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dissertation entitled

MULTINUCLEAR NHR STUDIES OF
MACROCYCLIC COMPLEXES

presented by

ROGER DONALD BOSS

has been accepted towards fulfillment
of the requirements for

Ph.D. degmeinLHEMlSlRL

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Date 9/26/85

 

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MULTINUCLEAR NMR STUDIES OF MACROCYCLIC COMPLEXES

By

Roger Donald Boss

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry

1985

ABSTRACT
MULTINUCLEAR NMR STUDIES OF MACROCYCLIC COMPLEXES
By

Roger Donald Boss

Although many physiochemical techniques have been
used in the study of complexation reactions, none is
useful in every case. An NMR technique has been
developed for the determination of formation constants of
metal ion complexes which utilizes competition of two
cations for a common ligand. The competitive method is
applicable in both protic and aprotic solvents, and has
been shown to be very reliable. The method may be used
to measure formation constants for cations (including
paramagnetic cations) whose NMR properties are not
particularly well-suited to conventional NMR study and
formation constants which are too large to be measured
directly. As well as some systems which exhibit slow
exchange are amenable to this technique. The precision
of formation constant determination is limited by the
precision of the known formation constants used in the
competitive reaction and the precision of the chemical
shift measurement. Formation constants as large as
logK=8.88 have been measured by the repeated application
of competitive NMR, and values as large as logK=11.4 by

the use of the technique for slow exchange systems.

Roger Donald Boss
Results obtained by the competitive NMR technique

are given for a series of 18—crown-6 complexes with a

variety of cations (including the paramagnetic
nickel (II) ion) in N,N—dimethylf0rmamide. Formation
constants are also given for 18—crown—6 and

1,10—diazo—18—crown—6 complexes with the alkali metal,
thallium (I), and barium cations in acetonitrile,
acetone, and propylene carbonate. These results are
interpreted on the basis of the solvating ability of the
solvent towards both the cation and the ligand, the size,
charge, 'hard/soft' nature, and geometry prefered by the
cation, and the 'hard/soft' nature and steric effects of
the ligand donor groups. The complexation of Na with
dibenzo—30—crown—10 in nitromethane has been
investigated. Values for the formation constants of the
Na+.DB3OClO and (Na+)2.DBBOClO complexes are obtained,
but the data do not support previous studies which

suggested the formation of a (Na+)3.(DB3OClO)2 complex.

To Pam

ii

ACKNOWLEDGMENTS

The author would like to thank Dr. Alexander I.
Popov for his suggestions and guidance during the course
of this study.

He also wishes to thank Dr. George Leroi for his
many useful comments on the material contained within
this thesis, and Dr. Andrew Timnick for his friendship
and encouragement during the course of the author's
graduate studies. Also Dr. Klaas Hallenga must be
recognized for his assistance concerning the 'care and
feeding' of the NMR.

Gratitude must be expressed to his advisor and the
National Science Foundation for financial support.

Great thanks must be extended to the past and
present members of the group (esp. Bruce, John, Patrice
and Rick) for their friendship, encouragement, and many
'enlightening' discussions.

The moral support of both Pam's and my families
could not be replaced, and a thank you is insufficient to
convey my appreciation.

Matt and Nathan, it cannot be expressed how your

love and smiles have cheered me. Finally, to Pam, my

iii

wife, life, and love, no words can begin to tell you how
the support, patience, and love that you have given me

was needed and is appreciated, all I can say is I love

you.

iv

TABLE OF CONTENTS

LIST OF TABLES. . . . . . . . . . . . .viii
LIST OF FIGURES . . . . . . . . . . . . xii
CHAPTER I - INTRODUCTION . . . . . . . . . 1
A. INTRODUCTION . . . . . . . . . . . 2

B. HISTORICAL PART . . . . . . . . . . 3

1. Measurement Techniques . . . . . . . 3

2. Competitive Studies . . . . . . . . 10

3. Comparison Studies of 18C6 and DA18C6 . . 14

4. Dibenzo-BO-Crown-IO . . . . . . . . 21
CHAPTER II - EXPERIMENTAL PART . . . . . . . 30
A. MATERIALS . . . . . . . . . . . . 31

1. Salts. . . . . . . . . . . . . 31

2. Solvents. . . . . . . . . . . . 33

3. Ligands . . . . . . . . . . . . 35

B. METHODS . . . . . . . . . . . . . 36

1. Sample Preparation . . . . . . . . 36

2. NMR Measurements . . . . . . . . . 37

C. DATA TREATMENT. . . . . . . . . . . 39

1. General . . . . . . . . . . . . 39

2. Competitive NMR . . . . . . . . . 40

a. Fast Exchange . . . . . . . .
b. Slow Exchange . . . . . . . .
i. KM is known, KN is unknown. . .
ii. KM is unknown, KN is known . .

3. Dibenzo-30—Crown-10 . . . . . . .
CHAPTER III - COMPETITIVE NMR. . . . . . .
A. INTRODUCTION . . . . . . . . . .
B. MODEL CALCULATIONS . . . . . . . .

C. TEST CASES . . . . . . . . . .
D. STUDIES ON THE COMPETITIVE METHOD . . .

E. SLOW EXCHANGE COMPETITIVE NMR. . . .

F. CONCLUSIONS. . . . . . . . . .

CHAPTER IV - STUDIES ON THE COMPLEXATION
OF 18-CROWN-6 AND DIAZO-18 -CROWN-6

A. INTRODUCTION 0 o o o o o o o o o
B. l8-CROWN-6 COMPLEXATION IN DMF . . . .

C. COMPLEXATION OF 18C6 AND DA18C6 IN ACETONE,
ACETONITRILE, AND PROPYLENE CARBONATE . .

1. General . . . . . . . . . . .
2. Results for 18C6 Complexation.
3. Results for DA18C6 Complexation . .
4. Discussion . . . . . . . . . .
5. Conclusions. . . . . . . . . .
CHAPTER V - DIBENZO—BO-CROWN-lo . . . . . .
A. INTRODUCTION . . . . . . . . . .
B. RESULTS AND DISCUSSION . . . . . . .

C. CONCLUSIONS. . . . . . . . . . .

vi

4O
44
44
45
46
50
51
52
62
71
108

113

115
116

117

131
131
133
141
152
170
171
172

175
183

CHAPTER VI - SUGGESTIONS FOR FURTHER STUDY . .
A. COMPETITIVE NMR . . . . . . . . .
B. DIBENZO-30-CROWN-10 . . . . . . . .
APPENDICES O O O O O O C C I O O I 0
APPENDIX I - DERIVATION OF EQUATIONS TO USE
TO CORRECT FOR MAGNETIC
SUSCEPTIBILITY . . . . . .

APPENDIX II - SUBROUTINE EQN WHICH INCLUDES
SOLVING A GENERALIZED POLYNOMIAL

APPENDIX III - SUBROUTINE EQN WHICH WILL CHECK
FOR THE CORRECTNESS OF A
SOLUTION TO A GENERALIZED
POLYNOMIAL . . . . . . .

REFERENCES 0 O O O O O O O O O O O 0

vii

184

185
186

188

188

195

203

207

LIST OF TABLES

Table. . . . . . . . . . . . . . . . . . . . . . . . page

1 Comparison of formation constants for 16
complexes of metal cations with 18C6 and
DA18C6.

2 Formation constants for metal ion complexes 25

with DB30C10.

3 Cesium-133 chemical shifts as afunction of 63
18—Crown-6 concentration for solutions
containing cesium chloridea, potassium

chlorideb, and 18—crown-6 in methanol.

4 Results for the test cases of the competitive 64
NMR method.

5 Cesium—133 chemical shifts as a function of 67
18—Crown—6 concentration for solutions
containing cesium tetraphenylboratea, sodium
tetraphenylborate , and 18-crown-6 in
N,N—Dimethylformamide.

6 Sodium-23 chemical shifts as a function of 68
18—Crown-6 concentration for solutions
containing sodium nitrate8 and l8—crown-6 in
N,N-Dimethylformamide.

7 Cesium-133 chemical shifts as a function of 72
1,10-Diazo-18—Crown-6 concentration for
solutions containing cesi m

tetraphenylboratea, sodium tetraphenylborate ,
and 1,10-diazo—18-crown-6 in Acetonitrile.

8 Sodium—23 chemical shifts as a function of 75
18-Crown—6 concentration for solutions
containing sodium tetraphenylboratea,

potassium tetraphenylborateb, and 18—crown—6
in Acetonitrile.

viii

Table. . . . . . . . . . . . . . . . . . . . . . . . page

9 Results obtained from the competitive NMR 77
method.

10 Cesium-133 chemical shifts as a function of 80
18—Crown—6 concentration for solutions
containing cesium tetraphenylboratea, sodium
tetraphenylborateb, and 18—crown-6 in

Acetonitrile.

11 Cesium-133 chemical shifts as a function of 83
Dibenzo-27-Crown-9 concentration for solutions
containing cesium thiocyanatea, potassium
thiocyanateb, and dibenzo-27—crown—9 in
Acetonitrile.

12 Cesium-133 chemical shifts as a function of 86
l8-Crown-6 concentration for solutions
containing cesium nitratea, nickel (II)
nitrate , and 18—crown—6 in

N,N—dimethylformamide.

13 Cesium—133 chemical shifts as a function of 88
18-Crown-6 concentration for solutions
containing cesium tetraphenylboratea, barium
tetraphenylborateb, and 18-crown-6 in
propylene carbonate.

14 Cesium-133 chemical shifts as a function of 90
18-Crown-6 concentration for solutions
containing cesium tetraphenylboratea and

18—crown-6 in propylene carbonate.

15 Results of the fit of the data for the system 91
Cs /Ph B /18C6/PC.

16 Cesium-133 chemical shifts as a function of 96
18-Crown-6 concentration for solutions
containing cesium tetraphenylboratea and

18-crown—6 in Acetone.

17 Results obtained from the competitive NMR 97
method in acetone.

ix

Table. 0 O O O O O O O O O O O O O O O O O O O O 0 0 page

18 Sodium-23 chemical shifts as a function of 99
18-Crown-6 concentration for solutions
containing sodium tetraphenylboratea, cesium
tetraphenylborateb, and 18-crown-6 in Acetone.

19 Sodium-23 chemical shifts as a function of 102
18—Crown-6 concentration for solutions
containing sodium perchloratea, thallium

perchlorateb, and 18-crown-6 in acetone.

20 Thallium-ZOS chemical shifts as a function of 104
18—Crown-6 concentration for solutions
containing thallium perchloratea, barium

perchlorateb, and 18—crown-6 in acetone.

21 Corrected parameters for the slow exchange 109
sodium-23 spectrum for a nearly 1:1:1 solution
of NaClOaa, LiC104b, and 0222C in

acetonitrile.

22 Results for slow exchange competitive NMR for 110
C222 complexes in acetonitrile.

23 Corrected parameters for the slow exchange 112
sodium-23 spectrum for a nearly 1:1:1 solution
of Na0104a, TlClOab, and c222c in
acetonitrile.

24 Sodium-23 chemical shifts as a function of 118
18-Crown-6 concentration for
N,N-dimethylformamide solutions containing

sodium ion in competition with another cation.

25 Formation constants for some metal ion.1806 123
complexes in N,N-dimethylformamide.

26 Sizes of some cations.a'b 130
27 Properties of solvents used in complexation 132
studies.

Table. . . . . . . . . . . . . . . . . . . . . . . . page
28 Cesium—133 chemical shifts as a function of 134
18—Crown-6 concentration for solutions
containing cesium tetraphenylboratea, barium

b _ _ .
tetraphenylborate , and 18 crown 6 in
acetonitrile.

29 Results for competitive studies of 18C6 135
complexation.

30 Sodium—23 chemical shifts as a function of 137
18-Crown-6 concentration for solutions
containing sodium ion in competition with
another cation in variuos solvents.

31 Cesium-133 chemical shifts as a function of 145
diazo-18—crown-6 concentration for solutions
containing cesium ion in competition with
another cation in various solvents.

32 Results for competitive studies of DA18C6 150
complexation.

33 Lithium—7 chemical shifts as a function of 156
diazo-lB-crown-6 concentration for solutions
containing lithium perchloraté% thallium
perchlorate? and DA18C6 in acetonitrile and
acetone

34 LogK's for 18—crown—6 in acetone (AC), 159
acetonitrile (AN), and propylene

carbonate (PC).

35 LogK's for diazo-18-crown-6 in acetone (AC), 160
acetonitrile (AN), and propylene
carbonate (PC).

36 Sodium—23 chemical shifts and linewidths as a 176
function of mole ratio of

dibenzo-30-crown-10:sodium ion for solutions
containing 0.05000i0.0005 M sodium
tetraphenylborate in nitromethane.

37 LogK's for dibenzo—30—crown—1O using various 179
models in nitromethane.

xi

LIST OF FIGURES

Structures of some macrocyclic ligands.

Crystal structure of the ((Na+)2.DBBOC1O).(SCN_)
2
complex (reference 94).

Vacuum line attachment for the drying of salts.

Calculated chemical shifts XE mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
not monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the formation constant for the observed
metal ion is 103 M‘l.

Calculated chemical shifts XE mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the formation constant for the non—observed
metal ion is 103‘M71.

Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the ratio of the monitored formation
constant to that of the non—observed formation
constant is 0.01.

Calculated chemical shifts XE mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the ratio of the monitored formation
constant to that of the non-observed formation
constant is 0.1.

xii

23

34

53

54

57

58

Figure. 0 O I O O O O O O O O O O O O O O O O O O 0 .page

8

10

11

12

13

14

Calculated chemical shifts .lé mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the ratio of the monitored formation
constant to that of the non-observed formation
constant is 1.

Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the ratio of the monitored formation
constant to that of the non-observed formation
constant is 10.

Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function of
the formation constant for the metal ion which is
monitored by NMR, for solutions of two metal
ions, both at 0.01 M, which form 1:1 complexes,
when the ratio of the monitored formation
constant to that of the non-observed formation
constant is 100.

Experimental and calculated ce ium-133 chemical
shifts as a function of 18C6/Cs mole ratio for
solutions containing CsCl, KCl, and 18C6 in
Methanol.

Experimental and calculated cesium-133 chemical

shifts as a function of 18C6/Cs mole ratio for

solutions containing CsPh B, NaPh B, and 18C6 in

N, N-dimethylformamide. TBe minimum of the curve,

is+ a clear indication of formation of the
.(18C6)2 complex.

Experimental and calculated cesium-133 chemical
shifts as a function of DA18C6/Cs+ mole ratio for
solutions containing CsPh4B, NaPhAB, and DA18C6
in acetonitrile.

Experimental and calculated sodium—23 chemical
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaPh B, KPh B, and 18C6 in
acetonitrile. The curv calcfllated from the
current results ( ) and that obtained using the
value of Lin as a constant (---9 are both plotted
for comparison.

 

xiii

59

60

61

65

69

73

78

Figure. 0 O O O O O O O O O O O O O O O O O O O O O Opage

15 Experimental and calculated cesium-133 chemical 81
shifts as a function of 18C6/Cs+ mole ratio for
solutions containing CsPhaB, NaPhaB, and 18C6 in
acetonitrile.

16 Experimental and calculated cesium-133 chemical 84
shifts as a function of DB27C9/Cs+ mole ratio for
solutions containing CsSCN, KSCN, and DBZ7C9 in
acetonitrile.

17 Experimental and calculated cesium-133 chemical 87
shifts as a function of 18C6/Cs+ mole ratio for
solutions containing CsNO3, Ni(NO3)2, and 18C6 in
N,N-dimethylformamide. The minimum of the curve
is a clear indication of the formation of the
Cs+.(18C6)2 complex.

18 Experimental and calculated cesium-133 chemical 92
shifts as a function of 18C6/Cs+ mole ratio for
solutions containing CsPhaB and 18C6 in propylene
carbonate. The minimum of the curve is a clear
indication of the formation of the Cs+.(l8C6)
complex. 2

19 Experimental and calculated cesium-133 chemical 93
shifts as a function of 18C6/Cs+ mole ratio for
solutions containing CsPh4B, Ba(PhaB)2, and 18C6
in propylene carbonate.

20 Experimental and calculated cesium-133 chemical 98
shifts as a function of 18C6/Cs+ mole ratio for
solutions containing CsPh4B and 18C6 in acetone.

The minimum of the curve is a clear indication of
the formation of the Cs+.(18C6)2 complex.

21 Experimental and calculated sodium-23 chemical 100
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaPh4B, CsPhaB, and 18C6 in
acetone.

22 Experimental and calculated sodium-23 chemical 103
shifts as a function of 1806/Na+ mole ratio for
solutions containing NaC104, T10104, and 18C6 in
acetone.

23 Experimental and calculated thallium-205 chemical 106
shifts as a function of 18C6/T1+ mole ratio for
solutions containing T10104, Ba(C104)2, and 18C6
in acetone. The points at mole ratios greater
than 2 were not included in the fit.

xiv

Figure. 0 O O O O O O O . 0 C O C C C O O O O O O O Opage

24 Experimental and calculated sodium-23 chemical 124
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaPh4B, RbPh4B, and 18C6 in
N,N-dimethylformamide.

25 Experimental and calculated sodium-23 chemical 125
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaN03, Mg(N03)2, and 18C6 in
N,N-dimethylformamide.

26 Experimental and calculated sodium-23 chemical 126
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaN03, Ca(N03)22 and 18C6 in
N,N-dimethylformamide.

27 Experimental and calculated sodium-23 chemical 127
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaN03, La(N03)3, and 1806 in
N,N-dimethylformamide.

28 Experimental and calculated sodium-23 chemical 128
shifts as a function of 18C6/Na+ mole ratio for

solutions containing NaN03 and 18C6 in
N,N-dimethylformamide (0») and solutions
containing NaN03, M(N03)m and 18C6 in
N,§-dimethylformagide, where M+= Sr2+ (c1),
Pb+(A),andBa+(O).

29 Experimental and calculated cesium-133 chemical 136
shifts as a function of 18C6/Cs+ mole ratio for
solutions containing CsPh4B, Ba(PhaB)2, and 18C6
in acetonitrile.

30 Experimental and calculated sodium-23 chemical 140
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaPhaB, CsPh4B, and 18C6 in
propylene carbonate.

31 Experimental and calculated sodium-23 chemical 142
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaClOa, T1C104, and 18C6 in
acetonitrile.

32 Experimental and calculated sodium-23 chemical 143
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaPhaB, MPh4B, and 18C6 in
propylene carbonate, where M+- K" (I) and
Rb+ (a ).

XV

Figure. 0 O O O O O O O O O C O O C O O O O O O O 0 .page

33 Experimental and calculated sodium-23 chemical 144
shifts as a function of 18C6/Na+ mole ratio for
solutions containing NaPh4B, MPh4B, and 18C6 in
acetone, where M = K+ (N!) and Rb+ ( a).

34 Experimental and calculated cesium-133 chemical 153
shifts as a function of DA18C6/Cs+ mole ratio for
solutions containing CsPhAB, MPhaB, an DA18C6 in
acetonitrile, where M+ = K+ (o) and Ba + (O ).

35 Experimental and calculated cesium— 133 chemical 154
shifts as a function of DA18C6/Cs+ mole ratio for
solutions containing CsPhaB, +MPhaB, and DA18C6 in
propylene carbonate, where M+ +(o), K+ (A ),

b+ (o), and Ba (A).

36 Experimental and calculated cesium-133 chemical 155
shifts as a function of DA18C6/Cs+ mole ratio for
solutions containing CsPh4B, MPhAB, and DA18C6 in
acetone, where M+= Na+ (<3), K+ (13), Rb+ (O ),
and Ba2+ (A ).

37 Experimental and calculated lithium-7 chemical 157
shifts as a function of DA18C6/Li+ mole ratio for
solutions containing LiC104, TlC104, and DA18C6
in acetonitrile.

38 Experimental and calculated lithium-7 chemical 158
shifts as a function of DA18C6/Li+ mole ratio for

solutions containing LiC104, TlC104, and DA18C6
in acetone.

39 Experimental sodium-23 chemical shifts as a 173
function of DBBOClO/Na+ mole ratio for solutions
containing NaPh4B and DBBOClO in nitromethane
obtained by Shamsipur and Popov (35).

40 Experimental and calculated sodium-23 chemical 174
shifts and linewidths as a function of
DBBOClO/Na+ mole ratio for solutions containing
NaPh4B and DB30C10 in nitromethane obtained by
Stover, si si. (100).

41 Experimental and calculated sodium-23 chemical 177
shifts (v) and linewidths (O) as a function of
DB30C10/Na+ mole ratio for solutions containing
NaPhaB and DBBOClO in nitromethane. The
calculated curves are based upon a model using
1:1 and 2:1 Na+:D830C10 complexes.

xvi

Figure. I O I . . I O . . . . . . . I . I . I I . . .page
Experimental and calculated sodium-23 chemical 180

42

43

shifts (V) and linewidths (O) as a function of
DB30C10/Na+ mole ratio for solutions containing
NaPh4B and DB30C10 in nitromethane. The
calculated curves are based upon a model using
1:1, 2:1, and 3:2 Na+:DBBOC10 complexes.

Experimental and calculated sodium-23 chemical
shifts (v) and linewidths (O) as a function of
Db30C10/Na+ mole ratio for solutions containing
NaPh4B and Db30C10 in nitromethane. The
calculated curves are based upon a model using
1:1, 2:1, and 2:2 Na+:DB30C10 complexes.

xvii

181

CHAPTER 1

INTRODUCTION

A. INTRODUCTION

The study of complexation reactions in solution has
been a rich field for many years, and during this time
practically every known physiochemical technique has been
used for the determination of formation constants of these
complexes. There have been many studies of the class of
uncharged macrocyclic polyethers called crowns, which were
discovered by Pedersen (1,2), and the macrobicyclic
ligands called cryptands, which were first synthesized by
Lehn and co—workers (3-5).

The methods used for these complexation studies
include potentiometry, polarography, conductance,
ultraviolet-visible spectroscopy (UV-vis), infrared
spectroscopy (IR), nuclear magnetic resonance spectroscopy
(NMR), calorimetry, and liquid—liquid .partion
(extraction). Each of these techniques has its advantages
and disadvantages.

A review of the techniques which have been used in
the past, as well as a review of those previous results
which bear upon the results to be presented later is now

in order.

B. HISTORICAL PART
1. Measurement Techniques

The techniques used to measure formation constants
are covered in detail in general texts (6,7). Techniques
which have been used to measure crown and cryptand forma-
tion constants have been recently reviewed by Popov and
Lehn (8). A quick review of the major advantages and
disadvantages of these standard techniques follows.

The electrochemical techniques of
potentiometry (9-11) and polarography (12-14) have been
used to study crown and cryptand (Figure 1) complexation
reactions for various reasons. Both methods (as well as
conductance which will be discussed next) have the
advantage that they can be performed on solutions of low
concentrations, which helps to minimize insolubility as
well as ion pairing effects. These two methods also have
the distinct advantage that the observed quantity
(equilibrium potential or half-wave potential) is directly
proportional to the logarithm of the activity of the free
metal ion (the activity is generally nearly equal to the
concentration of the metal ion). As a consequence it is
possible to measure, quite accurately, small
concentrations of the free metal ion and, hence, small
differences in small concentrations of the metal ion.

This ability enables the determination of large formation

(‘9. pm

C. ::DCI 07:1) (CI: :JQ
bod boy Lov'

IBZngzg-6 D1cyclohexy1-lB—Crown—6 Dibenzo-lB-Crown-b

(DC18C6) (D818C6)

. 3 .
cm “is

   

 

H
1,10-Diazo-18—Crown-6 Dibenzo-27-Crown-9
(DA18C6) (0327c9)
. ‘:::’ [:::::;:::::::)
Dibenzo-30-Crown-10 Cryptand-2,2.2
(naaoc10) (C222)

Figure 1: Structures of some macrocyclic ligands.

constants. Potentiometry has the additional advantage
that the electrodes available are often quite selective
for certain cations.

The primary disadvantage of these techniques is that
the electrode system must be reversible. Often the
reverSiblity of the electrode is dependent upon the
solvent, and, therefore, an electrode which may be
reversible in one solvent may or may not be reversible in
another. The potential measured with an irreversible
electrode is not proportional to the logarithm of the
activity of the metal ion. Clearly, if the observed
potential is not reflective of the metal ion activity
(concentration), then it is impossible to extract any
useful information concerning the formation constant from
the potential.

The other commonly—employed electrochemical
technique, conductance (15-20), differs markedly from
potentiometry and polarography in that there are, ideally,
no redox reactions occurring at the electrode, and
therefore there is no requirement for reversiblity.
However, this brings about a disadvantage in that the
observed quantity, the conductivity, is directly
proportional to the concentration rather than to the
logarithm of the activity. Consequently, it is much more
difficult to measure small differences in small

concentrations, which results in an inability to

accurately discriminate between large formation constants.

Further, because the uncompexed cation is more likely
than the complexed cation to form an ion pair it is
possible that the act of complex formation will increase
the conductivity (due to the breakup of ion pairs), rather
than to decrease the conductivity (due to the lower
mobility of the larger complexed cation). These effects
may partially cancel out, which serves to complicate the
interpretation of the data (21). All of these
considerations result in the inability to measure forma-
tion constants which are greater than about 105M-1 by
conductance. One further disadvantage is that conductance
requires very precise temperature control, beyond that of
the other techniques.

The complexation of crowns and cryptands have also
been studied by spectroscopic techniques such as
UV-vis (2,22-26), IR (27), and NMR (22,28-40) (circular
dichroism measurements also have been used (41) for those
systems involving chiral ligands). Ultraviolet-visible
spectroscopy has the advantages that the absorptivities
can be quite high (allowing for low solute concentrations)
and that with double—beam referencing techniques it is
possible to observe subtle changes in a spectrum which may
be due to the complexation reaction. Ultraviolet-visible
spectrophotometry has the disadvantage that a chromophore

of some sort must be present on at least one of the

participants of the complexation reaction, and that this
chromophore must be sensitive to the complexation
reaction. This severely limits the possible macrocyclic
systems which may be studied by this technique.

Infrared spectroscopy has the advantage that
information concerning the conformation of the ligand in
the complex (and hence something about the form of the
complex) can be obtained. Infrared spectroscopy does,
however, have severe disadvantages: upon complexation a
band may gain or lose degeneracy; bands may appear and/or
disappear (due to combinations, overtones, or Fermi
resonance); the background due to the solvent may
interfere. Couple these effects with the difficulty of
doing quantitative IR (because of the difficulty in
establishing constant path lengths), and it becomes clear
that IR spectrophotometry is not extremely useful for
formation constant measurements.

Nuclear magnetic resonance spectrometry has been used
widely for the study of complexation reactions since
nearly every reaction involves a change in the proton
and/or carbon-13 spectrum of the ligand. Furthermore, due
to the high symmetry of the ligands, these spectra are
often simple and hence easily interpretable. Also, NMR of
the cation (especially alkali nuclei and thallium-205) can
be an extremely sensitive probe of these complexation

reactions, since the electron density at the nucleus often

changes greatly upon complexation. Nuclear magnetic
resonance spectrometry, however, has various disadvantages
including: low natural abundance (which can sometimes be
offset by enriching the compounds, perhaps at considerable
expense), low sensitivity, small chemical shift changes
upon complexation, problems with exchange kinetics (which
may excessively broaden the resonance lines), the general
necessity of high concentrations, complete loss of signals
when a paramagnetic species is intimately involved in the
complexation, and - for proton and carbon-13 NMR -
possible overlap of solvent peaks with the resonance of
interest.

All spectroscopic techniques suffer from the relative
disadvantage that the observable quantity (absorbance in
UV-vis, integrated oscillator strength in IR, and chemical
shift in MNR) is directly proportional to concentration,
which, as in conductance, limits their applicability (with
few exceptions) to those formation constants smaller than
104 to 105 5‘1.

Calorimetric titrations have been used to study a
wide variety of ligand systems (42-54), primarily in
water, methanol, and water/methanol mixtures, even though
they are applicable as well to nonaqueous solvents. One
particular advantage of calorimetry over other techniques
is that besides the value of AG° (which is equivalent to

determining the formation constant), the value of AH°

(and hence AS°) is directly determined. If one wants to
determine AH° (and/or A80) by all other techniques, it is
necessary to determine the formation constant at various
temperatures and then to construct a van't Hoff plot (and
hope that the plot is linear). Calorimetry, like
conductance and the spectroscopic techniques, measures a
quantity (the heat evolved/absorbed) which is directly
proportional to the concentration, and hence it is
impossible to directly measure formation constants greater

than 105 M-1 (44). Furthermore, calorimetry requires that

the value of AH0 be such that the temperature change due
to the reaction is at least 0.01K (44).

The technique of liquid—liquid partition (55-58), or
extraction, has been used since the beginning of the study
of crown complexation (55). Extraction has several severe
problems, chief among them is that there will always be
some water dissolved into the organic phase and some of
the organic solvent in the aqueous phase. This automatic
mutual pollution of the solvents makes the results, at
best, only partially reliable when results determined by
the extraction technique are compared to those of other
techniques measured in a more pure solvent. Also, the
quantity of the materials in each (or one) phase must be
determined by some methodology. All the advantages and

disadvantages of this other methodology are compounded

onto those of the basic extraction technique.

10

It is clear that there is a considerable need to
extend the range of utility of many of the above
(especially spectroscopic) techniques. Many have been

improved by performing competitive studies.
2. Competitive Studies

The first competitive study of crown complexation was
a UV study of the K +ion competition between DBl8C6 and
DC18C6 in water done by Pedersen (2). Because neither
DC18C6 nor its K+ complex absorb UV light in the region
near 275 nm (where DBl8C6 absorbs) the observed
differences between the spectra of DBl8C6 with K+ and
those observed for the DBl8C6 with K+ i_ £22 presence 2;
DC18C6 are due to the formation of the K+ complex of
DC18C6. Thus it was possible to use UV spectroscopy to
study a complexation reaction which, due to the absence of
a chromaphore is not particularly amenable to UV
spectroscopy. In a similar manner Smid and
co-workers (22,59) have used the UV spectrum of the
fluorenyl anion to determine selectivity series for alkali
metal ion.crown complexation via the competition between
the crown and the fluorenyl anion.

Just as Pedersen was the first to use a competitive
technique to study the crown compounds he discovered, so

were Lehn and co-workers (3,60,61) the first to use a

competitive technique to study the cryptands they first

11

synthesized. Lehn and co—workers studied the competition
of H+ and metal ions for cryptands in water and
water/methanol mixtures by use of H+ potentiometry.

The competition is in fact forced, since the
cryptands are di-tertiary amines and, therefore, are
bases. Consequently, in any protic solvent there is a
competition between the hydrogen ion and the metal ions of
interest. This necessary complication was turned to
advantage by using hydrogen ion potentiometry to follow
the competition. If the acid dissociation constants of
the ligand are known it is possible to use this very
sensitive method, which is selective to hydrogen ions, to
determine formation constants involving other cations.
Since the hydrogen ion selective electrode can only be
used in a competitive study for those protic solvents in
which the electrode is reversible, and for those systems
in which the complexation of the hydrogen ion is resonably
large, this is not a universally applicable technique.

Another, similar technique has been used by Cox,
Schneider, and co—workers (62—64) and others (65,66)
wherein the Ag+ ion is used as a competing cation with
detection by a Ag/Ag+ electrode. This electrode is
reversible in many non—aqueous solvents including many
(but not all) aprotic solvents.

In this technique the formation constant for the

Ag+.cryptand complex is first determined. This value is

12

then used, along with the measured potential of the Ag/Ag+
electrode as a function of added ligand in the presence of
the cation of interest, to determine the desired forma-
tion constant. This method works best for those systems
where the formation constant for the AgI complex is
101+M-d'or greater. Also, the Ag/Ag' electrode must not
only be reversible but must also be insensitive to the
other metal ion and the anion which are present.

In order to extend the usefulness of the calorimetric
technique Genthe and Hansson (67) and Eatough (68) have
used a competitive technique to study the complexation of
two metal ions for a common ligand. By doing so, the
upper limit of the conventional technique, K<10L"M-l (44),
is eliminated, and, in fact, Eatough (68) has determined
that the formation constant for Cu(II).1,10-phenanthroline
in water is logK=9.14£0.06.

Jagur-Grodzinski and co-workers (69,70) used a
competitive NMR method to study the complexation of Bra
with D318C6 and DC18C6 in carbon tetrachloride and in
carbon tetrachloride-ethyl bromide (3:1 v:v) solutions.
In their method the formation constant of chloroform with
the crown is determined by the change in the proton
chemical shift of the chloroform proton. This is then
used, along with the observed change in the chemical shift
due to complexation, to determine the formation constant

for the Br2.crown complex via an experiment in which Bra

13
is added to a solution of the chloroform.crown complex.
In the analysis it is presumed that there is no
cloroform.Br2 complex formed and that the chemical shifts
of the chloroform proton in the free and complexed states
are unchanged due to the presence of the Br .

2

DeJong, ££,2l° (71) used a competitive NMR experiment
to determine the ratio of the formation constants for a
series of crown ethers with the t-butylammonium ion. The
experiment involved an extraction of the cation from an
aqueous solution by a chloroform solution of the crown.
The chloroform solution was then 'titrated' by another
crown, and the observed chemical shift of the ammonium
proton were analyzed for the ratio of the equilibrium
constants. More recently, Zink and co-workers (72) have
described a method wherein thallium-205 NMR is used to
probe the competition of the thallium ion and another
cation for the same ligand.

Both the methods of DeJong, _£._l- and Zink and
co-workers provide relative formation constants, and hence
selectivity orders, but not actual formation constants,
unless one of the formation constants is known in advance.
These methods are applicable to systems where only
complexes of 1:1 stoichiometries form. Furthermore, the
method of Zink and co-workers requires that the ligand is

always completely complexed (i.e. both formation constants

are greater than about lOlIMTL), which makes prior

14

knowledge of one of the formation constants less likely.

Even with these restrictions these methods can be
quite useful. Reid and Rabenstein (73) have used the
proton NMR of mercaptoacetic acid, as a function of pH, to
monitor the competition of the mercaptoacetic acid with
various thiol—containing compounds for the CH3Hg+ ion.
These authors have also used the proton NMR of glutathione
to study the competition of glutathione and hemoglobin for
the CH3H8+ ion (74). In both cases, their methodology is
analogous to that of Zink, except that it is the CHng+
ion which must be compleufly complexed, instead of the
ligand. By the use of this method they have been able to
measure formation constants as large as 1017 MRI.

To summarize, essentially every known physiochemical
technique has been used in one way or another to study the
complexation reactions of crowns and cryptands. Each of
these techniques has its own special advantages and
disadvantages, and it is often possible to greatly extend
the usefulness of these techniques by using a competitive

method.

3. Comparison Studies sfi 18C6 and DA18C6

There have been several recent reviews of the general
literature of crown and cryptand complex formation
constants (75—80). While the literature for 18C6 and

DA18C6 are both rather extensive, there are relatively few

15
cases in which both ligands have been studied with the

same cation in the same solvent, which would be necessary
for the data to be directly comparable.

Frensdorff (9) determined the formation constants for
several monovalent cations with crown ligands in methanol
and water by the use of ion selective potentiometry. Some
of these results are given in Table 1. The results for
the K+ ion complexation with 18C6 and DA18C6 in methanol
indicated a large decrease in the stability upon the
change from 18C6 to DA18C6 (approximatly four orders of
magnitude). This was explained by the lowered
electronegativity of the —NH— vs. the —O- moieties. By
contrast, the formation constants for these complexes of
the Ag+ ion in water increased dramatically (about six
orders of magnitude) when the ligand was changed from 18C6
to DA18C6. This may be explained as being due to the
greater covalency of the bonding, which increases when -0-
is replaced by -NH- in the complexing agent for Ag+.

Izatt, _£._l- (49) used calorimetry to determine the
formation constants for several monovalent and divalent
cations with 18C6 in aqueous solutions. Several of these
results are given in Table 1. The agreement of their
results for the K+ and Ag+ complexes with 18C6 in water
with those of Frensdorff is excellent.

Anderegg (47) used pH titration to determine the

formation constants for several divalent cations with

16

 

 

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19

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20

DA18C6 (as part of a study of noncyclic, monocyclic, and
bicyclic nitrogen containing ligands) in water. Some of
these results have been reproduced more recently by Gramain
and Frere (81), who also used pH titrations to determine
the formation constants for the alkaline earth cations
(excluding Mg2+ and Be2+) with DA18C6 in water. Some of
these results are given in Table 1 and are in reasonable
agreement with one another.

Similarly, Arnaud-Neu, ££.fll- (82) have studied
several transition metals with a few macrocyclic ligands in
water by pH titration (see Table l for some of these
results). They explain their results in terms of the size
of the cation and the ligand cavity, and the extent of the
covalency for these ions as opposed to that for the alkali
and alkaline earth cations.

Kulstad and Malmsten (83) have used conductance to
study the formation constants of alkali metal ions with
DA18C6 in acetonitrile. They explain their results (which
may be found in Table 1) as being due to the difference in
solvation caused by the varying ion size.

Popov and co-workers (32c,36,38,40,84) have used
alkali metal and thallium-205 NMR to study the complexes of
these cations with various macrocyclic ligands in a variey
of solvents. The results for 18C6 and DA18C6 are given in
Table 1. Shamsipur and Popov (38) have proposed that the

selectivity order for DA18C6 is Tl+>Li+>Na+>Cs+. Their

21

explanation for the difference between this order and the
analogous one for 18C6 (Tl+>Cs+>Na+>Li+ (76)) is based on
the differences in the 'hard/soft' nature of the cations
and the 'hard/soft' nature of the —NH- and —0— moieties.
In summary, the data available for comparison of 18C6
and DA18C6 are relatively sparse, and have been, in
general, explained in terms of the nature of the cation
(the 'softer', more covalent tending, is the cation, the
greater the affinity for DA18C6 vs. 18C6). The data for
the individual crowns are interpreted on the basis of the
size of the cation vs. the size of the cavity, the
solvating ability of the solvent, and the 'hard/soft'

nature of the cation.

4. Dibenzo—30-Crown—10

 

Since the original report of the synthesis of
dibenzo—30—crown—10 (2), DBBOClO, there has been interest
in the complexes which form between the ligand and the
alkali and alkaline earth cations, because the size of the
cavity of the 30—membered ring is similar to that of some
naturally occurring antibiotics such as nonactin and
valinomycin. With DBBOClO having been shown to induce
transfer of cations through membranes (85,86), and with a
permeability order for the alkali ions reported to be
Li+<Na+<Cs+<K+<Rb+ (86) it is clearly of interest to

determine as much as possible concerning the complexes

22

formed between DBBOClO and the alkali metal cations.

Poonia and Truter (87) have reported the preparation
in ethanol of crystals of both Na+2.DBBOC10 and K+.DB30C10
with either I- or NCS- as counter ion. Similarly,
Parsons, Truter and Wingfield (88) reported the synthesis
of the DB30C10 complexes of several alkali tetraphenyl-
borates. With this anion only the complexes K+.DB30C10,
cs*.DB3oc1o, and Na+.DB30ClO were formed, although when
hydrated, the complex Na+2.DB3OC10'(H20)2 was obtained.

There have been several reports of x-ray crystal
structures for DB30C10 complexes. Bush and Truter (89,90)
reported the structure for (K+.DBBOC10)I-, while Hasak,
s; _i. (91—93) have reported the structures for
(K+.DB3OC10)NCS- and (Rb+.DB30ClO)NCS'-H20. In each case
the DB30C10 assumes the form of a toroid (the seams of a
tennis ball or baseball are toroids). For the potassium
complexes the ligand fits tightly around the cation with
the anion isolated from the potassium. For the rubidium
complex the ligand, although in the same conformation,
does not completely isolate the cation from the one
molecule of water, which is in contact with the cation.

Owen and Truter (94) have reported the structure for

the (Na+ .DBBOC10)(NCS-)2 complex, which is shown in

2
Figure 2. For each sodium ion there is coordination to

six oxygens of the ligand (two ether oxygens bridge the

sodium ions) and the nitrogen and of a thiocyanate anion.

23

 

Figure 2: Cryspal structure of Ehe
((Na )2.DBBOCIO).(SCN )2 complex

(reference 94).

24

The two bridging oxygens lie on the C2 axis of the
complex. When viewed down the C2 axis the ligand forms a
figure-eight with the benzo groups 'up' and the
thiocyanate anions 'down'.

The first report of formation constants for DB30C10
complexes was by Frensdorff (9) in methanol for the Na+
and K+ ions (see Table 2). Since then there have been
various formation constants determined; these are compiled
in Table 2, along with the method used in the
determination.

Live and Chan (31) used proton NMR to study the
complexation of the Na+, K+, and Cs+ ions in acetone.
Their results indicate that for the K+ and Cs+ complexes
the conformation of the ligand is extremely similar to the
conformation taken in the K+.DB30C10 crystals. The ligand
conformation in the Na+ complex is not, however, similar
to that of the K+.DBBOC10 crystals. Hence the authors
conclude that the sodium ion is not at the center of a
torioidal shaped ligand molecule.

In all of the studies of DB30C10
complexation (26,31,35,95-100), only for the Na+ ion in
nitromethane and acetonitrile (35,100) have there been any
indications of the formation of complexes with
stoichiometry other than 1:1, other than the formation of

Crystals. For the unusual cases Shamsipur and Popov (35)

observed behavior of the chemical shifts in the sodium-23

25

Table 2: Formation constants for metal ion complexes with

 

 

0330010.
Solventa Cation Anion logK Technique Reference

AC Na+ (310:;- 2.54¢0.09 1 H 31
K+ 0101; 4.30i0.11 1H 31

cs+ 0101;” 4.23:0.13 1 H 31

Pic- 4.04i0.05 133 Cs 35

SCN- 3.99.1008 153 Cs 35

PhnB' 4.01:0.05 133 Cs 35

AN 11+ Pic- 3.6 :? pot. 99
Na+ Clq: 3.60:? pol . 96

K+ 0101'; 4.70:? pol. 96

126+ Clog” 4.70:? pol. . 96

Cs+ C10; 3.50:? pol. 96

SCN" 3.39:0.09 153 Cs 35

11+ Clo]:L 5.60:? pol. 96

MeOH 1.1+ Cl" <0 UV 26
Na+ Cl' 2.11:0.07 0v 26

Cl- 2.0t 0.2 pot. 9

SCN- 2.80:0.04 pot. 95

K+ Cl' 4.57:0.05 UV 26

Cl' 4.60i0.08 pot. 9

010; 3.9 :? pol. 96

 

26

 

 

Table 2: continued.
Solventa Cation Anion logK Technique Reference
MeOH K+ SCN' 4.23i0.08 pot. 95
Rh+ Cl‘ 4.64i0.0S 0v 26
Cs+ Cl 4.23:0.05 CV 26
SCN 4.18i0.07 133 Cs 35
NHu+ Cl' 2.43:0.05 uv 26
T1+ C10; 4.51i0.05 uv 26
Clo; 4.1 :2 p01. 96
NM Na+ Ph B >5 23Na 100
2.1ao.3 23Na 100
C
2.5i0.3 23Na 100
0st 010- 4.30:0.05 133Cs 35
PC Mga+ C10; 2.8930.06 pot. 97
Ca2+ C10; 5.23:0.04 pot. 97
Sr2+ C10; 7.6730.03 pot. 97
Ba2+ Clo; 9.33:0.04 pot. 97
La3+ Clo; 4.29:0.04 pot. 98
Ce5+ C10; 4.10:0.03 pot. 98
Pr3+ C10; 4.12:0.04 pot. 98
Nd3+ C10; 4.10:0.05 pot. 98

 

27

Table 2: continued.

 

 

 

Solventa Cation Anion logK Technique Reference
5+ .-
PC Sm Cth 3.75i0.03 pot. 98
Cd3+ C10; 3.53i0.04 pot. 98
+ -
Tb5 C104 4.0730.06 pot. 98
3+ -
Er Cloh 4.48i0.05 pot. 98
+ -
Yb3 C104 4.7610.04 pot. 98
+ .—
Lu3 C104 4.80:0.05 pot. 98
FY Cs+ Ph#B- 4.41:0.10 133Cs 35
a. AC = acetone, AN = acetonitrile, MeOH = methanol,
NM = nitromethane, PC = propylene carbonate,
PY = pyridine.

b. for formation of 2:1 complex.
c. for formation of 3:2 complex.

28

and carbon-13 NMR spectra which were explained by the
formation of complexes of Na+ with DBBOClO in the
stoichiometries 1:1, 2:1, and 3:2. For the solvent
nitromethane, Stover, _£._l- (100) used a model based upon
these complexes to calculate the formation constants given
in Table 2, while for the solvent acetonitrile, Hofmanova,
._E _i. (96) report a formation constant for a 1:1 complex
without any correction for (or even mention of) the
existence of other complexes.

It is worth mentioning that Frensdorff (9),
Chock (26), and Petranek and Ryba (95) have measured the
formation constant for the 1:1 complex of the Na+ ion with
DBBOClO in methanol. In each case the possibility of
other stoichiometries was neglected. Poonia and
Truter (87) specifically report the preparation of the 2:1
complex from an ethanol solution. Given the similarity of
methanol and ethanol, the formation of a 2:1 complex in
methanol must be considered as a distinct possibility.

In summation, the crystal data for the K+ complexes
of DB30C10 uniformly indicate the complete encapsulation
of the cation by a toroidal ligand; Cs+ and Rb+ seem to
form only 1:1 complexes, and although these cations are
too large to be completely encapsulated, the ligand is
likely to take a toroidal shape; and Na+ often forms other

than 1:1 complexes with DB30C10 and, therefore, the data

avilable for the formation constants for sodium with

29

DB30C10 must be viewed with caution.

CHAPTER _I_I

EXPERIMENTAL PART

A. MATERIALS

 

hm

Sodium tetraphenylborate (Aldrich Gold Label) was
used as received except for drying for two days under
vacuum at 4§)C. Cesium tetraphenylborate, potassium
tetraphenylborate, and rubidium tetraphenylborate were
prepared by the metastatist reaction as described by
Mei (101) for the cesium salt, then dried for two days
under vacuum at 700C. Barium tetraphenylborate was
prepared by the method of Khol'kin, ss si. (102).
Approximately two grams of sodium tetraphenylborate was
dissolved in about 30 ml of diethylether to which about
one m1 of water is added. Approximatly 100 m1 of a 1 M
(or greater) aqueous solution of the desired metal ion was
prepared using the metal chloride (for example in the
preparation of barium tetraphenylborate a 1.5 M solution
was used). The solution was then divided into three
nearly equal fractions. Each of the three portions was
shaken for two minutes with the sodium tetraphenylborate
solution. The metal tetraphenylborate was then
precipitated from the ether phase by the addition of "a
non-polar solvent" (102); hexane was used to precipitate
the barium tetraphenylborate. The salt was then filtered,
washed (with the non-polar solvent), and dried, being
careful to note that the stability of the tetraphenyl-

borates decreases in the order (102): alkali metal >

31

32

alkaline earth > transition metal > lanthanides. For
example the barium tetraphenylborate was dried under
vacuum, in the dark, at 400C for two days.

All tetraphenylborate salts were tested for C1-
contamination by digesting the tetraphenylborate salt in
approximately 5 m1 warm (circa 400C) concentrated nitric

acid. To the resulting dark brown/black solution an equal

 

portion of approximately 0.1 M aqueous silver nitrate
solution is added and the solution is inspected for a
white precipitate. It should be noted that a very small
grain of NaCl (circa 0.5 mg) dissolved in the warm acid
solution results in a very obvious precipitate. It should
also be noted that incomplete digestion of the
tetraphenylborate ion will result in the precipitation of
silver tetraphenylborate which is also a white
precipitate. All tetraphenylborates were tested for
sodium ion content by atomic emission spectrophotometry
and found to contain not more than 0.5% sodium ion, on a
molar basis.

Cesium chloride (Alfa), potassium chloride (Fisher),
sodium nitrate (Baker), cesium nitrate (Alfa), strontium
nitrate (Baker), and barium nitrate (Allied Chemical) were
used as received except for drying at 120°C for one week.
Calcium nitrate (Fisher) and nickel (II) nitrate (Allied
Chemical) were used as received except for drying at

5

-
10 torr at room temperature on a vacuum line which was

33

fitted with an attachment which was specially designed to
be used for the drying of salts (Figure 3) for three days.
Magnesium nitrate (Baker) and lanthanium (III) nitrate
(Alfa) were used as received except for drying at
10- torr at room temperature for two days followed by
drying at 10.5 torr at 50 to 600C for one day.

Cesium thiocyanate (Pfaltz and Bauer) was
recrystallized twice from methanol then dried at 450C
under vacuum for two days. Potassium thiocyanate (Fisher)

was used as received except for drying at 453C under

vacuum for two days.

2. Solvents

Acetone (Baker), AC, was refluxed over anhydrous
CaSOu for two to four days, followed by fractional
distillation with the middle 60% fraction retained.
Acetonitrile (Baker), AN, was refluxed with CaEE for one
week, followed by fractional distillation with the middle
60% fraction retained. The solvent N,N—dimethylformamide
(Fisher), DMF, was refluxed over CaH2 under slightly
reduced pressure for two to four days, followed by
fractional distillation with the middle 60% fraction
retained. Methanol (MCB), MeOH, was reacted with Mg

(5 gm/l) and I (0.5 gm/l) then refluxed for two days,

2
followed by fractional distillation with the middle 60%

fraction retained. Propylene carbonate (Aldrich), PC, was

refluxed over CaH at about 90 torr (a pot temperature of

2

34

 

p I
l

. £7

/

TO VACUUM LINE

 

 

 

11

 

 

 

 

 

 

 

 

 

 

 

SALT

 

 

 

 

 

 

Figure 3: Vacuum line attachment for the drying of salts.

35

1000C) for two days, followed by fractional distillation
with the middle 60% fraction retained. All these solvents
were stored in a dry box under dry nitrogen over freshly
activated Linde 3 E molecular sieves. In addition, PC was
further treated by transfer to a new portion of freshly
activated sieves for at least 24 hours immediatly prior to
use. Solvents treated in this manner were analyzed by gas
chromatography (103) for the presence of water and always
found to contain less than 70 ppm water.

House distilled water was further purified by passage
through a Sybron/Barnstead Organic Removal Column (#D8904)
followed by passage through a Sybron/Barnstead Ultrapure
Mixed Bed Column (#D8902). The conductance of water

-1 -l

purified in this manner is about 5 x 10 g cm .

3. Ligands

The ligand 18-crown-6, 18C6, was obtained from the
Aldrich Chemical Co. and purified as described
previously (39); this purified ligand was then vacuum
dried for two days at room temperature. Kryptofix-2,2
(1,10-diazo-18-crown-6), DA18C6, was obtained from the MCB
Chemical Co. and used as received except for drying for
two days at room temperature under vacuum.
Dibenzo-27-crown-9, DB27C9, was obtained from the Parrish
Chemical Co., recrystallized twice from n-heptane, and
then vacuum dried for two days at room temperature.

Kryptofix-2,2,2 (cryptand-2,2,2), C222, was obtained from

36

the MCB Chemical Co. and used as received except for
drying for two days at room temperature under vacuum.
Dibenzo-BO—crown-IO, DBBOClO, was obtained from the
Parrish Chemical Co. and recrystallized from acetone, then
desolvated under vacuum at room temperature for three

days.

B. METHODS

1. Sample Preparation

The experimental solutions were prepared in one of
the following three ways:

Method 1: A stock solution containing the ligand and
one of the salts (at mole ratio 1:1) was prepared, and
another stock solution of the other salt was also
prepared. Appropriate volumes of these two stock
solutions were then mixed in a 2 ml volumetric flask so as
to prepare solutions of the desired mole ratio of the two
salts, but of constant ligand concentration. The volumes
of the stock solutions were measured by an Eppindorf
digital micropipette (cat. no. 22 33 360-7) which is
adjustable in 1 pl volumes from 80 to 1000 pl.

Method 2: Separate stock solutions were prepared for
each of the salts as well as the ligand. These stock
solutions were then micropipetted together into 2 ml
volumetric flasks to prepare solutions of constant, and

nearly equal, concentration of both salts and varying mole

37

ratios of ligand to salt.

Method 3: A stock solution was prepared of nearly
equal concentrations of the two salts. The ligand stock
solution was diluted with the salt stock solution (thus
the ligand stock solution contains the ligand and both
salts). The ligand stock solution was then micropipetted
to add the desired amount of ligand, and diluted with the
remaining salt stock solution to 2 ml. In this way it is
possible to ensure that each and every solution has the
same salt concentration.

The method used will be indicated in each case.

2. NMR Measurements

All nuclear magnetic resonance measurements were made
on a Bruker WH-180 multinuclear NMR spectrometer with a
field strength of 43.2 kG. At this field cesium-133,
sodium-23, thallium-205, and lithium-7 resonate at 23.62,
47.61, 103.88, and 69.951 MHz, respectively.

All solutions were measured in 10 mm od tubes (Wilmad
513-5PP) with a 4 mm od insert (Wilmad cat# WGS-lOBL)
coaxially placed inside. The insert contained a chemical
shift reference and the lock compound (except for
lithium-7 which was run without lock). For cesium-133 the
insert was 0.5 M CsBr in 020 (8.943 ppm vs. infinite
dilution cesium ion in water). For sodium-23 the insert
was 0.1 M NaCl in D20 (-0.081 ppm vs. infinite dilution

sodium ion in water). For thallium-205 the insert was

38

0.1 M TlNO3 in D20 (-1.5 ppm vs infinite dilution thallium
ion in water). For lithium-7 two inserts were used; one
was 0.1 M LiCl in D20 (0.0 ppm vs infinite dilution
lithium ion in water) and the other was 0.01 M LiCl in
pyridine (2.83 ppm vs infinite dilution lithium ion in
water).

The chemical shift of the sample peak was determined
by either: 1) performing a parabolic fit of the three most
intense 'smoothed' points (a smoothed point is obtained by
averaging the true point intensity with the intensity of
the two nearest neighbors), 2) an automatic computer fit
of the three most intense points to a Lorentzian function,
or 3) manual fit of the band profile to a Lorentzian
function. Method 1 was used for all data taken on the
WH—180 prior to the installation of the operating system
which utilizes the program NTCFTB. Methods 2 and 3 are
software options in NTCFTB. The choice between methods 2
and 3 was made based upon the apparent width of the band.
For all bands which were sufficiently narrow so that one
tenth the line width was less than f2'times the frequency
difference of adjacent points in the spectrum (i.e. there
were 14 or fewer points with intensities greater than 1/2
the maximum intensity) method 2 was chosen. For the other
case method 3 was used. The uncertainty of the measured

chemical shift was taken to be either J2. times the

frequency difference of adjacent points or one tenth the

39

apparent line width, whichever was larger. In the case of
dibenzo—30—crown-10, method 3 was used, but it was
repeated three times, with the average and standard
deviation of these three trials taken as the measurement
and its uncertainty. Downfield chemical shifts were taken
to be positive. All measurements were taken at ambient

probe temperature, which is approximately 220C.

A. DATA TREATMENT

1. General
All chemical shift measurements were corrected for
the magnetic susceptibility of the solution by the
equation of Live and Chan (104) as corrected for Fourier
transform experiments utilizing a superconducting magnet,
which is, as given by Martin, ss sl. (105),
An 6

+._. - lO , l
6corr .6obs ,3( xref xsol) X ( )

where X is the volumetric susceptibility of the solution

1

is the observed chemical shift, and 6 is the
obs Corr

true chemical shift. Due to some confusion as to which

i. 6

sign should appear in equation 1, a derivation of this
expression is given in Appendix I. Inasmuch as the salt
concentrations were always low, the magnetic suscept-
ibility of the solution was taken to be the diamagnetic

susceptibility of the solvent, as Templeman and

40

Van Geet (106) indicate, except for those cases where
there was reason to believe that one of the cations was
paramagnetic, in which case the magnetic susceptibility of
the solutions were directly‘ measured by conventional
techniques (107) using a Gouy balance.

The chemical shifts thus obtained as a function of
concentration (for the ligand and both salts) were then
analyzed by the use of the non-linear weighted least
squares program KINFIT (108). For nearly all the cases
analyzed, the exchange kinetics of the probe cation were
such that the free and. complexed sites underwent fast
exchange and only one time-averaged signal was observed.
In the case of systems containing C222 there were separate
resonances for the free and complexed cations (i.e. the

systems were in slow exchange).
2. Competitive NMR

3. Fast Exchange. For two cations, M+ and N+, which
form only 1:1 complexes with the ligand, L, there are the

two simultaneous equilibria

+ KM +
M + L ._.. ML (2)
and
+ KN +

The mass balance equations for the analytical

41

. + + .
concentrations for the cat1ons M and N and the ligand,

CM’ CN’ and CL’ respectively, may then be written

Cu = [M*1 + [ML*1. (4)
Cu = [N*1 + [NL*1. <5)

and
CL = [L] + [ML+] + [NL+], (6)

where [i] is the concentration of the species 1.
By solving the equilibrium constant equations for the

free cation it is easy to show that

[ML+1(KM[L1 + 1)/KM[L]. (7)

and

[NL*1<KN[L1 + 11/KN1L1. <8)

2
I

Equations (7) and (8) are solved for the concentration of
the complexes. These are substituted into equation (6),
and the resulting equation is then rearranged to give the
following cubic polynomial for the concentration of the

free ligand:

3 2
KMKN[L] + EMKNUZM + CN - CL) + KM + Kiln]

+ [3an - CL) + KN(CN - CL) + 1:'[L] — CL = 0. (9)

For a fast exchange of cation M+ the chemical shift,

42

' ' he ex ression
acorrected’ 1s glven by t p

0 +6 [L]K
0 1 M, (10)

corrected - 1 + [LIKM

 

where 61 is the chemical shift of the metal ion complexed
with i ligands.
If the metal ion N+ forms both 1:1 and 1:2 complexes

according to the equilibria

K
+ N1 +
N + L +———+ NL (11)
and
+ KNZ +
NL + L +——> NL2 (12)

then the polynomial equation for the free ligand analogous

to equation (9) becomes:

4
KK K [L]
MNINZ

3
+ [RMKNIKN (CM + ZCN — CL) + KMKN + KNlKNé][L]

2 1
r— ‘1
KMKN1 (CM + CN — CL) + KM
2
+ [L]
+ K K (2C - C ) + K
_ N1 N2 N L N1—

 

 

+ [RM(CM - CL) + KN (CN - CL) + I][L] - CL = 0. (13)

1

It should be noted that the absence of a 1:2 complex is

43

equivalent to KN being equal to zero. Substitution of
2

zero for KN in equation (13) does result in
2

simplification back to equation (9).

The chemical shift for the cation M+ would still be

given by equation (10), but if the metal ion N+ is the

probe nucleus, then the chemical shift would be given by

the equation

2
00 + 61[L]KN1 + 62[L] KNIKN2
= (14)

2
1 + [L]K + [L] K K

 

corrected

where all symbols are defined analogously to those in
equation (10).

The polynomial for the free ligand, equation (9) or
(13), is then solved iteratively by the subroutine EQN
given in Appendix II, and the value (or values) of the
unknown formation constant (or constants) are calculated.
The calculated values for the formation constant(s) are
sometimes reported with two uncertainties. These arise
whenever a previously-determined formation constant is
used as a known constant (as opposed to an unknown). The
first uncertainty (the value inside the parenthesis) is
the uncertainty for the calculated value when the known
formation constant is used as a constant .EIEE ss

uncertainty. These results are then combined with the

uncertainty of the known formation constant to give the

44

overall uncertainty, which is the second reported value,

for the measured formation constant.

b. Slow Exchangs If at the temperature of

 

measurement the NMR spectrum for one of the cations, M+,
shows slow exchange between the two cationic sites and if
a solution which has a mole ratio of 1:1:1 for M+:N*}L
also exhibts slow exchange, then it is possible to
determine the actual fractions of the species MI' and MU’
by simply integrating the corrected bands. Unfortunately,
the observed bands and the corrected bands are not quite
the same, since, as indicated by' Strasser (109) and by
Szyzgiel (110), a FID collected with a delay between the
end of the rf pulse and the beginning of acquisition will
not be Lorentzian. Moreover, when line broadening is
applied (to improve signal-to—noise) the apparent band
intensity is not the true intensity. Therefore, it is
necessary to correct the observed intensity for these
effects prior to the integration of the band profiles.
All reported band areas are corrected for these effects.
Once the correct band areas are obtained there remain
two possible cases to deal with, either 1) K1118 known and
KN is unknown, or 2) KM is unknown and KN is known.
i. KM is known, KN is unknown. From the values for
the fractions of M+ and MB’, and KM? it is possible to

directly determine the concentration of the free ligand

45

from

[ML+]

[L] = —_ (15)
(11%,,

Given [L] and [ML+], it is trivial to calculate [NL+] from
equation (6) and consequently [N+] from equation (5). The
formation constant KN is directly calculated from the
known values of [L], [N+], and [NL+]. The uncertainty in
KN is then determined by a propagation of errors for the
uncertainties of CH, CN, CL, KM, and in the integrated

areas of the slow exchange peaks.

ii. KM is unknown, KN is known. The value of [ML+]
from the slow exchange areas is used to modify the mass
balance equation for the total ligand, equation (6). This
modified equation is then combined with equation (8) to

obtain an expression for the free ligand concentration

 

 

[L] = -b +/ b2 '1' 46C (16)
23
where
a = KN, (17)
_ _ _ _ +
b — 1 (CN CL + [ML ])KN (18)

and

. (19)

The value of KM is then directly calculated from the
determined values of [L], [M+], and [ML+]. As in case 1

the uncertainty is calculated from a propagation of errors

for the uncertainties of all known or measured values.

3. Dibenzo—30—Crown-10

 

For the equilibria proposed by Shamsipur and

Popov (38) to exist for the sodium ion, M+, and

dibenzo-30-crown—10, L, in NM:

K
M+ + L +_i+ ML+, (20)
K2 2
ML+ + M+ +——+ MZL +, (21)
and
+ 2+ K3 3+
ML + MZL +——+ M3L2 , (22)
the mass balance equations become:
C = [L] + [ML+] + [M L2+] + 2[M L 3+] (23)
L 2 3 2 ’
and
_ + + 2+ 3+
CM — [M ] + [ML ] + 2[M2L ] + 3[M3L2 ]. (24)
Rearrangement of the formation constant expressions

followed by the appropriate substitutions gives:

47

[ML+1 = K1[M+][L].
2+ _ + 2
and [MzL ] - K1K2[M ] [L].
3+ _ 2 + 3 2
[M3L2 ] _ K1 K2K3[M ] [L] ,

Equation (23), multiplied by 3, minus 2
(24), along with equations (25) and (26)

expression for the free ligand:

3C - 20 + 2[M+]
[L] = L M

 

3 K M+ — K K M+ 2
+ 11 1 1 21 ]

(25)

(26)

(27)

times equation

results in an

(28)

Equations (25) - (28) are then substituted into equation

(24) which is rearranged to yield the final polynomial:

[M+]5(K12K22 - 4K12K2K3)
+ [M+]4|;(2C

- 2 2 _
L 01%)le2 + (80M 12C

2 2
4 _
- [M+]3 ( CM 12CMCL + 9CL )K1

2 2
K K K 2K K
+ CL 1 2 + 1 + 1

)K 2K K
L 1 2 3

2K K
2 3

2 (29)

+ 2 _ 2 _ _
+ [M ] [:(CM CL)K1 + (2CM 6CL)K1K2 4K1]

+ —
+ [M ] (4CM 3CL)K1 3

+3C

48

This is the polynomial which must be solved in
subroutine EQN in program KINFIT. Unfortunately, this
polynomial may have more than one root in the region
0<[M+]<CM. Hence it is necessary to modify the subroutine
EQN from Appendix II to include a 'step' which checks for
the correctness of the solution by calculating all
concentrations (from equations (25) - (28)) then checks
that these values do satisfy the mass balance conditions.
That is, equations (23) and (24) must be satisfied, and no
concentration maybe negative. This modification is
included in the subroutine EQN given in Appendix III.

It is also possible that, rather than an M L 3+

3 2

species, a dimer, MZLZZT, is formed. In this case the

equilibria would be described by equations (20), (21), and

K
2ML+ +—Q+ M2L22+, (30)

with the mass balance equations becoming

_ + 2+ 2+
CL — [L] + [ML ] + [MZL ] + 2[M2L2 ], (31)
and

_ + + 2+ 2+
CM — [M ] + [ML ] + 2[M2L ] + 2[M2L2 ]. (32)

The concentration of the dimer is given by

49

2+ = 2 + 2 2
[MZLZ l K1KD[M] [L] . (33)

and the concentrations of [M2L2+] and [ML+] are given by
equations (25) and (26), respectively.
The derivation then follows analogously to that given

previously, with the final polynomial being:
+5 2
[M 1 “(121(2)
+ 4 2 2 2 2
+ [M l [E1 K2 (CM ~2CL) + K1 K2 - 2K1 Kg]
+ 3 2 2
+ [M ] (K1 K2 - 4K1 KD)(CL - CM) (34)
+ 2 2 2
- [M ] 2K1 KD(CL - CM) + 2K1K2CL + K;]

+ [M+] K1(CM - CL) - I

This polynomial is also solved using the subroutine EQN

given in Appendix III.

CHAPTER II

COMPETITIVE NMR

A. INTRODUCTION

The conventional NMR technique has proven to be an
excellent method for the determination of formation
constants in nonaqueous solutions (111-114). There are,
of course, the disadvantages that it is not possible to
measure formation constants which are greater than about
105 M71 and that the NMR properties of many cations are
not particularly well suited to such studies (due to low
receptivity, low natural abundance, large quadrupole
moment, small chemical shift range, and/or
paramagnetism). Just as Cox, Schneider, and their
co—workers (20,62-64) extended the usefulness of the
potential of the Ag/Ag+ electrode by the use of a
competitive technique, Zink and his co-workers (72)
attempted to extend the usefulness of thallium-205 NMR by
using a competitive technique. However, their method is
not applicable to systems in which the ligand is not
completely complexed, due to their assumption that the
concentration of the free ligand is negligible. Nor is
their method applicable to systems in which complexes of
stoichiometries other than 1:1 are formed. In chapter II
the methodology was described for a general competitive
NMR method, in which the free ligand concentration is
explicitly included, and in which additional equilibria
may also be included.

It is the goal of this Chapter to explore the

51

52

applicability and sensitivity of the general competitive
NMR technique. The disadvantages of the technique will

also be discussed.

B. MODEL CALCULATIONS

In order to illustrate the sensitivity of the

competitive technique model calculations have been
performed in two ways. In both cases the formation
3 l

constant for one of the complexes was fixed at 10 M- ,
and the other formation constant was allowed to vary over
several orders of magnitude. The fixed formation
constant may be thought of as being the known value,
while the variable formation constant is the unknown
value. For the case where the observation nucleus is the
cation which forms the complex with the fixed formation
constant, the calculated chemical shift vs. mole ratio
(ligand to metal ion) plots are shown in Figure 4. For
the case where the observation nucleus is the cation
which forms the complex with the variable formation
constant, the calculated curves are shown in Figure 5.
Inspection of these two plots indicates that the
observed chemical shift behavior does contain the
information needed to determine the unknown formation
constant over a wide range of its values (circa six

orders of magnitude), regardless of whether the

observation nucleus is involved in the formation of the

53

 

8(ppm)

 

 

 

 

'00 I 2 ' 3

MOLE RATIO
IL
(M 1

Figure 4: Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function
of the formation constant for the metal ion
which is not monitored by NMR, for solutions of
two metal ions, both at 0.01 M, which form 1:1
complexes, when the formation constant for the
observed metal ion is 10 ,M‘l.

54

 

lOOOO

000

 

6" 100

94
IO

 

'0 1 fi‘
0 . l

MOLE RATIO (L/M)

 

”a:
09

Figure 5: Calculated chemical shifts .lé mole ratio of

ligand to one of the metal ions, as a function

'0f the formation constant for the metal ion

. which is monitored by NMR, for solutions of two

metal ions, both at 0.01 ‘M, which form 1:1

cmmflexes, when the formationaconstant for the
non-observed metal ion is 10 {M-l.

55

complex with known or unknown formation constant. It is
also quite apparent in Figure 4, although less so in
Figure 5, that the greatest distinction among possible
values of the unknown formation constant occurs in the
region of the curve near the mole ratio of 1. Further
inspection indicates that the maximum change in the
overall shape of these plots occurs when the unknown
formation constant is nearest in value to that of the
known formation constant. This implies that the best
precision of a determination will occur for those unknown
formation constants which have values most nearly equal
to the known formation constant.

Besides the 'match' of the known and unknown forma-
tion constants, the precision of the determination (and
the sensitivity of the method) is also greatly affected
by the chemical shift change upon complexation and the
precision of the chemical shift measurement. The change
in the chemical shift upon complexation would be,
essentially, a vertical scale factor for plots as shown
in Figures 4 and 5, and hence would affect the [overall
spread of the plots, while the precision of the chemical
shift measurements reflects the extent to which the
various plots may be resolved from each other. Clearly
the best overall precision should result from a large
chemical shift change with high precision (low

uncertainty) in the chemical shift measurement.

56

Furthermore, it is clearly impossible to calculate a
value for an unknown formation constant with better
overall precision than the precision of the
previously—known formation constant.

Figures 6-10 are plots of some other model
calculations. In each figure the ratio of the formation
constant for the complex involving the observation
nucleus and the non-observed formation constant is held
constant. For any ratio it is clear that the plots are
unique and that as the formation constants increase in
value the plots approach a limiting curve, but that so
long as the formation constant of the observation nucleus
is such that it could be directly determined in a
conventional NMR experiment (i.e. K <10S M-l) the
limiting curve is not obtained. Comparision of Figures
6-10 indicates that the limiting curve depends upon the
ratio of the formation constants. Furthermore, the
portion of the plot near the mole ratio of 1 is
reflective of the ratio of the formation constants, while
the region near the mole ratio of 2 is reflective of the
formation constant of the complex involving the
observation nucleus.

From these model calculations it is clear that the
competitive method should be applicable to cases in which
the known and unknown formation constants differ by no

more than about 4 or 5 orders of magnitude. Also it

10

Figure 6:

 

57

 

100000

' 10000

'1000

00

10
l 2 . 3
MOLE RATIO (L/M)

Calculated chemical shifts is mole ratio [of
ligand to one of the metal ions, as a function

.of the formation constant for the metal ion

which is monitored by NMR, for solutions of two
metal ions, both at 0.01 M, which form 1:1
complexes, when the ratio of the monitored
formation constant to that of the non-observed
formation constant is 0.01.

Figure 7:

58

 

[ 100000
1- 10000

1000

6~ loo

 

10 1 l 1
0 1 2 3
MOLE RATIO (L/M)

Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function
of the formation constant for the metal ion
which is monitored by NMR, for solutions of two
metal ions, both at 0.01 M, which form 1:1
complexes, when the ratio of the monitored
formation constant to that of the non-observed
formation constant is 0.1.

59

 

 

 

O I 100000
1 _ 0000
2 b 1000
3" ,
[+-
(6)
ppm
5 100
6 .
7 .
8 .
9 _ 10
10 l l j
,0 . 1 2 3

Figure 8:

Mom: RATIO (L/M)

Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function
of the formation constant for the metal ion

'which is monitored by NMR, for solutions of two
.metal ions, both at 0.01 M, which form 1:1

complexes, when the ratio of the monitored
formation constant to that of the non-observed
formation constant is 1.

6"
(ppm

Figure 9:

60

 

 

 

 

O r
10000010000
1 .
1000
2 .
3 ..
1, .
00
5 r
6 D
7 P
8 L
10
9 .-
10 ‘ ‘ ‘
0 1 2 3

MOLE RATIO (L/M)

Calculated chemical shifts is mole ratio of

_ligand to one of the metal ions, as a function

of the formation constant for the metal ion

.which is monitored by NMR, for solutions of two

metal ions, both at 0.01 M, which form 1:1
complexes, when the ratio of the monitored
formation constant to that of the non-observed
formation constant is 10.

(Ppm)'

61

fl

100000
10000

1000

100

10

 

10 l . A

Figure 10:

.0 i 2 3
MOLE RATIO (L/M)

Calculated chemical shifts is mole ratio of
ligand to one of the metal ions, as a function
of the formation constant for the metal ion
which is monitored by NMR, for solutions of
two metal ions, both at 0.01 E, which form 1:1
complexes, when the ratio of the mOnitored
formation constant to that of the non-observed

formation constant is 100.

62

should be possible to determine both formation constants
simultaneously if the previous condition is met and if
the formation constant involving the observation nucleus
could be directly determined in a conventional NMR

experiment.

C. TEST CASES

To test the competitive method a cesium-133 chemical
shift study was performed on a series of solutions,
prepared using method 2, containing CsCl, KCl, and 18C6
in MeOH. The value for the formation constant for the
Cs+.18C6 complex determined potentiometrically by
Frensdorff (9) (108KC8+18C6 =4.62i0.04) was used as the
known formation constant in a computer fit of the
experimental data given in Table 3 based on 1:1 complexes
of both cations. The results of this fit are given in
Table 5. The value calculated for the formation constant
of the K+.18C6 complex (logI(K+1806 =6.18(10.04)10.08) is
in excellent agreement with that of Frensdorff
(logK-Ilac6 =6.1010.04). The experimental data and the
calculated curve, both of which are plotted in Figure 11,
show excellent agreement.

As a second test of the competitive method a
cesium-133 NMR study was performed on a series of
solutions containing CsPW+B, NaPth, and 18C6 in DMF

which was prepared using Method 1. The data obtained in

63

Table 3: Cesium—133 chemical shifts as afunction of
18-Crown-6 concentration for solutions
containig cesium chloridea, potassium
chloride and 18-crown-6 in methanol.

 

 

Concentrationc Chemical
of 18-Crown—6 Shift
(fl) (ppm)

0.0 -42.05
0.0051 -41.26
0.0081 -39.98
0.0097 —38.74
0.0102 -37.79
0.0107 -36.78
0.0112 -36.33
0.0168 -21.39
0.0194 -13.50
0.0204 -12.61
0.0214 -12.67

 

a. [CsCl] . 0.0100 t0.0002 E.
b. [KCl] - 0.0100 10.0002 5.
c. uncertainty is 2%. d. uncertainty is 0 .04 ppm

64

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65

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66

this study are given in Table 5. From a previous
cesium-133 NMR study by Mei, gt g1. (32c), it is known
that the cesium ion forms the complexes Cs+.18C6 and
Cs+.(18C6)2. The value of the formation constant of Mei
for the formation of the 1:2 complex

(K +
CS 0(18C6)2
Before the data could be fitted it was necessary to

-l
=2.44¢0.05 M ) was used as a known value.

determine the value for the formation constant of the
Na+.18C6 complex.

A conventional sodium—23 NMR study of NaNOB and 18C6
in DMF was performed (these solutions were prepared
according to method 2). The data obtained, which are
given in Table 6, were fitted and the formation constant

was calculated to be =125i20lfl-1. With this

KNa+1806
value in hand the data for the competitive system could
then be analyzed. The results of the computer fit for
these data are given in Table 4. The value calculated
for the formation constant of the Cs+.18C6 complex
8 i t . u
(108KC8+18C6 4.03( 0.09) 0.20) agrees with that of Mel
(logK + =3.9Si0.14). The experimental data and
Cs 18C6
calculated curves are given in Figure 12. It should be
noted that the reversal of the chemical shifts clearly
indicates the formation of a second (1:2) complex for the
cesium ion.

These two test cases are of particular interest when

compared to the equivalent results of Zink and

67

Table 5: Cesium—133 chemical shifts as a function of

18—Crown—6 concentration for solutions
. . . a .

containing ce51um tetraphenylborate , sodium

tetraphenylborate , and 18—crown-6 in

N,N—Dimethylformamide.

 

 

ConcentrationC Chemicald
of 18-Crown-6 Shift
(M) (ppm)
0.0 —0.24
0.0051 1.21
0.0086 2.08
0.0093 2.35
0.0096 2.40
0.0101 2.36
0.0106 2.42
0.0120 2.68
0.0130 2.76
0.0152 2.78
0.0202 2.79
0.0253 2.78
0.051 2.49

 

a. [NaPhAB] = [18C6]. b. [CsPhaB] = 0.00995:0.0002 M.
c. uncertainty is 2%. d. uncertainty is 0.04 ppm.

68

 

 

 

Table 6: Sodium-23 chemical shifts as a function .
18-Crown-6 concentration for solutions
containing sodium nitratea' and 18-crown-6
N,N-Dimethylformamide.

Concentration Chemical
of 18-Crown-6 Shift
(fl) (ppm)
0.0 _4038*0012
0.00293 -5.7210.17
0.0058 -6.82t0.19
000097 -804 i003
0.0146 -907 $003
0.0293 -11.0 10.3
0.049 —12.4 10.4
0.097 -13.3 $0.4
a. [NaNO ] a 0.0108 10.0002 M.

b. uncer ainty is 2%.

69

 

 

 

O
0.5
Cesium-BS
Chemical
SN"
(mm) |
L5
2
2.5
I 1 l l L
3O I 2 3 4 5
Mole Ratio EBCGJ
iCs")
Figure 12: Experimental and calculated cesium-133

chemical shifts as a function of 18C6/Cs+ mole
ratio for solutions containing CsPth, NaPh B,
and 18C6 in N,N—dimethylformamide. he
minimum of the curve, is a clear indication of
formation of the Cs+.(18C6)2 complex.

70

coworkers (72). One test case performed by Zink was of
Cs+ and K+ with 18C6 in MeOH. Their result
(KC +/KKf=0.026i0.005) is in good agreement with that of
Frefsdorff (9) (KCs+/KK+=0.033i0.007), as is the current
result (K +/K +=0.02710.003). But both of the
... CS K. 5-1
1nd1v1dual formation constants are greater than 10 M ,
and hence the assumption of Zink and coworkers, that the
free ligand concentration is always negligable, holds.

By contrast, for the Na+ and Cs+ complexation with
18C6 in DMF, the results of Zink and coworkers indicate
that KCs+/KNa+=10.0i0.8, while that of the current work
is KCs+/KNa+=86i18. The results of Mei (32c) and this
work, from conventional NMR experiments, indicate that
KCs+/KNa+=71t26, which clearly does not agree with that
of Zink and his coworkers, but does agree with the
results of the general competitive NMR method. In this
case the formation constants are both less than 105 M-1,
and the assumption of Zink and coworkers does not hold.
Indeed, for 18C6 in DMF they report the ratio of the
formation constants for M+ to that of T1+ _to be
O.IOOi0.006, 2.3io.3, and 1.00i0.06 for Na+, K+, and 03*,
respectively. The direct ratio of the formation
constants determined by the conventional NMR method are
[lg T1+ (85)] 0.05610.012, 0.25:0.04, and 4.0t1.4 for
Na+ (this work), K+ (115), and Cs+ (32c), respectively.

As a test to see if both formation constants could

71

be determined simultaneously a cesium-133 NMR study was
performed on a series of solutions containing CsPhAB,
NaPhaB, and DA18C6 in AN, which were prepared using
method 3. The data obtained (which are given in Table 7)
were then fitted to a model using 1:1 complexes for both
cations. The results of this fit are given in Table 4
and the experimental data and the calculated curve are
given in Figure 13. The values thus calculated
(lOgKCs+.DA1806=2'254iO'009 and logKNa+.DA1806=4°49iO'02)

are in acceptable agreement with the values of Kulstad

and Malmsten (83) (logK + =2.48i0.04 and

Cs .DA18C6

logK =4.30i0.06), which were obtained by

Na+.DA1806
conductance measurements, and the formation constant for
the Cs+.DA1806 complex is in excellent agreement with
that of Shamsipur and Popov (38) (logK=2.26i0.02), which
was obtained from a cesium-133 NMR study.

The results for these test cases, all of which are
given in Table 4, agree well with the previously—reported
literature values, also given in Table 4. These results

clearly show that the described competitive NMR method

does give reliable values.

D. STUDIES 9! THE COMPETITIVE METHOD

 

A previous cesium-133 NMR study by Mei, _t _l. (32c)
of the complexation of Cs+ by 1806 in AN indicated the
formation of a 1:1 Cs+.18C6 complex and a 1:2 Cs+.(18(:o)2

complex. Because of the type of curvature obtained, the

Table 7:

72

Cesium-133 chemical
1,10-Diazo-18—Crown-6
solutions containing cesium tetraphenylborate ,

tetraphenylboratéi,

sodium

shifts

as a
concentration

function

1,10-diazo-18-crown—6 in Acetonitrile.

of
f r

and

 

 

Concentration ofC Chemical
Diazo-lS—Crown-6 Shift

(M) (9?!!!)
0.0 17.60
0.00299 18.07
0.0060 18.27
0.0080 18.73
0.0089 19.20
0.0094 19.54
0.0097 19.90
0.0099 19.83
0.0101 20.38
0.0104 20.61
0.0109 21.48
0.0119 23.31
0.0139 26.85
0.0169 32.33
0.0199 36.53
0.0299 44.62
0.050 50.32

 

a.

[NaP

B]

0.0099 10.0002 M.

b. [03? [p] a 0.0099 10.0002 M.
c. uncertainty is 2%.

d.

uncertainty

is 0.036 ppm.

73

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74

formation constant of the 1:2 complex could be precisely
determined (KCS+(18C6)2 =3.7i0.6 Mfl), while only a lower
limit for the formation constant of the 1:1 complex could
be determined (logK + >4). In order to determine
Cs 18C6

the actual value of the formation constant for the 1:1
complex it was necessary first to determine the value of
a 'known' complex.

A sodium-23 chemical shift study was performed on
the system NaPhqB, KPhQB, and 18C6 in AN (these solutions
were prepared using method 3). The experimental data
thus obtained are given in Table 8. These data were
fitted to a model containing a 1:1 sodium and a 1:1

potassium complex. The results for this fit are given in

Table 9. The value obtained for the Na+.18C6 complex

(logK Na+1806 =4.2110.10) does not agree within
experimental error with that of Lin (113)
(logKNa+18C6 =3.8i’0.2). In Figure 14 the experimental

data and the calculated curve (solid line) are shown, as
well as the curve calculated when the value of Lin is
used as a constant (broken line). The curve obtained
when the value of Lin is used clearly does not agree with
the experimental data, while the curve calculated from
the current values does. Hence, the current result for
the Na+.18C6 complex should be considered more reliable
and it will be used in all further calculations. It must

be noted that this improvement does not come about from

 

 

Table 8: Sodium-23 chemical as a function of
l8-Crown—6 concentration for solutions
containing sodium tetraphenylboratea, potassium
tetraphenylborate l8-crown—6 in
Acetonitrile.

Concentration Chemical

of 18—Crown-6 Shift

(fl) (ppm)

0.0 -7.49 $0.05
0.00300 -7.67 £0.05
0.0060 -7.99 10.07
0.0090 -8.62 £0.08
0.0095 -8.85 10.10
0.0100 -8.94t 0.10
0.0105 —9.10¢ 0.11
0.0120 -9.64i 0.13
0.0150 -11.22i:0.13
0.0185 -13.58 10.09
0.0196 -14.09 10.08
0.0199 -14.31 10.07
0.0201 -14.36 $0.07
0.0203 -l4.52 $0.07

 

76

Table 8: continued

 

 

Concentration C Chemical

of 18-Crown-6 Shift

(31) (ppm)
0.0206 —14.66 10.07
0.0215 —14.79 10.07
0.0250 -14.93 i0.07
0.0300 -14.93 i0.08
—14.93 i0.11

0.0400

 

a. [NaPh B] = 0.0100 10.0002 M.
b. [KPh 0] = 0.0099 10.0002 M.
c. unce tainty is 2%.

77

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79

the competitive method, but rather is the result of the
experiment being performed on a more powerful instrument
(a 43.2 kG magnet rather than a 14.4 kG magnet as for
Lin).

Next, a cesium—133 chemical shift study was
performed on a series of solutions containing CsPh B,

4
NaPh B, and 18C6 in AN (these solutions were prepared

4

using method 1). The data obtained are given in
Table 10. These data were then fitted to a model
comprised of 1:1 sodium complex and both 1:1 and 1:2
cesium complexes, with the known values for the forma—
tion constants of the sodium complex and the 1:2 cesium
complex. The results of this fit are given in Table 9,
and the experimental data and the calculated curve are
shown in Figure 15. The value calculated for the 1:1
cesium complex formation constant
(logKCs+.18C6=4°83iO°18) clearly agrees with that of Mei
(logK>4). This shows that the competitive method can
succeed where the conventional method gives only lower
limits.

The value reported from a previous potassium-39 NMR
study of the complexation of K+ with DB27C9 in AN (116),
logK=3.9i0.8, has a very large uncertainty (K has an
uncetainty of 140%) due to the potassium—39 nucleus

—4

having a very low receptivity (4.73 x 10 of that of the

proton) and very broad lines. By contrast, a cesium-133

80

 

 

 

Table 10: Cesium-133 chemical shifts as a function of
18-Crown-6 concentration for solutions
containing cesium tetraphenylboratetl sodium
tetraphenylboratea, and 18-crown-6 in
Acetonitrile.

Concentration C Chemical
of 18-Crown-6 Shift
(11) (ppm)
0.0 24.58
0.0049 19.67
0.0079 17.78
0.0084 17.55
0.0089 17.23
0.0094 16.94
0.0099 16.76
0.0104 16.59
0.0109 16.37
0.0114 16.08
0.0118 15.89
0.0148 15.25
0.0198 14.63

a. [NaPth] = [18C6]. b. [CsPhuB] = 0.0098 10.0002 M.

c. uncertainty is 2%. d. uncertainty is 0.04 ppm.

Figure 15:

81

M'-

 

 

 

‘ I ' i
MOLE RATIO [18061/[Cs+]

Experimental and calculated cesium-133
chemical shifts as a function of 18C6/Cs+ mOle
ratio for solutions containing CsPth, NaPth,
and 18C6 in acetonitrile.

82

NMR study of the complexation of Cs+ with DB27C9 (117)
resulted in the value 108KC8+DB2709 =4.0610.04, which has
only 10% uncertainty due to the narrow lines and wide
chemical shift range of the cesium—133 nucleus.
Therefore, a series of solutions containing CsSCN,
KSCN, and DBZ7C9 in AN were prepared using method 2, and
their cesium-133 chemical shifts measured. The
experimental data are given in Table 11. Because in this
solvent both the K+ and Cs+ cations form ion pairs with
the SCN- anion , it was necessary to correct for these

additional equilibria - =0.59iO.42 (115) and

(KK+SCN
KCS+SCN- =41i14 (118)). The data were then analyzed
using a model which contained 1:1 complexes and ion pairs
for both cations. The calculated results are given in
Table 9, and both the experimental data and the
calculated curve are plotted in Figure 16. The value
obtained (1°8KK+DB27C9 =4.10(i0.02)i0.08) is much more
precisely determined using the competitive method and the
cesium-133 nucleus, rather than the potassium-39 nucleus.
The advantage of being able to use a sensitive nucleus
with narrow lines and a wide chemical shift range, rather
than a relatively insensitive nucleus with broad lines
and a small chemical shift range is obvious.

A cesium-133 chemical shift study was performed on a

series of solutions containing CsNOS, Ni(NOB)2, and 18C6

in DMF (prepared using method 2), in the hopes of

83

Table 11: Cesium—133 chemical shifts as a function of
Dibenzo-27-Crown-9 concentration for solutions
containing cesium thiocyanatea, potassium
thiocyanate , and dibenzo-27-crown-9 in
Acetonitrile.

 

 

Concentration ofC Chemical
Dibenzo-lB-Crown-6 Shift
(M) (ppm)
0.0 35.26
0.00400 24.77
0.0070 16.83
0.0085 12.29
0.0095 10.19
0.0105 7.22
0.0115 5.13
0.0160 -5.06
0.0190 -10.73
0.0210 —11.84
0.0230 -12.84
0.0270 -13.24
0.0300 -13.38

 

a. [CsSCN] = 0.0099 £0.0002 M.
b. [KSCN] = 0.0100 $0.0002 M.
c. uncertainty is 2%. d. uncertainty is 0.04 ppm.

a‘c:

IO

20

84

 

 

 

 

l l

b

 

Figure 16:

l 2 3
MOLE RATIO [DBZ7C91/[Cs+]

Experimental and calculated cesium-133
chemical shifts as a function of DBZ7C9/Cs+
mole ratio for solutions containing CsSCN,
KSCN, and DB27C9 in acetonitrile.

85

extending the competitive method to the study of
equilibria involving paramagnetic species. It is known

that the N12+

ion is paramagnetic in DMF (119,120), but
due to its low concentration in these solutions the
measured magnetic susceptibility of the solutions is
insignificantly different from that of pure DMF.
Consequently, the experimental data given in Table 12 are
corrected only for the bulk diamagnetic susceptibility of
the solvent. These data were then fitted to a model
containing 1:1 and 1:2 Cs+.18C6 complexes (the known
values of these formation constants are given in Table 4)
and a 1:1 Nia'tl8C6 complex. The calculated results are
given in Table 9 and both the experimental points and the
calculated curve are plotted in Figure 17. These results
clearly indicate that in some cases it is possible to
measure the formation constant for a paramagnetic
species. Further discussion of the value obtained for
this formation constant will be found in Chapter IV.

The experimental data for a cesium-133 chemical
shift study of a series of solutions containing Cst+B,

Ba(Ph4B)2, and 18C6 in PC, prepared using method 3, are

given in Table 13. These data were fitted to a model

using 1:1 and 1:2 Cs+.18C6 complexes and a 1:1 Ba2+.18C6
complex. The formation constants for the cesium
complexes (logKCs+ 180624.4510.06 and

KCS+(1806)2='11°192‘-0'49 M-l) were determined from a

86

Table 12: Cesium-133 chemical shifts

as a function of

18-Crown—6 concentration for solutions
containing cesium nitratea, nickel (II)
nitrate , and 18-crown-6 in

N,N-dimethylformamide.

 

 

ConcentrationC Chemical
of 18-Crown-6 Shift
(11.) (ppm)

0.0 0.44
0.00248 1.37
0.00398 2.64
0.00447 2.78
0.00472 2.84
0.0049 2.96
0.0052 2.96
0.0054 3.00
0.0059 3.04
0.0074 3.05
0.0094 2.95
0.0099 2.89
0.0124 2.67
0.0255 1.19

 

a. [CsNO ] = 0.0049 i0.000131.
b. [Ni(N03)2] = 0.0049 10.0001 m.

c. uncertainty is 2%. d. uncertainty is 0.02 ppm.

87

 

1.33066

2.0 "

 

 

 

 

3.5
0

MOLE RATIO [18061/[Cs+1

Figure 17: Experimental and calculated cesi m-133
chemical shifts as a function of lBC6/Cs mole
ratio for solutions containing CsNO3,

Ni(N03)2, and 18C6 in N,N-dimethylformamide.
The minimum of the curve is a clear indication
of the formation of the Cs+.(18C6)2 complex.

88

Table 13: Cesium-133 chemical shifts as a function of

 

 

 

18-Crown-6 concentration for solutions
containing cesium tetraphenylboratea, barium
tetraphenylborate , and 18-crown-6 in
propylene carbonate.
ConcentrationC Chemical Concentrationc Chemical
of 18-Crown-6 Shift of l8-Crown-6 Shift
(5) (ppm) (5) (ppm)
0.0 -36.95 10.01 0.0095 -12.86i 0.05
0.00250 -36.99 i0.03 0.0097 —11.21 i0.03
0.00400 -36.99 10.03 0.0100 —10.73 $0.03
0.00475 -36.94 $0.03 0.0102 —10.07 10.03
0.0049 ~36.84 10.01 0.0105 -9.65 $0.03
0.0050 -36.81 $0.01 0.0107 -9.45 10.03
0.0050 -36.81 10.03 0.0110 -9.30 20.03
0.0052 -35.67 $0.03 0.0125 -9.36 10.03
0.0070 -26.51¢ 0.11 0.050 -19.53 £0.03
0.0090 -15.16* 0.09
a. [CsPh B]=0.0050 £0.0001 _
b. [Ba(P 4Bé.l=0'00499 i0.0001 M.

C.

uncertainty is 2%.

89

conventional cesium-133 study of Cqu+B and 1806 in PC,
and are in reasonable agreement with the results of Mei,
_g_l. (32c) (logK1:l=4.l4:t0.19 and Kl=2=10.9i0.4 E1).
The experimental data for the conventional study are
given in Table 14, the results of the computer fit are
given in Table 15, and both the experimental data and the
calculated curve are plotted in Figure 18.

The results of the fit of the competitive study are
given in Table 9, and the experimental data and the
calculated curve are shown in Figure 19. Only a lower
limit could be obtained for the formation constant of the
barium complex (logK > 9), due to the large difference
between the formation constant of the 1:1 cesium complex
and that of the barium complex (at least 4.5 orders of
magnitude). These results show that the competitive
method requires that the known and unknown formation
constants differ by no more than 4 or 5 orders of
magnitude (which is similar to the requirement that the
formation constant be less than 101+ to 10 5E1 in a
conventional study).

An attempt to determine the formation constant for
the Rb+.18C6 complex in AN was unsuccessful due to the
insolubility of the RbPth. Likewise, an attempt to
measure the formation constant for the Tl+.18C6 complex
in PC was unsuccessful since T1C104 is insoluble.

Similarly, the first attempt to measure the formation

9O

Cesium-133 chemical shifts as a function of
18-Crown-6 concentration for solutions
containing cesium tetraphenylboratea and
18—crown-6 in propylene carbonate.

Table 14:

 

Concentrationb Chemical C Concentrationb ChemicalC

 

 

of 18—Crown-6 Shift of 18-Crown—6 Shift
(fl) (ppm) (M) (ppm)
0.0 -36.08 0.0120 -8.92
0.00300 -28.54 0.0130 -9.13
0.0060 -20.15 0.0150 -9.70
0.0080 -l4.51 0.0175 -10.61
0.0090 -12.33 0.0200 -11.32
0.0095 -10.72 0.0300 -14.09
0.0100 -9.65 0.050 -18.55
0.0105 -9.18 0.098 -25.37
0.0110 -9.01 0.195 -32.51
a. [CsPh B] a 0.0100 10.0002 M.
uncertainty is 0.04 ppm.

b. uncer ainty is 2%. c.

91

Table 15: Res 1ts of the fit of the data for the system
Cs /Pth‘/18C6/PC.

 

a
Complex Calculated logK Literature Value

 

cs+.1aco 4.45i0.06 4.14:0.19

03+.(1806)2 K=11.14:0.49M‘1 K=10.910.4M‘1

 

a. reference 32c.

92

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by

wO—I

omomma

1°”!

 

 

ran:

93

 

 

 

-38«
-30.
133
Cs 6
-204
-1 OJ
0 i ' 5 5
MOLE RATIO [18061/[CS+1
Figure 19: Experimental and calculated cesium-133
chemical shifts as a function of 18C6/Cs+ mole
ratio for solutions containing CsPh B,

Ba(P B) , and 18C6 in propylene carbonate.
2

94

constant for the Ba2+.1806 complex in AC failed due to
the formation of a precipitate when Ba(Phl‘LB)2 and 1806
were mixed. These experiments demonstrate that the
competitive method has the serious constraint that the
cation of interest, the competing cation, and all the
cationic complexes must be soluble in the presence of the
same anion. This disadvantage can be partially
circumvented by a proper choice of the anion.

In fact, in some cases it is possible to avoid the
mutual solubility constraint, and the constraint
requiring that the known and unknown formation constants
be within 4 or 5 orders of magnitude, through the
repeated application of the competitive technique using
an 'intermediate' cation. The difference between the
'known' and 'unknown' formation constants may be greater
than 5 orders of magnitude if the 'intermediate' cation
has a formation constant which is intermediate between
the known and unknown values. In this way both steps,
'known' to 'intermediate' and 'intermediate' to
'unknown', may be less than 4 or 5 orders of magnitude,
but with the overall difference being greater than 5
orders of magnitude. Similarly, the 'known' and
'intermediate' measurements may be performed with one
anion, the 'intermediate' and 'unknown' with another,
while with neither of these anions would RQEM the 'known'

and 'unknown' be soluble. The following series of

95

experiments illustrate these possibilities.

Cesium-133 chemical shift data, which are given in
Table 16, for a conventional NMR study of CsPhuB and 1806
in AC, were fitted to a model using 1:1 and 1:2 CS+.18C6
complexes. The results are given in Table 17, and both
the experimental points and the calculated curve are
shown in Figure 20. Although the value of the formation
constant of the 1:1 03+.1806 complex is logK=4.62i0.05),
it is not possible to use this value to determine the

2+
.1806 complex or for the

formation constant for the Ba
T1+.l806 complex, not because the formation constants
differ by too many orders of magnitude, but rather
because of the lack of mutual solubility (CsClOQ is
insoluble in AC, Ba(PhuB)2 is insoluble in A0 in the

presence of 1806, and TlPh B is insoluble in A0).

4

These cesium complexation formation constants can,
however, be used as knowns in a competitive sodium-23
study of NaPhAB, CsPhaB, and 1806, in A0. The
experimental data, obtained from a set of solutions
prepared using method 3, are given in Table 18. The
results of a computer analysis, using the known values
for the cesium formation constants and an unknown forma-
tion constant for a 1:1 sodium complex, are given in
Table 17, and the experimental data and the calculated

curve are shown in Figure 21. The calculated value for

the Na+.1806 complex formation constant

96

Table 16: Cesium-133 chemical shifts as a function of
18-0rown-6 concentration for solutions
containing cesium tetraphenylborate a and
18—crown-6 in Acetone.

 

 

Concentration b Chemical
of 18—Crown-6 Shift
(fl) (ppm)
0.0 -37.41
0.00323 -25.72
0.0097 -6.69
0.0102 -6.07
0.0105 -6.00
0.0109 -6.11
0.0118 -6.77
0.0140 —8.56
0.0188 -13.50
‘ 0.0323 -22.40
0.053 -30.23
0.113 -37.87

 

a. [03? B] = 0.0100 iO-OOOZ M.
b. uncer ainty is 2%. c. uncertainty is 0.04 ppm.

97

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Tm Hamil N 802000

 

I. q
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.ocoUmom cw venues mzz m>HuHuanoo on» scum conflMuno muaammm "NH wanmh

98

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may mo :owpmsuow ocu ww coaumoavcfl cmoau m ow o>u=o 0:» mo aaawcfia one
:

.o:Ouoom :H coma new m moo wcwcfimucou maoausaom mow ofiumu macs +mo\oom~
mo coauocam m on muwflcm HmOHaono mmHIasflmou voumH=OHmo was Hmucoawuoqu "om ouzwflm

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Vonl

 

99

Table 18: Sodium—23 chemical shifts as a function of
18-Crown—6 concentration for solutions
containing sodium tetraphenylboratea, cesium
tetraphenylborate , and 18—crown-6 in Acetone.

 

 

Concentration C Chemical
of 18-0rown-6 Shift
(31) (ppm)
0.0 -7.9110.06
0.00399 -9.89i0.15
0.0079 -12.2310.15
0.0109 -13.7710.15
0.0119 -14.38i0.14
0.0149 -15.96i0.14
0.0179 -16.18i0.14
0.0189 -16.1210.14
0.0199 -16.1110.l4
0.0209 -16.11i0.13
0.0219 -16.15i0.14
0.0249 -16.17i0.14
0.0308 -16.16i0.14
0.050 -16.1610.14

 

b. [cspth] = 0.0100 :0-0002
c. uncergainty is 2%.

100

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101

(logK =4.57(i0.02)i0.06) cannot be used to

+
Na 1806
determine the value for the formation constant of the

2

Ba +.18C6 complex, because the difference between the two
formation constants is larger than can be determined with
the chemical shift change (”8.3 ppm) and the uncertainty
of the chemical shift measurement (~0.14 ppm) of the
sodium-23 nucleus.

Although TlPhuB is insoluble in AC, T1010# is

soluble, and so is NaClO#. Therefore, a competitive

sodium-23 study of solutions of NaClO TlCth, and 1806

4.
in AC was performed (the solutions were prepared by
method 3). The experimental data are given in Table 19.
These data were then fitted to a model containing 1:1
complexes for both sodium and thallium (I). The results
are given in Table 17, and the experimental points and
the calculated curve are plotted in Figure 22. The value
calculated for the T1+.18C6 complex formation constant
(108KT1+1806 =6.19(i0.03)t0.09) can then be used to
determine the formation constant for the Ba2+.1806
complex.

A competitive thallium-205 NMR study of a series of
solutions containing T10104, Ba(010#)2, and 1806 in AC,
prepared by method 3, resulted in the experimental data
which are given in Table 20. Those solutions which

contain an exesss of ligand (beyond that needed to form

both 1:1 complexes) do not show a constant chemical

102

Table 19: Sodium-23 chemical shifts as a function of
18-0rown-6 concentration for solutions
containing sodium perchlorate , thallium
perchlorate , and 18—crown-6 in Acetone.

 

 

ConcentrationC Chemical
of 18-Crown-6 Shift
(M) (ppm)

0.0 -8.41 10.07
0.00300 -8.49 10.07
0.0060 —8.64 10.07
0.0098 -9.25 10.07
0.0101 -9.49 10.07
0.0103 -9.48 10.07
0.0105 -9.50 10.07
0.0108 -9.62 10.07
0.0138 -11.25 10.08
0.0169 -13.42 10.08
0.0199 —15.54 10.08
0.0299 -16.02 10.08
0.049 -15.98 10.08

 

a. [NaCth] = 0.0099 10.0002
b. [T1010 ] = 0.0104 10.0002
c. uncertainty is 2%.

M.
_M-.

103

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vV—l

vfl— I.

 

 

104

Table 20: Thallium-205 chemical shifts as a function of
18-0rown—6 concentration for solutions
containing thallium perchloratea, barium
perchlorate , and 18—crown-6 in Acetone.

 

 

ConcentrationC Chemical
of 18-0rown-6 Shift
(M) (ppm)

0.0 —219.0210.05
0.00281 —218.6610.06
0.0091 -217.6010.16
0.0093 -217.7010.16
0.0095 —217.4110.15
0.0098 -217.3410.16
0.0112 -213.8610.15
0.0140 -206.4410.l6
0.0187 -194.8410.16
0.0281 -196.2610.13
0.046 —l98.2810.12

 

a. [T1010 ] = 0. 0093 10. 0002 M.
b. [Ba(Cll0n ] = 0. 0094 10. 0002 M.
. uncerta y is 2%.

105

shift, nor do they continue to change in a manner which
might indicate 'weak' 1:1 complex formation. Rather
these points reverse the direction of the chemical shift
change, as was originally observed by Rounaghi (121),
possibly indicating the formation of a 1:2 Tl+.(1806)a
complex. Since the thallium (1) ion has the right size
to fit into the 1806 cavity, the formation of a 1:2
complex would not be expected, or, at most, it should be
very weak. Furthermore, if a 1:2 complex is formed, it
would have distorted the previous competitive sodium-23
study of the thallium complexation, by slightly reducing
the fraction of the sodium ion complexed at the mole
ratio of 2. Since the experimental point and the
calculated curve for that system (see Figure 22) do not
show significant deviation near the mole ratio of 2, the
formation constant for such a 1:2 complex must be more
than 4 orders of magnitude smaller than the 1:1 Na+.1806
complex; hence 108KT1+(1806)2 (0.6.

Thus given that 103KT1+1806 =6.19t0.09 and
logKTl+(1806)2 (0.6, the formation of the 1:2 complex may
be neglected, and the data in Table 20 for mole ratios
less than or equal to 2 may be fitted to a model
containing only 1:1 complexes for both cations. The
results are given in Table 17, and the experimental data
and calculated curve are shown in Figure 23.

4..
Because the formation constants for the Ba .1806

106

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h h

h
b

.03.

o
Hsnow

TO—NI

 

mos-

107

and Tl+.1806 complexes are both larger than 106M-l,
there is essentially no free metal ion at mole ratios
greater than 2. Therefore, any variation of the chemical
shift from the chemical shift of the Tl+.1806 complex, at
mole ratios greater than 2, may be attributed to the
formation of the 1:2 Tl+.(1806)2 complex. There are two
unknown parameters for the 1:2 complex, the formation
constant and the chemical shift. Since there are two
data points at mole ratios greater than 2 it is possible
to directly calculate that logKlz2=-0.3 and
61:2=-470 ppm. Although these values agree with the
previous reasoning, they should not be considered very
accurate.

Clearly, the repeated application of the competitive
method can result in the determination of formation
constants which are otherwise too large to be measured in
one experiment and can partially mitigate the constraint
of mutual solubility. The repeated application of the
technique does, however, result in ever-increasing
uncertainties. (For the 03+.1806 formation constant the
uncertainty is 11%, for Na+.1806 it is 14%, for Tl+.1806
it is 21%, and for Ba2+.1806 it is 74%.) This growth in
the uncertainty will, eventually, result in unreasonably
large values. Furthermore, the repeated application of

the competitive method requires that for each experiment

at least one of the two cations should be a nucleus which

108

is suitable for observation by NMR.

E. SLOW EXCHANGE COMPETITIVE NMR

The previous discussion has been limited to the fast
exchange cases; however, exchange involving cryptates is
often slow on the NMR time scale. Thus it is of interest
to determine if slow exchange spectra may be used in a
competitive experiment.

To test whether the integrated areas of slow
exchange resonance bands may be used in a competitive
study, the sodium—23 spectrum for a nearly 1:1:1
Na010#:LiClOu:0222 solution in AN was obtained. The
spectrum showed a slow exchange, and the resonance bands
were fitted to Lorentzian profiles. Parameters obtained
were then corrected for the effects of the line
broadening and the delay time, and Lorentzian bands
defined by the corrected parameters were then integrated.
The corrected parameters and the integrated areas are
given in Table 21. The value of the formation constant

determined by Cox, 31 Q1. (64) (logK =6.9:0.1) was

Li+0222
used as the known value and the formation constant of the
Na+.0222 complex calculated. The agreement of the
calculated value (logKNa1C222 =9.8t0.3) with that of Cox,

£1 31. (logK =9.63i0.1) is excellent (see

Na+0222
Table 22).

A similar sodium-23 study of a 1:1:1 solution of

109

 

 

 

Table 21: Corrected parameters for the slow exchange
sodium-23 spectrum for a nearl 1:1:1 solution
of 11.301043, LiClogb, and 0222 in acetonitrile.

Species Position Linewidth Intensity Area

(ppm) (H2) (H2)

Na+ -7.59t0.09 35:12 27001800 850012500

Na+.0222 40.231.10.09 27:2 7500011700 23500015000

a. [NaClq+] = 0.00568t0.0001 M.

b. [LiClOu] = 0.00575i0.0001 M.

c. [0222] = 0.00569t0.0001 M.

110

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111

N 010 , T1010 ,
a 4 4

in Table 23. The value calculated for the formation

and 0222 in AN resulted in the data given

constant of the T1+.0222 complex (logK =11.4iO.2)

Tl+C222
is nearly equal to that of Cox, t 1. for the K+.0222

complex (logKK+C222 =11.3i0.1), which almost certainly
reflects that K+ and Tl+ are approximately the same size
and, therefore, fit the 0222 cavity nearly equivalently.
Attempts to use both sodium-23 and thallium-205 to
measure the formation constant of the Ba2+.0222 complex
in AN failed due to the absence of a resonance band for
the complexed probe cation in the 1:1:1 solution. These
results indicate that 0222 complexes the barium ion so
strongly that insufficient amounts of the ligand are left
to complex the probe cation. Because it is known (121)
that the resonance of the Tl+.0222 complex is less than
twice as broad as the resonance of the free Tl+ in AN, it
is possible to use the observed signal-to-noise for the
free Tl+ band (S/N2128) and the certitude that the
signal-to-noise of the 'non-observed' complex band must
be less than 1, to calculate a lower limit for the
Baa+.0222 complex formation constant: 108KBa2+0222 >15.0.
The lower limit calculated for the formation
constant of the barium complex is only 3.5 log units
greater than that of the thallium complex used to

determine it, which indicates a problem with the slow

exchange competitive method. In the slow exchange case

112

 

 

Table 23: Corrected parameters for the slow exchange
sodium— 23 spectrum for a nearly 1: 1: 1 solution
of NaClQha, TlClOQIK and 0222C in acetonitrile.

Species Position Linewidth Intensity Area

(Ppm) (H2) (H2)

Na+ -7.5910.09 15.310.2 317001400 9960011300

Na+.0222 -10.9110.09 7313 38001600 1190011900

 

a. [NaClOLJ = 0.0107310. 0002

b.
c.

[T1010]
[0222]

‘9 0. 01059+0. 0002 M.

M.
= 0. 01076+O. 0002 E

113

the known and unknown formation constants must be within
3 or 4 orders of magnitude, which is more restrictive

than the 4 or 5 orders of magnitude difference available

in fast exchange case. Still, the use of the slow
exchange competitive NMR method may allow for the
determination of some cryptate complex formation

constants which would not otherwise be measurable.

F. CONCLUSIONS

 

The competitive NMR method can be applied to any
solvent system, within the constraints of solubility.
The method is applicable to the measurement of formation
constants for nuclei which are not well suited to direct
observation by NMR, and can even be used to study
paramagnetic cations. The method can be used to
determine formation constants which are larger than
105 M01, and very large formation constants can be
determined by the repeated application of the method.
The method is not adversly affected by the formation of
species other than the 1:1 complexes, provided that the
additional equilibrium constants are known, and ‘it may
give information concerning these additional equilibria.
It is not necessary to perform a separate experiment to
obtain a known formation constant, if the value could be
determined in a conventional NMR experiment. Finally,
the method can be applied to slow exchange systems, such

as metal ion.cryptand complexes.

114

The need to dissolve the ligand of interest with two
cations and a common anion in a given solvent places
restrictions on the systems which may be investigated.
To determine the desired formation constant there must be
a known or a determinable formation constant within 4 or
5 orders of magnitude (except for the slow exchange
method, where the more stringent requirement of only 3 or
4 orders of magnitude difference applies), and one of the
cations must be amenable to the NMR technique. Because
the uncertainty of the determined formation constant will
be greater (on a precentage basis) than that of the known
formation constant, repeated application of the method

will eventually result in very large uncertainites.

CHAPTER 11

STUDIES 93 THE
COMPLEXATION,Q§
18-CROWN-6 AND DIAzo-la-CRowu-o

A. INTRODUCTION

In order to evaluate the relative importance of the
various factors involved in the formation of crown
complexes it is necessary to measure the formation
constants for many analogous systems. These systems may
differ in any of several factors: the number or type of
donor groups in the crown; the flexibility or size of the
ligand; the solvating ability of the solvent; the size,
charge, or 'hard/soft' nature of the cation; or the
anion. The anion, while known to influence the exchange
kinetics of the complex (109), should not actually
influence the value of the thermodynamic constant for
complex formation. In fact the measured formation
constant is usually a concentration constant, which will
be affected due to the effect the anion has on the
activity coefficients and due the ion pair formation,
which will probably be different for the free and
complexed cation.

In this chapter complexation studies on several sets
of analogous systems will be reported. These systems
will differ in the solvent used, the cation, and the
types of donor groups on the crown ligand. The results
will be interpreted based upon the influence of each of

these factors.

116

117

B. 18-CROWN-6 COMPLEXATION 1__2_£

In order to investigate several cations, it is
necessary to have a solvent with relatively good
solvating properties so that a wide variety of cations
will be soluble. Moreover, the use of a solvent with
good solvating characteristics, such as the dielectric
constant and donor ability, helps to minimize any ion
pairing which would complicate the equilibria,
particularly for di- and tri-valent cations. To further
minimize ion pairing the anion is chosen to have a small
charge density (i.e. a large singly-charged anion such as
Pth', 010; , or NO; ).

The solvent DMF has relatively good solvating power
(Gutmann donor number =26.6 (122), dielectric
constant=36.71 (123), and dipole moment=3.86 D (123)).
Hence, a series of studies of the complexation of 1806 in
DMF were performed using the competitive technique and
the previously-determined value for the formation
constant of the Na+.1806 complex in DMF (K=125120'M-l).

The data obtained from sodium-23 chemical shift
measurements for competitive studies of the complexation
of 1806 with RbPhqB and with magnesium, calcium.
strontium, barium, lead (II), and lanthanum (III)
nitrates are given in Table 24. These solutions were

prepared using method 2. For each case the sodium salt

used was of the same anion as the salt of the cation of

118

Table 24: Sodium-23 chemical shifts as a function of
18-0rown-6 concentration for
N,N-dimethylformamide solutions containing
sodium ion in competition with another cation.

 

 

Concentration Chemical Concentration Chemical
of 18-Crown66C Shift of 18-Crogna6e Shift
(11) a’ ' (ppm) (fl) ’ ’ (ppm)

0.0 -5.06 10.09 0.0 —4.3210.08
0.0049 -5.23 10.13 0.0047 -6.2810.17
0.0079 -5.66 10.16 0.0076 -7.9 10.2
0.0089 -5.93 10.18 0.0086 -8.0 10.2
0.0099 -6.29 10.18 0.0095 —8.5 10.2
0.0109 -6.5 10.2 0.0105 -8.8 10.3
0.0119 -7.0 10.2 0.0115 -9.0 10.3
0.0149 -8.4 10.3 0.0143 -10.4 10.3
0.0199 -10.1 10.4 0.0172 -11.3 10.5
0.0299 -12.1 10.5 0.0191 -12.3 10.5
0.059 -l3.5 10.6 0.0287 —13.5 10.5
0.099 -13.8 +0.7

 

a. uncertainty is 2%.

b. [NaPm+B] = 0.0101 10.0002
c. [Rme+B] = 0.0099 10.0002
d. [NaNO = 0.0099 10.0002 M.
e. [Mg(N 3)2] = 0.0094 10.002

M.
M.

M.

Table 24: continued.

119

 

 

Concentration Chemical Concentration Chemical
of 18-Crown-6 Shift of 18— --Crow:h-’l Shift
(fl)aaf:8 (ppm) (M)a (ppm)

0.0 -4.5410.10 0.0 -4.5810.10
0.00401 -6.5210.16 0.00400 -5.2010.12
0.0080 -8.2 10.2 0.0080 -5.9010.13
0.0090 -8.7 10.2 0.0100 -6.3610.16
0.0100 -9.1 10.2 0.0120 -7.1010.19
0.0110 -9.2 10.2 0.0200 -9.7 10.3
0.0120 -9.7 10.2 0.0250 -10.6 10.3
0.0201 -11.2 10.3 0.0376 -12.0 10.3
0.0301 -12.1 10.3 0.094 -13.1 10.4
0.078 -13.1 10.4
0.095 -13.5 +0.4

 

uncertainty is 2%.

[NaNO .0100 +0. 0002 M.
‘[Ca(N8] )2 10 . 0. 0101 +0. 0002 Mo
[NaNO = 0. 0099 +0. 0002 M.
[Sr(N83) 2] = 0. 0099 +0. 0002 M.

120

Table 24: continued.

 

 

Concentration Chemical Concentration Chemical
of 18-Crown-6 Shift of 18-Crown-6 Shift
(mamfl: (ppm) (whim (ppm)
0.0 -4.4810.09 0.0 -4.6210.07
0.00398 -4.6010.10 0.0071 -5.0610.10
0.0079 -4.7810.11 0.0092 -5.4410.13
0.0099 -5.1610.13 0.0102 —5.8510.13
0.0119 -5.7410.14 0.0113 -6.0310.16
0.0199 -8.9 10.3 0.0123 -6.3 10.2
0.0248 -10.4 10.3 0.0174 -8.4 10.2
0.0393 -12.6 10.4 0.0205 -9.2 10.3
0.082 -13.6 10.5 0.0308 -11.5 10.3
0.051 -12.3 10.4

 

a. uncertainty is 2%.
j. [NaNOa] .0102 10. 0002 M.

k. [Ba(N0 )2 ]O = 0. 0099 10. 0002 M.
l. [NaNOB T: 0. 0099 10. 0002 M.
m. [Pb(N0 3)2] = 0. 0100 10. 0002 M.

121

Table 24: continued.

 

 

Concentration Chemical
of 18-Crown-6 Shift
(fl)a,n,o (ppm)

0.0 -4.5610.09
0.00392 -6.7210.18
0.0078 -8.5 10.2
0.0098 —8.9 10.2
0.0117 -9.4 10.3
0.0196 -10.6 10.3
0.0245 -11.6 10.4
0.0387 -13.2 10.5
0.102 -14.0 10.5

 

a. uncertainty is 2%.
n. [NaN08]= .0098 10. 0002 M.
o. [La(N 5);]0 = 0. 0100 10. 0002 M.

122

interest. Each system was fitted using the
previously-determined formation constant for the sodium
complex as known and the formation constant for a 1:1
complex of the cation of interest as unknown. The
results of these fits are given in Table 25. The

experimental points and the calculated curves for the

Rb+, Mg2+, 032+, and La3+ systems are given in

Figures 24-27, respectively, while those for the Sr2+,

2+

Ba2+, and Pb systems are plotted in Figure 28 along

with the experimental points and calculated curve for the
conventional sodium-23 study of Na+ complexation (Table
6). The similarity of Figure 28 for these data and
Figure 4 for the model calculations is obvious, although
the value of the formation constant of the observation

complex is 125 M.1 for these data, while for the model

calculations it was 1000 M-l.

The values of the formation constants in Table 25,
along with those previously determined by Mei,

1. (32c) for Cs+ (logK=3.95iO.14), by Shih (118) for

EE
K+ (1°8K=2.7010.04), by Rounaghi and Popov (84) for Tl+
(108K33-35i0-06). and in this work for N12+

(logK=l.85¢0.26), result in the selectivity series

Ca2+,L33+<N12 2+ 2 2+

+<mkog <x+<sr +<Tl+(?Rb+)<(?Rb+)Pb2+<Cs+<Ba

L33+

Neglecting, for the moment, 032+, , and N12+, the

123

moo: omao .o

.ummmm commmfi mm coHumo comum>momno mzz .m

 

 

m~.:v oumm.+mom o.mo.oHom.N oum:.+oz moz\+mom\+oz
mm.ommko.omvoo.m comm.+mom Ammo.omom.m ouw:u.oz mOZ\+mom\+oz
om.ommmm.ouvmw.e comm.+mom Ammo.oH0m.~ oumm.+oz moz\+mom\+oz
O 'I O I. O O O I O m
o: o+Aom o+voo m comm +mom o.mo 0+0: N comm.+oz Ioz\+mtm>.oz
m.mv oum:.+moo o.mo.omom.m oom:.+oz M©z\+mou\+oz
m:.ommwo.oavmm.m oum:.+mw: Ammo.omom.m ouwm.+oz .mo2\+mw:\+oz
mm.oflmom.omvkm.m oom:.+om o.ko.oflom.~ oum:.+oz Im::m\+om\+oz
xon woumaaoamo onquo sownsum xon :3ocx xofiqeoo onomm soumxm

 

.mwwEmEmomecumEvaz.z cm moonaeou cow~.:om Hmuwe meow mew mucmumcoo cowumEmom "mm oHnt

 

124

 

Figure 24:

J J 1 l 1

i 2 3 4 5 o 7

MOLE RATIO [18061/[Na+]

Experimental and calculated sodium-23 chemical
shifts as a function of 1806/Na+ mole ratio
for solutions containing NaPn+B, .RbPhMB, and
1806 in N,N-dimethylformamide.

125

 

23“,

CH! MICAL
SH} I

 

 

 

 

not: nno ӣ3-
No

Figure 25: Experimental and calculated sodium-23 chemical
- shifts as a function of 18C6/Na+ mole ratio
for solutions containing NaNOB, Mg(N03)2, and

1806 in N,N-dimethylformamide.

126

 

 

 

 

4 1 1 1 14 L 1 1 1

0 1 2 1 4 5 ‘BC 7 I 3 10
I
Mmmlxwojgg

 

Figure 26: Experimental and calculated sodium-23 chemical
shifts as.a function of 18C6/Na+ mole ratio
for solutions containing NaNO}, Ca(N03)2, and
1806 in N,N-dimethylformamide.

127

 

 

 

 

 

 

"5 I I I l t I r u y y
'11-
'11»-
IJN. -w-
CNEMICAI.
SKI"
In ”a
o, q
-. . '1
-7 d
-‘ '
as -I
-‘ 1 1 1 1 J 4 1 I - I I ‘
0 l 2 J A 5 6 7 I 9 10 ll
MOLE RATIO "a—Cé
No.

Experimental and calculated sodium-23 chemical
shifts as a function of 1806/Na+ mole ratio
for solutions containing NaNO}, La(N03)2, and
1806 in N,N-dimethylformamide.

Figure 27:

323Na
(ppm)

128

 

 

 

 

 

 

 

 

Figure 28:

 

o I 2 3 4 3 6 7 s 9 l0
MOLE RATIO
[IBC6]
[NM]

Experimental and calculated sodium-23 chemical
shifts as a function of 1806/Na+ mole ratio
for solutions containing NaNO} and 1806 in

N,N-dimethylformamide (CI) and solutions
containing NaN% M(NOE)n and 18 6 in
ere M=Sr +(Ill).

N, dimethylformam de
g“ (A), and Baél'e (o).

129

order indicates that, for a given charge, as the size of

the cation increases (see Table 26), the formation
constant increases. This increase in the formation
constant probably reflects the decreasing solvation

strength, and apparently overwhelms the effect due to the
'fit' of the cation into the cavity of the 1806 molecule.
Similarly, for a given size cation, as the charge
increases, the formation constant increases. This
increase is almost certainly due to the increase in the
ion-dipole interactions. It should be noted that an
increase in charge by a factor of 2 should not double
logK. Although AHO may be doubled (because the
interactions of the cation with the ligand and with the
solvent are both twice as strong), ASO will not
necessarily be doubled. For example, if cations of the
same size are solvated equally the the desolvation would
release the same number of solvent molecules, resulting
in equivalent translational entropies. Hence AGO is not
doubled and, consequently, neither is logK. Comparison
of the formation constants for K*' and Ba2+
(1ogK=2.70i0.04 and logK=4.21i0.19, respectively) shows
an increase by a factor of about 1.6, which agrees with
the above reasoning.

The formation constant for the L33+.18C6 complex is

quite small. This may be due to strong ion pairing with

the nitrate ion, which, while not precluding the forma-

130

 

 

Table 26: Sizes of some cations.a’b
Ion Radius Ion Radius
(R) (R)
Li+ 0'6 M22+ 0.65
Na+ 0 95 Ca2+ 0.99
K+ 1.33 sr2+ 1.13
Rb+ 1 48 Ba2+ 1 35
cs+ 1 69 Ni2+ 0.69
T1+ 1 5 Pb2+ 1.3
La3+ 1 2

 

a. for comparison Pedersen gives as the radius for 1806,
and its analogues, 1.3-l.6 R.
b. taken from refernces (80,125,127).

131

tion of the complex, could reduce the relative amount of
complex formed, possibly so much that it is impossible to
obtain a measurable formation constant without prior
knowledge of the extent of ion pairing. The small value
may also be due to very strong solvation between the

.2+

trivalent cation and the solvent. The low value for Ni

2+

is easily explained in terms of the geometry Ni prefers
for its complexes, which is octahedral. The ligand 1806
has its 6 oxygen donor atoms in a basically planar
arrangement, and is, therefore, poorly suited to this
type of geometry. The apparently low formation constant
for the Ca2+ complex is quite interesting, but currently
unexplainable. It is of further interest to point out

2+
that this behavior for Ca has been observed previously

in water (49) and 70/30 methanol/water mixtures (50).

C. COMPLEXATION QM 1806 AND DA1806 1M

ACETONE, ACETONITRILE, AND PROPYLENE CARBONATE

1. General
Since the complexation of 1806 in DMF, a strongly
solvating solvent, seems to be dominated by the solvation
of the cation, it was of interest to perform a series of
studies with some solvents of intermediate solvating
ability. The solvents AN, PC, and AC which are of
intermediate solvating ability were chosen. Their

properties are collected in Table 27. To ensure that ion

132

Table 27: Properties of solvents used in complexation

 

 

 

studies.

Solvent Gutmann Dielectric Dipole
Donor Constant Moment

Number (D)
b b

acetonitrile (AN) 14.1a 37.5 3.44

a C d

propylene carbonate (P0) 15.1 65.0 5.2
a b b

acetone (A0) 17.0 20.7 2.69
a b b

N,N-dimethylformamide (DMF) 26.6 36.71 3.86
a. reference 122. b. reference 123. c. reference 124.

d. reference 113.

133

pairing is minimized only tetraphenylborate and

perchlorate salts were used in these studies.

2. Results for 1806 Complexation
The cesium-133 chemical shift data for a competitive
NMR study of a set of solutions, prepared by method 3,

containing CsPh B, Ba(PhnB)2 and 1806 in AN are given in

4
Table 28. The results of a computer fit of these data to
a model containing an unknown formation constant for a
1:1 Ba2+.1806 complex and the previously reported values
for the formation constants of the 1:1 and 1:2 Cs+.1806
complexes are given in Table 29, and the experimental
data and the calculated curve are shown in Figure 29.

A set of sodium-23 competititve NMR studies were
performed on the systems; NaPhMB, CsPh4B, and 1806 in PC;
NaPhAB, KPth, and 1806 in PC; NaPhqB, RbPhAB, and 1806
in PC; NaPhuB, KPth, and 1806 in AC; NaPhMB, RbPhMB, and
1806 in AC; and NaClO4, TlClO#, and 1806 in AN. Each of
these systems was prepared using method 3, and the
experimental data are given in Table 30. The data for
the NaPhuB, CsPhAB, and 1806 in PC system were fitted to
a model using an unknown formation constant for the
Na+.18C6 complex and the previously reported values for
the formation constants of the 1:1 and 1:2 Cs+.1806
complexes. The results of this fit are given in

Table 29, and the experimental points and calculated

curve are plotted in Figure 30. The calculated value for

Table 28:

Cesium-133 chemical shifts as a

134

function of

 

 

18-Crown-6 concentration for solutions
containing cesium tetraphenylboratea, barium
tetraphenylborateb, and 18-crown-6 in
acetonitrile.
ConcentrationC Chemicald Concentrationc Chemical
of 18-Crown-6 Shift of 18—Crown-6 Shift
(fl) (ppm) (11) (ppm)
0.0 21.84 0.0095 16.65
0.00250 21.87 0.0097 16.40
0.00401 21.87 0.0100 15.97
0.0047 21.86 0.0102 15.85
0.0049 21.83 0.0105 15.75
0.0050 21.82 0.0110 15.60
0.0050 21.81 0.0125 15.05
0.0052 21.59 0.0150 14.48
0.0055 21.36 0.0225 12.67
0.0070 19.69 0.050 6.57
0.0090 16.99

 

a.

[CsPhMB] = 0.00499 10.0001 M.

b. [Ba(PhMB)2] = 0.00500 10.0001 M.
c. uncertainty is 2%.

d.

uncertainty is 0.04 ppm.

135

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136

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b

 

 

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137

 

 

 

Table 30: Sodium-23 chemical shifts as a function of
18-Crown-6 concentration for solutions
containing sodium ion in competition with
another cation in variuos solvents.

Concentration Chemical Concentration Chemical

of 18-Crown-6 Shift of 18-errqr61 Shift

(5)5111)“: (ppm) (fl) ’ ’ (ppm)

0.0 -903 i002 0.0 -904 i002
0.00400 -11.1 10.3 0.00300 —9.7 10.2
0.0080 -13.2 10.3 0.0060 -10.1 10.2
0.0090 -13.2 10.3 0.0080 -10.6 0.3
0.0095 -13.3 10.3 0.0090 —lO.7 10.3
0.0100 -14.0 10.3 0.0095 -10.9 10.4
0.0105 -13.9 10.3 0.0100 -10.9 10.3
0.0110 ~14.0 10.3 0.0105 -ll.2 10.3
0.0120 -14.4 10.3 0.0110 -11.4 10.3
0.0150 -14.8 10.3 0.0120 -11.7 10.3
0.0175 -15.5 10.3 0.0140 -12.6 10.4
0.0250 -15.7 10.2 0.0200 —15.7 10.3
0.0450 -15.8 10.3 0.0250 -15.8 10.2

0.0400 -15.7 10.3

a. uncertainty is 2%.

b. [NaPh B] a 0.0099 10.0002 in PC.

c. [CsPhEB] a 0.0099 10.0002 in PC.

d. [KPh ] = 0.0100 10.0002 M in PC.

1.,

138

Table 30: continued.

 

 

 

Concentration Chemical Concentration Chemical
of 18-Crown-6 Shift of 18-Crown- Shift
(11) a.e.f (ppm) (11) a’g’ (ppm)

0.0 -9.3 10.2 0.0 —8.17 10.07
0.00201 —9.9 10.2 0.00300 -8.26 10.07
0.00301 -10.6 10.2 0.0060 -8.49 10.08
0.0050 -11.3 10.3 0.0080 -8.89 10.09
0.0056 -ll.3 10.3 0.0090 -9.21 10.11
0.0062 -11.6 10.3 0.0095 -9.36 10.11
0.0068 -12.1 10.3 0.0100 —9.40 10.10
0.0075 -12.2 10.3 0.0105 -9.59 10.10
0.0080 -12.5 10.3 0.0110 -9.79 10.10
0.0090 -l2.9 10.3 0.0120 -10.50 10.14
0.0 100 -13.1 10.3 0.0150 -12.35 10.13
0.0 110 -13.6 10.3 0.0175 -14.15 10.13
0.0 120 -14.0 10.3 0.0200 -15.74 10.11
0.0150 —15.2 10.2 0.0250 -16.22 10.12
0.0163 -15.6 10.2 0.0400 -16.23 10.10
0.0201 -15.9 10.2
0.0402 —15.9 10.2

a. uncertainty is 2%.

e. [NaPh#B] = 0.0100 10.0002 M in PC.

8: 18888481 : 8888888881812 I.28:

h. [KPh 11] = 0.0100 10.0002 M_in AC.

1+

139

Table 30: continued.

 

 

 

Concentration Chemical Concentration Chemical
of 18-Crown76. Shift of 18—Crown—6 Shift
(1) 9:193 (ppm) (maflml (ppm) 9
0.0 -8.3310.07 0.0 -7.59
0.00300 -8.6710.07 0.00299 -7.65
0.0060 -9.3710.08 0.0059 —7.81
0.0080 -10.0610.11 0.0079 -8.06
0.0095 -10.5410.11 0.0094 -8.50
0.0100 —10.7410.12 0.0099 -8.48
0.0105 -10.9310.12 0.0101 -8.70
0.0120 -11.6510.11 0.0104 -8.69
0.0140 -12.5210.11 0.0119 -9.42
0.0170 —14.1710.11 0.0139 —10.52
0.0200 —15.7510.10 0.0169 -12.41
0.0300 —16.1010.10 0.0199 -14.47
0.050 -16.2210.10 0.0299 -14.96
0.049 -l4.98

a. uncertainty is 2%.

i. [NaPh B] a 0.0100 10.0002 M’in AC.

j. [RbPh ] a 0.0099 10.0001 M in AC.

k. [NaClO ] a 0.0099 10.0002 M in AN.

1. [TlClOM] = 0.0099 10.0002 M in AN.

m.

uncertainty is 0.07 ppm.

140

5
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141

the formation constant of the Na+.1806 complex was then
used as the known and the other PC systems were fitted to
models using 1:1 complexes for both metal ions (Na+ and

+, Rb+, or Tl+). The previously-reported values for the

K
formation constant of the Na+.1806 complex in AC and AN
(logK=4.57i0.06 and logK=4.2110.10, respectively) were
then used as known in precisely similar fits for the AC
and AN systems. All of the results are given in
Table 29. The experimental data and calculated curves
are plotted in Figure 31 for the system NaClOM, T10104,
and 1806 in AN, and. for the PC and A0 systems in

Figures 32 and 33, respectively.

3. Results for DA18C6 Complexation
The data for a series of cesium-133 competitive NMR

studies for the systems; CsPhAB, KPhuB, and DA1806 in PC,

4
B, and DA18C6 in PC and A0; and CsPhuB,

AC, and AN; CsPh B, NaPth, and DA18C6 in PC and AC;
CsPhuB, RbPhh
Ba(PhuB)2, and DA1806 in PC, AC, and AN, are given in
Table 31. These solutions were prepared using method 3.

The systems CsPhuB, NaPh B, and DA1806 in PC and AC were

4
fitted to models containing unknown formation constants
for 1:1 complexes for both cations. The results of these
fits are given in Table 32. The remaining cesium-133
systems were fitted to models containing 1:1 complexes

for both cations, with the previously-determined forma—

tion constant of the 03+.18C6 complex as the known, and

142

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145

Table 31: Cesium-133 chemical shifts as a function of
diazo-18-crown-6 concentration for solutions
containing cesium ion in competition with
another cation in various solvents.

 

 

 

Concentration of Chemical Concentration of Chemical
Diazo-18—Crown—6 Shift Diazo-18-Crown- Shift
(11) a,c,d (ppm) b (11) a,e, (ppm) b

0.0 -37.03 0.0 -38.73
0.00300 -36.85 0.00299 -38.29
0.0060 -36.54 0.0060 -37.18
0.0080 -35.89 0.0080 -35.55
0.0090 —35.21 0.0089 -34.04
0.0095 -34.49 0.0094 -32.93
0.0098 -34.25 0.0097 -32.55
0.0100 -33.58 0.0099 -31.78
0.0102 -33.59 0.0101 -32.14
0.0105 -33.23 0.0104 —31.68
0.0110 -32.24 0.0109 -30.49
0.0120 —30.12 0.0119 -27.73
0.0140 —24.92 0.0139 -22.67
0.0170 -16.50 0.0169 -l4.07
0.0200 -9.37 0.0199 —5.52
0.0300 5.51 0.0299 10.81
0.050 19.73 0.050 24.03

a. uncertainty is 2%. b. uncertainty is 0.04 ppm.

c. [CsPh B] . 0. 0099 +0. 0002 M in PC.
d. [KPh 8] a 0. 0099 +0. 0002 M in PC.
e. [0328 B] a 0. 01007 +0. 00027 M in AC.
f. [Kphufi] = 0. 0100 10. 0002 M7 in AC.

146

Table 31: continued.

 

 

Concentration of Chemical Concentration of Chemical
Diazo-18-Crown-6 Shift Diazo—18—Crown—6 Shift
(11) a,g,h (ppm) b (1)5111” (ppm) b

0.0 18.44 0.0 —37.19
0.00299 18.60 0.00300 -37.13
0.0060 18.91 0.0060 -36.91
0.0080 19.64 0.0080 -36.59
0.0089 21.46 0.0090 -36.13
0.0094 20.99 0.0095 —35.82
0.0099 21.74 0.0100 -35.15
0.0109 22.56 0.0105 -34.02
0.0119 24.62 0.0110 -32.92
0.0139 28.10 0.0120 -29.61
0.0169 33.37 0.0140 —24.41
0.0199 36.98 0.0160 -l8.45
0.0299 45.48 0.0180 -13.50
0.050 50.81 0.0200 -8.38
0.0220 -5.42

0.0250 -0.49

0.050 19.87

 

a. uncertainty is 2%. b. uncertainty is 0.04 ppm.
g. [CSPWBB] = 0.0100 10.0002 M in AN.
h. [KP ] = 0.0094 10.0002 M in AN.

1. [CsP 43] = 0.0100 10.0002 M in PC.
j. [NaPth] = 0.0099 10.0002 M in RC.

147

Table 31: continued.

 

 

Concentration of Chemical Concentration of Chemical
Diazo-18-Crown-6 Shift Diazo-18-Crown—6 Shift
(menial (ppm) (1)“,n (ppm) ‘0
0.0 -39.09 0.0 —37.14
0.00399 -38.17 0.00299 -35.37
0.0080 —34.96 0.0059 -32.58
0.0094 -32.24 0.0079 -30.20
0.0104 -29.76 0.0089 -28.28
0.0119 —25.77 0.0094 -27.20
0.0159 -14.40 0.0099 -26.52
0.0199 -6.07 0.0104 -25.48
0.0299 10.15 0.0109 -24.88
0.0399 18.26 0.0119 -22.36
0.050 22.72 0.0139 -l8.16
0.0169 -11.91
0.0199 -6.43
0.0299 7.11
0.049 19.74

 

uncertainty is 2%.
[CSPth]
[NaPth]
[CSPhQB]
[RbPhMB]

in A0.
in A0.
in PC.
in PC.

b. uncertainty is 0.04 ppm.
0.0100 10.0002 M
0.0100 10.0002 M
0.0100 10.0002 M
0.0100 10.0002 M

148

Table 31: continued.

 

 

Concentration of Chemical Concentration of Chemical
Diazo-18-Crown-6 Shift Diazo-18-Crown-6 Shift

(11) 31°:P (ppm)b (fl) a’q’r (ppm) b
0.0 -40.01 0.0 -37.88
0.00301 -37.75 0.00299 -37.91
0.0060 -33.22 0.0059 -37.88
0.0080 -29.57 0.0084 -37.86
0.0095 —25.80 0.0094 -37.85
0.0100 -25.37 0.0099 -37.82
0.0105 -24.19 0.0099 —37.82
0.0120 -20.63 0.0100 -37.78
0.0140 -l7.03 0.0104 -36.92
0.0170 -9.80 0.0114 —33.69
0.0200 -3.62 0.0139 -24.97
0.0301 11.08 0.0169 -16.44
0.050 23.76 0.0199 -9.01
0.0299 6.99
0.049 19.49

 

uncertainty is 2%. b. uncertainty is 0.04 ppm.
o. [CsPth] = 0.0100 10.0002 M in AC.

p. [RbPh B] . 0.0100 10.0002 M in AC.

q. [csphflB] = 0.0099 10.0002 M in RC.

r. [Ba(ph4B)2] = 0.0100 10.0002 M in PC.

149

Table 31: continued.

 

 

Concentration of Chemical Concentration of Chemical
Diazo-lB-Crown—6 Shift Diazo-lB-Crown-6 Shift
(M)a,s,t (ppm)b (fl) a,u,v (ppm)b
0.0 -42.31 0.0 21.03
0.00299 -42.14 0.0049 21.85
0.0060 -42.06 .0050 21.88
0.0084 -41.91 .0051 22.15
0.0098 —41.84 .0099 38.82
0.0100 -41.72 .050 51.82
0.0102 -40.37
0.0114 -34.84
0.0139 -24.86
0.0169 -13.68
0.0199 -4.90
0.0299 10.23
0.050 22.31

 

uncertainty is 2%.

b.

uncertainty is 0.04 ppm.

s. [CsPh B] = 0.0100 10.0002 M in AC.
t. [Ba(thp)2] = 0.0100 10.0002 M in AC.
u. [CsP B] = 0.0050 10.0002 M in AN.
v. [Ba(P 1+ma] = 0.0050 10.0002 M in AN.

150

 

cc.cHAmc.chmo.N

mc.cHAac.chcc.m

sc.cHAmc.chmm.o

oc.cm:mc.cmccc.m

sc.cH:mc.cham.o

cc.cmak.m
mc.cmmc.m
mc.cHNc.s

cac.cmmsc.a

occaac.+om

ccmaac.+om

ccwa<c.+a

ccwaac.+a

occaac.+a

ccwa<c.+mz

occaac.+mc

ccca<c.+oz

ccwaac.+mc

mc.chc.N
cac.choc.a
oocc.cHomN.N
mc.chc.N

cac.cmmoo.a

oowfi<m.+mo

ouwfi<m.+mo

oomfi<n.+mo

©0®~<Q .+ m0

cowa<a.+mo

ca\ocma<c\-mmam\+oa\+oc

cm\ccwa<c\-aoco\+cm\+mc
o

z<\ccca<c\1m am\+a\+mc

c<\ccca<c\1msam\+a\+mc

cm\ccma<c\1maam\+a\+oc

c<\ccma<c\umoam\+m2\+mc

co\ccca<c\-acaa\+mz\+oc

 

xon cmumfiscfimu

meQEOU cmmcsum

mon czocx

xmaaeoo mpomm

memumxm

 

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we mmmcsum m>mumumqeou mow mufismmm "mm mHan

151

.mm mocommwom

.>oaom cam unnamemcm an coupoamm coon mm: mAxon mo o=Hm> m .c

.mm oocommwom .o .xmo: mmzu .n .ummmw coumwa mm cowumo coaum>momno mZZ .m

 

NA

NA

NA

oomH<Q.+HH
ouw~<a.+ah

oowH<Q.+Nmm

occaac.+ mm

m

occaac.+mom

oao.cHom.o
occ.c+ma.m
accc.cHomN.N

mc.cmkc.m

cac.choo.a

1a
cccaac.+aa z<\ccca<c\ Icac\wam\+aa

cocaac.+aa c<\ccma<c\ Mcac\+am\+aa
. a
cccaac +mc z<\ccca<c\1m ao\+mom\+mc

ccca<c.+mc c<\ccca<c\Imaam\+mom\+mc

ouw~<o.+mo om\oowa<n\lm:cm\+mmm\+mo

 

xon cummasuflmo

xmaqaou vmwcsum

xon czocx

xmfiaeoo mnomm Emumxm
m

 

.coscmucou

mm man

152

the value of the formation constant for the other cations
as unknowns. These results are also given in Table 32.
The experimental data and the calculated curves for the
AN, PC, and AC systems are shown in Figures 34-36,
respectively.

Two competitive lithium-7 studies for the systems
LiClO , TlClO , and DA18C6 in AN and AC have been
performed on solutions prepared using method 3. These
data, given in Table 33, were fitted to models containing
1:1 complexes for both cations with the formation
constant of the Tl+.DA18C6 complexes as unknown and the
values of Shamsipur and Popov (38) for the Li+.DA1806
complexes as known (logKAN=4.39i0.41 and
logKAC=2.l3iO.08). The results of these fits are given
in Table 32, and the experimental data and the calculated
curves are shown in Figures 37 and 38, respectively, for

the AN and AC systems.

4. Discussion
The formation constants for the 1806 and DA1806
complexation in AN, PC, and A0 with Na*, K+, Rb+, 03+,
T1+, and Ba2+ obtained in this work and those results
obtained previously by other workers for these systems,
and for the complexation of Li+, are complied in
Tables 34 and 35. The current results for these systems

are much more complete (and reliable) than previously

possible, due to the use of the competitive NMR method.

153

:H oum~<a cam .m

N

a :

cm: .m

‘

.Aouv

n

N

am can A0 V... M u : mums: .oamuumcououm

mom omuam macs +mu\oow~<n
mo coauocaw m on mummsm Hmoaaocu mmHIsammoo commasonmo can Hmucoaauoqu "an whammm

ammo mcmcmmwmro macauaaom

a+mca\acccaaa_ caeam mac:

N

d

d

on

O?

oocnna

on

 

 

ON

154

.A‘V + mm cam .on + m .AQV ...: .AOV +mz .... z mums: .oumconmmo 23130.3
cm ouw~< c:m..m¢nmz .m ammo wcmcHMucoo mcomuzaom mow omumm macs +mo\oowa<n
mo coauocsu m mm muwmnm Hmomsmnu mmHIsammoo commaaoamo cam Hmucoammoaxm ”mm omammm

a+mca\acccaaaa camam mac:
n o n m _ o

q d d

d
d

 

 

 

155

A<c +mom cam A07. 2 Adv +0. .Aoc to: u : moon: .233.
pa occa<c coo .msam: .msamoc moaoaooooo mooaooaoo tom oaooo oaos +oc\ccwa<c
mo acmuucsw m mm muwwzm Hmomeocu mmfiIazmmoo commaaoamo cam Hmu:OEHmqum "om omawmm

a+oca\accca<cc camam mac:

 

 

.. a a A _
I.I/.. . ON
10—
.c
”a. moomna

OT

OMI

 

 

Table 33:

156

Lithium-7 chemical shifts as a function of

diazo-18-crown-6 concentration for solutions

containing

perchlorate,

acetone .

lithium perchlorate, thallium
and DA1806 in acetonitrile and

 

 

 

Concentration of Chemical Concentration of Chemical
Diazo-18-Cr%w%-6 Shiftd Diazo-18-Crown—6 Shift
(M) ’ (ppm) (MW:c (ppm)
0.0 -2.87 0.0 2.03
0.00400 —2.89 0.00303 2.05
0.0080 -2.87 0.0098 2.03
0.0095 -2.83 0.0100 1.97
0.0100 -2.82 0.0102 1.97
0.0105 -2.64 0.050 0.85
0.0120 -2.34
0.0150 -1.60
0.0180 -1.06
0.0195 -0.69
0.0200 -0.57
0.0205 -0.55
0.0220 -0.43
0.0300 -0.37
0.050 —0.40
a. [LiClQu] = 0.0101 10.0002 M in AN.
[TlClQh] = 0.0099 10.0002 M in AN.
b. [LiClQM] = 0.0100 10.0002 M in AC.
[TlClQu] = 0.0100 10.0002 M in AC.
c. uncertainty is 2%. d. uncertainty is 0.03 ppm.

157

¢ 3 .oammmm:Ouoom cm
833 cam . cacaa. . cacaa mcaoaoocoo maoaooaom tom oaomo oaoe +aa\ccca<c

mo coauucam m mm muwmnm Haemeoco Blesmcuma commaauamo cam Hmucosmmoqu .Nm omsmmm

a+aaa\accca<ca camam mac:

 

 

n v n a _ c
d d a d d 0
+1? hon 1
IT
omam
LNI

 

 

I
C)
('0
I

158

oum~<o cam

MO

acmuucsm

. 1a

m

OHUHH
mm

.ocouoom cm

.+€Homa wcmcmmucoo mcowusaom mow cmumm macs +Hq\oowH<o
mummnm Hmomeoco NIE=mcumH cmmmazoamo cam Hmucosmmoaxm "mm omswmm

H+HAH\Hmo®H¢QH 0H9<m mac:

 

 

m #1 n N — o
1—
oaas
L m.—
.. ...N
E a ..

 

159

 

 

 

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mm.cmqm.w cc.cmma.c mc.cmmc.o cc.chN.m mc.cmcc.c cc.cmkm.m omc.cmcm.a ca
ooa.cmsa.o cox
ox IIIIIIIII cc.cmmo.o ca.cmmm.m oa.cmoa.c ma.cmca.m oaa.cmoc.m co
o mA ooA om.c+c.m
ao.cmcc.c oa.cmaw.m ca.cmmc.o IIIIIIIII ca.cmca.m ca.cmam.q ooc.cmsm.m z:
+Nom +am +mc +am +m +oz +aa poo>aom
.Aomv wmmcocmmo mamaxaomq
cam .Az<v mammuHCOuwum .Ao<v mcoumom cm oIczoCOIwH mow m.xwoq "em mHan

160

.mw mucmmmmmm

.mm wucwhwmmh .m

 

 

omx mac.cmcc.a
AA m.mA mc.cmmc.m cc.cmco.m mc.cmcw.m cc.cmak.m owc.cHMa.N ca
oNc.cmmo.a
AA ---- occ.cmmoo.a mc.cmcc.m cc.cmam.o mc.cmmc.o omm.cmmc.m cm
mmc.cmcm.m
mmA aqc.cmco.m amc.cmkm.m acc.cmmm.o acc.cmcm.o
AA AA occ.cmomm.m 111111111 oc.cmmm.o Nc.cmoo.o oao.cmom.o z:
+Nmm +am +mc +am +m +oz +aa ooo>aom

 

.Aomv camconmmu mamamaoma
cam .Az<v mHHCuHCOumum .AU<V QCOumum CH clc3omuleIONwHU mow m.xwoq "mm manmh

161

The only major point of conflict between the current
results and those obtained previously is for the forma-
tion constant of the NaI.DA18C6 complex in AC.

The previous result, of Shamsipur and Popov (38) is
logK=1.96t0.18, while the current result is
logK=3.71i0.06. The previous result was obtained by a
conventional sodium—23 NMR experiment in which the
chemical shift of the sodium nucleus changed about 1 ppm
and had an uncertainty of nearly 0.3 ppm at high mole
ratios (excess ligand). By contrast, the current value
was determined from. a competitive cesium-133 NMR
experiment in which the chemical shift changed more than
40 ppm and had an uncertainty of only 0.04 ppm. The
tremenous increases in chemical shift range and precision
result in a more reliable result. The plot of the
experimental data for this competitive system, which is
shown in Figure 36, shows that the Na+ ion is complexed
first, clearly indicating that the formation constant for
the Na'fil806 complex must be the larger of the two. It
should also be noted that the result for the formation
constant for the Cs‘hDA18C6 complex determined in this
manner (logK=2.07i0.03) is in rather good agreement with
that of Shamsipur and Popov (logK=1.89i0.01),
particularly considering that the previous study used
CsSCN while the current study used CsPh B. (The use of

L.

the tetraphenylborate ion would reduce the extent of ion

162

pairing and might remove any slight decrease in the
measured formation constant caused by ion pairing of the
thiocyanate ion.)

From the results in Tables 34 and 35, it is possible
to extract the general selectivity series for 1806
complexation as being

Ba2+ > Tl+ > K > Rb > Cs , Na > Li+,

and that for DA18C6 as

332+ (2) Tl+ > K+ , Na+ > Rb+ , L1+ > 03+.

The series for 1806 agrees with the previously-reported
series (49), while that for DA1806 differs in the
relative order of Na+ and Li+ from that reported
previously (38):

T1+ > L1+ > Na+ > 03+.

The previously-reported series was based upon rather few
results, hence the current series is considered more
general and reliable. It must be stressed that none of
these series are universally correct, but rather seem to
reflect general trends.

The selectivity series for 1806 is rather easily

163

explained as being due to an interplay of the strength of
the solvation of the cation, and the strength of the
interaction between the cation and the crown. The
solvation, for a given charge, should be strongest for
the smallest cation and decrease steadily as the size of
the cation inreases. The interaction with the crown
should be, again for a given charge, nearly constant for
those cations small enough to fit into the cavity, and
then should decrease steadily as the cation size
continues to increase past the size of the ligand cavity.
This would suggest that the strongest net interaction
should be for those cations which just fit into the
ligand cavity, and should decrease as the size of the
cation varies in either direction from this best fit.
Indeed, T1+ and K+ (radii=1.5.x and 1.4.1 (125),
respectively) are just the right size to fit into the
cavity of the 1806 molecule (radius=1.3—l.4 K (125)), and
they show the largest interaction (formation constant) of
the +1 cations. Barium is also the right size to fit
into the cavity of the 1806 molecule
(radius=1.36.x (125)) and due to the larger charge all
the interactions are stronger, thus resulting in the
strongest interaction. It is difficult to predict
whether Na+ or Rb+ should be next strongest, based upon
these simplistic arguments.

There have been attempts (125,126) to describe

164

theoretically the interactions which ocurr in these
complexation equilibria, and to use these models to

predict the behavior of the formation constant as the

cation size varies. For example, Lamb _1 £1.(125) have
proposed a six—term expression to calculate AG.
Unfortunately, this expression has three unknown

(adjustable) parameters; thus the equation is useful less
for g priori predictions than for after-the-fact
rationalization. Consequently, no further efforts have
been made to interpret the formation constants for the
1806 complexes as a function of cation size.

The selectivity series for DA1806 given above can be
explained similarly to the series for 1806. The
solvation strength of the cations must, of course, vary
in the same manner as for the 1806 systems, since the
solvation of the cation is independent of the ligand.
The interaction between the DA18C6 and the cation should
be nearly constant for cations able to fit into the
cavity and decrease steadily as the cation size increases
beyond the cavity size. Because 1806 and DA18C6 are both
18-membered rings with 6 donor moieties, it would seem
that the size of the cavities ought to be very nearly the
same. From these arguments there is no apparent reason
that the DA18C6 selectivity series should differ from
that of 1806. However, there are three effects, caused

by the presence of the two -NH- moieties in DA1806 which

165

need to be considered.

The first effect is that the nitrogens of the DA1806
are 'softer' than the 1806 oxygens they replace. This
will tend to cause a stronger interaction for 'softer'
cations, and a weaker interaction for 'harder' cations.
Indeed, the dramatic increase for the complexation of Ag+
in water when the ligand is changed from 1806 to DA1806,
and the equally dramitic decrease for the complexation of
the K+ ion in MeOH for the same ligands, was explained by
Frensdorff (9) by this type of effect. However, this
reasoning does not work in the curret case. The 03* ion,
which is the 'softest' of the alkali metal cations (127),
shows the weakest complexation. Furthermore, the K... ion,
which ought to fit the cavity better than, and be less
solvated than the Na+ ion, is also 'softer'. All of
these considerations suggest that the K+.DA1806 complex
should have a larger formation constant than the
Na+.DA18C6 complex, whereas they are comparable.

The second effect is that the proton of the -NH-
moiety may be inside the cavity, forming an
intramolecular hydrogen bond to one of the -0-
moieties (128), thus effectively blocking the cavity, for
all but possibly the smallest of the cations. This
should reduce the formation constant equally for all of
the cations, with the possible exception of the smallest

ion (Li+). This cannot explain the position of the Li+

166

ion in the selectivity series or the apparent similarity
of the formation constants of the complexes of the Na+
and K+ ions.

Finally, it can be seen from space-filling models
that even when the proton of the -NH- moiety is not
inside the cavity, it will still be partially blocking
the entrance of the cavity, and the face of the ligand.
This effect should reduce the formation constant slightly
for those cations which would otherwise just fit into the
cavity, and should greatly reduce the formation constant
for those cations which are too large to directly enter
the cavity (and would otherwise complex with the face of
the cavity). This third effect seems to explain quite
nicely why the formation constant for the K... ion is not
larger than that for the Na+ ion, and why the formation
constants for the Rb+ and Cs+ ions are much lower than
that for the K+ ion. Interestingly, the T1+ ion seems
not to be affected the way the K+ ion is, possibly due to
the T1+ ion being substanially 'softer' (127), which
would allow it to 'slip' past the —NH- proton (and then
would be more likely to complex strongly, since the
nitrogen of the DA18C6 is also 'softer' than the -0-).

It is also of interest to compare the results, for a
given cation and solvent, between 1806 and DA18C6. For
example, in AN the formation constant of the Li+ ion

increases about 2 orders of magnitude when the ligand is

167

changed from 1806 to DA1806. In light of the previous
discussion there is no reason that the formation constant
should increase; in fact a slight decrease might be
expected (due to the 'hard' Li+ ion "perferring" the
'harder' oxygens of the 1806 rather than the 'softer'
nitrogens of the DA18C6). There is, however, an
explanation for this apparently odd result.

It has been shown (103,129-131) that AN complexes
1806. Indeed, this complexation occurs between the AN
methyl protons and every alternate one of the 6 oxygens
of 1806, on both sides of the 1806 ligand (103), thus
completely blocking the entrance to the cavity. In order
to correct for this effect, it is necessary to divide the
formation constants measured in AN by the fraction of the
1806 which is uncomplexed by the AN. This fraction has
been shown by Mosier-Boss to be 0.02 (103,131). Thus, to
correct the values of logK given in Table 34 for 1806
complexation in AN, it is necessary to add 1.7 log units.
By contrast, the solvation of DA18C6 by AN occurs between
the -NH- protons of the DA1806 and the lone pair on the
nitrogen of the AN. This solvation will only slightly
increase the blocking effect due to the -NH- proton, and
thus no correction need be made to the formation
constants. As a result, for AN solutions, the formation
constants for the Li+ ion complexes of DA18C6 and 1806

are equal (to within the uncertainty of the

168

measurements), and for all other alkali cations the
DA1806 formation constant is lowered Mg that of the 1806,
probably due to a combination of the effects due to the
-NH- proton being inside the cavity (reducing all the
formation constants) and due to the blocking of the
cavity entrance of the -NH- proton outside the cavity
(further reducing the K7 ion formation constant slightly,
and the Cs+ ion formation constant more substantially).
Similar arguments apply to AC solutions.
Mosier-Boss has determined that the fraction of the 1806
which is uncomplexed is not less than 0.37 (i.e., the
values given in Table 34 for 1806 complexation in AC must
have 0.44 added to their values). Also, it would seem
most likely that a hydrogen bond between the -NH- proton
of the DA18C6 and the oxygen of the AC ought to be the
primary interaction, thereby not requiring a correction.
When the correction is applied to 1806 the values for the
Li+ ion complexes become nearly equal in A0, with the
DA18C6 being slightly larger. There is no apparent
raeson for DA1806 to complex the Li+'more strongly than
does 1806. The remaining alkali metal cation complexes,
however, follow the same trend as was seen in AN.
Currently there are no data available for the
solvation of 1806 or DA18C6 in PC, hence there can be no
corrections applied to the values in Table 34. The most

likely interaction for the PC and the DA18C6 molecules

169

would be a simple hydrogen bond between the -NH— proton
of the DA18C6 and the 0:0 oxygen of the PC, which is
similar to that which occurs between A0 and DA18C6. The
PC molecule does posses a methyl group, which may feel a
sufficient reduction of its electron density, due the
electron withdrawing effects of the carbonate moiety, to
form an interaction with 1806, which could be similar to
that of the acetonitrile methyl group. Of course these
interactions are just supposition at this point. Hence,
the results for the PC systems are not currently
interpretable, other than to say that the general trends
seem to follow those found in AN and AC.

It is also of interest to compare results between
the solvents for a given cation and ligand. After
applying the solvent.1igand complexation corrections to
the values of Table 34 one can conclude that the forma-
tion constant for AN is larger than that for A0, with the
relative position of the PC formation constants being
undeterminable. The relative values for the formation
constants in AN and AC follows what would be expected if
the donor numbers reflected the solvating ability of the
solvent (the weakest solvating solvent will have the
largest formation constant), but not if the dielectric
constant (or dipole moment) was reflective of the
solvating ability of the solvent. The results reported

previously for the complexation of 1806 in DMF also fits

170

into this reasoning. The formation constants are reduced
in DMF (neglecting any effect due to the complexation of
the ligand by the solvent). Furthermore, the extent of
this reduction is greatest for the smallest cation and
the amount of the reduction diminishes steadily as the

cation size increases.

5. Conclusions

 

The formation constants for the alkali metal
cation.1806 complexes in AN, AC, and PC follow the
expected trends for a solvent in which the interplay
between the strength of the solvation and the strength of
the interaction with the ligand define the relative
complexation strength. The formation constants for the
alkali metal cation.DA1806 complexes do not strictly
follow the same trend, but show also a substantial steric
effect due to the -NH- proton, with the 'hard/soft'
interaction being significant in these studies only for
the Tl+ ion complexation. Indeed, the primary difference
between the formation constants for the 1806 and DA18C6
complexes, after correction for solvation of the ligand,
is also due to the steric effect of the -NH- proton, not
to 'hard/soft' interactions. Finally, the formation
constants, as a function of solvent, follow the trend

expected on the basis of the solvent donor numbers.

W1

DIBENZO-BO-CROWN-lO

A. INTRODUCTION

There have been several studies of the complexation
of alkali metal cations with DB30010 in nonaqueous
solvents (9,26,35,95,96,100). A sodium—23 chemical shift
study of the complexation of Net by DB30010 in NM by
Shamsipur and Popov (35) resulted in the data shown in
Figure 39. The chemical shifts were not analyzed to
obtain the formation constants, but because of the
presence of the minimum at the mole ratio of 0.5, the
maximum near the mole ratio of 0.7, and a leveling beyond

the mole ratio of 1, they suggested the presence of the

complexes Na +.DB30010, (Na+ )2.0330010, and
(Na*)3.(DB30010)2. Recently, Stover, 21,11. (100)
repeated the study and obtained the sodium-23 chemical
shifts and linewidths shown in Figure 40. These workers
analyzed the linewidths using a model based upon the
formation of the complexes proposed by Shamsipur. The
formation constants were calculated to be logKl>5,
logK2=2.1;fl.3, and logK =2.5¢0.3, where the formation
constants are as defined in equations (21), (22), and
(23).

Interestingly, the chemical shifts of Stover do not
show the maximum near the mole ratio of 0.7, which was
observed by Shamsipur. Furthermore, the linewidths

obtained by Stover (which were measured on both 80 and

200 MHz instruments), differ markedly (as much as a

172

173

 

 

 

 

 

-.5 ""
8
(ppm)
A

1 ._J

‘IO 77 Y I
l l l l L
(15 L0 IS 2() 25

[DB3OCIo]/[No*]
Figure 39: Experimental sodium-23 chemical shifts as a

function of DB30010/Na'+ mole ratio for
solutions containing NaP B and DB30010 in
nitromethane obtained y Shamsipur and
Popov (35).

174

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175

factor of 2.5) from those Shamsipur obtained on a 60 MHz
instrument (132). Due to these substantial differences a
new sodium-23 NMR study was performed on the complexation

of NaPth with DB30010 in NM.

A. RESULTS AND DISCUSSION

The sodium-23 chemical shifts and linewidths
obtained for a series of solutions of NaPh#B and DB30010
in NM in collaboration with John Rovang are given in
Table 35. The chemical shifts, which are plotted in
Figure 41, do not show the maximum near the mole ratio of
0.7 observed by Shamsipur, in agreement with the results
of Stover, _£‘_1. The linewidths, also shown in
Figure 41, are also in agreement with those of Stover,
_£ 11., not with those of Shamsipur. The cause of the
difference for Shamsipur's data is not clear.

The linewidths in reference (100) were fitted to a
model which assumed 1:1, 2:1, and 3:2 Na+:DB30010
complexes; however, the polynomial for the free metal ion
is not the same as that given in equation (29).
Everywhere that K3 appears in the equation of Stover,

21 al., apears in equation (29). Whether this is a

— KlKS
misprint in their paper is not clear, and hence one
cannot be sure whether their value of 'K3' is actually KB
or K K . If it is in fact KIKB’ then logK} is not
2.5 . , but rather logK <-2.2.

In an effort to clarify Stover and coworker's value

176

 

 

 

Table 36: Sodium-23 chemical shifts and linewidths as a
function of mole ratio of
dibenzo-30-crown-10:sodium ion for solutions
containing 0.0500010.0005 M sodium
tetraphenylborate in nitromethane.

a . b . .
[DB30010] Chemical L1new1dth
[Na+] Shift (Hz)
(ppm)
0 l3.04110.02 171 2
0.1 12.04 10.12 1221 5
0.2 11.29 10.17 209110
0.3 10.05 10.17 294123
0.4 9.50 10.28 4021 7
0.48 8.66 10.34 459114
0.5 8.10 10.06 4931 8
0.52 8.29 10.08 ‘ 481124
0.55 8.35 10.2 477132
0.6 8.16 10.20 428131
0.65 8.23 10.33 406125
0.7 8.62 10.05 4141 3
0.75 8.85 10.28 363123
0.8 8.28 10.21 2951 2
0.9 8.60 10.26 2651 3
0.98 8.84 10.11 242110
1.0 8.84 10.10 2371 3
1.02 8.80 10.06 2431 9
1.1 9.01 10.07 2261 5
1.2 8.90 10.18 2211 9
1.3 8.60 10.20 214118
1.5 8.91 10.07 206113

 

a. uncertainty is I%.
b. not corrected for magnetic susceptibility.

 

177

 

 

 

4
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q
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23".
Chemical
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00 23".
Linewidth
(HZ)
"0 ‘ f L300
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-7 I I I I
° °-5 1.0 1.5 2.0

Figure 41:

OBJOCIO
Na

Experimental and calculated sodium-23 chemical
shifts (V) and linewidths (O) as a function

of DB30C10/Na * mole
containing NaPhuB and
The calculated curves
using 1:1 and 2:1 Na+

ratio for solutions
DB30010 in nitromethane.
are based upon a model
:DB30C10 complexes.

178

of 'KB" the sodium-23 chemical shifts and linewidths
given in Table 36 were analyzed. The data were first
fitted to a model using only 1:1 and 2:1 Na+:DBBOC10
complexes. The results obtained are given in Table 37,
and the experimental points and the calculated curves are
plotted in Figure 41. Next the data were fitted to the
model used by Stover, _£ _1. (100): (1:1, 2:1, and 3:2

Na+:DB30C10 complexes). The results of this fit are also

given in Table 37, and the experimental points and the

calculated curves are given in Figure 42. The values
calculated for the formation constants are vastly
different from those of Stover, t al., and are so

uncertain that they are essentially meaningless. Finally
the data were fitted to a model containing 1:1, 2:1, and
2:2 Na+:DB30C10 complexes. The results for this fit are
also given in Table 37, and the experimental points and
the calculated curves are plotted in Figure 43. Again,
as for the model containing the 3:2 complex, the
calculated formation constants are so uncertain that they
are meaningless.

Comparision of Figures 41-43 indicates that the
model which employs only the 1:1 and 2:1 complexes
describes the data just as well as the more complicated
models do. Since the chemical shift and linewidth data
show only one extremum followed by a leveling off, it is

not necessary to include either a 2:2 or a 3:2

179

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- 600

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” 400 23Na

Linewidth
0d)

'300

.200

.100

 

 

T’ l I ‘T
0.5 1.0 1.5 2.0

DB30C10
Na

Figure 42: Experimental and calculated sodium-23 chemical

shifts (V) and linewidths (O) as a function
of DBBOClO/Na+ mole ratio for solutions
containing NaPh B and DBBOCIO in nitromethane.
The calculated fiurves are based upon a model
using 1:1, 2:1, and 3:2 Na+:D330C10 complexes.

-13
~12

23Na

Chemical

Shifts-11
-10
-9
-8

Figure 43:

 

181

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. 500

1 f 400 23"a

L1new1dth
‘ (HZ)

+ '300

 

‘L .200

1 1 .1.

 

 

I l I ”T
0.5 1.0 1.5 2.0
9830C10
Na

Experimental and calculated sodium-23 chemical
shifts (V) and linewidths (O) as a function
of DB30C10/Na+ mole ratio for solutions
containing NaPth and DB30C10 in nitromethane.
The calculated curves are based upon a model
using 1:1, 2:1, and 2:2 Na+:DB30C10 complexes.

182

Na+:DB30C10 complex. Indeed, this explains why the fits
using the complicated models result in such uncertain
formation constants. The unacceptably large
uncertainties are due to trying to extract more
information from the data than they are able to yield.
How Stover, ‘_£ _1. were able to obtain the results
reported in the literature is not clear. (In fact a fit
of the data using the formation constants and calculated
chemical shifts and linewidths from reference (100) as
the initial guesses gave the results given in Table 34.)
A variable temperature study was performed on the
system in an attempt to determine whether there in fact
complexes of stoichiometries other than 1:1 and 2:1. For
solutions having DB30C10:Na+ mole ratios of 0.5, 0.7, and
l at room temperature the observed sodium-23 spectrum is
a single resonance (with linewidths in the hundreds). As
the temperature is lowered to -25°C, each solution shows
steady broadening, but at no point is it possible to
identify more than one resonance. A similar study was
also performed in 2—nitropropane. In this solvent, the
resonance broadened to over 5000 Hz at —97°C, but again,
at no temperature was it possible to identify more than

0118 resonance.

183

C. CONCLUSIONS

The observed data do not require the presence of
other than the 1:1 and 2:1 Na*:D830C10 complexes. The
conclusions of Stover, _£ 11. are not supported by the

current results, although the data are in substantial

agreement.

CHAPTER y;

SUGGESTIONS FOR FURTHER STUDY

A. COMPETITIVE NMR

Sometimes the study of the complexation of a ligand
in a particular solvent results only in a lower limit for
all cations under investigation (see for example
reference 38, Table II, the data for 18C6 in NM). In
these cases it could prove useful to employ the
competitive NMR technique, using two ligands and one
cation. For example, note that in reference 38,
Table II, there is a value for the formation constant of
the Li+.DA18C6 complex which might be used to obtain the
formation constant for the Li+.18C6 complex - and this in
turn could be used to study the remaining 18C6 complexes.

Performance of such a two ligand/one cation study,
using the NMR of the cation, would require that the
solutions be of constant concentration with respect to
the cation and the ligand with the smaller formation
constant, while the concentratin of the other ligand is
varied. The concentration of the 'weaker' ligand should
be sufficiently large that the cation is essentially
completely complexed, so that the free metal
concentration is negligable, and hence its chemical shift
is unimportant. Except for the different solutions, the
methodology would be equivalent to that of the two
cation/one ligand method. The equations for the two
ligand/one cation method would be identical to those of

the two cation/one ligand method, except that in

185

186

equations (2) - (9) the symbols 'M' and 'N' would
represent the two ligands and 'L' would be the cation,
and in equation (10) the chemical shifts 60 and 61 would
be the chemical shifts for the weaker and stronger
complexes, respectively.

It should be possible to use the competitive NMR
method to determine the thermodynamic parameters AH and
AS, by the repeated application of the technique and the
consequent determination of the formation constant at
various temperatures. The formation constants for these
various temperatures may be used in a van't Hoff plot to

obtain AH, and subsequently AS may be calculated.

B. DIBENZO-BO—CROWN-IO

The results for the complexation of Na+ with DB30C10
in NM show no indications of the 3:2 complex proposed by
Shamsipur (35). This also cast doubt on the results for
the complexation of Na+ with DB30C10 in AN, where he also
proposed the existence of a 3:2 complex. Because the
formation constants are known for the Cs+.DB30C10
complexes in many solvents (35), it should be possible to
obtain formation constants for many other cations using
the competitive technique. Furthermore, since cesium-133
NMR tends to have large chemical shift changes and
because these chemical shift measurements are usually
very precise, such experiments may well yield a great

deal of information about the formation constants of

187

other cations.

APPENDICES

w;

DERIVATION 0F EQUATIONS TO USE TO CORRECT FOR MAGNETIC

SUSCEPTIBILITY

Recall that the resonance (Larmor) frequency, V, is

given by the Larmor equation

yH
__ Eff, (1)
2n

 

where Y is the gyromagnetic (magnetogryic) ratio, which
is characteristic of the nucleus on which the NMR
experiment is being performed, and Heff is the effective

magnetic field strength at the nucleus. The effective

field strength is usually expressed as

Heff = HO(1 - o). (2)

where H0 is the applied magnetic field and O is the
sheilding constant.
In order to correct for the effect of the

diamagnetic susceptibility on a chemical shift, equation

2 must be replaced by

Heff = HO(1 - o - Sfx). (3)

where X is the magnetic susceptibility of the solution
(generally this is approximated by the magnetic

susceptibility of the pure solvent (106)) and S is the

f
188

189

shape (or geometry) factor, which is dependent on both
the shape of the sample cell and the orientation of the

sample in the magnetic field.

For spherical sample cells Sf = 0 regardless of the
magnetic field orientation. However, for the more
commonly used cylindrical tubes Sf = 21V3 for magnetic

fields applied perpendiculary to the long axis of the
tube (this is the case for permanent and/or
electromagnets), while Sf = -41V3 for magnetic fields
parallel to the long axis of the tube (which is the case

for superconducting magnets).

A. gag; 11 Continuous Wave (CE) Experiments

In a continuous wave experiment the frequency is
held constant and the applied magnetic field is varied
until the resonance condition is reached. Thus from
equation 1 it can be seen that the effective field
strength is the same for each nucleus, regardless of its
environment, when it obtains the resonance condition.
But from equation 3 it is clear that nuclei in different
environments will achieve resonance at different applied

magnetic fields. Thus the chemical shift, 6, is given by

 

(S: .10 9 (4)

where H0 is the applied magnetic field at the resonance

3
condition of the nucleus in environment 3, H0 is the
b
applied magnetic field at the resonance condition of the
nucleus in environment b, H0 is the applied field at the
c

resonance condition of a free nucleus (i.e., one for

which both C and S are zero, hence H = H = H ), and

f 0 0 eff
c

the factor of 106 is to convert to parts per million
(ppm).

Thus if one desires to correct an observerd chemical
shift, 5 , in solvent 1 to what it would be in solvent

obs

2 the corrected chemical shift, acorr' is given from

 

Ho ’ H0
2 1 6
- 5 = '10. (5)
corr obs H
eff
Thus if equation 3 is solved for HO/Heff and subsituted

in equation 5 above, it is easily shown that

1 l
_ 5 = ( )_( ) '10 . (6)
5corr obs _ _ _ _
1 02 Sfx2 1 01 Sfx1

 

 

Equation 6 can be rearranged to yield

191

 

corr - 6obs
= (7)
(l-ol-Sfx1)-(1-02—SfX2) 6
.10
2
1' 01‘ 02+ 0102‘S f X1“S f X2+ C’25 {X1+ 0‘15 f X2+S f X1X2
Because we are attempting to correct a particular

chemical shift for the solvent diamagnetc susceptibility
it is clear that CH=Cb(=CD. Also, because, generally,
chemical shifts do not exceed 50,000 ppm, must be less
than 0.05 (it is of interest to note that for the
carbon—13 nucleus, where the total chemical shift range
is approximatly 300 ppm, would be less than 0.0003), and

is generally on the order of 10-6, equation 7 may be

simplified to the approximate form

_ _ 6
%orr - 6obs - Sf(Xl X2)10 ’ (8)

(for example the approximation is accurate to within
0.06% for carbon-l3).
Choosing solvent 2 to be the reference solvent, and
because is generally tabulated as -xx106 the factor of
v

6 . . . . .
10 is incorporated into the x 3, resulting in the

equation

192

 

 

 

 

'6 =8 _ o 9
corr obs f(xref Xsol) ( )
Thus for a continuous wave experiment utilizing a
permanet or electromagnet
21f
= 6 - 10
corr obs + jrfixref Xsol) ( )
while for a continuous wave experiment utilizing a
superconductingfimagnet
4n
corr obs - (Xref - X301) (11)

These equations (10 and 11) are those of Live and

Chan (104).

B. Case 21 Fourier Transform (FT) Experiments

In a Fourier transform experiment a constant
magnetic field, H0, is applied. The resonance condition
is then satisfied at different V's, as given by
equation 1, where Heff is as given in equation 3. For

this case, the chemical shift, 6, is given by

(12)

or equivalently

 

(13)

193

where the subscripts a, b, and c have the same
significance in equations 12 and 13 as they do in
equation 4. Since H is the effective field for a free

nucleus “eff = H0 and equation 13 becomes

 

5 = '10 (14)

If, as in Case 1, we assume that we are trying to

correct an observed chemical shift, 5 , in solvent 1 to

obs

the corrected value, acorr’ in solvent 2 (the reference

solvent), then equation 14 becomes

 

6 - 6 = '10 (15)

solving equation 3 for Heff/HO and substituting into

equation 15 yields that
(16)

$orr ‘60bs = [El'oz-Sfxz) - (l-Ol-Sfxlir106

where again identical sample geometries are assumed.

194

Again 01:02:0’ and the factor of 106 is included into the

X's resulting in the equation

6 - 6

corr obs

= Sf(x1 _X 2) (17)

Thus for a Fourier transform experiment utilizing a

permanet or electromagnet

 

 

2n
6corr — Gobs _' 3(Xref - X301) (18)
while for a Fourier transform experiment utilizing a
superconductingpmagnet
ATT
= 6 —— —
corr obs +' 3(Xref X301) (19)
Equations 18 and 19 are the equations of Martin,

t 1. (105).

APPENDIX 11

SUBROUTINE EQN WHICH INCLUDES SOLVING A GENERALIZED

POLYNOMIAL

 

In order to use the program KINFIT to fit
competitive NMR data it is necessary to solve a high
order polynomial (either a third or fourth order
polynomial). The subroutine EQN which follows includes a
part which solves such high order polynomials.

For this subroutine to operate properly it is
necessary to define the coefficients of the polynomial
such that the polynomial is positive when the polynomial
is evaluated at zero. If the polynomial may have more
than one root in the possible search region (O<[M+]<CM)’
then this subroutine is not reliable, and the subroutine
given in Appendix III should be used. Finally, it should
be noted that in the particular version which follows the
subroutine is set up for two competing 1:1 complexes,
with the observation nucleus being the cation with the

known formation constant.

195

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zmshmm
MOZHHZOU
zmzhmx
MOZHHZOU
zmzhmm

Hmvxxuoa<quHmEE

mszHHzoo
zmskmm

mm CHOU AHI.mz.:HmzHVmH

MOZHHZOU

HHHOHmzoo*EEEEE+o.Hv\HAHOHmzoo*HEEEE*AmO=+HNOEOuQE<u
**************x*********************************************************

mOzm mzHHOOm zOHHOOOm 4<Hzoz>40m mze mxmz3 mH mHm9

OH

ON

mm

NOOm

*
*
*

********%***************************************************************

AE.oHE.

mazHHzoo

O.qummmm

mzzHHzou

Hoom OHou
A_vxx EOE EZEOE onHEEom Oz **=mm.xm.\ve<zEOE aoa
AHOHH HEEE.EE<H5OEHHE3

meow oeoo Hm.Ez.E<aOEH

NOON

wOON

************************************************************************

*

x

202

Ozm
zmshmm
mzzHHon NH
zmsbmm
mazHezoo HH
szHmm

APPENDIX III

SUBROUTINE EQN WHICH WILL CHECK FOR THE CORRECTNESS OF A

SOLUTION TO A GENERAL POLYNOMIAL

In order to use the program KINFIT to fit NMR data
to some models in which there is a possibility of the
polynomial having more than one solution in the search
region 0<[M+]<CM, it is necessary to solve a high order
polynomial and to check the solution for correctness.
Also, should the solution be incorrect it is necessary to
restart the search from the incorrect solution. The
subroutine EQN which follows includes a part which does
exactly this.

The particular version which follows is set up for
the solution of the polynomial given as equation (34),
for a model in which there are 1:1, 2:1, and 2:2

metal:ligand complexes formed.

203

2100

2101

2021

2015

2000

2007

204

SUBROUTINE [ON

CONNON (JUNTQITOP[0JTAP[9INTQLAPQXINCRoNOPToNOVARoNOUNNoloUoITNAIO

INIXQT[STQIoAVoRESIDoIONe[PSoITYPQXXQNXTVPQDXIIQFOPOFOQFUQPOZLQTOQE

ZIGVOLQXSIQTOOTOLQNQJJJQYQDYQV[CTQNCSToCONSTeNDATOJDAIoHOPTeLOPTe
STTYQCONSTS

:ONNONI:§EDTIINETH

CONNON/POINT/KOPTQJOP'ONXX

OINENSIO‘ XIOOSOOIQUI20)oNTXIOeBOOIoXX(OIeFOPI3OOIQFOCSOOIQFUCSOOI

10P(2002119V[CT¢200213oZLISOOIcTOIZODo[IGVAL(20’9XST(300)oY‘lO)o

231(10)QZJNSTSISOQISIoNCSTCSOD9!SNIN¢50).RXTYP(50)OOXII(SOIQIRX(50)

SoNOPT(501oLOPTISODoYYYCSOIoCONSTI16)oXXXIIS)
GO TO (2030O05'1970809010911912) ITYP
CONTINUE
ITAPE=60
JTAPE=61
RETURN
CONTINUE
‘OUNK87
NOVAR=3
RETURN
CONTINUE
RETURN
CONTINUE
UCII=ABSIUIITI
UIZ):ABS(U(2))

U(3)=ABS(U(3))
IFCXX(1).GT.(XX(3)IZ.0)) GOTO 2100
‘NNIN3XNISI'200'XX(I)
GOTO 2131
CONTINUE
FHHI~:003
CONTINUE
:NNOX2XIIB)
FNNOXI=EONAX
FNNIN1=:1NIN
A=U(2)'U(2)
3=U(2)-2o00U(3’0U(2)0U¢2I0(2.0iXX(ID'XXCBII
2:(U(2)-O.0‘U(3)DOCXXCID-XX(3))
33-100-2oOOUCZIOXXCII-ZoOIUCII'UI3"(XXIl)-XX(3))0(XX(I)-XX(3))
[=-I.O'J(1)0(XX(I)-XX(3))
F=XX(3)
IF!XXII).[0.0.0) GOTO 2002
CONTINUE
VHIN=F
IF(ABSIVOIN).LToooOOOOOOOI) GOTO 2003
CONTINUE
IFIVNIN.3T.0.0) GOTO 2000
CONTINUE
=-|
B=-B
C=-C
D=-O
£=-E
:=-:

VNIN=-VOIN

CONTINUE

TINC=(FNNIX-FNHIN)I(I.0512)

III=1

CONTINUE

=HTST=F141N¢TIN2

VTST=(((IOOFNTSTOB)OFNTSTOC)IFHTST'UIIIOOIOFHTSTOUII)O[)*FNTSTOF
IF(A8$(VTST).LT.0.00000001) GOTO 2020

[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO
[ONO

[ONO
[ONO
[ONO
[ONO

2008

2006

2011

2010

2020

2009

2003

2002

2012

2013

2016

205

IFIVTST.-T.C.J) 6010 2326

=nn1V=FWIST

VHIV=VTST

IFIFHTST.ST.FHHAIT GOTO 2016
IFITINC.3T.(FNPAx-FHNINI)II.0[¢0O) GOTO 2007
1F111103201000) GOTO 2008

111:11101

SOTO 2017

CONTINUE

TINC=TIV3010.0

111:1.0

SOTO 2007

CONTINUE

t~'MT0P=F\IT$T

VTOP=VTST

CONTINUE

IFIVNINoEOoVTOPI GOTO 2009
‘NTST=FOOINO(FNTOP-FNNINIIIVNIN-VTOP10VNIN
IF(ABSIIENTST-FNNINIIFNTSTIoLTo0o00000000011 GOTO 2009
IF(ABS(CENTST-FNTOPDIFHTST1oLTo0o0000000001) GOTO 2009
VTST=(((1OOFNTSTOB)OFNTSTOCIOFNTSTOUC110010FNTSTOUC110[1OFNTSTOF
IFIABSCVTST)oLTo0000000001) GOTO 2009
IFCVTSToLToOoOISOTO 2010

ENNIN=FNTST

VNIN=VTST

SOTO 2011

CONTINUE

FNTOP=FOTST

VTOP=VTST

GOTO 2011

CONTINUE

VTOP=VTST

ENT0P=F1TST

CONTINUE

FH:FNTST

GOTO 2012

CONTINUE

VTOP=VN10

‘NTOP=FOOIN

FH=FHNIN

GOTO 2012

CONTINUE

=n=xx¢3)

:L3300

:HL3000

FHZL=000

FN2L2=0o0

SOTO 201O

CONTINUE
EL=¢NXIID~XXI3IOFNIII1.0-0(110UIZIOFN0FN1
FNL=U1110FN0FL

FN2L=U(2)oFHLtFN

FH2L2=U(3)¢FNL'=HL
TH=FHOF9;92.0¢F12L02.00FH2L2
TL=FL0FHEOFH2L02.0-F92L2

IFCFL.LT.0.0) GOTO 2013
IFIABSCITN-XXC3))ITN).GT.0.01) GOTO 2013
IFCABSIITL-XX(111/TL1oLT00001) GOTO 201O
CONTINUE

VNIN=VTO’

FNNINzFOTOP

GOTO 2021

CONTINUE

FN=KX(31

‘L=XX(11

FHL=0o0

FH2L=0oC

ICOO

20

10

11

12

206

:H2L2:Oo:

IIII=1.3

CONTINUE

°1=FHOCOVSTSIJ0IT911
‘HL111=((8.O'U(3)fiXX1310110'0o5-1)lIOoOfiUIS))
IF(JDAT.E0.2) GOTO 1000
3NL=1COVSTSIJDAT.210lX131-(Xx131-FHL111)'U(5))/FHL111
a3:2-OIEOZL‘UIO)

PO=2o0"‘2L20U(5)

GOTO 1001

CONTINUE
JHL=ICOVSTSIJDATo21~lX(3)-(XX(3)-FHL111)*UIT))/FNL111
P3=2.0¢"2L'U(6)

PO=2.00=‘2L2'UIT)

CONTINUE

P2=DHL0=WL
CALC=IP1'°20P393O)IIX(3)
IFCINETfloNE.-1) 00 T0 35

RETURN

CONTINUE

RESID=CALC-XX(2)

RETURN

CONTINUE

RETURN

CONTINUE

RETURN

CONTINUE

IFIINETHoNE.-1) GO TO 20

R[TURN

CONTINUE

RETURN

CONTINUE

RETURN

CONTINUE

QETURN

CONTINUE

RETURN

CONTINUE

RETURN

END

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