
M esolv.

Strongly solvating solvents such as ammonia tend to shift
the equilibrium all the way to solvated cations and sol-
vated electrons. Solvents such as hexamethyl phosphoric

triamide and methylamine tend to yield mixtures of M“, M

27

and egolv . Less polar amines and ethers give mainly the

solv and M as minor constituents. Addi—

M- species with e
tion of an excess of a complexing agent such as C222 cryp-
tand can cause the equilibrium to shift all the way to the

right (similar to ammonia) in suitable solvents and for

some of the metals.

III. GENERAL FEATURES OF ALKALI METAL ION NMR

3.1 Introduction

 

All alkali metals possess at least one isotope with a
nuclear magnetic moment and therefore can be examined with
the NMR technique. Many studies of the resonances of these
nuclei have been performed on aqueous and non—aqueous salt
solutions as well as on crystals. In solution the ions
exist as separate entities with negligible covalent bonding
between opposite charged species. At high concentrations,
association among ions can occur, but these associations
are short lived and exchange between different sites is
rapid. Rapid exchange among sites results in only one
resonance signal with an average frequency determined by
the magnetic shielding o and life-time T of the nucleus
in each of the many sites. Because of the fast exchange,
no fine structure is observed and the only measureable pa-
ramaters are the chemical shift and line width of the
resonance.

Although the intensity of alkali metal resonances
relative to that of protons is low, the range of magnetic
shielding constants (except lithium) is considerably larger
and increases with atomic number. The chemical shifts
result primarily from changes in the paramagnetic contribu—
tion Up, to the total magnetic shielding 0 (except for

lithium, where diamagnetic, 0 and paramagnetic shielding

DI

28

29

both contribute).

All of the alkali metal nuclei possess a nuclear
quadrupole moment, since their spins are greater than 1/2.
The dominant relaxation mechanism in solution is quadru-
polar, except that a dipole-dipole relaxation mechanism
may partially contribute to some of the observed relaxation
rates of lithium and cesium ions in solution. In cases
where quadrupole relaxation dominates, an investigation
of linewidths can yield information about the magnitude
of the electric field gradient at the nucleus. Since
electric field gradients are produced by ion-solvent and
ion-ion interactions in solution, information which per—
tains to ion rotational and translational motion is obtained.
It is experimentally possible to determine the product
(qu)2TC (qu is the quadrupole coupling constant and TC
is the correlation time), but the separation of TC from
(qu)2 cannot be made unless TC or (qu)2 are measured by
other methods. Generally, independent measurements of TC
or (qu) are unavailable for alkali ions in solution.

To first order, the quadrupole moment along with an
electric field gradient at the nucleus can perturb the
Zeeman energy levels. Figure 5 shows the effect of quad—
rupole coupling on the energy levels of a nucleus with spin
I = 3/2. The selection rule for the transition is given
by AM = :1 and the degeneracy of the Zeeman transitions
is lifted with this coupling. Experimentally, three tran—

sitions are observed for sodium in single crystals of

30

.on mo mHm>wH wmnocm
on mcflocommmuuoo Ednpoomm Hoveuosuommm ADV .Hoouo umnfim cfl
moflmuoco cmEooN Hmoaosc com: mcflamsoo DHOQSHUMSU mo uommwm Amy .m oudmflm

Q m

IILIIINE

0T;

 

‘—

 

 

31

NaNO391 (hexagonal crystal structure). The NMR spectra of
crystals such as the alkali halides do not exhibit quadru-
pole splitting since the crystals have cubic symmetry and
no field gradient exists. In solution, the effect of quad—
rupole splitting is not observed since for normal liquids,
the time scale of solvent fluctuations (which produce field
gradients) is 4 to 5 orders of magnitude shorter than the
time scale corresponding to the quadrupole coupling.

In this chapter we will describe some of the general
features of alkali metal ion NMR. The description is by
no means complete. It is only meant to give the necessary

background for the NMR studies described in Chapters V

and VI.

3.2 Shielding Constants of Alkali Metal Ions

 

The shielding constant, 0, is defined by mo = y(l—0)HO,
where Y is the gyromagnetic ratio of the nucleus and H0 is
the external magnetic field. When the gaseous atom is
taken as the reference state, then 0 = 0 and y refers to
that for the gaseous atom. A negative value for o is inter-
preted as a paramagnetic (low field) shift relative to the
reference state and correspondingly a positive value for
o is interpreted as a diamagnetic (high field) shift rela-
tive to the reference state. Note that this sign is op-
posite that frequently used to express chemical shifts

but its use provides an internally consistent sign conven-

tion.

32

3.2.1. Alkali Metal Ions in Crystals

 

The shielding constant of alkali metal ions in crystals
is paramagnetically shifted (shifted to lower field) from
that of the free gaseous ion. In crystalline salts the
chemical shift also depends upon the counter anion.92
The factors governing these shifts are qualitatively under—
stood, but are not well accounted for quantitatively.

During the late 1950's and up to the mid 1960's a number
of attempts had been made to calculate paramagnetic shield—
ing constants for alkali metal ions in solid alkali halides.

The starting point for all these calculations was Ramsey's

expression93 for the total shielding of a nucleus, given

 

by
2 r i—f f
k k k
0 = ( e )[(9 I) -——-————-|w )
2mc2 O k rk3 O
+ 2 (E0 - Em)"l{(w | X Ek | Wm)
m k
E A
k k
(wm I Z ;_3 lqlo).+ (Yo I E ;_3 I Wm)
k k
(9m I E 1k I NO)}], 3.1

where To and Wm represent the many-electron ground- and

excited—state wave functions, EO and Em are the ground-

and excited-state energies, Ek is the angular momentum

 

33

th electron and rk is the radial distance

of the kth electron from the origin at the nucleus.

operator of the k

The first term in Equation 1 is the diamagnetic con—
tribution to the total shielding. For a gaseous alkali

metal ion, the diamagnetic shielding, is proportional

0D,
to the magnetic field produced at the nucleus by induced
currents which arise from the Larmor precession of electrons
in the external magnetic field. The second term is the
paramagnetic contribution to the total shielding and is
zero for an isolated gaseous alkali metal atom or ion. A
paramagnetic shift is produced by introducing orbital an-
gular momentum into the wavefunction. For alkali metal
cations in alkali halide crystals and in solution, the
paramagnetic contribution to total shielding is not zero.
In the crystal, the wave functions are distorted from those
of the hypothetical ideal crystal (considered as combina—
tions of distinct positive and negative ions, each con—
stituent ion having a spherically symmetric closed shell
electronic configuration identical to that expected for

the isolated ion, with the complete assembly being held
together by electrostatic forces) and hence orbital angular
momentum is introduced and produces a paramagnetic shift.
As can be seen from Equation 3.1, both 0D and Up are

tensor quantities in the general case. For all the systems
discussed, cubic symmetry is assumed and the scalar part

will be used. In order to evaluate op, a knowledge of

Wm is needed. Since in almost all cases, W is not known,

In

 

34

Ramsey93

introduced the average—energy approximation.
With the assumption of cubic symmetry and the average energy

approximation, the total shielding is now given by

 

 

a= (ill—III)
3mc2 O rk
2 E,
+ e22” I ”EkTI Io“ 3'2
Am c kk' rk

where A is the average excitation energy.

Two models have been proposed for the origin of mag—
netic shielding based on the perturbation—theory approach
of Ramsey. The first is the charge~transfer—covalency model

94

due to Yosida and Moriya, and the second the overlapping-

ion model by Kondo and Yamashita (KY).95 Ikenberry and Das96
have pointed out that calculations of quadrupole coupling
constants in diatomic—alkali-halide molecules clearly in-
dicate that there is little, if any, covalent bonding of
the charge-transfer type in these crystals. Thus, in the
most recent calculations, only the KY model has been con—
sidered. The KY model assumes that short range repulsive
forces between adjacent ions cause a change in the op value
of M+ upon going from the gas phase (op = 0) to the nonideal
crystalline state. From the KY model only overlap between
outermost s and p orbitals for both positive and negative

ions is considered. Since inner—core orbitals are tightly

bound and do not extend appreciably into the region between

 

35

the ions, they remain spherical and are not considered.
Also calculations show that the change in CD for M+ gas +

M+ crystal is two to three orders of magnitude less than

96 + +
op. Thus, for crystal 0 (Mcrystal YE Mgas) ~ op (assum_
ing a reference state 0 = Up a 0 for the gaseous metal ion).

Under these conditions with the application of Equation
3.2, Ikenberry and Das96 have calculated chemical shifts

for Rb+ ions in halide crystals. Their final expression for

O (M+ 97

+ - u
p crystal is. Mgas) is given as follows

160I2

_ < —3> [ISOSIZ + ISOOIZ + ISUWI
Op ' A ri p ij ij ij
CO TT'TT

where d is the fine structure constant, <rl3>p is the ex—

pectation value for an outer p—electron of the central ion
i, Sij are the two—center overlap integrals between outer
p orbitals of the central ion i and the outermost s and p
orbitals of other ions j, s represents an s orbital, and

o and n are p orbitals parallel with the line of nuclear

centers and perpendicular to the line of nuclear centers

respectively.

In summary, the features that are important for mag-

netic shielding as given by Equation 3.3 are:

1. The expectation value <r£3>p for the outer p

orbital of the central ion.

 

36

2. The average excitation energy A, usually taken to
be the energy of the np + np + 1 electronic transi-
tion of the central ion.

3. Overlap between neighboring ions, which depends

upon the internuclear separation.

The average excitation energy determines the amount of ex—
cited state p character introduced into the wavefunction.

This causes a deformation from spherical symmetry and

produces the paramagnetic shift. Some values of <r;3>p

and A along with their ratios are shown in Table I. Ex—
perimentally, the chemical shift range increases as atomic

number increases and this increase is in agreement with

the increasing values of % (ri3>p'

At the time Ikenberry and Das, and Hafmeister and Fly-
gare performed calculations for magnetic shielding of ions
in crystals, there were no experimental values available
for 0(M+ vs M+ ). It has been only within the last

crystal —— gas
few years that these values could be obtained. Experimental

values were determined from a combination of precision

99-101 102 103,104
I

NMR atomic beam, and optical pumping

experiments. From these measurements it is now possible to

obtain values for o(M+ vs M ) and since many determina—
H20 —— gas

+ +
I f - —
tions 0 0(Mcrystal vs MHZO) have been reported, an experi

+ .
mental value for 0(Mcrystal XE Mgas) can be obtained. How

ever, calculated values of 0(M+

crystal) from theory are

referenced to the gaseous ion. The difference between

 

37

Table I. Values of the average excitation energy A, and

the expectation value <rl3>p for alkali metals.a

 

 

 

-3
<r. > A

1 p l —3
Ion a.u. Rydbergs A <ri >p
Na+ 16 2.72 5.9
K+ 12.94 1.62 7.98
Rb+ 20.22 1.47 13.8
Cs+ 23.42 1.25 18.7

 

 

a) All values taken from Reference 98.

 

38

+
crystal 35

+
Mgas) and 0(M vs M

+ +
crystal —— ga (M

0(M D gas

S) is o
23 Mgas) which is the diamagnetic contribution caused by
the addition of an electron to a gaseous ion. The term

GD (Mgas 23 M ) can be reliably calculated from accurate

gas

atomic wavefunctions by applying the first term in Equation
3.2. Values for these diamagnetic shielding constants for

Li, Na and K are less than 5 ppm and tend to get smaller

105 Thus, for Rb and Cs, the

. + + + .
assumption 0(Mcrystal gs Mgas) ~ 0(Mcrystal gs Mgas) is

as atomic number increases.

reasonable. Comparison of the chemical shift values cal-

106

culated by Hafmeister and Flygare, and Ikenberry and

Das96,97 +

With the measured values of 0(Mcrystal XE Mgas)
are given in Table II. The agreement is qualitative only.
However, it should be pointed out that theoretical values
for the change in shielding with pressure for alkali halide

96:97,106 107 are in much better

crystals and for xenon gas
agreement with the experimentally observed chemical shift
changes. From these calculations it appears that the KY
model offers a reasonable explanation of magnetic shield—

ing.

3.2.2. Alkali Metal Ions in Solution

 

Solvated cations also undergo large paramagnetic shifts
from the gaseous ions as shown in Table II for rubidium
and cesium. Changes in the diamagnetic shielding as a
function of solvent are expected to be small compared to

changes in op.109'llo Thus, as for the crystals, changes

39

.NOH moawnwmmm he
.woa mocmummom A0
.mm mucoummom An

.NOH 8:8 mos .Na mmocmnwwwm eons Ammo: ms em fineszvmxmo new .iem HHUIHz

 

 

 

m> we powzvmxoo .Awm new: m> mhnwzvmxoo mcflfifidm an omcflmuno DMD: modao> Hmpcmfifluwmxm Am

comm- ems- Hmo +mo

comm- mam- ammo +mo

comm- amm- Home +mo

em.eem- fine 8 on comm- ewe- emu +mo

coma- mam- Hem +nm

Dome- mmm- umnm +nm

UOMHI mHmI HUQM +Qm

ooeHI cam- mam +nm

ee.HHNI fine 8 on seam- mmm- umnm +nm

Ammo: .m> .wwwo ucm>aom mmmmmvm mmMvam wofluqu coH
>Homzvmxoo A +2 .m> MA 2 .m>
+ mwuwzvoamoo mhuwzvmxmo

 

 

.coHu9H0m msoosom one mampmwuo ocflams
EH mQOH Edemoo one Eseoensu mom mamanm Hmoflsmco oopmasono tom Hmucoswuomxm .HH Danae

 

40

in magnetic shielding are reflected predominantly through
changes in Up.

An interesting correlation between the Gutmann donor
number (D.N.) and the relative chemical shift of sodium

111,112

ions in different solvents has been reported. The

Gutmann donor number of a solvent is a measure of its Lewis

113 As the D.N. increases, the solvent donor

basicity.
ability increases and an increasing paramagnetic shift of
the sodium cation is observed. A linear correlation be—
tween Gutmann's donor number and the relative magnetic
shielding of sodium ion in different solvents is observed.
For sodium, the solvent effect on the magnetic shield—
ing occurs primarily in the first solvation or coordination
layer of the sodium cation. If a sodium is trapped within
the cavity of a complexing agent such as C222 (the first
coordination layer of solvent is completely replaced by
C222), the chemical shift of the cation is nearly solvent
independent. On the other hand, the free sodium ion chem—
ical shifts change appreciably in these solvents as shown
by Table III. The same behavior is observed for lithium
ion complexed by a smaller cryptand ligand.114
Calculation of shielding constants for alkali metal
ions in solution is a much more difficult task than for
ions in crystals. As a consequence, only one semiquantita-
tive calculation based upon the KY model has been performed
for Rb+ in aqueous solution. The theoretical value for
0(Rb;

XE Rb;a ) = -65 ppm is in poor agreement with the

20 s

41

Table III. Chemical shifts of free and cryptated sodium
ions in solution.

 

 

 

 

 

+ +

Concentration 0(Nasolv VS Nam-dil—HZO)

(M) Solvent (ppm)
0.2 NaI H20 -0.1
0.6 NaBr EDA —13.7
0.4 Na¢4B THFa +7.4
0.2 Na¢4B PYRb -0.9

+ .—
0.2 Na C222I H20 +8.5
0.3 Naiczzzsr‘ EDA +10.6

4. ..
0.2 Na C222¢4B THF +11.9
0.2 Na+C222¢4B— PYR +12.4
a) THF = tetrahydrofuran.
b) PYR = Pyridine.

42

experimentally determined value 0(RbH20 XE Rbgas) = -212
ppm.97 However, the model used for the calculation is one

in which a Rb+ is surrounded by six water molecules with

the oxygen end oriented towards Rb+ and the O-H bonds point—
ing away. The wavefunctions for H20 were based upon a model
of localized electron-pair bonds. In view of the uncertainty
of the model and the crudeness of the wavefunctions, the

poor agreement between theoretical and observed values is
understandable. It seems that Equation 3.3 at least quali-

tatively predicts the effects of a paramagnetic shift for

ions in solution.

3.3 Quadrupole Relaxation of Alkali Metal Ions in Solution

 

The magnetic relaxation of nuclei with spin greater
than 1/2 is almost always caused by the interaction of
their electric quadrupole moment with the electrical field
gradient at the nuclear site.~ Thermal motion of ions and
solvent molecules can produce fluctuating electric field
gradients at the nuclear site. The time evolution of these
fluctuations contain Fourier frequency components which are
at the Larmor frequency of the alkali metal ion and hence
can induce a transition through coupling with the quadrupole
moment. The quadrupole relaxation rate for a nucleus in the

motionally narrowed limit (wTC<<l) is given by115

2 2
(1 + 937-) (e??- -—---3 V2
32'

1 .SL 21+3

.__ = ______——— )T ,
T1 40 12(21—1) C

43

where I is the spin of the nucleus, n is the asymmetry
parameter (n = 0 for a symmetric field gradient), Q is the
quadrupole moment of the nucleus, 32V/BZ'2 is the Z compon-
ent of the electric field gradient at the nucleus, and TC
is the correlation time which characterizes the fluctuations
of the field gradient. For solutions, (wTC<<1), T1 = T2,
and the resonance lineshape is Lorentzian.

The field gradient at the nucleus can be expressed as
BZVO/az2 (1 + 7”) where Ym is the Steinheimer antishield—

117 The term BVO/az2 represents the field grad-

ing factor.

ient at the nucleus produced by an external charge. The

external charge also causes deformation of the spherical

symmetry of the inner closed shell electrons and this

leads to the correction term (1 + yw). Values of (l + ym)

are calculated from theory and range from 0.74 for Li+ to

111 for Cs+.117 Thus the effect of (l + ym) can be enormous.
Information obtained from the linewidth contains the

product (eQ/h 82V/32'2)21C. Only for cases where TC can

be determined from other measurements can the field gradient,

82V/3Z'2, be determined. This has been done recently by

118 for sodium nuclei encapsulated in

13

Kintzinger and Lehn
the C222 cryptand. The C relaxation times T1(13C) of
the CH2 carbons of the sodium cryptate complex were measured.

The dipole-dipole relaxation equation

2 2 2 -6 '

_ 2
I" I C) " n h YHYCrCHTc

44

13C relaxation

can be used to obtain ré values from the
rates. Then, by making the assumption that, in fairly rigid
complexes Té also represents reorientational motions which
modulate the 23Na quadrupolar interaction, they calculated
the quadrupole coupling constant.

For a simple process one would expect that TC =

A where Er is an activation energy for solvent re—

98 If the value of the quadrupole coupling

organization.
constant is assumed not to change with temperature, then
the relaxation rate will vary exponentially as a function
of temperature. This behavior is observed for sodium bro-
mide in ethylenediamine solution as shown in Figure 6.

For many monodentate liquids the infinitely dilute
sodium linewidth varies from 4 to 30 Hz at 25°C. When the
cation is placed in an environment which does not have
cubic symmetry, such as within the cavity of a crown ether
(see Figure 1), the linewidth increases by large amounts.
This increase is caused by asymmetry of the electric field
at the sodium nucleus because of the planar structure of
crown ethers. If a bicyclic ligand such as C222 cryptand

is used, the Na+C linewidth is not broadened nearly as

222
much as in the crown case. This indicates that the electric

field produced by C222 is much more symmetric than that
produced by crown complexes.

The difficulty in predicting relaxation rates from
Equation 3.4 is in the evaluation of the field gradient.
119-123

Electrostatic models have been proposed in which

.dom cfl Hmmz 2 mH.o
mcwcflmucoo GOHDSHOm m How musumumeou DDDHOmnm

4S

 

 

Hmooumaoon onu.mw Mme How NB\H mo uoam moaflsom .m onsmflm
:. x... .59
v.0 0.0 No no 0.»... ad
4 . a _ a _
I on
\o\H
\o\ .I 00—.

\\\1. I;

.\\\\C. 7v.
. It

0 \ 1%)

\.\ w
. Iooa ...

\ O\

 

 

46

the field gradients are produced by electric dipoles or

110 has proposed a model in which

point changes. Deverell
repulsive forces between molecules and ions are related to
a distortion from spherical symmetry of the ionic electron
cloud which results in the production of a field gradient.
With this model Deverell was able to derive a correct order
of magnitude for the relaxation rate of the nucleus. The

124 who

most recent calculations have been done by Hertz,
assumes an electrostatic model. Hertz includes water-water
correlations and ion-ion correlations in his calculations.
Calculated values from his electrostatic model agree sur—
prisingly well with the experimentally observed relaxation
rates for a number of quadrupole relaxed nuclei. However,
it is difficult to determine how much of this agreement is

caused by the presence of parameters in the model which

must be estimated and cannot be independently measured.

IV . EXPERIMENTAL

4.1 General Techniqpes
4.1.1. Glassware Cleaning

All glassware was cleaned by a two step procedure
(except glassware used with normal salt solutions). First,
the glassware was pre-rinsed for several minutes with a
solution of HF cleaner (33% HNO3, 5% HF, 2% acid soluble
detergent, 60% water by volume) followed by a thorough
rinsing with distilled water. The glass vessels were then
filled with boiling aqua regia which remained in the vessel
at least six hours. They were then thoroughly rinsed with
distilled water (five times) followed with a second rinsing
with conductance quality water (five times). The vessels

were allowed to dry over night in an oven (110°).
4.1.2. Vacuum Techniques

Standard high vacuum techniques were employed in this

6mm Hg were obtained in Pyrex vacuum

work. Pressures of 10-
lines by using a dual stage mechanical pump and a two-stage
oil diffusion pump. Greaseless Teflon valves (Fischer-
Porter, Delmar, and Kontes types) were employed for high

vacuum work to avoid contamination of metal-amine and metal-

ether samples with grease.

47

48

4.2 Metal Purification

 

Alkali metals were purchased as follows:
Na: J. T. Baker Co. (99.99%).

Rb: Fairmount Chemical Co.

Cs: A gift from Dow Chemical Company.

All metals were distilled several times before use.
4.2.1. Storage of Alkali Metal in Small Quantities

4.2.1.1. Sodium Metal - Sodium was cut with a knife

 

into small pieces. The pieces were placed into the bottom
of a quartz tube (40mm O.D.) as shown in Figure 7. Twenty
to thirty smaller diameter Pyrex tubes were sealed at one
end and placed into the quartz tube on top of the sodium
with their open ends down. The system was evacuated to

a pressure of 10"5

mm Hg and then the sodium was gradually
heated until it formed a liquid pool at the bottom. Next,
helium gas was introduced at a pressure of 1/2 to 1 atm.

to force liquid sodium into the small Pyrex tubes. After
cooling, the small diameter tubes were then exposed to the
atmosphere and small quantities of relatively pure sodium

metal could be isolated by simply cutting a specified length

of Pyrex tubing.

4.2.1.2. Cesium and Rubidium Metals

 

Cesium and rubidium burn very easily in air. Large

ampoules (greater than 20 gms) of these metals can be

49

f High vacuum

 

<$—' Helium
Signaly

 

 

 

A/// TS 40/50

’\ q [ I{ k”EZ/»#4O mm O.D.

 

I /7 _//—I4Imn O.D.

 

90 cm

 

<§ Jfl/x—Sodium metal
91-
Q

 

 

 

 

 

 

fii\fl

 

 

 

EX

 

Figure 7. Apparatus for the preparation of storage tubes
for sodium metal.

50

subdivided into ampoules containing 10 to 20 gms metal by

the method described by Dewald.125

To obtain even smaller
samples the apparatus shown in Figure 8 was used. An
ampoule containing the metal was scored with a glass—cutter
and placed into an open-ended Pyrex tube #1 at position A.
The Pyrex tube was then connected to a second tube #2, by
using a piece of flexible heat shrink tubing (Pope Scien-
tific Company), which made a vacuum tight seal. The system

5mm Hg and the

was evacuated to a pressure of at least 10-
glass ampoule was moved to position B where it was broken.
The fragmented ampoule was next moved to position C and two
vacuum seal-offs were made at D and E. The metal could

then be melted into the long Pyrex tube and a small quantity

could easily be obtained by sealing off a portion of this

tube.

4.3 Solvent Purification

 

Ethylendiamine (EDA) was purified by the method des—

cribed by DeBacker.88

Tetrahydrofuran was dried over
calcium hydride for at least 48 hours. After initial
drying, THF was distilled into a vessel containing benzo-
phenone and an excess of sodium-potassium alloy. A blue-
purple color resulted, due to formation of the ketyl, and
served as an indicator of dryness. If the blue color
faded, the THF was redistilled onto a fresh mixture of

benZOphenone and Na—K alloy. These blue solutions were

stable for months.

51

.HmumE Edflmwo
tam EDAUHQDH mo moasomfio Hanan mo coaumuwmmum How msuoummmd .m musmflm

Manson Hopes

 

 

 

E
I.
8"“

 

 

 

//Nl.
m a
we when _ 1 scenes xaeuzm as when
M new: menexmee
m .
m

_J

Essom> noes ou

52

Methylamine and ethylamine were dried over calcium
hydride and then vacuum-distilled into a vessel contain-
ing Na-K alloy. If a blue solution did not form, the sol-
vent was repeatedly vacuum distilled into vessels containing
fresh Na—K alloy until a stable blue solution did form.
Once a stable blue solution formed (usually no observation
of color change after one to two days is a good criterion
for stability) the solvents were distilled into Pyrex stor-
age bottles. Pyridine was refluxed over granulated barium
oxide and then fractionally distilled in a nitrogen atmos-

phere.

4.4 Preparation and Purification of 2,2,2 Cryptand

 

During the progress of this research, 2,2,2 cryptand
was not commercially available and had to be synthesized
by following a brief outline in the literature.34 The
synthesis was carried out in collaboration with M. T. Lok
and F. J. Tehan. Several major improvements in the pro—
cedure were developed by us in the process of synthesizing
the material. The details are reported in the Ph.D. thesis
of M. T. Lok52 and will not be described here. However,
an improvement of the purity of one of the precursors is
described.

Triglycolic acid (HOCOCHZOCH CHZOCHZOCOH) is a pre-

2

cursor in the synthesis of the 2,2,2 cryptand molecule.

The diacid is produced by oxidation of the corresponding

53

glycol with 60% nitric acid and a vanadium catalyst (NH4VO3).
Many by—products are formed in the oxidation and it is dif—
ficult to separate the acid from these by-products. The
following procedure, partly based on a synthesis reported

126 I

by Micovic, enables us to obtain triglycolic acid with'

reasonable purity.

4.4.1. Synthesis of Diethyl Ester of Triglycolic Acid

 

Add 256 gms of crude diacid to a one neck, 2 liter
flask equipped with a magnetic stirring bar, a downward
condenser and a collection pot containing 253 gms of K2C03.
Add 570 ml of 100% ethyl alcohol, 285 ml of reagent grade
toluene and 1.3 ml of reagent grade H2804 to the flask.

The flask is heated and an azeotropic mixture of ethanol,
toluene and water distill at 75°C. The heating is continued
until 300 to 400 ml of distillate are collected and then it
is suspended. The distillate is shaken well with K2C03,
next filtered through a fritted glass disk, and is poured
back into the reaction flask. The mixture is heated again
until 95% of the volatile distillate is removed. The solu-
tion is allowed to cool slightly and then it is vacuum dis-
tilled (without fractionation).

Next the liquid is redistilled with an efficient frac-
tionation column. The pure diethyl ester boils at 142°
under a pressure of 4 mm Hg. The PMR spectrum of the neat

liquid consists of a triplet (-CH3) St 1.3 ppm, a singlet

u
(~OCH2CH20) at 3.8 ppm, a singlet (~C—CHZ—O) at 4.2 ppm

54

and a quartet (-O-CH2-CH3) at 4.25 ppm.

4.4.2. Hydrolysis of the Diester

 

Add 130 ml of diethyl ester, 130 ml of distilled water
and 1.3 gms Dowex 50-WX-2 ion exchange resins to a 3-neck
500 m1 flask. The solution is heated to a temperature of
approximately 90-95°. The diester is not 100% miscible in
water and two phases appear at the start of the reaction.
After an hour of heating the solution becomes one phase and
liquid starts to boil off between 70-95°C. The distillate
is a mixture of water and ethanol. When all the ethanol
is used, the boiling point of the distillate goes up to 100°
and the hydrolysis is completed. Next, the residual solu—
tion is filtered to remove the ion exchange resin and then
the remaining water is stripped off with a roto-evaporator.
The viscous liquid is placed under vacuum until it solidifies.
The PMR of the diacid in D20 shows two sharp singlets with

an area ratio of 1:1 and the melting point range is 65—75°C.

4.4.3. Purification of 2,2,2 Cryptand

 

2,2,2 Cryptand is purified by recrystallization in
hexane followed by a vacuum sublimation. If the crude 222
cryptand contained precursor impurities such as the mono-

/ CHZCHZOCHZCHZOCHZCH2\
CHZCHZOCHZCHZOCH2CH2

recrystallization was found to be effective for separating

cyclic diamine,

a major portion of this impurity. However, some residual

55

diamine (approximately 5%) could always be detected by PMR
studies. The 2,2,2 cryptand in this work gave a PMR spec—
trum that did not show impurities and had a melting point

range of 70.2-71.1°C.

4.5. Synthesis of a Crystalline Salt of the Sodium Anion

 

The first authentic salt containing a sodium anion
was prepared by the following procedure:

A Pyrex vessel of the design shown in Figure 9 was
used to prepare polycrystalline samples of NaC+ ' Na- in
which C is 2,2,2 cryptand (see Figure l). A convenient
amount (50 mg to l g) of C was placed in compartment B and
sodium metal was placed into the side-arm shown which was
then sealed off. The vessel was evacuated to “:10-6 torr
and the sodium was distilled into compartment A. Ethyl—
amine was distilled into B by cooling B with a dry-ice
isopropanol bath. The quantity of ethylamine (EA) used
was adjusted so as to form a 0.1 M solution of C. After
removal from the vacuum line, the solution of C in ethyl—
amine was transferred through the glass frit into compart-
ment A. Upon contact with the sodium mirror a dark blue
solution formed immediately. The contact with sodium
was maintained with shaking for several minutes between
0° and -60°C. The solution was then warmed to 0° to 10°C
and allowed to filter through the frit by cooling B. Upon

cooling, shiny gold—colored crystals of Na+C ' Na— formed.

56

pcoloxtU
.1
QQOO

 

o>_o>
E33o0>

 

 

 

 

 

 

 

 

 

 

.Imz . o+mz mo cofluoummmum HON Hommm> .m ousmflm

2.;
omeooU

BEE 02
e

 

 

 

Nessa

 

“*0 _Omm

 

 

Eanoo> toe
cdcgtmcou

 

57

The excess liquid was again poured into A to insure that
all of the sodium which could be dissolved was in solu—
tion. Since sodium is insoluble in ethylamine in the

absence of C, the solubilization stopped when the reaction

2Na (5) + C + NaC+ + Na7

had used up all of the free complexing agent, C.

After the final crystallization process, the super—
natant solution was poured into A, the vessel was again
connected to a vacuum line and all of the ethylamine was
removed by distillation. Purified diethyl ether (purified
in a similar way to THF) was distilled into B. The crystals
were only very slightly soluble in diethyl ether, which
therefore serves as a convenient washing solvent. The very
light blue solution formed in diethyl ether was poured into
A and then redistilled back into B. This was repeated
several times until all traces of white or blue material
had been removed from the crystals. The diethyl ether was
poured into A and then distilled out of the vessel. Pure
crystals of Na+C ° Na- remained in the vessel. The elemental
analysis, some properties, and the crystal structure have

been reported elsewhere.36.38'52'53

58

4.6 Solution Preparation

 

4.6.1. Salt Solutions for NMR Exchange Studies

 

Reagent grade NaBr, NaI and Na¢4B were dried and used
without further purification. Samples were prepared in a
dry box or glove bag under an inert atmosphere of dry nitro-
gen or argon. 10 mm O.D. thin-wall high resolution NMR
tubes purchased from Wilmad Glass Company were modified
by placing a standard ground glass joint at the open end.

This provided an air-tight seal.

4.6.2. Preparation of Metal Solutions

 

Figure 10 shows the Pyrex apparatus used in most of
the alkali anion NMR studies. Preparation of sodium solu-
tions was done by two methods. In the first method, the
2,2,2 cryptand was dropped into the vessel and rested on
the glass frit. An excess of sodium metal was sealed into
the glass side arm and the entire vessel was evacuated.
Sodium was distilled through the side arm and into bulb
A to form a shiny mirror. Ethylamine was distilled into
B and a method similar to that discussed in 4.5 was used
to form a blue solution, which precipitated gold crystals
at dry ice temperatures. The crystals could be rinsed off
with diethyl ether as discussed previously and then any of
the solvents could be distilled into the vessel to form a
blue solution which contained Na+C : Na- (%O.l to 0.2 M).

The solution was then poured into the bottom of the NMR

59

 

.22.] .

 

 

 

 

Teflon valve Q

 

 

I i vacuum

 

 

 

 

 

 

 

 

C
glass 9%3
frit 10 mm NMR tube
V
B

2,2,2 cryptand

.-
‘vA

:. sodium metal

Figure 10. Vessel for preparation of NMR samples.

60

tube and frozen with liquid nitrogen. The vessel with its
frozen solution was pumped to a pressure of «’10-5 mm of Hg
and the NMR tube was sealed off at constriction C.

In the second method, the solutions were prepared
directly by distilling the solvent to be used into the vessel
containing sodium and 222 cryptand. The 2,2,2 cryptand was
dissolved and a blue solution was formed with the previously
discussed method. However, in this case no crystals were
isolated, the blue solution was poured into the NMR tube and
sealed off under vacuum as before. Cesium and rubidium anion
solutions were prepared by the second method. Although no

+ — +
222 Rb and CsC222 Cs were observed

to precipitate in solution, shiny bronze films were observed

gold crystals of RbC

on the glass walls of rubidium samples and copper colored
films were observed on the glass walls of cesium samples.
Concentrations of all the solutions were adjusted to approxi—
mately 0.1 M in 2,2,2 cryptand. The equilibrium

solvent + _
C + excess M 2 (C222M ) + (M )

222
lies very far to the right for all metals and all solvents
used.

Sodium solutions were stable at temperatures of +5°C
for several days. Rubidium and cesium solutions were stable
at dry ice temperatures for a week, but at ice temperatures
decomposition occurred within an hour. Thus, the working

temperatures of rubidium and cesium solutions were maintained

61

below —30°C where no significant amount of decomposition

occurred on the time scale of NMR experiments (3 W 6 hrs.).

4.7 The NMR Spectrometer

 

A pulsed multinuclear NMR spectrometer was used for
most of the studies. The design is similar to one reported

127 A block diagram of the spectrometer is

by Traficante.
shown in Figure 11. The spectrometer consisted of three
main parts. The first is a tuned transmitter/receiver sec—
tion which operates at 56.44 MHz. The second part consisted
of a network of double balanced mixers coupled to a frequency
synthesizer. The third part is a wideband transmitter/re-
ceiver network coupled to a single coil tunable probe. A
magnet from a Varian DA-6O spectrometer was used and main-
tained at 14.09 Tesla. With the mixing network, the broad
band amplifiers and tunable probe it was possible to observe
NMR signals in the range of 5 to 30 MHz. Changing frequen-
cies simply required adjustment of the probe, the tunable
power amplifier and the frequency synthesizer (which could
be done in less than 15 minutes).

A key feature of the spectrometer is the external
look. In collaboration with David Wright a small single
coil probe (lock probe) was constructed and tuned to the
proton frequency. The probe was filled with doped water
(linewidth approximately 4 Hz) and made to insert into the

main NMR probe. The lock probe was connected to the normal

62

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63

proton lock circuitry of an unused Varian DA-60 spectrometer.

In this manner it was possible to lock the magnetic field on

a proton signal and perform magnetic resonance experiments

in the frequency range of 5 to 30 MHz. The maximum drift

in an eight hour period was less than 6 Hz. The details of

the external lock probe construction are given in David

Wright's Ph.D. thesis.128
The spectrometer itself is controlled by a Nicolet 1080

computer system equipped with a Diablo magnetic disk. The

hard-wired interface and software are described elsewhere.128

4.8 Temperature Control and Calibration

 

Temperature regulation was accomplished by using a
standard Varian heater-sensor and V-4343 variable tempera-
ture controller. Temperatures were measured with a cali—
brated Doric digital thermocouple. A thermocouple was
placed in a fixed position inside the probe, at a height
which is just below the bottom of a sample tube. To make
sure that the temperature at the thermocouple and the tem—
perature at the sample tube were the same, a calibration
procedure was used. A mercury thermometer and a thermo—
couple were placed inside the bottom of an NMR tube with
1 ml of solvent. The thermometer bulb and thermocouple
were positioned at the center of the receiver coil of the
NMR probe. The temperature was varied from 0° to 100°C

and the thermometer reading along with the readings from

64

the thermocouples inside and outside the sample tube were
recorded. The results are given in Table IV. From these
results, it was not felt necessary to perform any tempera-
ture correction and all thermocouple readings were used as

read.

 

4.9 Data Reduction

Free induction decays were stored on magnetic disk.
The data were Fourier-transformed without applying smooth—
ing or exponential weighting. The transformed data were
zero-order phase corrected and punched onto paper tape with
a modified version of RELAX 2 (a program writtEn by David
Wright).128 The modification to RELAX 2 is given in Appendix
A. The data from paper tape were punched on keypunch cards
in octal format. The octal formatted data were converted
to decimal format by program CONVERT (Appendix B). The
decimal formatted data were analyzed by a generalized

I“
weighted non-linear least-squares program (KINFIT).129

65

Table IV. Temperature calibration for NMR.

 

 

 

Thermometer Inside Thermocouple Outside Thermocouple
(°C) (°C) (°C)
+4.1 +2.9 +2.9

8.5 7.6 7.9
13.2 12.3 12.3
18.8 18.2 18.3
26.0 26.0 25.9
24.1 23.7 23.7
31.9 32.0 32.1
37.9 37.7 37.7
47.2 47.0 46.9
51.9 51.7 51.5
57.0 56.9 56.6
61.7 61.6 61.4
66.4 66.3 66.2
73.4 73.4 73.2
78.4 78.6 78.3
86.5 86.7 86.3
93.9 94.3 93.9
98.9 99.4 99.1

 

 

V. SODIUM-23 NMR STUDY OF SODIUM ION - SODIUM

CRYPTATE EXCHANGE RATES IN VARIOUS SOLVENTS

5.1 Introduction

 

Macrocyclic polyethers (crown ethers), first synthesized

by Pederson,32 and macroheterobicyclic diamines (cryptands)

34

firSt synthesized by Lehn 2; al. form very stable complexes

with alkali metal and alkaline earth metal cations. X-ray
structure determination of cryptate complexes formed from

272:2 cryptand (C see Figure l) and alkali metal salts

222'
show that the alkali cation is contained within the central

cavity of the ligand.l30’131 Association constants for complex
formation between many of the synthetic complexing agents of

both the crown and cryptand classes and a variety of metal

132-134

salts are known for aqueous solutions. Except for

association constants in methanol, very few others have

been determined in nonaqueous solvents.l32-134 Even fewer

rate data exist for the exchange of metal ions between
solvated and bound sites. Exchange rates at the coales-
cence temperature have been reported from PMR studies on

D20 solutions which contain C222 and half the stoichiometric

39

amount of alkali metal salt. From these results it was

clear that sodium cation exchange might be slow enough to

23

be observed directly by using Na NMR techniques. Ceraso

40 investigated the kinetics of complexation reactions

of Na+C222 cryptates in EDA solutions by using 23Na NMR

and Dye

66

67

techniques. Their work is the first example of sodium cation

exchange which is slow enough to exhibit clearly defined

separate signals for two environments. Cahen 33 al.135

studied the Li+—cryptate exchange kinetics in water and in
several nonaqueous solvents by using 7Li NMR. Cryptands

smaller than C222 were used. No other quantitative informa—

tion exists for alkali cation exchange rates in the presence

136-138

of C Schori e: 21. studied the kinetics of com—

222'
plexation of crown ethers with sodium and potassium cations

23 39K NMR lineshape anal-

in several solvents by using Na and
ysis. Since for the crown case the chemical shift between

the free and bound site is negligible compared to the 23Na

and 39K linewidth of the bound site, their experiments only
exhibited one apparent resonance. Under their conditions,

it was possible to reduce the complete lineshape expression
for two site chemical exchange to a single Lorentzian line
shape function. This is a special case of the treatment

used here.

In this chapter an NMR lineshape analysis of the tempera-
ture dependence of sodium ion exchange in the presence of C222
in H20, EDA, THF and PYR solutions is given. Lineshapes
are calculated from the exact expression for a general two
site exchange of uncoupled spins and are fitted to the ex-
perimentally observed lineshape with the aid of the generalized

weighted non—linear least—squares program KINFIT.129

23

We have chosen to use the Na pulsed Fourier transform

NMR technique because the advantages over continuous wave

68

NMR techniques are threefold:

1. No modulation distortion from sidebands occurs
(particularly a problem with sodium, due to its
range of relaxation times);

2. No saturation broadening occurs; and

3. Signal averaging is accomplished in a much shorter

time period.

Despite the low sensitivity of 23Na NMR compared to that of

PMR, its use has two advantages over PMR:

l. The chemical shift range of sodium nuclei is much
greater than that of protons; and

2. Deuterated solvents are not required.

5.2 Determination and Interpretation of the Line Shapes

The bloch equations which describe the motion of the

X and Y components of magnetization in the rotating frame,

when modified to include chemical exchange, are given byl39’140

E— + GAGA = ‘lYHlMOA + TB GB — TA GA 5. 1
—Ci-‘E— + (XBGB : —1YH1MOB + TA GA "' TB GB , 5 . 2
where
G = u + iv G = u + iv a - T_l~i(w m)
A A A’ B B B' A 2A A ’

69

0‘B 28 B

frequency field, MOA B

of magnetization for sites A and B, and TA and TB are the

= T -i(w -w), w is the variable frequency, H1 is the radio

and MO are the equilibrium 2 components
mean lifetimes in sites A and B respectively. Other symbols

have their usual meaning. The solution to these equations

dGA dGB
for slow passage conditions (?fi7 = TEE = 0) and for transient
conditions (Hl = 0) have been shown to form a Fourier trans-

141,142

form pair. The solution for slow passage conditions

is given in Appendix C. The shape function is given by

 

 

 

 

 

 

G(w) = YHlMoiIcose - Rsin0} 5.3
I = 82+T¥; R = Hg:§%- 5.4

S +T S +T

P P

A B T
S = ——— + ——— +-—————— - T(w -m)(w -m) 5-5

T2A T2B TZATZB A B

P P
U = 1 + T(TB + T—é- 5.6
2A 2B
w -m w -w
A B

T = P w + P w - w + T[ + ] 5.7

A A B B TZB TZA
V = T[PBmA + PAwB-w] 5.8

T T
T = A+ B 5.9

T T
A B

p , p = 5.10
A TA+TB B TA+TB

70

where I represents the absorption mode lineshape and R

represents the dispersion mode lineshape. wA,mB and T2A’

T2B are the Larmor frequencies and transverse relaxation

times of sites A and B in the absence of exchange. PA and PB
are the relative pOpulations in sites A and B. Equation 5.3
predicts the lineshape throughout the entire range of ex-

change from the extreme slow limit to the extreme fast limit

(slow exchange occurs for T >> ‘ 1' ), fast exchange occurs
w -w
A B
for T << ——¥L——-). The exchange time I together with the
(MA-MB)

relative pOpulations PA and PB contain all of the kinetics

information.

5.2.1. Measurements in the Absence of Exchange

 

In order to evaluate exchange times through application
of Equation 5.3, we must obtain information about the Larmor
frequencies and transverse relaxation times for sites A and
B in the absence of exchange (A denotes a solvated sodium
cation and B denotes a cryptated sodium cation). In addi—

tion, the populations P and P

A for exchanging systems must

BI
also be known. In many studies of systems which undergo two
1 d 13

site chemical exchange, H an C NMR lineshape analysis is

used to obtain T values. In some of these studies the assump-
tion that l/T2A = l/T2B = 0 is made. This assumption is not
justified for sodium since its relaxation rates are usually
much larger (broader lines) than those of 1H or 13C and

these relaxations contribute significantly to the observed

NMR lineshapes.

71

Since the equilibrium constant (Ka) for complex forma-
tion between Na+ and C222 is large (Ka > 103) in all sol-

vents and at all temperatures, PA and P are directly deter-

B
mined from the mole ratios of C222 and sodium salt added to
solution.
To obtain MA,wB, T2A and TZB’ two solutions in each

solvent were prepared. The first contained a sodium salt
with no C222 and the second contained a sodium salt and

equimolar C Because Ka is large, the second solution

222'
contains only bound sodium cations and these ions cannot
undergo chemical exchange since the concentration of unbound

23Na NMR of each of these solutions

sites is too low. The
was studied as a function of temperature. All experimental
lineshapes were found to be Lorentzian.

The values of w and T2 were determined by fitting a
Lorentzian line to the observed signal. Complete character-
ization of the intensity of a Lorentzian signal by the Fourier
transform NMR technique requires determination of six param—
eters. These are the amplitude, K, the Larmor frequency, w,
the linewidth parameter, T2, the height of the baseline, C,
the zero—order phase correction, 00, and the first-order
phase correction, 0'. The zero—order phase correction is
constant and independent of frequency. It determines the
contribution of dispersion and absorption mode signals to
the observed lineshape. Electronic filtering and the finite

length of a 90° pulse that initiates a free induction decay,

as well as delays in the start of data acquisition can all

72

lead to a first-order phase correction. The first-order
phase correction varies linearly with frequency (and hence
channel number, j) according to 0' = 01 ° % in which N is
the total number of channels in the spectrum and 01 is the
total change in phase over the entire spectrum.

In terms of these parameters, the intensity is given

as a function of frequency by

 

K’T
GIN) = 2 2 2 {cos(00+0') — T2(IIIO-III)Sin(90+9') + C
1+T2(wO—m)
5.11

Commonly the phase parameters and the baseline height
are instrumentally adjusted by visual inspection of the
signal to obtain a symmetric absorption—mode signal with a
zero baseline. The value of 01 is constant for given
instrument settings and may be accurately determined by
measuring the signal from a reference sample at several
magnetic field settings which span the entire frequency
range to be used. Once 01- is evaluated in this way it need
not be changed from sample to sample and is not an adjust-
able parameter. By contrast 00 is influenced, not only by
instrument settings, but also by sample position, tempera—
ture, etc., and therefore it must be adjusted for each
sample.

Since in any event, the parameters must be adjusted
(either numerically or instrumentally), we have chosen to
evaluate all parameters except 01 by fitting the Lorentzian

Equation (5.11) to the observed spectrum by a non—linear

73

least—squares procedure. A typical example of a fit for
0.6 M NaBr in EDA solution at 26.3°C is shown in Figure 12.
The variation in linewidths and chemical shifts with tem—
perature for free and unbound sodium in each of the four
solvents is listed in Tables V-XII. The measurements of T2
and w for free Na+ in H20 and PYR were made visually. The
data for each solvent are plotted in Figures 13-16, (semi-
1og plot of l/T2 ys 103/T). Simple exponential behavior of
the variation of the relaxation rate with temperature is
observed for THF, EDA and H20 solutions but not for PYR solu—
tions. As shown in Figure 16, the relaxation rate levels
off between 90 and 140°C. This deviation from exponential
behavior might be caused by changes in ion-pairing with
temperature. In all cases the activation energy (see Chap—
ter III) is smaller for free sodium cations than for bound
sodium cations in the same solvent. All chemical shifts
are referenced to the infinitely dilute aqueous sodium
cation (a positive shift corresponds to a high field shift).
The Larmor frequencies show only a slight dependence
upon temperature. The value of m at any temperature between
those examined was determined by graphical interpolation.
A sample of saturated aqueous sodium chloride at 25°C was
used as an external reference for both chemical shift and
linewidth calibrations. (The chemical shift of saturated
aqueous sodium chloride relative to infinitely dilute aqueous

sodium ion is —0.7 ppm). Linewidth contributions from

magnetic field inhomogeneties ranged from 2 to 6 Hz and

74

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75

 

 

 

Table V. Variation of the relaxation rate and chemical
shift of free sodium cation with temperature
in ethylenediamine.a

T(°C) 103/T(°K) 1/T2B(sec)b 6(pmeC
20.6 3.404 255.3 —13.86
26.3 3.340 220.3 —l3.75
32.1 3.276 192.8 -l3.67
38.0 3.214 173.3 -l3.65
43.5 3.158 154.7 -13.61
49.1 3.103 139.7 —l3.59
54.9 3.048 124.0 -l3.56
60.0 3.002 113.8 -l3.53
64.5 2.962 104.8 -13.47
70.1 2.913 94.79 -l3.42

 

 

a) 0.6 M NaBr in EDA solution.
b) Natural relaxation rate.

c) Referenced to infinite dilute aqueous Na+.

76

 

 

 

Table VI. Variation of the relaxation rate and chemical
shift of bound sodium cation with temperature
in ethylenediamine.a

T(°C) 103/T(°K) 1/TZB(sec)b 6(PPm)C
20.2 3.409 273.6 10.41
26.6 3.336 231.5 10.65
32.3 3.274 202.8 10.90
35.1 3.244 182.6 10.83
41.4 3.179 158.0 10.92
48.3 3.111 138.3 11.21
52.4 3.072 127.0 11.10
59.0 3.011 110.4 11.17
67.7 2.934 95.79 11.24

 

 

a)
b)

C)

0.3 M Na+C - Br—
Natural relaxation rate.

Referenced to infinite dilute aqueous Na+.

in EDA solution.

77

Table VII. Variation of relaxation rate and chemical shift
of free sodium cation with temperature in water.a

 

 

 

T(°C) 103/T(°K) l/T2B(sec)b 6(ppm)C
7.8 3.556 37.5 0.3
13.9 3.484 27.3 0.3
21.2 3.397 24.9 0.3
33.3 3.263 18.6 —-—
36.2 3.233 17.1 0.6

 

 

a) 0.2 M NaI in H20 solution.

b) Natural relaxation rate.

c) Referenced to infinite dilute aqueous Na+

78

Variation of relaxation rate and chemical
shift of bound sodium cation with temperature
in water.a

Table VI I I .

 

 

 

T(°C) 103/T(°K) l/T2B(sec)b 5(ppm)c
2.8 3.624 520.7 7.45
8.3 3.553 438.1 7.68

13.4 3.490 355.3 7.84
19.2 3.421 311.3 8.12
21.0 3.400 282.3 8.45
25.0 3.354 245.5 8.54
29.7 3.302 233.1 8.53
35.3 3.242 184.3 8.83
40.6 3.187 164.5 9.07
45.9 3.134 149.3 9.28
50.7 3.088 134.3 9.46
54.6 3.051 122.4 9.54
60.8 2.995 110.5 9.72
66.1 2.948 100.5 9.86

 

 

a)
b)

C)

0.2 M Na+C - 1'

Natural relaxation rate.

in H20 Solution.

Referenced to infinite dilute aqueous Na+

79

 

 

 

Table IX. Variation of the relaxation rate (1/T2) and
chemical shift of free sodium cation with
temperature in tetrahydrofuran.a

o 3 o b C
T( C) 10 /T( K) l/T2B(sec) 5(ppm)
25.7 3.346 96.92 +7.43
30.7 3.291 94.29 +7.53
35.4 3.241 91.97 +7.58
42.8 3.165 88.60 +7.72
47.9 3.114 87.43 +7.82
53.1 3.065 85.79 +7.93

 

 

a) 0.4 M Na¢4B in THF solution.
b) Natural relaxation rate.

c) Referenced to infinite dilute aqueous Na+.

80

 

 

 

Table x, Variation of relaxation rate and chemical shift
of bound sodium cation with temperature in
tetrahydrofuran.a

T(°C)I 103/T(°K) l/T2B(sec)b 6(ppm)C
19.7 3.415 169.5 11.89
25.1 3.353 154.3 12.03
30.3 3.295 139.0 12.17
35.4 3.241 129.5 12.26
42.1 3.172 119.7 12.52
46.6 3.127 111.1 12.48
53.2 3.064 101.4 12.62
59.5 3.006 94.72 12.57
64.2 2.964 89.25 12.67
68.4 2.928 86.46 12.74
70.9 2.907 84.57 12.81

 

 

a) 0.2 M Na+C ° ¢ B— in THF solution.

4

b) Natural relaxation rate.

c) Referenced to infinite dilute aqueous Na+.

81

Table XI. Variation of relaxation rate and chemical
shift of free sodium cation with temperature

 

 

 

in pyridine.a
T(°C) 103/T(°K) l/T2B(sec)b 6(ppm)C
22.6 3.383 86.8 —1.2
45.0 3.145 70.4 -0.6
57.6 3.025 62.1 -0.3
69.0 2.924 57.2 —o.2
80.3 2.830 53.9 0.0
88.3 2.768 55.5 0.1
100.8 2.675 53.9 0.3
112.4 2.595 53.6 0.4
125.4 2.510 53.9 1.0
133.8 2.458 58.8 1.1
140.3 2.420 57.2 1.3
144.8 2.393 58.8 1.3

 

 

a) 0.2 M Na¢4B in PYR solution.
b) Natural relaxation rate.

c) Referenced to infinite dilute aqueous Na+.

82

 

 

 

Table XII. Variation of relaxation rate and chemical
shift of bound sodium cation with temperature
in pyridine.a

T(°C) 103/T(°K) l/TZB(sec)b 6(ppm)°
25.5 3.348 150.9 12.38
32.9 3.267 134.8 12.54
38.6 3.208 124.9 12.56
43.7 3.156 116.5 12.65
55.1 3.047 97.43 12.76
61.4 2.989 90.14 12.82
68.8 2.924 83.87 12.93
74.9 2.873 78.12 12.98
82.6 2.811 72.75 13.05
88.6 2.764 67.45 13.10

102.2 2.664 63.73 13.22
109.2 2.615 59.06 12.79
114.0 2.583 61.01 13.28
121.2 2.537 60.24 13.18
128.6 2.489 60.50 13.19
133.8 2.457 57.71 13.18
140.2 2.419 59.33 13.07

 

 

+ - . .
a) 0.2 M Na C ° ¢4B in PYR solution.
b) Natural relaxation rate.

c) Referenced to infinite dilute aqueous Na+

83

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500-

 

 

 

Figure 14.

3.2 3.4 3.6
103/T(°K")

Semilog plots of l/T2 for 23Na ys reciprocal
absolute temperature for solutions containing
0.2 M NaCl (0) and 0.2 M Na+c222 . Cl“ (0)

in H20.

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ICON

 

 

 

86

.msm an loo
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ousuouomfiou musHomnm Hmooumflomu m> 62mm How NB\H mo muoam moHHEmm .oa mucosa

 

 

1.61.5.2
«.6 ad TN
_ l l _ l s cc
0 O O O
o oo
o . .,....
O 0 \Sn.
0 109 w
0 7w
0
o
o

 

 

OON

87

were, for all cases except aqueous solutions, a small frac-
tion of the measured width. Inhomogeneous line broadening
varied from one set of experiments to the next. This con-
tribution to the linewidth was determined for each set of
experiments by using an aqueous reference sample with a
known relaxation time (saturated aqueous NaCl; natural line—
width is 8.0 Hz at 25°C), according to

(l/Tz)

(l/Tz) (l/Tz)

obs. nat.

inhomo.

This value was then added to the previously determined value
Of (1/T2)nat. for each of the sites so that the values of
l/T2A and l/TZB used in the following line shape equations
include both the natural contribution to the linewidth and
the inhomogeneous contribution. This method assumes that
the shape function of the field inhomogeneity also has a
Lorentz form, which is often not true. However, for all

cases but free sodium cation in H O, the inhomogeneous con-

2

tributions to the observed linewidth are small and are ap-
proximated well by a Lorentz shape function (see Figure 12).

Even the narrow lines observed for free Na+ in H20 were Loren-

tzian.
Values for (1/T2) at any temperature were evaluated
by fitting the following exponential equation to the observed

data (corrected for inhomogeneity).

eEr/R (l/T-1/298.15)

(l/T nat.

) = (l/T )
2A Or B nat' 2298.15

88

This was done for all solutions except free sodium in H20
and free and bound sodium in PYR. In these cases graphical
extrapolation and interpolation was used. The values for Er

are listed in Table XIII.

5.2.2. Evaluation of Exchange Times

 

To evaluate the exchange time T, Equations 5.3, 5.5,

5.7 and 5.8 were modified as follows

G(w) = K{Icos(eo+e') - Rsin(00+e')} + C 5.3'
P P
A B T
S = ——— + ——— +-—————— - T(w +A—w)(w +A—w) 5.5'
T2A T2B TZATZB A B

wA+A-w wB+A-w

T = P w + P w + A - m + T[
A A B B T2B T2A

 

V = [PBwA + PAwB + A - w]. 5.8'

Application of Equation 5.3' requires evaluation of six
parameters. These are amplitude, K, baseline height, C,
zero-order phase correction, 00, first-order phase correc—
tion, 0', frequency shift, A, and the exchange time, T.
Again the first-order phase correction was not adjusted num—
erically, but was measured visually for a given set of in-
strumental settings as described previously. Thus, in most
cases, we chose to adjust five parameters to obtain the best
fit of Equation 5.3' to the observed data. The frequency

shift parameter was introduced because of experimental

Table XIII

89

Activation energy, Er
in various solvents.

, for solvent reorganization

 

 

 

Concentration Er
Ion (M) Solvent (Kcal)
Na+ 0.6M NaBr EDA 3.6
Na+C 0 3M N +C 'B I EDA 4 4
Na+ 0.4M Na¢4B THF 0.86
+ + —
Na C222 0.2M Na C222 94B THF 2.7
+ + —
Na 0.2M Na C222 I H20 4.8

 

 

90

difficulties with referencing absolute frequencies from one
set of data to the next. The relative chemical shifts at
the two sites were not adjusted. The errors in precise
referencing of one set of data to another were caused by the
method of external referencing. If an internal reference

in each sample and an internal lock had been employed, there
would be no need for the correction term A. The frequency
shift parameter allows the absolute frequency in Equation
5.3' to shift, without changing the shape of the function.
In most cases A was less than 0.5 ppm.

For each spectrum analyzed, 90 to 99 data points were
found to be more than sufficient to determine T. The program
used (KINFIT) gave complete statistical information about
the fit to the data, including standard deviation estimates
for each of the parameters and the multiple correlation co—
efficient, which gives a measure of the coupling of each
parameter to all of the others. Coupling between T and the
other four parameters was lowest at intermediate rates of

exchange (I e l/(w This is expected, since I has its

greatest influence upon the lineshape in the intermediate

region of exchange.

5.2.2.1. Exchange Times in EDA Solutions — Three solu-

 

tions (EDA l, 2, and 3) each containing 0.6 M NaBr but with
variable amounts of C222 (0.15, 0.30 and 0.45 M respectively)
were examined. Selected spectra for EDA l, 2 and 3 are shown

in Figures 17-19. Spectra from solutions EDA 1 and EDA 3

91

 

 

 

Figure 17. Spectra at various temperatures for a solution
of 0.15 M C222 and 0.6 M NaBr in EDA
(1 ppm = 15.87 Hz).

92

1 76 . 40
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n
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I 21.30
Figure 18,

Spectra at various temperatures for a solution
of 0.30 M C2 2 and 0.6 M NaBr in EDA
(1 ppm = 15.87 Hz).

 

 

10 ppm H—~—+>

70.2O

 

58.8O

 

 

Figure 19. Spectra at various temperatures for a solution
of 0.45 M C2 and 0.6 M NaBr in EDA
(1 ppm = 15.§% Hz).

94

were analyzed by using Equation 5.3'. The spectra from EDA
2 were also analyzed by using Equation 5.3', but the value
of 61 was determined by computer adjustment of a modified
form of Equation 5.3'. The A term was dropped and ”A' wB
and 91 were allowed to float (along with K, C, T, 60) to
obtain the best fit of Equation 5.3' to the experimental
data. The three lowest temperature spectra were fitted and
the average value of 61 was computed. This value (61 =
264°) was then used to analyze all the spectra from solution
EDA 2 by using the unmodified form of Equation 5.3'. Some
typical fits for these data are shown in Figures 20-25,

Variations in T values with temperature are listed in

Tables XIV-XVI.

5.2.2.2. Exchange Times in THF, H20 and PYR Solutions -

 

A single solution of each solvent was examined. Equation
5.3' was used and no 91 corrections were made (61 = O).
For the H20 solution, the A parameter was not used. Some
of the fits for H20 solutions are shown in Figures 26 and
27. Noticeable intensity differences between calculated
and observed values at low temperatures in the vicinity of
the broad peak (bound cation) occurs with the experimental
intensity lower than the calculated intensity. This may
be partly caused by the spectrometer delay time. After
the pulse, a delay time of 200 to 300 microseconds occurs
before collection of the free induction decay. The area
under a peak in the frequency domain is proportial to the

intensity of the free induction decay at time zero. If a

95

 

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Figure 20. Computer fit of spectra obtained with 0.15 M
2 2 and O. 6 M NaBr in EDA. (a) 42. 60 C;
(b? 25. 5 OC.

96

 

 

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Figure 21.

Computer fit of spectra obtained with 0.15 M
C222 and 0.6 M NaBr in EDA. (a) 64.9OC;
(b) 53.9Oc.

97

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”unanauuxrg

Figure 22. Computer fit of spectra obtained with 0.30 M
c222 and 0.6 M NaBr in EDA. (a) 45.00c;
(b) 30.40C.

98

 

 

 

 

 

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Figure 23.

Computer fit of spectra obtained with 0.30 M

3%?

2 and 0.6 M NaBr in EDA.
50.2Oc.

(a)

76.4OC;

 

 

 

99

 

 

 

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Figure 24. Computer fit of spectra obtained with 0.45 M
c2 2 and 0.6 M NaBr in EDA. (a) 30.6Oc;
(b? 19.30c.

100

 

 

 

 

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Figure 25. Computer fit of spectra obtained with 0.45 M
and 0.6 M NaBr in EDA. (a) 41.9OC;

C
(ggz 36.10c.

101

 

 

 

Table XIV. Temperature dependence of the exchange time
in EDAl and corresponding relaxation rates
in the absence of exchange.a

T(°C) T(msec) l/T2A(sec) 1/TZB(sec)
19.9 6.65 (0.16)b 272 283
25.5 4.353 (0.08) 237 247
31.3 2.851 (0.03) 211 222
36.8 2.042 (0.02) 190 192
42.6 1.376 (0.009) 170 170
48.3 0.9508 (0.007) 153 151
53.9 0.6633 (0.009) 139 136
59.5 0.4856 (0.01) 127 123
64.9 0.3462 (0.003) 116 112
70.3 0.2500 (0.002) 106 102

 

 

a) 0.15 M C222 + 0.6 M NaBr.

b) Standard deviation.

 

 

 

102

Table XV. Temperature dependence of the exchange time
in EDA2 and corresponding relaxation rates
in the absence of exchange.a

 

 

 

 

 

T(°C) T(mseC) l/T2A(sec) l/T2B(sec)
30.4 2.338 (0.03)b 256 270
36.2 1.603 (0.02) 189 191
38.0 1.413 (0.01) 182 184
41.4 1.126 (0.008) 171 171
42.4 1.048 (0.008) 168 167
45.0 0.8913 (0.008) 160 159
50.2 0.6154 (0.004) 145 143
53.8 0.4862 (0.004) 136 133
60.8 0.3111 (0.003) 121 117
69.0 0.1918 (0.002) 106 101
76.4 0.1238 (0.001) 93.9 84.0

a) 0.30 M C222 + 0.6 M NaBr.

b) Standard deviation.

103

Table XVI. Temperature dependence of the exchange time
in EDA3 and corresponding relaxation rates
in the absence of exchange.a

 

 

 

T(°C) T(msec) l/T2A(sec) l/T2B(sec)
19.3 2.154 (0.04)b 271.5 288.3
24.4 1.448 (0.02) 243.8 255.0
30.6 0.956 (0.02) 215.1 221.0
36.1 0.600 (0.02) 193.3 195.8
41.9 0.486 (0.02) 173.4 173.4
47.4 0.3586 (0.005) 157.0 155.3
53.3 0.2295 (0 002) 141.6 138.7
58.8 0.1626 (0.0007) 129.1 125.4
64.4 0.1162 (0.0007) 117.9 113.7
70.2 0.08232 (0.0005) 107.6 103.2

 

 

a) 0.45 M C + 0.6 M NaBr.

222

b) Standard deviation.

 

104

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Figure 26. Computer fit of spectra obtained with 0. 2 M
C andO 0. 4 M NaI in H20. (a) 23. 6 C;
222
(b) 3. 30 C.

 

 

105

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Figure 27. Computer fit of spectra obtained with 0.2 M

c2 2 and 0.4 m NaI in H o. (a) 39.3Oc;
? o 2
(b 26.9 c.

 

106

delay occurs and one relaxation time is much shorter than

the other, as in this case, some of the intensity of the

faster relaxing site will be lost. As a consequence, the
observed intensity of the broad peak will be lower than that

of the calculated. Spectra from the PYR solution were analyzed
with Equation 5.3'. In the slow exchange limit, the A param—

eter was dropped and MA and w along with the usual parameters

B
were allowed to be adjusted to obtain the best fit of 5.3'
to the experimental data. Some fits for spectra from PYR
solution are shown in Figures 28 and 29. Spectra from the
THF solution were also fit with an unmodified form of 5.3'.
A few of the fits for THF are shown in Figures 30 and 31.

Variations of T with temperature for H20, PYR and THF solu—

tion are listed in Tables XVII and XIX.

5.3 Results and Discussion

 

5.3.1. Some Sources of Systematic Error

 

Many sources of systematic error occur when the Fourier
transform NMR technique is used. These can cause distor-
tion of the observed lineshapes. Some sources are pulse
feed-through, the first—order phase correction and narrow—
band audio filtering. The effects that they produce can
sometimes be eliminated instrumentally and/or the calculated
lineshape can be modified to include these effects. For
example, the calculated NMR lineshapes included the first—

order phase correction as described previously.

 

107

 

 

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Figure 28.
and 0.4 M Na¢4B in PYR.
66.7OC.

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93.20c;

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108

 

 

 

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Computer fit of spectra obtained with 0.2 M

C222 and 0.4 M Na¢4B in PYR. (a) 135-40C;
(b) 116.4OC.

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109

 

 

 

 

 

 

 

 

 

 

 

 

 

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(b 44.1 C.

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(E)? 62. 80 c.

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111

 

 

 

 

 

Table XVII. Temperature dependence of the exchange time
in H20 and corresponding values for relaxation
rates in the absence of exchange.a
T(°C) T(msec) 1/T2A(sec) 1/T2B(sec)
3.3 34.5 (3.1)b 61.0 503
12.0 11.34 (0.4) 49.4 389
22.2 4.335 (0.07) 42.3 294
23.6 3.830 (0.05) 41.5 284
26.9 2.877 (0.04) 39.8 261
29.2 2.178 (0.02) 38.7 247
30.6 2.030 (0.02) 38.0 238
33.8 1.616 (0.02) 36.8 221
37.0 1.120 (0.02) 35.8 205
39.3 0.892 (0.01) 35.4 195
45.9 0.5122 (0.009) 32.3 168
52.3 0.3333 (0.008) 31.3 147
a) 0.2 M C222 + 0.4 NaI.

b)

Standard deviation.

112

Table XVIII. Temperature dependence of the exchange time in
PYR and corresponding relaxation rates in the
absence of exchange.a

 

 

 

T(°C) T(msec) l/T2A(sec) 1/T2B(sec)
55.2 32.0 (4.3)b 83.8 115
66.7 21.9 (2.1) 78.8 102
73.3 15.2 (1.4) 76.3 98.0
81.4 9.82 (0.5) 74.8 88.4
93.2 5.31 (0.2) 73.3 80.4
98.7 3.82 (0.1) 73.3 77.8

102.0 3.157 (0.09) 73.3 77.4

105.4 2.815 (0.06) 73.8 77.4

109.6 2.333 (0.06) 73.8 76.9

116.4 1.609 (0.02) 74.1 76.5

125.8 1.013 (0.011) 74.8 75.4

129.4 0.8607 (0.008) 75.8 75.4

135.4 0.6611 (0.006) 76.8 74.9

142.1 0.5051 (0.006) 77.8

 

 

a) 0.2 M c222 + 0.4 M Na¢4B

b) Standard Deviation.

113

 

 

 

 

 

Table XIX. Temperature dependence of the exchange time
in THF and corresponding relaxation rates in
the absence of exchange.a
T(°C) T(msec) l/T2A(sec) l/T2B(sec)
35.5 24.2 (1.2)b 108 146
39.4 20.2 (0.8) 106 139
44.1 15.0 (0.4) 105 132
45.8 12.7 (0.3) 104 129
49.4 10.2 (0.2) 103 124
52.2 8.43 (0.1) 102 120
56.8 6.089 (0.09) 100 114
59.1 5.334 (0.08) 99.3 111
62.8 4.063 (0.05) 98.1 107
65.0 3.510 (0.03) 97.5 105
68.2 2.876 (0.03) 96.5 102
71.3 2.363 (0.03) 95.6 98.7
74.6 1.872 (0.02) 94.6 95.7
a) 0.2 M c + 0.4 M Na¢4B.

b)

222

Standard deviation.

114

It is not at all obvious by inspection of the spectra
that a first-order phase correction is needed. This is be-
cause a single-line spectrum can be phased to appear as an
absorption mode signal by using only a zero—order phase cor—
rection. Even in the case of a doublet, the spectrum can
be visually phased to an apparent absorption mode signal
without using a first-order phase correction (an example of
this is shown by the spectra in Figure 17, in which the total
change in phase from one end of the spectrum to the other is
44.5°). By contrast 13C NMR spectra usually exhibit many
narrow lines which span the entire frequency range sampled.
In this case Visual evaluation of the first—order phase cor—
rection is easily made from a single spectrum.

The first-order phase correction will have its maximum
effect on the lineshape for an exchanging system at the slow
exchange limit (low temperatures), where the spectral in—
tensities are spread out over a broad frequency range.
Figures 32a and 32b, which contain the same experimental
data, show the effect of 8' upon the fit. The lineshape
calculated in Figure 32a does not include a first-order phase
correction term whereas that calculated in Figure 32b includes
the proper first-order phase correction. The fit in Figure
32b is slightly better than in 32a.

Failure to make such a correction usually only causes
small differences between the calculated and observed line-
shapes. However the effect is magnified for large chem—

ical shift differences such as we observed with EDA solu-

 

 

 

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ooooooonaooooooaoooo.o ( ‘A‘QLHA o .|','t Cowl 25.8

Figure 32. Computer analysis of the 23Na lineshape for a
solution containing 0.15 M C 22 and 0.6 M NaBr
in EDA at 25.5 C. (a) No first-order phase
correction; (b) first-order phase corrected.

116

tions. In addition as shown in Figure 33, straight line
Arrhenius plots result in either case, but give different
activation energies. The experimental data are the same for
both sets of calculations shown in Figure 33, but the T values
were evaluated with and without first-order phase correction.
This shows that failure to make the proper first—order phase
correction might not be readily apparent but it can have a
pronounced effect on the results. In this case (EDA l),
neglect of 0’ correction gives an 8% error in the calculated
activation energy.

Another source of error can come from the 4-Pole Butter-
worth active audio filters which are frequently used in Fourier-
transform NMR spectroscopy. All the experiments discussed
were performed with a sweep-width of 5000 Hz. To obtain an
optimum signal-to-noise ratio, a narrow band filter (0 -

5000 Hz) was used. A perfect filter would be one which passes
any frequency between 0 and 5000 Hz and has an infinitely
sharp cutoff at 5000 Hz. However, no such filter exists.

The attenuation characteristics of the filter employed in
these experiments is shown in Figure 34. An input sine wave
which is passed through the filter at 1 volt (peak to peak)
and 5000 Hz frequency is attenuated by 40%. The attenuation
at 3000 Hz is only 3.1%. The intensity function shown in
Figure 34 can be matched to within better than 1% with an

equation of the form

I = ax2 + bx + c,

117

 

 

‘Q\
i\
o
103»
5 ...
,r
1*
U _.
an
U)
U
.x
2
10 ~
_
.1 I J l l l 1 '

 

 

 

l l
2.9 3.0 3.1 3.2 3.3 3.4
103/T (°K‘1)

Figure 33. Arrhenius plot of k (rate of release of Na+ from

C222) for EDAl solution. (0) No first-order

phase correction; (O) first-order phase
corrected.

.umuaflm m>fluom nuuozumnusm maomus

um ooom m How mocmsvmum MN 0H\H wuflmcmucfl omumscmuum mo uoam .vm muswflm

ANIVme x .09.“—

 

118

 

3.. o.» o.~ 3 ed
_ fl _ _
L ed
.. n
I/n. mwguml
/. ..
/./. ..
/o/
./In. 1. 1.. 3

 

 

 

119

where x represents frequency and I is the intensity. A least-
squares fit of the above equation to the data in Figure 35

was performed to evaluate the coefficients, a, b and c. This
calculated intensity function was then inserted into Equation
5.3' as an amplitude adjustment. The corrected intensity form
of Equation 5.3' was fit to the EDA 3 data (these data were
used since, of all the spectra, they had the most spectral
intensity at the highest frequency and this is where most
attenuation would occur). A comparison of T values calculated
from the best fit of 5.3' with and without this intensity
correction to the observed data from EDA 3 solution is given
in Table XX. From these results it is clear that no intensity
corrections are needed for this work.

Another source of error comes from the digital sampling
which is characteristic of a Fourier transform spectrum. Even
if an ideal spectrometer with no baseline distortion from
pulse-feedthrough were used, baseline artifacts could occur
because of the digital sampling. If we are interested in a
spectrum with frequencies as high as 6 Hz, we must sample
the free induction decay at a rate which is at least 26 in
order to properly represent the spectrum in digital form (this
is known from information theory). If we sample at a rate
26, and frequency of 6 + e (where e is positive) is examined,
then there will be less than 2 points per cycle representing
the frequency 6 + e and the frequency 6 - s also has the same
value at each of the sampled points. Thus the frequency

6 + e is indistinguishable from the frequency 6 — e , and any

120

 

 

 

Table xx, Comparison of exchange times with and without
intensity correction for EDA3.

Temp(°C) T(msec) Tcorr(msec)
19.3 2.154 (0.04)a 2.151 (0.04)
24.4 1.448 (0.02) 1.447 (0.02)
30.6 0.956 (0.02) 0.956 (0.02)
36.1 0.600 (0.02) 0.601 (0.02)
41.9 0.486 (0.02) 0.486 (0.02)
47.4 0.3586 (0.005) 0.3584 (0.005)
53.3 0.2295 (0.02) 0.2293 (0.002)
58.8 0.1626 (0.0008) 0.1625 (0.0008)
64.4 0.1162 (0.0007) 0.1161 (0.0007)
70.2 0.0823 (0.0005) 0.0823 (0.0005)

 

 

a)

Standard deviation.

121

information of the former is aliased to the lower frequency
6 - 8.

Taking a simple case, if a spectrum is obtained which
has a single peak which is broad (say a factor of 20 times
smaller than the sweep width) then baseline distortion will
occur and might be observable with a good signal-to-noise
ratio. Any intensity on the wings outside the sweep width
is folded back into the spectrum. The dispersion mode
spectrum is much more distorted than the absorption mode
spectrum because of higher intensity in the wings. This fold-
ing back of the wings causes a baseline distortion. If a
phase correction is performed, the larger distortion folded
into the nearly pure dispersion mode spectrum is mixed into
the phase corrected absorption mode spectrum. Foldover from
the wings of the dispersion line becomes worse as the width
of the line is increased compared to the width of the spec-
trum. Normally, the linewidth of a peak is smaller than two
percent of the total width of the spectrum and the signal-to—
noise ratio is smaller than 100, so that the spectral dis-
tortion is negligible. In conclusion, even a perfect spec-
trometer can give Fourier transformed spectra which are base-
line distorted because of digital sampling which leads to

only a finite range of distinguishable frequencies.

5.3.2. Mechanism of Exchange

 

Two possible mechanisms of exchange were considered.

The first (I) is given by Equation 5.12 and assumes exchange

 

 

 

122

proceeds through an association—dissociation process.

k
1

+ (Na+) : (Na+C222) 5.12
k—1

(C222)

The second mechanism (II), given by Equation 5.13, is bi-

molecular and also represents the overall exchange process.

* + + * + +
(Na ) + (Na C222) 2: (Na C222) + (Na ) 5.13
Results of Lehn et 31.39 combined with those of Ceraso and
Dye4O indicated a preference for mechanism I, but mechanism

II was not shown to be inconsistent with the data. The com-

plexation of crown polyethers with sodium ions proceeds via

mechanism I. To determine whether mechanism I or II is con—

sistent with the data at all temperatures, we examined the

concentration dependence of T. The data from EDA l, 2 and

3 were used since PA varies as 0.25, 0.5 and 0.75 respectively.
The relationship of T to a mechanism is made through the

definition of Ti

l/T * rate of removal of nuclei from sites of type i

i number of nuclei in sites of type i

 

5.14
From Equations 5.9, 5.10 and 5.12—5.14 we obtain the following

equation for T.

Mechanism I T = PA/k—l 5.15

123

Mechanism II T = 1/2k2(Na+)total
Mechanism I predicts a dependence of T upon the relative
population of site A while mechanism II predicts a dependence
of T upon the total concentration of sodium ion. Table XXI
gives the calculated activation energies for each solution
from the best fit of an Arrhenius expression to the data.

To test for consistency with either mechanism I or II an

exchange time, Tc was calculated from the average value

alc’
of the activation energies and relaxation times of all three
solutions. Then Tcalc values were calculated for equal popu-
1ations, PA = PB = 0.5, at each temperature for which the
experimental exchange time, Tobs' had been evaluated. The

ratio of Tobs/T is plotted against temperature for each

calc
solution in Figure 35. It is clear that the data at all
temperatures are consistent with mechanism I, since the
values are proportional to PA' Measurements with solution
EDA 2 were performed before the importance of an instrumentally
determined first-order phase correction had been realized and
a computer estimate of 0' was used (previously described)
to calculate lineshapes. This might be the cause of the
systematic deviations shown for this solution.

Activation energy plots, log k_l vs l/T, are shown in
Figures 33, 36 and 37 for EDA l, 2 and 3 respectively. Ac-

tivation energy plots for H O, PYR and THF are shown in

2

Figure 38. Activation energies, rate constants (k_l) and

values of AH:, As: and AG: for the release of Na+ from the

124

 

 

 

 

 

 

 

O C O
1.5 0—o*—.~—-———.—o . .
0. .g.
o ’ o
O
O
.—
.2 10 9
8
L
>
‘8
I-
O: C . .—
U o o 0 . . ° ’
I l l l I l
20 30 40 5O 60 70
t(°C)
Figure 35. Plot of the ratios TobS/T vs temperature (°C)

1 .
for EDAl, EDA2 and EDA3 sgiugions.

125

 

103 __ .
\

1'1
0

k (seC°1)
I I
/

 

 

2 l 1 J 1 I '
1° 2,9 3.1 3.3

103mm")

 

Figure 36. Arrhenius plot of k (rate of release of Na+ from
C222) for EDA2 solution.

 

 

 

 

126

 

.l
(3
u

k(sec4)

 

 

'\
2 1 I I 1 1
1° 3.0 3.2 3.4

103/T(°K")

 

Figure 37. Arrhenius plot of k (rate of release of Na+ from
C222) for EDA3 solution.

127

 

 

 

 

_ \ 0 H20
0 D THF
103,. \e 0 PYR
B
:'\ \
._ R. 20
7 \ \3. ‘00
3 - ‘\ D. \
O.
a“. 0. CE] 0\
x C D O
1 \ . O
10 )— . E
I D
1— \
: \ 80b 0
~ '\ \
5 ‘1‘
\1 O
l L, I l l l
2.4 2.6 2.8 3.0 3.2 3.4 3.6
10‘} (°K“)
'I
Figure 38. Arrhenius plots of k (rate of release of Na+ from

C222) for H20, THF and PYR solutions.

128

cryptate complex are given in Table XXI. Rate constants were

calculated from T values by assuming that the pathway of
sodium ion exchange for H20, PYR and THF solutions also
proceeds via mechanism I. A complete error analysis, in—
cluding the cross correlation terms, which account for the
coupling of the parameters was performed in all cases. The
free energy of activation is directly determined from k_l
and has the smallest standard deviation.

As expected, the average value of the activation energy
for EDA solutions (listed in Table XXI) is in good agreement

with the value of 12.2:l.1 kcal obtained by Ceraso and Dye4O

23Na NMR techniques. For the H20

solution a forward rate of association k1 is calculated from
6 1 -l

by using continuous wave

k_l and Ka to be 1.2 x 10 l

was reported for sodium ion exchange in D20 solution at

314°C and is in fair agreement with our calculated value of

k_l = 16 sec-l, at 3°C for sodium ion exchange in H

tion.

20 solu-

Activation energies vary by nearly 4 kilocalories, in-
dicating the definite presence of a solvent dependence. A
variation in activation energy with solvent for Li-cryptate

135 They

decomplexation has been reported by Cahen et 31.
observed a rough correlation between activation energy and

donicity of the solvent as expressed by the Gutmann donor

number (D.N.). As solvent donor number increases the activa-

tion energy for release of Li+ from the cryptate complex

increases. In our case, no correlation is indicated (the

M- sec . A value of k_ = 27 sec-

1

129

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130

donor numbers for THF, H O, PYR and EDA are 20.0, 33.0, 33.1

2
and 55.0 respectively). In both the lithium case and our

case, the exchange rate in PYR solution is very much slower
than the corresponding rates in H20 solution. By contrast,

Shchori gt gt.136—138

found that the activation energy for
release of a Na+ ion from certain crown ethers was independent
of solvent (to within 11 kcal). They suggest that the energy
barrier to exchange may be determined by the energy barrier

for a conformational twist of a crown molecule. However, their
data are restricted to three solvents with very similar donic-
ities and more solvents are needed to test their hypothesis.

The positive entropy of activation of H O is significant.

2

It indicates that solvent participates in the transition

state. Values for entropies of transferAStr of univalent

electrolytes from water to other solvents show that the
standard partial molar entropy of the cation in water is
higher than in other solvents143 (after corrections have
been made for differences in dielectric constants). This is
due to extensive structure-breaking of bulk water when an

i in H20

is therefore a strong indication that the solvent participates

ionic solution is formed. The positive value for AS

in the transition state.

VI. ALKALI METAL NMR STUDIES OF

SODIUM, RUBIDIUM AND CESIUM ANIONS

6.1 Introduction

 

It had been evident for some time that solutions of the
alkali metals in amines and ethers contain species of stoichi—
ometry M- (see Chapter II). The shift of the optical absorp—

tion band with metal, solvent and temperaturezg'30

suggests
strongly that the species is a centro-symmetric anion. How—
ever, other models cannot be ruled out on the basis of optical
evidence alone. Figure 39 shows three other contenders for
the M- structure. Indeed, one or more of such structures
might be responsible for the diamagnetic species in metal—

ammonia solutions which, to date, show no specific evidence

for the existence of centro-symmetric anions.

6.2 Magnetic Shielding Constants of Alkali Metal Ions

 

103,104 102 99-101

Optical pumping, atomic beam and NMR

techniques have established the shielding constants of the

133CS+

aqueous cations 23Na+, 87Rb+ and relative to the

gaseous atom with an accuracy of at least 2%. Reliable

105

calculations of the shielding constants of Na+(g) and

Na"(g) relative to the free atom have been made by using

Lamb's complete expression for atomic diamagnetic shielding144

(first term in Equation 3.2) and analytic Hartree—Fock

145

wavefunctions. The changes in shielding constants are

131

132

 

H

// \N/ \\ \N/ x/ \\
[I H\ :1 /H \‘ H\ :4 /,H = \
IH—N ...... M ...... Nqu H—N ...... M ...... NTH 92 IL...—

H/ H l’ H/ i \H /
\ ; \

/ \ /
\ /N /N\ \ \ ///
\\ H I H H I H \e—a’ \
\1e5,,/ H

EXPANDED ORBITAL ION PAIR WITH DIELECTRON MIG?)

Figure 39. Three possible models for a species of stoichiom-
etry M" (other than an alkali anion). All of
these models permit solvent interaction with the
outer p electrons of the cation. Ammonia is used
to represent any amine or ether solvent.

133

relatively small, amounting to only 7.7 ppm (diamagnetic)
for the addition of two 3g_electrons to gaseous Na+ to form
Na'(g). Corresponding shifts for Rb_(g) and Cs‘(g) are also

expected to be small. Diamagnetic contributions from solva-

109,110

tion are generally only a few ppm and the major effect

of the solvent, both from theoretical expectations and experi-

98

mental results is a substantial paramagnetic shift (45 to

75 ppm for Na+) upon solvation. The magnitude of this shift

correlates well with the donicity of the solvent,llllllzvl46';47

that is, the ability of the solvent to donate electron den-
sity to the cation. It is via the interaction of this sol—
vent electron density with the outer p orbitals of the alkali

metal cation which gives the observed paramagnetic effect.

6.3 Results

The key feature which permits us to study the NMR

spectra of alkali metal anions is the complexation of the

32

cation by macrocyclic polyethers of the crown and cryptand

34

classes. There are two reasons for the importance of this

complexation. First, the pronounced enhancement of metal

30'31'33'36 permits the use of metal concentrations

solubility
which are high enough to study by alkali metal NMR techniques.
Second, the complexed cation is released slowly enough by
the complexing agent so that, at low enough temperatures,

the exchange of M+C with solvated cations is slow on the

222
NMR time scale as shown by Chapter V. This makes it possible

134

to observe separate resonances for M+C222 and M‘.

Figure 40 shows a typical spectrum of Na+C222 ' Na-
in ethylamine. On the basis of the positions and linewidths
of NMR spectra of salt solutions which contain the cryptated
cation, NaC+, the broad peak in Figure 40 is attributed to
this Species. The narrow peak at high fields is then
assigned to the sodium anion. Although detectable amounts
of free Na+ cannot be present (because of reaction with Na-
to precipitate sodium metal) its normal position in this
solvent is also indicated on the figure. As expected from
the solution stoichiometry the areas under the two peaks are
equal within the error of their determination. The existence
of two peaks rather than a single averaged peak, which would
result from rapid exchange between NaC+ and Na", is expected
on the basis of the results from the previous chapter.

The 23Na NMR spectrum of Na+C222 - Na— has been studied
as a function of temperature in three solvents, tetrahydro—
furan (THF), ethylamine (EA) and methylamine (MA). The 87Rb
NMR spectrum of Rb+C222 ' Rb- in BA and THF and the 133Cs NMR
spectrum of 133Cs+C222 ° Cs“ in THF have also been studied.

The results are summarized in Table XXII.

6.4 Discussion

 

The spectra for Na+C222 ° Na_ in THF, EA and MA are
compared in Figure 41. The most striking feature is the

absence of a solvent-induced paramagnetic shift for Na- and

135

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137

 

 

 

 

 

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111 11111-1611111-11111
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1 I _ l I l J l
--20 O 20 40 60 80 100

Figure 41. 23Na NMR spectra of Na+C222 ° Na- solutions
(=0.1 M) in three solvents. All chemical shifts

are referenced to aqueous Na+ at infinite
dilution.

140

the narrowness of this line. The complexed cation, Na+C222
has a chemical shift which is also nearly independent of
solvent and is at the same position as for ordinary salts
of Na+C222 in these solvents. By contrast the solvated
cation, Na+, is strongly solvent—dependent (Table XXII).

The chemical shift of Na- is not only independent of
solvent, but is also nearly the same as that of Na- in
the gas phase. This is completely different from that of
any ion with filled outer p orbitals (including halide
anions) as indicated in Table XXII. As discussed in Chapter
IV, a paramagnetic shift of an ion is caused by the overlap
(KY model) of outer s and p orbitals of the solvent molecules
with the outer p orbital of the ion. Inner orbitals are
not considered, since they are tightly bound and do not
extend appreciably between nearest neighbors. The absence
of a chemical shift for Na“ shows that the 22 orbitals
are well shielded from the solvent by the presence of the
filled 3g_orbital. This would not be the case for any
model shown in Figure 39. We conclude therefore that the
most reasonable model for Na‘ is that of a centro-symmetric
anion with two electrons in the outer s orbital. It is not
obvious why the shift is as small as it is, since interaction
with the solvent to cause mixing of s and p character could
yield a paramagnetic shift. Perhaps the large size of the

anion causes the chemical shift to be small.

 

 

 

141

The extreme narrowness of the line for Na“ also attests
to the high spherical symmetry of this species. Quadrupolar
broadening of 23Na NMR lines is common (see Table XXII) and
results from an electric field gradient at the nucleus. Even
such presumably symmetric cations as Na+(aq) are quadrupole
broadened to 5 Hz (full width at half-height). By contrast,
the true linewidth of Na" in THF is less than 3 Hz compared
with 23 Hz for Na+ in THF. Since the lines may also be

broadened by the presence of e; via a paramagnetic inter-

olv
action, it is difficult to obtain the true quadrupole-broadened
linewidth. The relative concentration of esolv tends to vary
from one sample to another depending upon the solvent used

and the method of preparation. Therefore, we find that the
linewidths are not completely reproducible. Since exchange

of sodium between Na‘ and either Na+C or Na+ would also

broaden the line we cannot completely rule this out. However,
it seems unlikely since the linewidth of Na“ does not decrease
markedly as the temperature is lowered.

Just as for Na‘, Rb_ and Cs- give narrow lines which are
diamagnetically shifted from the corresponding cations by a
large amount. The NMR absorptions of Rb+C and Cs+C were not
observed in the M+C, M' samples, probably because of line—
broadening. The signal-to-noise ratio was satisfactory for
observation of the narrow Rb” and Cs‘ lines but not for the

broad lines expected for Rb+C and Cs+C. Studies with salts

indicate that the linewidth of Rb+C is far too broad to have

142

been observed in the metal solution case. The situation for
the case of Cs+C is not as clear. If the linewidth were in
excess of 200 Hz the signal would have been lost in the noise.
In methanol at 250C the linewidth of Cs+C (iodide salt) is

30 Hz. It might be expected to be much broader in THF at
—7lOC. The aqueous Rb+ and Cs+ ions are paramagnetically
shifted 212 and 344 ppm from the respective gaseous atoms.
Values for the gaseous anions are not known but are presumably
shifted diamagnetically a few ppm from the atoms. The reson—
ance positions of Rb’ in EA and THF are shifted 26 and 14 ppm
paramagnetically from the atom and Cs“ in THF is shifted 52
ppm. Although the shielding constants are not as close to the
gaseous anions as for the case of sodium, they are very close
compared with the range of chemical shifts for the correspond—
ing solvated cations.]-l0'148 The linewidth of Rb" in THF,

15 Hz, is much narrower than that of the Rb+ ion in any
solvent. However, this is not the case for Rb" in EA or Cs‘
in THF which have linewidths comparable to those of the sol—

vated cations. It is likely that the lines of Rb" and Cs-

r b ad-
solv or a e ro

are either paramagnetically broadened by e
ened by exchange.

In conclusion, the NMR studies described in this chapter
and the recent isolation of a crystalline salt of the sodium

36'37 are the most convincing evidence that genuine

anion
alkali anions exist in solution as well as in the crystalline

state.

APPENDICES

APPENDIX A

MODIFICATION OF RELAX 2

The data output portion of RELAX 2, a program written
by David Wright128 of Michigan State University for computer
controlled timing and data acquisition for two—pulse experi—
ments was slightly modified in order to dump data from the

Nicolet 1083 computer. The modifications are

 

 

143

Core Location Instruction
1310 2001607
1311 2001607
1312 2110577
1313 2404606
1314 2332600
1315 0005144
1316 0000001
1317 2000206
1320 0001346
1321 3110606
1322 3001326
1323 0001327
1324 2000206
1325 0001346
1326 0005051
1327 2124606

1330

1331

1332

1333

1334

1335

1336

1337

1340

1341

1342

1343

1344

1345

1346

1347

1350

1351

1352

1353

1354

1355

144

2000206
0001346
3110606
3001326
0001340
2000206
0001346
3001563
2001607
2134606
0006454
0162000
0000155
0001314
2404040
0000000
0000037
0001646
2165350
2001404
2001413

2125560

APPENDIX B

PROGRAM CONVERT

Program CONVERT converts data from octal to decimal

in a form compatible with KINFIT.

100
10

105

110

15

115

116

999

PR¢GRAM C¢NVERT(INPUT=65,¢UTPUT=65,PUNCH=65)
DIMENSI¢N IX(2), IY(2),X(2),Y(2)
DATA(MASK=77777777777773777777B)

READ 100,A,B

IF (E¢F(5LINPUT))999,10

F¢RMAT (2310.2)

READ 105,(IX(I),IY(I),I=1,2)

IF (E¢F (5LINPUT))5,8

F¢RMAT (2¢10)

PRINT 110,(IX(I),IY(I),I=1,2)

F¢RMAT (1x,2310)

D¢ 15 K=1,2
IF(IY(K).GE.2000000B)IY(K)=IY(K)+MASK
X(K)=IX(K)

Y(K)=IY(K)

PRINT 115,(X(K),A,Y(K),B,K=1,2)
F¢RMAT (2(20X,F10.0,F10.8,F10.0,F10.0))
PUNCH 116,(X(K),A,Y(K),B,K=1,2)

F RMAT (2)F10.0,F10.8,F10.0,F10.0))
G¢ T¢ 10

C¢NTINUE

END

145

APPENDIX C

SOLUTION TO MODIFIED BLOCH EQUATIONS

The Bloch equations which describe the motion of the X
and Y components of magnetization in the rotating frame, when

modified to include chemical exchange, are given by

1

G 1

dGA/dt + a G = -1YH + B-TA GA C1

A A 1MOA TB

1

_ . - 1
dGB/dt + aBGB _ 1YH1MOB + TA G

A-TB GB C2

The solution to these equations for slow passage conditions
is obtained by setting dGA/dt = dGB/dt = 0 and solving C1
and C2 for the total complex moment G = G + GB. Solving

A
for GA in C1 gives

1
(a + -—)
A TA

 

Substitute C3 into C2 and solve for G

 

 

aBGB = -1YH1MOB + - TB GB C4
(a +-JL)T
A TA A
iYHlMOA
(”lYHlMOB - WT)TB(GATA + 1)
GB = C5

[(aBIB + l)(aAIA + 1)-1]

146

147

and from inspection

in M
. 1 OB
( 1YH1MOA " WHAWBTB + 1)
B B
[(dATA + 1)(aBIB + 1) -1]

 

G = G + G = u.+ iv C7

inlMOB
IMOA — GBTB+1)TA(aBTB

G = {(-in + 1)

lYHIMOA

IMOB ’cfigfi;fif"°TB(aATA + 1)}/

+ (—in

{(aATA + l)(C1BTB + 1) — 1} ca

T T
. __ A __ B

 

 

and for low values of the radio frequency field P M = M

A O OA'
PBMO = MOB
PB
G = ~inlMO{(PA + 3;?31T)TA(aBIB + 1)
P
+ (P +—-—L—)T (0LT +1)}/
B GATA+1 B A A

{(aAIA + l)(aBTB + 1)—l} C9

 

 

 

 

148

or G = -in1MO{(PAaBTB + PA + PB)TA + (PBaATA + PB + PA)TB}/
{(aAIA + 1)(aBIB + 1) — 1)} C10
Since PA + PB = 1
G = -inlMO{(PAaBTBTA + TA + PBQATATB + TB)}/
{(aAIA + 1)(0LBTB + 1) - 1} C11
or
G = -inlMO{(TA + TB) + IAIB(aAPB + aBPA)}/
{(aAIA + 1)(0LBIB + 1) - 1} C12

as first obtained by Gutowsky, McCall, and Schlicter.139

To obtain the absorption and dispersion mode shape functions,

one must separate the real and imaginary parts of Equation C12.
TATB
TA+TB

 

Define T =

G IA+TB+TATB(aAPB+aBPA)

. = C13
—inlMO aAaBTAIB+1+aBIB+aAIA-1

 

Let Y =

dividing numerator and denominator of C13 by (TA + TB)

 

T T T T
A B A B

TA+TB + TA+TB + IA+TB(QAPB+QBPA)

Y = C14

TATB a
TA+TB A B

 

 

 

149

 

 

 

notePA+pB=1= f + +3
TA TB TA TB
Thus
1 + T(a P + a P )
Y = A B B A (:15
TaAaB + PBaB + PAaA
1 1
Let k = ——-, k = ———
A TZA B TZB
then 0A = kA-1(wA-w), aAPA = kAPA-iPA(wA-w)
dB = kB-1(wB—w), aBPB = kBPB—IPB(wB-w)

 

 

Let kAPA - KA, kBPB - KB
and QA = PA(wA-w), QB = PB(wB-w)
aAaBPAPB (KA—iflA)(KB-108)
Then aAdB = P P = P P
A B A B

and C15 becomes

1+I{(k p +k p )-i[P (w -w)+P (w -m)]}
Y: ABBA BA AB C16
(K -i0 )(K —i0 )
T[ A 2 P B B ] + (KA+KB)-i[QA+QB]
A B

 

 

1+I{(kAPB+kBPA)-1[PB(wA-w)+PA(wB-w)J}
Y = C17
(K K -0 Q -i(0 K +0 K )
A B A B A B B A .
T[ PAPB J + KA+KB-1[QA+QB]

 

 

150

 

 

 

 

 

or
Y = l+I{(kAPB+kBPA)-1[PB(wA—w)+PA(wB-w)]}
(K K -0 Q ) (0 K +0 K )
A B A B . A B B A
K +K +1 -1[(Q +9 )+T
A B PAPB A B PAPB
(K K -0 Q )
B P P
A B
R K +9 K
T = 9A + QB + T( A B B A)
P P
A B

U = 1 + T(kAPB + kBPA)

V = T[PB(wA-w) + PA(wB-w)]
Substituting C19-C22 into C18 gives

U~iV (U-iV)(S+iT)

 

 

 

Y=-——-.—-=
S-lT 82+T2

Y (SU+TV) + i(UT—SV)

‘ 2 2

S +T
and

— _- - [-i(SU+TV) + (UT-SV)]

G — inlMOY - +YHlMO 2 2

S +T

C18

C19

C20

C21

C22

C23

C24

151

 

 

 

 

 

 

Define I = + Léfligyl' absorption mode shape function
2 2
S +T
R = igglgyl, dispersion mode shape function
2 2
S +T
and G = u + iv = yHlMO[R-iI] C26
where
P P PP
_ A B 1: [AB
S——+—-—+ —PP(w-w)(w-w)] C27
T2A T2B PAPB T2AT2B A B A B
P P
A B T
S = ———--+-——— + ——~———--'r0n -w)(w -w) C28
T2A T2B TZATZB A B
P P
U = 1 + T(TIL + TEL) C29
2A 2B
P P P P
B A A B
T=P(w-w)+P(w-w)+ T[ (w-w)+-—(w-w)] C30
AA B B PAPB T2B A T2A B
wA—w wB-w
T = P w -P w+P w -P w + T( + ) C31
AA A BB B T2B T2A
wA-w wB-w
T=Pw +Pw—w+( + )T C32
AA BB T2B T2A
and
V = T[PB(wA—w) + PA(wB-w)] C33

152

V = TEPBwA + PAwB-w]

In summary, the complex moment, G(w), is given as

 

 

G(w) = u + 1V = yHlMO[R—11]
R = 12%:§%L, dispersion mode
S +T
I = 1§§i§¥1l absorption mode
S +T
where
P P
A B T
S=—+-———+———-—-I(w -w)(w -w)
T2A T2B TZATZB A B
P P
U=1+T(-,i,—§—+-T-B—)
2A 2B
w —w w —w
A B
T = P w + P w - w + T( + )
AA BB T2B T2A
V = TEPBwA + PAwB-w]

C34

C35

C36

C37

C38

C39

C40

C41

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’b’b’b’b

 

 

 

 

   

 

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