ESTIMATES OF SOME mmmovmw
mom-mas or SALTS pf ALKAU
METAL moms AND A33Na NMR'

sm IN or EXCHANGE was
we METAL sowmns

Thesis for the Degree of M. S.
MICHzeAN ST ATE UNIVERSITY
CHARLES WESLEY ANDREWS

1975

 
  
 
 

  
 

I

L I If .3: A R Y
Michigan State
University

a
'v
'— mw—w—V s—u— -——— vv—

35337-915

 

 

ESTIMATES OF SOME THERMODYNAMIC PROPERTIES
OF SALTS OF ALKALI METAL ANIONS AND A
23Na NMR STUDY OF EXCHANGE RATES

IN METAL SOLUTIONS
By
Charles Wesley Andrews
ABSTRACT

Extensive use was made of Born-Haber type calculations
in order to estimate thermodynamic properties of the salts
of the alkali metal anions. One cycle used to illustrate
the ease with which M- forms involved the formation of a
hypothetical salt M+M- by the process ZMS + M+M_. The
most reasonable values for the enthalpy of formation indi-
cate that since a crystalline salt which contains Na- has
been synthesized, such solid salts should be possible for
all of the other alkali metals as well provided the cation
can be suitably stabilized. A second cycle was employed
in which the enthalpy change was estimated for the reaction
ZMS + CS + MC+M-, in which C is a cryptand complexing agent.
However, several terms in this cycle could be evaluated
only by using additional energy cycles and questionable
assumptions. This led to the use of a more reliable "dif-

ference calculation". The difference calculation invoked

Charles Wesley Andrews

a stability criterion in which the alkali anion salts (MC+M-)
were compared to a reference salt, NaC+Na_, which is known

to be stable. In the reference salt, C represents 2,2,2

I I . . . O O —
Cryptand (C222). The stability criterion is AGM AGNa —
0 O o o . .
AHM AHNa T (ASM ASNa) : O in which M and Na represent

the salts MC+M- and NaC+Na-, respectively. Results of this
difference calculation indicate that except for CsC§52Cs-
all the alkali metals should be able to form salts which
contain anions of the alkali metals. The calculation in
the case of the lithium salt involved 2,1,1 cryptand.

The NMR investigation utilized 18—crown—6 (18-C-6) to
study the exchange of Na_ with NaC+ gig NMR. Unlike metal
solutions which contain NanzzNa- and are in the slow ex-
change limit between 0° and -40°C, solutions which contain
18-C-6, Na, and methylamine are exchange-broadened and the
NaC+ and Na_ peaks coalesce at —5°C. The line shapes of
the NaC+, Na- spectra were fit with a generalized nonlinear
least squares program to determine the exchange time T.

The variation of T with temperature and the concentration
of various species permits the exchange pathways to be
examined. While the results are very preliminary at this

stage, two mechanisms appear to be competing in the NaC+,

Na- exchange. They are

Nac+ Z Na+ + c
_ (A)

Na : Na+ + 2e

and

Charles Wesley Andrews
(B)

These mechanisms are qualitatively consistent with the
fact that the exchange times and the apparent activation
energies, Ea' are dependent upon the ratio [Na-]/[NaC+]
as well as the presence of excess crown. The values for Ea
range from l8.2:.3 kcal mole"l for equimolar amounts of
Na- and NaC+ to 25.2:l.2 kcal mole_l when excess crown is

present.

ESTIMATES OF SOME THERMODYNAMIC PROPERTIES
OF SALTS OF ALKALI METAL ANIONS AND A
23Na NMR STUDY OF EXCHANGE RATES

IN METAL SOLUTIONS

BY

Charles Wesley Andrews

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirement

for the degree of

MASTER OF SCIENCE
Department of Chemistry

1975

To My Family

For Their Prayers

ii

ACKNOWLEDGMENTS

The author wishes to express his appreciation to Professor
James L. Dye for his guidance and encouragement as a teacher,
a scientist, and a friend.

He would also like to thank Captain Steve Landers, USAF,
and Joe Ceraso for their assistance with the NMR studies.

The author would also like to acknowledge Mike DaGue,
Elizabeth Mei, Guan-Huei Ho, and Mike Yemen for their friend-

ship and assistance.

iii

TABLE OF CONTENTS

Chapter

LIST OF TABLES. . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . .

CHAPTER 1 - Historical. . . . . .
The Nature of Alkali Metal
Solutions. . . . . . . . . . .
The Alkali Anion . . . . . . . . .

The Role of Complexing Agents. . .

The Role of NMR Studies. . . . . .

CHAPTER 2 - Experimental. . . . . . . .
Instruments. . . . . . . . . . . .
Data Analysis. . . . . . . . . . .

Chemical and Solvent Purification.
Sample Preparation . . . . . . . .

Temperature Measurement. . . . .

CHAPTER 3 - Thermodynamic Considerations

of Alkali Anion Formation .
Rationale. . . . . . . . . . . . .
A Hypothetical Salt. . . .

Complete Born-Haber Cycle for
MC+M‘ Formation. . . . . . . .

Enthalpy of Cryptand Sublimation .
Enthalpy of the Gas Phase Reaction
Lattice Energy . . . . . . .

A Difference Calculation of the
Born-Haber Cycle . . . . . . . . .

iv

Page

Vi

viii

11
12
12
14
15

15

18
19
19

23
26
27

3O

33

Chapter Page

Discussion. . . . . . . . . . . . . . . . . . 36

Possible Experimental Verification
of the Thermodynamic Cycles . . . . . . . . . 40

CHAPTER 4 — NMR Exchange Studies of
Alkali Metal Anion Solutions . . . . . 43

Rationale . . . . . . . . . . . . . . . . . . 44
Three Site Exchange Processes . . . . . . . . 47

Reduction of the Three-site Equa-
tions to Two-site Equations . . . . . . . . . 50

Information From Non-Exchanging
Systems . . . . . . . . . . . . . . . . . . . 54

18-C-6 Salt Exchange System . . . . . . . . . 56

Results of Na‘, 18-C-6 Exchange
Studies . . . . . . . . . . . . . . . . . . . 59

Uses of Other Complexing Agents . . . . . . . 63
Discussion of Results . . . . . . . . . . . . 74

REFERENCES....................78

Table

LIST OF TABLES

Page
Qualitative Trends in Metal Solution
Equilibria . . . . . . . . . . . . . . . . . . 7
Results for Hypothetical Salt
Calculation. . . . . . . . . . . . . . . . . . 24
Results of Energy Cycle Used to
Determine the Enthalpy of the Gas
Phase Reaction . . . . . . . . . . . . . . . . 31
Results of Born-Haber Cycle Calcula-
tion for MC+M- Formation . . . . . . . . . . . 34

Results of the Difference Calcula-

tion Using the Stability Criterion . . . . . . 37
Possible Exchange Mechanisms and

Expressions for l/Té . . . . . . . . . . . . . 53
The Variation of the Linewidth and

Chemical Shift of the Free and Com-

plexed 23Na Cation with Temperature. . . . . . 55
The Variation of the Chemical Shifts,

A, and the Transverse Relaxation Times,

T2 for 18-C-6, NaI Exchanging System.
Concentrations of Complexed and Free

Sodium Ions are Equal. . . . . . . . . . . . . 58
Composition of Samples Used for

Line Shape Fitting . . . . . . . . . . . . . . 60

vi

Table Page

10 The Temperature Dependence of the

Exchange Time T and l/TB for

Sample 1 . . . . . . . . . . . . . . . . . . . 64
11 The Temperature Dependence of

the Exchange Time T and l/TB for

Sample 2 . . . . . . . . . . . . . . . . . . . 65
12 The Temperature Dependence of

the Exchange Time T and l/TB for

Sample 3 . . . . . . . . . . . . . . . . . . . 66
13 The Temperature Dependence of

the Exchange Time T and l/TB for

Sample 4 . . . . . . . . . . . . . . . . . . . 67
14 The Temperature Dependence of

the Exchange Time T and l/TB for

Sample 5 . . . . . . . . . . . . . . . . . . . 68
15 Apparent Activation Energy and l/TB

(0°C) for Alkali Anion to Complexed

Cation Exchanging Systems. . . . . . . . . . . 70
16 The Variation of the Linewidth

and Chemical Shift With Temperature

for Two Solutions Which Contain the

lS-C-S Complexing Agent and NaI. . . . . . . . 71
17 The Variation of the Linewidth and

Chemical Shift of NaC+ and the Chemical

Shift of Na‘ with Temperature for the

lS-C-S System in Methylamine . . . . . . . . . 73

vii

LIST OF FIGURES

Figure Page
1 Examples of Two Classes of Complexing
Agents . . . . . . . . . . . . . . . . . . . . . 5
2 Vessels for Sample Preparation A. For

Air Sensitive Solutions B. Sealable
NMR Tube for Salts . . . . . . . . . . . . . . . 16
3 Energy Cycle for a Hypothetical Solid

Salt . . . . . . . . . . . . . . . . . . . . . . 21

4 Born-Haber Cycle for MC+M- Formation . . . . . . 25
5 23Na NMR Spectra of Na+C222 and Na+

(18-C-6), Na- in Methylamine . . . . . . . . . . 45
6 23Na NMR Spectra of Na+ (18-C—6), Na—

in Methylamine at Various Temperatures . . . . . 46
7 Semilog Plot of Transverse Relaxation

Times vs Reciprocal Temperature for Free

NaI (CD) and a 1:1 Complex of NaI and

18-C—6 (0 ). The log of the Viscosity

of Methylamine is Plotted for Compari—

mmn (C) . . . . . . . . . . . . . . . . . . . . 57
8 Line Printer Plot of Sample 1 at +5.7°C

and -15.9°C. . . . . . . . . . . . . . . . . . . 61
9 Line Printer Plot of Sample 1 at —26.4°C

and -32.9°C. . . . . . . . . . . . . . . . . . . 62

viii

Figure

10

ll

12

Page
Arrhenius Plots of l/IB vs Reciprocal
Temperature for Sample 1 (0 ), Sample 2 ( 9),
Sample 3 (1:), Sample 4 ( a), and Sample
5 (x.) . . . . . . . . . . . . . . . . . . . . 69
23Na NMR Spectra of: A. Equimolar NaI
and lS-C-S in Methylamine B. 15-C—5, Na
in Methylamine . . . . . . . . . . . . . . . . 72

Plot of l/TB at 0°C vs (A) Na— Concentra-
tion (B) Population of Na_ Site/Population

of NaC+ Site (PC/PB) for Various Samples . . . 76

ix

CHAPTER 1

HISTORICAL

The Nature of Alkali Metal Solutions

The discovery by W. Weyl in 1863 of solutions of alkali
metals in ammonia opened up a new field of challenging chem-
istry that has to this day remained, in part, a mystery.
Metal ammonia solutions are characterized by high metal
solubility (SM-6M), large molar extinction coefficients,
rapid cation-electron exchange, phase separation at high con-
centrations and low temperatures (for Li, Na, K, and Rb) and
thermodynamic instability. These characteristics, coupled
with the lack of agreement among theoreticians about a suit-
able model, illustrate the complex nature of metal ammonia

solutions.1

For example, at the time of this writing a
controversy persists about the nature of the intermediate con-
centration range in metal ammonia solutions. One school
describes this concentration range as a solution composed of
microscopically inhomogeneous regimes in which the concentra-
tion fluctuates locally about either of two well-defined
concentration values. Opposing their view are those who
believe the intermediate range to be a region of continuous
concentration change.2

In general, metal ammonia solutions are described by
models which place reducing species in potential wells formed
by solvent molecules. The exact number, and nature of these
species, and how and when the trap is formed is still a matter
of debate.

Metal-amine and metal-ether solutions are very different

from metal-ammonia solutions. The former are characterized

by low solubility, distinct optical bands, greater instability,
and the presence of a number of distinct species.3 These
differences make the study of amine and ether solutions worth—
while. For example, the identification of a monomer, M,
(sometimes described as an ion pair between the solvated
electron and the cation) and the alkali anion M’, were made
possible because of the clear-cut esr spectra of M and the
metal-dependent optical absorption bands for M-. If these
species are present in ammonia solutions they give spectral
peaks which are buried under other bands or in some other

way do not yield distinct spectra.

The Alkali Anion

 

An interesting and controversial subject is the presence
or absence of alkali anions in metal solutions. Although
they were proposed a number of years ago for ammonia solutions
there was no specific evidence for their existence and it was
not until 1969 that Matalon, Golden, and Ottalenghi suggested
that the metal-dependent visible bands observed in metal-

amine solutions were due to Na”, K , Rb-, and Cs- metal ions.4
Much confusion about the metal-dependent bands existed prior
to that time because of contamination by sodium from the Pyrex

5 This contamination

glass used to make up the solutions.
obscured the interpretation of the spectra for a long while.
In addition to the evidence provided by the optical

absorption hand, there is now a host of other evidence which

verifies the existence of alkali anions. ESR measurements

indicate the diamagnetic nature of this species and the con-

solv.’ The

ductance of M- is very different from that of e
Faraday effect, oscillator strength, and kinetics studies
verify the stoichiometry of this species in amines and ethers.6
The isolation and characterization of a crystalline salt of Na-
and the NMR spectrum of the M- ion has caused the most excite-
ment since these studies provided the most convincing argu-

ment for the existence of "genuine" alkali anions.7'8

The Role of Complexing Agents

 

When a complexing agent of the crown9 or cryptandlo

class (see Figure 1) is added to a solution of an alkali metal
in an amine or ether, the solubility of the metal is greatly
increased. This increase in solubility is caused by the
ability of the cyclic polyether to complex the alkali cation.
This technique was suggested by V. A. Nicely11 when he noted
that many salts in the presence of a crown cyclic polyether
dissolve in nonaqueous solvents in which they are normally
insoluble. The effect of the crown and cryptand on the
equilibrium among the various species present in the amines

and ethers is clearly shown by the following set of equilibria:
M + M (1.1)

K
M_ 2,2 M+ + 2e (1.2)

2,2,2 C rypta nd

(C222)

W“.
C D

o o
k/°\)
2
18-C row n- 6
(18-C-6)

Figure 1. Examples of Two Classes of Complexing Agents.

M 1 M+ + e" (1.3)
K4
M+ + c : MC+ (1.4)

In general the equilibrium constants are not known and are
very difficult to obtain. However, certain trends as listed
in Table 1 can be established on the basis of the solubility,
optical spectra and esr spectra.

The proper choice of the type and concentration of the
complexing agent in many cases permits one to tailor the
nature of the solutions to meet his need. In general the cryp-
tand gives a higher metal solubility than the corresponding
crown compound. The symmetry of the complex also appears to
be an important factor in both crystal growth and NMR spec-
troscopy. When crown complexes are formed, the interaction of
the bound cation and the solvent is much greater than for
cryptates. This can cause large solvent effects and lead to
inclusion of solvent in many of the solid complexes. Similarly,
the alkali metal NMR line is greatly broadened as a result of
the asymmetric electric field gradient present in most crown

complexes.

The Role of NMR Studies

 

A major breakthrough came in 1974 when Dye and Ceraso
reported the NMR spectrum of the sodium anion in tetrahydro-

furan and in ethylamine.l3 Previously, only the paramagnetic

.Uw>uwwno soon #0: mm: ad

I. . U

.pm>ummno soon was mcfluufiamm mafimummwn AA 020

.Esnuommm mmm wnu CH mcfluuflamm mcfimnwmmn mw>wm £UH£3 mmflommm umEocoe map on muwmmu 2

Q

.mma ammfi .dm .dam 8 42 .flmzm .mmz "HOUHO ucw>HOmm

 

 

 

 

 

mmmmuocH
0 mo ousumc coma mocmmmo ou owuommxm usn :30cxca o+z m“ O++z Avv
M
3.: :3 .nm .m 62 $6865 2 M 3+ 2 2:
U l MM. I +
s s s \
oxflqv 62 x gm mo wmmmnocH n2 mw Imm++z Ame
mz .x .Qm .mo .Hq mmmmuoma Im++z mu Amy: AHV
M
ucmumcou Esflunflafisqm ucmumcou Esflunwawsqm so coauomwm
mewmmwnomo mo umpuo mucm>aom mo uommmm
maunfiafisqm coausHom Hmumz ca mucous 0>Humufiam50 .H manna

shift (Knight shift) of the alkali cations could be studied

14'15 This recent study showed

due to solubility problems.
that the alkali metal anions in solution are indeed centro-
symmetric species with two electrons in the outer s orbitals.
This conclusion was based on two factors. First, the very
small shift of the Na- peak in solution from that of Na(gas)
indicates that the p electrons are well shielded. Second, the
narrow line width of Na- indicates a spherical field gradient
about the species.

One use of NMR techniques which is growing in importance
is the determination of reaction rates. Lehn recognized the
importance of proton NMR techniques for the study of cation
exchange rates between the solvated and the cryptated states.16
Shchori and co-workers extended this type of work further with
a 23Na NMR kinetics study of sodium cation exchange in methanol,
dimethoxyethane and N,N-dimethy1formamide in the presence of

17'18 More recent work by Dye and Ceraso,

dibenzo-l8-crown-6.
who first observed separate lines from sodium in two different
environments,established the techniques which have been used

19 and provide the background for the NMR

in this laboratory
work in this thesis.

The basis for NMR rate studies is a set of phenomenological
equations proposed by Bloch and modified by McConnell. The
modified Bloch equations are:

dGA -1 -1

E-E- + GABA = "lYHlMOA + TB GB - TA GA 105

dGB 1 -1

TE? + aBGB = '1YH1MOA + TA GA ' TB GB 1'6

in which G and G are the complex magnetizations caused by

A B
the nucleus in sites A and B, respectively. The definition of

~w) in which T2A is the transverse relaxa-

is the corresponding Larmor fre-

. _ —1 .
aA is aA - T2A - i(w

tion time of nucleus A and w

A

A

quency; a is similarly defined. H1 is the amplitude of the

B
R.F. magnetic field and y is the magnetogyric ratio of the
nucleus being studied. Equations 5 and 6 are different from
the original Bloch equations in that they allow for exchange.
The tgl term is the probability per unit time that a nucleus
in position A will jump to position B. That is, TA is the mean
lifetime in position A. TE has the same definition for position
B. If needed, a third site can be added. This possibility
will be discussed later.

The solution to equations 5 and 6 which is used in this work

is as follows.

UT-SV

G = [T‘EJYHiMo ‘ iYHlMOE§L2Ifl§2£J 1'7
S +T S +T
where
s = is. + P_B_ + __T___
T2A TZB TZATZB - T(wAew)(wB-w) 1.8
P P
U = 1 + 1(fli + 61L) 1.9
2A ZB

10

 

 

 

wA—w wB—w
T = (P w + P w -w) + T( + ) 1.10
A A B B TZB TZA
V = (PBmA + PAmB-w) 1.11
and
T T
r==Tfif 1J2
A B

This solution describes the line shape function in the general
case, even when the transverse relaxation times in the two
sites are different.

In the absence of exchange, the single complex moment is

described by:

dG 1
EE+[T_

‘ i(wO-w)]G = in
2

1M0
The solution to this equation is:

KT (w -w) KT

0
1+T (w -w)2 1+T2(w -w)
2 O 2 O

 

 

NNN

These line—shape functions allow complete line-shape fitting
to be done on the experimental data. Although there are exam-

22 it has seldom been

ples of this method in the literature,
applied to such complex NMR data or as routinely as in this

laboratory.

CHAPTER 2

EXPERIMENTAL

11

12

Instruments

 

The 23

Na NMR spectra were obtained with an NMRS-MP-IOOO
spectrometer which uses a Varian DA-60 magnet, a lock system
built in our lab, and a Nicolet 1083 computer system. The
computer system allowed the use of pulsed fourier-transform
techniques and permitted data to be punched directly onto
paper tape for analysis with a CDC 6500 computer.* The
stability of the lock system (less than 2 Hz drift per hour)
made it possible to take a reference spectrum only at the

beginning and end of each series of temperature runs. The

reference sample was measured at 25°C.

Data Analysis

 

The Nicolet 1083 computer and an ASR-33 Teletype were
used to punch the raw data onto paper tape as octal numbers.
Computer cards were then punched from the octal tape and

23 to a second set of cards as decimal numbers with

converted
the proper format for the curve fitting program.

The NMR spectra line shapes were fit in most cases with
five parameters using a generalized nonlinear least square
program called "Kinfit".24

The form of the line shape function used to fit the two

site exchange system follows.

 

*

For other details of the NMR system the reader is referred to
the theses of David Wright and Joseph Ceraso, Michigan State
University (1975).

13

yHlMO 0

 

 

 

_ _____ - 1 _ _
G(w) - 2 2 {(SU+TV)cos(6O + 3??) (UT SV)
S +T
e1
Sln(60 + 3F)} + C 2.1
where
P P
A B T
s=—+—-—+-————-T(m +A-w)(w +A-w) 2-2
T2A T23 TZATZB A B
P P
U=l+T(F-BL+T-§—) 2.3
2A ZB
wA+A-w wB+A-w
T = P (w +A) + P (w +A) - w + T(-————— + ——————) 2.4
A A B B T2B T2A
v = TEPB(mA+A) + PA(wB+A) -w] 2.5
and
T T T T
PA: J? PB = +B T = A+B 2'6
TA TB TA TB TA TB
T and T are natural relaxation times in absence of exchange.

2A 2B

“A and wB are the Lamor frequencies in the absence of exchange.
The five parameters which the computer adjusted were the .
amplitude (yHMO), baseline (C),mean lifetime (T) for exchange,
the phase of the signal (00) and the frequency shift (A)

which adjusts w to compensate for frequency drift between

T and m were measured in

sample and reference. TZA’ “A’ 23 B

14

separate experiments and entered as constants. The four
other constants used in the line shape function were the
second order phase correction (61), number of points in
digitalized spectra (N), and the population of the sites

(PA and PB). In several cases P was used as a sixth param-

A

eter when it could not be determined due to decomposition of

 

the sample.

For the rumr-exchange systems in which wA, T2A' wB and T2B
were determined the complete shape function is

KT2 l'
G = 2 2Lcos(eo+el)-T2(wO-w)Sin(60+81)] 2.7
1+T2(w -w)
o

The five parameters are the amplitude (K), C, T2, mo and

00. The two constantswused are 61 and N.

Chemical and Solvent Purification

 

Methylamine, MeNHz, the solvent used, was purified by
distilling it onto BaO where it was allowed to stand for
several weeks with occasional freeze-pumping cycles.* The
MeNH2 was then distilled from BaO onto a fresh film of Na-K
alloy where it was allowed to stand at room temperature with
occasional freeze-pumping. The amount of decomposition at

this stage was small as indicated by the amount of hydrogen

formed. The MeNH2 was then distilled into a thick-walled

 

*
Methylamine was purchased from J. T. Baker Co.

15

storage vessel. All distillations were done after evacuation
to a pressure of less than 10-5 torr. Ethylamine was similarly
purified.

18-crown-6 was recrystallized twice from acetonitrile
and vacuum-dried.* Its melting point. was in the range of
38 - 40 degrees centigrade. The 2,2,2 cryptand was synthesized

by a modification of Lehn's procedure.25

Sample Preparation

 

All reactive metal solutions for the NMR experiments
were prepared in specially cleaned25 glass vessels of the
design shown in Figure 2A. The metal solutions were saturated
at 0°C for one half hour by allowing the solution to stand
over a metal mirror and shaking the solution. The metal
was purified by no fewer than three vacuum distillations.
Less reactive salt solutions were prepared by quickly load-
ing the dried, weighed sample into a sealable NMR tube (Figure
28). The sealable tube was pumped to 10.5 torr, the solvent

distilled in, and then sealed off in the normal fashion.

Temperature Measurement

 

The temperature was controlled with a Varian NMR tempera-
ture controller model number V-4S40. The temperature was

measured with a calibrated Doric digital readout thermocouple.

 

*
l8-crown-6 was purchased from PCR Incorporated.

16

.m mcoflusaom m>fluflmcmw Ham Mom

 

 

.wuamm MOM made mzz mHQmHmom
.d coflumummmum mHQEmm Mom mammmm>

 

 

 

.N munmfim

<

17

One thermocouple wire was placed approximately 1 cm below the
10 mm NMR tube in the probe. A second thermocouple wire was
placed in the 10 mm tube containing 1nu_of isopropyl alcohol.
A calibration plot of the temperature in the tube gs. the

temperature below the tube was made. The plot was linear

and reproducible to il°C.

CHAPTER 3

THERMODYNAMIC CONSIDERATIONS OF

ALKALI ANION FORMATION

18

19

Rationale

 

The evidence for alkali anions is very convincing; how-
ever, certain puzzling facts remain. One of the most in-
triguing is the absence of a lithium anion in any lithium
solutions. Is this absence due to some anomalous thermodynamic
behavior or simply that the right conditions have not been met?
The second puzzling phenomenon is the fact that to date only
one salt (of the sodium anion) has been produced by crystalliza-
tion even though solutions which contain K-, Rb-, and Cs- can
be readily prepared.

With these questions in mind, the thermodynamics of forma-
tion of the solid anion salts has been investigated. This in-
formation may then be used to predict the feasibility of com—
pound formation and thermodynamic stability of salts of the

alkali anions.

A Hypothetical Salt

 

The alkali metals have certain properties which, taken
together, make them unique among the elements. They have a
low first ionization potential, positive electron affinity,
and small heat of vaporization. All of these properties work
together to make it relatively easy to form a salt which
contains both cations and anions rather than neutral atoms.
This is clearly illustrated by an energy cycle in which the

alkali metal forms a hypothetical solid salt (H.S.) as shown

20

in Figure 3. Other than AHF the only term which is not known
is the lattice energy. Several methods are available to cal-
culate this term. However, most require a knowledge of the
structure and other parameters of the salt. From the Born—

Lande equation

2
NMZ+Z_e

_ l
U — r (l n) 3.1
We know that the lattice energy varies as % from one salt to
another. Therefore, the lattice energy of the hypothetical

salt may be obtained from that of a reference salt of similar

structure by the use of the multiplicative scaling factor

rR.S./rH.S.

r
UH.S. = URef. salt X r

 

R.S.
H.S.
The difficulty is to choose the proper structure for the
hypothetical salt so that an appropriate reference salt can
be chosen, and to predict the radius of the hypothetical salt.
Three methods have been used for comparison.

The first method assumes the interatomic distance in the
H.S. is the same as the interatomic distance in the metal
except that structure of the H.S. is similar to the struc-

ture of sodium iodide. This is reasonable in view of X-ray

 

*

U is the lattice energy, N is Avogadro's number, M is the Made-
lung constant, Z+ and Z- are the valences of the ions, e is

the charge on the electron, r is the interatomic distance,

and n is the electronic shell's repulsion exponent.

21

 

 

4.
"(9) + ”(9)

AP!
Lo.

 

 

AHiP A
2'“ (9) AHfia 7
A
AHvap
* AH
2mm F

Figure 3. Energy Cycle for a Hypothetical Solid Salt.

22

measurements of the NaC+Na_ solid which show that the radius

of Na- is approximately equal to the radius of I-. This causes
the radius ratio, an important factor in determining crystal
packing, to be about the same for Na+/I- and Na+/Na-. Hence,
the lattice energy of sodium iodide is scaled by a factor of
rM+M'/rNa+I' where rM+M‘ and rNa+I' are the interatomic dis-
tances in the metal and salt respectively.

The second model used to calculate the lattice energy of
the H.S. is to keep the density of the H.S. the same as the
density of the metal but change the crystal structure from a
body-centered cubic (metal) to a face-centered cubic (salt).
This then has the effect of changing the interatomic distance
to maintain the same density in the transition from metal to
H.S. salt. The NaI lattice energy is still used. This is
illustrated when we recall that the alkali metals form a B.C.C.
lattice with two atoms per unit cell.

3 4

Volume per atom = % a = r; = 3.3
V27 '

C.C. M+M-

where a is the length of the unit cell and r is the inter-
atomic distance. If this structure is changed to a F.C.C.

with the same density, we then have

3.4

or

23

The scale factor then becomes

4 1/3
rNa+I‘/rB.c.c. (jg?)

The third model used to calculate the lattice energy of the
H.S. assumes that both the interatomic distance and the lattice
structures of the H.S. stay the same as that of the metal.

This structure was then scaled using a CsCl lattice energy.
CsCl of course has a B.C.C. lattice. This model is not as

reasonable as the first two but it serves a purpose in that
it allows comparison with the first two models.

The results of these calculations are shown in Table 2
for all the alkali metals along with some of the data used

in the calculations.

Complete Born-Haber Cycle for MC+M- Formation

A more complete understanding of the thermodynamics can
be achieved by using an energy cycle which considers a com-
plexing agent such as a cryptand. One such cycle is shown

in Figure 4 which represents the process

+ c + M+CM’ 3.6

2” (S) (S)

(S)

The terms in Figure 4 have the following meanings. AHvap

is the heat of sublimation of the alkali metal, AHip and AHea

are the enthalpy due to the ionization potential and the

24

.Amnmflv ems .ww ..em .ewno .n .nuuosucmz .m .3 .cmno .2 ;m

 

 

 

 

 

 

 

m
.onma ..OO umnnsm HmoHEmno ..Um nuom .moflmwmm one muumfifimnu mo xoonpcmmm
.Aemmav aw .muuomum mucuosuum .uumuumm .m .0H
m.H m.m m.ma o.m| n.mm mm.ma mv.m mo
m.n m.m m.HH H.HHI m.om vm.ma em.q gm
o.on n.Hn m.n m.HH| H.ooa mm.mH m.v x
n.nn m.Hu m.oa m.maa m.mHH mo.¢m mn.m mz
m.HN| m.vau ¢.o m.bHu m.vma na.mm mo.m HA
mm Q a
me me H# m ma N Ame m m>m< mwfmmmmwzmmw. Hmumz
Hmooz Hobo: Hobo: a .
mma Ema use
Am musmwm ommVAHImHOE Hmoxv mmcmnu amamnucm
.cofiumasoamo uamm Hmoauwnuommm MOM muHSmmm .m wanna

25

.COAquwom Iz+uz How macho Hmnmmlcuom .w mwsmwm

Amvn2+u2i§u + ASSN

 

 

 

 

 

4 .14
3 card
Ame lav;
.7”: DIG u Qfl>14
+ +
if
so: + Es?) ...:IE£«

26

electron affinity respectively, AH is the enthalpy of sub-

sub
limation of the cryptand, AHg is the heat of formation of the
gaseous complex between the cation and the cryptand, and
lastly,U is the lattice energy of the solid compound. The
terms which are not available from the literature are AHsub'
AHg, and U. Fortunately, some data are available which allow
estimates to be made,but the reliability of these estimates is
questionable. An attempt is made to evaluate these terms,

point out possible errors, and finally to use these estimates

to draw conclusions about the MC+M- salt.

Enthalpy of Cryptand Sublimation

 

The enthalpy of sublimation of the cryptand was determined
by neglecting the enthalpy of fusion and using Trouton's

rule.

AH
AS = vap 3 21 cal/deg mol 3.7

 

where Tb is the boiling point of the compound. Tb was cal-

culated by use of the Clausius-Claperyron equation

p2 Hvapcrz-Tl)
log(——) = 3.8
pl 2.303R(T2T11

 

which relates the vapor pressure p to the absolute tempera—
ture T by means of the enthalpy of vaporization. The values

of p2 and T2 are one atmosphere and the boiling temperature

27

respectively. p1 and T1 were calculated by using the Langmuir

free-evaporation method26

with sublimation data. In the
Langmuir free-evaporation method, the rate of loss of mass
(dw/dt) by vaporization from a sample of area a in a vacuum

is related to the equilibrium vapor pressure by the equation

(-dm/dt)(2nRT/M)is

3.9
aa

The factor a is the coefficient of evaporation and is often
assumed to be unity. M is the molecular weight. One dif-
ficulty with this method is that the area (a) is not easy

to evaluate. The data used were as follows.

Weight of C222 evaporated = 0.7 g.

*
Temperature of vaporization = 110°C
Duration of vaporization = 2% hours

3.14 cm2

Surface area of material

A value of 22.1 kcal/mol was obtained for AHsub by using this

method.

Enthalpy of the Gas Phase Reaction

The enthalpy of the gas phase reaction of metal and cryp-

tand may be estimated by the following set of reactions.

 

*
This is above the melting point of C222.

28

AH
+ l +
M .
M(g) + (aq) 3 10
AH2
AH
+ 2 +
M(aq) + C(aq) MC(aq) 3°12
AH4
MC+ + MC+ 3.13
(9) (aq)
AH
+ 5 +
+ .
“(9) cm " “Cm 3 14
From these reactions it is clear that
AH = AH + AH + AH — AH 3.15

5 1 2 3 4

Everything on the right hand side of this equation is known
or can be calculated. For instance, the heat of hydration of

the alkali metals is fairly well known27

from both experimental
work and theory. The heats of aqueous cryptation are small

and are also known for most of the compounds used here. AH4

was calculated by using a modification of the Born equation28
-Zze2NO l ZzezNO 3D
AH = ———————(l - —) + T (-—) 3.16
solv. 8ne.r D 2 8T
0 o BTEOrOD

in which 2 is the valence of the ion, e the charge on the

electron, NO is Avogadro's number, go the permittivity of free

space, rO the radius of the ion and D the dielectric constant.

29

By using the values of these quantities with water as a sol-

vent we have:

2 2
166Z + T(.0094)_]Z:‘__(kca1

AH = mole
o

) 3.17

 

O

Lehn introduced a technique for the evaluation of the
radius of the complexed cation by adding the ligand thick-
ness to the radius of the free ion.29 The procedure used to
determine the ligand thickness (3) consists of spreading the
volume of the ligand around the cation and calculating the
thickness of the layer. The value of the ligand thickness

is given by:

s = (ri + ———) - r. 3.18

where ri is the radius of the cation and VL is the volume

of the ligand. VL is the sum of the Van der Waals volume of
the atoms and groups forming the ligand.

One of the major problems with the Born equation is that
the dielectric constant is not a constant as the Born equation
assumes. It is a function of the field strength about the ion.
However, two factors increase the validity of the Born equa-
tion in this case. First is that in a high dielectric
constant medium where e/e:o >> 1, the errors will not be too

serious and secondly, the radius of the cryptated cation is

greater than 5.0 A so that the electric field gradient is not

30

as high as for most bare ions.

In order to proceed with this calculation, a critical
assumption had to be made about the enthalpy of transfer of
cryptand from the gas phase to water (AHZ). The Born equation
calculates only the free energy of solvation which is due to
the electrostatic interaction of the ion. It neglects all
the non-electrostatic terms. The assumption is made that
the non-electrostatic term in AH4 cancels the enthalpy of
transfer for the cryptand (AHZ). There are problems with this
assumption; the biggest is the fact that there are probably
large conformational changes between the cryptand and the
cryptate which will have a pronounced effect on the enthalpy
of transfer. However, the magnitude of these effects is un-
known and very hard to measure. If we assume that the error
from one alkali cryptate to another is approximately the same,
we can still use this result for our purposes. The results
of this calculation are shown in Table 3. The difference
calculation described later in this chapter will prove to be

more reliable for doing this.

Lattice Energy

 

The determination of the lattice energy of the cryptated
anion salt poses another interesting problem. The classic
method used to calculate the lattice energy of a salt is the
Born-Lande equation which has already been mentioned. The

problems with this equation, although it gives good results,

31

s a
.Ummfi 0H03 H H NU .HOM mODHMNV
t.

 

 

 

 

m.vv| m.m~u o.~n o.~n: wm.m +mu
>.oon o.m~n m.oan m.mn| mm.m +Qm
n.5mu >.m~| H.HHI m.mm| mm.m +M
o.mmn m.mmu m.mu o.ooan om.m +mz
m.voa v.mm| m.vu H.~man «mo.m +fiq
HImHoE Hmox HumHOE amox HImHoE Hmox HIwHoE Hmox ANV GOHDMO coH
mma «ma mma Hm omumummuo Hmumz
< mo msflcmm
.cofiuommm
mmmnm who on» mo amamnusm may mcflfiumumo on com: macho hmumcm mo muasmmm .m canoe

32

are two-fold. First, a certain crystal structure must be
assumed before this equation can be used. Second, the calcula-
tion of the Madeling constant is a formidable task requiring
much mathematical manipulation for complex structure types.

A reasonable alternative to the Born-Lande equation is the

Kapustinskii30 equation

287.2V Z+Z_ = [l _ 0.345]

r++r_ r++r_

U:

 

 

where v is the number of ions in the chemical molecule, (r++r_)
is used for rO the interionic distance, and Z+ and z_ are the
valences of the ions.

Kapustinskii found that the Madelung constant, the inter-
nuclear distance, and the empirical formula of an ionic com-
pound are all interrelated. This is not surprising when one
considers that, given a certain number of ions of a certain
size, the number of ways of packing them efficiently is
limited. Calculation of rock salt type lattice energies by
both the Kapustinskii and the Born-Lande equation gives
results that are within a small percentage difference of one
another in most cases.30'31

In calculating the values of the lattice energy for the
alkali anion salts, the same value of the cation radius was

used as in the previous calculation of AH The value of the

4.
radius of the anion was estimated by using the suggestion of

Matelon, gt 31. in which

33
3.20

In this equation rM- is the radius of the anion, rM—M is the
interatomic distance in the metal, and rM+ is the ionic radius
of the cation. Justification for the use of this anion radius
is presented in the discussion of these results. The results

of the complete Born-Haber cycle are shown in Table 4.

A Difference Calculation of the Born-Haber Cycle

Many of the problems of the previous thermodynamic cycles
can be overcome by computing only energy differences in the
cycles of the alkali cryptates and by using sodium cryptate
as a reference. The sodium case is used because it is known
that the sodium cryptate solid is a stable compound. We
know that Equation 21

2Na 3.21

+ _
(s) + C222(s) * Na C222Na(s)
describes the formation of a stable gold-colored solid.

Therefore

0 = o _ o
AGNa AHNa TASNa i o 3.22
For other alkali cryptate salts of this type, the following

could also be written.

34

Table 4. Results of Born-Haber Cycle Calculation for MC+M-
Formation.

 

 

Radius of

 

. 0 U _ AH
Anion (A) MC+M f
Compound (Zrm-rm+) kcal mole.l kcal mole-l
. + .-
Nac+Na‘ 2.8 -72. 35.
KC+K- 3.2 -64. 19.
RbC+Rb- 3.4 -63. 22.

Csc+Cs' 3.6 -60. 38.

 

 

35

o _ o _ o _ o _ o

o

AGM - AG
where M refers to a salt of MC+M_ type and Na to the NaC+Na—
salt. This (more than adequate stability condition) is

referred to as the stability criterion. We can rewrite the

Born-Haber cycle in Figure 4 as follows.

0
AH
+ 5 +
M(g) + C(g) + MC (9) 3.24
AH:
C(S) -> C(g) 3.25
AH
7 + -
2M(S) + M(g) + M(g) 3.26
o
M+C + M' A28 M+CM‘ 3 27
(g) (9) (s) '

If we substitute the appropriate terms for AHM and AHNa and

apply the stability criterion, we have:

M M
Acg - Agga = (AHgM — augNa) + (AH? — AHgNa) + (AH: - AHgNa)
—o -o —o —o
T(sMCM SNaCNa) 2T(sM sNa) : o 3.28

o . . . .
The term (SMCM SNaCNa) is the difference in the molar entropies

of the salts. This term is not known but it is assumed to be

small. All other terms with the exception of (AHM 2a)

s-AH

36

are known so that Equation 3.28 can be replaced with the

following

oNa

oNa 0M oNa
) 8

OM-AH < -(AH -AH

AH5 5 — 7 7

_ oM_ —o_-o
(AH8 AH ) + 2T[sM sNa] 3.29

This expression represents the maximum value that (AHOM -

5
AHgNa) can have for the stability criterion to hold. The

result of this calculation is shown in Table 5.
Using the same energy cycle that was used to calculate

the absolute value of the gas phase enthalpy, we can esti-

Na
5 )°

than the absolute calculation because terms involving sub-

mate (AH? - AH This calculation is much more reliable
limation and aquation of the cryptand cancel out and the use
of the Born equation for a difference calculation is more
reliable. The result of this cycle is also given in Table

5.

Discussion

 

The results of the hypothetical salt calculations are
interesting. Of course, the net free energy of the reaction
must be greater than zero since we know the alkali elements
to be metallic rather than ionic. However, it is evident that
not very much stabilization energy is needed to form the
anions. Model one, for example, has values which range from
-3.1 kcal mol—1 for Li to +15.3 kcal mole"1 for Cs. This is

the most conservative and reasonable estimate of the three

37

Table 5. Results of the Difference Calculation Using the
Stability Criterion.

 

 

 

(AHH-Aflga)max (AHE-AHga)est
Metal (kcal mole-1) (kcal mole-1)
Li ~12.4 -22.
Na ---- ----
K 24. 15.
Rb 25. 21.

Cs 31.8 38.

 

 

38

models, having a larger interatomic distance in the salt
compared with model 2 and a lower density than model 3. This
serves to illustrate the importance of the radius and struc-
ture in determining the stability of a compound. From this

it can be argued that the radius of the anion cannot be much
smaller than the interatomic distance in the solid minus the
metal cation radius as in Equation 3.20. This idea is in
accord with the suggestion of Matalon, Golden, and Ottolenghi.4
They used this assumption, based on ideas of Slater and Pauling,
to test the applicability of a charge transfer to the solvent
(CTTS) interpretation of M- spectra.

The calculations also indicate that if one anion can be
found, all the alkali metals should form anions. In particu-
lar, there does not seem to be any reason why lithium anions
should not form in solution under proper conditions.

The results obtained from the cycle shown in Figure 4
for formation of a salt of the cryptated cation and the alkali
anion are not very encouraging. In all cases, the enthalpies
are positive. This however, is not too surprising in view of
the rough approximations and estimates that were made. Examina-
tion of the possible errors in this calculation indicates that
the major errors, if corrected, would make the value of AHf
more negative. For example, the Kapustinskii equation usually
gives a value for the lattice energy which is low. This is
due to the fact that while the Kapustinskii equation accounts
for terms in the lattice energy due to electrostatic inter-

action, it ignores all contribution due to polarizability

39

and dispersion energies.
The thermochemical cycle used to calculate AHgas is even
more in question. The biggest error occurs with the assumption

thattjmgnon-electrostatic parts of the AH4 cancel AH . Of

2

the three conformations in which the cryptand can exist, two
allow for electron pairs to be oriented toward the solvent.
These electron pairs interact very strongly with the solvent
(water in these calculations). This would cause the enthalpy
of transfer to water from gas for the cryptand to be much more
negative than for the non-electrostatic part of the enthalpy
of transfer of the cryptate. The cryptate is formed by an
ion-dipole interaction of the metal ion with the electron
pairs of the complexing agent. Therefore, in the cryptate

the electron pairs would be pointing toward the ion, and the
solvent would not interact with them. In addition to this

are the effects of hydrogen bonding which would be expected

to interact differently with the cryptand and cryptate. For-
tunately, the error caused by these interactions is expected
to remain nearly constant from one ion to the next so that the
values that are obtained from this calculation may be used to
compare one metal with another. Of course, the value of

AHsub for the cryptand should be viewed as only a rough esti-
mate. Again, this error is constant regardless of the metal
ion used. We might conclude that if one of the alkali metals
form a salt of the anion and the cryptated cation then it might

be expected that they all would form such a salt.

When the difference in AHf for different cryptates are

40

evaluated, we have a much more reliable calculation. The
AHsub cancels out and the error in the lattice energy is not
severe. The biggest error comes with the use of C211 for

lithium. This was used because lithium forms only a very weak

complex with C and as a result some of the terms may not

222'
cancel out. But, this is assumed to be small. Similar argu-
ments apply to the case in which (AH? - AHga) was estimated.

As mentioned, the terms involving aquation of the cryptand
cancel out and the Born equation is more reliable.

From Table 4 it is evident that except for the Cs case,

Na . M Na
(AH? - AH5 )max is larger than (AH5 - AH5 )

that Li, K and Rh form a stable salt as does the sodium cryptate

est' This implies
salt of Na'. The fact that this predicts CsC+Cs- to be un-
stable with respect to NaC+Na- is not surprising in view of
the low complexation constant for Cs++C + CsC+. The choice

of a different cryptand would change this result.

Possible Experimental Verification of the Thermodynamic Cycles

 

With several experiments the values in the thermodynamic
cycles described above could be determined much more accurately.
In fact, if proper experiments were done, these cycles could
be used to determine the value for some of the terms that are
difficult to measure. For example, the electron affinity of
sodium and the enthalpy of the interaction of the cryptand with
the solvent could be evaluated. A summary of needed experiments

follows.

41

l) The enthalpy of sublimation of cryptand could be
determined by the Knudsen effusion method. The sublimation
used to purify the compound indicates that this could be easily
done. A novel modification of the Knudsen method uses the mass
spectrometer.32 This technique utilizes the intensity of
the parent peak as a function of temperature to obtain AHsub'

2) The enthalpy of the gas phase reaction between the
cryptand and the positive sodium ion could be determined by
two methods. The most direct and reliable method would be
the use of ion cyclotron resonance spectroscopy. The second
method is to measure the enthalpy of cryptation in a poor
coordination solvent and use a thermochemical cycle to find
the heat of the gas reaction. In the poor coordination sol-
vent, hydrogen bonding and the electron pair interaction
with the solvent would be much smaller than in water.

3) The enthalpy and free energy of the sodium cryptate

solid could be determined by the following set of thermo-

chemical studies.

+ Na + +

(a) Enthalpy of solution [NaCNa C(solv.)

(S)

Na(solv.)] in an amine or ether.

(b) The enthalpy for the complexation reaction
+ - .
[Na(s) + C(s) I Nac(solv.) + Na(solv.)] 1“ the

same amine or ether.

(c) The third law entropy for NaC+Na-(s) and for

C(s).

42

All of these studies would involve a great deal of experi-
mental work and time because of the reactivity of the reduc-

ing species and the care necessary in handling the solution.

CHAPTER 4

NMR EXCHANGE STUDIES OF ALKALI METAL

ANION SOLUTIONS

43

44

Rationale

 

The impetus for this study came from the work of Dye

and Ceraso, in which the NMR spectrum of Na" was observed.15
It was felt that the use of a different complexing agent
would yield new and different information about the nature
of the anion interactions in solution. Although C222 had‘
been used for the original work, l8-crown-6 (l8-C-6) was
tried for several reasons. First, solution studies showed
that 18-C-6 increased the solubility of sodium in methyl—
amine (MA) to more than .35M which is high enough to give
good NMR spectra. In addition this system can form unusual

33

solid complexes. Secondly, l8-C-6 is commercially avail-

able and is much lower in price than C
23

222. Figure 5 shows

a comparison of the Na NMR spectrum of a solution of C

222
and Na in MA with that obtained with 18-C-6 and Na in MA at
nearly the same temperature. It is evident from these
spectra that the 18-C-6 system is affected by exchange
broadening. This exchange broadening is reasonable since
it is known that with salt solutions the crown exchange
rates are faster34 than cryptate exchange rates.35 This im-
mediately suggests that a detailed study of the temperature
dependence of the NMR spectra of solutions which contain
both the 18-C-6 complex and Na- would yield information
about exchange processes. Figure 6 shows the changes which

23

occur in the Na NMR spectra of the Na', NaC+ system (with

C=18-C-6) as a function of temperature. Fortunately, the

45

H-—>

 

   
 
   
  

 

 

 

 

 

 

[I 2.2.2 Cryptand, Na in MeNH2
-2l.4°

 

 

 

 

 

 

18Crown6, Na in MeNH2
-2OD

 

 

 

1 1 1 l
-200 -400 0 100 200
ppnt

23

Na NMR Spectra of Na+C and Na+ (18-C-6), Na-

in Methylamine.

Figure 5. 222

46

“—9 MeNH2
IB-Crown-é
+Sodium

 

 

 

 

 

l
W 1 -32°

NaC+ Na—
P J l I l J
-400 0 100 200
.ppnI

 

23Na NMR Spectra of Na+ (lB-C-6), Na- in Methyl-
amine at Various Temperatures.

Figure 6.

47

coalescence temperature (-10 to 0°C) is low enough to avoid
rapid decomposition of these reactive solutions. A study
of this exchange process might yield two types of information.

Since the relaxation time is given by

JL Rate of leaving site i 4 1

Ti Concentration of species in site i

 

a study of the concentration dependence of the relaxation
time could yield the mechanism by which the exchange is
occurring. From the mechanism the rate of exchange of
electrons between the anion and the cation might be mea-

sured.

Three Site Exchange Processes

 

The anion exchange system differs from the previous
crown and cryptate systems studied in that three sites are
available for the nucleus. The sites are Na+ (site A),
NaC+ (site B) and Na' (site C). (It is even possible that
a fourth site, the sodium monomer, might be important).
The modified Bloch equations for the three site case are

similar to the two site equations and are given as follows.

1 1 1
‘[a + ——]G + __(; + ——G = in mP 4.2
A TA A TBA B TCA C 1 0 A
-[aB + 3.168 + ____(1 ;A + ——-—(l ;C = iYHlMOP 4.3
TB ' TAB TCB B
”[0. + LJG + .—__(l ; + ———-(l 3 = i'yH M P 4.4
C TC C TAC A TBC B l o c

48

The terms have the same meaning as in the two site case
except for the terms involving T. For a nucleus at any
given site there exist two other sites to which it can jump.

For example, ¥l— = average lifetime in position A before the
AB

nucleus jumps to position B. T and T

TAc' TBA' BC' CA CB

are similarly defined. In addition a term 5; can be defined
A

T

as

L: —-——l +——1 4.5
TA

so that iL-is the average lifetime in site A before a jump
A
to either site B or site C. The definition of Ti and E}—
B C
are similar.

Dr. Dye has suggested several possible mechanisms to
describe the process of exchange in the Na- system. These

are:

l
NaC+ I Na+ + C 4.6
k-l
%k2
Na + NaC+ Z NaC+ + Na+ 4.7
kkz
k
Na- 3 Na+ + 2e- 2.8
k-—3
_’5k _ +
Na + Na + Na + Na 4.9

49

Na- + C E NaC+ + 2e- 4.10
R4-
-5
%k6 _
Na- + NaC+ I NaC+ + Na 4.11
%k_6

By using mass and charge balance considerations it is not
difficult to relate the mean lifetime of a nucleus in any
site to the rate constants and the concentrations of the

various species. When this is done with the six exchange

mechanisms (4.6-4.11) the following expressions are obtained

 

for :
1 + - 2 -
.__ = k [c] + k [NaC ] + k [e ] + k (Na ) 4.12
TA -1 2 -3 4
or
P k k P
l ._ + 2 _ C 2 -l -5 B +
'?— — (NaC ) (1 5-0 [-—§f§———'+ k_3] + k2[NaC J
A B 5 C
P
+ k4 59mm 4.13
B
1 + + 2 PC 2 Pc +
__ = k + k [Na ] + k [NaC ] (l - ——) + k ——(NaC ) 4.14
T l 2 -5 P 6P
B B B
and
‘3; = k + k3K4 Pc +
Tc 3 k_3 PB (NaC+)(l — Eg)2
PB
P P
B +2 C 2 +
+ k_5§-(Nac (1 - P‘) + k6(NaC ) 4.15

C B

50

These expressions provide a powerful probe for determining
the mechanism which dominates the exchange of the 18-C-6
system. From measurements on the salt and crown system
without Na- present,mechanism 4.6 can be distinguished from

mechanism 4.7 because of the dependence of éL-on the Na+

concentration. Mechanism 4.10 can be distinguished from
mechanism 4.11 by the dependence of g; on NaC+ concentra-
tion. The relative concentrations of NaC+ and Na- can be
changed by adding NaI to the crown before the solution is
placed on the metal mirror. This produces a system which

contains NaC+, Na- and I" provided decomposition is not

severe .

Reduction of the Three-site Equations to Two-site Equations

Although there are three possible sites for the sodium
nucleus only two sites can be detected as a result of the
large complexation constant of the crown. It would be easy
to assume that because the concentration of the third site
is very small tflfijs case reduces automatically to a two site
system. This however is not always the case. Since the
relative concentration of a site is related to the mean
lifetime of a species in that site, when pA is small, TA
may also be small and terms involving pA can make a signi—
ficant contribution to the exchange time through the ratio

PA

TA

side of equation 4.2 becomes negligible and, as suggested by

. For the case in which pA is very small the right—hand

51

Dye, we can solve for G We then have

 

 

A'
- 1 O 1
BA A T CA A T
A A
If we assume that the contribution of “A is very small
compared with gL-we then have
A
T T
GA = ?lL GB + ?1L GC 4.17
BA CA

The neglect of “A is reasonable except when the lines are
very broad in the absence of exchange. Only when TA becomes
very small or the line in question is very broad will a site
of very low concentration affect the spectrum. Substitut-

ing Equation 4.17 into 4.3 and 4.4 gives the following:

 

-[aB + €L.- ¥—:%——]GB + T1+ET T? JGC = in1M PB 4.18
B AB BA CB AB CA °

-[aC +.%; - ?—:§——]GC + [?l—+ ?—:$——JGB = in1M PC 4.19
C ACTCA BC AC BA 0

It can be shown that the coefficient of GB in Equation 4.18
is equal to the coefficient of GA in 4.19 and the same is
true with the coefficients of GC' Therefore we can rewrite

these two equations as follows:

_ 1 1 _ .
[a8 + :JGB + -T—-;- GC - lyHlMopB 4.20
B C
1 1 _ .
”[GC + :TJGC + :7 GB — lYHlMOpC 4.21
C B

52

where
T
-T-l.-=.-r-l—+;—1—(1+}£) 4.22
3 BC BA AB
and
T
_1'_ ._. __1 + _1 (1 + —AB) 4.23
TC TCB TCA TAC

Since Equations 4.20 and 4.21 are identical in form to the
two-site Bloch equations, we can use the solutions for the
two site case to deal with a three-site case provided the
concentration of one of the sites is very low and provided
also that this site is not paramagnetic (which would give

a large value of a). Once T' and T' have been obtained

B C
from a fit of the line shapes, they can be related to a

mechanism. For example, if the exchange occurred via
mechanisms 4-6 and 4.8. gg-would be related to the concentra-

B
tions and the rate constants as follows:

 

 

 

 

.3? = 1 4.24
T k P
B [1 + kl PB]
3 C
and
k
%%-= 3 4.25
C k P
3 C
[l + k P ]
l B

Table 6 lists several mechanisms and their expressions

 

53

Table 6. Possible Exchange Mechanisms and Expressions for
l/T'.
B

 

 

Mechanism through which

 

 

 

 

 

 

 

Na- to NaC+ exchange occurs Expression for §+
B
k
NaC+ % Na+ + C
k_1 k
Mech. A A; = 1
T k P
_ k + B l + 1 B]
Na 2 Na + 2e k3 PC
k-3
k
NaC+ % Na+ + C
k k
‘1 1 1
Mac“ B P“ " k_ (c -(Nac*3)
k B 1 T
— 4 - + [1 +
Na + Na 2 Na + Na 2k (Na-)
R4 4
- + k + — l -
Mech. C Na + NaC I NaC + Na IF"- = 2k6(Na )
k B
6
k k
— § + - ]_ = -S
Mech. D Na + C k+ NaC + 28 FT (C -NaC+)K P
_5 B T 5 C]

PB

 

 

 

54

for TB. These expressions allow the different exchange

mechanisms to be tested by the concentration and relative

population dependence on T of the species Na-, NaC+, e-

B
and C.

Information From Non-exchanging Systems

 

In the process of independently measuring wA, T2A'

wB and T23, other information can be extracted from the non-

exchanging system. One such piece of information is the
activation energy for molecular reorientation of solvent

molecules Close to the ion. In general if a simple activa-

tion process is assumed, then

TC = Aexp (—Er/RT) 4.26

Where A is a constant and TC is the correlation time.36

Furthermore, if the quadrupole coupling constant and the

field gradientanxainsensitive to temperature changes then

T aTC = A' exp (Er/RT) 4.27

The activation energy, Er’ is the slope of a plot of the log
of the line width (T31) versus reciprocal temperature.

The agreement between this method and other methods for

determining Er is good.36

T w and w are given in Table 7.

The values of T2 A B

A' 28'

55

Table 7. The Variation of the Linewidth and Chemical Shift
of the Free and Complexed 23Na Cation with Tempera-

 

 

 

ture.
Temp(°C) Av;i(Hz)1 T2(msec)2 Appm3'4
Free Cation
12.4 7.0 45.4 -9.4
5.7 6.9 45.8 -9.3
+ 0.7 7.6 42.1 -9.2
- 6.7 8.1 39.5 -9.3
-1l.0 8.4 37.9 -9.3
-l7.8 9.6 33.2 -9.3
-23.9 10.6 30.1 -9.3
-32.8 12.3 25.8 -9.3
-4l.6 15.4 20.7 -9.3
Complexed Cation
10.7 244.9 1.30 5.6
- 2.5 320.3 1.00 6.0
-l3.5 391.5 0.81 5.6
-20.0 481.7 0.66 6.3
-29.0 656.3 0.50 8.6

 

 

1For all tables, full-width at half-height in Hertz corrected

for field in homogeneity.
210.5 msec for free cation and 1.03 msec for complexed cation.

3For all tables, relative to aqueous Na+ at infinite dilution
(actual reference solution was saturated aqueous NaCl).

41.4 ppm.

56

-1

The plots of log T2 vs. reciprocal temperature are pre-

sented in Figure 7. A plot of log n vs. reciprocal tempera-
ture for pure MA is also included in Figure 7. The values

for the activation energy, E for the free and complexed

r!

NaI are

Er for = .15 MNaI = 1.8i.1 kcal mole-l

R

Er for .15 MNaC+I— = 3.21.2 kcal mole-l
T2C and we (line width and Larmor frequency of Na-)
were obtained from the C222 Na and MA system which is in

the slow exchange limit from -40° to 0°C. The line width
of Na" changed only 2H2 over the entire region (12.5-14.5
Hz). The average value of this was obtained and corrected
for inhomogeneous broadening. The average value was used
for T2C'

18-C-6 Salt Exchange System

The work on the sodium salt exchange with 18-C-6 proved
to be very difficult. Sodium iodide was chosen for the
salt because its solubility appeared to be higher than
that of either NaBo4 or NaSCN. Even with NaI, precipita-
tion occurred in a .1 M solution at about -40°C. At this
temperature the system was in the rapid exchange region.
Typical results for the linewidth and chemical shift are

shown in Table 8. It is unfortunate that the exchange is

57

 

 

 

5.
‘4
3.1
2. u
"7‘
U
I.“
U) D
F103. 0
d d
d
6' ..
1 ”.3
4_ .-
00 . x
d . 0 3:
o ‘3 fig
0
2. . ‘2’
>
10 r I I I U i 1
3.5 3.6 3.1 3. 3.9 4.0 4.1 4.2
101m“)

Figure 7.

Semilog Plot of Transverse Relaxation Times vs

Reciprocal Temperature for Free NaI (p) and a
The log of

the Viscosity of Methylamine is Plotted for

1:1 Complex of NaI and l8-C-6 (n).

Comparison (0).

58

Table 8. The Variation of the Chemical Shifts, A, and the
Transverse Relaxation Times, T for 18-C-6, NaI
Exchanging System. Concentrations of Complexed
and Free Sodium Ions are Equal.

 

 

 

Temp(°C) Appm Av%(Hz) T2(msec)
0.0 -1.6 191.3 1.7
-15.0 -1.8 254.8 1.3
-l9.8 -2.2 341.5 .93

-30.4 -1.6 403.0 .79

 

 

59

so fast since it is important to distinguish between
mechanisms 4.6 and 4.7 for the release of Na+ from the com-
plex. It is fair to assume however that this exchange
occurs via mechanism 4.6 based on previous studies on the

crowns and cryptates.:M’37

Results of Na-, 18-C-6 Exchange Studies

Three types of Na' solutions can be made for study.
The first is a solution in which the populations of Na-
and NaC+ are equal (PB = PC). This type of solution can
be studied at different absolute concentrations. The second
type of solution is one in which a non-reducible salt is
added (NaI) along with an equimolar amount of l8-C-6. This

has the effect of making P > PC which allows the effect

B
due to the relative populations to be quantitatively studied.
The third type of solution which can be readily prepared
contains 18-C-6 in excess. By using solutions of these three
compositions a severe test can be made of the mechanisms
previously discussed.

Five samples were prepared for rigorous data analysis.
The nature of these solutions is listed in Table 9. The
lineshapes of these five samples were fit as described.
A few representative line printer plots from program KINFIT
are present in Figures 8 and 9. In the figures x corresponds

to the input data, 0 corresponds to the calculated value

and = to the points in which the calculated value is equal

60

Table 9. Composition of Samples Used for Line Shape Fitting.

 

 

 

[NaC+] [Na’]
Sample Mole liter‘1 Mole liter
1 .1 .1
2 .17 .12 NaI Added
3 .17 .17
41 .15 .15 Excess Crown Added
5 .19 .l NaI Added

 

 

1Relative populations determined by allowing the computer to

adjust a sixth paramater (PA).

61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_‘_ O I O
y I. _...--..-
" __SJ[32
I II I ‘
o—m —— o a..-“ l . —-———-—.———
0 0
. O I
o 3
IO. 0
I II _
I0 I ‘
I O I
.. _ .. o...— u -. __ _. -_ __
l o 3.
I OII O
o 0 II
- — -lI-I won I- M ._ - —
l I O I g
I” , I .0 l I
F‘I' can“ I. I Tau-aunt
I .-... . I... -' .- ...,..l. .
I I moon I I n
9000000 I I I IOOOOO‘ I
hr..- i--....|._. I. -'°OOI”00
I I I II
I
_ _. .. -_.- I._..__-..
I I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r :W
I
.. ___..._ - -- “1--.... _.._ .. --- - _
I 1., _. ..
II I
_. ‘C .__—u I __ -
_.15_9_ I -. ._
- - -_-__ . . ._
I L 2 1.!
" ' ' .A‘ ’T"”
. '45:. -I I'-.— —-- ...__. I - I
' ' accomm- I 0: '°
I I on I II ".00 "'"ml" "'0' "_ a. "7
I I I I” . I
I ooo I can on In.
_ l—- _ . ——_._‘._ .I _--.I-o--onoo "'4 —--.——————. on I
I SW? .‘ ‘ I I. ' I.”
4m .4- _I_ - I—_—-
0 I I I
'I l ' I
-_, —— — I
I
'35"'3"0"b"b"I "L"

'- . 3
CHEMICAL SHIFHPPM)

Figure 8. Line Printer Plot of Sample 1 at +5.7°C and
-15090C.

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\
' .
L |___- ..
I o
I I II II I u
I 000 I II I 9.0!
_-._..nooao¢o ”moo. I— I -—~ -I on
III u too- 0 I II on I o IIT
so“. .9- I I on I.
no. I o o- 0! I I l
- I mmm—mmm I r
I I I I I
I I I I
I I I- I I _,
-_..__. _-.-,___ _—-—_———.—~_——_~_—_——_.-I.—— .... ..___._
_;:3249 -
I
Y I
O
I
' 2- . l
O
5'. E! I I——'I ..._.
I I l4 I I I I I I o Ian- I
no I 330; no. .0 0000 .0. .00. 02° :1 .033 no; no- o-o II I I cc. .3: I II ‘
I
U. .-_ _--.—.._._-—.—_.- ... --.— -._ 3‘.-. I»--oom.ouo 0.0 noo- -_—.— . .
I I II I
. . l . . .
l ---I t T I' I II I I 'l I ' I
- :oo

o 20
CHEMICAL SHIFT(PPM)

Figure 9. Line Printer Plot of Sample 1 at -26.4°C and
-32.9°C.

63

to the actual data within lineprinter resolution. The

values of T, reciprocal temperature andng for the samples
B
are listed in Tables 10-14. The apparent activation energy

(Ea) can be obtained by fitting the data with the equation
._1_ : Ae-Ea/T.

T
B
Figure 10 and the results are tabulated in Table 15.

These data are plotted for the samples in

Uses of Other Complexing Agents

 

The great variety of complexing agents available offers
unlimited opportunity for studying alkali metal NMR. One
system in which preliminary results have been obtained is
lS-C-S, sodium and MA. Unlike the lB-C-6 complexing agent the
lS-C-S compound gives a relatively narrow NMR line. Values
of the linewidth and chemical shift for 1:1 and 3:1 ratio
of [NaI] to [lS-C—S] solutions are tabulated in Table 16.
The 3:1 solution is in the rapid exchange limit even at
-40°C as was the case with the 18-C-6 system. The 15-C-5
was used to prepare a sample containing Na-. The sample
gave a very weak Na- peak in the NMR which coalesced with
the NaC+ peak at approximately 33.0°C. Several spectra
are shown in Figure 11. Other data are presented in Table
17. The reason for the small intensity of the Na- peak in
the lS-C-S system may be due to the presence of solvated
electrons or to solution decomposition. If solvated elec-
trons are present then the crown would be present in excess

and the concentration of the anion would not be as high

64

Table 10. The Temperature Dependence of the Exchange Time

T and 1/1B for Sample 1.

 

 

 

Temp-1(103K-1) 1(secx103) ¥]L--x10m3 ofiLé

B B
3.586 .04409 11.34 1946.9
3.658 .08733 5.725 747.0
3.731 .1703 2.936 610.0
3.800 .3151 1.587 127.0
3.887 .7676 .651 60.0
3.974 1.678 .298 25.0
4.012 1.998 .250 12.0
4.119 5.389 .0928 3.9

 

 

aFor all tables gfiL-is linear estimate

tion of

1

B

B

of the standard devia-

65

Table 11. The Temperature Dependence of the Exchange Time
T and 1/1B for Sample 2.

 

 

 

Temp-1(103K-1) T(S€CX103) -T-:L-x10~3 ogL
B B

3.571 0.05766 4.960 700.0
3.629 0.1398 2.046 200.0
3.719 0.3477 0.822 55.0
3.803 0.9352 0.3058 32.0
3.889 1.840 0.1554 13.0
3.950 2.899 0.987 6.5
4.054 8.588 0.0333 3.5
4.178 30.19 0.009 0.4

4.296 314.88 .000909 0.3

 

 

T

66

able 12. The Temperature Dependence of
T and 1/1B for Sample 3.

the Exchange Time

 

 

 

 

 

Temp-1(103K-1) oi_1x103 T(SeCX103) €ix10-3 0%:
3.518 .0248 .04344 11.51 900.
3.610 .026 .08899 5.619 470.
3.684 .0271 .1444 3.463 440.
3.773 .0285 .4780 1.046 64.
3.883 .0301 1.723 0.3283 20.
3.979 .0316 4.767 .1049 4.
4.106 .0337 21.9 .02282 .6

1 1

Estimate of Standard Deviation in Temp-

67

Table 13. The Temperature Dependence of the Exchange Time
T and 1/TB for Sample 4.

 

 

 

Temp-1(103K-1) (secx103) .-T!'—-x10"2 GEL-1:10-2
B B
3.607 .09523 49.3 5.3
3.668 .1663 28.3 2.3
3.732 .4493 10.46 .48
3.793 .8769 5.36 .37
3.8424 1.731 2.71 .16
3.9085 4.505 1.04 .03

3.9896 9.129 .51 .01

 

 

68

 

 

 

Table 14. The Temperature Dependence of the Exchange Time
T and l/TB for sample 5.
Temp(IOBK-l) (secx103) «l—xlo-2 (Ii-x10"2
T T
B B
3.569 .1914 10.0 .80
3.661 .3688 5.2 .7
3.770 1.383 1.388 .218
3.842 3.946 .48 .08
3.982 10.56 .18 .01
4.243 80.26 .0239 .0036

 

 

Figure 10.

 

69

(sec 1‘
3.
43/

It?“ .15 9.9!. .t
Ina
/%
‘ kiH DI
///////:;
/

7

I
W

 

 

‘1 1 1 I ' I T ' fir

3.5 3.6 3.1 3.8 3.9 4.0 4.1 4.2 4.3
111(K")

Arrhenius Plots of l/TB vs Reciprocal Temperature

for Sample 1 (0), Sample 2 (9), Sample 3 (0),
Sample 4 (I), and Sample 5 (x).

70

Table 15. Apparent Activation Energy and 1/TB (0°C) for
Alkali Anion to Complexed Cation Exchanging

 

 

 

Systems.
a —1 1a —3
Sample # Ea (kcal mole ) ?— (0°C)x10
B
1 18.2: .3 5.61.2
2 20.7: .7 1.7i.2
3 21.2: .9 3.31.3
4 25.2il.2 2.61.3
5 19.0i .1 4.2i.5

 

 

aDeviations listed are linear estimates of the standard
deviations obtained with program KINFIT.

71

Table 16. The Variation of the Linewidth and Chemical
Shift With Temperature for Two Solutions Which
Contain the 15-C-5 Complexing Agent and NaI.

 

 

Temp Av15 T2(msec) Appm

 

1:1 Ratio of Na+ to Crown

+ 2.5 24.4 13.0 -3.1
- 9.7 34.2 9.3 -2.8
-17.4 39.0 8.2 -2.8
-26.2 53.7 5.9 -2.8
-38.3 73.2 4.3 -2.6

3:1 Ratio of Na+ to Crown

1.4 29.3 10.9 -9.3
- 9.0 29.3 10.9 -8.1
-22.3 43.9 7.2 -6.8
-34.3 63.5 5.0 -4.7

-4l.8 87.9 3.6 -3.5

 

 

72

H-—-——’

 

- 33.3%

 

 

 

 

 

 

 

ab' '-oB"-3b' ' 6"‘36 ’W
CHEMICAL SHIFT (PPM)
23 Na NMR Spectra of: A. Equimolar NaI and

15-C-5 in Methylamine B. lS-C-S, Na in Methyl-
amine.

Figure 11.

73

Table 17. The Variation of the Linewidth and Chemical Shift
of NaC+ and the Chemical Shift of Na‘ with Tem-
perature for the lS-C-S System in Methylamine.

 

 

 

 

 

 

Temp(VC) 0% NaC Appm NaC+ Appm Na— -— (msec-l)1
—28.8 175.8 -1.85 ---- 3.4
-39.8 190.4 -l.85 64.9 2.7
-45.1 233.5 0.0 65.8 2.1
-50.8 243.3 0.0 64.3 2.0
-56.0 268.6 -3.0 63.7 1.80
1Estimate from spectra 120%.

74

as in the 18-C-6 case. More work is needed to characterize

the lS-C-S crown exchange. However, it appears that this

will be an interesting system to study.

Discussion of Results

 

For the systems in the absence of exchange, the results

38 in which the donor

are reasonable. From the work of Popov
number of basic solvents was correlated with the sodium
chemical shift it is expected that the chemical shift of Na+
in MA would be near that in ethylamine (~ll.3) and ammonia
(~13.1). The chemical shift for the salt in MA was not
extrapolated to infinite dilution so the results are not
exactly comparable. HoWever, the results given in Table

7 are in good agreement with expectation.

The results of the Na“ systems which show exchange are
very interesting. Several facts are evident from the data
presented previously. First, the apparent activation energy
(Ea) is very high ranging from 18.2 - 25.2 kcal mole-l.
This is in sharp contrast to the results of Shchorigt al.34
who found that the dibenzo—lB—crown-G activation energy for
cation exchange was relatively low (8.3 kcal mole-l) and in-
dependent of solvent. Studies in this laboratory of the
decomplexation of C222 give activation energies in the
range of 12-16 kcal mole”1 depending upon the solvent. It

also appears that when 18~C-6 is added to a solution con-

taining Na- the reaction

75

Na + Na+ + 2e-

does not proceed to a great extent.

by allowing the computer to adjust PC and P

This was determined

B for a sample

in which 18-C-6 was added after the solution had been pre-

pared.
sensitive to the presence of free crown.

it is clear that fiL-is very dependent on
B

of various species in the sample.
This evidence suggests the presence

mechanisms of exchange. Figure 12 shows

P

P

0°C vs.[Na-] and l; at 0°C vs.
TB B

The activation energy also appears to be extremely

In view of this

the concentration

of two competing

a plot of l; at
TB

for the five samples.

Again we see the presence of several distinctive trends.

Examination of the possible mechanisms shows that a combina-

tion of mechanisms A and B could be consistent with this

behavior.

k1

 

 

NaC+ z Na+ + C
k-l
k
- 3 _
Na : Na+ + 2e
k—3
The expression
.3; z 1
TB [1 + :1 :B]
3 C

From Table 6 we have for mechanism A which is

4.31

76

 

 

 

 

5..
to 4‘
$2
x 3. 03
km o4
b 2.
O2
11
i5
.10 f .15 ' .13 ‘ .13 '
[NA-J
5‘ 01
C”)
2 4.
X
m3~ 03
\k °4
"' 2
1 02
1.
05
T 1 F I I
.2 .4 .6 .8 1.
Pc/
Pb

Figure 12. Plot of l/rB at 0°C vs (A) Na' Concentration (B)
Population of Na- Site/POpulation of NaC+ Site
(PC/PB) for Various Samples.

77

While for mechanism B which gives exchange via

 

 

 

 

 

 

1
NaC+ z Na+ + C
k—l
k
- 4 -
Na+ + Na 1 Na + Na+
k-4
we have
.1. _ k1
' _
TB (CT-NaC+)
[1+k_1 _
2k4(Na )
When A and B are combined we obtain
1 k1 k1
F = + +
B k P [c -NaC
[1 + El-—§] [1 + k —_E____Y
+
k1 PA k_l[CT-NaC 1
if k P >>l and _ >> 1
3 C k4(Na )

then we have

JL.— k PC + Zklk4 (Na )
T' _ _—' k +
B B -1 (CT-NaC )

 

4.39

Equation 4.39 predicts that when the concentration of free

P

crown is large, gg-is proportional to —E. When the free

B PB

crown concentration is small mechanism B dominates the

exchange. This would qualitatively explain the variation

78

P

of iL-with 5—. Points 1, 2 and 5 are reasonably linear and
B B

could represent the effect of mechanism A. Points 1, 3,

and 4 show the effect of excess crown in which case mechanism
B would become operative. This assumes that sample 3 which
is of high concentration has excess crown present in solu-
tion because of solubility limitations on the concentration

P

of Na-. Other experiments are needed in which FE and excess
B

18-C-6 are systematically varied so that these effects can
be studied further.

The results of the lS-C-S system are very intriguing
because of the relatively narrow line of the complex NaC+.
This narrow line could be caused by several phenomena. The
principal reason for variation in alkali metal NMR line width
is the quadrupolar relaxation of the nucleus. This kind of
relaxation is dependent on the field gradient about the
nucleus. The compound with the larger gradient has a
broader line. Therefore, the narrow line in the lS-C-S
system could be because the 15-C-5 has a more symmetrical
structure in solution than the other crowns. A second ex-
planation could be that the correlation time is different
in the lS-C-S case. It is not reasonable to believe that
the intermolecular motion of the two crowns (15-C-5 and 18-C-6)
is different enough to cause tfifij; change in correlation
time. Therefore, it would require some type of intramolecu-
lar motion to cause this difference in correlation times.

This may be a reasonable explanation for the difference
in line broadening by crowns and deserves more attention in

future work.

REFERENCES

10.

11.

12.

13.

14.
15.
16.

17.

REFERENCES

J. L. Dye, Pure Appl. Chem., 1 (1970).

 

For discussion of current models of Ammonia solutions,
see proceedings of Colloque Weyl IV, J. Phys. Chem. (to
be published).

 

J. L. Dye in "Electrons in Fluids", J. Jortner and L. R.
Kestner, Ed., Springer-Verlag, West Berlin, 1973, p. 77.

S. Matalon, S. Golden and M. Ottolenghi, J. Phys. Chem.,
1%, 3098 (1969).

 

I. Hurley, T. R. Tuttle, Jr. and 8. Golden, J. Chem.
Phys., 48, 2918 (1968).

J. L. Dye in "Electrons in Fluids", J. Jortner and L. R.
Kestner, Ed., Springer-Verlag, West Berlin, 1973.

F. J. Tehan, B. L. Barnett and J. L. Dye, J. Amer.
Chem. Soc., 26, 7203 (1974).

 

 

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

J. C. Petersen, J. Amer. Chem. Soc., 89, 7017 (1967);
23, 386 (1970). “m

 

B. Dietrich, J. M. Lehn, and J. P. Savvage, Tetrahedron
Letters., 2885 (1969); 2889 (1969); J. Amer. Chem. Soc.

23. 7§Is (1970).

J. L. Dye, M. G. DeBacker, V. A. Nicely, J. Amer. Chem.
Soc., 22, 5226 (1970).

 

 

 

J. L. Dye, C. W. Andrews, 5. E. Mathews, J. Phys. Chem.,
(to be published).

 

J. M. Ceraso and J. L. Dye, J. Chem. Phys. 6%, 1585
(1974). 7‘—

 

D. E. O'Reilly, J. Chem. Phys., 41, 3729 (1964).

 

D. E. O'Reilly, J. Chem. Phys., 31, 3736 (1964).

 

J. M. Lehn, J. P. Savvage, B. Dietrich, J. Amer. Chem.
Soc., 22, 2916 (1970).

 

E. Shchori, J. Jagur-Guodzinski, Z. Luz, and M. Shporer,
J. Amer. Chem. Soc., 3%, 7133 (1971).

 

79

18.
19.

20.

21.

22.

23.

24.

25.

26.
27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

80

E. Shchori, gt 31., J. Amer. Chem. Soc., 25, 3842 (1973).

 

J. M. Ceraso and J. L. Dye, J. Amer. Chem. Soc., 35,
4432 (1973).

 

J. A. Pople, W. G. Schneider, and H. J. Bernstein, "High
Resolution Nuclear Magnetic Resonance", McGraw-Hill,
New York, NY, 1959.

J. M. Ceraso and J. L. Dye (1974).

For example, S. 0. Chan and L. W. Reeves, J. Amer.
Chem. Soc., 25, 670 (1973); J. Amer. Chem. Soc., 95,

 

Pat Smith, M. S. Thesis, Michigan State University,
East Lansing, Michigan, 1975.

 

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

Fred Tehan, Ph.D. Thesis, Michigan State University,
East Lansing, Michigan, 1975.

 

I. Langmuir, Phys. Rev., 2, 329 (1913).

S. Goldman, R. G. Bates, J. Amer. Chem. Soc., 24,
1476 (1972).

 

G. N. Lewis, M. Randall, B. S. Pitzer, and L. Brewer,
Thermodynamics, p. 503, 523. McGraw-Hill Book Co.,
New York, 1961.

 

J. M. Lehn, Struct. Bonding, (Berlin), 16, 1 (1973).

 

T. C. Waddington, Adv. Inorg. Chem. Radiochem., 1,
157 (1956).

 

C. J. Moody and J. D. R. Thomas, J. Chem. Ed., 32, 205
(1965).

M. R. Arshadi, J. CFTAR., 1Q, 1569 (1974).

J. L. Dye, C. W. Andrews, and S. E. Mathews, J. Chem.
Phys. (to be published).

E. Shchori, et al., J. Amer. Chem. Soc., 93, 7133 (1971);
95, 3842 (1973).

 

J. M. Ceraso, J. L. Dye, J. Amer. Chem. Soc., 25, 1958
(1973).

 

C. Deverell, Progress in Nuclear Magnetic Resonance
Spectroscopy,fig, 235 (1968).

 

 

37.

38.

81

J. L. Dye, P. Smith, S. Landers and J. Ceraso (to be
published).

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

   

”11111111111111[11131111fiifiliufiflfljmfix'ES

 

082 217