A CESIUM - 133 NMR STUDY OF THE STAT'ICS AND ‘
DYNAMICS OF CESIUM ION COMPLEXATION BY CROWNS
AND CRYPTANDS IN VARIOUS SOLVENT S

Dissertation for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
ELIZABETH HUN-I MEI
1977

 

 

 

 

 

 

 

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This is to certify that the

thesis entitled
A CESIUM-133 NMR STUDY OF THE STATICS AND

DYNAMICS OF CESIUM ION COMPLEXATION BY

CROWNS AND CRYPTANDS IN VARIOUS SOLVENTS.
presented by

ELIZABETH HUN-I MEI

has been accepted towards fulfillment -
of the requirements for

_Eh._D..__ degree in Lhamisiry

c» y/f’fl “/4 wbjéz/x/

Major profes

Date NOV. LI', 1976

 

0-7 639

 

 

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.081“ 1 '9 23
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A CESIUM-l

CESIUM ICI

 

ABSTRACT

A CESIUM-l33 NMR STUDY OF THE STATICS AND DYNAMICS OF
CESIUM ION COMPLEXATION BY CROWNS AND CRYPTANDS IN

VARIOUS SOLVENTS

BY

Elizabeth Hun-I Mei

Chemical shifts of the cesium-133 nucleus were measured
in six nonaqueous solvents relative to 0.5 M aqueous cesium
bromide. Cesium tetraphenylborate (CsTPBT triiodide and
thiocynate were used to determine the infinite dilution
chemical shifts in pyridine (PY), propylene carbonate (PC),
dimethylformamide (DMF), dimethylsulfoxide (DMSO), aceto-
nitrile (MeCN), and acetone. The corresponding ion-pair
formation constants were determined from chemical shift
concentration data with the aid of a weighted nonlinear
least squares program (KINFIT). The association constant
for CsSCN in pyridine is 9001200 while for CsTPB in pyridine
it is 370120, in PC it is 1617, in MeCN it is 40:10, and in
acetone it is 2213. The uncertainties given are standard
deviation estimates.

Cesium-133 NMR studies were also performed on cesium
tetraphenylborate complexes with five ligands in the six

nonaqueous solvents mentioned. These ligands were 18-Crown-6

I18C6), dibenzo-
tad-€222 (C222)
have different t
cotplexation abi
1:1 and 2:1 (lig
solvents with th
103. A new £le

to analyze data

I2le formation.
fected by the ge
It IIas also show

in the equilibri

Complexation by

 

 

 

Elizabeth Hun-I Mei

(18C6), dibenzo-18C6 (DBC), dicyclohexyl-18C6 (DCC), cryp-
tand-C222 (C222), and monobenzo-C222 (C2228). These ligands
have different topologies and substituents which affect the
complexation ability. Cesium tetraphenylborate forms both
1:1 and 2:1 (ligand/Cs+) complexes with 18C6 in all six
solvents with the first formation constant (K1) larger than
103. A new EQN subroutine of the KINFIT program was written
to analyze data which show both 1:1 and sandwich complex
(2:1) formation. It was found that both K1 and K2 are af-
fected by the geometry and substituents of the crown ligands.
It was also shown that the solvent plays an important role
in the equilibrium process. For example, the K values for

8, K = 71:1,

2
in PC K1 = (1.5t0.6) x 104, K2 = 8:2, in acetone K1 > 107.

x2 = 3410.5, in our K1 = (9:3) x 103, K2 = 2.44:0.05, in

DMSO K

complexation by 18C6 in pyridine are 2K1>10

1 = (1.1:0.1) x 103, K2 = (110.4) and in MeCN K1 >

105, K2 = 4.4:0.3. The attachment of a substituent on the
ring of 18C6 yielded values of K1 in the order 18C6 > DCC >
DBC. However, probably because of steric effects, the K2
values are in the order DBC > 18C6 > DCC (at least in pyri-
dine).

A thorough study of 18C6 complexes with CsTPB in pyri—
dine was made at various temperatures (from 25° to -44°C).
For the purpose of this study a new temperature independent
reference was designed. Its validity was tested and it

was used to show that ion-ion and ion-solvent interactions

give temperature-dependent chemical shifts. The values of

 

the first format
too large to be c
were determined
changes for the
152 = -6.2:0.1 K
152 = -ll.2:0.3
reaction of (35+.

KCdl/mole.

 

The fomati
Vere also obtain
t .

*Cmatlon consta

solvents . For i

x102 (Dm) ' (27
2228, with a bet:
weaker complexes
ZPYI to Zero (DH!

a?
45
‘endent studie

F .
o. kinetics B
' C

i
n the Solution

A;
”- th

e formation
0f CS+

 

Elizabeth Hun-I Mei

the first formation constant at various temperatures were
too large to be determined by NMR techniques but K2 values
were determined and used to obtain the enthalpy and entropy
changes for the second complexation step. The results are:

AH2 = -6.210.l Kcal/mole (A63) = -2.8310.004 Kcal/mole,

298
A82 = -ll.210.3 e.u. A kinetics study of the decomplexation
reaction of Cs+-18C6 gave an activation energy of 810.3
Kcal/mole.

The formation constants of C222 and C2228 complexes
were also obtained from the NMR chemical shift data. The
formation constants showed the same trends with various
solvents. For instance, K1 values for C222 are >105 (PY),

3 (pc), (10.810.8) x 103 (acetone), (1.510.1)

4

(1011) x 10
x 102 (one), (2713) (DMSO), and (411) x 10 (MeCN). Cryptand—
2228, with a benzo group on one of the ether chains forms
weaker complexes, with K values ranging from (5.710.8) x 103
(FY) to zero (DMSO). Chemical shift-mole ratio temperature
dependent studies were also carried out, as well as studies
of kinetics. Both gave evidence for two types of complexes
in the solution. The results are interpreted on the basis
of the formation of both inclusive and exclusive complexes
of Cs+ by C222. Enthalpies and entropies of formation were
also calculated by using the KINFIT program and it was found
that both quantities are sensitive to the solvent for the
complexation of free cesium ions to form the exclusive

complex. The conversion of the exclusive to the inclusive

complex is much less sensitive to solvent. The activation

 

energy (Ba) for t
I

CsTPB in PC is 1~
obtained from kit
are Ea = 8.510.5
(for 18C6) . It 5
restricted geome°

the largest acti~

ion.

 

 

Elizabeth Hun-I Mei

energy (Ea) for the complexation reaction of C2228 with
CsTPB in PC is 14:0.6 Kcal/mole. By comparison the values
obtained from kinetics studies of crown complexes in PC

are Ea = 8.5i0.5 Kcal/mole (for DCC) and E3 = 814 Real/mole
(for 18C6). It appears that the higher rigidity and
restricted geometry of the ligand combine to give C2228

the largest activation energy for removal of a cesium

ion.

A CESIUM
ornnnn

CROWN S

 

1n Par+

 

 

A CESIUM-l33 NMR STUDY OF THE STATICS AND
DYNAMICS OF CESIUM ION COMPLEXATION BY

CROWNS AND CRYPTANDS IN VARIOUS SOLVENTS

BY

ELIZABETH HUN-I MEI

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirement

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1977

To My Parents.

ii

 

The author
Professors Jan
guidance, enc<
out this study

Gratitude
Michigan State
Ildmirtistratior,
financial aid.

Special th
brother Dr. Ed
meflt and SuggeI
to the memberd
and PrOfeSSOr
moral Support,

Natty thaw
Frank Bennie. A
eter in operaq

I am deepl
love and Cordi

I dedicate thi

 

ACKNOWLEDGMENTS

The author wishes to express her sincere gratitude to
Professors James L. Dye and Alexander I. Popov for their
guidance, encouragement and whole-hearted support through-
out this study.

Gratitude is also extended to the Department of Chemistry,
Michigan State University, the 0.8. Energy and Development
Administration and the National Science Foundation for
financial aid.

Special thanks go to my Uncle Dr. Tony S. Shen and my
brother Dr. Howell H. Mei for their constant encourage-
ment and suggestions in many ways. Thanks are also extended
to the members of the research groups of both Professor Dye
and Professor Popov for their constant stimulation and
moral support.

Many thanks also go to Mr. Wayne Burkhardt and Mr.

Frank Bennis for their efforts in keeping the NMR spectrom—
eter in operating condition.

I am deeply grateful to my parents for their great
love and cordial concern throughout all my life. To them

I dedicate this thesis.

iii

 

Chapter

LIST OF TABLES

 

LIST 01’ FIGURE

   
   
 
 

omens I. n:

l. INTROU

II. HISTOE
3- Ma

P

3 Co

Ma

C Nu

(j

(1‘

(ii

III CONCLr
AND L]

II' SOLVEe
PREPAI

III, THE: N»
AND D}:
EESIUM is
VOMPLBXES
ARIOU So
INTRO);

I1_ .
bIINVEST

Chapter

LIST OF

LIST OF

CHAPTER
1.

II.

III.
CHAPTER

I.
II.
III.

CHAPTER

TABLE OF CONTENTS

TABLES. . . . . . . . . . . . . . . .
FIGURES . . . . . . . . . . . . . . .
I. HISTORICAL. . . . . . . . . . . .
INTRODUCTION. . . . . . . . . . . . .
HISTORICAL BACKGROUND . . . . . . . .

A. Macrocyclic Polyether-Crown Com-
plexation of Alkali Metal Ions. .

8. Complexation of Metal Ions by

Macroheterocyclic Ligands-Cryptands

C. Nuclear Magnetic Resonance. . . .
(i) Introduction . . . . . . . .

(ii) Chemical Shift Studies of
Electrolyte Solutions. . . .

(iii) Cesium Nuclear Magnetic
Resonance. . . . . . . . . .

CONCLUS IONS . O C O O C C O O O O O C
II. EXPERIMENTAL PART. . . . . . . .

SYNTHESIS OF CESIUM TETRAPHENYLBORATE
AND LIGAND PURIFICATION . . . . . . .

SOLVENT PURIFICATION AND SAMPLE
PREPARATION . . . . . . . . . . . . .

THE NMR SPECTROMETER; MEASUREMENT
AND DATA HANDLING . . . . . . . . . .

III. STUDY OF FORMATION CONSTANTS OF

CESIUM TETRAPHENYLBORATE ION PAIR AND OF
COMPLEXES WITH MACROCYCLIC LIGANDS IN
VARIOUS SOLVENTS. . . . . . . . . . . . .

I.

II.

INTRODUCTION. . . . . . . . . . . . .

INVESTIGATION OF CESIUM SALTS IN
NONAQUEOUS SOLVENT s o o o o o o o o 0

iv

Page

vii

xiv

15
25
25

27

38
43
44

45

47

52

57
58

59

Chapter

III. FORMA'
PHENYI
AND Cl

IV. TEMPE?
SHIFT
omen.

 

 

 

Chapter

III. FORMATION CONSTANTS OF CESIUM TETRA-
PHENYLBORATE COMPLEXES WITH cnowns
AND CRYPTANDS IN VARIOUS SOLVENTS . . . .

(i) Complexation Reactions with
Crowns . . . . . . . . . . . . .

(ii) Complexation Reactions with
Cryptands. . . . . . . . . . . .

IV. TEMPERATURE DEPENDENCE OF THE CHEMICAL
SHIFT AND ITS RELATIONSHIP TO THE THERMO-
DYNAMICS OF COMPLEXATION REACTIONS. . . .

A. CESIUM TETRAPHENYLBORATE COMPLEXES
WITH 18C6 IN PYRIDINE . . . . . . . .

B. CESIUM TETRAPHENYLBORATE COMPLEXES
WITH C222 IN VARIOUS SOLVENTS . . . .

CHAPTER IV. A STUDY OF THE DYNAMICS OF
CESIUM TETRAPHENYLBORATE COMPLEXES
WITH CROWNS AND CRYPTANDS . . . . . . . . . .
I. INTRODUCTION. . . . . . . . . . . . . . .

II. DETERMINATION AND INTERPRETATION OF
THE LINESHAPES O O O 0 C C O O O O O O O O

A. MEASUREMENTS IN THE ABSENCE
OF EXCHANGE O O O I O O O C O O O O O

B. EVALUATION OF EXCHANGE TIMES. . . . .
III. RESULTS AND DISCUSSION. . . . . . . . . .
A. LIGAND EFFECT ON EXCHANGE RATE. . . .

B. SOLVENT EFFECT ON THE EXCHANGE
PROCESSES O O O O O O O O I O O C O O

C 0 DISCUSSION 0 O C C C C O C C I O O O 0
CHAPTER V. A CESIUM-133 NMR STUDY OF THE
COMPLEXATION OF CESIUM TETRAPHENYLBORATE
BY C222: DISCUSSION OF THE TYPES OF
COWLEXES O I O C O C O O O O I O O O O O O O

I 0 INTRODUCTION 0 O O O O O O O O O O I O O O

Page

68

89

99

109

109

125

142

143

143

144
151
152
152

168
183

186
187

 

Chapter
II. EVIDENI
COMPLEZ

CHAPTER VI. ST.
FUTURE STUI

I. L'nvaet
II. scones:
termites
APPENDIX A.
APPENDIX 3.
APPENDIX c.
APPENDIX D.

PEFEREXCES ,

 

 

Chapter Page

II. EVIDENCE FOR TWO TYPES OF CRYPTATE

COMPLEXES . . . . . . . . . . . . . . . . 187
CHAPTER VI. SUMMARY AND SUGGESTIONS FOR

FUTURE STUDIES. . . . . . . . . . . . . . . . 201

I. SUMMARY . . . . . . . . . . . . . . . . . 202

II. SUGGESTIONS FOR FUTURE STUDIES. . . . . . 205

APPENDICES

APPENDIX A. . . . . . . . . . . . . . . . . . 208

APPENDIX B. . . . . . . . . . . . . . . . . . 212

APPENDIX C. . . . . . . . . . . . . . . . . . 221

APPENDIX D. . . . . . . . . . . . . . . . . . 235

REFERENCES. . . . . . . . . . . . . . . . . . . . 238

vi

 

Table N

l Thermodyne

Reactions
2 Thermodan

Cryptate

by Calorie
3 Trends in

crYPtands
4 Values of
A. and thé
Alkali Me‘
Values of
TechfiiqUES
The phYsi
Nucleus .
Physical 3
Correctior
on DA-GO.
cesium-l3

Salt SQIUI

10

 

LIST OF TABLES
Table Page

1 Thermodynamic Quantities for Complexation

Reactions of Macrocyclic Polyethers . . . . ll
2 Thermodynamic Quantities for Alkali

Cryptate Complexation Reaction Measured

by Calorimetry at 25°C in Water . . . . . . . 22
3 Trends in Thermodynamic Parameters with

Cryptands . . . . . . . . . . . . . . . . . . 21
4 Values of the Average Excitation Energy,

A, and the Expectation Value <r;3>p for

Alkali Metals . . . . . . . . . . . . . . . . 33
5 Values of qu Obtained by Various

Techniques. . . . . . . . . . . . . . . . . . 37
6 The Physical Properties of the Cs-133

Nucleus . . . . . . . . . . . . . . . . . . . 38
7 Physical Properties of Solvents and

Correction for Magnetic Susceptibility

on DA—60. . . . . . . . . . . . . . . . . . . 55
8 Cesium-133 Chemical Shifts of Cesium

Salt Solution at 25°C . . . . . . . . . . . . 60
9 Ion Pair Formation Constants of Cesium

Salts in Various Nonaqueous Solvents. . . . . 67
10 Mole Ratio Study of 18C6 Complexes

with Cesium Salts in Various Solvents

by Cs-133 NMR at 25°C . . . . . . . . . . . . 72

vii

 

Table

11

12

13

14

15

16

17

18

19

Hole Ratit
CsTPB in J
at 25°C .
Mole Rati'
CsTPB in 1!
NMR at 25'
Mole Ram
CsTPB in x
at 25°C .
Ible Ratig
CsTPB in I
at 25°C .
Formation
with LigaI
Mole Ratic
with CSTpr
‘38°C .
Limiting (

SOlVents .

 

 

Half‘heig3
I

1 Va]

+ 0
CS ‘nganc

L09 K

 

Table

11

12

13

14

15

16

17

18

19

Mole Ratio Study of BBC Complexes with
CsTPB in various Solvents by Cs-133 NMR
at 25°C . . . . . . . . . . . . . . . . .
Mole Ratio Study of DCC Complexes with
CsTPB in Various Solvents by Cs-133

NMR at 25°C . . . . . . . . . . . . . .
Mole Ratio of C2228 Complexes with

CsTPB in Various Solvents by Cs-133 NMR
at 25°C . . . . . . . . . . . . . . . . .
Mole Ratio Study of C222 Complexes with
CsTPB in Various Solvents by Cs-133 NMR
at 25°C . . . . . . . . . . . . . . . . .
Formation Constants of CsTPB [0.01 M]
with Ligands in various Solvents (25°C) .
Mole Ratio Study of 18C6 Complexes

with CsTPB in Pyridine at 24°C, -6°C,
-38°C . . . . . . . . . . . . . . . . . .
Limiting Chemical Shifts in Various
Solvents. . . . . . . . . . . . . . . . .
Half-height Linewidth (Ava Hz) of
Cs+-Ligand Complexes at 24°C. . . . . . .

Log K Values of Cesium Salts with

1
Ligands in Various Solvents (25°C). . . .

viii

Page

75

77

79

81

88

93

97

101

108

Table

20 Concentr
Shift at
Complex

21 Data fro
Referenc

22 hole rat

Chemical

 

0f 18C6 :
23 The Simui
and Least
for the c
borate by
TemPeratu
24 Limiting
Complex a
for the p
1" Pyridi
25 Hole RatN

ChemICal

26 Hole Rati

ChemiCal
the preSq
27 Hole Rati

ChemiCal

presenCe

 

Table

20

21

22

23

24

25

26

27

Concentration Dependence of the Chemical
Shift at 25°C for CsTPB and its 1:1

Complex with 18C6 in Pyridine . . . . . . . .
Data from the Test of the Insulated
Reference Tube. . . . . . . . . . . . . . . .
Mole ratio-Temperature Data for the

Chemical Shift of CsTPB in the Presence

of 18C6 in Pyridine . . . . . . . . . . . . .
The Simulated Formation Constant (K1)

and Least-Squares Adjusted Constant (K2)

for the Complexation of Cesium Tetraphenyl-
borate by 18C6 in Pyridine at various
Temperatures. . . . . . . . . . . . . . . . .
Limiting Chemical Shift of the Cs+-(18C6)2
Complex and the Thermodynamic.Parameters

for the Reaction Cs+-18C6 + 18C6 I Cs+-(18C6)2
in Pyridine at Various Temperatures . . . . .
Mole Ratio-Temperature Data for the

Chemical Shift of CsTPB [0.02 M] in the
Presence of C222 in PC. . . . . . . . . . . .
Mole Ratio-Temperature Data for the

Chemical Shift of CsTPB [0.01 M] in

the Presence of C222 in PC. . . . . . . . . .
Mole Ratio-Temperature Data for the

Chemical Shift of CsTPB [0.02 M] in the

presence of C222 in DMF . . . . . . . . . . .

ix

Page

111

119

121

123

126

128

129

130

 

Table

28

N

30

31

32

M

Mole Rati
Chemical
Presence
Mole Rati
Chemical
Presence
Formation
Chemical
0f CsTPB
Temperatt
FOrmatior
Shifts f<
C222 in E
“manor
Chemical
Cf CSTPB

AcetOne a

Table

28

29

30

31

32

33

34

Mole Ratio-Temperature Data for the
Chemical Shift of CsTPB [0.01 M]in the
Presence of C222 in DMF . . . . . . . . .
Mole Ratio-Temperature Data for the
Chemical Shift of CsTPB [0.02 M] in the
Presence of C222 in Acetone . . . . . . .
Formation Constants and Limiting
Chemical shifts for the Complexation

of CsTPB by C222 in PC at Various
TemperatureS. . . . . . . . . . . . . . .
Formation Constants and Limiting Chemical
Shifts for the Complexation of CsTPB by
C222 in DMF at Various Temperatures . . .
Formation Constants and Limiting
Chemical Shifts for the Complexation

of CsTPB [0.02 M] by c222 in

Acetone at Various Temperatures . . . . .
Thermodynamic Parameters for the
Complexation of CsTPB by C222 in

Various Solvents. . . . . . . . . . . . .
Temperature Dependence of the

Transverse Relaxation Times for

Free and Complexed Cesium Cations

in Propylene Carbonate. . . . . . . . . .

Page

131

132

137

138

139

140

147

 

Table

36

37

38

39

40

TemperatuI
RelaxatioI
in the Pre
Temperatu:
Time T, o
Propylene
Reciproca
Time of c
B). . .

TemPeratu
Time in PI
the Corre
RElaxaticI
IB) . . .
Exchange I
Parameter
Some Cesi
proleene
Tempe”tu
RelaXatiC‘
Com918xed
Temperatu
Relaxatio

(C222) CE)

 

Table Page

35

36

37

38

39

40

Temperature Dependence of the Transverse

Relaxation Times in Propylene Carbonate

in the Presence and Absence of C222 . . . . . 148
Temperature Dependence of the Exchange

Time I, of Some CsC+ Complexes in

Propylene Carbonate and Corresponding

Reciprocal Transverse Relaxation

Time of Cs+ (Site A), and CsC+ (Site

8). . . . . . . . . . . . . . . . . . . . . . 161
Temperature Dependence of the Exchange

Time in PC in the Presence of C222 and

the Corresponding Reciprocal Transverse

Relaxation Times of Cs+ (A) and Cs+C222
(8)162
Exchange Rates and Thermodynamic

Parameters for Release of Cs+ from

Some Cesium Macrocyclic Complexes in

Propylene Carbonate . . . . . . . . . . . . . 166
Temperature Dependence of the Transverse

Relaxation Times of Free and 18C6-

Complexed Cesium Cation in Pyridine . . . . . 172
Temperature Dependence of the Transverse

Relaxation Time of Free and Complexed

(C222) Cesium Cation in DMF . . . . . . . . . 173

xi

 

Table

ll Temperatu

Q

43

44

4S

46

47

Relaxatio
Cesium Ca
Temperatu
Time in t
and the (

Vers e R~e

CsC+ (B)
Temperat
Time in
and the
Verse F
Csc+ (r
Tempere
Time it
the CO
Relaxa

Table

41

42

43

44

45

46

47

Temperature Dependence of the Transverse

Relaxation Time of Free and Complexed (C222)

Cesium Cation in Acetone. . . . . . . .

Temperature Dependence of the Exchange

Time in the Presence of 18C6 in Pyridine

and the COrresponding Reciprocal Trans-
verse Relaxation Times of Cs+ (A) and
Csc+ (B). . . . . . . . . . . . . . . .
Temperature Dependence of the Exchange
Time in the Presence of C222 in Acetone
and the Corresponding Reciprocal Trans-
verse Relaxation Times of Cs+ (A) and
Csc+ (8). . . . . . . . . . . . . . . .
Temperature Dependence of the Exchange
Time in the Presence of C222 in DMF and

the Corresponding Reciprocal Transverse

Relaxation Times of Cs+ (A) and CsC+ (8).

Exchange Rates and Thermodynamic Param-
eters of 18C6 Complex Exchange in
Propylene Carbonate and Pyridine. . . .
Test of the Dependence of the A82 Value
onde.................
Estimated Enthalpies of Formation of
the Exclusive (A81) and Inclusive (A82)

in Acetone, PC and DMF. . . . . . . . .

xii

Page

174

176

177

178

184

195

195

 

Table

48 Estimate
Complexa
49 Activati

Release

 

 

Table Page

48

49

Estimated Entropy Values for the
Complexation Reaction at 298°K. . . . . . . . 198
Activation Parameters for the

Release of Cs+ from Cs+C222 in DMF. . . . . . 200

xiii

 

Figure

10
11

12

Diben
NaBr-
CsNCS
Crypt.
Newly
CIth;
The F:
near
field
centre

133CS

t0 inI
tempe]
(C) 3:
Paris)
APpar;
Prepai
VESSe)
vesSeI
Block
magnet
Concer
Chemit

VarioK

 

Figure

UIthH

10
11

12

LIST OF FIGURES

Dibenzo-lB-Crown-G (DBC) . . . . . . .
Na8r-D8C-2H20 Crystal Structure. . . .
CsNCS-tetramethyl-DBC (1:1). . . . . .
Cryptand, C (k+1, mwl, n+1). . . . . .
Newly Synthesized macrotricyclic
cryptand . . . . . . . . . . . . . . .
The Frequency of the Cs resonance
near 28.013 MHz at fixed applied
field as a function of molar con-

centration in H2160, D2160, and H

133

18
2 o.

Cs Shift data (CsCl'MeOH) relative
to infinite dilution shifts at three
temperatures (a) 298°K; (b) 308.3°K;
(c) 326°K and (d) CsCl+H20 for com-
parison. . . . . . . . . . . . . . . .
Apparatus for storing solvent in the
preparation of NMR sample. . . . . . .
Vessel for solvent purification. . . .
Vessel for DMF purification. . . . . .
Block diagram of the multinuclear
magnetic resonance spectrometer. . . .
Concentration dependence of the Cs—133
chemical shifts of cesium salts in

various solvents . . . . . . . . . .

xiv

Page

15

19

41

41

49

50

51

53

64

 

Figure

13
14

15

l6

17

18

19

20

Crowns
Chemic
functi
TPB’]
0.01 N
Chemic
functi
in var
Chemic
a func
[CS+T
[CSTP
Chemi
a fun
[CS+T
[CSTP
Chemi
a fun
[CS+Tr
[Csrpg
N°nli
shift
Nonlir

Figure Page

13 Crowns and [2]-cryptands . . . . . . . . . 71
14 Chemical shifts of Cesium-133 as a

function of mole ratio of [l8C6]/[Cs+

TPB'] in various solvents. [CsTPB]T =

0.01 M . . . . . . . . . . . . . . . . . . 83
15 Chemical shifts of Cesium-133 as a

function of mole ratio of [D8C]/[Cs+TP8']

in various solvents. [CsTPB]T = 0.01 M. . 84
16 Chemical shifts of cesium-133 as

a function of mole ratio of [DCC]/

[Cs+TP8-] in various solvents.

[CsTPB]T = 0.01 M. . . . . . . . . . . . . 85
17 Chemical shifts of cesium—133 as

a function of mole ratio of [C2228]/

[Cs+TP8-]in various solvents.

[CsTPB]T = 0.01 M. . . . . . . . . . . . . 86
18 Chemical shifts of cesium-133 as

a function of mole ratio of [C2228]/

[Cs+TP8-] in various solvents

[CsTP8]T = 0.01 M. . . . . . . . . . . . . 87
19 Nonlinear curve fitting of chemical

shifts gs [18C6]/[Cs+TP8'] in DMSO . . . . 91
20 Nonlinear curve fitting of Chemical

shifts Kg [18C6]/[Cs+TP8-]in MeCN. . . . . 92

XV

   

Figure Page

21 A study of cesium-133 Chemical shift

!§_mole ratio [18C6/Cs+] at 24°, -6°,

-38°C in pyridine. [CsTPB]T = 0.01 M. . . 95
22 A typical fitting of a two step

reaction . . . . . . . . . . . . . . . . . 96
23 The interaction of solvent molecules

with complexed cesium ion. . . . . . . . . 102
24 Mole ratio - Cesium-133 chemical shift

study for various ligands in DMF . . . . . 104
25 Cesium-133 chemical shift variation

with the concentration of cesium salts

in pyridine. . . . . . . . . . . . . . . . 112
26 Insulated NMR reference sample . . . . . . 116
27 Test of the insulated reference

tube . . . . . . . . . . . . . . . . . . . 118
28 A three-dimensional plot of the cesium-

133 chemical shift gs mole ratio and

temperature (°C) for solutions of CsTPB

and 18C6 in pyridine. The concentration

of CsTPB was 0.01 M. . . . . . . . . . . . 122
29 A comparison of simulated data (0 )‘with

experimental data (A) for a chemical

shift-mole ratio study at 297°K and

235°K for solutions of CsTPB and 18C6

in pyridine. . . . . . . . . . . . . . . . 124

xvi

 

Figure

30

31

32

33

34

35

Cesiur

 

ratio
PIOPY
tempe
Cesiu
ratio
Prepy
tempe
Cesiu
ratic
at V6
A Plc
tion
aCet
A ty
133

Figure

30

31

32

33

34

35

Page

Cesium—133 chemical shift y§_mole

ratio of [C222]/[Cs+TP8'] in

propylene carbonate at various

temperatures . . . . . . . . . . . . . . . 133
Cesium-133 Chemical shift 22 mole

ratio of [C222]/[Cs+TP8-] in

prOpylene carbonate at various

temperatures . . . . . . . . . . . . . . . 134
Cesium-133 chemical shift !g_mole

ratio of [C222]/[Cs+TP8-] in acetone

at various temperatures. . . . . . . . . . 136
A plot of 2nK gs l/T for the complexa-

tion reactions of Cs+ with C222 in

acetone, PC, and DMF . . . . . . . . . . . 141
A typical KINFIT analysis of cesium—

133 lineshape for a solution containing

0.01 M CsTPB in propylene carbonate at

-46°C. . . . . . . . . . . . . . . . . . . 146
Semilog plots of 1/T; for the cesium-

133 nucleus gs 1/T for solutions containing
0.02 M CsTPB in the presence and absence

of various complexing agents. l/T; values

1

below about 15 sec- represent inhomogeneous

broadening . . . . . . . . . . . . . . . . 149

xvii

 

Figure

36

37

38

39

40

41

Semil
|
133 T:

tempe

 

0.02
PC..

Spect

repr
Ilef
of e
Spect
a so]
and I
Spec.
80
and

Spec

Wit

Figure

36

37

38

39

40

41

Page

Semilog plots of 1/T; for cesium-

133 nucleus reciprocal absolute

temperature for solutions containing

0.02 M CsTPB and 0.02 M Cs+C222 in

PC.. . . . . . . . . . . . . . . . . . . . 150
Spectra at various temperatures for

a solution containing 0.02 M CsTPB and

0.01 M C222 in PC. The dotted lines

represent the chemical shifts of CsC+

(left) and Cs+ (right) in the absence

of exchange. . . . . . . . . . . . . . . . 153
Spectra at various temperatures for

a solution containing 0.02 M CsTPB

and 0.01 M C2228 in PC . . . . . . . . . . 154
Spectra at various temperatures for

a solution containing 0.02 M CsTPB

and 0.01 M DCC (A) in PC . . . . . . . . . 155
Spectra at various temperatures for

a solution containing 0.02 M CsTPB and

0.01 M 18C6 in PC. . . . . . . . . . . . . 156
Computer fit of the spectrum obtained

with 0.02 M CsTPB and 0.01 M C222 in PC.

The mixture of dispersion and absorption

modes occurs because the first-ordered

phase correction was not made with the

spectrometer . . . . . . . . . . . . . . . 158

xviii

 

Figure

42

43

44

45

46

47

Com}
witl
(A)

Com;
witl
in I
Arrh
rate
1/T

Arrh
time
Pros:
SPCC'
a so.
18C6
CoaL
and .
POOr
chem:
the e
SPEC)
a soI
0.01
Show

in t.

Figure

42

43

44

45

46

47

Page

Computer fit of a spectrum obtained

with 0.02 M CsTPB and 0.01 M DCC

(A) in PC. . . . . . . . . . . . . . . . . 159
Computer fit of a spectra obtained

with 0.02 M CsTPB and 0.01 M 18C6

in PC. . . . . . . . . . . . . . . . . . . 160
Arrhenius of plots of 1 (Exchange

rates of Cs+ ion from ligands) gs

1/T for PC solution. . . . . . . . . . . . 163
Arrhenius plot of 1 (exchange

time of Cs+ ion from C222) for

propylene carbonate solutions. . . . . . . 164
Spectra at various temperatures for

a solution of 0.01 M CsTPB and 0.005 M

18C6 in pyridine. The linewidth at

coalescence were W400 Hz. This fact

and the low concentration lead to the

poor S/N. The dotted lines show the

chemical shifts of CsC+ and Cs+ in

the absence of exchange. . . . . . . . . . 169
Spectra at various temperatures for

a solution containing 0.02 M CsTPB and

0.01 M C222 in DMF. The dotted lines

show the chemical shifts of CsC+ and Cs+

in the absence of exchange . . . . . . . . 170

xix

 

Figure

48

49

50

51

52

Spec

 

0.01
line
CsC
exch

Semi

 

nucl
eith
in p
abOu‘
inhc
Sem:
133
tai
CSC
1/1
in'
Ar

CS

br

Figure

48

49

50

51

52

Page

Spectra at various temperatures for

a solution containing 0.02 M CsTPB and

0.01 M C222 in acetone. The dotted

lines show the chemical shifts of

CsC+ and Cs+ in the absence of

exchange . . . . . . . . . . . . . . . . . 171
Semilog plots of l/T; for cesium-133

nucleus 23 l/T for solutions containing

either 0.02 M CsTPB or 0.02 M Cs+-18C6

in pyridine. Values of l/T; less than

1 represent the effects of

about 10 sec-

inhomogeneous broadening . . . . . . . . . 175
*

Semilog plots of l/T2 for the cesium-

133 nucleus 35 1/T for solutions con-

taining either 0.02 M CsTPB or 0.02 M

CsC222+ in DMF and in acetone. Values of

1 represent

1/T; less than about 10 sec-
inhomogeneous broadening . . . . . . . . . 179
Arrhenius plots of 1 (exchange time for

Cs+ ion from 18C6) in propylene car-

bonate . . . . . . . . . . . . . . . . . . 180
Arrhenius plots of 1 (exchange time

for Cs+ ion from the ligand C222) in

DMF solution . . . . . . . . . . . . . . . 181

XX

 

Figure

53

54

SS

56

 

Arrh

for 1
solud
A le
0f CS
15 te

(dott

 

ConVe
SP801
Cs+cz
low

dOtt

Figure

53

54

55

56

Page
Arrhenius plot of r.(exchange time
for Cs+ ion from C222) in acetone
selution O O O O O O O O O O O O O O O O O 18 2

A plot of limiting chemical shift

of Cs+C222 in DMF, PC and acetone

XE temperature. The extrapolations

(dotted lines) for all three solvents

converge to the same value . . . . . . . . . 189
Spectra of solutions which contain the

Cs+C222 complex and uncomplexed Cs+ at

low temperatures in five solvents. The

dotted lines indicate the peak positions

of CsC222+ at room temperature . . . . . . 190
A comparison of simulated plot of limit-

ing chemical shifts of CsC222+ in PC
y§_temperature (°K) with experimental

value where 0 means simulated value

and x means experimental value . . . . . . 197

xxi

CHAPTER I

HISTORICAL

 

 

not C1
becau:
were :
fact,
and C
tion

teres
devel
POint
in th
thEir
trans
more

Ethel
SeSSt
alka
SYnt
1i9a
Sand
tion
one

“hit

rea<

We.

1. INTRODUCTION

For many years, complexes of alkali metal ions were
not considered an exciting area for chemical investigation,
because it was assumed by most chemists that the complexes
were neither stable nor important, and, as a matter of
fact, alkali salts were frequently used to achieve high
and constant ionic strength in solutions, when complexa-
tion with other metal ions was occurring. Recently, in-
terest in these alkali metal coordination complexes has
developed, both from the chemical and the biological
points of view, the latter because of their importance
in the metabolism of plants and liver mitochondria and
their significance as models for investigation of active
transport processes in general. The first synthetic ligand,
more or less specific for alkali catiors was a cyclic poly-
ether obtained by Pedersen in 1967 (1). The ligand pos-
sesses a bidimensional cavity which can accommodate an
alkali cation. Soon thereafter Lehn and coworkers (2)
synthesized cryptands which are diazapolyoxamacrocyclic
ligands with tridimensional cavities. Both types of li-
gand can form very stable alkali metal complexes in solu-
tion as well as in crystalline form. This fact enables
tone to more easily control and investigate the parameters
which determine the characteristics of the complexation
reaction.

During the past decade, it has been found that alkali

NMR spectra are very sensitive probes of the immediate

 

 

 

envir
mainl
ion b

nonaq

II

1964,
bioti
rat 1
and s
on mo
indue
Phore
the s
in ma
macro
promo
Chara.

in? S.

M!

Sized

environment of the alkali metal ion (3-7). This work
mainly concerns some aspects of the complexation of cesium
ion by crown and cryptand complexing agents in various

nonaqueous solvents as studied by Cs-133 NMR.

II. HISTORICAL BACKGROUND

Interest in the polyether type ligands has grown since
1964, when Pressman and Moore discovered that the anti-
biotic valinomycin exhibits alkali cation specificity in
rat liver mitochondria (8). Later, in 1966, Stefanaé
and Simon (9) showed by electromotive force measurements
on model membranes that alkali ion selectivity is mainly
induced through complex formation of the antibiotic ion-
phore with the cation in question. This observation was
the starting point which stimulated scientific interest
in macrocyclic complexation of metal ions. Synthetic
macrocyclic polyether- crowns and cryptand ligands have very
pronounced complexation abilities. Their special physical
Characteristics will be reported separately in the follow-

ing section.

(A) MACROCYCLIC POLYETHER-CROWN COMPLEXATION OF ALKALI

METAL IONS

 

More than 50 macrocyclic "crown" ethers were synthe-

sized by Pedersen, and many were found to solubilize

 

 

 

alka

of t

numbt
respe
the I

comp]

alkali metal salts in non-polar solvents. The structure

of the first crown compound, dibenzo-lB-crown-G (DBC)

is shown in Figure l, where ”18" and "6" indicate the total
number of atoms and the number of oxygen atoms in the ring
respectively. Ultraviolet and infrared measurements of

the D8C-KSCN system indicated the formation of a 1:1

complex (10). It was further shown that when the cation

. /
\._/°\__/

Figure 1. Dibenzo-lB-crown—G (88C).

was too large to fit in the central hole of a cyclic
polyether ligand, complexes with mole ratios of 1:2 or 2:3
(meta1:ether) could also be obtained (11). Some of the
larger ethers have been shown to complex two metal ions
simultaneously (12).

Truter 35 31. (13) determined the crystal structures

of several crown complexes. They showed that in the solid

 

 

tt
fO
in

Pec

(ii)

state, the alkali metal ion is located in the middle of
the polyether ring and the ligands are in a gauche con-
formation about the aliphatic carbon-carbon bonds. The
interesting features revealed in their work and that of

Pedersen are the following:

(1) When the number of oxygen atoms is even and no
larger than six, they are coplanar in the ring,
and the apex of the C-O-C angle is centrally
directed in the same plane. Symmetry is at a
maximum when all the oxygen atoms are evenly
spaced in a circle. When seven or more oxygen
atoms are present in the polyether ring and the
complexed cation is larger than the cavity diam-
eter, the oxygen atoms cannot assume a coplanar
configuration and, consequently, arrange them-
selves around the surface of a right circular
cylinder with the apices of the C-O-C angles

pointed toward the center of the cylinder.

(ii) The second interesting feature revealed was that,
even in the crystalline state, there are inter-
actions between the cation, anion and solvent
molecules, as shown in Figure 2 for the NaBr-
DBC-ZHZO complex (14). In this case, one sodium
ion in ring A, is in a hexagonal bipyramid of
oxygen atoms, six from the ligand and two axial.water

molecules. The sodium ion in ring 8 is attached

 

Figure 2. Na8r-D8C-2820 crystal structure.

(iii)

to a bromide ion, at one apex of a hexagonal
bipyramid, the ligand forming the equator and
water the other apex. The structure is held in

a chain by water-bromide and water-water hydrogen
bonds. Another example is the structure of the
1:1 compound CsNCS-tetramethyl-dibenzo-18C6 as
shown in Figure 3. The compound shows equal
sharing of the two thiocyanate ions between the
two metal ions and a somewhat unsymmetrical en-

vironment for cesium.

It was also found that the stoichiometry in a
unit cell may not necessarily be the stoichiometry

of the complex. For instance, the unit cell of

 

The

“are MC

 

 

Figure 3. CsNCS-tetramethyl-DBC (1:1).

a 3:2 RbSCN complex (15) contains four molecules
of a 1:1 RbSCN-08C complex and two uncomplexed

polyether molecules of crystallization.

The stability constant, K, of a complex is defined
by

K = [MCr+]/[M+JICr]

where MCr+ is the complexed ion formed from metal ion (M+)

 

 

and 1:

Va
stants
techni
select
(18).
goes t
P01yet
crown-l
betwee]
Sizes ;

the Ca.

and ligand (Cr) by the following reaction:

K
M+ + Cr 2 MCr+ (1.1)

Values of the stability constants (or formation con-
stants) have been measured by a calorimetric titration
technique (16), by potentiometric measurements with ion-
selective electrodes (17) and by spectroscopic methods
(18). These studies revealed that the stability constant
goes through a maximum for each cation with increasing
polyether ring size. The maximum for Na+ is between 15—
crown-S and lB-crown-6, for K+ is 18-crown-6: for Cs+
between 18-crown-6 and 21-crown-7. These optimum ring
sizes are those which provide the closest fit between
the cation and the ”hole".

Pedersen and Frensdorff (19) noted that very few data
are available on complexation reactions in solvents less
polar than methanol. In solvents of lower polarity, ion-
pair formation becomes significant so that the anion ef-
fects would be appreciable. Smid gt 21. (18,20-22) in-
vestigated the interactions of alkali metal ions and their
fluorenyl ion pairs with crown ethers in tetrahydrofuran
(THF) and tetrahydropyran (THP) by using Optical spec-
trosCOpy, distribution equilibria, conductances, and
viscosities. From their early conductance study (23,24)

in THF, it is known that at room temperature, the salt

 

exi

CIOI
5011
only
two

plex

pair

where

sents

s°lver
iOn pa
dipole
asSOci
Consta:
tic“, 1
metal j
detail.
talcum
alkali

exists predominantly as a tight ion pair but changes into
a solvent-separated ion pair at lower temperatures. When
crown ethers are added to fluorenyl salts in ethereal
solvents, complex formation occurs. In systems where
only 1:1 crown-ion pair complexes are formed, at least
two isomeric complexes can be found, i.e., a crown com-
plexed tight ion pair (FE,M+Cr) and a crown separated ion

pair (FI,CrM+) (25). The equilibria in the solution are,

F2“,M+ + Cr 2 F£-,M+Cr (1.2)
-+ +_+
Fe ,M + Cr + F£,CrM (1.3)
+ + +
ns + FI,M Cr + FI,CrM ,ns (1.4)

where MCfIdenotes a complexed crown molecule, Fn' repre-
.sents the fluorenyl carbanion and ns is the number of
solvent molecules interacting with the crown-separated
ion pair. A semi-theoretical calculation of the electric
dipole moment was used by Grunwald (26) to obtain the
association constant for ion-pairing. From the formation
constant, K, one can obtain the free energy of complexa-
tion, AGO. However, the entropy and enthalpy of alkali
metal ion complexation have not been studied in muCh
detail. Simon gt 31. (27-29) used a computerized micro-
calorimeter to study the thermodynamic properties of

alkali complexes of antibiotics, while Izatt gt_gl. (30-32)

 

 

 

also

to st
synth
1 rev
cycli
tive.
by Me
tingt
addit
from

IEplg

is al
Plexg
(DCC)
using
of e)
that

equi:

10

also use a precision thermometric titration calorimeter

to study the thermodynamics of formation of complexes of
synthetic macrocyclic polyethers. The data shown in Table
1 reveal that, for the complexation reaction of macro-
cyclic ligands, usually AHc and quite often, ASc are nega-
tive. This is caused by the macrocyclic effect described
by Margerum (37,38). He used this term in order to dis-
tinguish it from the chelate effect because there is an
additional enhancement in stability beyond that expected
from the gain in translational entropy when chelates
replace coordinated solvent from metal ions.

Kinetics information about these complexation reactions
is also very limited. Shchori gt_gl, monitored the com-
plexation of the sodium ion by DBC and dicyclo-hexyl-18C6
(DCC) in dimethylformamide and methanol solutions (4) by

using 23

Na NMR measurements. From a study of the variation
of exchange rates with concentration, they postulated
that the exchange mechanism involved the complexation

equilibrium,

Na+(X-), Crown 2 Na+(X-) + Crown (1.5)

In both solvents, the activation energy is 12.610.6 Kcal/
mole for D8C and 8.3 Kcal/mole for DCC. The lower activa-
tion energy for releasing Na+ ion from DCC was attributed
to the flexibility of the macrocyclic ring. Recently

the above authors also studied the decomplexation kinetics

 

 

 

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11

 

 

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12

 

 

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mm ueoumoa u--- eo.ea- mm

mm moo: m.esu m.e~- mu +s

mm moan u--- e.~a-e mm

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mm cum m.H- mH.e- ee

mm cam e.mu eo.m- mm

mm o~m «.mau me.ma ea +1

mm mom: a.H- e.m- mm

mm moan u--- e.u-e mm

mm omzo v.0: m.~u mm oz m uoEOnH

mm Owe ~.H- eH.~- mu mmz

mm cum «.m- em.~u ee

mm Omm e.mu He.~u ma

mm o~m a.n- ee.~- OH +eo

mm cum H.4a a~.nu as

an ca: «.4- mm.m- mm

mm ON: s.e- me.mu ea +nm

am can e.~- em.mu ee

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mm moms -- o.HH- mm +He

mm mow: -- m.m- mm wmz

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mm moms -- e.ua- mm +am

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mm mow: -- e- mm +ez onom-ONSmnAa
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mm cum m.e- He.m- mm wmz

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.ooscwucou .H OHACB

 

of I
of e
the
for
stil
as -
x-re
Shoe
very
same
to p

less

gate

1.8a

14

of DEC-K+ and DEC-Rb+ complexes in MeOH solutions by means
of alkali metal NMR (5). The activation energy (Ea) for
the decomplexation of the K+ ion is 12.6 Kcal/mole, while
for Rb+, the exchange between free and complex sites was
still indicated as being rapid even at temperatures as low
as -50°. They interpreted these results as follows: The
x-ray crystallograph study done by Truter gt_gl. (15),
shows that both Na+ and K+ can fit the cavity size of BBC
very well, therefore for these two ions they obtained the
same Ea value. However, Rb+, a larger cation, is forced
to protrude from the cavity plane and, consequently, is
less tightly bound to the BBC molecule.

The complexation reaction of dibenzo-30C10 with Na+,
K+, Rb+, Cs+, NHI, Tl+ in methanol solution was investi-
gated by Chock (39). The reaction mechanism he postulated
is as follows:

fast
+
+

Cr

k
2
+ M+ % MCr+ (1.7)
k21

Cr2
That is, a conformational transition was prOposed. The
symbol Cr1 represents an unreactive species, Cr2 is an
Open configuration which is ready to complex the cation,
and MCr+ is a Closed configuration which is stabilized

by a monovalent cation. His results also emphasized that

the stability of the complex is dependent on the ionic

 

radi
Cuss
DBC
Thei
is 2

thus

Witt.

15

radius and the hydration energy of the cations under study.
Cussler and coworkers (40) made conductance studies of

BBC and DCC in acetonitrile (MeCN) and in methanol (MeOH).
Their results indicated that the stability of the complex
is affected by the solvation of the cation under study and
thus solvent effects on the complexation reaction cannot

be overlooked.

(B) COMPLEXATION OF METAL IONS BY MACROHETEROCYCLIC

LIGANDS-CRYPTANDS.

Cryptands are polyaza and polyoxa macrocyclic compounds

with tri-dimensional cavities (Figure 4). In order to

Figure 4. Cryptand, C (k+1,m+1,n+l).

accommodate different cations, the cavity size can be
varied by changing the length of the ether bridge. The
selectivity of complexation and stability of complexes,

in general, are several orders of magnitude greater than

 

for

in

tand
For

has

firs
ture
Na
PIOC
than
caus
is i:
WOrk,
in e1

16

for crown compounds with the same number of oxygen atoms
in the ring.

In general, the term cryptand is ascribed to the
free ligand and the term cryptate to the complex. The
notation C(n+l,m+l,k+1) is an abbreviation for a cryp-
tand with n+l,m+l,k+1 oxygen atoms in each branch.

For instance, if a hexaoxadiamine macrocyclic compound
has a value n=m=k=1, then it can be written as C222.

The kinetics of the complexation by cryptands was
first studied by Lehn 2E.El° (41) through a PMR tempera-
ture study on the complexation of C222 with K+, Tl+, and
Na+ in D20. They concluded that the exchange mechanism
proceeded by a dissociation-complexation process rather
than a bimolecular process. The symmetrical splitting
caused by Tl+-H spin-spin coupling indicated that the ion
is in the center of the molecular cavity. Dye and co-
workers (42) studied the exchange rate of sodium cryptate
in ethylenediamine. The activation free energy value
they obtained is similar to that of Lehn obtained in aqueous
solution. They also dissolved pure sodium in ethylamine
(EA) and in THF in the presence of C222. Due to the com-
plexation of the cryptand with Na+, the concentration of
dissolved metal was greatly enhanced and a gold-colored
(NaC222)+Na- salt was formed (433), At low temperatures (43b)
they observed two NMR resonances, i;g;, (NaC222)+ and Na-,
with the Na- peak shifted upfield about 63 ppm from

saturated aqueous NaCl for both solvents, i.e., EA and THF.

 

 

Kint
com;
the
with
The
solu
for
C222

2911

by C-
energ
is re
This
23 a]
Studj

and I

17

Kintzinger and Lehn (44) also used 23Na-NMR to study the
complexation of Na+ ion with cryptands. They found that

the 23

Na nuclear quadrupole coupling constant decreased
with an increasing number of oxygen atoms in the ligand.
The chemical shift (referred to a 0.25 M aqueous NaCl
solution as external reference), had values of 11.15 ppm
for Na+-C211,-4.25 ppm for Na+-C221, and -ll.45 ppm for Na+-
C222. The line widths at halfheight were 13213, 4612 and
2911 Hz, respectively.

Lithium-7 NMR kinetics studies have also been performed
by Cahen, gt El° (6). They found that the activation
energy for the decomplexation of the Li-cryptand complex
is related to the Gutmann donor number of the solvent.

This result contrasts with the kinetics studies of Shchori
gt El! who used crown complexing agents. The latter authors
studied the exchange rate of Na-DBC in DMF and methanol

and noted that there seemed to be no solvent effect on

the activation energy. However the donor number for DMF

and methanol are very nearly same.

In addition to the study of the complexation of metal
ions with macrobicyclic ligands (denoted as [2]-cryptands),
Lehn 25 31. also synthesized macrotricyclic ligands (de-
noted as [3]-cryptands) (45,46). Later, they also studied
the cation exchange rate between binding sites on two rings

130 NMR. Their

inside the cavity of a [SJ-cryptate by
observation for this study is summarized as follows:

(1) Complexes display an intramolecular cation exchange

 

proces
is loc

shown

(2) '1
decree
energk
(3) z

Preser

18

process which interconverts two species in which the cation
is located unsymmetrically in the molecular cavity, as

shown below.

‘Wfl \0/
.-.: ““0 v— ~~ 2.»0
(“Hi ‘ 33"

(2) The free energies of activation, AG: for this process
decrease with increasing size and decreasing hydration
energy of the cations in the order Ca+2 > Sr+2 > Ba+2.

(3) An intermolecular cation exchange process is also
present, but its rate is much slower and its free energy

of activation is much higher than those of the intramolecu-
lar process. (4) Both intra and intermolecular cation
exchange is fast for the weak complexes which form with
alkali cations.

Another [3]-cryptand has been synethsized recently
(47). As shown in Figure 5, the attractive feature of
this molecule is that it possesses a spherical intra-
molecular cavity into which the cation may be placed.
Preliminary measurements show that the logarithm of the

stability constants for the K+, Rb+, and Cs+ complexes

in water are about 3.4, 4.2 and 3.4, respectively; and

 

 

 

Fig

the]

Pera‘

(at.

cryp
Obta
flow
kins
mure
ca+2
exo-
and

fiQU;
the 1

has .

19

no

Q 521}
(We?)
UV

Figure 5. Newly synthesized macrotricyclic cryptand.

the PMR kinetic study obtained from the coalescence tem-
perature showed that the free energies of activation for
K+, Rb+ and Cs+ are 15.5 (at 28°), 16.7 (51°) and 16.1
(at 41°C) Kcal/mole.

Kinetics information about the complexation between
cryptands and metal ions is scarce and has been mainly
obtained by NMR techniques. Very recently, a stopped-
‘flow technique (48) was used for a kinetics study by Wil-
kins g£_al. They followed the color variation of the

+2 *2

murexide-Ca and

+2

complexation reaction of murexide-Ca
Ca -cryptate. In this study, conformational changes, i;g;,
exo-exo endo-endo (41,49), were also considered. Endo
and exo configurations are shown below. The endo con-
figuration has the lone pair electrons directed toward

the interior of the cavity while the exo configuration

has the lone pair electrons turning outside.

Formation constants of alkali metal cryptates in

 

 

 

aque
SiVe
niqt
tior
an a
com;
a pc
C22:
reSt
ing

This
the

Of p
Valu

the

from

Stil

20

exo-exo endo-endo exo-endo

aqueous and methanolic solutions have been studied exten-
sively by Lehn and coworkers who used potentiometric tech-
niques. Recent reviews (50,33) contain extensive compila-
tions of complexation constants. Cahen 22.2l- (7) used
an alkali NMR technique to study formation constants of
complexation in several solvents. They found that, in
a poor donor solvent such as nitromethane, the addition of
C222 or C221 cryptand to a lithium perchlorate solution
resulted in a drastic chemical shift which reached a limit-
ing value at higher than 1:1 (ligand/metal) mole ratios.
This phenomenon indicates that the formation constant of
the resulting cryptate is large in contrast to the case
of pyridine, a better donor solvent, in which the limiting
value is not reached even at a 25:1 mole ratio because of
the competitive action of the solvent.

The thermodynamic quantity AGO can be obtained directly
from the formation constant, but AH0 and AS0 values are

still very limited in extent. Only very recently Lehn

 

 

 

and

an a
“YE
Tabi
com;
char
The:
and

cal<

Sr+j

Na+

//“'1

[Ca'

hav‘

S‘flm

21

and coworkers (51) made calorimetric measurements under

an argon atmosphere to avoid the problems caused when
cryptand solutions absorb C02. Their data are listed in
Table 2. In this work, they stressed explicitly that the
complexation reactions to form cryptates have large negative
changes in enthalpy, sometimes, negative entropy changes.
These are important factors in determining the stability

and selectivity of the complexation reaction. From their
calorimetric study they observed the trends shown in Table

3.

Table 3. Trends in Thermodynamic Parameters with Cryptands.

 

 

 

 

 

Cation Complex With Cryptand Dominant Minor

+2 +2 . +
Sr ,Ba (not With C222),Na (C222) AH<0 TAS>O
Na+,K+,Rb+,Cs+ AH<O TAS<0
Ca+2 TAS>O AH<0

. ' .+ +2
In addition, they noted that [L1 CC ], [Ca CC ],
221 211
+2

[Ca CZC222] are entirely entropy stabilized with about zero
heat of reaction.

Crystal structures of a number of alkali cryptates
have been determined by Weiss and coworkers (52-55). For

[2]-cryptates it was observed that the metal ion is centro-

symmetrically located in the cavity. In some cases, solvent

.HOUQK CH OomN U6 NHuTEfiHONQU
>n~ mumwhfinflmuz COfiUOUGK COfiUflXTHQEOU @uuuflxnhUlfiHMXHaw MO WTHUflUEQDU UsEfiCkmuOEMWCL. .N @HQQE

 

 

22

.cofiusuoan mouocop s
.musum omxoameoo o» Hommcsnu monocoo o
.UMHAUG+ZH + UuAAV +
Amsscc+z smusnssa saucmumsufis was mo coaussuom spas sssmsa swusussa was

oucw mmsnm msm on» Eoum coauso on» no Hmmmcsuu ..o.w .acowusmflq: movocmv a muonz

 

 

 

 

 

nms + oms u «ms ans + ems u ass "maoz
~.o~ h.a~ m.ma 1111111111 am<| Anw.mv
H.mh m.vm «.mw llllllllll «ms: «mm
an Inn: Hm mm 111:: amqu Afim.mv
Hm lulu hm maa lllll «ms: «mm
In: m.ma h.am m.ma m.HN am<| A«N.~V
nan m.vm m.~m m.HHH H.~ma amsn Ham
:1: In: In: m.mm mm «ms: Ano.av
In: 1|: 1|: ~.HHH ~.>ma «as: Haw
laws.ac+mo Asms.av+nm Asmm.av+m Asmm.oc+sz Assn.oc+fiq meos\Hsoxv sass“;
o o o o o . nouoEsHsmosuosa
.uousz ca comm us muuosauoaso
>n omHSmsoz cowuoswm cowusxoameoo manuaauolaasxa< mo mowuwucsso oafiscmoosuona .m magma

23

molecules are also linked to the complex, e.g., Rb+(C222)

2 +2

sew-H20, 13:1+ (c222) (somzazo (56) and Ba (c322) (somz-
2820 (57). The solvent molecule or anion can extend into
the ligand cage and coordinate with the trapped metal ion
in the center. It was also found that for [2]-cryptates the
preferred configuration is endo-endo in the crystal. For
[3]-cryptates (58,59) the metal ion is also located in

the cavity. Monovalent ions usually form weaker complexes
with [3]-cryptands but 1:2 (ligand/metal) complexes can

be formed. The crystal structure of an Ag+-[3]-cryptate
complex actually shows two silver ions located in the
two rings and linked with a third Ag+ through the oxygen
of the nitrate group of AgNO3. This third Ag+ is outside
of the cage.

In summary, the complexation reactions of metal ions

with macrocyclic ligands depend on the following factors:

(1) The type of binding site in the ring. For a ligand
with a donor atom such as 0, N or S, the stability usually
follows the trend, 0 > N > S for small ions such as Li+,
Na+. For a large ion such as NH: or a group B ion such

as Ag+ the same trend may not necessarily hold because of
some covalency in the coordination.

(2) The number of binding sites in the ring. Compare

for example the log R value for the Na+ and K+ complexes
of C222 (with Na+ or K+ in MeOH log K is larger than 8)

and 'czzc8 (with Na+ in MeOH log K is 3.5 while for K+

 

 

 

it

“Y
the
sit
of

(3)
(60
she
the

sig

sut
dex
his

Cai

th:
th.
Qf;

is

11.

24

it is 5.2). In this comparison, C22C8 denotes a [2]-
cryptand with one aliphatic branch. Both ligands have about
the same cavity radius but C22C8 contains two fewer oxygen
sites. This results in a decrease in stability by a factor
of 104-105 (50).
(3) The relative sizes of the metal ions and the ligand
(60). The K value as a function of the cation radius
shows a maximum for any given ligand. This indicates that
the ratio of cavity radius to the ionic radius contributes
significantly to the selectivity of these ligands.
(4) Steric hinderance and ligand thickness (61). The
substituents on the ring will introduce rigidity and hin-
derance in the ligand. These can make the ligand have a
higher selectivity and ability to discriminate against
cations which are either smaller or larger than the preferred
one.

The ligand interposes a layer between the cation and
the outside medium. Therefore the thicker the ligand,
the better the cation is shielded from the medium. This
effect decreases long range ionic stabilization. The effect
is larger the higher the dielectric constant of the solvent.
(5) The solvent and extent of solvation of the ion and
ligand. For example, Cahen's study illustrates that in
solution the complexation reaction competes with solvation.
Media which can solvate cations more strongly usually
result in weaker complexes.

(6) The electrical charge of the ion. Previous studies

25

have shown that, with a similar cation radius, a bivalent
ion forms a stronger complex than a monovalent ion (6)).
However, in this case ligand thickness becomes very im-
portant because the long range interaction energy varies

as the square of the ionic charge.

(7) Topology of the ligand. The dimensions and geometry
of the ring can greatly affect the stability of the complex.
This is most pronounced when the complexing groups are held
in favorable positions by the ligand framework. The extent
of ion-pairing also depends on the geometry of the ligand.
In addition to the recent work of Smid gt 31,,electron spin
resonance studies (62,64) have been made of alkali metal
hyperfine splittings in the presence of macrocyclic poly-i
ether ligands. These results illustrate that several

types of ion-pairs are formed with crown complexes in low
dielectric media. However this effect was not observed

when cryptates were in the same media.

(C) NUCLEAR MAGNETIC RESONANCE

( i ) INTRODUCTION

 

Electrolyte solutions are particularly suited to in-
vestigation by nuclear magnetic resonance techniques. The
7 presence of extremely rapid and generally random molecular
motions averages local magnetic and electric fields to
very small values and can result in narrow resonance lines

even for quadrupolar nuclei. This fact is important

 

 

bec
and
In
Che
eff
in
in
in
In
th
at
of
ar.
si

tC

m

1‘4

m.-

i}

W;

fl

26

because it enables small differences in magnetic shielding
and/or fine structure of the resonance signal to be detected.
In addition, broadening of the resonance line because of
chemical exchange, hyperfine interaction or quadrupolar
effects may be studied and chemical information derived
from the observed behavior. Proton NMR is useful in the
investigation of solvent or ligand behavior and can provide
information about ion-solvent or ion-ligand interactions.
In favorable cases, non-proton NMR can be used to study

the ions themselves and thus provide direct information
about such interactions. Although resonance frequencies

of metal ions are sensitive to ion-solvent, ion-ligand,

and inter-ionic interactions, the generally weak resonance
signals and the special instrumentation required combined
to make such studies rare prior to the last decade. All
alkali metals possess at least one isotope with a magnetic
nucleus; e. ., 7Li, 23Na, 39K, 87Rb, and 13303. The in-
herent intensity of the resonance is much lower than that
of the proton. However, the sensitivity of the nuclear
magnetic shielding constants to the nature of the surround-
ings is considerably larger and increases as the atomic
number of the ion increases. This condition leads to a
wide range of chemical shifts, from a few ppm to hundreds
of ppm. Variations in the chemical shift result primarily

from changes in the paramagnetic shielding constant, op.

 

 

spi

the

in
and
tex
Var
at

ma)

whe

27

(ii) CHEMICAL SHIFT STUDIES OF ELECTROLYTE SOLUTIONS

For an assembly of identical but isolated nuclei of
spin I and magnetic moment u in a static magnetic field Ho,

the simplest expression for the resonance condition is

v0 = uHo/Ih = yHo/Zn (1.8)

in which v is the frequency at which energy is absorbed

o
and y is the magnetogyric ratio. The latter has a charac-
teristic value for each isotopic species. However, a
variety of mechanisms may produce secondary magnetic fields

at a nucleus. The actual field experienced by the nucleus

may be written as

H = Ho (1-0) (1.9)
where o is a dimensionless quantity known as the shielding
(or screening) constant.

Ramsey (65,66) has developed general theoretical expres-
sions for chemical shifts caused by magnetic shielding of
nuclei in molecules. This treatment has been applied succes-
fully to simple molecules but the approximations required to
apply it to more complex systems yield only qualitatively cor-
rect results. Saika and Slichter (67) attempted to explain the
difference in the shielding constants of F2 and F-. They

divided the contributions into separate terms: (1) the

 

 

diam
a pa

cont

expa
envi
be;
have
ider

Rams

ind;

sone

Fret

The)

Mutt

28

diamagnetic contribution for the atom in question. (2)
a paramagnetic contribution for the same atom and (3)
contribution from the electrons of other atoms.

When investigating an electrolyte solution, one can
expand Ramsey's formulation as applied to a solid state
environment. If alkali halide crystals are considered to
be purely ionic in character, each constituent ion will
have a spherical closed-shell electronic configuration
identical to that expected for the isolated ion. In
Ramsey's expression, the shielding constant of the ionic
nucleus is determined only by the diamagnetic term, ad,
for an isolated ion. Therefore, the observed large.para-
magnetic contributions found for crystals (usually 102-
103 times larger than ad) indicate that there are additional
interactions present which are able to distort the symmetry
of the electron distribution and introduce some net
orbital angular momentum into the ion. This perturbation
gives rise to a paramagnetic chemical shift. Such inter-
actions might be considered in terms of electrostatic,
covalency or overlap effects. However, the calculations
indicate (68) that neither electrostatic effects nor rea-
sonable estimates of the degree of covalency can account
for shifts of the magnitude observed. The best inter—
pretation so far is that of Kondo and Yamashita (69).

They suggested that the cause of the paramagnetic shift is
due to the short range repulsive forces between ions.

Mutual overlap of atomic wave functions of neighboring

 

 

 

i0:
Pa
ra
to
9C.

fc

t}
ac

La

L, h

29

ions produces a strong repulsive force mainly due to the
Pauli exclusion principle. This force acts over a short
range and competes with the electrostatic forces which tend
to reduce the separation of oppositely charged ions. At
equilibrium in the crystal the attractive and repulsive
forces are in balance. Kondo and Yamashita used L6wdin's
(70) orthogonalized-atomic-orbital model and considered
that the overlap integrals are significant only for inter-
actions of orbitals which belong to nearest-neighbor ions.
Later, both Ikenberry and Das (71) Hafemeister and Flygare

(72) gave more exact derivations of the paramagnetic shift

to be expected from overlap forces in alkali halide crystals.

But at that time they ran into difficulty in comparing

theoretical results with experiments because the experimental

shielding data are usually referred to a reference sample

in which the shielding constants are not known. Therefore

it was thought that this problem could be solved by referring

all experimental shielding constants to the infinite dilution

chemical shift in water which, in principle, is supposed to
be constant because of the strong hydration properties of
water.

When the alkali salt is put into a solvent, the cal-
culated paramagnetic shielding constant, op, from the
crystal state and the experimentally measured shift,

6, referred to the aqueous solution are related by the

equation:

 

 

ar

0‘

p]

mc
on
si
re
Va
in
ac

fr

Ci
Di

5‘!

re

90:

30

o = o - 6 (1.10)

where gig is the paramagnetic shift of the hydrated ion

0
aq
of the partner ion in any alkali metal or halide series,

relative to the "free ion". Since a should be independent

0

aq obtained by a combination of theory

the constancy of o
and experiment, therefore, provides a test for the proposed

overlap mechanism and the accuracy of the wave functions em-

0
aq
is not constant. Attempts were made to explain the dis—

ployed in the calculation. However, in reality, a

crepancy by Hafemeister and Flygare (73), Ikenberry and
Das (74) and Y. Yamagata (68) individually by using various
models in the calculations. However, all of them could
only illustrate that ion-solvent interactions can produce
sizable paramagnetic shifts of the ionic nucleus, but their
results were still not comparable with the experimental
values. Therefore, it was suggested that chemical shifts
in solutions may be caused not only by ion-solvent inter-
actions in dilute solution, but also may have contributions
from direct interionic effects.

By using the Rondo-Yamashita model one could in prin-
ciple account for the chemical shifts in aqueous solutions.
Direct collisions between ions will distort the spherical
symmetry of the electron distribution and also can produce
paramagnetic chemical shifts. In the solid state, the
relative positions and distances of separation of the

component ions are known, and, therefore, the theoretical

ur
se
ma
sh
fo
bo
wa
th.
se]
ma]
the
fir
the

Pa:

“he

31

attack is easier. In solution the environment of each ion
varies randomly with time as the ion and solvent molecules
undergo rotational and translational diffusion. The ob-
served chemical shift is an average value resulting from
many separate contributions corresponding to the various
short-lived associations in solution. An exact expression
for the shielding constant would require a knowledge of
both the radial distribution function of other ions and
water molecules about the central ion and the magnitude of
the appropriate overlap integrals as a function of the
separation. This information is difficult to obtain. To
make this problem tractible, Deverell gt El! (75) modified
the Rondo-Yamashita theory in the following way: At in-
finite dilution, the only interactions present are between
the ion and the water molecules. This contribution to the
paramagnetic chemical shift can be expressed by

0 -16a2 -3 o

an =‘—_K_— (ri >p Ai-HZO (I'll)
where A is the average excitation energy,

a is the fine-structure constant,

<r'3>p is the expectation value of r;3 for an outer p-
electron of the central ion, i.
Ai-H O is an appropriate sum of the squares of overlap
2

integrals between the outer p-orbitals of the ions,
i, and the outermost orbitals of neighboring water

molecules. The superscript denotes zero

the

The

wher

 

tegr
all
ion
The
and

501v

Prob

and

 

the:
<r‘3
f0r

Shif

deSc

Stud

the :

 

32

concentration of the counter ion.
As the concentration of the solution is increased,
the presence of interionic processes has to be considered.

The experimental shift, 6, can be expressed as

2
o _ -160 3 c
p aq - A (ri >p[ZAi-j

+ (AC -A° )] (1.12)

where Ai-j is the sum of the squares of the overlap in-
tegrals for the interionic contribution and is taken over
all ions in solution other than the central ion, 1. The
ion j may be of like or unlike charge with respect to i.
The superscript c denotes the concentration of the salt,
c o .
and (Ai_H20 Ai-HZO) represents changes in the effect of
solvent-ion overlap integrals.
c c

Both terms, Ai-j and Ai-HZO' are dependent upon the

probabilities of collision occurring between the central ion

and other ions or water molecules in solution and are

therefore concentration dependent. Also, from the factor

-3
i

for the observation that the magnitude of the chemical

<r >/A, as shown in Table 4, it is possible to account
shift increases with the atomic number of the alkali ion.
The following is a recapitulation of the previously
described development of alkali metal ion chemical shift
studies:
Ramsey used standard perturbation theory to express

the shielding constant as (67):

 

Tab]

II

I»

33

Table 4. Values of the Average Excitation Energy A, and

the Expectation Value <r;3>

for Alkali Metals.a

 

 

 

p
-3 -3
(1:1 >p A (1:1 >
Ion a.u. Rydbergs A
+
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

 

 

aReference 76.

 

Si

no

ti

EX

 

it

tc

CI

t1

34

 

 

o = Gd + op
2A A A
2 r 2 - r r
= 62 {(lpolék 3 kkl wo>+
2mc rk
-1 A Ek
{(so-Em) [(Wollszl‘pmxi’mlg "3W0” etc]} (1.13)
m r

k

Since excited state wavefunctions and energies are usually
not known, Ramsey introduced the average energy approxima-
tion and the paramagnetic shielding constant was then
expressed as follows:
0 - (- e2)<w I (3’9: /r3)ltl) > (I 14)
_ _____ ' ,
P AM2C2 o ké' k k k 0
A :average excitation energy.
e :electronic charge
M :electron mass.

C :velocity of light.

p)

:angular momentum of the k'th electron, and

rk :radial distance of the k'th electron from the origin

at the nucleus.

The subscript 0 refers to the ground state and m refers to
the excited state.

For a crystal, an additional interaction force was
introduced. Two models have been proposed in an attempt
to rationalize the large paramagnetic shifts, op, of ionic
crystals. These are Yosida and Moriya's (77) charge-

transfer covalency model (YM model), and Kondo and Yamashita's

 

(69) over

of the Qt

 

halide m
plausibl
derivati
transfer
18p betwe
ion with
introduce
in Ramse}
integral

1' and ti

 

Their cori
Pulsive 1
By Combix
mOre C10:
from 51k.-
also uSe.
the KY m.
atomic w

but also

Their Ca

Can be
(next he
”911 as
P01.
relate w

35

(69) overlapping-ion model (KY model). Later, calculation
of the quadrupole coupling constants in diatomic alkali-
halide molecules (78) showed the KY model to be more
plausible. However, Das gt_gl. (71) gave a more exact
derivation by including the effects of overlap and charge
transfer covalency. For the KY model they considered over-
lap between the outmost s and p orbitals of the central
ion with those of neighboring ions. Das gt El: not only
introduced <r'i'3>p for a p electron of the central ion, i,
in Ramsey's expression, but also included the overlap
integral between the outer p—orbitals of the central ion,
i, and the outmost s and p orbitals of all other ions, j.
Their conclusion was that the KY model (short-range re-
pulsive force) is predominant over the YM model (covalency).
By combining the two effects, the resultant calculation
more closely approximates the experimental data obtained
from alkali halide crystals. Hafemeister and Flygare (72)
also used the symmetrical orthogonalization method as did
the KY model, but they not only considered the overlap of
atomic wavefunctions of nearest-neighbors in the lattice
but also included the next nearest-neighbor's interaction.
Their calculations indicate that alkali-alkali interactions
can be neglected but for the halide ions, halide-halide
(next nearest-neighbor interactions) should be included as
well as halide-alkali interactions.

For the case of solutions, however, op still does not

relate well to the observed values. Yamagata (68) considered

the dipc
molecule
shifts <
ions bui
computec
approacl
meantime
Hartree-
Give the
Stantia]
and cowc
Cept to
eXpresSj
describe
be made
about t}
when Lut
results.
optiCall
obtaine
pariSOn
Shifts 1

given in

 

36

the dipole polarization of the ion by adjacent water
molecules. Calculations based on this mechanism predict
shifts of the correct order of magnitude for the halide
ions but not for alkali metal ions. Ikenberry and Das
computed c§2+ for a model of Rb+(H20)6 by using the same
approach as they did for alkali-halide crystals. In the
meantime, Hafemeister and Flygare also used D. Mayer's
Hartree—Fock wavefunction to calculate 022+. Both results
give the right order of magnitude but still disagree sub-
stantially with the experimental observations. Deverall
and coworkers applied a short-range repulsion force con-
cept to solutions, as shown in Equation (1.12). With this
expression, the concentration-dependent phenomena can be
described but complete calculation of the shifts could not
be made at the time because of the lack of information

about the experimental value of egg, This problem was solved

0

when Lutz (79) determined 0a directly by combining the

results obtained from precision NMR, atomic beam, and

optical pumping experiments. A summary of 0:

values
obtained by different means is listed in Table 5. A com-
parison of experimental results with calculated chemical
shifts in halide crystals and aqueous solution has been

given in Ceraso's thesis (95), Page 39.

 

 

 

 

 

Um. .
mmwSmufiCSUmwB TDOflHflxw \AQ VGCHQUQO 00 N0 mums-N85 M THQUE

 

37

 

 

 

me «use x a.u- passeuomxm coeusaom +nm muse
oouuomou macauosuoucfl
osasb oz coe1s0fi Hoowmcoo
mu van msHHo>o soflusaom +bm moussoflm was Haouo>oo
ms «use x eo.ou :oeusueusaom seamen Acmmv+am assumes» osxsw
cofiuocsum>s3
xoomnoouuusm
no vuoa x «.0: a.uoasz .m .0 coavoaom +bm snowman was Houmonomsm
vb sled x mm.o1 mmauo>o macamv+nm use was humoncoxH
.mom coH ooum m> Emacssooz H0002 Honusm
woo
+2

 

 

mmsvwsnooa msowus> ha omswmuao

Us

on no mosas> .m manna

(iii)

The

in Tabl

Table 6

 

The
was fir:
authors

with Cor

 

large 6}
cesium i
adding ‘
linearl.

the Shi

38

(iii) CESIUM NUCLEAR MAGNETIC RESONANCE

 

The physical properties of the Cs-133 nucleus are shown

in Table 6.

Table 6. The Physical Properties of the Cs-l33 Nucleus.

 

 

Resonance frequence in MHz
for a 1.4 T. field 7.87

Natural abundance, % 100
Relative sensitivity (vs. 1H)

for an equal number of nuclei _2
at constant field. 4.74 x 10
Magnetic moment in multiples

of the nuclear magneton

(eh/4n mc) 2.5642

Spin 1, in multiples of h/2n 7/2

Electric quadrupole moment Q,
in multiples of barns2 0.003

 

 

The magnetic resonance of cesium ions in solutions
was first studied by Gutowsky and McGarrey (80). The
authors observed that the 133C8 resonance frequency varied
with concentration. Carrington 22.21: (81) also observed
large shifts of the cesium resonance upon variation of the
cesium halide concentration. They studied the effects of
adding various salts to CsCl solutions. The shift varied
linearly with the mole fraction of added salt and in general

the shift was greater the larger the anion.

 

 

 

rise to

 

39

More recently Deverall and Richards (75) studied the
chemical shifts of alkali halide and nitrate aqueous
solutions by the alkali NMR technique. The magnitudes
of the shifts increased considerably with increasing
atomic number of the cation, and shifts to both higher
and lower fields relative to the cation at infinite dilu-
tion were observed. The resonances of K+, Rb+ and Cs+
were observed to vary linearly with the mean activity of
the salt and, for all alkali cations, anions showed a
definite series of Shielding effects, geee, the order of
increasing shielding was 1' < Br- < Cl' < F' < H20 < N03.
The authors concluded that the chemical shifts of the cation
resonances were not only caused by changes in the inter-
actions with solvent molecules, but also with counter-
ions. By a modification of the theory of Kondo and
Yamashita, and the expression of Das EE.El-v the chemical
shift at infinite dilution was formulated as Eq. 1.11.

The concentration dependence of the chemical shift may
result from two processes. Firstly, the addition of other
ions may modify the ion-solvent interactions which give
rise to an' and, secondly, direct interactions between
the ions during collisions may also contribute to the
shift. So the chemical shift at concentration C, relative

to the free ion can be written as

2 1 l C C ]

O = -16a '<_3’>np A Aion-ion + Aion-water (1'15)

 

   

40

where Ac is a sum of the squares of overlap integrals at
concentration of salt C. Deverall eg_gl.(77) also found
that the approach of the two oppositely charged ions will
be activity dependent, and the term Igon-ion in the above
equation should increase linearly with the activity of the
solution. The increased paramagnetic shielding caused

by halide ions of high atomic number is mainly caused by
the higher values of the overlap integrals for the larger
anions. The small shifts observed for Li+ and Na+ with
concentration in aqueous solution are probably caused by
strong hydration which inhibits direct cation-anion inter-
actions. The increase in the interaction from K+ to Cs+
may be partly due to a decreasing strength of hydration
and greater facility of approach of the anion to the larger
cations, as well as to the increase in size and greater
degree of overlap.

Halliday and coworkers (82) experimented with isotopic
solvents and observed Cs+ resonance shifts in dilute salt
solutions. They studied the Cs+ resonances, at fixed
applied field and as a function of molar concentration,
2160, D2160 and H2180. The results are shown in
2160 and H2180 are

indistinguishable and extrapolate to the same value at

in H

Figure 6. The shifts observed in H

infinite dilution. However, the shift at infinite dilu-

tion in n215

that the isotope effects cannot simply be a function of

0 lies at a lower value. These results showed

the masses of the molecules and suggest strongly that at

 

Figure 5

Figure 7

 

41

"32Ur .
/

L c: at 28 MHz ,

* /

/

I)

, ./
: //
v’ /

-4OU

 

 

N
I . Hfo
0 H,'°o
o 02:60
b /o
O
- 500/
0 on 04 06
C (Molar)

Figure 6. The frequency of the Cs resonance near 28.013
MHz at fixed applied field as a function of molar
(82)

concentration in H2150, D2150, and H2130.

//

100

Shin/Hz

 

 

l L l l 1 J

.05
leCHlmol/dm’l

   

l l J

 

Figure 7. 133Cs shift data (CsCl-MeOH) relative to infinite
dilute shifts at three temperatures (a) 298°K;
(b) 308.3°K; (c) 326°K (84) and (d) CsCl + H20

(83) for comparison.

 

infinitii

in the s
from Hzi
ance cat
from “ox
somewhat
Wlth Hzc
to cause

 

 

At
PUblishe
solvents
They ft:
their 0‘
of 0.03
which a
gives a
the Val
aqueOus
F01- the
Cs-l33

42

infinite dilution, the isotOpe effect is caused by a change
in the strength of the solvent hydrogen bonds in passing
from H20 to 020. The paramagnetic shift of the Cs+ reson-
ance caused by adjacent water molecules arises mainly

from "overlap" interaction of the water molecules. The
somewhat stronger hydrogen bonds formed by D20, compared
with H20, might easily modify the paramagnetic shift so as
to cause the observed diamagnetic shift.

At about the same time, Sharp and coworkers (83,84)
published an alkali metal NMR study of Cs+ in various
solvents at lower concentrations and at various temperatures.
They first studied cesium salts in aqueous solution and
their observations indicated that in the concentration range
of 0.03 to 2 M, the data follow an empirical relation in
which a plot of log (shift) 23. log (molar concentration)
gives a straight line with slope 9. Later, they also tested
the validity of this empirical logarithmic law for non-
aqueous solutions and found it was much less satisfactory.
For the investigation of the temperature dependence of the
Cs-l33 chemical shift, they studied the systems CsCl-MeOH
and CsBr-Hzo at a series of different concentrations.

The shifts varied only slightly with temperature as shown
in Figure 7. It should be noted that the reported chemical
shift value at various temperature was obtained by first
referring to a 2 M CsCl aqueous solution as an external
reference measured at the same temperature and then further

related to the value at infinite dilution at that temperature.

 

III. Ct

Fro
of alkar

interes

 

tions.
tion re:
nonaque
IS a $8
SOlutio
StUdy o

 

Prepert
IV) of ‘

tands 14

 

43

III. CONCLUSIONS

 

From the above discussion, it is evident that a study
of alkali complexes with macrocyclic ligands is chemically
interesting. In addition, it should have many useful applica-
tions. Information on the thermodynamics of these complexa-
tion reactions is very sparse, especially for reactions in
nonaqueous solvents. It is also evident that alkali NMR
is a sensitive probe of the complexation of alkali ions in
solution and therefore is a very useful technique for the
study of cryptate complexes. This thesis reports an in-
vestigation by the Cs-133 NMR technique of the equilibrium
properties (Chapter III) and dynamic properties (Chapter
IV) of the complexation of cesium ion by crowns and cryp-

tands in various nonaqueous solutions.

CHAPTER II

EXPERIMENTAL PART

44

I. SYNTHESIS OF CESIUM TETRAPHENYLBORATE AND LIGAND PURI-

 

FICATION.

 

Cesium tetraphenylborate (CsTPB) was made by mixing a
tetrahydrofuran (THF) (Burdick and Jackson Laboratories
Inc.) solution of sodium tetraphenylborate (NaTPB) with a
concentrated aqueous solution of cesium chloride (Ventron
Alfa Products, 99.9% pure). The fine white precipitate
was washed continuously with conductance water: sodium
contamination was checked with a flame emission spectrom-
eter (EU-703) and was found to be less than 0.01%. Cesium
triiodide solutions were made by mixing equimolar amounts
of cesium iodide (Ventron Alfa Products, 99.9% pure) and
iodine (Baker and Adamson) in an appropriate solvent.

Crown ligand 18C6 (PCR, Inc.) was purified by forming
a complex with acetonitrile (Mallinckrodt A. R. grade).
When about 50 grams of 18C6 was dissolved at ambient tem-
perature, in 125 m1 of acetonitrile (MeCN), fine white
crystals of the 18C6°MeCN complex were formed. The flask
was cooled in an ice-acetone bath to precipitate as much
complex as possible and the solid was then collected by
rapid filtration. The hygroscopic crystals were trans-
ferred to a round-bottom flask equipped with a magnetic
stirring bar and a vacuum take-off. The weakly bound
MeCN was removed from the complex by pumping under vacuum
for a few hours. The m.p. of recrystallized 18C6 was

39°C, the same as that reported (85).

45

 

Cry
Inc. an
hexane I
of the
with 8

Cry
was use
chased
and 8),
these t

used f0

 

rEports

46

Cryptand C222 was obtained from E. M. Laboratories,
Inc. and was purified by two recrystallizations from n-
hexane followed by vacuum sublimation. The melting point
of the snow-white sublimate was 68° (reported 68°C (86))
with a melting range of less than one degree.

Cryptand C222B was a gift from E. M. Laboratories and
was used as received. Dicyclohexyl-18C6 (DCC) was pur-
chased from duPont Co. as a mixing of the two isomers (A
and B). For lineshape analysis purposes, a separation of
these two isomers was carried out, and only isomer A was
used for the study. The method used was based on two
reports (87,88). Approximately 100 g of Alumina Absorption
(Fisher) was weighed and packed slowly in a column (2 cm
I.D.) which already contained n-hexane. During the packing
process, the column was checked constantly to insure that
no air bubbles were trapped. After packing was completed,
the column was eluted several times with n-hexane. Five
grams of DCC were dissolved into 10 ml n-hexane and the
solution was poured into the column, which was then washed
with n-hexane a few times. A mixture of n-hexane and
diethyl ether (Mallinckrodt A.R. grade) was then used to
elute the column. The mole fraction of ether in the elut-
ing solvent was increased gradually for each addition.
Isomer A was eluted first and then the solvent was removed
by a flash-evaporator. Isomer A was recrystallized twice
from ether and then the crystals were taken out with

ivory forceps to avoid contamination by metal ions.

 

 

 

WE

ar

C:

II

me
We
SL1
dC
an.

She

47

Then the crystals were pumped on in a container on a vacuum
line overnight. The white crystals melted at 61-62°C.

If the m.p. range was larger than 1% degrees, the separation
was repeated again using a newly-packed column. Isomer

B could be stripped off from the column by eluting with
anhydrous methyl alcohol (Absolute, Mallinckrodt A. R.

Grade), then recrystallized from n-hexane (m.p. 69-70°C).

II. SOLVENT PURIFICATION AND SAMPLE PREPARATION.

Propylene carbonate (Aldrich), acetone (Fisher), di-
methylsulfoxide (Baker, Reagent grade) and acetonitrile
were first dried with calcium hydride under reduced pres-
sure and then transferred by vacuum distillation to newly
activated molecular seives (Linde Type-4A,(Matheson Coleman
and Bell)) through a T-shaped joint with a coarse frit as

shown below.

 

   
 

% (15mm Fisher Porter joint
and

Ire/Penton coopllng

 

 

 

1's
fid:".- I I. . ’

Ca H2 molecular
selves

48

After 12 hours this solvent was vacuum distilled to another
container (Figure 8). Before vacuum distillation, this
bottle was pumped on the vacuum line for a few minutes
through joint (1) and heated gently to get rid of adsorbed
moisture on the surface. The distilled solvent was kept
in the drying vessel and transferred to the sample tube
when needed. The sample compartment was first pumped
on line through joint (2) for a few minutes before transfer.
After the desired volume of solvent had been transferred,
the solution was cooled with dry ice and the sample tube
was flame sealed off. During transfer, the pressure in
the stock bottle must be higher than that in the sample
tube; otherwise "bumping" of the solution can occur.
Pyridine (Fisher) was dried over CaH2 under reduced
pressure overnight and then further dried by the following
method: Sodium and potassium (J. T. Baker Co. 99.99%
pure) were packed into small ampoules as described in F.
Tehan's thesis (89). A three-to-one ratio of potassium
and sodium in the small ampoules was put into the sidearm
of the bottle and sealed as shown in Figure 9. Benzo-
phenenone (Matheson Coleman and Bell) was placed into the
vessel in an amount slightly less than the stoichiometric
amount of metals, then the vessel was vacuum-line pumped.
When the pressure in the line went to 10'6 torr, the metal
was heated by a gas flame until all metals left the first

section and glass ampoules: leaving some impurities in

49

 

 

 

Kontes valve

(1)

TO vacuum

 

 

TO vacuum

(2)

TV

‘ \J

 

 

 

 

 

CIEEN
’" 5 mm Fisher-Porter
and
Penton Coupling
l' ‘l

 

 

Figure 8. Apparatus for storing solvent in the preparation
of NMR sample.

 

thi
PUr
off

Sue]

50

constriction

1:12;)

I‘d/K

v

v

 

 

w benzophenone

Figure 9. Vessel for Solvent Purification.

this section. The first constriction to isolate the im-
purities away from the Na/K alloy was made by flame seal-
off. The sidearm was repeatedly heated and sealed off, in
such a way the metal was finally distilled into the bottle.
After the Na/K alloy was in the bottle, the last constric-
tion was sealed-off and pumping was continued for awhile
and then pyridine was distilled over. When pyridine was
distilled through the vacuum line, a blue-colored solution
(caused by the formation of benzophenone radical anions)
indicated that the solvent was dried. The above method had

to be modified for drying DMF, since it decomposes when

pl

TH

pc

n
.1

po

si

 

 

reln

51

placed in contact with an alkali metal in basic solution.

An anthracenide radical anion was first formed by distilling
THF into the bottle which contained freshly distilled
potassium and anthracene. A blue solution formed indicat-
ing that the anthracenide radical anion was present. After
pouring the blue solution into vessel B (Figure 10) the

side bottle with metal was sealed-off. Then the THF was

 

 

 

An

 

 

Figure 10. Vessel for DMF Purification.

.removed by vacuum distillation and the blue salt was
Pumped overnight to make sure that all THF was removed.

I‘~7,N-dimethylformide (DMF) (Burdick and Jackson Laboratories,

 

Ir
ar
ex
bl

di

wi
Ph

PP

II

in
am
loe
60
of
Ste
Us
The
mix
is
sin
”or:
etel

35,

52

Inc.) was dried over CaH2 under reduced pressure overnight
and the dried DMF was distilled into the vessel after
evacuation to 10"6 torr. If the solution was greenish-
blue, it indicated that the solvent was dry; if not, the
distillation was repeated.

All solvents except acetone were analyzed for water
with an automatic Karl Fisher Titrator (Aquatest II) from

Photovolt Corp. The water content was always below 100

ppm 0

III. THE NMR SPECTROMETER; MEASUREMENT AND DATA HANDLING.

A Varian DA-60 NMR spectrometer was modified to operate
in the pulsed mode at a field of 1.409 T. The 133Cs reson-
ance frequency at this field is 7.8709 MHz. The field is
locked by a home—built (90) lock probe which uses the DA-

60 console to lock on the proton resonance. A Block diagram
of the spectrometer is shown in Figure 11. The spectrom-
eter consists of three main parts. The first is a tuned
transmitter/receiver section which operates at 56.44 MHz.

The second section consists of a network of double balanced
mixers coupled to a frequency synthesizer. The third part

is a wideband transmitter/receiver network coupled to a
single coil tunable probe. By utilizing the mixing net-
work, broad band amplifiers and tunable probe, this spectrom-
eter can observe NMR signals in the range of about 2 to

35 MHz.

 

1

53

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54

The NMR spectrometer is interfaced to a Nicolet 1083
computer for time averaging of spectra and also for on-
line Fourier transformation of data. Chemical shift read-
out was directly obtained from the spectra during the ex-
periment, and all the shifts were calibrated with 0.5 M
CsBr in water being an external reference during measure-
ment. However, all data reported in this thesis are ulti-
mately referenced to infinitely dilute Cs+ in water at
25°C. The reported data are also corrected for differences
in bulk diamagnetic susceptibility between sample and

reference according to the following equation:

_ 21_ ref _ sample
corr - obs + Z3 (Xv Xv ) (11°1)
where xgef and xgample are the volume susceptibility of the
reference and sample solutions respectively and Gobs and
acorr are the observed and the corrected chemical shifts,
respectively. Values of acorr were calculated on the basis

of published magnetic susceptibilities of various solvents
(91). It was assumed that the concentration of added salt
was low enough that the magnetic susceptibilities of the
solvent were not affected. The magnitude of the correc-
tion for various solvents is shown in Table 7. Lineshape
analysis data were stored on magnetic disc in the form of
free induction decay signals. Later these data in the time
domain were Fourier-transformed without any smoothing or

exponential multiplication. They were then transferred to

l u . It flifilillfdc b ghr‘nupr

 

55

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.ocsauoouoHnofio mo coquHom oousafio Magma: s as maunm auw3 uocov “Hum
souuooao osu mo cowuosuoucfi man How oHOE\HsoM cw osas>nm< o>wusmmc may as omswmmv
me guess .uco>H0m mo mmfiuuomoum owaflcmooaosc ecu mmoumxo o» kuoesusm HsowuHmEo eds

 

 

 

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.osusn
assesses .5 sense

56

paper tape as octal numbers. This paper tape was then
read and punched onto computer cards in octal form. The
CDC 6500 computer program CONVERT transferred the octal
numbers to decimal numbers in a format which is compatible
with the KINFIT program. The program CONVERT and its deck
structure are listed in Appendix c.

The equilibrium and kinetics data were all fitted with
the appropriate equations by using the least-squares curve
fitting program, KINFIT. The related equations and deck

structure are listed in the Appendices.

CHAPTER III

STUDY OF FORMATION CONSTANTS OF CESIUM TETRAPHENYLBORATE
ION PAIR AND OF COMPLEXES WITH

MACROCYCLIC LIGANDS IN VARIOUS SOLVENTS

57

58

I. INTRODUCTION

 

Previous studies in our laboratories (92-95) and
elsewhere (75,83,96,97) have shown that alkali NMR offers
a very sensitive probe of the environment of ions in
electrolyte solutions; for example, sodium ions in various
solvents, and solvent mixtures. The linear relationship
between sodium-23 infinite dilution chemical shifts and
solvent Gutmann donor numbers illustrates the capability
of this technique (98) for predicting donor abilities of
various solvents. Of all the alkali metal ions, cesium-
133 has the widest range of chemical shifts and its shift
is therefore most sensitive to variations in the immediate
environment.

In 1975 Cahen gt 31. (93) showed that nuclear magnetic
resonance of the lithium nucleus could be used to measure
the stability constants studies of lithium complexes in
solution. The purpose of the study described in this chapter
was to extend the NMR investigation of alkali salt solutions
to cesium salts and complexes in solutions.

It should be noted that in solvents of low dielectric
constant and/or in concentrated solutions, cesium salts
may form ion pairs or even higher ionic aggregates.
Naturally, it was important for us to determine the extent
of ionic association of cesium salts in nonaqueous solvents

prior to the study of the complexation reaction.

59

II. INVESTIGATION OF CESIUM SALTS IN NONAQUEOUS SOLVENTS.

 

The concentration dependence of 133Cs chemical shifts
as a function of the salt concentration was studied for

CsTPB,CsI and CsSCN in pyridine, acetone, MeCN, PC, DMF,

3
and DMSO. The results are shown in Table 8 and Figure
12. It can be seen from Figure 12 that only in the case
of solutions in pyridine, acetone and MeCN did we observe
the variation of chemical shift with concentration,which
is characteristic of contact ion pair formation. Of the
solvents listed in Table 7, pyridine has the highest donor
number (DN=33.1) and the lowest dielectric constant (e =
12.40), yet the curvature of the plot indicates that in this
solution there is relatively strong contact ion pairing.
Cesium triiodide is known to be a strong electrolyte
(99) and the virtual absence of a concentration dependent
chemical shift in pyridine solution indicates that the
extent of ion pairing is very small in this case. Cesium
thiocynate has a very low solubility in pyridine, so that
chemical shifts were determined at only five points in the
concentration range of 0.007 to 0.0005 M. The chemical
shift becomes more diamagnetic as concentration is decreased.
Although the change in chemical shift is small compared,
for example, to that for CsTPB, the curvature indicates
that both CsTPB and CsSCN form ion-pairs, since the curva-
ture changes dramatically as the concentration decreases.

It should be noted that it is the curvature of the chemical

60

 

 

Table 8. Cesium-133 Chemical Shifts of Cesium Salt Solution
at 25°C
Salt:CsTPB CsSCN CsI3
Solvent:Pyridine Pyridine Pyridine
Conc. (M) ppm Conc. (M) ppm Conc. (M) ppm
0.015 37.81 0.007 -35.10 0.02 -32.93
0.0121 37.18 0.005 -34.94 0.019 -32.31
0.01 33.0 0.003 -34.32 0.013 -3l.69
33.15 0.001 -32.46 0.008 -30.76
0.009 31.29 0.005 -31.69 0.007 -30.45
0.008 29.12 0* -30.76 0.002 -28.90
29.13 0* -29.41
0.007 26.94
0.006 24.46
24.01
0.005 22.29
0.004 17.95
17.34
0.003 14.23
0.0025 11.74
0.002 8.03
0.001 1.27
0.0005 -8.25
0* -15.64

 

61

 

 

Table 8. Continued
Salt:CsTPB Cs13 CsI3
Solvent:PC PC Acetone

Conc. (M) Appm Conc. (M) Appm Conc. (M) Appm
0.02 36.63 0.02 34.43 0.05 20.73
0.01 35.89 0.01 34.43 0.03 21.81
0.008 35.89 0.008 34.74 0.01 22.90
0.006 35.52 0.006 34.74 0.008 23.21
0.005 35.27 0.004 35.05 0.006 23.52
0.003 35.27 0.002 35.05 0.004 23.83
0.001 35.02 0.001 35.21 0.002 23.83
0* 34.02 0* 34.45 0.001 24.30

0* 23.96

 

62

 

 

Table 8. Continued
Salt:CsI3 CsI3 izigf

Solvent:DMSO MeCN

Conc. (M) Appm Conc. (M) Appm Conc. (M) Appm
0.3 -70.47 0.3 -4l.31 0.015 -20.88.
0.05 -69.23 0.1 -37.59 0.012 -22.74
0.03 -68.77 0.05 -35.42 0.009 -23.77
0.01 -68.46 0.03 -34.17 0.007 -25.44
0.008 -68.46 0.01 -34.01 0.005 -26.93
0.006 -68.15 0.008 -33.86 0.003 -27.59
0.004 -68.15 0.006 -33.24 0.002 -28.89
0.002 -68.15 0.004 -33.24 0.001 -30.38
0.001 -67.99 0.002 -33.24 0* -34.03
0* -67.96 0.001 -33.09

0* -32.61

 

 

0*

Data

NOTE:

 

63

 

 

Table 8. Continued
Salt:CsI3 C313 C313

Solvent:DMF MeOH Formic Acid

Conc. (M) Appm Conc. (M) Appm Conc. (M) Appm
0.30 -3.38 0.05 37.43 0.3 12.34
0.10 -0.12 0.03 39.61 0.1 20.87
0.06 -0.12 0.01 42.25 0.05 23.51
0.04 0.34 0.008 42.35 0.03 25.06
0.02 0.34 0.006 43.64 0.01 26.45
0.01 0.34 0.004 43.64 0.008 27.07
0.008 0.49 0.002 44.42 0.006 27.23
0.006 0.49 0.001 44.88 0.004 27.54
0.004 0.65 0* 45.03 0.002 27.85
0.002 0.80 0.001 27.85
0* 0.9 0* 28.23

 

 

*
Data obtained by extrapolation.

NOTE:

CsTPB in acetone, DMF, DMSO are collected by L. L. Liu.

 

Fieu

64

 

 

 

 

 

 

 

 

 

L.
* —
_----—g -—--m-==«_—.o;-_-.-:&:_-.o:_-:::-:.:t=.:.- "'7‘“ TPB
0 I5
TPB'__,°
E e ————————— .----
o. __...o--“""
d "°__,_...-1:r"'"
D" - c s - ..
L1- ‘-----fi-—--——.—.&.--:__* ..... ---- '5 fi‘ '3
- scu‘
L.
-5ot
)-
*TPB-
"'1“ '3:' ‘7"- ‘."" '1'”"."‘7“"‘.“"T"‘.‘""I—T '3 . .
. 1
* l..L.LlU 0.005 ‘ C ‘4] 0°
PYRIDINE ------- MeCN
................. pc __ __ .__ DMSO
——--—---- ACETONE ._..__.__ DMF

Figure 12. Concentration dependence of the Cs-133 chemical
shifts of cesium salts in various solvents.

shift
that
the (
shifi
value
show:
CsSC)
pyric
and J
the j
The j

in t}

iOn I
One

giVeI

 

”hare

the

fa
the

 

65

shift !g_concentration together with the limiting shift
that determines the association constant. Thus even though
the CsTPB curve shows a much larger change in chemical
shift than does CsSCN, the latter reaches its limiting
value at lower concentrations than does CsTPB. iThis clearly
shows that the ion-pair association constant is larger for
CsSCN. The infinite dilution chemical shifts of Cs+ in
pyridine were -15.6, -30.8, and -29.4 ppm for Tea“, SCN‘,
and I3, respectively. The value -29.4 ppm was chosen as
the infinite dilution chemical shift of Cs+ in pyridine.
The ion pairing constants of CsTPB and CsSCN were calculated
in the following way.

The exchange between free solvated cesium ion and the
ion pair is fast on the NMR time scale, consequently, only
one resonance signal is observed and the chemical shift is
given by the expression (97)
= x

+X

Obs fo ipdip = 1p
where 6f and 61p are the chemical shifts characteristic of
the free and ion paired cesium ion respectively, while

Xf and xip are the corresponding relative mole fractions of
the two cesium species.

Obviously,

whe

sti

The

mat

Sul

ree

to
St.
tt
91

T)

66

where CfM is the concentration of the free cesium ion and

CtM is the total concentration of the cesium salt. Sub-

stitution of Equation (111.2) into (111.1) gives

M
Cf
60138 = E—E (6f - 61p) + in (111.3)
I:

The concentration equilibrium constant for the ion pair for-

mation is

M M
+ - c - c

2 (111.4)

 

 

Substituting Equation (111.4) into Equation (111.1) and

rearranging gives

{-1 + (1 + 4KainCtM)1/2]
1P

2 M 19
2Kayi C

6

 

obs
t

Equation (111.5) relates the observed chemical shifts
to the total concentration of the salt (CtM), the chemical
shift characteristic of the free Cs+ ion (6f) and that of
the Cs+ ion in the ion pair (dip), the mean activity co-
efficientyt and the ion pair formation constant Kip’
The values of CtM and 6f are obviously known and those
of Y: were calculated using Debye-Huckel Equation (111.6)
(3_= 5.3 A (100)). Equation (111.5) cannot be solved

directly since it has two unknowns 6ip and K1 The values

p.
of dip and of Kip were obtained with the help of a non-linear

lea

The

the

be

the

Tab

//

67

least squares curve-fitting program KINFIT (101).

 

6
1.823 x 10
3/2 |z+ z_|/I
(DT)

 

-log y: = (111.6)

9
1 + 5.029 x 10 a ,3

(DT)1/2 ‘—

The results are shown in Table 9. The ion pairing constant
(Kip) for the thiocynate salt is over twice as large as
that of the tetraphenylborate salt. This phenomenon may

be caused by the different extents of polarization of

the Cs+ ion by the two anions.

Table 9. Ion Pair Formation Constants of Cesium Salts in
Various Nonaqueous Solvents.

 

 

 

Solvent Salt Kip
pyridine CsTPB (3.7:0.3) x 102

CsSCN (9.3:0.2) x 102
Acetone CsTPB (2.110.3) x 10
MeCN CsTPB (3.8:1. ) x 10
PC CsTPB (1.610.?) x 10
DMF CsTPB m0

DMSO CsTPB m0

 

 

III.

have t
Cs+ ic
and 10
and co

a POpu

Shift a
free Cs
IESpect
ComPle
reaceic

rEPreSE

 

 

Ce.

68

III. FORMATION CONSTANTS OF CESIUM TETRAPHENYLBORATE

 

COMPLEXES WITH CROWNS AND CRYPTANDS IN VARIOUS

 

SOLVENTS.

 

In a solution of a cesium salt and a ligand we may
have the following solute species: ligand molecules, free

+ ions, ion—paired Cs+ ions, complexed Cs+ ions and, free

Cs
and ion-paired anions. When the exchange between the free
and complexed Cs+ ion is fast on the NMR time scale, only
a population averaged chemical shift is observed.

5 + 5. 5 x (111.7)

obs = GFXF 1pxip + c c
In the above equation 6obs is the observed chemical
shift and Xf, X.

1p'
free Cs+ ions, ion-paired Cs+ and complexed Cs+ ions

Xc are the relative mole fractions of

respectively. The corresponding chemical shifts of free,

complexed and ion paired Cs+ ions are 6f, 6 6 The

c' ip'
reactions which take place in a CsTPB solution may be

represented by:

Cs+ + solvent I Cs+'solvent

Cs+ + TPB- + Cs+'TPB-

4.

Cs+ + ligand I Cs+-ligand.

Cesium ions are not as strongly solvated as smaller

ions
actio
that
large
compe

be 51

 

 

CdUSe

We Wr

Where

WQr‘

as

EC.

(21

69

ions and therefore, the ion pairing and complexation re-
action may be more important. In this study it was found
that the formation constants of the complexes were much
larger than the ion-pairing constants: therefore, the
competitive reactions of ion-pairing and complexation can
be simplified by assuming that complexation is the major
cause of the variation of the chemical shift. That, is

we write

_ v
obs — GFXF + GCXC (III.8)

where

0:
>4
ll

6FxF + 61px ip
The formation constants of the complexation reactions

were determined by measuring the cesium chemical shifts

as a function of ligand/Cs+ mole ratio, then followed by

a computer fit of the data with the equation

_ M _ L_ 2 L2 2 _ 2
aobs — [(K ct K 0t 1) + (K ct + K cfiz 2K c EC:
L 1/2 Gf-ac
+ 2K ct + 2K cM + 1) II“ M] + 6c , (111.9)
t 2K cM
t

Equation (111.9) has two adjustable parameters, the forma-
tion constant K, and the limiting chemical shift of the

complex 5c (for details see Appendix B). In the above

70

M
t

the metal ion and ligand respectively. Due to solubility

equation C and c: are the analytical concentrations of
limitations, the concentration of CsTPB was kept at 0.01
M for all complexation studies. The crowns used in this
study were l8-Crown-6, dicyclohexyl-18C6 (DCC), and dibenzo-
18C6 (DBC). Their cavity diameters are reported to be in
the range of 2.6-3.2 A (16). The cryptands used were
C222 and C222B where B indicated the benzo group on the
ther chain (Figure 13). The cavity diameters of the cryp-
tands are about 2.8 A (102). All the results of this study
are given in Tables 10-14 and shown in Figures 14-18. Cesium
NMR resonance signals are usually very narrow (E 2H2).
Therefore no error bars are indicated in the chemical shift
XE! mole ratio graphs. The corresponding K value from each
mole ratio study was computed by using KINFIT and is listed
in Table 15.

Two techniques were involved to compute K values with
KINFIT: 112;! curvefitting and simulation. When the K

5 or larger, it is difficult to fit the

value is about 10
region around the sharp break at the stoichiometric mole
ratio. Usually the fitting process will either fail to
converge or will give a very large standard deviation.
The simulation technique uses KINFIT to imitate a system
which is fully defined by a set of given conditions. For

example, the initial estimate for a curvefitting process

is the starting value which is varied by iteration. For

A /O/-—-V—\O\ A

/__\

\
O
M

 

71

Amused
“12$.an .. mum

m nxuo .

.mocsumwuolnmu was mc3onu .mH ousmwm

A mummo V

QZ<PQ>EUINNNIONmeOZOE

_ r\

Anomo V

®IZ>>OmUImFIJ>XwIOJ O>O_Q leEOmUImFIONmeE

n21»?
R/lxwlxob , \

\nlJ,\(|/

o o

ZQ

O

.66.

“mosey
slzsomolme

 

72

Table 10. Mole Ratio Study of 18C6 Complexes with Cesium
Salts in Various Solvents by Cs-133 NMR at 25°C.

 

 

Salt:CsTPB
Solvents:Pyradine Acetone PC
|18C6| |18C6| |18C6|
[08+] Appm [08+] Appm [08+] Appm
0 32.38 0 35.41 0 36.16
0.28 17.66 0.36 23.77 0.27 28.80
0.51 9.37 0.72 10.42 0.5 21.44
0.78 -3.48 0.90 7.19 0.77 14.73
1.0 -9.91 1.00 6.35 1.00 10.72
1.19 —6.56 1.46 9.89 1.28 9.79
1.46 -0.222 1.19 7.47 1.58 10.54
1.90 5.65 1.80 13.15 1.74 10.54
2.04 8.91 2.00 14.46 2.12 11.93
2.56 15.90 2.50 18.28 2.60 13.42
3.03 20.08 2.77 19.67 3.10 14.54
4.09 26.06 5.15 28.99 5.40 19.29
6.28 34.06 7.08 33.18 6.89 21.53
6.91 35.45 10.3 36.81 8.90 24.51
12.62 40.95 16.54 40.54 22.40 33.27
18.95 41.38 31.3 35.88

 

73

 

 

Table 10. Continued.
DMF MeCN DMSO

[18C6] [18C6] [18C6]

[Cs+] Appm [Cs+] Appm [Cs+] Appm
0 0.81 0 —24.51 0 -67.96
0.33 -0.37 0.33 -21.16 0.23 -58.18
0.63 -l.98 0.62 -18.55 0.59 -44.76
0.90 -2.73 0.77 -l7.15 0.90 -34.98
1.00 -2.82 1.00 -15.48 1.00 -33.40
1.35 -2.82 1.28 -14.45 1.24 -30.51
1.45 -2.63 1.40 ~14.18 1.45 -29.21
1.69 -2.54 1.89 ~12.96 1.80 -27.25
1.99 -2.17 2.06 -12.68 2.19 -25.95
2.72 -l.42 2.49 -ll.75 2.33 -25.67
3.0 -0.96 3.23 -10.26 3.12 -24.08
5.19 1.37 4.85 -6.81 4.72 ~22.22
7.60 3.70 7.26 -2.62 7.24 -20.08
10.23 5.94 11.05 2.78 9.85 -18.50
30.74 18.23 19.7 -12.81

 

74

 

 

Table 10. Continued.
Salt:CsI CsI CsCl

Solvent : DMF H20 H20

|18C6| |18C6| |18C6|

[Cs+] Appm [08+] Appm [Cs+] Appm
0 -l.89 0 -0.55 0 -0.19
0.32 -3.01 0.28 -0.65 0.5 -0.19
0.51 -3.10 0.51 -0.65 1.0 -0.19
0.82 -4.03 0.72 -0.74 1.5 -0.59
1.00 -4.31 1.00 -0.74 2.0 -0.59
1.55 -4.03 1.48 -0.74 2.5 -0.75
1.81 -3.75 1.26 -0.93 4. -0.90
2.15 -3.47 1.82 -1.11 6. -1.06
2.67 -3.01 2.05 -l.11

3.15 -2.35 3.20 -l.38 8. -l.37
5.08 -0.40 2.49 -1.30

6.90 1.47 7.31 -l.86

4.06 5.19 11.41 -2.16

20.7 11.71

24.35 13.67

 

75

Table 11. Mole Ratio Study of BBC Complexes with CsTPB in

Various Solvents by Cs-133 NMR at 25°C.

 

 

 

 

Solvent:
Pyridine Acetone PC
L9§§l Appm LQEEl' Appm L2§§l Appm
[Cs ] [Cs ] [C8 J
0 32.23 0 35.52 0 36.01
0.15 28.77 0.06 34.90 0.19 34.28
0.46 20.46 0.32 30.19 0.46 30.55
0.65 17.48 0.63 26.72 0.685 28.82
0.99 13.88 1.00 25.10 1.00 27.08
1.29 15.62 1.38 26.96 1.20 26.71
1.50 17.97 1.49 27.58 1.39 26.71
1.92 24.92 1.79 29.69 1.40 26.71
1.98 25.30 2.00 30.81 1.55 27.20
2.18 33.49 *2.91 32.30 2.17 28.20
2.41 29.02 2.24 28.32
3.22 34.11 *3.0 29.69
6.17 39.57
7.48 40.31
*9.81 40.68

 

*DBC not completely dissolved.

76

Table 11. Continued.

 

 

 

 

Solvent:

DMF MeCN DMSO
L2§§l. Appm L2§§l. Appm LEEEl Appm
[Cs J [Cs 1 [Cs ] ‘

0 1.89 0 -24.41 0 -68.08
0.13 2.51 0.29 -20.07 0.13 -66.60
0.36 3.63 0.45 -16.84 0.32 -63.99
0.57 4.74 0.61 -15.23 0.55 -61.14
1.00 5.86 1.00 -8.90 1.00 -55.93
1.13 6.73 1.25 -5.18 1.14 -54.81
1.33 7.10 1.48 -2.57 1.20 ~54.31
1.54 7.71 1.59 -1.33 1.69 -49.60
1.86 8.59 2.04 3.13 1.84 ~47.74
2.06 8.96 2.27 5.62 2.14 —56.00
2.12 9.33 2.65 8.59 2.31 -44.76
2.61 10.82 2.95 10.95
3.33 11.82 4.07 17.15

3.74 12.44 5.82 23.36

 

 

77

Table 12. Mole Ratio Study of DCC Complexes with CsTPB in

Various Solvents by Cs-133 NMR at 25°C.

 

 

 

 

Solvent:
Acetone PC Pyridine
fiE§§% Appm £E§§% Appm %%§%% Appm
0 36.26 0 35.77 0 32.25
0.27 24.48 0.22 23.23 0.19 23.19
0.56 10.59 0.40 17.28 0.39 5.07
0.89 -6.29 0.75 —3.32 0.71 -l3.41
1.00 -9.14 1.00 -13.00 1.00 -30.78
1.15 -l4.97 1.10 —18.58 1.23 -33.76
1.44 -l8.45 1.50 -21.06 1.52 -34.13
1.87 -18.82 1.70 -21.19 1.64 -34.13
1.99 -18.82 2.14 -21.56 2.09 -33.76
2.17 -18.82 2.49 -21.68 2.13 -33.89
2.42 -18.57 2.97 —21.43 2.76 -33.02
2.83 -18.32 3.09 -21.43 2.93 -32.77
3.07 -18.08 3.25 -21.31 2.99 -32.40
5.86 -15.35 4.45 -20.56 4.53 -30.04
7.79 -13.61 6.29 -l9.32 6.11 -27.93
8.74 -17.84 9.35 —23.96

 

78

Table 12. Continued.

 

 

 

 

 

Solvent:

DMF MeCN DMSO
£2991 Appm £2991 Appm [DCC] Appm
[c.+] [es+1 [cs*]

0 1.15 0 ~23.88 0 -68.27
0.17 -3.07 0.22 -26.36 0.25 -65.17
0.46 -9.77 0.55 -30.58 0.45 -62.44

‘0.73 -14.86 0.89 -34.67 0.72 -60.08
1.00 —20.32 1.00 -35.66 1.00 -57.60
1.25 -23.05 1.14 -36.41 1.26 -55.86
1.46 -24.66 1.65 -37.03 1.47 -55.24
1.60 -25.78 1.94 -37.03 1.89 -54.25
2.03 -27.39 2.02 -37.03 1.99 -53.51
2.19 -28.01 2.43 -36.66 2.6 -52.88
2.49 —28.63 2.75 -36.90 3.03 -51.77
2.91 -29.01 3.04 -36.78 3.37 -51.77
3.27 -29.25 3.71 -36.28 6.54 -49.78
5.06 -29.38 5.53 -35.29 8.52 -49.03
6.12 -29.50 6.74 -34.92
9.81 -29.38 8.86 -33.68

 

 

79

Table 13. Mole Ratio Study of C2228 Complexes with CsTPB
in Various Solvents by Cs-133 NMR At 25°C.

 

 

 

 

Solvent:
PC Pyridine Acetone

L—lfiif'i L—lizfi: L433?

0 36.34 0 32.25 0 34.90
0.21 22.74 0.32 15.37 0.36 14.38
0.52 -1.29 0.6 -3.61 0.5 -24.95
0.69 —14.71 0.83 -49.40 0.75 -39.47
1.04 -31.94 1.00 -66.89 1.00 -44.31
1.05 —35.11 1.16 -70.33 1.50 -50.14
1.16 -37.90 1.27 -74.83 1.70 -51.01
1.32 -39.67 1.36 -74.33 2.00 -51.75
1.49 -42.84 1.41 -75.33 2.50 -52.25
1.67 -44.87 1.64 77.56 3.53 -53.12
1.74 -46.06 1.77 -78.06 *w -54.0920.23
1.75 -45.73 1.99 -78.81
1.92 -46.75 2.52 -79.55
2.2 -48.05 3.20 -79.67
2.7 -49.45 *w -80.60:0.15
3.34 -50.2
*w -52.55:0.14

 

*
Obtained by the curve-fitting program.

80

Table 13. Continued.

 

 

Solvent:

DMF MeCN DMSO

 

|C22ZB| Appm ICZZZBI Appm

[C2228]

 

[03+] [cs+3 [03+] Appm

0 1.17 0 -24.09 0 -68.31
0.28 -4.12 0.35 -40.07 0.21 -68.46
0.41 -5.30 0.54 -50.62 0.53 '63.46
0.82 -11.20 0.68 -54.19 0.83 -68.46
1.00 -12.51 1.00 -65.51 1.00 '68.77
1.39 -17.07 1.32 -70.63 1.23 '68.46
1.53 -18.19 1.61 -72.33 1.42 -68.93
1.67 -19.77 1.98 -73.26 1.76 -68.93
2.0 -22.01 2.04 -73.26 2.18 '68.46
2.47 -24.99 2.41 -73.58 2.46 -68.46
2.90 '27.60 3.13 -73.89 3.07 -68.46
*m -51.8211.61 *W -74.-4i0.04

 

 

81

Table 14. Mole Ratio Study of C222 Complexes with CsTPB
in Various Solvents by Cs-133 NMR at 25°C.

 

 

 

 

Solvent:
PC Acetone MeCN

[c222] Appm [c222] Appm [c222] Appm

[Cs ] [Cs ] [Cs 1

O 36.45 0 35.83 0 -24.40
0.13 17.37 0.30 -17.17 0.26 -97.14
0.48 -56.72 0.58 -102.26 0.51 -132.97
0.72 —113.68 0.89 -165.60 0.72 -166.31
1.00 -175.56 1.00 -182.52 1.00 -206.17
1.19 -184.87 1.18 -192.51 1.37 -208.81
1.45 -189.21 1.58 -199.42 1.55 -209.58
1.93 -191.38 1.86 -200.36 1.72 -209.74
2.08 -191.69 1.97 -200.92 2.27 -210.20
2.23 -191.54 2.42 -201.29 2.36 -209.89
2.93 -l92.62 2.89 -201.85 2.87 -210.05
3.17 -192.62 3.03 -201.85 3.11 —210.20
*m -193.75:0.16 *m -202.96¢9.19 *m -210.39:0.11

 

82

 

 

 

 

 

 

Table 14. Continued.
Solvent:
DMF Pyridine

L—lizzi. —-‘E::i% ——‘:::i§

0 0.80 0 -67.01 0 30.81
0.19 -13.31 0.25 -70.56 0.25 -----
0.45 -35.02 0.57 -74.67 0.45 -----
0.60 -41.85 0.92 -79.90 0.72 -----
1.04 -63.30 1.00 -81.21 0.96 -217.33
1.20 -78.60 1.12 -82.52 1.28 -223.85
1.40 -87.60 1.46 -86.07 1.46 -224.47
1.70 -95.51 1.82 -89.99 1.81 -224.18
2.13 -105.90 2.12 -92.61 1.97 -224.18
2.40 -111.95 2.57 -95.97 3.05 -224.25
3.18 -121.25 2.75 -96.72
3.56 -124.51 3.26 -100.64
*w -155.80:2.30 *w -144.3413.52
1

Data collected by L. L. Liu.

83

 

 

 

 

 

._ j 1..Cssph4 1n pv; II--C58Ph4 in MezCO; Ill--CsBPha in pc; .3
'1' IV--CSBPh4 in DMF; V--CSI in DMF; Vl--C58Pha in New;
__€5() _y v11 --c:1 in H20; VIII-~C58Pha 1n onso __
1D"
1 1 1 1 1 _1 L L 1 1 1
2 4 6 8 l0
4.
18C6/[Cs]
Figure 14. Chemical shifts of cesium—133 as a function of
mole ratio of [18C6]/[Cs+TPB’] in various sol-

vents.

84

 

5C)

,_,..__...—i——-—o—-*—-u PYRI DINE

/./
/.
,....~-y6*/ ACETONE

PC

 

 

APPM

DMSO

 

 

1 1 l l I l L

1 2 3 4 5 6 7 8 9
[DBC]/(Cs+)

Figure 15. Chemical shifts of cesium-133 as a function of

mole ratio of [DBC]/[Cs+TPB'] in various sol-
vents. [CsTPB]T = 0.01 M.

 

85

 

0‘.

  
      

  

\‘K
K‘u-mo—o-M"""-°

\‘M-u-Hh --------------

 

APPM
,;

A—
f

 

 

 

V

1 2 3 4 5 6 7 8 9 10

Figure 16. Chemical shifts of cesium-133 as a function of
mole ratio of [DCC]/[Cs+TPB'] in various sol-
vents. [CsTPB]T = 0.01M.

86

 

 

 

 

 

 

40
20
0'
F" . .
0..
E 20, . . .
&’ ~ InwF
d
-40~ °
_ . PC
. ACETONE
-60 1-
1;? DMSO
94 A". i A MeCN
'80 ' V v PYRIDINE
-100-
l l l l l
1 2 3 4 5
lczzzsl
[05" I

Figure 17. Chemical shifts of cesium-133 as a function
of mole ratio of C2228]/[Cs+TPB'] in various
solvents. [CsTPB T = 0.01M.

87

 

 

    

 

 

 

4C
0
2 4
O.
0.
Id \3.
“100 ‘K\\* DMSO
*4 cm
'\
04%, PC
‘200 °*D‘°*wo~~ ACETONE
""°‘"" MeCN
" “1" W“ PYRIDINE
l L L 1 l J l

 

031-
N
m

2 3 4 5
[cad/[05+]

Figure 18. Chemical shifts of cesium-133 as a function of
mole ratio of 5C2228]/[Cs+TPB'] in various sol-
vents. [CsTPB T = 0.01M.

 

.1

 

 

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89

simulation the initial estimate may be used to mimic the
behavior of the system. For this reason, whenever the K
value was too high to fit an experimental curve, the simula-
tion technique was used to get a rough estimate of the
association constant. However, such estimate cannot be

taken very seriously,

(i) COMPLEXATION REACTIONS WITH CROWNS

The variation of the Cs—133 chemical shift as a func-
tion of the 18C6/Cs+ mole ratio in different solvents
is shown in Figure 14. It is immediately obvious that
the solvent plays an extremely important role in the com-
plexation process. The behavior in pyridine, acetone, and
propylene carbonate solutions is especially interesting in
that the Cs-133 resonance shifts linearly downfield until
a 1:1 ligand/Cs+ mole ratio is reached and then shifts
upfield as the concentration of ligand is further increased.
The data seem to indicate a two-step reaction. First the
formation of a stable 1:1 complex and then the addition
of a second molecule of the ligand to form a "sandwich"
complex (13) .

In DMSO and MeCN solutions the Cs-133 resonance shifts
only upfield with some indication of a weak "break" at
the 1:1 mole ratio. The resonance continues to shift

upfield even after the formation of a 1:1 complex but

90

there is no clear-cut evidence of a 2:1 complex. However,
least-squares fitting of the data (Figure 19,20) based on
the formation of only the one-to-one complex gave a large
standard deviation and the fit was poor especially at lower
concentrations of ligand. Therefore, a model was used
which assumed that both one-to—one and two-to-one complexes
are formed. The fit was much better as shown in Figure

19-

Cesium tetraphenylborate complexes with 18C6 in MeCN
showed similar features to those in DMSO. Once again,
attempts to fit the data, as shown in Figure 20 by assum-
ing formation of only the 1:1 complex gives large devia-
tions of the calculated curve from the experimental one.

An attempt was made to include the 2:1 complex in the
calculation. This resulted in a reasonably good fit of

the data but a big standard deviation for the first forma-
tion constants (K1). This big standard deviation is mainly
caused by the large value of K1.

When 18C6 forms a complex with CsTPB in pyridine solu-
tion, the change in-direction at 1:1 mole ratio clearly
indicates the formation of a second complex. However, the
variation of the chemical shift with mole ratio does not
clearly indicate the stoichiometry of the subsequent
complexation. In order to discriminate a sandwich complex
(2:1) from a club sandwich complex (3:2), a study of the
temperature dependence of the chemical shift was carried

out. From the data listed in Table 16 and plotted in

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vs. [18C6]/[Cs+TPB ] in DMSO.

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Table 16. Mole Ratio Study of 18C6 Complexes with CsTPB
in Pyridine at 24°C, -6°C, -38°C.

 

 

Appm (X§° 1:1 Complex)

 

[1806]

[03+] 24°C -6°C -38°C
1.00 0 0 o
1.34 6.36 13.80 20.01
1.45 10.24 22.49 31.95
1.77 15.51 32.41 45.78
2.00 18.15 35.52 51.83
2.20 21.71 40.01 .58.19
2.50 24.66 29.77 61.91
2.83 27.61 32.25 64.24
3.00 29.62 34.88 65.94
5.44 41.41 44.33 69.98
7.90 46.99 47.29 71.06
9.75 48.85 47.60 71.22

 

 

94

Figure 21, it is clear that the subsequent reaction forms
a sandwich complex. The mole ratio plots in acetone, PC
and DMF also exhibit a dip at a mole ratio of one. There-
fore, by analogy, sandwich complex formation is postulated.
However, one interesting feature in the mole ratio-chemical
shift plots is different. In pyridine solutions the plot
exhibits a sharp change in direction and a discontinuous
slope. The other three solvents give a somewhat different
shape. These differences reflect different values of K1
and K2. In pyridine, K1 is much larger than K2 but the
latter is also large. Therefore, a sandwich complex
starts to form only when most of the Cs+ ions have already
formed the Cs+°18C6 complex. This condition gives a sharp
discontinuity in the mole ratio-chemical shift plot at

the 1:1 ligand/Cs+ mole ratio. For the other solvents, K1
is not as large as in pyridine and K2 is also smaller.
Therefore, a "rounded-off" dip is produced, because at
mole ratios around unity both complexation reactions
(1.3;, formation of Cs+118C6 and Cs+- (18C6)2) are taking
place. A typical fit of the data obtained in PC at 25°C
with an equation which assumes a two step reaction with
shifts in the opposite direction is shown in Figure 22.

It is also important that, in spite of the great dif-
ferences in the shape of the curves, the limiting chemical
shift of Cs+-(18C6)2 complexes as determined by the KINFIT
program (Table 17) seem to be independent of solvent.

This contrasts with the large solvent dependence of the

95

 

 

 

 

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97

 

 

 

Table 17. Limiting Chemical Shifts in Various Solvents.
Solvent Cs+ Cs+-(18C6) Cs+-(18C6)2
PC 36.45 8.1:0.2 46.5:0.9
Acetone 35.83 6.35 47. t9.
Pyridine 32.38 -9.35 48.2:0.2
DMSO -67.96 -23.7¢0.4 49. :24.

 

 

chemical shifts of the free cations and of the one-to-one

complexes.

This observation indicates that the primary

solvation shell of the Cs+ ion is more or less completely

displaced by the ligand when the two-to-one complex is

formed.

The attachment of two benzo groups on 18C6 to form

DBC, was expected to result in weaker complexes. This

aromatic group decreases the basicity of the oxygen atoms

(10) and also decreases the 0-1-0 distance which causes a

decrease in cavity size (50).

complexes with CsTPB in six solvents was made.

A mole-ratio study of DBC

The results

showed some similarity to the case of 18C6: i.e., in pyri-

dine, propylene carbonate and acetone we also observed 2:1

complex formation, while in DMF there was no change of

direction, but only a continuous shift to higher fields

which continued up to the solubility limit of DBC. In

98

MeCN and DMSO solutions, although the shift is in the same
direction as in the case of 18C6, the curvature of the plot
is much smaller. This shows that the complexation is
weaker. An investigation of the half-height linewidth
(Avg) at room temperature shows that DBC also forms more
labile complexes with Cs+ than does 18C6. In the exchange
region, i.e., when the mole ratio of ligand to total Cs+
is approximately 0.5, the half-height linewidth for 18C6
in pyridine (36.59 Hz) is much larger than it is with DBC
(<le). This phenomenon indicates that the 18C6 complex
is less labile than the DEC complex and has a slower ex-
change rate at a given temperature. Even though it is
hazardous to draw conclusions about thermodynamics from
rate phenomena, we expect the more labile complex in these
systems to be also the more weakly bound.

It was of interest to test the effect of a complexing
agent which does not have aromaticity: therefore, dicyclo-
hexy1-18C6 (DCC) was used. This ligand has five isomers
of which only two have been isolated (termed isomers A and
B). A mixture of these two isomers was used in this study.
Figure 16 shows that some features of the plot of chemical
shift Kg. the mole ratio (DCC)/(Cs+) are different from
those with 18C6 and DBC. There is no clear-cut change
in direction (or reflection point) at a mole ratio of
one-to-one as found for 1806 and DBC in pyridine, propylene
carbonate, and acetone solutions. The extent of the down-

field (paramagnetic) shift is much greater for DCC in DMF

 

(5741' ILIIII I." 747‘ ' III-I'll.

99

and the direction of the shift in the case of MeCN is also
changed. This phenomenon may be caused by the higher
rigidity of the DCC framework which results in a larger
overlap of the lone pair electrons of oxygen with the
cesium ion. This will introduce more orbital angular
momentum, and thus more paramagnetic shift.

All three crown complexing agents form 2:1 complexes
in PC, acetone and pyridine. Formation constants were
obtained by fitting the appropriate equation to the data
with the KINFIT program. The results are listed in Table
15. When the formation constants were too large, lower

limits were estimated by simulating the data with KINFIT.

(ii) COMPLEXATION REACTIONS WITH CRYPTANDS.

 

Cryptands are tridimensional ligands which can completely
enclose a metal ion within the cavity. This property would
make the complexation of cesium ion by cryptands stronger
than that with crowns, except that the cation may be too
large to fit into the cavity easily. The change of the
chemical shift of Cs+ with the concentration of cryptand
is in the paramagnetic direction. The magnitude of the
shift for Cs+ complexes with cryptands is much larger than
with crowns. This phenomenon, which is especially pro-
nounced with C222,indicates that cryptands can perturb
the Cs+ ion more;probably by increasing the overlap because

of short range repulsions and introduce a larger orbital

100

angular momentum. With an ortho-benzo group in place of

a -CH2-CH2- group in one of the ether chains, C2223 not
only has a decrease in the O-o-O distance, and more rigidity
of the ligand but also a decrease in the basicity of the
oxygen atoms on that branch. Therefore C2228 should have
less ability to "swallow" the cesium ion into its cavity
which should lead to a (thermodynamically) weaker complex
than with C222. This speculation is confirmed by the ther-
modynamics of complexation. The kinetics of exchange also
indicates a more labile complex. At room temperature and
(ligand)/(Cs+)=0.5, the resonance line of Cs+ with C222

in pyridine was so broad that the signal is barely obser-

vable (Av >400 Hz), while for C2223, A08 in this region is

15
approximately 15 Hz (Table 18). Another interesting fact
is that in DMSO with C222B, there is no chemical shift
variation as more ligand is added, while with C222, weak
complexation is observed. On the other hand, all crown
ligands form relatively strong complexes in DMSO. Perhaps
this is because the solvent can still play an important
role when crown complexes are formed. When Cs+ is com-
plexed by cryptand but before it has been completely
surrounded by the cage, a strong competition between ligand
complexation and solvation may be taking place as illus-
trated in Figure 23. Dimethylsulfoxide is a good donor
solvent, so that a weaker complexing agent such as C2228

cannot compete for Cs+ and no chemical shift variation

results as the mole ratio is increased. However, in the

101

'k
Table 18. Half-height Linewidth (Av15 Hz) of Cs+-Ligand
Complexes at 24°C.

 

 

 

 

 

Ligand Ligand/Cs+ Avg (Hz)
DCC z0.5 69.65
DBC zO.5 1
C222 20.5 >400 Hz
C222B zO.5 14.47
18C6 40.5 36.59
0 1.00
0.39 16.17
1.00 2.22
1.5 51.00
2.0 51.00
2.5 51.00
*
Av% = (v%)sample - (Vk)ref°

 

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102

 

 

IB-CROWN‘G

The interaction of Solvent Molecules With Complexed Cesium Ion.

Figure 23.

103

case of C222, a stronger complexing agent, the Cs+ can be
complexed more readily so that there is some chemical shift
variation with ligand concentration. Because of the deli-
cate balance between solvation and complexation, it seems
that cryptands can serve as good ligands for the investiga-
tion of solvent effects and ligand effects on the complexa-
tion reaction.

The expression of Das (Equation 1.15) for the chemical
shift in an electrolyte solution, indicates that the extent
of the paramagnetic shift is determined by the overlap
integrals of ion-solvent and ion-ion interactions. This
idea, together with considerations of size and complexing
ability can be used to explain the direction and magnitude
of the shift which occurs upon complexation as well as
solvent effects in electrolytic solutions. When a complexa-
tion reaction occurs in an electrolyte solution, there is
competition between the donating ability of the solvent
molecules, the counterions, and the donating sites of the
complexing agent. This competition will have two effects
on the variation of the chemical shift with the concentra-
tion of the complexing agent. For example, Figure 24 shows
graphs of the chemical shift (in ppm) XE the mole ratio in
DMF for all five ligands. This example clearly shows the
two features referred to above. The "sharpness" of the
curvature tells how easily the complexing agent can compete

with the solvent, leading to displacement of the solvent

104

 

 

50
_ 93C 18C6
.__”_.u£p—~—""W—O
011" I III 4"”k
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g C2228
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C222
L J L 1 J l L 1 1 I l

 

 

 

5 1O
LIGAND/[cg] IN DMF

Figure 24, Mole ratio-cesium-l33 Chemical Shift Study for
Various Ligands in DMF.

105

shell and the counter ion. That is, the curvature gives

us thermodynamic information. However, the direction

 

of the chemical shift variation and the ultimate extent of
the shift depends upon how much the donating electron pairs
of the complexing agent can perturb the electron cloud of
the cation. This perturbation, when greater than that of
the solvent, leads to a paramagnetic shift. Dibenzo-18C6
appears to have weaker interaction of the lone pairs with
the cesium ion than is the case for the other crowns,
probably because of its rigidity and lower basicity of
the oxygen atoms. In DMF solution, the chemical shift
moves upfield with an increase in the mole ratio (that is,
as the concentration of BBC increases). This phenomenon
implies that the donating ability of the lone-pairs on
oxygen in BBC is weaker than those of DMF. However it
should be noted that repulsive interactions at short range
contribute to the shift so that one cannot equate the
magnitude of the shift only with an attractive interaction.
Indeed, when the interaction is "forced" as when Cs+ is
inside of a cavity which is too small, the repulsive inter-
actions can lead to large paramagnetic shifts. In any
event, the chemical shift variation indicates that complexa-
tion is taking place.

In the case of 18C6 which shows a change in direction
of the shift at the 1:1 mole ratio, the upfield shift
shows that the net contribution of the lone pair electrons

of the 12 binding sites in a 2:1 complex is smaller than

106

that of the 6 binding sites of the 1:1 complex. This ob-
servation probably results from a large decrease in the in-
dividual overlap integrals in the 2:]. complex as the short-
range repulsions are relaxed. The half height linewidth
(Table 18) also decreases when the sandwich complex is
fornmed. This phenomenon would be expected if the 12 oxygen
atcuns were symmetrically distributed around the cesium
ion.

For DCC, the aliphatic cyclic substituent results in a
better donating environment (_i_.£._, closer oxygen-Cs+
contacts) as manifested by the chemical shift-mole ratio
plot. Among all three crowns, DCC has the largest para-
magnetic shift even though it does not form the strongest
(unmplex. The second formation constant of DCC complexes
‘With Cs+ is the smallest of all three crowns in a given
SOlyent. Both cryptands, with two more binding sites, and
Probably much closer oxygen-Cs+ contacts because of steric
lfiJnitations can perturb the Cs+ electron cloud more and,
therefore, introduce a larger paramagnetic shift than any
(If the crown ligands. However, probably because of the
rigidity and size of the tridimensional ligands the stoich-
ixmmetry of the complexes stops at 1:1.

A close examination of the K values for a given ligand
shows clearly that the solvent plays an important role in
the complexation. With crown type ligands, probably
because the complexed (in 1:1 complexes) and the free

cation both interact with the solvent appreciably, the

107

complexation constant is not as sensitive to solvent as
with the cryptands. Figure 23 shows schematically how
complexation and solvation might take place on opposite
sides of the cation which could make this complexation
system more affected by the solvent. Therefore, C222
was chosen to examine the relationship between solvent
properties and the complexation equilibrium. The values

of log K for C222 obtained in six solvents and in H O

2
and MeOH from another source (50) are listed in Table 19.
Pyridine has the highest donor number but the lowest di-
electric constant of all the solvents listed and it forms
the strongest complexes. In PC, a solvent with the highest
dielectric constant and the next to lowest donor number,

an intermediate value log K is obtained. When water,

DMF and DMSO are all solvents of high donor ability and
high dielectric constant and all have small values of log
K. These phenomena follow exactly the behavior found for
ion pair formation. This fact may indicate that for a
weakly solvated cation such as Cs+, the interactions
between cations, anions, ligand molecules and solvent mole-
cules depend on both the donor ability and the bulk di-

electric constant of the solvent. The size and geometry

of the solvent molecules may, of course, also play a role.

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109

IV. TEMPERATURE DEPENDENCE OF THE CHEMICAL SHIFT AND ITS

RELATIONSHIP TO THE THERMODYNAMICS OF COMPLEXATION

REACTIONS.

(A) CESIUM TETRAPHENYLBORATE COMPLEXES WITH 18C6 IN

PYRIDINE.

In this section, a detailed study of the two step re-
action of the 18C6 complexed with Cs+ ion in pyridine will
be considered. The possible equilibria for this system

were first prOposed as follows:

When the mole ratio of (18C6) to (Cs+) is zero,ion

pair formation can occur:

K.
Cs+ + TPB- $9 Cs+°TPB— (111.3)

The observed chemical shift can be expressed as

6 X (III.4)

6 = 6 F F

obs ipxip +

When 18C6 is added to the cesium tetraphenylborate

solution the possible reactions may be expressed as

110

 

 

+ - ip +
Cs + TPB -...:_ Cs -TPB- (III.3)
+ +
18C6 18C6
K!
+ — lp - +
C8 ~18C6 'I' TPB =_——-.__=' TPB 0C8 ~18C6 (111.5)
+ +
18C6 18C6
+ + -
Cs 1(18C6)2 Cs -(18C6)2 + TPB

In order to see if the above reaction scheme can be
simplified, two studies of the concentration dependence of
the chemical shift were carried out. The data obtained
for reactions III.3 and III.5 are shown in Table 20 and
Figure 25. It can be seen that the salt solution shows
substantial ion-pairing (Kip =(3.7:0.3) x 102 as mentioned
in Section 111.1) while the 1-to-l complex of 18C6 with Cs+
gives no evidence for contact ion pair formation. That is,
K! = 0, and the above scheme can be reduced to three re-

1P
actions, i.e.

p Cs+:TPB- (III.3)

+04

Cs + TPB-

111

 

 

 

Table 20. Concentration Dependence of the Chemical Shift
at 25°C for CsTPB and its 1:1 Complex With 18C6
in Pyridine

Cs¢4B Cs¢4B + 18C6 (1:1)
Conc. 6conc. Conc. 6conc.
0.015 37.81
0.121 37.18 0.020 -7.25
0.010 33.15 0.015 -8.49
0.009 31.29 0.010 -9.58
0.008 29.12 0.008 -9.73
0.007 26.94 0.006 -10.35
0.006 24.46 0.004 -10.97
0.005 22.29 0.001 -10.66
0.004 17.95
0.003 14.23
0.0025 11.74
1.002 8.03
0.001 1.27
0.005 -8.25

 

 

112

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Edwmmo mo coaumuucmocoo map nufi3 coaumwum> umwnm a80fiEmno mMHIEdwmoo .mm whomwm

:2. ZO_._.<m._.Zm 0200

 

 

 

 

90.0 .00 wood .ood
. q 4 J 4 — 1 q a u _ d u q 1
I: x :1! Ln 1 1 of.
Ju‘l 4 41
14 8948
1 O
1 Dr
V
.d
_d
“W
1 ON
.
1 Om

+mo

 

113

+ K; +
Cs + 18C6 + Cs ~18C6 (111.6)
K
+ .2, +
Cs -18C6 + 18C6 + Cs ~(18C6)2 (111.7)

The observed chemical shift can be expressed as

6obs

GFXF + GiPXip4-6clxcl + SC XC (III.8)

Where F, ip, 01' c2 denote uncomplexed Cs+, ion-paired
Cs+, Cs+-18C6 and Cs+-(18C6)2 respectively. By convention,
diand Xi denote the chemical shift and the relative mole
fraction of Cs+ in state i respectively.

In order to express the relative mole fractions in terms

of overall concentrations the equilibrium constants are

used as follows:

Let C denote 18C6, then

Kip = [Cs+-TPB-]/[Cs+][TPB-] (111.9)
K1 = [Cs+-C]/[Cs+][c] (111.10)
K2 = [CS+'C2]/[CS+C][C] (111.11)

Let C total concentration of cesium salt.

ISM-336

total concentration of 18C6.

114

then

c; = [c5+] + [Cs+-TPB‘] + [CSCI] + [Cscg] (111.12)
CE = [C] + [CsC+] + 2[CsC§] (111.13)

Equation 111.12 can be further expressed in terms of

[Cs+] through

c; = [Cs+] + Kip[cS+][TPB'] + K1[Cs+][C] + K1K2[Cs+][C]2

+- _ T - 2
[Cs ] - CM/{l + Kip[TPB ] + K1[C] + K1K2[C] } (I11.14)

Equation 111.13 can be rewritten as

CE = [c] + xltc8+][c] + 2K1K2[Cs+][c]2 (111.15)
[C]2{2K1K2[Cs+]} + [C]{l + K1[Cs+]} - CE = 0
therefore

 

-{1+K1[Cs+]} +‘V]1+K1[Cs+])2+8K1KZCE[Cs+]

 

[C] = (111.16)

+

4K1K2[Cs ]
The negative root was discarded because a negative

[C] value has no physical meaning. If [Cs+] and [C] can

be obtained then

115

xC = K1[Cs+][C]/C§
x l - K K [c +][c]2/cT
c2 ‘ 1 2 S M
xf = [Cs+]/C§
xip = [Cs+-TPB-]/C§ = Kip[cS+][TPB‘]/c§

Thus, Gobs could be easily calculated with information about

6f, 6. 6

1p'
contains [C], while that for [C] also contains [Cs+]. In

and 6 . However, the expression for [Cs+]
C1 C2

order to solve for [C] and [Cs+] without solving a cubic
equation, an iteration technique was used to obtain both the
concentration of Cs+ and that of 18C6. An initial estimate

of [Cs+] was made which depended upon the ratio of CT

L
T T T + ~ T _ T
M! When CL < CM' then [Cs ] ~ CM CL because K1

is large. When CE z C3; [Cs+]:K(-1 +‘Vl+4K1C§)/2K1 and

when CE > C3, [Cs+] is very low. For the third case, an

arbitrary small number was chosen, [Cs+] z 10-7, as an

to C

initial estimate. Starting with an initial estimate, the
first value of [C] was obtained and used to calculate a
more accurate estimate of [Cs+]. This procedure was re-
peated until the ratio of the "current" value of [C] to
the previous value of [C] was close to unity. Then the
final values of [C] and [Cs+] were used to calculate rela-
tive mole fractions and thus Gobs‘ The Fortran expression
and EQN subroutine deck structure which were used are listed
in Appendix B-II.

As the data listed in Table 1 indicate, most macro-

cyclic complexation reactions are exothermic. It was

116

therefore of interest to investigate the temperature de-
pendence of the complexation of Cs+ by 18C6 in pyridine.
In previous work, Lehn and coworkers (41) and Cahen 93 31.
(93) both noted that the apparent chemical shift of the
complexed metal ion varied with temperature. However no
detailed study was made,probably because of difficulty in
finding a prOper absolute reference. For the present
temperature study, an absolute reference was designed

which was suitable for all temperatures (Figure 26).

/ TO VACUUM

5 MM A
wanm 1%
NMR was f

 

 

.flONfll\NHJIAD
NMR TUBE

 

 

0.5 M Cst
AQUEOUS
SOLUTION ‘

Figure 26. Insulated NMR Reference Sample.

117

A 0.5 M CsBr aqueous solution was sealed into a 5 mm pre-
cision Wilmad NMR tube which was concentrically sealed in
a 10 mm precision Wilmad NMR tube. The space between the
tubes was evacuated to 10"6 torr and then sealed.

The validity of this reference was tested and the
results are shown in Figure 27 and are given in Table 21.
The chemical shift of a 0.5 M CsBr aqueous solution in a
10 mm NMR tube was recorded as a function of temperature
from the readout of the spectrometer. It was measured at
the same temperature as the probe. The chemical shift
of the absolute reference in the insulated tube was also
recorded from the readout of the spectrometer. The measure—
ment was made under exactly the same conditions as with the
10 mm NMR reference tube, but the insulated reference was
left in the probe only during the time of data collection
(ELEL' less than one minute). In this way, the temperature
of the solution in the insulated tube is at or near room
temperature. The constancy of the chemical shift for the
sample in the insulated tube demonstrates the validity of
this technique in providing an absolute reference. Of
course, the results also indicate that the interaction of
the solute with the solvent changes with the temperature
to give a temperature-dependent chemical shift.

Sharp and coworkers (83,84) also observed this phenom-
enon, but they compared their chemical shift to an external
reference which was measured at the same temperature as

sample. Their major interest was to measure the variation

118

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0e mm3h<mmafiwr

om<oz<hw awh<43wz. OEEmIb o
meh :22 52°F fl

0'

on

“66

 

119

Table 21. Data from the Test of the Insulated Reference

Tube.

 

 

Varian DA-60 1.4T
Mixing Frequency 48.585800 MHz
Sweep width = 1000 Hz
200 ns.

Dewell time = 500 us

Delay time =

 

Temperature (°C) 10 mm NMR Tube Insulated Standard

 

81.0 44.17 52.17
71.5 45.54 51.06
57.0 47.83 52.17
48.0 49.13 52.11
38.0 50.56 51.80
27.6 51.99 51.99
14.0 53.91 52.30
5.8 55.15 52.55
-0.6 56.39 52.48
-15 ----- 52.67
-26 ----- 52.42
-42 ----- 52.24

 

 

120

of the chemical shift with concentration at various tempera-
tures and they did not emphasize the temperature dependence
of the shifts.

With the aid of this new reference, a series of measure-
ments were made of the temperature dependence of the
chemical shift for the 18C6 complexes with CsTPB and for
CsTPB itself. The results are listed in Table 22 and
shown in Figure 28. The figure shows not only the marked
change in chemical shift which occurs when 1:1 and 2:1
complexes form, but also how the chemical shifts of free
and complexed cesium ions respond to variations in tempera—
ture. As the temperature decreases, the difference between
the chemical shifts at mole ratios of zero and one gets
smaller because the chemical shift of the 1:1 complex is
less sensitive to temperature. As shown for the region
of mole ratio larger than one, the second formation constant
increases as the temperature decreases and eventually the
"break" in the curve is sharp enough to show clearly that
the stoichiometry of the second complex is 2:1. It can
also be seen that the limiting chemical shift for the 2:1
complex is not very sensitive to temperature. All of the
chemical shift-mole ratio curves at different temperatures
show very sharp changes in direction at a mole ratio equal
to one. This condition makes it impossible to extract a
complexation constant from the data between mole ratios of
zero and one by the nonlinear least-squares technique.

However, it is possible to obtain an order of magnitude

1J21

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122

A ppm

 

 

 

 

.; [IBCG]
IO [C5¢4d

 

 

 

 

 

Figure 28. A three-dimensional plot of the cesium-133
chemical shift !§_mole ratio and temperature
(°C) for solutions of CsTPB and 18C6 in pyridine.
The concentration of CsTPB was 0.01 M.

 

123

estimate of K1 through simulation of the data by the
iteration technique previously described. All such simu-
lated "data" were compared with experimental results and
adjustments in K1 were made as needed. The values used for
K2 were obtained by a least-square fit of the data obtained
at mole ratios higher than one. Two representative results
are shown in Figure 29. The corresponding K1 and K values

2
are listed in Table 23.

Table 23. The Simulated Formation Constants (K ) and Least-
squares Adjusted Constant (K ) for the Complexa-

tion of Cesium Tetraphenylborate by 18C6 in
Pyridine at Various Temperatures.

 

 

 

Temperature °K K1 K2
297 5 x 108 71.3
285 5 x 108 116.6
272 5 x 108 209
255 109 414
244 3 x 109 605
235 6 x 109 1140
229 3 x 1011 3440

 

 

Since the K1 values are much larger than K2, at mole
O + 0
ratio equal to one, most Cs can be con31dered to have been
+ . . .
converted to Cs ~18C6. Therefore, it is p0831b1e to obtain

K2 values by fitting the data beyond a mole ratio of 1:1 with

124

 

 

 

 

 

 

 

 

E

Q

0.
G --::::::::::-;::;:W
235'K
I 1 L g L L 4 .1 l 1
‘30 23456789l0

[mod/[05+] IN PYRIDINE
Figure 29.

A Comparison of simulated data (0) with experi-
mental data (A») for a chemical shift - mole

ratio study at 290°K and 235°K for solutions
of CsTPB and 18C6 in pyridine.

125

the KINFIT program (Table 24) and thus obtain the enthalpy
of the second complexation reaction. This procedure gives
H2=-6.l6i0.09 Kcal/mole. The relevant thermodynamic param—

eters are calculated by the following relationships:

@— : 1%?- (111.17)
d(1/T)
AG = — RTan (111.18)
as = Af-‘g—AE (111.19)
and the resultant values are (AG2)298 = -2.8310.004 Kcal/mole,

A82= -ll.l810.31 cal/(mole K°). Again, it is worthwhile
to note that the limiting chemical shifts of Cs+°(18C6)2
are nearly temperature independent. This phenomenon may
imply that the first solvation shell has been completely
displaced by the ligand and also that there is no pro-

nounced conformational change between 24° and -44°C.

(B) CESIUM TETRAPHENYLBORATE COMPLEXES WITH C222 IN

VARIOUS SOLVENTS

 

The variation of chemical shift with temperature
was also studied for the cryptand—Cs+ complexation reac-
tion. The implications of these variations will be discus-
sed later but in this section the overall formation con-

stants of C222 complexes with CsTPB in DMF, PC and acetone

126

us.eumeos.emo m.os~.eeu n «ma meosxemox eoo.osomm.~1umm~l~oae

 

 

 

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no.0Hm~.¢ u mmmxmsaev «Hoaxemom H.¢H~.mI umma
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m~.mv ~o.ose~.e efl.ee emm.m new

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127

will be considered. The relevant thermodynamic parameters
of the complexation reaction can be calculated from the
temperature and concentration dependence of the chemical
shift, just as was done for complexation by crowns.

For this study two concentrations of CsTPB were used,
0.02 M and 0.01 M. The external reference was 0.5 M
CsBr aqueous solution in a vacuum-jacketed tube. All of
the chemical shifts measured at various temperatures are
listed in Tables 25-29 and shown in Figures 30-32. The
formation constants and limiting chemical shifts were
computed by the KINFIT program and the results are listed
in Tables 30-32. The corresponding thermodynamic param-
eters are listed in Table 33 and plots of fin K v§_l/T
are shown in Figure 33. An interesting observation, which
has consequence to be discussed in Chapter V is that the
limiting chemical shift varies with temperature and as the
temperature gets lower, this variation becomes smaller.
In addition, the chemical shifts at low temperatures
approach a value which is independent of the solvent used.
These data indicate that the C222 complexation reaction
with Cs+ is not validly described by a simple complexa-
tion reaction, such as

Cs+ + 0222 I Cs+C: c222

in which CSEZZCZZZ denotes a complex with a Cs+ ion in the
center of the cavity. More discussion of this anomaly will

be given in Chapter V.

128

 

 

 

 

 

 

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129

 

 

 

 

 

 

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130

 

 

 

 

 

 

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131

 

 

 

 

 

 

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132

 

 

 

 

 

 

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133

W( PCS
wfl

-50. x.
E \
‘ I
‘ I
'Q
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I
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' 105°
’ I
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O
: ‘ 96
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g . O
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I
' I
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h I o
I 46
I
I
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» .‘****—*-* -----l- -2°
0
. 133:: 22:22:: :1: :33.
' 1 l L. L k [c222]
1 2 3 4 5 11

 

(5‘7
Cesium-133 Chemical Shift vs Mole Ratio of 0222 to 03+

in Propylene Carbonate at various Temperatures.

Figure 30.

134

 

 

 

O I
$1 DMF
I
r I
-50 I- \
I
r , .
I. \\ .~
P ‘x' 3
1. .
I- '1‘ o
-100"' a 54°
:1 o o
E L a I 46
t II
)- I
" 'I'I
‘ I!
. 1) 2"
n
-150 - ‘3‘ ‘
II
I- II
N .
b- “‘ 1' .. _2°
|
I- ‘3‘
. 1} - 1 -21°
-200 L- I": .
II ’40
L- II
Ig___
r. 'I' “‘----——-o ————— -o- -58°
I
.. Luau-x ------- 46- ----- *- “13°
L 4 lie 1 1 : [czn
1 2 3 4 5 [Cs

Figure 31.

Cesium-133 chemical shift vs mole ratio of [C222]/
[Cs+TPB’] in DMF at various temperatures.

Figure 32.

135

Cesium-133 chemical shift vs mole ratio
of C222 to Cs+ in acetone at various
temperatures.

 

136

50

 

0 in
i
9
-50 I- '
f!
(.
.400. ’
» ;:
1
. 1
II
-450' i
r "I
3
\\ . _ 54°
. \. 46°
—2m- a“ séuiue—t—i—g 32:
. I \k
x-II-x-mII-«II- ----- -II- -2°
\H+--o--¢.-----.- .21"
I o—o-o-«x-ouo-«ue- 44°
bs-Ih-a-«r-a-ut-u-«o- -64°
-250T
1 l l l

 

a».

Figure 32.

#_ C222
Cs

137

Table 30. Formation Constants and Limiting Chemical Shift
for the Complexation of CsTPB by C222 in PC at
Various Temperatures.

 

 

Temperature (Appm)lim K

 

[Cs+]= 0.02 M

 

378 -129 11 (1.7 1.1)x102
369 -138.710.7 (3.610.3)x102
345 -156.110.6 (1011)::103
319 -176.910.3 (4.010.9)x103
302 -191.1810.04 (6.710.4)x103
271 -208.80 -------------
252 -216.35

 

 

[Cs+]= 0.01 M

 

373 -184 12.0 '(2.610.2)x102
343 -202.910.5 (8.610.4)x102
313 -220.510.2 (4.110.3)x103

298 -230.210.2 (10.il)x104

 

 

138

Table 31. Formation Constants and Limiting Chemical Shift
for the Complexation of CsTPB by C222 in DMF
at Various Temperatures.

 

 

 

 

 

 

 

Tempeiature (Appm)lim K

[03*]= 0.02 M

327 -134.410.4 44.310.5

319 -136 12 70 16.

297 -156.410.2 148.1 2.

271 —178.2410.07 512.1 6.

252 -193.810.2 (11.110.8)x102

233 -209. 11. (6.12)x103

215 -219.5 ----------

200 -231. ----------
[03*]= 0.01 M

298 -155 11 156 6

288 -159 13 (2.6i0.3)x102

271 -172.010.s (6.910.3)x102

258 -185.51o.8 (9.210.9)x102

 

 

139

Table 32. Formation Constants and Limiting Chemical Shift
for the Complexation of CsTPB (0.02 M) by C222
in Acetone at Various Temperatures.

 

 

 

Tempeiature (Appm)lim K
327 -183.910.2 (1.910.2)x103
319 -189.310.8 (3.810.3)x103
302 -199.710.2 (1.811.1)x104
297 -202.710.9 (1.810.5)x104
271 -216.15 —————————————
252 —223.28 —————————————
229 -23o.02 .............

209 -236.57 —————————————

 

 

140

Table 33. Thermodynamic Parameters for the Complexation
of CsTPB by C222 in Various Solvents

 

 

AH AG an AS
Solvent (Kcal/mole) (Kcal/mole) (298°K) (cal/mole°°K)

 

DMF -7.510.3 -2.9410.01 4.9710.08 -1511

PC —lO.9iO.9 -5.50i0.01 9.310.2 -18i4
*-lO.810.l -S.4 10.001 9.1910.03 -l8.110.3

Acetone -15 12 -5.910.2 9.9 10.2 -31i7

 

 

*[Cs+] = 0.01 M. All other cases [Cs+] = 0.02 M.

141

 

 

”ACETONE

an

 

DMF

 

l _L _L

.1 3.0 3.5 4 0

1,6 (K")

Figure 33. A plot of an E l/T for the complexation re-
actions of Cs+ with C222 in acetone, PC and DMF.

CHAPTER IV

A STUDY OF THE DYNAMICS OF
CESIUM TETRAPHENYLBORATE COMPLEXES

WITH CROWNS AND CRYPTANDS

142

INTRODUCTION

 

The complexation studies described above showed that
the stabilities of crown and cryptate complexes strongly de-
pend on the nature of the solution and that the topology of
the ligand dramatically affects the extent of the complexa-
tion reaction in a given solvent. Therefore, NMR line-
shape analysis at various temperatures was used to study
the kinetics of the complexation reaction. The rates of
cesium ion exchange in the presence of the macrocyclic
ligands in PC, pyridine, acetone and DMF were calculated
from the exact expression for a general two site exchange
of uncoupled spins. The equations were fitted to the ex-
perimentally observed lineshape with the aid of the generalized
weighted non-linear least squares program KINFIT. It was
suspected that the activation parameters obtained from line-
shape analysis at various temperatures might help to
further investigate how the topology of the ligand and

the nature of the solvent affect the complexation process.

II. DETERMINATION AND INTERPRETATION OF THE LINESHAPES

 

The modified Bloch equations (103,104) which describe
the motion of the X and Y components of magnetization in

the rotating frame, are expressed as follows:

d6 1 _1

A = _. ‘
dt +0IG iyfllMo +1 G

A A A B B " TA (1v.1)

GA

143

144

"d? + aBGB = ’iYH1M°B 4' TAlGA ' T131613 (IV°2)

with
GA = uA + ivA (1V.3)

where v represents the absorption mode lineshape and u
represents the dispersion mode lineshape. Then G(m) is a
general expression for the lineshape which can predict the
entire range of exchange from the extreme slow limit to the
O 1

f . f << ;
extreme ast limit At the ast exchange limit 1 753:5;7
and only one signal is observed, while at the slow exchange

. l . . .

limit, 1 >> 13;:5377 one can distinguish separate signals

from the two sites. The exchange times, 1, at different

temperatures supply all of the kinetics information.

(A) MEASUREMENTS IN THE ABSENCE OF EXCHANGE

In order to determine the linewidth of the two dis-
tinguishable sites at various temperatures in the absence
of exchange, separate lineshape analyses were made of the
salt (site A) and the completely complexed Cs+ ion (site
B) at various temperatures. The values of TZB were studied
over the temperature range where the formation constant is
larger than 103. Therefore, the populations PA and PB

can be determined directly from the mole ratios of ligands

and cesium salt added to the solution. All experimental

145

lineshapes in the absence of exchange were found to be
Lorentzian.

The values of m and T2 for the free and the complexed
ion were determined by fitting a Lorentzian line to the
observed signal. A typical example for a fit of 0.01 M
CsTPB in PC is shown in Figure 34. The five adjustable
parameters were the amplitude, K, the Larmor frequency, w,
the linewidth parameter, T2, the height of the baseline,

c, and the zero-order phase correction, 8. The first-order
phase correction, 81, can be determined experimentally by
following the procedure in the NMR Manual from the Nicolet
Instrument Corp. (105). Therefore, the first-order phase
correction is introduced as an externally determined quantity
while all of the other five parameters were adjusted by KIN-
FIT. The factors which can affect these parameters are
described in detail in reference 95.

The variations in linewidths with temperature for the
free and complexed cesium ion, in the presence of 18C6,
DCC(A), C222B and C222 in PC solution are listed in Tables
34 and 35 and the data are plotted in Figures 35 and 36.

The natural linewidth of the cesium ion is very narrow (since
the quadrupole moment, Q = 0.003 barns, is small) and the
linewidth is predominantly determined by the inhomogeneity

of the field. Therefore, only T; values are reported.

*1 df'db(T*’1-(T )"1
2 s e lne Y 2’ ‘ zinh

where TZinh is caused by inhomogeneous broadening

The quantity T
( “1

+

T2nat)
and T2nat is the natural linewidth of the species under

146

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148

Table 35. Temperature Dependence of the Transverse Relaxa-
tion Times in Propylene Carbonate in the Presence
and Absence of C222.

 

 

 

 

 

 

 

CsTPB
Temperature *
°K T2(sec)
284 0.08 (0.01)
273 0.07 (0.01)
252 0.06 (0.01)
227 0.037 (0.007)
Cs+-C222
Temperature *
°K T2(sec)
298 0.015 (0.003)
286 0.012 (0.0007)
273 0.006 (0.002)
258 0.0050 (0.0003)
241 0.0028 (0.0002)

230 0.0013 (0.0002)

 

 

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1000:
,
I CsC222+
b
'I; r
O L
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93. .
1- l
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100:-
L
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,
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L 1 1 1 1 1 I 1 1 l l L 1
35 .40 45

(TEMPERATURE °I<I"x103

*

Figure 36. Semilog plots of l/T for Cs-133 nucleus
reciprocal absolute emperature for solutions
containing 0.02 M CsTPB and 0.02 M Cs+-C222
in PC.

151

study. As Figure 35 shows, the broadening of the lines by
increased viscosity occurs only at very low temperatures.
The exchange study was carried out under exactly the
same field conditions as the nonexchange case to avoid
systematic errors. In order to insure that saturation
effects were absent, a smaller than 90° pulse (usually 20°)
was used. In addition, tests were made to be sure that the
S/N ratio of the FID (Free Induction Decay) was not de-
creased by a slight increase of the pulse power or repeti-
tion rate. The spectra were also collected within the first
3/5 of the sweep width used. This procedure was followed
to insure that the signal intensity was not attenuated by

the filter.

(B) EVALUATION OF EXCHANGE TIMES

 

To evaluate the exchange time, 1, Equation 1V.7 can

be rewritten to include the baseline correction.

G(w) = K(vcose - iusine) + C (1V.l7)
wheree=0o+81andu=9¥§% v=Q—§flT§
s +T s +T
P P
S = —1L.+ —£L + —-JL—— - (wA+A-w)°(mB+A-w) (IV.18)
T T T T
2A 2B 2A 2B

152

wA+A-w wB+A-w

_] . __
123 T

T = P + P ”B + A-w + 1[ ] (IV.19)

AwA s
V =(PBwA + PAwB-A-w)1 (IV.20)

The frequency shift parameter, A, was introduced because
of field drift of the NMR spectrometer (m2 Hz per day).
The values of “A and “B were determined separately but
under exactly the same experimental conditions as those
used to collect exchange data.

All the data were stored on a magnetic disc and punched
out on paper tape when needed. Up to this step in the
process, neither data smoothing nor parameter adjusting
were used except that an approximate zero-order phase cor-
rection was made. This correction had no effect on the
fit of the data since 80 was re-adjusted by the KINFIT

program.

III. RESULTS AND DISCUSSION

 

(A) LIGAND EFFECT ON EXCHANGE RATE

 

Except for DBC, all the complexes which were used in
the equilibrium study were also used for the exchange
study in PC solution. Their spectra, collected at various
temperatures are shown in Figures 37-40. Figure 37 shows
that the resonance at the fast exchange limit is not half-
way between the two peaks of the slow exchange limit.

However, this is not unexpected because the chemical shift-

24°

10°

fi

I

' I
l

I

  
 

  

 

i
I
5
. A151 h
I'
I
Q

3906.25 0 9+ 6222 C
CS+ =O.5 IN PC

Spectra at various temperatures for a solution

containing 0.02 M CsTPB and 0.01 M C222 in PC.

Dotted lines represent the chemical shifts of

CsC+ (left) and Cs+ (right) in the absence of

exchange.

Figure 37.

154

‘GOOC Vi/
W"
W

70752 Cs c+ Cs+ 2680.7Hz

B
C222—2: 0.5 IN PC

CsP

Figure 38. Spectra at various temperatures for a solution
containing 0.02 M Cs¢4B and 0.01 M C222B in PC.

 

155

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- 60°C

v \vw \w \ILV‘MJ $0.7 H3
7075.2 csc+ Cs+

039105 IN PC
Cs

 

Figure 39. Spectra at various temperatures for a solution
containing 0.02 M Cs¢4B and 0.01 M DCC (A) in
PC.

156

 

2
§
1

-60°c \
‘0, \ -
\J'J Wf‘JCSC-f C8+ \r\-/\M'V‘/J\
7075.2
2680.7Hz

113.92.: 05 IN PC
CS‘

Figure 40. Spectra at various temperatures for a solution
containing 0.02 M Cs¢4B and 0.01 M 18C6 in PC.

157

temperature dependence study showed that the limiting
chemical shift of the complexed Cs+ is very temperature
dependent.

Examples of the computer fitting are shown in Figures
41-43. Figure 41 illustrates how the absence of spectrom—
eter first and zero order phase corrections affects the
shape of the peak. In Figures 37-40, by contrast, the
spectra were plotted after both phase corrections had
been instrumentally made. For the computer fitting pro-
cess only an approximate zero order phase correction was
made on the raw data. The first order phase correction was
not made by the spectrometer in order to avoid distortion
of the baseline. Therefore, for example, the spectra shown
in Figure 41, have two peaks which are 180° out of phase.
Figures 41—43 also illustrate how the first order phase
correction depends on frequency. In Figure 41 the two peaks
are approximately 2000 Hz apart and the two resonance lines
are 180° out of phase, while in Figure 42, the two peaks
are only about 300 Hz apart: therefore, the phase difference
of the peaks is very small. The exchange times (I) obtained
by fitting the data are listed in Tables 36 and 37 and
the Arrhenius plots of exchange times (semi-log scale) XE:
the reciprocal of the absolute temperature are shown in
Figures 44 and 45. Of the four complexes, the one with
C222, at room temperature, has the slowest exchange rate

in PC. This fact suggests that the process has the highest

158

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_c.upon. u h:u:uau:_.3c.uo~_. u exceo 01» pa u:4<:.::.uo__. u rum; wt» »4 u:4<> ..~.o<>x.x :0 ._...x v— wvcmu<

161

 

 

 

Table 36. Temperature Dependence of the Exchange Time 1,
of some CsC+ complexes in propylene Carbonate
and the Corresponding Reciprocal Transverse
gelgxation Time of Cs+ (Site A), and CsC+ (Site

Temperature 1(msec) —l—(sec) ¥——(sec)
°C 2A 28
(A) 18C6 -60.0 3.3 (0.3)b 50.00 58.00
-55.0 2.2 (0.2) 41.00 48.01
-52.0 1.8 (0.1) 40.49 42.99
-44.0 0.59(0.03) 33.00 32.00
(B) DCC -55.0 20. (7.) 43.50 130.55
-47.5 8. (1.) 34.97 92.00
-36.0 3.4 (0.7) 26.50 54.00
-23.0 1.4 (0.2) 20.49 33.00
-10.5 0.73 (0.06) 16.00 20.49
-4.7 0.33 (0.06) 13.70 16.21
(C) C222B —42.0 13.3 (0.70) 30.00 73.00
-36.0 1.8 (0.4) 27.00 55.87
-29.0 0.8 (0.2) 22.99 42.02
-22.7 0.40 (0.06) 20.28 32.47
—10.5 0.08 (0.01) 16.00 20.49
-32.0 1.0 (0.2) 24.51 46.95

 

 

a0.02 M CsTPB + 0.01 M

b

Standard deviation.

ligand.

162

Table 37. Temperature Dependence of the Exchange Time in
PC in the Presence of C222 and the Corresponding
Reciprocal Transverse Relaxation Times of Cs+
(A) and 03+ 0222 (B).6

 

 

Temperature 2 1

 

°C 1(msec)x10 Tr—4sec)-1 -,I.--]-'-—l(sec)-'l
2A ZB

24 1.6 (0.2)b 10.53 68.03
10 4.6 (0.8) 6.08 144.93
0 56. (29.) 13.50 172.41
-12 119. (19) 16.00 178.57
-25 314. (16) 19.01 270.27
-35 523. (19) 21.98 384.62
—37 538. (97) 22.99 429.19
-41 688. (14) 24.51 500.00

 

 

a0.02 M CsTPB + 0.01 M 0222

bStandard deviation.

163

 

T DCC

J_J._..LA_LL

 

 

 

5 4 2
‘9’. 1/
3.
'1
1
r -(
~10F‘ 1
y 4
h 4
* C2228 ‘
J 1 L l J L 1 L l 1 1

 

 

4.0 ‘ 3 4.5
(TEMPERATURE 'K )' x 10
Figure 44. Arrhenius of plots of T (exchange rates of Cs+

from ligands) vs T'1 for propylene carbonate
solutions.

164

 

' I

 

 

3 .
u:
(n
2 F
Iv-
OJ:-
L
b
“ I
p
1 1 1. 1 L 1’1 1 1 4— 4 1 l 1
3.5 4.0 4.5
103 -1
-:r- ( K )
Figure 45. Arrhenius plot of T (exchange time of Cs+

from C222) for propylene carbonate solutions.

 

165

steric hindrance. The broad temperature range from co-
alescence to the slow limit indicates that C222 processes
the highest activation energy, but because of the com-
plexity of the plot of r 35 (temperature)"1 as shown in
Figure 45, the interpretation will be deferred until the
next chapter.

The activation energies and the exchange times at 298°
for the other three ligands were obtained from the Arrhenius

equation. Then by using the following relationships:

1‘ = _2_]]<.__ (IV.21)
b
# = _
AHO Ea RT (IV.22)
g
AH
7‘ = .. £2 _9
Aso Rinkb Rzn 11 + T (IV.23)
AG: = AH: - TAS: (IV.24)

all related activation parameters could be calculated (Table
38). In the above equations, AGfi, AH: and A8: are the
standard free energy of activation, the standard enthalpy

of activation and the standard entropy of activation,
respectively, for the decomplexation reaction. The symbols
k and h in the above equation represent the Boltzmann
constant and Plank's constant, respectively. The activa-

tion energy values in Table 38 illustrate that the nature

of the ligand significantly influences the complexation

166

 

 

 

 

 

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+

 

 

{Ilif ()

167

reaction. Cryptand-2223 has the highest rigidity and also
possesses the largest activation energy. In addition, DCC
with a substituent, is more rigid than 18C6, and its activa-
tion energy is slightly larger. Dibenzo-18C6 has a higher
rigidity than DCC but its smaller cavity size and the
weaker donor ability of its oxygens makes the complexation
with Cs+ much weaker. In addition, it may form exclusive
complexes in which the cesium ion is not able to penetrate
into the center of the ring. This fact may also be the
reason that DBC has the fastest exchange rate at room
temperature of all the ligands. If the slow exchange limit
for DBC complexes in PC could be observed, it would probably
have the lowest activation energy if only exclusive complexes
are formed. If this assumption is valid then the activa-
tion energy for release of Cs+ ion from crowns would be
generally lower than from cryptands. This is in contrast
to the trend of the formation constants, which is 18C6
> DCC > DBC m C222 > C2228. It is not difficult to ration-
alize the trends caused by rigidity and donor ability of
theligand in regard to the complexation reaction. The
ligand 18C6 has both flexibility and proper cavity size.
Therefore it can form the strongest complexes. 0n the
other hand, C2228 has a greater rigidity and, perhaps,
the smallest cavity size, and thus forms the weakest
complexes.

TheAS: values of all three ligands are negative,

the magnitude of this value is usually determined

168

by factors such as the reorientation of solvent molecules
or conformational changes of the ligand. It seems likely
that for the case of C2223 both factors are involved in
the transition state. Therefore complexes with C2223 show

the largest negative entropies of activation.

(B) SOLVENT EFFECT ON THE EXCHANGE PROCESSES

Lineshape analysis of exchange rates has also been
carried out for the complexes of Cs+ with 18C6 in pyri-
dine, and C222 in DMF and acetone. The relevant spectra,
collected at various temperatures, are shown in Figures
46-48. For the pyridine case the S/N is poor because of
the low concentration of the cesium tetraphenylborate (0.01
M was used) and broad linewidth (m400 Hz) of the resonance
line. The nonexchanging T; values for Cs+ in various sol-
vents are listed in Tables 39-41, and are shown graphically
in Figures 48 and 49. Again, in these solvents the line-
widths of Cs+ in the absence of exchange processes are
narrow and are dominated by inhomogeniety of the field
except at very low temperatures where viscosity broadening
starts to become more important. The exchange rates were
obtained by fitting the lineshapes with the KINFIT program
and the results are listed in Tables 42-44. The Arrhenius
plot of log T 2g l/T for the system 18C6 :Cs+ in pyridine
is shown in Figure 51. The Arrhenius plots for the cases

of C222 in DMF and acetone are complicated (Figures 52,53)

169

 

Figure 46.

1806
08*

:05 IN PYRIDINE

Spectra at various temperature for a solution
of 0.01 M CsTPB and 0.005 M 18C6 in pyridine.
The linewidth at coalescence were N400 Hz.
This fact and the low concentration lead to
the poor S/N. The dotted lines show the chem-
ical shifts of CsC+ and Cs+ in the absence of
exchange.

170

 

 

 

 

A ' -780 C
3906.25 040+ 5: 0 Hz
0222 _
c. -0.5 IN DMF

Figure 47. Spectra at various temperatures for a solution
containing 0.02 M CsTPB and 0.01 M C222 in DMF.
The dotted lines show the chemical shifts of
CsC+ and Cs+ in the absence of exchange.

Figure 48.

171

 
     

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3905.25

_£c33:3..-_- o 5 m Acevoua
Spectra at various temperature for a solution
containing 0.02 M CsTPB and 0.01 M C222 in
acetone. The dotted lines show the chemical
shifts of CsC+ and Cs in the absence of ex-
change.

172

Table 39. Temperature Dependence of the Transverse Relaxa-
tion Times of Free and 18C6-Complexed Cesium
Cations in Pyridine.

 

 

 

Temperature Cs¢4B Temperature Cs+-18C6
9C T;(sec) °C T;(sec)
-47 0.021 (0.003) -47 0.05 (0.01)
-38 0.035 (0.007) ~38 0.07 (0.01)
-32 0.05 (0.01) -32 0.07 (0.01)
-26 0.059 (0.007) -26 0.087 (0.008)
-15 0.087 (0.008) ~15 0.10 (0.01)
-7 0.007 (0.01) -7 0.07 (0.01)
9 0.08 (0.01) 9 0.08 (0.01)
23 0.072 (0.008) 23 0.10 (0.01)

 

 

NOTE: T2(ref) = T2(inh) = 0.1453 sec.

173

Table 40. Temperature Dependence of the Transverse
Relaxation Time of Free and Complexed (C222)
Cesium Cations in DMF

 

 

 

Tempe;ature T;(sec)
(A) 03+

297 0.111 (0.009)
279 0.12 (0.01)
251 0.115 (0.006)
234 0.117 (0.007)
220 0.104 (0.00)
209 0.073 (0.005)

 

(B) Cs+-C222

301 0.03 (0.01)
287.5 0.0230 (0.009)
264.5 0.014 (0.003)
243 0.007 (0.001)
226 0.004 (0.001)
209 0.0019 (0.0005)

 

 

NOTE. T2 (ref) = = 0.1305 sec.

T2(inhomogeneous)

1f74

Table 41. Temperature Dependence of the Transverse Relaxa—
(inn Time and Complexed (C222) Cesium Cations in
Acetone.

 

 

 

Temperature ,
°K T2(sec)
(A) Cs+

297 0.11 (0.01)
285 0.0 (0.01)
273 0.09 (0.01)
253 0.084 (0.007)
242 0.072 (0.005)
232 0.065 (0.005)
216 0.082 (0.006)
200 0.103 (0.007)

 

(B) Cs*-0222

297 0.067 (0.007)
280 0.048 (0.003)
273 0.043 (0.006)
260 0.03 (0.005)
249 0.040 (0.003)
236 0.031 (0.004)
223 0.028 (0.002)
207 0.020 (0.001)
195 0.015 (0.001)

 

 

NOTE: - 0.1632 sec.

72(rer) ’ T2mm)

175

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176

Table 42. Temperature Dependence of the Exchange Time in
the Presence of 18C6 in Pyridine and the Cor-
responding Reciprocal Transverse Relaxation
Times of Cs+ (A) and CsC+ (B).a

 

 

 

Temperature 1(msec) fi—(sec) Tl—(sec)
C 2A 28

-47 4.9 (0.7)b 19.19 _ 47.39

-38 2.6 (0.5) 15.20 28.65

-32 1.4 (0.2) 13.50 21.65

-26 1.0 (0.2) 11.79 16.95

-15 0.4 (0.1) 9.83 11.49

-7 0.4 (0.1) 9.83 14.58

9 0.14 (0.03) 9.83 12.15

23 0.06 (0.01) 9.92 13.86

 

 

a0.01 M CsTPB + 0.005 M 1806.

bStandard deviation.

 

 

177

Table 43. Temperature Dependence of the Exchange Time in the
Presence of C222 in Acetone and the Corresponding
Reciprocal Transverse Relaxation Times of Cs+ (A)
and CsC+ (B).a

 

 

 

 

 

 

 

Tempféature 1(msec) —%;(sec) _%;‘sec)
Experiment No. 1
10 2.1 (0.2)b 0.1042 0.0526
0 16 (8) 0.0971 0.0476
~24 63 (16) 0.769 0.0357
~37 233 (25) 0.0676 0.0299
~50 240 (24) 0.0741 0.0244
~78 1207 (100) 0.1064 0.0147
Experiment No. 2
*24 1.4 (0.2) 0.0300 0.0244
12 2.2 (0.8) 0.1031 0.0541
*0.7 3.4 (0.5) 0.0276 0.022
~31 107 (17) 0.0718 0.0323
~41 217 (33) 0.0646 0.0282
~58 423 (61) 0.0823 0.0213
~73 1759 (95) 0.1033 0.0161
*Exponential multiplication was used (TC = ~S).

a0.02 CsTPB + 0.01 0222.

b

Standard deviation.

178

Table 44. Temperature Dependence of the Exchange Time in
the Presence of C222 in DMF and the Correspond-
ing Reciprocal Transverse Relaxation Times of
Cs (A) and CsC+ (B).a

 

 

 

 

 

Temperature 2 1 1
C I(msec)x10 §—-(sec) fi——(sec)
2A 28
~8 0.26(o.02)b 0.116 0.0133
~12 0.61 (0.07) 0.1163 0.0119
~20 0.8 (0.2) 0.116 0.0095
~24 1.31 (0.35) 0.1163 0.0085
*~31 1.8 (0.1) 0.116 0.0056
~37 4.9 (0.9) 0.1163 0.0057
*~55 44 (9) 0.0290 0.0086
~67 288 (33) 0.0606 0.0019
~78 1944 (123) 0.0294 0.001
*Exponential multiplication was used (TC = ~5)

a0.02 M CsTPB + 0.01 M 0222.

bStandard deviation.

179

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35

Figure 51.

4.0 _ 45
l TEMPERATURE °Kl 1x103

Arrhenius plots of T (exchange time for Cs+
ion from 18C6) in pyridine,

181

 

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T

IO

lj I—I'W'I

'?
A P
U )-
w )-
(n .
E .
k .
OJ

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r

 

 

 

 

1 I 1 1 1 1 J 1 1 1 J 1 L4 1 1 l 1 .
3.5 4.0 4.5 5.0
3 -:
J— K)
T (

Figure 52. Arrhenius plots of T (exchange time for Cs+
ion from the ligand C222) in acetone solution.

182

 

 

 

 

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)-
'1—
A :
o h
u: .
co
:5 .
t- *
OJ :-
' I
0.0!:-
1 1 1 l 1 1 1 1 1 1 1 L 1 L 1 1
4-0 4.5 5.0
3
1o -1
T
Figure 53. Arrhenius plot of T (exchange time for Cs+

ion from C222) in DMF solution.

 

183

and will be discussed in the next chapter.

The activation parameters for the release of Cs+ by
18C6 in PC and pyridine are listed in Table 45. The Ea
values for both cases are similar ; however, the big stan-
dard deviations make the meaning of the difference ques-
tionable. Previously, Cahen had observed (6) in the Li-
cryptate study that the activation energy increases with
increasing donicity, Opposite to the overall energy change.
Therefore, he concluded that the transition state must in-
volve substantial ionic solvation. In the present study

such an effect seems to be small.

(C) DISCUSSION

 

Shporer and coworkers (4,5) studied the dynamics of
complexation of Na+ by DCC in DMF and methanol and reported
Ea values of 8.3 :1. (Kcal/mole) in both solvents, while
for the complexation of Na+ or K+ with DBC in methanol the
Ea values are 12.6 i l. (Kcal/mole) for both cations.
Therefore, they concluded that the complexation reaction
of Na+ with DBC has a larger activation energy than with
DCC because of the higher steric hinderance of DBC, they
also concluded that there is no solvent effect since the
activation energies for Na+ complexes with DCC in MeOH
happen to be the same. The value of Ba found by Shporer
and coworkers for Na+~DCC in methanol is about the same

as we have found for Cs+~18C6 in pyridine. However this

184

Table 45. Exchange Rates and Thermodynamic Parameters of

18C6 Complex Exchange in Propylene Carbonate
and Pyridine.

 

 

Activation
Parameters PC Pyridine

 

Ea

(Kcal/mole) 8.0:4.0 8.04:0.27

kbx1o'3 50.014.o 8.9 20.8

at 298°K
(sec‘l)

g
AHO
(Kcal/mole) 7.41:4.0 7.5i0.3
As:
(cal/ K mole) ~12.2 $0.2 ~15.5i0.2

AG#
0

(Kcal/mole)
298°K 14 14.0 12.1:0.4

 

 

185

could be coincidental because of the compensation of several
factors which affect the activation energy. For instance,
18C6 has less rigidity in the ring than does DCC, but a
larger cation such as Cs+ might introduce a higher activation
energy. Therefore, a coincidence could occur by compensa-
tion of the ligand effect and cation effect and solvent effect.
In other words, the factors which affect the reaction rate
are complex, and conclusions cannot easily be based upon
comparisons made with very different systems.

Together the solvent effect and the ligand effect
of the complexation reaction can be represented by the

reaction profile drawn below:

 

 

 

 

 

 

 

 

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I, ‘
\
,’ \
, 1
I I
1
0" /’-.\\ 1 EC!
. I
I I ’9- ‘
f,’ I \1 X
,' I ’ \\ 1
I I I’ 11 1
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\
“\ \ 1 +
\\ ‘ Cs DCC(AHPC)
\ ‘ * Cs+18C6 (pc)
\
X r

 

 

031806 (PY)

CHAPTER V
A CESIUM-133 NMR STUDY OF THE COMPLEXATION OF
CESIUM TETRAPHENYLBORATE BY C222:

DISCUSSION OF THE TYPES OF COMPLEXES

186

I. INTRODUCTION

The diameter of the cesium ion (3.3 A) is larger than
the estimated diameter of the C222 cavity (2.8 A). How-
ever, an X-ray study of the solid complex (55) showed that
the cesium ion can be accommodated into the cavity of C222.
In the present chapter the discussion will focus on the

nature of binding of Cs+ to C222 in solution.

II. EVIDENCE FOR TWO TYPES OF CRYPTATE COMPLEXES

Inclusive cryptate complexes were first designated by
Lehn (50) with the mathematical symbol (2i, M+C L).
It was considered that whenever the cavity diameter of
the cryptand (L) is larger than or equal to the diameter
of the metal ion (M+), inclusive complexes are formed in
which the cation is situated within the cavity. However,
in the present discussion, we need to include other pos-
sibilities. The symbol M+C: L, will be used to designate
a complex in which M+ is located entirely within the cavity
(inclusive complex). By contrast, whenever a complex is
formed in which the metal ion only partially penetrates
into the cryptand cavity it will be called an exclusive
complex and designated as M+lJ L.

It has already been mentioned in previous chapters
that the reaction of Cs+ with [2]~cryptands seems to give

more than one type of complex. A summary of the observations

187

188

which support this speculation are as follows:

(1) The limiting chemical shift of Cs+~C222 (measured
directly at large ligand/Cs+ ratio or obtained as a
parameter from data fitting) is very solvent dependent

at room temperature as shown below.

Solvent PC Acetone MeCN DMF DMSO Pyridine

(Appm)lim -l93.8 -203.0 ~210.4 -155.8 ~144.3 -224.3

(2) The limiting chemical shifts are also temperature
dependent, as shown in Figure 54. A special feature

is that the extent of variation with temperature de-
creases at low temperatures eventually extrapolating

to the same Cs+ chemical shift in all solvents. By
contrast Cs+-(18C6)2 complexes for example, show neither
solvent dependence nor temperature dependence of the
chemical shift. We would expect Cs+ inside of a C222
cavity to be well-shielded from the influence of the

solvent.

(3) The spectra obtained with samples which have only
enough C222 to complex half of the Cs+ (1:2; 0222/
(Cs+)t = 0.5) in five solvents were collected at various
temperatures including temperatures low enough to be
at the slow limit of the exchange process. As shown
in Figure 55, the chemical shifts for the complexed

+

Cs at low temperatues have about the same value.

However, in PC and in DMF solutions the linewidth of

189

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190

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Spectra of solutions which contain the Cs+C222
complex and uncomplexed Cs+ at low temperatures
in five solvents. The dotted lines indicate the

resonance frequency of CsC222+ at room tempera-
ture.

191

the CsC222+ peaks are much broader than in the other
solvents. The fact that the chemical shifts of CsC222+
are solvent independent at low temperatures is taken
to indicate that the complex is inclusive. The broad
linewidths of CsC222+ in PC and DMF may indicate the

presence of slow exchange between the inclusive and

the exclusive complexes.

Based on the above observations, an effort was made
to examine the data presented in Chapters 3 and 4 to see
if they are consistent with the assumption that two types
of complexes are found.

The proposed reactions which involve the two types of

complexes are as follows:

K K
+ 1 + 2 +
C8 +C=2 Cs U C = CSCC (v.1)
(exclusive) (inclusive)
where C denotes [2]~cryptand. At a given temperature the
observed chemical shift is given by

6 = 6 x + 6.x. + 6 x (v.2)

obs F F i 1 e e

where the subscripts e and i refer respectively to the
exclusive and the inclusive complexes. The apparent equi-

librium constant, K, is given by

K = [CsC+]/[Cs+][C] (v.3)

192

while
x1 = [es”u cytosine] (v.4)
and
[031::0] = [03+U CJ'K2 (v.5)
SO
[03"0]total = [03+u 0] + [051: 0]
= K1[Cs+][C]+ K1K2[Cs+][C]
= [Cs+][C]K1[l + K2] (v.6)
Therefore
K = K1[1 + K2] (v.7)

It is seen from the above results that at a given temperature,
chemical shift studies would not yield separate values of

K1 and K2. However, additional information can be obtained
from a study of the temperature dependence. Since we can
suppress the effect of K1 by studying the limiting chemical

shift at high (C)/(Cs+) ratios, the temperature dependence

193

of the limiting shift might reflect the temperature de-

pendence of K and permit its determination. This will only

2
be true if the variations of 6e and 61 with temperature are
small compared with the variation of the weighted-average
limiting chemical shift. From the solvent-independent
limiting shift at low temperatures one can find the chemi-
cal shift of the inclusive complex (~245 ppm) with some
confidence. However, it is difficult to find the charac-
teristic chemical shift for the exclusive complex.

As a first approximation it was assumed that the chemical
shift of the 1:1 complex with 18C6 in the solvent under
study is the same as the chemical shift of the exclusive
complex. Having estimated these two chemical shifts,
6e and 61, it is possible to determine AHZ' the enthalpy
change due to the conversion of the exclusive to the inclu-
sive complex.

For the limiting case where the analytical concentration
of the cryptand is much larger than that of Cs+ ion, the

concentration of free Cs+ must be negligible. Consequently,

the observed limiting chemical shift is given by 6 =

obs
Gexe + dixi, or
Gobs = 66(1-xi) + (Sixi = Xi(6i~6e) + Ge (V.8)
so that
6 ~6
xi = .22§__2 (v.9)
6 ~6

194

and

6 -6
x = _j_'._.2.13§. (Vol.0)

8
Gi-Ge

Since the concentration of free cesium ions is negligible,

only one equilibrium is involved, i.e.,

+ K2 +
[03 u 0222] I [Cs c0222] (v.11)
and
x .—
i obs e
K = = _:___. (v.12)
2 xe 1 Obs

Therefore, from each Gobs value at a given temperature, a
corresponding K2 value can be obtained. From the temperature
dependence of K2, the enthalpy change, AH2 can be calculated
(Equation III.l7) by using the KINFIT program. Since we
arbitrarily chose 6e to be the same as the chemical shift
of Cs+-18C6, it is important to test the sensitivity of
the calculated value of 4H2 to the value of Ge chosen. The
highest value used was 20 ppm above the value for the 18C6
complex and the lowest was that found for C222B complexes.
The results are given in Table 46.

It is obvious that AH2 is not very sensitive to the
choice of Ge. It is also small and insensitive to the sol~
vent. By using the chemical shift of Cs+-18C6 for Se, we

obtain K2 at each temperature and from the apparent formation

195

Table 46. Test of the Dependence of the AH2 Value on 6e.

 

 

 

Solvent 6e AH2 (Keel/mole)
PC 8.1 ~2.9i0.1
28. ~2.8:0.1
-52.6 -3.3:0.2
Acetone 6.4 ~2.5:0.l
-53.6 ~2.710.1
DMF ~3.37 ~2.610.1
-51.8 -2.810.l

 

 

constants (listed in Chapter III) at the corresponding
temperature, we can also calculate K1 and thus AHl. The

calculated results are listed in Table 47.

Table 47. Estimated Enthalpies of Formation of the Exclu-
sive (AHI) and Inclusive (AHZ) in Acetone, PC
and DMF.

 

 

Solvent 1 AH1 (Kcal/mole) AH2 (Kcal/mole) AHt(Kca1/mole)

 

Acetone ~12.9 ~2.5 ~15.4
PC ~8.6 ~2.9 ~ll.5
DMF ~S.7 ~2.6 ~8.3

 

 

196

It is interesting to note that AH2 is essentially in-
sensitive to the solvent. This agrees with the model,
since, when the exclusive complex is formed, most of the
solvent sheath has already been displaced by the cryptand
molecule. Simulation of the limiting chemical shift Kg.
temperature for the range from ~100°C to 500°C was done
for the three solvents. From Figure 56, a typical example,
one can see why it is not possible to obtain Ge,AH2 and

AS by fitting the data with program KINFIT. If the model

2
and the parameters used for simulation are correct, we have
examined only a small region of the temperature range

over which the inclusive 2 exclusive equilibrium exists.

The required extrapolation to obtain 5e is far beyond the
temperature region which is susceptable to experiment. From
a comparison of AHI and AH2 and the slow variation of K2
with temperature, it is also evident why a plot of log K

25 l/T gives a straight line even when K is a function of

K1 and K2. The value of AH2 is so small that variations of
the inclusive to exclusive ratio with temperature would lead
to only a slight curvature of the plot of log K 33 1/T.

It is also interesting to examine the entropy changes.

The factors which determine the change of entropy on com~

plexation can be expressed as
AS = ASS + ASc + ASn (v.13)

in which AS8 is the net entropy change due to changes in

197

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198

solvation between the complexed ion, the free salt and

the free ligand, ASC is the net entropy change due to con-
formational changes, and ASn is the change in entropy
caused by a change in the total number of particles. In
Cs+~[2]cryptate complexation, ASn should be nearly indepen~
dent of the type of complex formed, and it will be left
out of the present discussion. The term A88 is probably
positive because of the displacement of the well-ordered
solvation shell of the cation (except for a highly struc-
tured solvent). The ASc term is likely to be negative be-
cause of the decrease in the flexibility of the cryptand
when it forms a complex. According to these arguments, we
expect AS to be negative for the conversion of the exclusive
to the inclusive complex. This speculation fits the esti-

mated entropy changes given in Table 48.

Table 48. Estimated Entropy Values for the Complexation
Reaction at 298°K.

 

 

 

Solvent Asl(e.u.) ASZ(e.u.) AS(e.u.)
PC -l3.7 -7.0 -20.7

DMF -11.2 -7.6 -18.8

 

 

199

It is interesting to note that A81 is strongly solvent
dependent, but that A82 is much less dependent on the sol~
vent.

The existence of two types of complexes in the solu~
tion would also be expected to affect the apparent activa~
tion energy. Indeed, we obtained anomalous Arrhenius plots
as shown in Figures 45 and 52. The curved Arrhenius plots
for the acetone and PC cases could result if the exchange
process involves more than two sites. If we assume that the
reaction actually occurs in two steps as given by Equation
V.l then the activation energy for dissociation of the ex~
clusive complex must be higher than that for the inter-
conversion of the two complexes. This phenomenon is shown
by a collapse of the single line at low temperatures into
two lines, one of which occurs at the chemical shift value
of the free ion. If at low temperatures, the second re-
action becomes slow, then a broadening of the line for
the complex will occur which will give an anomalously
large value of T when only the two-site exchange process
is considered. It is simply not valid to use the two-
site expression when the rate of conversion to a third
site becomes slow.

This speculation is also reinforced by the exchange
spectra of Cs+C222 in PC and acetone at various temperatures
shown in Figures 37 and 48. It is interesting to note that
at low temperatures when the exchange rate between free

and complexed ions is slow enough to permit observation of

200

two distinct peaks as the temperature is lowered, the com-
plexed cesium peak is first broad, then narrow and finally
again becomes broad. This effect is especially pronounced

in PC solutions. The broadening of the signal for the
complexed Cs+ species could be caused by a slowing down of
the exchange equilibrium, [Cs+L)C] : [Cs+CZC] at low tempera-
tures.

The lineshape analysis for DMF solutions at various
temperature also shows a broad Cs+C222 line at low tempera-
ture. However, it was found that the exchange process
had not yet reached the slow exchange limit. This may be
the reason why the Cs+C222 kinetics study in DMF gave
a straight-line Arrhenius plot while it was curved in the
other two solvents. The activation parameters for the ex-

change reaction in DMF were therefore calculated.

Table 49. Activation Parameters for the Release of Cs+
from Cs+C222 in DMF

 

 

E = 13.520.3 Kcal/mole

a.

_ 6 -1
(kb)298 -(910.9)x10 sec
(10%) = 7.8:0.6 Kcal/mole

298
AHg = 12.910.3 Kcal/mole

#
A50

1721 (e.u.)

 

 

CHAPTER VI

SUMMARY AND SUGGESTIONS FOR FUTURE STUDIES

201

I . SUMMARY

Chemical shifts of the cesium—133 nucleus were measured
in six nonaqueous solvents relative to 0.5 M aqueous cesium
bromide. Cesium tetraphenylborate (CsTPB), triiodide and
thiocynate were used to determine the infinite dilution
chemical shifts in pyridine (PY), propylene carbonate (PC),
dimethylformamide (DMF), dimethylsulfoxide (DMSO), aceto-
nitrile (MeCN), and acetone. The corresponding ion—pair
formation constants were determined from chemical shift-
concentration data with the aid of a weighted non-linear
least-squares program (KINFIT). The association constant
for CsSCN in pyridine is 9002200 while for CsTPB in pyri-
dine it is 370120, in PC it is 1617, in MeCN it is 40:10
and in acetone it is 2213. The uncertainties given are
standard deviation estimates.

Cesium-133 NMR studies were also performed on CsTPB
complexes with five ligands in six nonaqueous solvents
mentioned. These ligands were 18~Crown~6 (18C6), dibenzo-
18C6 (DBC), dicyclohexyl~18C6 (DCC), cryptand-222 (C222)
and monobenzo-C222 (C2223). These ligands have different
topologies and substituents which affect the complexation
ability. Cesium tetraphenylborate forms both 1:1 and 2:1
(1igand/Cs+) complexes with 18C6 in all six solvents with
the first formation constant (K1) larger than 103. A new
EQN subroutine of the KINFIT program was written to analyze

data which show both 1:1 and sandwich complex (2:1) formation.

202

203

It was found that both K1 and K2 are affected by the geom-
etry and substituents of the crown ligands. It was also
shown that the solvent plays an important role in the
equilibrium process. For example, the K values for 18C6

in six solvents are in pyridine K1 > 108, K2 = 7111: in PC

x1 = (1.510.6) x 10‘, K2 = 8:2; in acetone K1 > 107, K2 =
3410.5; in DMF K1 = (913) x 103, K2 = 2.44:0.05: in DMSO
x1 = (1.1:0.1) x 103, K2 = (110.4); in MeCN K1 > 105, K2
= 4.4:0.3. When substituents are added to the ring of 18C6,
the resulting differences in geometry and rigidity affect
the K values substantially. The complexation reaction of
all three crowns in pyridine can serve as an example, the
ligand 18C6 is the most flexible of the three crowns and
has the highest K1 value, while DBC with the smallest cavity
and greatest rigidity has the lowest K1 value. On the other
hand, because of its small cavity and high rigidity, DBC
may form a non-symmetric 1:1 complex and this geometry
favor the formation of a 2:1 "sandwich" complex. In any
event, DBC gives the highest K2 value of the three crowns.
Dicyclohexyl~18C6 has a similar cavity size to 18C6 but
a higher rigidity of the ring. It has an intermediate K1
value, but the smallest K2 value.

A thorough study of 18C6 complexes with CsTPB in pyri-
dine was made at various temperatures (from 25° to ~44°C).
For the purpose of this study, a new temperature independent

reference for all temperatures was designed. Its validity

was tested and provided evidence that ion-ion and ion-solvent

 

 

 

 

204

interactions are temperature dependent. In this complexation
study, conclusive evidence for the 2:1 complex (18C6:Cs+)

was also found. The values of the first formation constant
at various temperatures were too large to be determined by
NMR techniques, but K2 values were determined and used to
obtain the enthalpy and entropy changes for the second com~
plexation step. The results are: AH = ~6.210.1 Kcal/mole

2

(AG -2.83i0.004 Kcal/mole, A82 = -11.210.3 e.u.

o) =
2 298

A kinetics study of the decomplexation reaction of Cs+o18C6
gave an activation energy of 820.3 Kcal/mole.

The formation constants of C222 and C2223 complexes
were also obtained from the NMR chemical shift data. The
formation constants for these two ligands showed the same
trends with various solvents. For example, the K1 values

5 3

for 0222 are > 10 (pr), (1011) x 10 (PC),(10.8:0.8) x 103

(acetone), (1.510.1) x 102

(DMF), (27:3) (DMSO), and (411)
x 104 (MeCN). By contrast, the 02223, with a benzo group
on one of the ether chains forms weaker complexes with K
values ranging from (S.7:0.8) x 103 (PY) to zero (DMSO).
Chemical shift-mole ratio temperature dependent studies
were also carried out, as well as studies of kinetics.
Both gave evidence for two types of complexes in the solu~
tion. The results are interpreted on the basis of the
formation of both inclusive and exclusive complexes of Cs+
by C222. Enthalpies and entropies of formation were com~

puted by using the KINFIT program and it was found that

both quantities are sensitive to the solvent for the

 

 

 

 

 

205

complexation of free cesium ions to form the exclusive
complex. The conversion of the exclusive to the inclusive
complex is much less sensitive to solvent. The activation
energy (Ea) for the loss of Cs+ from the Cs+C2223 complex
in PC is 14.910.6 Kcal/mole. By comparison, the values
obtained from kinetics studies for crown complexes give

Ea = 8.5:0.5 (Kcal/mole) for DCC complexes and Ba = 8:4
(Kcal/mole), for 18C6 complexes. It appears that the
higher rigidity and special geometry of the ligand give

C2223 the largest activation energy.

II. SUGGESTIONS FOR FUTURE STUDIES

The studies already made lead to the following sugges-

tions for further investigation:

(1) Calorimetric studies of the complexation reaction
can supply some complementary information to the alkali
NMR results. A joint study of Cs+~C222 in various sol~
vents by calorimetric and NMR lineshape analysis should
give more insight into the nature of the complexation

reaction.

(2) It has already been observed that the chemical

shift of cesium ion in electrolyte solutions is tempera-
ture dependent. By using a temperature independent
reference, a series of studies such as Kip for an electro-

lyte solution and formation constants for complexation

206

reactions could be made at various temperature and thus
one could obtain the corresponding thermodynamic
parameters. Also, it may be worthwhile to investi-
gate ion-ion and ion-solvent interactions at different

temperatures.

(3) At present a few studies have been made of the Cs+
counter ion effect on formation constants. Therefore,
a complete study of cesium salts complexed by [2]-
cryptand could be carried out. This information could
help to determine the conditions which favor inclusive
Kg exclusive complexes. It could also be used for the
study of competitive complexation reactions such as
that between Cs+~[2]cryptates and Na+~[2]cryptates.
Since the latter complexes are usually stronger than
those with Cs+ the extent of replacement of Cs+ by

Na+ could be used to obtain relative complexation

formation constants.

(4) Preliminary temperature studies of the C2223
complexation reaction with Cs+ in PC and acetone seem

to indicate that the chemical shift of complexed Cs+

is not very temperature dependent. Therefore, a thorough
temperature study of the Cs+~C2223 complexation reaction
in various solvents may give further information about

a system which probably forms only exclusive complexes.

(5) A lineshape analysis at various temperatures and

207

concentrations could be made of Cs+-[2]cryptate complexa-
tion reactions, to determine the order of the decomplexa-
tion reaction in low dielectric media. It has long

been of interest to find out whether the mechanism of
decomplexation involves a unimolecular or a bimolecular
process. If C221 or C2223 form only exclusive complexes
with the Cs+ ion, this condition may offer a very
favorable situation to test the nature of decomplexa-

tion mechanism.

APPENDICES

APPENDIX A
DETERMINATION OF ION-PAIR FORMATION CONSTANTS BY

THE NMR TECHNIQUE; DESCRIPTION OF THE COMPUTER
PROGRAM KINFIT AND SUBROUTINE EQN

The equilibrium for an ion pair reaction can be expressed

as

and

ip = I c

in which Kc is the concentration equilibrium constant and

y+ is the mean activity coefficient. By using the well

known Debye-Hfickel equation, y+ can be thus calculated as

 

 

follows:
1.823x106 | |/_
3/2 2 z_~ I
.109 7+ = ‘DT’ + (A.1)
’ 50.29
1 + —————7— 3 /I
In this equation 2+,Z_ are the charges of the ions, I is

i (C = Concentra—

the molar ionicstrength which is 1/2 ZCiz
tion summed over all species in the sglution), D is the
dielectric constant of the solvent and T and 3 are the

temperature (°K) and the closest distance of approach of

the ions in A.

208

209

The observed chemical shift is a p0pulation average

of those of the free ion and the ion pair; i.e.

obs 5 EXP + 6ipX ip

)XF + 6. . (A.2)

= (GFG ip 1p

where ME = [Cs+]/C¥; and Cg is the total concentration of

Cs+ in the system. Material balance gives

 

 

 

 

 

0: = [03*] + [Cs+ - x’]
= [Cs+] + Kc [Cs+]2
Therefore
M
~ 1 1+4K C
[CS+]= J C T
ZKC
+
x =C3 =-+J1+4KC 0?; 2
F EM M and KC = Kipyt
T 2K C
C T
So that, finally
-1 + (1+4K. ch yf)1/2
Gobs = (6F ~ 61p) + 61p (A.3)
2K CM ' 72
ip T 1

In order to make computation easier on the CDC 6500 com~

puter, Equation (A.l) was rewritten as:

210

1

6
1.823x10
_ 2.303 |z+z_|/f ‘

50.29 1
[(DT)1/2]3[1 + 73;;172 Eff]J

 

 

-791600|z+z_|/i

 

exP

1/2 3 50.29
[(DT) ] [1+—__—I77 Slf]
(DT)
Two unknown parameters must be obtained from the fitting
procedure. These are the limiting chemical shift of the
ion-pair (U(l)) and the activity equilibrium constant (0(2)).

The known parameters are introduced as constants; i.e.;

const(l) chemical shift of the free ion, const(2) =
(dielectric constant) x (temperature) and const(3) = average
distance parameter 3. In this study a value was chosen
from reference 100. The Fortran eXpression and deck struc-

ture are listed on the next page. It should be noted that

in these cases, all K

T
M

general a correction should be made by considering the degree

ip values were less than 400; therefore,

C was used to calculate the ionic strength. However, in

of dissociation.

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212

APPENDIX B
DETERMINATION OF COMPLEX FORMATION CONSTANTS BY THE

NMR TECHNIQUE; DESCRIPTION OF COMPUTER PROGRAM
KINFIT AND SUBROUTINE EQN

(l) DETERMINATION OF FORMATION CONSTANTS FOR A SINGLE

STEP REACTION

The equilibrium for a one-to-one complexation reaction

can be expressed as

M + L I ML (8.1)

and the concentration formation constant K will be

K = CML/CM‘CL (13.2)

where C stands for concentration in terms of molarity. In
this case we only considered the concentration formation
constant since there are no changes in the number of
charged species and the concentrations of the reactants are
very low (0.01 M). Therefore, we can consider that the mean
activity coefficient for the free salt and the complexed
cesium are the same.

The method used in this technique makes use of the fact
that at the fast exchange limit (on the NMR time scale).
the observed chemical shift of M (Gobs) is a weighted aver-

age of the characteristic chemical shift of M at each site

213
(free M and complexed M in bulk solution).
6 = X 6 + X 6 (3.3)

where 6M, 6 are the chemical shift for free and complexed

ML
M, respectively in a given solvent, and XM' XML are the

relative mole fractions for each species. Therefore

obs _ M
= XM(5M - 6ML) + GML (3.4)

The analytical concentration of M is CE = CM + C and for

. . T _
the ligand 18 CL — CML + CL

ML

_ T _ T _ T
so CML — CM CM CL - CL CM + CM
so
_ T T T
Then K - (CM CM)/(CM)(CL CM + CM)
2 T T T _
K CM + (K CL - KCM + 1) CM - CM - 0

 

_ 1 _ T _ T f”“T_ T *2 If
CM - if“ { (K CL K cM + 1) i. (K CL K CM+1) +4K CM }

(8.5)

Since physically C cannot be negative, therefore only the

M
positive root is chosen.

Let

T
D = (K CL K C

Then

214

+ 1)2

38

__ 1 T__ T ‘E—‘T
cM - if {—(K CL K cM+1) + +4K cM }

and

5 = 1 {-

 

obs T
2K CM

(K CE—K C13”) + \lD-MK C§}(6M - 5 + 5

ML) ML

(8.6)

In order to fit this equation, two constants and two param-

eters are used; namely:

u(l) = GML

const(l) = C:

The above equations

 

follows:
- T =
A - K CM u(2)
_ T =
B — K CL u(2)
C _ (GM-5m) =
T
2K CM

u(2) = K

const(2) = 6M

expressed in Fortran notation are as

* const(l)

* xx(l)

(const(2) - u(l))/(2.*A)

D = (B - A + 1.) ** 2

S = 6 = ((A - B - l.) + SORT (D + 4.*A))*C + u(l)

obs

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C0911 [Milt
DFTUPN
CONTINUE

a
RETURN

‘50fi‘l

a

Obs. “5350351

COMTTNH‘
DFTHQM
END

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1796

216
A listing of the deck structure is shown on the next page;
for details of the format refer to reference (106). Dr.

Mark Greenberg's thesis (1974).

(II) DETERMINATION OF FORMATION CONSTANTS FOR A TWO STEP

REACTION
The equilibria for this reaction can be expressed as
M + L + ML K = C /C °C (8.7)
ML '+ L 2 ML K2 = c /cML ~cL (3.8)

If the reactions also compete with ion pair formation then

the ion pairing reaction should also be considered; i.e.,

M+ + x' I M+.x’ KC = -——¥§——- (3.9)
C °C
M X
Where C stands for the molarity of the species. Let CE
and CE denote the total concentration of the metal ion and

ligand respectively. Then

T _
CM ‘ CM + CML + CML2 + CMX (3'10)
cT = c + C + 20

L L ML ML2 (3.11)

T (3.12)

II
0
II
0
+
O

217

(3.10) can be further written as

T _ 2

CM ' CM [1 + K1 CL + KIKZCL + KCCX]
Therefore

0 = cT/[l + K c + K c2 + K c ]

M M 1 L 2 L C X

Equation (3.11) can also be written as

 

 

 

T 2
= +
CL CL K1 CM CL + 2K1K2CMCL
lOeO'
2K K c c2 + c {1 + K c } - CT = o
1 2 M L L 1 M L
Therefore
1 2 T
- +
C = {1 KlCM} +‘V}1+KCM) +8K1§2CMCL
L
41(1chM

and (B.12) can be written as

therefore

__ T
Cx - CM/1+KCCM

(8.13)

(8.14)

(8.15)

218

Since the observed chemical shift is

6 = 6MX + X 6 + X 6 6 (b.16)

obs M ML ML ML ML + xip

2 2 19

In order to fit the calculated result with the experimental
data, an expression for the relative mole fractions of all
a and CE is demanded. However

the above equations (8.14-16) are all inter-connected. In

four species in terms of C

order to avoid using the solution to a cubic equation to
obtain values of CM and CL and thus Gobs' an iteration
method was used. This method is achieved by applying a

"do loop" in the EQN subroutine. The computer starts the
calculation from a given initial estimate and first cal-
culates CL' then uses this newly computed CL value to cal-
culate CM and ex“ Then, again these values are used to
calculate CL and so on until the ratio of-the previous CL
and the current CL is almost equal to one. The iteration
stops by jumping out of the do loop when the difference
between unity and the ratio of the new to the old CL values
is less than 10-5. Then the current CL, CM' Cx values are
used to compuete the mole fractions of each component and
thus Gobs'
Subroutine EQN of this calculation is listed on the next

page. There are four parameters and four constants as

follows:

219

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u(2)

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u(4)

220

_ T
K1 const(l) - CM
K2 const(2) = 6F
limiting chgmical
shift of ML (GML) const(3) = sip

limiting chemical

shift of ML+ (5

2 const(4) = K

)
ML2 c

APPENDIX C

NMR LINESHAPE ANALYSIS FOR TWO-SITE EXCHANGE;
DESCRIPTION OF THE COMPUTER PROGRAM AND SUBROUTINE EQN

The Bloch equations in the double rotating reference
frame apply to the macroscopic momentnd when all nuclei are
acted on by the same field Ho. When two positions in the
system under investigation have different screening con-
stants, the simple equations are no longer valid because
there are two possible fields and correspondingly two
Larmor frequencies, ”A and wB. McConnell (104) therefore

modified the equations by assuming that

(1) A11 nuclei remain in one state until they make a
sudden rapid jump to another, the nuclear precision
during the jump being neglected. This implies that a
nuclear exchange between positions of the same type will
have no effect and we need only consider the inter-

change between positions of types A and B.

(2) While a nucleus is in an A position, there is a
constant probability Tgl per unit time of its making a
jump to a B position. Likewise Tgl will be the prob-
ability of a nucleus in position B jumping to A. Con-

sider the following definitions:

0
II

A complex moment of magnetization

113
ll

radiofrequency magnetic field.

gyromagnetic ratio.

221

222

3
II

magnetization in the Z direction at A given

site.

”A'wB = chemical shifts (Hz) at sites A and B in the
absence of exchange.

TZA'T2B= Transverse relaxation times of the nuclei at the

two sites, in the absence of exchange.

. _ -l .
“A'GB are defined as “A — TZA 1(wA—w)
a = T‘1 -i(w -w)
B 2B B
TA,TB are the mean lifetimes on site A and site B,

respectively, at a given temperature.

With these definitions, the modified Bloch equations can

be expressed as:

d6 -1 -1
H—t— + GAGA = -1YH1MOA + TB GB " TA GA (C01)
31: + “BGB = ’“HiMoB + TA GA ‘ T13 GB
TBIGB represents the rate of increase of GA due to transfer
of magnetization from B to A sites. Similarly, TAIGA is

the corresponding rate of loss. For slow passage, it is

appropriate to use

dGA dGB

‘d'é’=‘<fi:‘=°

Let the fractional population in the A and B site be PA

 

 

 

223

 

and PB which are related to TA and TB through
T T
A B
P = P = P = 1
A TB+TA B TB+IA A B
then
M0A = PAMo MoB = PBMo
Solve for GA and GB by
(1) + (2) aAGA + aBGB = -iyfl1Mo (P A+PB) (C.3)
(1)-(2) a G - a G = -iyfi M (PA- ) + ZT-lG - 21-16
A A B B 10 PB B B A A
(C.4)
Then
(3)+(4) a G = -i H M P + T-lG - T-lG
A A Y 1 o A B B A A
in M P r 1'1
G _ 1 o A A TTA B G (C.S)
A ‘ ' 'J"7FT B
aA TA+1 aA TA
(3)-(4) a G = -in M P - 1‘16 + 1'16
B B 1 o B B B A A
in M p r T'lT
B a T +I A
aBTB+1 B 3

Therefore,

224

 

 

 

 

 

 

 

 

 

 

 

 

inlMoPA-rA TATgl inlMOPBrB TngB
GA _ - +-—————— {- + GA}
GATA+1 GATA+1 aBIB+l aBTB+l
-in M
GA{ 1 - 1 } = 1 o {PATA(GBTB+1)
(aArA+1)(TBaB+l) (aATA+l)(aBTB+l)
+ PETA}
-inlMo
_ 1’
GA - (a T +1)(T a +1)L PATA + PETA + PATATBGB}
A A B B
-iyfi1Mo
= {T + P T T a }
A A A B B
Substitute GA back into (6) to obtain
inlMotBPB TBrgl -inlM {TA+PATA?BaB}
GB = - + —— ° °
GBTB+1 TBaB+1 (GAIA+1)(TBaB+1)-1
= ‘1YHlMo { PBTB . (aA1A+1)(aBTB+l)-l
(aATA+l)(aBIB+l)-l aBTB+l l
2
T P T a
+ B + A B B }
TBaB+l TBdB+1
-in M P T T
(aATA+1)(aBTB+l)-1 dBIB+1 IBaB+l
2
P T a
+ A B B }
TBaB+l

225

 

-in M P T
= 1 ° {{PBTBTAGA + PBTB ‘ "E—E'
1
+ 57:; [TB(1+PATBGB]}
B B
Therefore
G = GA + GB = u + iv.

 

{TA+TATB(PAGB+PBGA) + TB-PBTB +9313}

hiynlMo

 

- {T +T +1 T (P a + P a }.
A B A B A B B A
(GATA+1) (“Bil-8+1) '1
Where u and v are the transverse components of M along and
perpendicular to the rotating field H1. The v (out-of-

phase component) is the one proportional to the absorption

intensity.

In order to separate the imaginary part from the real,

let
T = TATE/(TA + TB)
and, therefore,

TA = 'r/PA TB = ‘r/P

226

(TA+TB)+TATB(P +P BGA)

+1-1

G AaB

 

'iYfilMo aAaBTATBw A A+ “B B

:A;§‘ (FAG B PBGA’
TA TB

1 +

A B + “ATA+“BTB

B TA+TB

 

 

“A“B

Substitute the expression for a into that for Y to give

N = 1 + :§:§_ {P T-1 - iP ( - ) + P T.1 - iP ( ‘ )}
T +1 A 2B A ”B m B 2A B ”A w
A B
TT
_ 1 + ¥-—;-{ PATZB + PBTZA 1[PA(wB w) + PBU»A w)]}
+
A B
= 1 + T{[PT1+ P 1] - i[ P w + P w w]
AT 23 BT 2A A B B A

D = T[T-1 -

2A i(wA-w)][T;% — i(wB-w)] +

__§__ [T2'1_ 1(wA -w)] + —————ITZB - i(wB -w)]

 

 

TB+TB TA-l-TB
_ -1-1 _ _ _ _ . -1 _ -1 _
T T"1 r T“1 T (w -w) T ( - )
+ { A 2A + B 2B _ i A A + B “B “
TA+TB TA+TB TA+TB TA+TB
_ -1 _ _ _ -1 -1
_ TtTZAT 2B (”A m)(wB w) + TB T2A+TA1T2B1

227

-iT[TZB(wA -w) + T2A(mB- w) + 181(wA-w) + 1A1(wB-w)]

Let

-1 -1
A2B + PBTZA)

2
ll

1 + 1(PA T - i'r (PAMB + PBwA-w) = Q-iV

_ --1T -1 _ _ _ -1 -1 -1 -1
D — T{T2AT 23 (”A w)(wB w) + TB T2A + TA T23}

1

 

. - -1 -1 - _ .

-1T{ (wA-w) (T2B + TB ) + (wB-w) ('1‘2A + TA ) — S - 1T

Y = Q - iv ___, (Q-iV) (S+iT)

s - 1T 5 + 22
= W = 9_2§+_ + 19.4
S2 4, T2 5 2+1? 5 2+1?

Then

G=-in1MY=- %{-L-S-Y+iQ-2—1‘T}

o 2 2 32 +
s +T

and

u = yHlMo £921§YJ = [QT-8V]

sz+T2 52%-2
v = 'Y31M0{Lv—T}= 'K (QS+VT)

 

s 2+T2 32%2

However, in order to eliminate the broadening caused by

viscosity, one has to run separate calibration experiments

228

on the free salt and the completely complexed salt. In this
way the correct T51 values can be obtained.
The detector is located in the laboratory frame. In

conjunction with the rotating frame, My can be expressed

 

as
l
- 2MoYT2
M' = [2H1coswt - T2(w -w)2H sinwt]
2 o l
1+T2(wo-w)
y H M T
= -——§l—9—£— {coswt e T2(wo-w)sinwt}
1+T2(mo-w)
where
wt = 60 + 61 = zero order phase correction + first
order phase correction.
Let
K = 7H1Mo = u(l)
C = Base line correction = u(2)
* 0
T2 = T2T2inh/T2-I-Tzinh = u(3) T2: Natural Line w1dth
T . : Linewidth due to
21nh inhomogeneocity
mo = peak position (data point number) = u(4)
60 = zero order phase correction (degree) = u(S)

Then the above expression for My in the FORTRAN 4 language

appropriate to the KINFIT program can be written as follows:

Knowing that the frequency can be calculated at a given

229

data point number and sweep width by the relationship

2n* sweepwidth

= ' *
w (data p01nt number) memory storage

 

= (data point number) * PI

and degree = 1%6' rad.= -.017453293 rad.

CAL = u(1)*u(3)/(1+u(3)**2*(u(4)-XX(1))**2*PI**2)*

(cos(u(5)*0.017453293+Xx(1)* .0174532*const(l)/const(2))

-u(3)*(u(4)-XX(1))*PI*sin(u(5)*0.017453293* 222§E%%}))

const
+u(2)
where
const(l) = 61 in degree
const(2) = memory storage (total data points in the

memory)

From this fitting we obtain T2 for the nonexchange case,
and use these T2 values to calculate T for the exchange case.
Due to the combination of dispersion and absorption mode
which are mixed in the observed lineshape the expression

for the lineshape becomes

 

My = usine+vcose+C where C is a baseline offset.
u = K [QT-8V] v = 7:52— [OS-WT]
SZ+T2 S +T

where

230

'1 + P T-l)

Q = 1 + 1(PAT2B B 2A

v = T(PAmB + PBwA - w)

a B T

 

T T - 1(wA-w)(wB-m)
28 2A 2B

(DA-OJ (DB-(L)

 

 

2B 2A
Let K = u(l) C = u(2) T = u(3) 90 = u(4) A = u(S)
*
const(l) = PA (population fraction) const(2) = T2A
*
const(3) = PB const(4) = TZB const(S) = ”A
const(6) = wB const(7) = 61 const(8) = number point
= * const(3)
Q l + u(3) (const(l)/const(2) + const(d)’

V = u(3)*(const(3)*(const(5)+u(5))+const(l)*(const(6)

+ u(5))-XX(1))*PI

 

 

S = const(l) const(3) + u(3) _ u(3) +
const(2) const(4) (const(2)*const(4))
(const(5)+u(5)-XX(1))*(const(6)+u(5)-XX(1))*PI**2

T = (const(l)*(const(5)+u(5))+const(3)*((const(6)+u(5)-
XX(l))*PI+u(3)*((const(S)+u(5)-XX(1))/const(4)

+ (const(6)+u(5)-XX(1)) * PI

 

const(2)

My = u + 1v = yHlMo (R - iI)

K

82+T2

[(QS+VT)cose-(QT-SV)sine]+c

231

CALC = u(1)/(S**2+T**2) * ((S*Q+T*V)*sin((u(4) + XX(1)*

const(7)

const ) * 0'017453293) ' (0*T-S*V)*sin((u(4)+

const(7)
XX(1)* const(8))* 0.017453293))+u(2).

 

232

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APPENDIX D

DETERMINATION OF THE ACTIVATION ENERGY

For a complexation reaction

k

(A) _,t (B)
M + L + ML
kb

where M denotes the metal ion and is the nucleus at site A
under study, ML denotes the complexed metal ion and is the
nucleus at site B. At the fast exchange limits on the NMT
time scale one can calculate K = kf/kb from a chemical shift-
mole ratio study. At slow and intermediate ranges one can
obtain exchange time (T) values via lineshape analysis. By
studying the I value at various temperatures one can further
obtain information about the activation energy as shown in
the following way:

The relaxation time T in a magnetic resonance study is

defined as:

 

 

j; = rate of leavingofa nucleus from ith state by_exchange
Ti number of nuclei in the ith state
i.e.
l. _ dML ‘3; _ dM
T " dt/CML 'r " E/CM
B A
while‘
dML _ dM _
dt ‘ kbCML 3E " kaMCL

235

 

236

 

then
1 1
TB b TA F L
Since
T = TATE/(TA+TB)
PA = TA/(TA + TB) PB = TB/(TA + TB)
Therefore
T = PATB = PETA
1_PA_ l_kb PA
T-T-kb 1.8. 2.6-$— T=F
B A b

To calculate Ea' a reference value can be used to provide

faster convergence; namely,

E

_ _ -a 1__. 1
kb " kb(ref)exP[ T (T Tref”

 

(instead of kb = A exp[-Ea/RT]) then

const(l) R = 1.987 cal/mole °K
... O
const(2) - Tref ( K)

XX(1) = T (°K)

k

XX(2) b

 

237

 

 

u(l) = £nkb(ref)
u(2) = Ea
_ _ u(2) 1 _ 1
Calc - u(l) constTI) (xxllS const(2))

 

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