A NUCLEAR MAGNETIC RESONANCE STUDY OF :THE .

COMPLEXATION OF23Na+BY 2-2-2 CRYPTAND

Thesis for the Degree of M. S.
MICHIGAN STATE UNIVERSITY
PATRICK B. SMITH
1977

i
. ”‘4‘;

 

LIBR‘;.1Y

Michigan State
University

 

ABSTRACT

23

A NUCLEAR MAGNETIC RESONANCE STUDY OF THE COMPLEXATION 0F Na+ BY

2-2-2 CRYPTAND

By

Patrick B. Smith

An investigation of the complexation of 23Na+ by 2-2-2 cryptand in
several solvents has been initiated. The chemical shifts and line-
widths of the complexed and solvated ions have been measured by 23Na
NMR. Rate studies have also been performed on the exchange of Na+
between the two sites in four solvents; water, pyridine, tetrahydro-
furan (THF), and ethylenediamine (EDA). It has been found that the
solvent has a definite influence , not only on the solvated sodium
ion but also on the complexed ion. The chemical shift of this species
ranges from 9.2 ppm in water to 13.4 ppm in dimethylformamide. The
kinetics of exchange is also very solvent dependent. The activation

energy in Real mole.1 for the dissociation step in water is 16.7, in

THF it is 14.4, in pyridine it is 14.2 and in EDA it is 13.0.

A NUCLEAR MAGNETIC RESONANCE STUDY OF THE

COMPLEXATION OF 23Na+ BY 2-2-2 CRYPTAND

By
I'\

Patrick Bf” Smith

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Chemistry

1977

To my family

11

ACKNOWLEDGEMENTS

The author wishes to express gratitude to Professor James L.

Dye for his encouragement and guidance throughout this work.

Professor Alexander I. Popov is also gratefully acknowledged
for his counseling.

The author would also like to acknowledge Dr. Joseph M. Ceraso
for his many hours of instruction, encouragement and friendship.
Special appreciation also goes to Dr. David Wright for his many hours
of valuable assistance. Mr. Timothy Kelly is also acknowledged for
his help in computer programming and Mr. Stephen Landers for much
of the linewidth data in this thesis.

A high degree of respect and appreciation are extended to Dr.
Elizabeth Mei, Mr. Michael Yemen, Mr. Midhael DaGue, Mr. Charles
Andrews, Dr. Guan.Huei Ho and Dr. Yves Cahen for many helpful
discussions in the laboratory. Financial support from the United States
Atomic Energy Commission is also acknowledged.

Lastly, my heart-felt appreciation is extended to my wife and
family for their encouragement and love which has made the attainment

of this goal possible.

111

TABLE OF CONTENTS

Chapter

I.

II.

III.

IV.

VI.

VII.

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . .
HISTORICAL
THE NATURE OF INTERACTIONS IN SOLUTION. . . . . . .
EFFECTS INFLUENCING THE EXTENT OF INTERACTION . . .
MATHEMATICAL FORMULATION OF THE NMR RATE EXPERIMENT
ALKALI METAL RATE STUDIES . . . . . . . . . . . . .
EXPERIMENTAL
GLASSWARE CLEANING. . . . . . . . . . . . . . . . .
SOLVENT PURIFICATION. . . . . . . . . . . . . . . .
CHEMICAL PURIFICATION . . . . . . . . . . . . . . .
SAMPLE PREPARATION. . . . . . . . . . . . . . . . .
INSTRUMENTATION . . . . . . . . . . . . . . . . . .

Super Con . . . . . . . . . . . . . . . . . .
varian DA-60 o o o o o o o o o o o o o o o o 0

RESULTS
THE NON-EXCHANGING SYSTEM . . . . . . . . . . . . .
THE EXCHANGING CASE . . . . . . . . . . . . . . . .
SUSCEPTIBILITY OF ETHYL AMINE . . . . . . . . . . .
CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . .
LITERATURE CITED . . . . . . . . . . . . . . . . . . . .

APPENDIX 0 O O O O C 0 O O O O O O O O O O O O O O O O 0

iv

Page

. 11
. ll
. 11

. ll

. 11
O 12

. 14

. 15

. 27

. 52

Table

l.

10.

LIST OF TABLES

The Chemical Shift of 23Na in Several Solvents. . . . . . .

The Variation of th 3Lincwidth and Chemical Shift of the
Complexed and Free Na Cation with Temperature in EDA... .

The Variation of thEBLinewidth and Chemical Shift of the
Complexed and Free Na Cation with Temperature in THF. . .

The Variation of th§3Linewidth and Chemical Shift of the
Complexed and Free Na Cation with Temperature in Pyridine

The Variation of tthLinewidth and Chemical Shift of the
Complexed and Free Na Cation with Temperature in Water. .

The Temperature Dependence of the Exchange Time and
LineWid-lth in WA I O O O O O O O I O O O I O O O O O O O O O

The Temperature Dependence of the Exchange Time and
Linewidth in THF. . . . . . . . . . . . . . . . . . . . . .

The Temperature Dependence of the Exchange Time and
LineWidth in Pyridine O O O O O 0 O O O O O O O O O O O O O

The TEmperature Dependence of the Exchange Time and
LineWid-m in wawr. O O ' O 0 O O O O O O O O O O. O O O O O O

The Solvent Dependence of the Thermodynamic Parameters. . .

16

18

19

20

22

36

37

38

39
45

LIST OF FIGURES

2-2-2 Crypt Used for the Complexation of 23Na . . . . . . . .

Space Diagram of the Complexed 23Na Cation . . . . . . . . . .

FDA 0 O O O O O O I O O 0 O O
mF O O O 0 O O O O O O 0 I O
Mid-me O O O O O O O O O O O
blater O O O O O O O O O O 0 O
23 . .

Na NMR Lineshape for EDA. .
23Na NMR Lineshape for THFS .

23Na NMR Lineshape for

23Na NMR Lineshape for water.

23Na Lineshape in EDA . . . .
23

23
23

Na Lineshape in THF‘. . . .
Na Lineshape in Pyridine. .

Na Lineshape in Water . . .

Figure
1. Dibenzo-lB-crown-é. . . . . . . .
2.
3. Block Diagram of DA-6O . . . .
1+. Block Diagram of the Lock System
5.
6. The Variation of T2 with l/T for
7. The Variation of Té with 1/T for
8. The Variation of T2 with l/T for
9. The Variation of T2 with l/T for
10. Typical Spectra Illustrating the
11. Typical Spectra Illustrating the
12. Typical Spectra Illustrating the
Pyridine . . . . . . . . . . . .
13. Typical Spectra Illustrating the
14. A Typical KINFIT Analysis of the
15. A Typical KINFIT Analysis of the
16. A Typical KINFIT Analysis of the
17. A Typical KINFIT Analysis of the
18. The Variation of the Log of k with the Inverse of the
Temperature in EDA . . . . . . .
19. The Variation of the Log of k with the Inverse of the
Temperature in THF . . . . . . .
20. The Variation of the Log of k with the Inverse of the
Temperature in Pyridine. . . . .
21.

The Variation of the Log of k with the Inverse-of the

Temperature in Water . . . . . . .

vi

30

31

32

33

35

40

41

42

43

LIST OF NOMENCLATURE, ABBREVIATIONS AND SYMBOLS

EDA:

THF:

DMF:

DMSO:

NaTPB:

Ethylenediamine
Tetrahydrofuran
Dimethylformamide
Dimethylsulfoxide

Sodium Tetraphenylborate

Full width at half height
Chemical shift

Spin—spin relaxation time
Mean lifetime at site A
Exchange time = ._IE$IBE

TA+ TB
Population at site A

vii

INTRODUCTION

CHAPTER I

1

Recent work in this laboratory has concentrated on the production
and identification of alkali metal anions (23). Cryptands, which
selectively complex alkali metal cations in solution have provided
one means by which these species are produced in relatively high
concentration. Cryptands are the best alkali cation complexing agents
to date, yielding such tightly bound complexes (cryptates) that rate
studies can be done on these systems. This project, in continuation
of the preliminary rate study of Ceraso and Dye (16), has further
investigated the solvent dependence of this exchange phenomenon as well
as the solvent dependence of the chemical shift and linewidth of the

complexed sodium cation.

CHAPTER II

HISTORICAL

THE NATURE OF INTERACTIONS OF ALKALI METALS IN SOLUTION

In the past, alkali metal nuclear magnetic resonance has afforded
only two parameters to observers; linewidth and the chemical shift.
Unlike proton NMR, where specific interactions are long lived, no fine
structure is observed due to the extreme lability of these metal cations
in solution. In order for a particular interaction to be observed on
the NMR time scale, the ion must remain in a certain environment for
about a millisecond or longer. If however, the ion moves rapidly
throughout the solution experiencing many environments during this time
period, then the effect of these environments will be averaged into a
single absorption.

Although only two parameters may normally be obtained in alkali
metal NMR, considerable information is provided by them. The chemical
shift and linewidth both provide information concerning the nature,
extent and lifetime of interactions in solution. The linewidth is
related to T2, the spin-spin relaxation time by

T2 = 1 (1)
nAvg ‘

where Ava is the full width at half height in Hz, of a Lorentzian line.

Since 23

Na has an appreciable quadrupole moment, its relaxation is
dominated by the interaction of the quadrupole with electrostatic field
gradients at the nucleus. Interactions with species which produce field
gradients at the nucleus will be observed in line broadening. The
extent of line broadening is useful in determining the geometry of the

environment and the strength of the interaction.

These interactions affect the chemical shift in much the same

3
fashion since it is a measure of the shielding of the nucleus by the
electrons around it. Since the field which the nucleus experiences is
largely dependent upon the electronic shielding, any interaction which
alters the character of these electronic orbitals will cause resonance
to occur at higher or lower fields.

The chemical shift, relative to the bare nucleus, is made up of two
components, a diamagnetic part, 0d and a paramagnetic part, op. Cd is
usually the larger of the two and arises mainly from the electronic
distribution in the ground state. It is not strongly affected however
by the environment of the ion. On the other hand, op depends also on
excited states through the mechanism of spin-orbit coupling. Inter-
actions in solution have large effects on op because solvent molecules
and counter-ions tend to interact with valence electrons via unoccupied
orbitals. Paramagnetic shifts are downfield whereas diamagnetic shifts
are upfield.

There are several mechanisms by which interactions in solution are
produced, the more important being 1) polarization of electronic
orbitals by dipoles or ions, 2) ring currents from neighboring molecules
and 3) donation of electrons from one species into the p-orbitals of
another. Deverell and Richards (1) have undertaken a study in which
they varied several parameters such as concentration, the cation or anion
of various salts, etc., in order to determine which mechanism produced
the greatest effects in solution. They observed that the concentration
of cations and anions in solution had a definite influence on the
chemical shift. They also noticed that some ions had larger effects on
the counter ions than others, in fact that those with the greatest size

and lowest charges tended to produce the greatest effect. From this,

4
they concluded that the major contributor to interactions was not due to
polarization but was instead produced by donation of electrons into the
p-orbitals of the counter ion, exciting those p-electrons to higher

states 0

EFFECTS INFLUENCING THE EXTENT OF INTERACTION

There are three major effects which govern the character of inter-
actions of metal cations in solution in a given solvent. The anion
produces the largest effect in that collisions of cation and anion
produce excitation of ground state electrons as discussed earlier. As
the concentration of the anion is increased, the frequency of collision
is also increased, yielding greater effects (2-5).

The temperature also influences the linewidth, most.obv1031y
because of solvent viscosity. Also however, as the temperature is
decreased, the rate of exchange between sites is slowed down, producing
longer lived interactions.

Thirdly, although the solvent interacts directly with the cation,
another important effect on T2 and the chemical shift is of a more
subtle nature. The solvent controls the extent of dissociation of the
salt so that it may be either conducive to ion pairing or it may
solvate the ions very well so as to limit interaction between them.
There is an entire spectrum of solvents ranging from those conducive to
contact ion pairing, to those in which solvent-shared or solvent-
separated ion pairs exist, and finally to those which prohibit ion
pairing. Considerable documentation (2-7) has been recorded for these
systems; and of particular interest to this discussion is the work of
POpov and co~workers (2-3), in which they relate the Gutmann donor

number of the solvent (which is a measure of its solvating ability) to

. 5
the chemical shift of 23Na in that solvent. They found a linear

relationship between the two.

MATHEMATICAL FORMULATION OF THE NMR RATE EXPERIMENT

If the exchange of a species from one environment to another is
slow, NMR may be utilized to distinguish between a nucleus in site A
and in site B; that is, two separate absorptions will occur. If on the
other hand, the lifetime at a site is less than about 10'3 seconds, only
one absorption will occur (an average of the two) because the sampling
rate of the instrument is not rapid enough to "see" the nucleus in the
two separate environments. The classical equations which govern NMR
rate processes are the Bloch equations modified by McConnell (8) for

exchange. ‘We begin with the Bloch equations in the rotating frame

$3 + 9,172 + (mo-w)v = O (2)

$3 + i - (mo-Lu)u +yH1Mz = o (3)

£1.22. + 55.5% -yH1v = O (4)
where

Mx = u cos wt - v sin wt (5)

M? = -v cos wt -u sin wt - (6)

If we define a complex moment

G = u + iv (7)

then equations 1-3 become

dG l

——-+- —- - i - G = -i H 8

dt [T2 (000 on] y In. ( )
This equation governs the behavior of a system when all nuclei therein
experience the same magnetic environment. If instead, a system contains
two magnetic environments, there will be two independent macroscopic

moments. If no exchange of nuclei occurs between sites A and B we have

EEA.+ l. - i(woA-w) GA = ‘1YH1M0A (9)
dt TZA
—-BdG + l. - i(woB-w) GB = -1YH1MOB (10)
dt T23

These equations must be further modified to take account of exchange
between sites A and B. If we define TA and TB as the mean lifetime of a
nucleus in sites A and B respectively, and assume that nuclei jump
directly from one site to another with no intermediate states involved,

we may write

99A 2 Pl -1
dt + GAGA 'iYHleA + T3 GB- TA GA (11)

d_GB , g -1 _. -1

whens GB/TB is the rate of increase of GA due to chemical transfer of
magnetization from the B system to the A system and -GA/rA is the rate of
decrease in GA due to chemical transfer of magnetization from system A

to system B, and

1
“A = TZA ‘1(woA‘w) (13)

In order to solve these differential equations, we invoke the "slow
passage condition", which states that if we scan the frequency slowly
enough so as not to perturb the system's thermal equilibrium, we may

assert that

dG dG
——A.= ——B - O 14
dt dt ( )

The total complex moment (G) which is the sum of GA and GB then becomes

G = in1M{TA + TB + TATB(°‘APA + 013133)] (15)
(1+aArA)(1+aBTB) - 1
Since v is the component of G corresponding to the absorption line-
shape function, the imaginary portion of G is observed as the in-phase
component in the NMR experiment, which upon the assumption that

T2A - T23 10 and PA - pB, gives

v = -1ryH1Mo[ 1(wa-wB)2 J (16)
{%(mA+wB) - w} + Iz(wA-w)2(wB-w)

which is the expression often used in the case of very narrow lines such
as in proton NMR. In 23Na NMR however, the lines are much broader than
proton NMR and TZA is usually not equal to T23. The equations for this
case will be considered later.

In this study, we have used Fourier transform techniques in which
the validity of the adaptation of this derivation (ie. the slow passage

condition) is not completely obvious. Woessner (9) has verified its use

8
by solving these equations in the Fourier transform case with equivalent

results.

ALKALI METAL RATE STUDIES

In recent years, complexing agents have been synthesized which trap
these labile metal cations to the extent that an exchange phenomenon may
be observed. This has drawn interest from the biological community as
well as from chemists since these complexing agents might be used as
models in simulating the processes which govern ion-transport through
membranes in biological systems.

Crown ethers, developed by Pederson (10) were the first such

complexing agents to appear. A typical "crown" is shown in Figure l.

fU/jl)\
@0 .©
K/OJ

Figure 1. Dibenzo-l8-crown-6

Schori, Jagur-Grodzinski, Luz and Shporer (11) were the first
investigators to utilize these crowns to do an actual 23Na rate study,
applying the modified Bloch equations to the 23Na NMR experiment. They
studied the effect of temperature on the linewidth of the single broad
absorption which they observed with the solvent dimethylformamide.
Because of the broadness of the lines they did not observe two separate
peaks but were able to fit the line broadening of the single absorption
to the modified Bloch equations. For the case of equal populations, is,
the concentration of free sodium equal to that of complexed sodium at

_13o C, Schori,g£3‘§l, reported a I value of about 10"3 seconds and an

activation energy of 12.5 Kcal.

WOng, Konizer and Smid studied these systems by using proton NMR
with several ethereal solvents and pyridine. They observed two sets of
protons, one corresponding to complexed crown and the other from
uncomplexed crown which they analysed at the coalescence temperature,
obtaining results consistant with those of Schori, SE: El: (12).

At the height of the interest in crown ethers, Lehn (13) introduced a
class of complexing agents (cryptands or simply crypts) which selectively
complex metal cations to an even greater extent than do the crown ethers.
Crypts are bicyclic molecules in which the length of the three ether
strands may be changed in order to accommodate different cations. A

typical crypt is shown in Figure 2.

Ono
NQO ”yo/s N
poun/

Figure 2. 2-2-2 crypt used for the complexation of 23Na.

Lehn and co-workers (13-15) studied the complexing ability of these
molecules by utilizing proton as well as 13C NMR in aqueous solution.
They have tabulated rate constants and AG* values for many metal cations
at their coalescence temperatures. Of particular interest to this study
is the rate constant of 23Na in water which is 27 sec'1 at 3° C with AG*
- 14.2 Kcal.

In 1973, the first example of an actual two line rate experiment with
23Na NMR was published by Ceraso and Dye (16). They studied a solution

of O.6M.NaBr and 0.3M crypt in ethylenediamine, observing two lines whose

10

linewidths were not equal. For this case, the modified Bloch equations

 

become:
v - —yH1Mo w (16)
S + T
where
P P
S BITA +~¥p + T TT - 1(wAfw),(mB-m) (17)
2A 2B 2A 23
U = 1 + 1(pA/ T2A + pB/TZB) (18)
T

 

"' (Pawa + meB +

T T

- to) +1 (“If“) “if”? (19)
213 2A

V = r(pBwA + pAwB - w) (20)

where pA is the population at site A and r is the lifetime of inter-

action defined by
r r

p.
u:

 

(21)

+
,4

This experhment was unique in that the reaction times and chemical
shifts could be measured in separate experiments. A total lineshape
analysis was used, which employed a generalized weighted nonlinear
least-squares program (20) to fit the data at several temperatures.

A I value of about 10-3 sec. at 400 C with AG* - 14.8 Kcal at 500

(I was obtained, agreeing with Lehn's results in aqueous solution.

CHAPTER III

EXPERIMENTAL

GLASSWARE CLEANING

All glassware used for the NMR studies was soaked in ggggflgggi§_for
at least three hours and then rinsed in an HF cleaning solution. The
glassware was then rinsed several times with distilled water and then

with conductance water several more times and dried at 1100 overnight.

SOLVENT PURIFICATION
All solvents were purified in the lab of Dr. Alexander Popov and the
reader is directed to the thesis of Mark S. Greenberg for this infor-

mation.

CHEMICAL PURIFICATION

 

All salts were reagent grade and no further purification was done
except drying at 110° for at least ten hours. Salts were then stored in

desiccators over Ca804.

SAMPLE PREPARATION

 

Salts and crypt were weighed directly into NMR tubes and then
rough pumped for several hours in a vacuum desiccator. The NMR tubes
were graduated, which allowed the solvent to be delivered directly into

the tube in a dry box.

INSTRUMENTATION

Super Con- Many of the 23Na chemical shift data were taken on a
highly modified NMRS-MP-lOOO spectrometer, operating at 60.06 MHz at a
field of 53 k0. The time sharing method of Baker (17) was employed and
the instrument utilized 5mm crossed coil probes. This system was inter-

faced to a Nicolet 1083 computer for time averaging capabilities.

11

12

Varian DAr60- The DAr60 utilizes an extremely homogeneous
magnetic field at 15.87 MHz with a greatly modified NMRSéMP-lOOO
spectrometer in the pulse mode. The field is locked by a home-built
lock probe (21) which uses the DA-60 console to lock on a proton
resonance. The lock was very stable, drifting on an average of five Hz
in twelve hours. Block diagrams for the DA-60 and the lock system are
shown in Figures 3 and 4. The DA-60 is interfaced to a Nicolet 1083
computer for time averaging of spectra and also for on-line Fourier

transformation of data.

DATA,MANIPULATION

Data collected with the Nicolet 1083 computer were dumped onto paper-
tape in octal via program PATPRT (18), then converted to decimal by
using program CONVERT (l9), and ordered in a form compatable with
KINFIT (20). KINFIT, a generalized weighted non—linear least-squares
program, was then used to fit the lineshape data to the modified Bloch
equations.

A.modification to the Nicolet 1074 version of FTNMR was also

utilized to dump data as shown in the Appendix.

13

 

 

 

 

 

POWER
AM PLI FIE R

* PROBE

 

 

 

 

 

 

 

I

 

r

 

 

R.ELNIT

7

L

 

 

PREAMPLIFIER

 

 

 

 

RECEIVER

 

 

 

 

 

 

 

OSCILLOSCOPE

PULSE
PROGRAMMER

 

 

 

 

 

 

 

 

1
PHAS E

DETECTOR

 

 

NICOLET

 

 

 

Figure 3,

 

1083
COMPUTER

 

 

 

 

 

DIFFERENTIAL
AMPLIFIE R

 

 

 

I

 

TElETYPE

 

 

 

Block Diagram of the DA-60

 

 

R.F. UNIT

 

PRE‘AMP

 

 

 

Figure 4.

 

 

 

 

HYBRID
BOX

 

 

 

 

2 K Hz MODULATION

 

 

 

 

PROBE

 

 

Block Diagram of the Lock System

 

 

 

 

 

 

CHAPTER IV

RESULTS

THE NON—EXCHANGING SYSTEM

The goal of this study was to determine the extent to which the
crypt protects the complexed cation from neighboring species in
solution. Figure 5. shows a diagram of the complexed cation. From
the structure of the cryptate, one would expect very little inter-
action between the cation and the environment outside the crypt. A
rather symmetric environment is provided for the cation by the crypt
which, in the absence of distortion, would produce relatively narrow
lines. We expected therefore, that the chemical shifts and linewidths
of the complexed cation would be independent of the solvent. Table 1
shows the chemical shift of the complexed cation in several solvents.

In most cases, the chemical shift is relatively independent of
solvent but there are four noticable exceptions to this rule; namely
water, acetonitrile, acetone and ethylenediamine (EDA). One possible
explanation for the behavior of these four solvents might reside in
the fact that the geometry of the crypt provides small holes through
which interaction with polar groups might take place. water, acetone,
acetonitrile and EDA all have small, polar residues whereas the other
solvents (except methanol) have larger polar groups. The holes in the
crypt might be more conducive to interactions with small molecules or
polar groups than to large ones and could conceivably produce the
observed behavior. Another possibility is that the cation might not be
completely enclosed by the crypt in these solvents.

Naturally, this study was not without its problems, the most serious
of which was solubility. Table 1 also lists those systems in which the
solubility of the complex was not high enough to observe by using NMR.

It is worth noting that crypt and the salt were soluble in these

14

15

 

Figure 5. Space Diagram of the Complexed 23Na Cation.
solvents by themselves but together they precipitated from solution.

THE EXCHANGING CASE

 

In continuation of the results published by Ceraso and Dye (16), this
work was designed to investigate the solvent dependence of the release
of the sodium ion from the crypt. Four solvents were examined;
tetrahydrofuran (THF), water, pyridine and EDA. The exchange had been
studied in water previous to our work by utilizing proton NMR (13-15)
so that a comparison of the results from proton and 23Na NMR would be
interesting. The study of several other systems was also attempted but
was discontinued because the chemical shift was not large enough, or the
two absorptions were too broad, thus producing only one broad peak.

Sodium tetraphenylborate (NaTPB) in nitromethane and in propylene

Table l.

Solvent

PYRIDINE
DMF
PROPYLENE CARBONATE
THF

ACETONE
ACETONITRILE
METHANOL
WATER

EDA

DMSO
NITROMETHANE
WATER

WATER

ETHYL AMINE
ETHYL AMINE
ETHYL AMINE
METHANOL
BENZENE
ACETIC ACID
EDA

THF

Salt
NaTPB

NaTPB
NaTPB
NaTPB
NaTPB
NaTPB
NaI
NaTPB
NaBr
NaTPB
NaTPB
NaCl
NaTPB
NaI
NaTPB
NaSCN
NaTPB
NaTPB
NaClO
NaI

NaI

16

The Chemical Shift of 23

Cone.

0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
0.4

0.4

I —--

a) Full-width at half-height

b) Referenced to 3M aqueous NaCl at 40°C

c) Referenced to saturated aqueous NaCl at 40°C

COMPLEX

APPM
13.1

13.4
13.2
12.7
10.1

9.5
11.9

9.2
11.3
11.2

11.5

Na in Several Solvents

-13.0

0.7

15.6

17
carbonate as well as NaI in acetonitrile yielded this type of behavior.
The systems ultimately used for rate studies were 0.4 M Nal and
0.2 M crypt in water, 0.6 M NaBr and 0.3 M crypt in EDA, 0.4 M NaTPB
and 0.2 M crypt in pyridine and 0.4 M NaTPB and 0.2 M crypt in THF.

The modified Bloch equations appropriate to our system are

v Y 1 ° [:32 + T2
where
S = £A-+ EB +'__1;__,-T(w -w)(w 'm) (23)
T2A T23 T2AT23 B

 

U = 1 + T(pA/T2A + pB/TZB) (24)
= _ (wA-w) ( -w)

T (pAmA + pBwB w) + T [—13—]; + “32A (25)

V = r(pBwA + pAwB -w) (26)

where pA is the population at site A and T is the lifetime of inter-
action defined by

'l' ._. TATB (27)

TA + TB

TZA’ T23, wA and mg were measured directly in separate experiments, and
are tabulated in Tables 2 through 5; PA and p3 were fixed by the initial
concentration of salt and crypt so that r and the amplitude were the
only variables in our system.

These equations define the lineshape of a system at slow exchange

to be two separate absorptions corresponding to nuclei in two separate

18

Table 2. The Variation of the Linewidth and Chemical Shift of the
Complexed and Free 23Na Cation with Temperature in EDA
Temp(°K) -% x 103(°K) Av:(hz) T2(msec) PPMb
COMPLEXEDC
293.4 3.409 90.1 3.534 11.1
299.8 3.336 76.7 4.151 11.4
305.5 3.274 67.5 4.714 11.6
308.3 3.244 61.1 5.208 11.5
314.6 3.179 53.7 5.976 11.6
321.5 3.111 47.0 6.773 11.9
325.6 3.072 43.4 7.332 11.8
332.2 3.011 38.1 8.347 11.9
340.9 2.934 33.5 9.508 11.9
FREEd

293.8 3.404 85.1 3.742 -13.10
299.5 3.340 73.9 4.306 -13.0
305.3 3.276 65.2 4.886 -12.9
311.2 3.214 59.0 5.400 -12.9
316.7 3.158 53.0 6.001 -12.9
322.3 3.103 48.3 6.593 -12.84
328.1 3.048 43.3 7.355 -12.8
333.2 3.002 40.0 7.956 -12.88
337.7 2.962 37.1 8.570 -12.71
343.3 2.913 34.0 9.370 -12.77

a) Full-width at half-height in Herz i_2 Herz, referenced to
saturated NaCl of 11.9 Herz width.

b) Referenced to

c) Concentration

d) Concentration

saturated aqueous NaC1I:_3 Herz.

0.6 M NaBr.

0.3 M crypt, 0.3 M NaBr.

19

Table 3. The Variation of the Linewidth and Chemical Shift of the
Complexed and Free 23Na Cation with Temperature in THF

Temp(°K) -% x 103(°K) Av:(hz) T2(msec) APPMb
COMPLEXEDC
292.7 3.415 58.2 5.468 12.61
298.3 3.353 53.4 5.890 12.76
303.5 3.295 48.5 6.561 12.9
308.6 3.241 45.5 6.996 13.0
315.3 3.172 42.4 7.512 13.2
319.8 3.127 39.6 8.030 13.2
326.4 3.064 36.6 8.707 13.3
332.7 3.006 34.4 9.247 13.3
337.4 2.964 36.7 9.739 13.4
341.6 2.928 31.8 10.011 13.4
344.1 2.907 31.2 10.204 13.5
FREEd
298.9 3.346 35.3 9.007 8.1
303.9 3.291 34.5 9.226 8.2
308.6 3.241 33.8 9.428 8.3
316.0 3.165 32.7 9.737 8.4
321.1 3.115 32.3 9.849 8.5
326.3 3.065 31.8 10.011 8.6
332.9 3.004 31.3 10.179 2.9
338.0 2.959 31.1 10.245 2.9
343.3 2.913 30.9 10.317 3.0

a) Full-width at half-height in Herz :_2 Herz, referenced
saturated aqueous NaCl of 12.3 hz width.

n
O

b) Referenced to saturated aqueous NaCl :_3 Herz.

c) Concentration 0.2 M crypt, 0.2 M NaTPB.

d) Concentration 0.4 M NaTPB.

,-

20

Table 4. The Variation of the Linewidth and Chemical Shift of the

Complexed and Free 23Na Cation with Temperature in Pyridine

Temp(°K) -% x 103(°K) Av:(hz) T2(msec) APPMb
COMPLEXED C
298.7 3.348 52.3 6.084 13.1
306.1 3.267 47.2 6.746 13.2
311.8 3.208 44.0 7.227 13.3
316.9 3.156 41.3 7.699 13.4
328.3 3.047 35.3 9.021 13.5
334.6 2.989 33.0 9.666 13.5
342.0 2.924 31.0 10.278 13.6
348.1 2.873 29.1 10.924 13.7
355.8 2.811 27.4 11.605 13.7
361.8 2.764 25.7 12.364 13.8
375.4 2.664 24.6 12.96 13.9
382.4 2.615 23.1 13.796 13.5
387.2 2.583 23.7 13.435 14.0
394.4 2.537 23.4 13.575 13.9
401.8 2.489 23.5 13.527 13.9
407.0 2.457 22.6 14.057 13.9
413.4 2.419 23.2 13.714 13.8
FREEd
295.8 3.383 33.6 9.48 -0.3
318.2 3.145 28.3 11.23 0.3
330.8 3.025 25.2 12.38 0.6
342.2 2.924 24.1 13.19 0.7
353.5 2.830 23.1 13.78 0.9
361.5 2.768 23.6 13.48 1.1
374.0 2.675 23.1 13.79 1.3
385.6 2.595 23.0 13.84 1.4
398.6 2.510 23.1 13.79 1.7
407.0 2.458 24.7 12.91 2.1

21

Table 4 (continued)

413.5 2.420 24.1 13.19 2.3
418.0 2.393 24.7 12.91 2.3

a) Full-width at half-height in Herz + 2 Herz, referenced to
saturated aqueous NaCl of 12.3 hz width.

b) Referenced to saturated aqueous NaCl :;3 Herz.

c) Concentration = 0.2 M Crypt, 0.2 M NaTPB.

d) Concentration = 0.4 M NaTPB.

Table 5.

Temp(°K)

276.0
281.5
286.6
292.4
294.2
298.2
302.9
308.5
313.8
319.1
323.9
327.8
334.0
339.3

281.0
287.1

294.4 f

306.5
309.4
317.4
325.9
330.5

22

The Variation of the Linewidth and Chemical Shift of the

Complexed and Free 23Na Cation with Temperature in Water

%-X 103(°K) Av:(hz) T2(msec) APPMb
COMPLEXEDC
3.624 170.6 1.866 8.2
3.553 144.3 2.206 8.4
3.490 117.9 2.699 8.6
3.421 103.9 3.063 8.8
3.400 94.7 3.361 9.2
3.354 83.0 3.836 9.2
3.302 79.0 4.027 9.2
3.242 63.5 5.013 9.6
3.187 57.2 5.564 9.8
3.134 52.4 6.079 10.0
3.088 47.6 6.692 10.2
3.051 43.8 7.268 10.2
2.995 40.0 7.956 10.4
2.948 36.8 8.643 10.6
FREEd

3.56 17.8 17.88 ---

3.49 14.9 21.36 0.9
3.40 13.8 23.07 0.9
3.26 11.8 26.98 ---

3.23 11.3 28.17 1.2
3.15 11.1 28.68 1.5
3.07 11.1 28.68 ---

3.03 11.1 28.68 1.5

a) Full-width at half-height in Herz i.2 Herz in the complexed
case and l Herz in the free case, referenced to saturated
aqueous NaCl of 12.8 hz.

b) Referenced to saturated aqueous NaCl :_3 hz.

c) Concentration = 0.2 M Crypt, 0.2 M NaI.

d) Concentration = 0.4 M NaI.

10.0

9.0

8.0

Té(nsoc)

7.0

6.0

10.0

9.0

8.0

7.0

Té(nsoc)

6.0

4.0 '

 

 

23

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310 3.1 3.2 1 3.3 374 3.5
$03

 

10
\o
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complexed
O\\\\\‘
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*\~\“‘:;
3:0 3:1 . 3:2 1 323 3.4 3T5
rm” '

Figure 6. The Variation of T with 1/T for EDA

2

10.“

10.2

10.0

9.8
1%(nsec)
9.6

9.4

9.2

10.0

9.0
Té(nsec)

8.0

7.0

6.0

 

24

 

1
O
ITTT‘O
at \O
.. o
0
1h
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1t 0\
.. ¢>\\\\\>5
3.0 3.1 3.2 ' 4“
1 ‘ 3 3 3 4
T3103
W?
O
‘\
up 0
\O
\o

 

Figure 7. The Variation of T with l/T for THF

2

15.0

luflo

13.0

T2(nsec)

12.0

11.0

10.0

15.0

14.0

13.0

11.0
15(maoc)

10.0

9.0

700

Figure

 

25

 

 

 

 

.. /°
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2:.4 I 2:.6 TA 2:.8 I 5.0 J i2 4* 334 4
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The Variation of T2 with l/T for Pyridine

 

26

 

 

 

 

 

31.0 1'

p
2°° -o—o o“ o
27.0 1,. o
25.0 ""
23.0 I»

12(nec)
21.0 3‘
free
19.0 0
17.0 ..
31 32 I3, 0, 3.1» 35 36 3‘?
10.0 T
9.0 1r
8.0 .1 \
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M .. complexed ‘o
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2.0 .. \0
3° 3‘1 3.2 3.; a.» 3.5 3.6 3.7 3.8
T303

Figure 9. The Variation of T with l/T for Water

2

27

sites. As the exchange becomes more rapid, these lines broaden and
begin to move together until, at more rapid exchange, they coalesce
into one broad peak. If the rate of exchange is further increased,
the broad absorption narrows considerably. This behavior is
illustrated in Figures 10-13.

The lineshipes which are obtained in the four systems studied
were fit to the modified Bloch equations by KINFIT in order to
obtain T. A five parameter fit was utilized in each case. These
included a normalization constant, a baseline correction constant,

a second order phase correction constant, a frequency correction
constant, and T. Figures 14-17 show typical computer fits of these
lineshapes. X corresponds to the input data whereas 0 corresponds
to the calculated value and = to those points in which the calculated
value is equal to the input value within the resolution of the
print-plot. The exchange in each solvent yielded very good results,

with standard deviations in T less than 5%. r, and T for

T24 2B
each temperature are shown in Tables 6-9 and are displayed graphically

in Figures 18-21. Table 10 shows the activation energies and AGO+

for the exchange in each solvent.

SUSCEPTIBILITY OF ETHYL AMINE

 

It has been reported by Live and Chan (24) that the magnetic
susceptibility correction with an internal capillary reference to be

made in a Varian rA-60 spectrometer is different from that in a

28

 

21 .' 42

Figure 10. Typical2 pectra Illustrating the Temperature Dependence
of the Na NMR Lineshape for EDA

29

Figure 11. Typicalz§pectra Illustrating the Temperature Dependence
of the Na NMR lineshape for THF

 

30

116

 

102 121

 

Figure 12. Typicalzgpectra Illustrating the Temperature Dependence

01' the Na (NMR Lineshape for Pyridine

31

 

 

Figure 13. Typical2 pectra Illustrating the Temperature Dependence
of the Na NMR Lineshape for Water

32

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Table 6. The Temperature Dependence of the Exchange Time in EDA
T(°K) '%-x 103 1(msec) 0a k log k
288.7 3.464 4.81 0.176 103.9 4.64

294.5 3.396 4.01 0.104 124.6 4.83

303.6 3.294 2.338 0.033 213.9 5.366
309.4 3.233 1.603 2.016 311.9 5.742
311.2 , 3.214 1.413 0.013 354.0 5.869
314.6 3.179 1.126 0.008 444.0 6.096
315.6 3.169 1.048 0.008 477.0 6.168
318.2 3.143 0.0913 0.0076 561.0 6.330
323.4 3.093 0.6154 0.0045 812.4 6.700
327.0 3.059 0.4862 0.0035 1028.4 6.936
334.0 2.995 0.3111 0.0031 1607.2 7.382
342.2 2.923 0.1918 0.0016 2606.6 7.866
349.6 2.861 0.1238 0.0010 4040.1 8.304

a) Linear estimate of the standard deviation of

T.

37

Table 7. The Temperature Dependence of the Exchange Time in THF.

 

a) Linear estimate of the standard deviation of

To

T(°K) 1/T x 103 T(msec) 0? k log k
308.7 3.240 2.43 1.2 20.62 3.03
312.6 3.200 20.20 0.80 24.76 3.209
317.3 3.152 14.98 0.44 33.37 3.508
'319.0 3.135 12.75 0.31 39.22 3.669
322.6 . 3.100 10.21 0.20 48.98 3.891
325.4 3.074 8.43 0.14 59.29 4.08
330.0 3.031 6.090 0.090 82.10 4.408
332.3 3.010 5.334 0.081 93.74 4.541
336.0 2.977 4.063 0.050 123.1 4.813
338.2 2.957 3.510 0.035 142.5 4.959
341.4 2.930 2.876 0.030 173.9 5.158
344.6 2.903 2.363 0.025 211.6 5.355
347.8 2.876 1.872 0.019 267.2 5.588

38

Table 8. The Temperature Dependence of the Exchange Time in Pyridine

 

3) Linear estimate of the standard deviation of

To

T(°K) 1/1 x 103 T(msec) 0a k log k
328.4 3.046 32 4.3 15 2.7
339.9 2.943 22 2.1 23 3.1
346.5 2.886 15 1.4 32 3.5

- 354.6 2.821 9.81 0.53 50.9 3.93
366.4 2.730 5.31 0.17 94.2 4.55
371.9 ' 2.689 3.82 0.11 131 4.88
375.2 2.666 3.157 0.090 158.4 5.065
378.6 2.642 2.815 0.050 177.7 5.180
382.8 2.613 2.333 0.058 214.3 5.367
389.6 2.567 1.609 0.019 310.8 5.739
399.0 2.507 1.013 0.011 493.6 6.202
402.6 2.484 0.8607 0.0080 580.9 6.365
408.6 2.448 0.6611 0.0060 756.3 6.628
415.3 2.408 0.5051 0.0060 990.0 6.898

39

Table 9. The Temperature Dependence of the Exchange Time in Water

3 a

 

a) Linear estimate of the standard deviation of

T.

T l/T X 10 T(msec) o 1/2 T log k
276.2 3.621 35 3.1 14 2.7
285.2 3.507 11.34 0.46 44.10 3.786
295.4 3.386 4.335 0.067 115.3 4.748
. 296.8 3.370 3.875 0.050 129.0 4.860
300.0 3.333 2.877 0.040 173.8 5.158
302.4 ' 3.307 2.178 0.023 229.6 5.436
303.7 3.292 2.030 0.022 246.3 5.507
306.9 3.258 1.616 0.020 307.4 5.728
310.2 3.224 1.120 0.020 415.0 6.031
312.5 3.201 0.8918 0.013 566.7 6.340
319.1 3.134 0.5122 0.0090 976.2 6.884
325.4 3.073 0.3333 0.0080 1500 7.313

40

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44
superconducting HR-220 because of the different field geometries.

The equations are

20

___ ref

scorr = dobs + 3 (X0 ' Xv ) (DA-60) (28)
51. ref

acorr = dobs - 3 (X0 ‘ Xv ) (HR‘ZZO) (29)

Since spectrometers with both of these geometries were readily
available to us, we presumed that by running an internally referenced
sample in the two instruments, we could directly obtain the magnetic

susceptibility of that sample. Solving these equations for xgef we have

0 21T obs obs (30)

THF, internally referenced with a saturated aqueous NaCl solution
was run first as a check on the method and yielded a value of -0.557
which is only a four percent difference from -0.577, the literature
value (23). Next a .3 M NaTPB solution in THF was internally
referenced by a saturated NaI solution in ethyl amine. Since the

magnetic susceptibility of THF is known,

 

ref 1 385.5 1437.
= 0.577 + _ - - = _ , 31)
X" 211 [15.87 60.06] 0 634 (

This method of determining magnetic susceptibilities has one big
advantage over the usual Gouy balance method; namely, the ease of the

experiment. The entire undertaking can easily be completed in one

afternoon.

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CONCLUS IONS

CHAPTER V

In this study we have utilized extremely powerful methods of data
acquisition and analysis in order to precisely define these systems.

As previously mentioned, T and m were measured in separate experi-

2
ments, so the rate constants could be reliably determined. We also
used a complete lineshape analysis, fitting the spectra at many tem-
peratures to the appropriately modified Bloch equations, which was a
procedure heretofore rarely utilized in NMR rate analyses. This has
also been one of the first rate studies ever attempted in which T2A
and T2B were appreciably different and since these parameters were so
well defined, they provide a rigorous test of the applicability of the
Bloch formulation to these systems.

There are several sources of error which could become important in
this study since they could lead to serious distortion of the NMR line-
shape. These include filtering, pulse feedthrough, saturation, delay
time distortions and second order phase correction. Most of the above
may be minimized instrumentally or else made provision for in computer
fitting of data. Delay time distortion is the only variable which
causes lineshape distortion which is not easily compensated for.

The delay time is the time between the rf pulse and the beginning
of data acquisition. This is dead time which allows the receiver
circuitry to recover from the large rf pulse and causes distortions in
the following way. If two resonances in a spectrum are of very differ-
ent T2, then the faster relaxing nucleus would be attenuated to a much
greater extent than the more slowly relaxing nucleus by the delay time

and thereby "saturated" to a higher degree than the other. For example,

the exchange in water involves a very broad (mlOO hz) complexed sodium

46

47

resonance and a narrow (~10 hz) free sodium resonance. The error in
this case due to delay time distortions is less than 52 for a typical
delay of lOOusec, and can be corrected with PA and PB adjustments. In
general, these distortions cause little trouble and the data very
closely fit the lineshapea predicted by the modified Bloch equations

- with standard deviations in the computer fitting of less than 52.

The rate constants which are reported in Tables 6-9 are defined

by the following equations:

k
+ 1 +
Na ~1-C222 “___? NaC222
2

1A, the mean lifetime of the sodium ion resident in the cryptand, is
related to the rate constant for the release of the cation, k2, by the
following expression:

rate of removal of sodium ion from.cryptand by exchange_

1
?' the number of complexed sodium ions

A

_ k2 ’[NaC+] _ k

[1180*] 2

k +
‘l'_ 1 [Na ] [01, _ k [C]
TB [Na+] l

The values are reported as k2, the rate constant for the decouples?
ation.

NO trend was observed between either donor number or dielectric
constant of the solvent and the thermodynamic data reported in Table 10.
Cahen, Dye and Popov (25) reported a rough correlation between donor

number and the activation energy of exchange for lithium cryptates, but

48

this correlation is not observed with sodium. The positive entropy

of activation in the water case indicates participation of the solvent
in the activated complex. This may be explained by the fact that water
has a very high dielectric constant and interacts much more strongly
with the sodium ion than the large organic complexed ion. The transi-
.tion state seems to be composed of the partially solvated, partially
complexed ion.

Several areas of this study pose interesting problems for further
research. 0f most interest would be the determination of the formation
constants of sodium with 0222 in these and other solvents. Calorimetry
would be useful in determining heats of formation. Since the formation
constants are known in six non-aqueous solvents for cesium salts (26),
it has been suggested by Professor Dye that a competitive complexation
for the 0222 between sodium ion and cesium ion be undertaken. This
"bootstrap" approach could be undertaken using a variety of ligands and
metal cations to competitively complex sodium ion and 0222 in order
to determine this formation constant.

Another interesting problem for study is presented by the non-
exchanging system in pyridine. In this solvent, the plot of T2 with
the inverse of temperature showed a curved behavior which could not be
explained by normal viscosity effects. Since this effect was observed
in both the free and complexed case, ion-pairing and direct solvent
effects would seem to be ruled out. Perhaps a concentration depend-
ence of this phenomenon would provide insight into its origin.

Finally, a competitive study using two different cations of similar

49

formation constant with a cryptand would be very interesting since the
NMR facility at Michigan State University is fully multinuclear. The
exchange phenomenon of both nuclei could be documented easily and
utilized as a yet more rigorous test of the Bloch formulation. Forma-
tion constants and other properties of these cryptands will become
.increasingly important as both the chemical industry and the academic
community discover the complexing ability and selectivity of these
cryptands and as they begin to utilize them in areas such as ion chrom-

atography, specific ion leachers, etc.

LITERATURE CITED

CHAPTER VI

(l)
(2)
(3)
(4)
(5)
(6)

(7)

(8)

(9)
(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

LITERATURE CITED

C. Deverell and R. E. Richards, Mol. Phys., 10, 551 (1966).
R. Erlich and A. I. Popov, J. Amer. Chem. Soc., 93, 5620 (1971).

M. Harlem and A. I. Popov, J. Amer. Chem. Soc., 94, 1431 (1972).

 

E. G. Bloor and R. G. Kidd, Can. J. Chem., 46, 3425 (1968).

 

E. G. Bloor and R. G. Kidd, Can. J. Chem., 50, 3926 (1972).

R. Erlich, M. S. Greenberg and A. I. Popov, Spectrochimica Acta,
29A, 543 (1973).

M. S. Greenberg, R. L. Bodner and A. I. Popov, J. Phys. Chem.,
77, 2449 (1973).

 

J. A. Pople, W. G. Schneider and H. J. Bernstein, "High
Resolution Nuclear Magnetic Resonance", MbGraw-Hill, p. 218, 1959.

D. E. Woessner, J. Chem. Phys., 35, 41 (1961).

 

C. J. Pederson, J. Amer. Chem. Soc., 86, 7017 (1967).

E. Schori, J. Jagur-Grodzinski, Z. Luz and M. Shporer, J. Amer.

Chem. Soc., 93, 7133 (1971).

K. H. WOng, G. Konizer and J. Smid, J. Amer. Chem. Soc., 92,
666 (1970).

B. Dietrich, J. M. Lehn and J. P. Sauvage, Tetrahedron Letters,
2885 and 2889 (1969).

J. M. Lehn, J. P. Sauvage, B. Dietrich, J. Amer. Chem. Soc.,
92, 2916 (1970).

 

B. Dietrich, J. M. Lehn, J. P. Sauvage, J. C. S. Chem. Comm.,
15 (1973).

 

J. M. Ceraso and J. L. Dye, J. Amer. Chem. Soc., 95, 4432 (1973).

 

E. B. Baker, L. W. Burd and G. N. Root, Rev. Sci. Inst., 36,
1495 (1965)

See Appendix.
See Appendix.

50

(20)
(21)

(22)

(23)
(24)
(25)

(26)

51

V. A. Nicely and J. L. Dye, J. Chem. Ed. , 48, 443 (1971).

The lock probe was designed and built by Dr. David Wright and
Dr. Joseph Ceraso.

M. S. Greenberg, Ph.D. Thesis, Michigan State University, East
Lansing, Michigan, 1974.

J. M. Ceraso and J. L. Dye, J. Chem. Phys. , 61, 1585, (1974).

D. B. Live and S. 1. Chan, Anal. Chem. , 42, 791 (1970).

 

Y. M. Cahen, J. L. Dye and A. I. Popov, J. Chem. Phys. , 79,
1292 (1975).

E. Mei, Ph.D Thesis, Michigan State University, East Lansing,
Michigan, 1977.

APPENDIX

CHAPTER VII

DESCRIPTION OF THE MODIFICATION TO THE NICOLET 1074 VERSION OF FTNMR

IN ORDER TO DUMP DATA

The Nicolet 1074 version of FTNMR can be modified in order to dump

data in octal directly from the teletype.

The first channel to be

printed out may be selected as well as the number of points and the

increment between them. The changes to be made are listed below.

A core map for the output routine is also listed.

CORE LOCATION

0105

0106

3205

3206

3211

3357

DEPOSIT

First channel # to be
printed out in octal

# of points to be
printed out in octal

1106 / TAD 106
7000 / NOP
1105 / TAD 105

4020 / JMS 20

/ Subroutine to increment channel # by INCREMENT

20

21

22

23

52

0000
1111 / TAD WA
1025 / TAD INCREMENT

3111 / DCA.WA

24

25

0105
0106

0025

53

DEFAULT

5420 / JMP I 20

INCREMENT # 1n octal

0000
0000

0001

To dump data from.the memory of the Nicolet 1074 interfaced

to a PDP8-E, halt the program, load address 3200 and depress switches

10 and 11. Then depress start on PDP8-E and computer control on the

NICOLET 1074.

0 - 4
5 - 7
10 - 37
40 — 64
65 - - 67
70 - 77
100 - 102
103 - 106
107 - 177
200 - 362
365 - 374
400 - 447
450 -. 517
520 - 560
600 - 643
650 - 674
700 - 723
725 - 747
750 - 772
1000 - 1157
1200 - 1253
1255 - 1372
1400 - 1457
1460 - 1504
1510 - 1571
1600 - 1770
2000 - 2132
5 2150 - 2174
2200 - 2337
2340 - 2377
2400 - 2577
2600 - 2777
3000 - 3135
3142 - 3174

3200 - 3375 -
. 3400 - 5377
' 5400 - 5577
5600 - 7577

54

FFT MAP

 

FLOATING POINT POINTERS

----- 2 0-25 USED BY OUT PUT ROUTINE
USED BY FLOATING POINT PACKAGE

15' FT SUBROUTINE POINTERS

USED BY FFT PROGRAM

----- 105-106 USED BY OUTPUT ROUTINE
USED BY FFT PROGRAM

SORT, PASS ONE, and BIT INVERT
INITIALIZE 1070

FLOATING POINT GET

FLOATING POINT PUT

GET WITH FIXED TO FLOATING POINT CONVERSION
GET PROPER PAIR SUBROUTINE

PUT PROPER PAIR SUBROUTINE

. DATA CHECK ROUTINE

SPREAD SUBROUTINE
INCREMENT PROPER PAIR INDEX
FFT EXECUTNE PROGRAM

' FFT MAIN PROGRAM

FFT DISPLAY SUBROUTINES
MAGNITUDE PROGRAM

APODIZATION PROGRAM

CHANGE ANGLE SUBROUTINE
MULTIPLICATION BY COMPLEX WEIGHTS SUBROUTINE
ORDER SUBROUTINE
FIXED-FLOATING POINT CONVERSION
PHASE CORRECTION SUBROUTINE
CONSTANT'S STORAGE

FREE PAGE

FREE PAGE

DATA SORT SUBROUTINE

DFLOAT SUBROUTINE

FFT INPUT-OUTPUT PROGRAM

FFT SINE LOOKUP TABLE

SINE 8. COSINE SUBROUTINES
FLOATING POINT PACKAGE #1

WITH ADDRESSES:

65478 set to 54008
65503 set to 55038

55

DESCRIPTION OF THE MODIFICATION RELAX 2 IN ORDER TO DUMP DATA

The data output portion of RELAX 2, a program written by David
wright of Michigan State University for computer controlled timing and
_data aquisition for two pulse experiments was slightly modified in order
to dump data from the Nicolet 1083 computer. The modifications made

were

CORE LOCATION DEPOSIT
1326 3001332 JMS OCTOUT (Print X)
1327 1330 JMP to 1330 (Y value)
1331 1335 (Forget Dwell)
1332 5051 (Address of OCTOUT)

1337 3001332 JMS OCTOUT (Print Y)

56

DESCRIPTION OF PROGRAM CONVERT

Program CONVERT is a computer program to convert data from octal to

decimal and order in a form compatible with KINFI'I'.

PROGRAM CONVERT

5

100
10

105
8
110

PROGRNM CONVERI(INPur-6s,ouIPuT-6s,runcn-65)
DIMENSION IX(2),IY(2),X(2),Y(2)
READ 100,4,3
IF(EOP(5LINPUT))999,10
FORMAT(2£10.2)

READ 105,(IX(I),IY(I),I-1,2)
IF(EOF(SLINPUT))S,8
IDRMAI<2010)
PRINT110,(IX(I),IY(I),I-1,2)
FORHAI(1X,2010)

Do 15 KP1,2

X(K)-Ix (K)

15 Y (K) IIY (K)

115
116
999

PRINT 115,(X(K),A,Y(K),B,K-1,2)
FORMAI(2(20X,P10.0,F10.8,Fl0.0,F10.0))
PUNCH 116,(X(K),A,Y(K),B,K!l,2)
FORMAT(2(F10.0,F10.8,Fl0.0,?10.0))

co T0 10

CONTINUE

END