Title: Nuclear relaxation in fluorine-containing liquids
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Title: Nuclear relaxation in fluorine-containing liquids
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Language: English
Creator: Watkins, Charles Lee, 1942-
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Copyright Date: 1968
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Volume ID: VID00001
Source Institution: University of Florida
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NUCLEAR RELAXATION IN
FLUORINE-CONTAINING LIQUIDS













By

CHARLES LEE WATKINS


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY











UNIVERSITY OF FLORIDA
1968


















ACKNOWLEDGMENTS


The author wishes to express his appreciation to

Dr. Wallace S. Brey, Jr., who directed this research, and

to Dr. Willis B. Person and Dr. L. K. Krannich for helpful

discussions.

A special expression of gratitude is given to the

author's wife, Mary Lou, whose patience and understanding

helped make the completion of this work possible.

Also, the author wishes to thank the National Aero-

nautics and Space Administration for financial support during

the period of this investigation.
















TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS .. .. . . . . . .. . ..... . ii

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

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


LITERATURE REVIEW . . . . . . . . . ..... 1

Nuclear Spin-Lattice Relaxation in Liquids . 1
Hydrocarbon-Fluorocarbon Interactions . .. ... .. 13

INTRODUCTION . . . . . . . . .. . . . 16

EXPERIMENTAL . . . ... . . . . . . ... 18

NUCLEAR SPIN-LATTICE REIAXATION IN SEVERAL FLUOROBENZENE
DERIVATIVES . . . . . . . . . . . . 21

Experimental Results and Discussion . . . . ... 21

o-, m-, and p-Chlorofluorobenzene .... . . .. 21
o-, m-, and p-Fluoroiodobenzene .. . . . . 39
o-, m-, and p-Fluoroaniline . .. .. . .. 50
o- and m-Fluorophenol .. . . . . . . . 52

SPIN-LATTICE RELAXATION TIMES IN SOLUTION . . . . . . 54

Experimental Results and Discussion .... . . . .. 54

Hexafluorobenzene-Hydrocarbon Systems . . . . 54
2,2,2-Trifluoroethanol-Ethanol . . . ... 65
n-Perfluoroheptane-Isooctane . . . . . ... 68

SUMMA.RY ........... ........... .. 71

APPENDIX . . . . . . . . . . . .. .. 78

REFTRENCES .......... . . . . . . . 110

BIOGRAPHICAL SKETCH .... . . . . . . . 115















LIST OF TABLES


Table Page

1. The Temperature Dependence of T1 in o-Chlorofluorobenzene 79

2. The Temperature Dependence of T1 in m-Chlorofluorobenzene 80

3. The Temperature Dependence of T in p-Chlorofluorobenzene 81

4. The Temperature Dependence of TI intra' T inter T



5. The Temperature Dependence of T1 intra' 1 inter' 1 sr'

and T1 intra d in m-Chlorofluorobenzene . . . 83
6. The Temperature Dependence of T1 i T i T
I1 intra' 1 inter' 1 sr'


and T intra d in p-Chlorofluorobenzene . . . . .. 84
1 intra d



7. The Temperature Dependence of T T. Tt
1 intra' I inter 1 sr


in -Chlorofluor in -Chloren luorobnzene . . . . .... 8

8. The Temperature Dependence of T
1 intra


in m-Chlorof luorobenzene . . . .. . . . .. 8

9. The Temperature Dependence of T
1 intra


in m-Chlorofluorobenzene . . . . . . . . 87
9. The Temperature Dependence of T
1 intra
in p-Chlorofluorobenzenc .. .... ......... . . . .87

10. Bond Distances and Moments of Inertia for o-, m-, and
p-Chlorofluorobenzene ............ . . . 88

11. Energies of Activation for Rotational and Translational
Motion in o-, m-, and p-Chlorofluorobenzene .. . . . 88

12. Calculated Values of T1 intra d from BPP Theory at Various
1 intra d
Temperatures for o-, m-, and p-Chlorofluorobenzene . . 89

13. Calculated Values of T from Steele Theory at
V intra d
Various Temperatures for o-, m-, and p-Chlorofluorobenzene 90













LIST OF TABLES (Continued)


Table

14.

15.

16.


Temperature Dependence of

Temperature Dependence of

Temperature Dependence of


T in o-Fluoroiodobenzene .

T1 in m-Fluoroiodobenzene

T in p-Fluoroiodobenzene .


17. The Temperature Dependence of T
1 irttra
in o-Fluoroiodobenzene . . . .

18. The Temperature Dependence of T1 intra

in m-F luoroiodob nzene . . . . . . .

19. The Temperature Dependence of T
1 intra
in p-Fluoroiodobenzene . . . . . . .

20. The Temperature Dependence of T intra T in.er
1 intra' 1 inter'
and T intra d in o-Fluoroiodobenzene . . .


21. The Temperature Dependence of T intra T1 inter'

and TI intra d in m-Fluoroiodobenzene . . .


22. The Temperature Dependence of T intra T inter
1 intra d in p-Fluorointerodobenzene .
and T in p-Fluoroiodobenzene.......
1 intra d


T
1 sr'







Tsr'
1 sr'



T-
1 sr


23. Energies of Activation for Rotational and Translational
Motion in o-, m-, and p-Fluoroiodobenzene . . . . .

24. Calculated Values of T intra d from BPP Theory at Various
1 intra d
Temperatures for o-, m-, and p-Fluoroiodobenzene . . .

25. The Concentration Dependence of (fl/f ) T in the
o 1
Hexafluorobenzene-Cyclohexane System where X Represents

the Hexafluorobenzene Mole Fraction . . . . . .

26. The Concentration Dependence of (2/2 ) T in the

Hexafluorobenzene-Benzene System where Xf Represents

the Hexafluorobenzene Mole Fraction . . . . . .


Page

91

92

93


S. 94



S. 95


96



97




98




99



100



100





101





102











LIST OF TABLES (Continued)


Table Page

27. The Concentration Dependence of (01/l ) T1 in the
Hexafluorobenzene-Mesitylene System where X Represents
the Hexafluorobenzene Mole Fraction . . .. . . .. 103

28. The Concentration Dependence of the Proton Chemical Shifts
in the Hexafluorobenzene-Mesitylene System where X
Represents the Hexafluorobenzene Mole Fraction .. . .104

29. The Concentration Dependence of (/T) ) T in the
Hexafluorobenzene-Dimethylformamide System where X
Represents the Hexafluorobenzene Mole Fraction . .... 105

30. The Concentration Dependence of the Proton Chemical Shifts
in the Hexafluorobenzene-Dimethylformamide System where Xf
Represents the Hexafluorobenzene Mole Fraction . . .. 106

31. The Concentration Dependence of (1/Tf ) T in the
2,2,2-Trifluoroethanol-Benzene System where Xf Represents
the 2,2,2-Trifluoroethanol Mole Fraction .. . ... .107

32. The Concentration Dependence of (7/Tfo) T1 in the
2,2,2-Trifluoroethanol-Ethanol System where X Represents
the 2,2,2-Trifluoroethanol Mole Fraction .. . ..... 108

33. The Concentration Dependence of (//Tf ) T in the
n-Perfluoroheptane-Isooctane System where Xf Represents
the n-Perfluoroheptane Mole Fraction .. ..... . .109

















LIST OF FIGURES


Figure Page

1. The Temperature Dependence .of T1 in o-Chlorofluorobenzene 22

2. The Temperature Dependence of T1 in m-Chlorofluorobenzene 23

3. The Temperature Dependence of T1 in p-Chlorofluorobenzene 24

4. The Temperature Dependence of T1 intra' T1 inter and

T1 intra d in o-Chlorofluorobenzene . . . . . 26


5. The Temperature Dependence of T intra T1 inter and
1 intra' 1 inter
T intra d in m-Chlorofluorobenzene . . . .... .. .. 27
1 intra d

6. The Temperature Dependence of T intra T inter, and

T intra d in p-Chlorofluorobenzene . . . .... .. .. 28
1 nntra d i

7. The Temperature Dependence of the Macroscopic Viscosity
in o-, m-, and p-Chlorofluorobenzene . . . . .. 32

8. The Temperature Dependence of T1 in o-Fluoroiodobenzene . 41

9. The Temperature Dependence of T in m-Fluoroiodobenzene . 42

10. The Temperature Dependence of T in p-Fluoroiodobenzene . 43

11. The Temperature Dependence of T i T inter' and
1 intra' 1 Lnter
T1 intra d in o-Fluoroiodobenzene . ... ..... . 44


12. The Temperature Dependence of T intra inter' and
1 ntra' 1 inter
T intr d in m-Fluoroiodobenzene . .. . . . 45
1 intra d

13. The Temperature Dependence of T intra T inter, and
Sintra d in p-Fluoroiodobenzene .tra 1 enter
T in p-Fluoroiodobenzene . ..... . . . . 46
1 intra d


vii












LIST OF FIGURES (Continued)


Figure Page

14. The Temperature Dependence of the Macroscopic Viscosity
in o-, m-, and p-Fluoroiodobenzene . . . . . .. 48

15. The Temperature Dependence of T in o-, m-, and
p-Fluoroaniline ... .... .. ........ . . 51

16. The Temperature Dependence of T in o- and m-Fluorophenol 53

17. The Concentration Dependence of (T/i ) T in the
o 1
Hexafluorobenzene-Cyclohexane System where Xf Represents

the Hexafluorobenzene Mole Fraction . . . .... . . 56

18. The Concentration Dependence of (1/7 ) T1 in the
o 1
Hexafluorobenzene-Benzene System where X Represents

the Hexafluorobenzene Mole Fraction . . . . ... 58

19. The Concentration Dependence of (/l ) T in the
o 1
Hexafluorobanzene-Mesitylene System where X Represents

the Hexafluorobenzene Mole Fraction . . . . ... 60

20. The Concentration Dependence of (/TI ) T in the
o 1
Hexafluorobenzene-Dimethylformamide System where X

Represents the Hexafluorobenzene Mole Fraction . . .. 63

21. The Concentration Dependence of (f/P ) T in the
o 1
2,2,2-Trifluoroethanol-Benzene and the

2,2,2-Trifluoroethanol-Ethanol Systems where Xf Represents

the 2,2,2-Trifluoroethanol Mole Fraction ...... . 67

22. The Concentration Dependence of (P/P ) T in the
o 1
n-Perfluoroheptane-Isooctane System where X Represents

the n-Perfluoroheptane Mole Fraction . ... . . . 69
















LITERATURE REVIEW


Nuclear Spin-Lattice Relaxation in Liquids


In a typical magnetic resonance experiment energy is absorbed

from a radio-frequency (rf) source by a system of nuclear spins

immersed in a magnetic field, Ho, as a result of transitions among

the energy levels of the spin system. For each of N non-interacting

spins, characterized by I and [, the maximum z components of angu-

lar momentum and magnetic moment, respectively, there are 21+1 levels

spaced in energy by p H/I. Upon application of an oscillating mag-

netic field, transitions corresponding to stimulated emission and

absorption occur. If there is a net absorption of energy from the rf

source, there must be an initial surplus of spins in the lower energy

levels. This condition will be attained in time if there is some way

for the spin system to interact with its surroundings and come to

thermal equilibrium at a finite temperature. At equilibrium the popu-

lations of the 21+1 levels will be governed by the Boltzmann factor,

and there will be the necessary surolus of spins in the lower states.

The exposure of the system to radiation, with subsequent

absorption of energy, tends to uoset the equilibrium state previously

attained by equalizing the populations of the various levels. The new

equilibrium state in the presence of the rf field represents a balance

between the processes of absorption of energy by the spins from the











radiation field and the transfer of energy to the heat reservoir

comprising all other internal degrees of freedom of the substance

containing the nuclei in question. The latter process is called the

spin-lattice interaction and is described by T1, the spin-lattice

relaxation time [1]. Alternately, one may consider the spin-lattice

relaxation time as a measure of the time taken to attain equilibrium

after application of the constant magnetic field, Ho, to the spin

system.

Magnetic resonance can be used to obtain information about the

nature and rate of molecular motion in a liquid. The value of 1/T1 is

effectively the transition probability of a nuclear spin reorientation

and depends, in general, on the fluctuating interactions of the spin

with the lattice. These fluctuating interactions arise from molecular

motion in the liquid [2]. Random motion of the molecules produces

fluctuations in the local magnetic fields which can induce transitions

between nuclear Zeeman levels if there is an appropriate frequency

component [3].

The various magnetic interactions which are modulated by

molecular motion in diamagnetic liquids are the following [4,5]:

1. Relaxation by direct dipole-dipole interactions between
like or unlike nuclei,

2. Scalar interrupted interaction,

3. Anisotropic exchange interaction,

4. Local anisotropic shielding field, and

5. Spin-rotation interaction.












Paramagnetic molecules or ions, if present as dissolved

impurities, will often provide the most efficient relaxation mechanism

in liquids and must be excluded [1,51 if other mechanisms are to be

studied.

If the nucleus being observed possesses a quadrupolar moment,

the interaction of the quadrupolar moment with the magnetic field is

usually the dominant relaxation mechanism. Motional processes have

been studied by direct measurement of the Tl of the quadrupolar nucleus

[6-9]. If the quadrupolar nucleus is not the nucleus being observed,

there can still be a secondary coupling effect between the spin of the

observed nucleus and the quadrupolar moment. This effect is usually

considered to be negligible [5].

Dipole-dipole and spin-rotation interactions are the most

important relaxation mechanisms for diamagnetic liquids and will be

discussed at length. Relaxation due to the local anisotropic shield-

ing field will also be mentioned for historical reasons.

Dipole-dipole interactions may be classified as intermolec-

ular or intramolecular according to whether or not the two interacting

nuclei are in the same molecule. To be an effective relaxation process

the interaction Hamiltonian must be modulated by random variation of

the internuclear distance and the orientation of the internuclear

vector with respect to the external magnetic field. Molecular reori-

entation is the chief means of achieving intramolecular interactions.

Molecular vibrations are ineffective since the correlation time is too

short, and the change in bond length is too small. Therefore, only











molecular reorientation is to be considered [10]. However, for

intermolecular interactions both parameters are varied by a combina-

tion of molecular reorientation and translational diffusion. It is

usual to simplify the treatment of intermolecular interactions by

ignoring molecular reorientation as compared to translational diffu-

sion [5].

Wangsness and Bloch [11,12] give an approximate treatment of

intermolecular dipole-dipole interactions in which a single molecule

is isolated from the rest of the liquid. All spins outside that one

molecule are considered as belonging to the lattice. The spin relax-

ation of one molecule is considered as due to a randomly fluctuating

magnetic field caused by all the other spins in the liquid.

The basic theory of dipole-dipole interactions in magnetic

resonance was developed by Bloembergen, Purcell, and Pound [.l]

Briefly, the BPP theory considers a rigid lattice of dipoles for which

a general Hamiltonian is written. Those terms in the dipolar part of

the Hamiltonian are nicked out which will be effective in relaxation.

The local magnetic field produced at one nucleus by neighboring mag-

netic nuclei is spread out into a Fourier spectrum extending to fre-

quencies of the order of 1/T, where T is a correlation time associated

with local Brownian motion and closely related to the characteristic

time which occurs in Debye's theory of polar liquids [13]. Essentially,

the theory describes the rotational and translational motion of the

molecules by means of a classical diffusion equation. An expression












for the dipolar part of T1 as modified by Solomon [14], Kubo and

Tomita [15], and Powles and Neale [16] may be written


1 2 d f(Tda) + N oa- (r) (1)
T d g i>j5 2

where


f(T) = ] (2)
1 + W2 T 1 + 4m2 2
r r


y = magnetogyric ratio,

i = Planck's constant,

ng = number of nuclei in a group in a molecule interacting
with one another,

d.. = distance between i and t nucleus,
13
n = number of resonant nuclei in a molecule,
m
N = number of molecules per cubic centimeter,
o
a = effective radius of the molecule,

T = angular position correlation time involving functions
da as (3 cos2 9 1),

Td = complex position correlation time involving functions
as r-3(3 cos 9 1) involving nuclei in different molecules,

r) = resonant angular frequency, and

T = correlation time of the interaction.


In the extreme narrowing situation where ur d << 1, the case

in most liquids, the intramolecular and intermolecular dipole contribu-

tions may be calculated as












1 3/2 y 4t2 2 No (3)
T k. r
1 inter

and

1 2 4 6
S = 3/2 f2 y ( Z r..) T
T1 intra d i

+ 4/3 2 Y 2 y If(If+l)( r-6) (4)
f i

where 1 is the macroscopic viscosity of the liquid.

Richards [3] has calculated T1 by fluctuation theory in terms

of a correlation function G(T) which represents the probability that

some function F of the coordinates of the molecule in question has not

changed significantly after a time T. The Fourier transform J(u) of

G(T) gives the intensity of the fluctuations at frequency w. A rota-

tional diffusional model is introduced, and the spin-lattice relax-

ation time is obtained by treating the local fluctuating field as

a small perturbation.

The spin-rotation interaction arises from the breakdown of the

separability of the electronic and rotational Hamiltonians for a rotat-

ing molecule [17]. The interaction is the response of the ground-state

electrons to the rotational motion, the electronic response being

described mathematically as a linear combination of ground and excited

electronic states. Some of the excited states possess electronic

angular moment which produce rotationally dependent magnetic fields

at the nuclei.












If a molecule rotates at an angular velocity w, the rotation

may be described by an index of the angular velocity J, given by


I W = TJ (5)


where I is the moment of inertia of the molecule. If free rotation

exists, J is the angular momentum operator. However, J is not usually

a good quantum number in liquids. It is unlikely that a molecule

makes one revolution in a liquid without interruption so the molecular

rotational levels are blurred by lifetime broadening. Spin-rotation

fields can be much larger than dipolar fields [2]. They are fluctu-

ating since the angular velocity of a molecule in a liquid changes

rapidly.

The spin-rotation Hamiltonian is written as


H = -4 I.c.J (6)
sr


where c is a tensor quantity known as the spin-rotational interaction

constant. Hubbard [18] has calculated the spin-rotation contribution

to the spin-lattice relaxation time for a spherical molecule as
2 2
1 2kTI(2c + c,2 ) sr
1_1 sr (7)

1 sr 3(1 + u2 T2 )2
r sr


where cj and cl are the components of the spin-rotational tensor.

Gutowsky and Woessner [19] measured the T 's in several Freons.

The molecular structures are such that by considering dipole-dipole

relaxation only, the proton and fluorine Tl's should be about equal.

The observed proton T 's, however, are several times longer than the












corresponding fluorine T 's. Attempts were made to explain this fact

on chemical shift or local field anisotropies. Anisotropy in the

chemical shift tensor produces in the laboratory xy plane, at the

nucleus, a magnetic field axially symmetric about the z' axis.

Molecular reorientation produces fluctuations in the field which
2 2
contribute a term to T In narrowing limit, io T << 1, this contri-

bution should be proportional to H2 [5]. The contribution from shield-

ing anisotropy is the only field-dependent relaxation term. Thus, T1's

at various magnetic field strengths should indicate importance of this

term. Its contribution is negligible for several flourine-containing

systems [4,10,19-21]. The difference between proton and fluorine T 's,

especially at higher temperatures, has been attributed to the spin-

rotation interaction [2,4,10,21-23].

The most useful information from T1 measurements is obtained by

separating the magnitudes of the various motional processes. Since

1/T is effectively a transition probability, to a first approximation

the various contributions may be written

1 = 1 1 (8)
1 1 intra 1 inter


where dipole-dipole and spin-rotation interactions are considered only.

If each motion is described by a single correlation time which is an

exponential function of temperature, an Arrhenius plot may be used to

obtain the energy of activation of the motional process [1,24-26].

The simplest method for separating the intermolecular and

intramolecular contributions to T1 is by extrapolation to infinite











dilution in a nonmagnetic solvent. At infinite dilution the intra-

molecular contribution will remain (which includes spin-rotation),

but the intermolecular will not [3, 27-29].

There is the question, however, of whether or not the dominant

contribution at infinite dilution is the perturbation of the solvent

upon the intramolecular motion. Also, uncertainties in experimental

measurement due to very weak signal strengths are to be considered

[9,30].

A method of separating the intermolecular and intramolecular

contributions for proton spin-lattice relaxation times is successive

deuteration. The perdeuterated analog of the liquid to be investi-

gated is used as the solvent. There must be no hydrogen-deuteriun

exchange. For a solution of a liquid with its perdeuterated analog,

the proton T1 is given by


1 1 + 1 [a + (l-a)F] (9)
1 1 intra 1 inter


where Y is the percentage of ordinary liquid. The factor F is

introduced to take into account the intermolecular contributions due

to the perdeuterated molecules. For values of a up to about 0.25,

(l-a)F is negligible with respect to a, and a plot of 1/T1 versus a

yields a straight line with the intercept equal to /T1 intra at

equals zero [30-32]. Powles points out that in the case of benzene-

hexadeuterobenzene solutions it is a good assumption that the benzene

motion is not substantially changed upon addition of hexadeuteroben-

zene [30,31]. The method depends on the fact that, as a is decreased,











the intermolecular proton-proton interactions are replaced by deuteron-

proton interactions where the relative magnitudes are represented by

the factor F.

The spin-rotation contribution to T1 may be obtained by sub-

traction if the intermolecular and intramolecular dipole-dipole inter-

actions are known. Also, it may be calculated directly using Hubbard's

equation [18]. Powles obtained the spin-rotational contribution to

the fluorine spin-lattice relaxation time in fluorobenzene by extrap-

olation of the dipolar contributions at low temperatures [2]. If the

BPP theory is applicable, a plot of log T1 versus 1/T should be linear

for dipole-dipole interactions. This is the case for the proton T1 in

fluorobenzene. The fluorine T1 plot is linear at low temperatures,

but falls off rapidly at higher temperatures. Powles attributed this

decrease in T1 at higher temperatures to spin-rotation. By extrap-

olating the T1 fluorine curve at low temperatures parallel to the T

proton curve and by subtracting the T1 fluorine extrapolation for

dipole-dipole interaction from the actual fluorine T1 measurements,

the spin-rotational contribution is obtained.

Hubbard has calculated the intermolecular contribution in the

form of a Taylor Series [33]. He has also derived a relationship

between the intramolecular dipole correlation time and the spin-rotation

correlation time which is


T T = -
d sr 6kT











where I is the moment of inertia [34]. The change in orientation of

the molecule is assumed to be due to rotational isotropic Brownian

motion. These equations are based on Stokes' diffusional model for

spheroidal molecules.

The chief difficulty in calculating the various contributions

to the spin-lattice relaxation time from the derived equations is in

obtaining reliable correlation times. The BPP theory assumes that

dipole-dipole interactions are diffusionally controlled processes.

The correlation time is given by

T = 4n T] a3/kT (11)


For intermolecular dipolar interactions the BPP theory seems to give

an adequate representation. However, for intramolecular dipolar

contributions, the theory is adequate only for polar highly associated

liquids. In most cases, the relaxation times predicted are much

shorter than those observed [28,29,30,35]. Steele argues, in fact,

that there is no direct relationship between macroscopic viscosity

and molecular rotation [35].

Spernol and Wirtz [36] and Gierrer and Wirtz [37] suggested

that the macroscopic viscosity be replaced by a microviscosity coef-

ficient which reduces the Debye correlation time by a factor of six

for pure liquids. Steele has proposed an inertial model in which the

rotational motion is best described by classical equations of motion

for a rigid rotator. He calculated the rotational contribution to

the spin-lattice relaxation time in several hydrocarbons and derived











a maximum value of the rotational correlation time by assuming that

the molecule turns one revolution without interruption [35,38,39].

Also, a single correlation time may not adequately describe

the motions, but it may be necessary to have a distribution of corre-

lation times. This is especially true in viscoelastic liquids where

a minimum in T1 as a function of temperature is often observed.

Meister [40,41] has used the Kubo-Tomita [15] model as modified by

McCall [42] to accommodate a distribution of correlation times in

hydrogen-bonded liquids.

Also, spin-lattice relaxation may be used to study solution

phenomena. Information regarding the calculation of correlation times

and contributions of various motional processes can be obtained from

solution studies. Two such examples have already been given, the

methods of successive dilution and successive deuteration. A study

of the concentration dependence of T1 provides a method of obtaining

a model for calculating correlation times. Both the microviscosity

model [36,37] and the Hill model [43,44] give better agreement with

experiment than the BPP model for most solutions. The Hill model is

based on the calculation of a mutual viscosity between the solvent

and solute. Mitchell and Eisner [29] measured the proton T1 for

benzene, cyclohexane, chlorobenzene, and bromobenzene in carbon

tetrachloride and carbon disulfide solutions. The Hill model prop-

erly accounts for the variation of both the rotational and transla

tional relaxation times with concentration of solute.

The formation of molecular clusters and the presence of

solute-solvent interactions may be detected by T1 measurements.












The BPP theory states that the viscosity connected product (f/fo)T1

should not vary with concentration where 1 is the solution viscosity

and T0 is the solvent viscosity. Giulotto [27] studied chlorobenzene
o

in carbon tetrachloride and confirmed these results, concluding that

molecular association is not present. However, solutions of phenol

gave results inconsistent with BPP theory which Giulotto attributed to

the self-association of the phenol. C. R. K. Murthy [45] observed a

minimum in T1 at 0.5 mole fraction in the mixture phenyl isothiocyanate

and diethylamine. The viscosity shows a sharp maximum; there is a

large exothermic heat of mixing, and there is a volume contraction,

all indicating a high degree of association. If molecular association

occurs, T1 should possess a minimum. Since the correlation time is

inversely proportional to Tl, any associative process will make T

longer since it takes a longer time for rotation or translation to

occur.

Brownstein [46] has studied by spin-lattice relaxation measure-

ments various weakly interacting systems which do not show a chemical

shift change with change in concentration.


Hydrocarbon-Fluorocarbon Interactions


A large amount of information has been gathered in the last

twenty years on fluorocarbon-hydrocarbon solutions [47]. Various

thermodynamic, charge-transfer, and nuclear magnetic resonance studies

have been conducted, chiefly in order to explain their unusual solubil-

ities. What factors cause the large deviation from regular solution











theory is not known. A brief discussion of the physical properties

of fluorocarbon-hydrocarbon solutions and the possibility of using

spin-lattice relaxation measurements as a means of investigating their

unusual behavior is now presented.

The chief approach to the analysis of the thermodynamic prop-

erties of these solutions has been the regular solution theory first

proposed by Hildebrand and Scatchard [48]. Experimental data accumu-

lated after the first attempt by Scott [49] to apply the regular solu-

tion theory to fluorocarbon-hydrocarbon solutions was in disagreement

with that theory [50-57]

There have been various explanations of this unusual behavior.

Dunlap [51] proposed a mechanical model. The hydrocarbons, because of

their small size, could fit together like gears. Because of this close

approach, not possible for fluorocarbon-fluorocarbon or hydrocarbon-

fluorocarbon solutions, the hydrocarbon-hydrocarbon interaction energy

should be very large. Hildebrand [58] suggested that the solubility

parameters of hydrocarbons be arbitrarily increased. Dunlap [59] also

suggested that the large heats of mixing observed are a result of large

volume expansions, and corrections to constant volume would remove

most of the anomaly.

Another approach has been the application of corresponding

states theory [60]. A Lennard-Jones potential function is assumed,

and the excess free energy is calculated. The collision diameter is

taken to be the arithmetic mean of the diameters of the two inter-

acting molecules, and the potential energy function is taken to be the











geometric mean. However, there is evidence in these solutions that

the geometric mean law does not hold [47,51,61,62].

Recently, attempts to explain the anomalous behavior of

fluorocarbon-hydrocarbon solutions have been based on studies of

specific intermolecular interactions. A study of l-hydro-n-perfluoro-

heptane in various hydrocarbons indicates that specific interactions

of the highly polar CHFJ group seem to dominate solution behavior [63].

Brady, using X-ray analysis, found that n-perfluoroheptane-isooctane

solutions show a large degree of scattering near the consolute temper-

ature, indicating the formation of fluorocarbon clusters [64].

Studies of hexafluorobenzene with various solvents indicate

the possibility of charge-transfer complex formation [65,66]. Most of

the systems form a 1:1 solid complex. Strong n-electron donors give

rise to absorption in the ultraviolet with hexafluorobenzene. However,

no absorption attributed to charge-transfer formation has been reported

for n-electron donors [67]. This may be attributed to the poor overlap

properties of the n-donor obitals with the weak acceptor orbitals of

hexafluorobenzene. Phase diagrams, volumes of mixing, and dipole

moments have been reported by Swinton [68,69] for six hexafluorobenzene-

hydrocarbon systems. He concludes that the existence of a compound in

the solid state does not necessarily imply any specific interaction in

the liquid state. The compound formation could be due to packing in

a more stable, lower energy configuration [70].
















INTRODUCTION


Proton spin-lattice relaxation times in liquids are usually

described by the theory of Bloembergen, Purcell, and Pound which

assumes that dipole-dipole interactions are the means of achieving

spin-lattice relaxation. In equivalent molecular structures, fluor-

ine spin-lattice relaxation times should be about the same as proton

spin-lattice relaxation times since their magnetogyric ratios are

about equal. Experimentally, it is found that the fluorine values are

considerably shorter. This behavior has been ascribed to the influ-

ence of the spin-rotation interaction. In the present investigation

several fluorine-containing liquids have been studied in order to

determine the relative importance of the various contributions to the

fluorine spin-lattice relaxation time.

One method of obtaining this information is through a study of

several similarly related compounds. Also, from a knowledge of the

temperature dependence of the various contributions, energies of acti-

vation for the motional processes may be obtained. In this manner,

the nature of the molecular motion in these fluorine-containing liquids

can be studied.

Another purpose of the investigation is to determine the

feasibility of using spin-lattice relaxation times in the study of

solution phenomena. Specific interactions, as hydrogen bonding and






17




charge-transfer, should be easily adaptable to study by this method.

One area of particular interest is that of perfluorocarbon-hydrocarbon

systems where considerable work has been done in an attempt to explain

their unusual thermodynamic properties.















EXPERIMENTAL


The spin-lattice relaxation times were measured by adiabatic

fast passage. In adiabatic fast passage, the magnetization vector

follows the precession of the effective magnetic field obeying the

equation

dH
0 << Jl H2 (12)
dt 1

where H1 is the applied rf field [5]. If the static magnetic field,

Ho, is symmetrically modulated by a sinusoidal or triangular sweep,

and if the time spent in resonance is short compared to T1, then at

equilibrium the signal on the return trace will be equal in amplitude

but inverted from that on the forward trace.

The magnetization at any time t, M1, is given by

1 exp(-t /T)
M = M (13)
1 expl-t/T (3)


where M is the magnetization at equilibrium in the H field [5].
O O

A modification of the above method is useful for T1 measurement.

The signal is no longer centered in the sweep field so there are

unequal time intervals above and below resonance. The time interval

difference, At, may be adjusted such that the signal vanishes on the

return trace as the magnetization returns to equilibrium. By knowing

the period of the sweep, P, and At, T1 is determined from the equation












Pt 1 2
At TIn 2 (14)
P = + exp(-P/r1) (


Conger and Selwood [71] have plotted the above equation.
19
The F T1 measurements were obtained with a Varian DP60

spectrometer operating at 56.4 MHz. The linear sweep unit of the

DP60 was replaced by a Wavetek model 110 function generator which

provided a triangular sweep which was placed directly across the

sweep coils. The sweep was displayed on a Hewlett-Packard model

120B oscilloscope. The field position and period were adjusted

until there was a null point on the return trace. Since the spin-

lattice relaxation times are several seconds long, the period was

measured manually with a stopwatch. At least five independent

measurements were made.

The temperature was regulated by the flow rate of dry

nitrogen through a Varian V4340 variable temperature probe assembly.

For the low temperature measurements, the nitrogen was cooled by

passing it through a copper coil immersed in liquid nitrogen. The

temperature was determined by a copper-constantan thermocouple placed

within the Dewar insert accurate to one degree. Most of the T1 meas-

urements of solutions were made at normal probe temperature, about

thirty degrees.

The rf output was calculated by the method of Anderson [72]

to see if adiabatic passage conditionswere being satisfied. The

correct rf level could then be chosen.











The system was calibrated by measuring the temperature

dependence of T1 for fluorobenzene and hexafluorobenzene. The cor-

responding plots were compared with those of Powles [2,4].

The removal of molecular oxygen is very important since

paramagnetic species can provide a dominant relaxation mechanism

[1,5]. The pump-freeze-thaw method was used to remove any oxygen

present. The cycle was repeated at least ten times for each sample.

The proton nmr chemical shifts were obtained using a Varian

A60 spectrometer. Tetramethylsilane was used as the internal

reference.

The viscosity measurements were made using an Ostwald vis-

cometer. Four milliliters of solution were used in each case.

Each measurement was repeated five times. To regulate the temper-

ature for viscosity measurements, a water bath was constructed in

which the temperature could be regulated to one-tenth of a degree.

All the fluorocarbons in this investigation were obtained

from Peninsular ChemResearch, Inc. The hydrocarbons were obtained

from various vendors, the best grade being obtained whenever possible.

All the compounds except ethanol and 2,2,2-trifluoroethanol were

dried over calcium hydride or phosphorus pentoxide and distilled just

before using. Ethanol and 2,2,2-trifluoroethanol were used as

obtained. The purity of the compounds was checked by nmr.
















NUCLEAR SPIN-LATTICE RELAXATION IN SEVERAL
FLUOROBENZENE DERIVATIVES


Experimental Results and Discussion


Only fluorine spin-lattice relaxation times will be discussed.

Unless otherwise specified, spin-lattice relaxation time refers to the

spin-lattice relaxation time of the fluorine nucleus. All tables are

in the Appendix.


O-, M-, and P-Chlorofluorobenzene

The temperature dependence of the fluorine spin-lattice relax-

ation time, TI, has been measured for the pure liquids o-, m-, and

p-chlorofluorobenzene. Plots of the log of T1 as a function of the

reciprocal of the absolute temperature are illustrated in Figures 1,

2, and 3 for o-, m-, and p-chlorofluorobenzene, respectively. The

experimental values are given in Tables 1, 2, and 3, respectively.

In general, the temperature dependence is similar to that

found by Powles [2] for the pure liquids, fluorobenzene and

hexafluorobenzene. At lower temperatures the plots are essentially

linear, indicating that the dipolar contribution is perhaps the only

major contributing factor in this temperature region. At higher

temperatures the plots are no longer linear but begin to fall rapidly,

indicating the presence of another type of relaxation process.

Powles [2] attributed this decrease in T1 with increasing temperature

to the spin-rotation interaction.




















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The linear portions of Figures 1, 2, and 3 were extrapolated

to higher temperatures to obtain the dipolar contributions. The

extrapolated plots are designated by the symbol T1 d on Figures 1, 2,

and 3.

Since the various relaxation processes are additive in

contributing to the total spin-lattice relaxation process, and since

the reciprocals of the various relaxation times are effectively

transition probabilities, the spin-rotational contribution can be

obtained by subtraction. The spin-rotational contribution is indicated

in Figures 1, 2, and 3 by TI sr and calculated from the equation


1 1 1
T I I- (15)
1 sr 1 1 d


Calculated values of T1 sr at ten-degree intervals are listed in

Tables 4, 5, and 6 for o-, m-, and p-chlorofluorobenzene.

The intramolecular contribution to T1 is obtained by the method

of extrapolation to infinite dilution, which has been discussed pre-

viously. Carbon tetrachloride was the solvent. The quadrupolar moment

of the chlorine nucleus may be neglected. The intramolecular contri-

bution, T intra is plotted as a function of 1/T for o-, -, and
1 intra'
p-chlorofluorobenzene, respectively, in Figures 4, 5, and 6. The

values are tabulated in Tables 7, 8, and 9. Values at ten-degree

intervals, taken from the plots of T intra in Figures 4, 5, and 6, are
1 intra
listed in Tables 4, 5, and 6 for the purpose of calculating subsequent

quantities.





















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The intermolecular contribution to the spin-lattice relaxation

time, T1 inter' can be obtained by subtraction, using the equation


1 1 1
=I-- 1- 1 (16)
1 inter 1 1 intra


The log of T1 inter as a function of 1/T is plotted in

Figures 4, 5, and 6 for o-, m-, and p-chlorofluorobenzene, respectively.

The values are tabulated in Tables 4, 5, and 6 at ten-degree intervals.

The intramolecular dipolar contribution to the relaxation time,

T1 intra d is obtained from the equation
1 intra d1

1 1 1
--- (17)
T T T
1 intra d 1 intra 1 sr


The log of T1 intra d is plotted as a function of 1/T in

Figures 4, 5, and 6 for o-, m-, and p-chlorofluorobenzene, respectively.

The values are tabulated in Tables 4, 5, and 6.

In each case, plots of the log of T1 and T1 in as

a function of 1/T are linear over a wide temperature range.

This linearity indicates a single relaxation process which is

exponentially dependent on temperature. If this assumption is valid,

the energy of activation for the process can be calculated. The spin-

rotation contribution is almost linear in each case,although theory

does not necessarily predict this. As the temperature is increased,

T inter and T intra d become larger in magnitude and become less
1 inter 1 intra d

effective as relaxation processes. This type of temperature depend-

ence is exactly that predicted for dipolar interactions by Bloembergen,











Purcell, and Pound [1]. In each case, T1 sr decreases in magnitude,

and spin-rotation becomes a more effective relaxation process with

increasing temperature.

The Arrhenius plots of T inter and T1 intra d become non-

linear at higher temperatures. The relaxation processes can be con-

sidered to be interrelated and no longer additive. Also, the density

of the sample changes with temperature which affects T slightly
1 inter

since the relative neighboring population changes about the molecule

in question.

Some interesting conclusions may be gotten about the various

forces governing the molecular motion in these three liquids by a

comparison of the various contributions to the spin-lattice relaxation

times.

The intramolecular dipolar contribution, T intra d' follows

the sequence o > m > p throughout the entire temperature range. This

is predicted by BPP theory. Equation (4) indicates that there is a

contribution from the dipolar interaction with nonresonant nuclei which

is inversely proportional to the sixth power of the distance between

the fluorine nucleus and the nucleus in question. Ortho hydrogens

would give the greatest contribution, meta hydrogens the next in magni-

tude, and para hydrogens the smallest contribution to relaxation.

Gutowsky [10] has shown that interaction of the quadrupolar moment of

the chlorine nucleus with the fluorine nucleus is negligible in CHFC12

for spin-lattice relaxation. Powles [32] calculated the effect of the

quadrupolar moment of bromine on the proton TI intra d in bromobenzene












and found it to be negligible. Therefore, the effect of the quadru-

polar moment interaction with the fluorine nucleus may be neglected

for spin-lattice processes. o-Chlorofluorobenzene has one ortho

fluorine-hydrogen, two meta, and one para interactions. m-Chloro-

fluorobenzene has two ortho, one meta, and one para fluorine-hydrogen

interactions. p-Chlorofluorobenzene has two ortho, two meta, and no

para hydrogen-fluorine interactions. The fluorine-hydrogen dipolar

interactions in p-chlorofluorobenzene would therefore be efficient in

intramolecular dipolar relaxation, giving the smallest T intra d
1 intra d

The intermolecular dipolar contribution, T1 inter' follows the

sequence o < p < m at temperatures above 20 degrees Centigrade. Below

20 degrees Centigrade, T inter follows the sequence o < m,p until the
1 inter

freezing points are approached where the three values are about equal.

The BPP theory predicts that the intermolecular contribution, T1 inter'

is governed by diffusion, and T inter is inversely proportional to

the macroscopic viscosity as demonstrated in equation (3). A temper-

ature-dependence study of the macroscopic viscosity for the three

compounds was made. Figure 7 shows plots of the log of the viscosity

as a function of 1/T for o-, m-, and p-chlorofluorobenzene. Benzene

is shown as the reference material on the plot The plots are linear

as expected. The important point is that over the investigated temper-

ature range the magnitudes of the viscosities follow the sequence

o > p > m, or the inverse of T inter This result lends evidence to
1 inter

the fact that the intermolecular relaxation time is governed by

diffusional processes.






















































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The spin-rotation contribution, TI sr follows the sequence

o < m < p over the entire temperature range. This result indicates

that the position of the chlorine atom on the aromatic ring has

a significant effect on the molecular motion of the molecule. From

equation (7), which is written for a spherical molecule, the spin-

rotation relaxation time, to a first approximation, should be inversely

proportional to the mean moment of inertia. The moments of inertia and

bond distances for o- and m-chlorofluorobenzene have been measured by

microwave spectroscopy [73,74]. However, there were no reported values

for p-chlorofluorobenzene. Since the bond distances were almost

exactly equal in the ortho and meta molecules, a set of values was

chosen, and the moments of inertia were calculated for p-chlorofluoro-

benzene. These values are summarized in Table 10. The mean moments

of inertia are in the sequence o < m < p, or opposite to that which

would explain the experimental results. It seems that the spherical

approximation is not a good one.

Assume that the major portion of the internal motion consists

of rotation about the axis in the plane of the ring coincident with the

C-F bond. The moment of inertia about this axis, IA, lies in the

sequence p < m < o which explains the experimental results. The moment

of inertia about the C-F bond axis for each of the three molecules is

significantly smaller than the moments of inertia about the other two

axes. As the chlorine is moved on the ring from the para to the ortho

position, deviation from cylindrical geometry causes more restricted

motion [31] and introduces tumbling of the molecule. Another











explanation is that as the moment of inertia, IA, is increased in

going from the para to the ortho position, the rotational motion about

the C-F bond axis is more restricted, and rotational motion about the

other two axes becomes significant.

The Arrhenius energies of activation for the intramolecular

and intermolecular dipolar interactions may be obtained from Figures 4,

5, and 6. The values are listed in Table 11. These values agree with

those reported for other aromatic systems [32]. The energies of acti-

vation for intramolecular motion, or essentially rotation of the mole-

cule by BPP theory, lie in the sequence o > m > p. Rotation occurs

much easier in p-chlorofluorobenzene presumably because of the higher

symmetry of the molecule. The more asymmetric the motion due to the

deviation from cylindrical geometry, and the higher the moment of

inertia about the rotational axis coincident with the C-F bond axis,

the greater is the energy of activation for rotation.

The intermolecular energies of activation lie in the sequence

o > m > p, the same as the energies of activation for rotation. The

energies of activation for the ortho and meta molecules are almost

the same, whereas the para molecule has a significantly lower energy

of activation. This result may again be explained by higher symmetry

of the para molecule.

For comparison with the experimental values, the intramolecular

dipolar contribution to the spin-lattice relaxation time, T1 intra d'

has been calculated using equation (4). The correlation time was chosen

to be the Debye correlation time given in equation (11). This is the











correlation time in BPP theory. A comparison of the experimental

and calculated times would give an indication of the applicability

of BPP theory to nonspherical molecules. The two variables besides

the temperature in equation (11) are the macroscopic viscosity and

the molecular radius of the sphere. Plots of the log of the macro-

scopic viscosity as a function of 1/T are given in Figure 7. Close

packing of spheres was assumed to calculate the molecular radius.

The bond distances needed in equation (4) were obtained from microwave

spectroscopy [73,74]. These calculations for o-, m-, and p-chloro-

fluorobenzene at various temperatures are given in Table 12. A com-

parison of the experimental and calculated values shows that the BPP

theory predicts too efficient a relaxation mechanism. That is, the

relaxation times are too short. The assumption of spherical symmetry

might not be expected to apply in these molecules. However, the BPP

theory does show the proper ordering in regard to relative magnitudes

with o > m > p as found experimentally. Agreement is better in the

para molecule than in the ortho or meta molecule presumably because of

the cylindrical symmetry.

Steele has suggested that the relations described above, between

macroscopic viscosity and molecular rotation, are not valid [35]. In

their place he proposed an inertial model of rotation. A correlation

time may be obtained from the equation of motion for a rigid rotator

and is given by


T j (18)











where I is the mean moment of inertia calculated from


I-1 = 1/3 I 1 B Cl) (19)


T intra d may be calculated using equations (4) and (18). Values

of T1 intra d calculated by the Steele approach are given in Table 13

for o-, m-, and p-chlorofluorobenzene. The calculated values differ

from the experimental values by an order of magnitude. Steele pointed

out that the discrepancies which appear in his model were for the

values for molecules where a large molecular dipole is present. The

T intra d calculated by Steele is the maximum theoretical value based

on the fact that the molecule goes through one period of revolution

without spin exchange. The experimental values in each case are

shorter than the calculated values, indicating that there are possibly

several spin exchanges in one period of revolution.

Flygare [17,75] and Chan [20, 76,77] have shown that the spin-

rotation constant and the magnetic shielding constant for any molecule

can be related. Using LCAO-MO theory, Flygare showed that the para-

magnetic part of the shielding constant was equal to


2 iZN,
C 2 N (20)
3mc2 4(M)(gN) a C=a,b,c N1 N N'


where the nucleus in question is designated by N, and e is the electron

charge, RNN' represents the distance to the N' nucleus, m is the

electron mass, c is the velocity of light, h is Planck's constant, M is

the proton mass, pN is the nuclear magneton, g is the nuclear "g"











factor given by yN /N, and ZNM is the atomic number of the NI

nucleus. The I 's are the principal moments of inertia of the

molecule, and the C 's are the diagonal components of the spin-

rotation tensor about these principal axes. By use of the mean

moment of inertia defined in equation (19), the modulus of the spin-

rotation tensor may be written, after substituting for known con-

stants, as


-. 4.42 x 10 -44 13 ZN'
C 4.2 (1.06 x 101) a + Z (21)
Sp NIN RNN


for a fluorine nucleus. The paramagnetic contributions to the

shielding constants for o-, m-, and p-chlorofluorobenzene have been

calculated by Caldow [78]. He found the paramagnetic contributions

to be 7.49, -1.15, and 3.08 parts per million (ppm) from fluorobenzene

for o-, m-, and p-chlorofluorobenzene, respectively. Chan [20] has

measured the paramagnetic contribution for fluorobenzene to be -284

ppm. Using these paramagnetic shielding values, calculating the mean

moments of inertia, and using the previously mentioned bond distances,

the moduli of the spin-rotation tensors for o-, m-, and p-chloro-

fluorobenzene are obtained. The values are 3.85, 2.91, and 3.74 kHz

for o-, m-, and p-chlorofluorobenzene, respectively. Chan [76] found

the diagonal components of the spin-rotation tensor in fluorobenzene

to be -1.0, -2.7, and -1.9 kHz, giving a modulus of 2.0 kHz.

The modulus of the spin-rotation constant may also be experi-

mentally determined from equation (7), postulated by Hubbard to obtain












the spin-rotational correlation time. The modulus E may be written,

after substitution, as

3 t2 T, 1/2
12 T

1 sr


where I is the mean moment of inertia, and Td is the dipolar correla-

tion time. A relationship between TI intra d and Td may be obtained

by using equation (4). Substituting, one obtains


T = A(TI T1 d)-l/2 (23)
1 sr 1 intrad


where A is a parameter depending on the molecule for which the

calculations are being made. Powles argues that, for the Hubbard

relationship to hold, (T T d /2 should be independent
1 sr 1 intrad

of temperature [2]. He showed that this relationship is approxi-

-2 2
mately obeyed for fluorobenzene and calculated c to be 2.5 kHz in

good agreement with the molecular-beam values of Chan. Also, Hubbard

[23,34] has shown that equation (10) gives good agreement with calcu-

lated data for the spherical molecules, tetrafluoromethane and sulfur

hexafluoride. However, for o-, m-, and p-chlorofluorobenzene,

(T T 1/2 is not temperature independent. A mean value
1 sr 1 intra d

of the product (T T1 ) was taken over the temperature
1 sr 1 intra d
range from 0 to 100 degrees Centigrade. The values of c obtained in

this manner are 20.0, 13.5, and 15.8 kHz for o-, m-, and p-chloro-

fluorobenzene, respectively. The experimental values of the modulus

are somewhat high compared to those calculated from magnetic shielding











data. If the mean moment of inertia is replaced by the moment of

inertia about the axis in the plane of the ring coincident with the

C-F bond, IA, values of 14.4, 6.4, and 5.4 kHz are obtained for o-,

m-, and p-chlorofluorobenzene, respectively. These values give

somewhat better agreement, especially in the case of the meta and

para molecules. This lends evidence to the fact that most of the

rotational motion in the para molecule is about the axis coincident

with the C-F bond. To a lesser extent, this tendency occurs in the

meta molecule.

The lack of agreement between the values of the moduli calcu-

lated by magnetic shielding data, which have been assumed to be more

reliable, and the values experimentally determined by the Hubbard

relationship point to the inapplicability of Stokes' diffusional

equation in explaining the rotational motion of nonspherical molecules.


o-, m-, and p-Fluoroiodobenzcne

The fluoroiodobenzenes were investigated to determine how the

BPP theory would respond to systems even more asymmetric than the

chlorofluorobenzenes. The substitution of an iodine atom for a

chlorine atom will shift considerably the center of mass in each case.

Also, since the iodine atom is very large, the rotational motion of

the molecules should depend, to a large extent, on the iodine atom.

The iodine atom has a much larger quadrupole moment than the chlorine

atom, and this could interact with the nuclear magnetic moment of the

fluorine.












The plots of the log of TI as a function of 1/T are given in

Figures 8, 9, and 10, respectively, for o-, m-, and p-fluoroiodobenzene.

The experimental values are given in Tables 14, 15, and 16. The tem-

perature dependence of T1 in the fluoroiodobenzenes is similar to that

in the chlorofluorobenzenes.

The same procedures as for the chlorofluorobenzenes were

carried out in obtaining the various contributions to the spin-lattice

relaxation time. The intramolecular contribution was obtained by

extrapolation to infinite dilution,using carbon tetrachloride. Plots

of the log of T1 intra' T inter' and T1 intra d as a function of 1/T

are given in Figures 11, 12, and 13 for o-, m-, and p-fluoroiodo-

benzene, respectively. The experimental values of T intra as a func-

tion of 1/T are listed in Tables 17, 18, and 19, respectively, for

o-, m-, and p-fluoroiodobenzene. Values of TI in TI i
1 intra 1 intra d

T inter, and T are listed at ten-degree intervals in Tables 20,
1 inter' 1 sr

21, and 22 for o-, m-, and p-fluoroiodobenzene.

Plots of the log of T intra d and T inter as a function of
1 intra d 1 inter

1/T are linear over a wide temperature range. This linearity indicates

a single relaxation process which is exponentially dependent on tem-

perature. As the temperature is increased, the relaxation mechanisms

corresponding to T1 inter and T intra d become less effective.
1 inter 1 intra d

T becomes a more effective relaxation mechanism with increasing

temperature in each case.

At low temperatures, T intra d is about equal for all three
molecules. However, at higher intra d lies in the
molecules. However, at higher temperatures, T, i d lies in the
1 intra d






41





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-i0




C c





0 0 <


o o0 0 0
o 10)j CFJH
U)


CV\


C)
c)


c)
C)
C)

(l)
C)

c)
C)l
ic
-'C





O C) C

C) C:


C)a


C)r

C)C
C)
C) 4.

H C)












sequence m > p > o. The BPP theory predicts the sequence o > m > p.

The fact that the ortho molecule exhibits the smallest values for

Tintra d at higher temperatures can not be easily explained.

However, it is likely that an additional interaction between the

iodine and fluorine could occur.

An indirect spin-spin interaction is possible between the

fluorine and iodine nuclei. The contribution is not thought to be

significant. This effect is considered to be unimportant by Abragam

[5] and Gutowsky [10], and calculations by the author based on the

equations given by Abragam confirm this point. However, it is gen-

erally agreed that the fluorine atom transmits spin information

through its p electrons. There is the possibility in the ortho

molecule that spin information could be transmitted through the

n electrons.

Also, a direct magnetic dipole-dipole interaction between

neighboring atoms may occur. One example of the dipolar splitting

of a quadrupolar spectrum is that of iodic acid [79] where a splitting

occurs due to the interaction between the proton and the iodine

nucleus.

Plots of the log of the macroscopic viscosity as a function of

1/T are illustrated in Figure 14 for o-, m-, and p-fluoroiodobenzene.

The viscosities lie in the sequence o > p > m over the investigated

temperature range. T1 inter at low temperatures is about equal for

the three molecules. At higher temperatures, T1 inter lies in the

sequence o > p,m. The BPP theory predicts m > p > o. T1 inter does














LO





CV





0
CC


.1i
o cn q CC





Cr
o '~J Cr/ I




00
00
-4


CC
0

















00 CC
LO u
a-

a



Cr
CC
C7G~





Cr,











0 01 0 LC
I a Cd F
[C)V












not seem to be simply related to the viscosity. Again, the greatest

deviation from theory seems to be when the iodine atom is in the

ortho position.

The energies of activation for rotational and translational

motion, calculated from Figures 11, 12, and 13, are listed in Table 23.

The energies of activation for rotational motion lie in the sequence

m > o > p. The para molecule has the lowest activation energy for

rotation, as expected, due to cylindrical symmetry of the molecule.

It may be assumed, as in p-chlorofluorobenzene, that the major portion

of the rotational motion occurs about the axis in the plane of the

ring coincident with the C-F bond. The ortho value should be the

highest, but is not, probably due to an additional intramolecular

interaction between the fluorine and iodine nuclei. This value is

probably too low. The energies of activation for translational motion

lie in the sequence m,o > p with the ortho and meta values within

experimental error. Again, symmetry arguments may be used to explain

the value for the para molecule.

Values of the contribution to T1 lie in the sequence
1 sr
m < o < p at lower temperatures. At higher temperatures, the spin

rotational values are about equal and correspond to the dominant

relaxation mechanism.

Values of T intra d were calculated from BPP theory. The
1 intra d
Debye correlation time was used. The values of the viscosity were

obtained from Figure 14. The same values for the C-H and C-F bond

lengths were used as for the chlorofluorobenzenes, since no independent











values could be found for the fluoroiodobenzenes. Close packing of

spheres was assumed. The calculated values of T1 intra d at ten-

degree intervals are listed in Table 24 for o-, m-, and p-fluoro-

iodobenzene. Comparison of calculated and experimental values indi-

cates that the BPP theory provides too efficient a relaxation

mechanism.


o-, m-, and p-Fluoroaniline

The temperature dependence of the spin-lattice relaxation times

for o-, m-, and p-fluoroaniline was investigated to determine the

effect of the quadrupolar moment of the nitrogen on T1 and the possi-

bility of intramolecular hydrogen bonding between the amino group and

the fluorine when the amino group is in the ortho position.

The temperature dependence of the spin-lattice relaxation times

for o-, m-, and p-fluoroaniline has been measured. Plots of the log of

T1 as a function of 1/] are illustrated in Figure 15. The same general

temperature dependence of T is observed for the fluoroanilines as for

the chlorofluorobenzenes and the fluoroiodobenzenes. About the same

magnitudes of T1 are observed at various temperatures as for the fluoro-

iodobenzenes and fluorochlorobenzenes. This would indicate that the

quadrupole moment of the nitrogen atom has little effect. Also, since

the values of T1 for the fluoroanilines are relatively close in magni-

tude at the same temperature over the entire temperature range, there is

probably little contribution from any intramolecular hydrogen bonding.
















OC
OD<

cPa
co'o



(E1
033
dP





0
< c
0 0
I U3
0


C o








0 LO O
0 U
+- --' L_ L





0 I 0L





O 0 0 0 C\
S 0O C\jH-
i)n











o- and m-Fluorophenol

The temperature dependence of the spin-lattice relaxation times

for o- and m-fluorophenol was investigated to determine the effect of

intermolecular hydrogen bonding on T1. Also, there is a possibility of

intramolecular hydrogen-fluorine hydrogen bonding in o-fluorophenol.

The temperature dependence of T1 in o- and m-fluorophenol has

been measured. Plots of the log of T1 as a function of 1/T are given

in Figure 16.

Figure 16 yields some interesting results. The plots are

linear over a very wide temperature range, and, at any given temper-

ature, T1 is somewhat less in magnitude than for the other fluoro-

benzenes investigated. These two observations may be attributed to

intermolecular hydrogen bonding of the phenol. Since the dipolar cor-

relation time is inversely proportional to T1, any process which length-

ens T, as hydrogen bonding, shortens T1. The temperature dependence

of the hydrogen bonding effect is opposite to that of spin-rotation,

probably cancelling it to some extent. The linear plots over a large

portion of the temperature range are probably a result of this

cancellation.

Since the Tl's for o- and m-fluorophenol are about equal over

the investigated temperature range, probably intramolecular hydrogen

bonding between the hydroxyl proton and the fluorine in o-fluorophenol

is small and has little effect on T There is infrared evidence to

indicate that there is not enough overlap between the hydroxyl group

and the fluorine, because of the small size of the fluorine, to have

appreciable intramolecular hydrogen bonding [80].






















CP
cD

co


On

0 0

00
00
oo


OO


0 O


0 ,0
cy u -


OJ







0





r"
aQ


0



C'4

( o






4J
c



















oo
0











a-
IC


LO
co


I


I I



















SPIN-LATTICE RELAXATION TIMES IN SOLUTION


Experimental Results and Discussion


Hexafluorobenzene-Hydrocarbon Systems

The properties of aliphatic hydrocarbon-fluorocarbon systems

have been studied extensively [47]. There is a large deviation from

regular solution theory, the fluorocarbons being very poor solvents

for most hydrocarbons. Various theories have been presented,to account

for this behavior,which are discussed in the literature review.

A partial explanation for the large positive deviations in thermo-

dynamic measurements is that fluorocarbon-hydrocarbon interactions

are weaker than hydrocarbon-hydrocarbon interactions in aliphatic

systems [47].

Prosser and Patrick [66] and Swinton [68] have investigated

aromatic fluorocarbon-hydrocarbon systems and have reported the exist-

ence of 1:1 molecular complexes in the solid state. These molecular

complexes are also thought to exist in the liquid state. Charge-

transfer interactions were originally proposed to provide the chief

stabilization energy. Swinton [68] points out that any such inter-

actions would be extremely weak. No charge-transfer bands have been

reported in the ultraviolet region for interaction of hexafluoro-

benzene with n-electron donors [67]. X-ray studies show that systems

such as the benzene-hexafluorobenzene system are stacked in alternate











planes in the solid state [81]. Stacking, Swinton points out, if

present in the liquid state, might explain the difference between

alicyclic and aromatic systems.

Studies were undertaken to determine what interactions, if

any, exist in the liquid state in aromatic hydrocarbon-fluorocarbon

systems. Scott [82] divides any such interactions which might occur

in these systems into three categories; physical interactions such as

dispersion forces, specific chemical interactions such as charge-

transfer, and specific interactions between aromatic rings as

quadrupolar-quadrupolar and bond dipolar interactions.

The hexafluorobenzene-cyclohexane system was studied in order

to establish a reference system. Swinton [83] argues that only

physical interactions such as dispersion forces should be present.

The phase diagram [68] of this system does not show a congruent melting

point but several barely noticeable incongruent melting points, similar

to the benzene-carbon tetrachloride system [84]. In the hexafluorobenzene-

cyclohexane system the unlike interactions are 5 per cent weaker than

the value predicted by the geometric mean combining rule [83].

The plot of the viscosity-corrected spin-lattice relaxation

time as a function of hexafluorobenzene mole fraction is shown in

Figure 17. The values are listed in Table 25. (T/1 ) T, decreases
o 1
with decreasing fluorocarbon concentration, leveling off at about 0.5

mole fraction. This behavior may be interpreted as the initial breakup

of large fluorocarbon clusters with addition of cyclohexane into

smaller, more rigid clusters [46]. Further addition of cyclohexane

beyond 0.5 mole fraction provides a continuous hydrocarbon phase for

























N
C)








a) C)
o 1
o i





"4




LC) -0

bX C,

w




W 41
C)
41
"4 0



-0














El
o C)
-C
C) "


C)
C) C
C) "4


a C
Qa,


C)
C)
0 r
*,- (4
"45
C)
C) c)






O E
oC C)


Q) 0
Li)












the segregated fluorocarbon clusters. The proton chemical shift of

cyclohexane does not change over the investigated concentration range,

which indicates that any specific interaction present must be

extremely weak.

The hexafluorobenzene-benzene system has a congruent melting

point at 240C and 1:1 mole ratio [68]. Figure 18 shows a plot of

(TI/ ) T1 as a function of fluorocarbon concentration. The values are
o 1

listed in Table 26. Initially, the fluorocarbon clusters are broken

up, and (1/f ) T decreases as benzene is added. At 0.5 mole fraction
o 1

the plot levels off and remains constant with increasing benzene con-

centration. Similar behavior is noted in the benzene and cyclohexane

systems. Any specific interaction, such as charge-transfer, must be

extremely weak. The proton chemical shift of benzene is invariant

over the investigated concentration range.

Beaumont and Davis [67] investigated the ultraviolet spectra

of several hexafluorobenzene systems with various n- and n-electron

donors. No charge-transfer absorption bands could be obtained for

n-electron donors, but several n-electron donor systems indicated

charge-transfer absorption. Symmetry arguments forbid the direct

overlap of the n-molecular orbitals of the rings in T-electron donor-

acceptor systems such as benzene-hexafluorobenzene. The rings must be

displaced relative to each other for charge-transfer to occur.

However, superposition of the ring systems, as in the solid state,

provide the most attractive orientation for dispersion and polarization

forces.

























C)


0)
N















E 0

LO ><
0O
C) 0
C 4
C)










r vj
W 41
Cd









ci a
0
o -



o '


C) a




















El U
C) C)
.0 C)


-o o
a



o C)

c) N



a. w


C) B






-'- C)


Go u 0 Z c C\J 0


Pr

Pr












The hexafluorobenzene-mesitylene system has a congruent melting

point at 360C and 1:1 mole ratio [68]. Swinton [85] has measured the

free energy, enthalpy, entropy, and volume changes of mixing for the

hexafluorobenzene-benzene, cyclohexane, and -mesitylene systems. The

thermodynamic changes are positive for the hexafluorobenzene-cyclohexane

system. This is the expected result for a system where any specific

interaction present is very weak. Very small changes are noted for

the hexafluorobenzene-benzene system, and negative changes are measured

for the mesitylene system. The thermodynamic evidence indicates a

strong interaction in the hexafluorobenzene-mesitylene system. Also,

Swinton [86] indicates that since there is a lack of spectroscopic

evidence for charge-transfer interactions, perhaps these molecular

complexes are stabilized by electrostatic interactions, the third type

mentioned by Scott [82]. The most probable interactions are dipole-

quadrupole or dipole-dipole interactions. Such an interaction should

be at a maximum when the two molecules are lined up face-to-face.

This type of interaction can explain the thermodynamic evidence.

Since methyl groups have a negative inductive effect and would lower

the ionization potential, mesitylene should possess a somewhat stronger

r-quadrupolar moment than benzene.

Figure 19 shows a plot of (T/T0 ) T as a function of fluoro-

carbon mole fraction for the hexafluorobenzene-mesitylene system.

These values are listed in Table 27. All measurements were taken at

400C. Initially, the plot decreases with addition of mesitylene due

to the breakup of fluorocarbon clustering. At 0.5 mole fraction,

















C

3


IX
C,






U
0 c





N
-4 a,
o


4





0




00



Ln




c 0)
.~ cr

-C


a



o C
C 4-
C)
(1 4-4








0




rA
C. C
q- a.



Ci


4/C




C! .0


OD
Vc1 0
U')











a slight maximum is observed, indicative of a weak fluorocarbon-

hydrocarbon interaction. Finally, as more mesitylene is added, the

curve falls and begins to level off.

The proton chemical shifts have been measured. The methyl

chemical shift changes slightly with concentration, the peak being

farthest upfield at 0.5 mole fraction. The aromatic hydrogens are

farthest downfield in pure mesitylene. Upon addition of hexafluoro-

benzene, the aromatic chemical shift moves upfield to about 0.5 mole

fraction. The aromatic proton shift does not change with further

addition of fluorocarbon. The chemical shifts are difficult to

interpret. The aromatic chemical shift trend indicates that probably

in puremesitylene the hydrocarbon-hydrocarbon interaction is fairly

strong. Physically, the mesitylene molecules can line up face-to-face

rather easily, and the molecules probably are held together by disper-

sion forces. The addition of fluorocarbon and subsequent completing,

increases the shift since the unlike interaction is much weaker.

The methyl chemical shift trend indicates that the mesitylene cluster-

ing is broken up to 0.5 mole fraction in favor of hexafluorobenzene-

mysitylene completing. After that point, with further addition of

hexafluorobenzene, mesitylene shows a tendency to recluster in the

fluorocarbon phase. The chemical shift values are listed in Table 28.

Whether or not these in-molecular complexes are held together

primarily by charge-transfer or electrostatic interactions is not known.

The negative inductive effect of the methyl groups in mesitylene would

increase the possibility of both charge-transfer and electrostatic











stabilization. Chemical shift data has been used to argue for charge-

transfer complexes in such systems as 7,7,8,8-tetracyanoquinodimethane-

benzene [87]. In such complexes, the chemical shift of the electron

acceptor increases with increasing electron-donor concentration.

However, the fluorine chemical shift in hexafluorobenzene decreases in

going from 0.9 mole fraction hexafluorobenzene in mesitylene to 0.1

mole fraction hexafluorobenzene by two Hz at 56.4 MHz operating fre-

quency. The lack of any spectroscopic evidence favors electrostatic

forces.

The hexafluorobenzene-dimethylformamide (DMF) system was

studied to investigate further any possible charge-transfer effects.

There is a possibility that the lone pairs of electrons on the oxygen

or nitrogen atom could be an n-electron donor with hexafluorobenzene

being the electron acceptor. A plot of the viscosity-corrected T1 as

a function of hexafluorobenzene concentration is shown in Figure 20.

These values are listed in Table 29. After the initial breakup of

hexafluorobenzene clusters, there is a linear decrease in T1 with

decreasing fluorocarbon concentration, indicating a specific interaction

with DMF.

The proton chemical shifts of DMF are given in Table 30. The

carbonyl proton chemical shift moves upfield with increasing fluoro-

carbon concentration, indicative of self-dissociation of DMF. The

methyl shifts change slightly. The a-methyl shift moves downfield

about two Hz in going from pureDMF to 0.1 mole fraction DIF in

hexafluorobenzene. The $-methyl shift moves upfield about two Hz in































































































cou (Q '
OD -
0)


a;

N
C
1;

0

cc





a;
4C




Lo









Iz


2;
C;







C;
C)






C;
C;

0
CC

C;
C;
C)
c;

0



CN


Q! .


CM Q












going from pure DMF to 0.1 mole fraction DMF in hexafluorobenzene.

The proton chemical shifts were also measured in 0.1 mole fraction

DMF in carbon tetrachloride. The carbonyl chemical shift moves upfield

in going from pure DMF to 0.1 mole fraction DMF in carbon tetrachloride,

but only about one-half as much as in hexafluorobenzene, about eight Hz.

The C-methyl chemical shift moves downfield about one Hz, and the

B-methyl chemical shift moves downfield about one Hz in going from

pure DMF to 0.1 mole fraction DMF in carbon tetrachloride. In DMF-

benzene, Hatton and Richards [88] pointed out that the DMF molecule

is situated such that the carbonyl group is as far away as possible

from the benzene ring. The Y-methyl shift changes appreciably with

concentration while the B-methyl shift is unchanged. They interpreted

these results to mean that the a-methyl group was positioned over the

center of the ring to retain the planar configuration of the amide.

In the present case, since hexafluorobenzene is a better electron

acceptor than benzene, the carbonyl group is not repelled as greatly.

The carbonyl group may complex slightly with the hexafluorobenzene

which would explain the chemical shift results. The upfield chemical

shift of the carbonyl group with increasing hexafluorobenzene concen-

tration could be explained as a combination of the self-dissociation

of DMF and interaction with the hexafluorobenzene. The fact that the

methyl shifts change very slightly in hexafluorobenzene and carbon

tetrachloride, indicate that the geometry involved in any complex

formation is considerably different from that in the DMF-benzene system.











Preliminary UV studies of the hexafluorobenzene-DMF system

were carried out. Beaumont and Davis reported a range of 265-353 mg

for several amines with hexafluorobeenzene. No new band was noted in

this region although both hexafluorobenzene and DMF absorb at

about 255 mg, and this absorption may obscure the band. What type of

specific interaction is occurring in the hexafluorobent'ene-DTM can

not be determined from the present study.


2,2,2-Trifluoroethanol-Ethanol

Ethanol and 2,2,2-trifluoroethanol (TFE) resemble each other

in their molecular structures, boiling points, and dielectric constants,

but differ considerably in acidity, basicity, and solvating ability.

Since the two liquids are miscible in all proportions, the TFE-ethanol

system is of interest in studying hydrogen bonding and relative solvat-

ing ability between the two components. Any strong hydrogen bond

should be detected by a study of the concentration dependence of the

spin-lattice relaxation time.

Using infrared spectroscopy,Mukherjee and Grunwald [89] found

TFE to be a better hydrogen-bonding donor to itself in an inert solvent

than ethanol. Infrared bands corresponding to monomer, dimer, and

higher complexes were assigned by Mukherjee and Grunwald. Rao [90]

showed, using nmr, that TFE is a better hydrogen-bonding donor than

ethanol to itself in an inert solvent.

In mixtures of TFE and ethanol, a new infrared band appears

with a maximum at 34001 cm. This is attributed to formation of mixed

hydrogen-bonded species, the most important being the TFE-ethanol dimer.











The calculated equilibrium constant for mixed dimer formation is about

10 times greater than for ethanol dimer formation [89].

Figure 21 is a plot of the concentration dependence of (T/TI ) T

for TFE in benzene. TFE shows self-association over the concentration

range studied. The value of (]] o) T decreases with decreasing TFE

concentration, indicating the breakup of large complexes. This breakup

is still incomplete, even at 0.1 mole fraction. The values are listed

in Table 31.

Figure 21 also shows a plot of the concentration dependence of

(1/o ) T in the TFE-ethanol system without solvent. As ethanol is
o 1

added, there is a decrease in (1/T ) T This decrease, however, is
o 1
not as great as in benzene, because the formation of mixed complexes

lowers the degree of self-association. Instead of the TFE breaking

into smaller units in an inert solvent, it is tied up in large hydrogen-

bonded clusters or chains. Mukherjee and Grunwald [89] postulate that

when TFE is in excess, there are hydrogen-bonded chains with ethanol

being the terminal acceptor. Also, when TFE is added to ethanol, there

are hydrogen-bonded chains formed with TFE being the terminal donor.

The motion of the perfluoromethyl group in TFE seems unaffected from

0.1 to 0.4 mole fraction TFE. This fact indicates that any chains

formed are breaking and reforming faster than can be detected on the

nmr time scale. Also, probably there is little hydrogen-fluorine

hydrogen bonding present. However, at about 0.42 mole fraction TFE

there is a discontinuity indicating very strong hydrogen bonding

involving the hydroxyl groups [27,45]. Probably the chief species is































































































S0

^ g )


Q u
if) Q!)
U.)


Q)
0
N
0
0
O a0

o a N

















O Av
-C 0
C 0 IM
0S 4J I
4o a 14

o c6
0 O
3 0) I



c *


















000~
*M OO
0 o
0N 2 C)
arl s,







-4 4J4 i1 ,^


4O



.= C K)
'.^ -E .4 0I
1- 4 0 4 0
0 c..
0 0- C4l
0 (0 4J
ue ai











0 (t U
'0 40 0 H
C 0
0. 0 0.0,
0,




(D C CI 4J






0 -4 1-'
1 4J G



4J1 IN -c
0 IN o 07
O4' 3 CIT:
Ci JT
11 CM *r4







C) 0 1 01

00 H

0J'0 (N 03
t -i ;I (N
[















b0
r-H
PL.S











the mixed dimer with higher complexes present. Mixed hydrogen bonding

seems to be a much stronger interaction than the self-association of

either ethanol or TFE. The above is a good example of the use of

spin-lattice relaxation times to detect associated species.


n-Perfluoroheptane-Isooctane

The n-perfluoroheptane-isooctane system is a typical aliphatic

hydrocarbon-perfluorocarbon system. Regular solution theory predicts

a consolute temperature of -2030C. The experimentally determined value

is 23.6 C [52]. The thermodynamic parameters, such as free energy of

mixing, are positive [91].

Brady [64] has investigated this system by small-angle X-ray

measurements. He finds both hydrocarbon-hydrocarbon and fluorocarbon-

fluorocarbon cluster formation. Starting with pure isooctane, which

exhibits no scattering, the scattered intensity increases with increas-

ing fluorocarbon concentration in a manner which indicates that the

clusters are increasing in size. The maximum size is attained at 0.5

mole fraction at which point the clusters are made up of about 140

n-perfluoroheptane molecules. With a further increase in fluorocarbon

concentration, a phase reversal takes place giving use to smaller

clusters of hydrocarbon in the fluorocarbon phase.

Figure 22 shows a plot of (1/l0 ) T as a function of fluoro-
O 1
carbon mole fraction for the n-perfluoroheptane-isooctane system.

The values are listed in Table 33. There is a decrease in (1/7 ) T
o 1
with decreasing fluorocarbon mole fraction throughout the concen-

tration range. No maximum or minimum which would indicate a strong

























a)
02






02
CC













41
U
C)
























L4
C) 0



02 0






a)




a~

-a
02 a,


~0 0

a'. ou

2 C)
O a'.

a~



0 02
02 -,
U a~
a
o r
U 02



Crl
bflX
U-


0U 0 0Q
cD If) -s- (Y)
if)











specific interaction is observed. Probably the addition of isooctane

to n-perfluoroheptane breaks up the weak fluorocarbon clusters through-

out the concentration range. This physical interaction adds a large

correction to the entropy of mixing term which is not accounted for

by regular solution theory.

A main feature of aliphatic perfluorocarbon-hydrocarbon systems

is that the fluorocarbon-fluorocarbon interaction is stronger than the

fluorocarbon-hydrocarbon interaction. The hydrocarbon-hydrocarbon

interaction is probably stronger than either the hydrocarbon-fluorocarbon

or fluorocarbon-fluorocarbon interaction. Probably the isooctane

molecules preferentially cluster, segregating the fluorocarbon molecules

from solution.
















SUMMARY


The temperature dependence of the fluorine spin-lattice

relaxation time has been measured in several pure liquids. In general,

the temperature dependence is similar to that found by Powles [2].

Plots of the log of T1 as a function of 1/T are, at lower temperatures,

essentially linear, indicating that the dipolar contribution is the

only major relaxation process in this temperature region. At higher

temperatures the plots are no longer linear, but they begin to fall

rapidly indicating the presence of another type of relaxation process.

This decrease in T1 with increasing temperature has been attributed to

the spin-rotation interaction.

The various contributions to the spin-lattice relaxation time

have been obtained for o-, m-, and p-chlorofluorobenzene and o-, m-,

and p-fluoroiodobenzene. The dipolar contribution to T was gotten

by extrapolating the linear portion of the T1 plot to higher temper-

atures. The intramolecular contribution was obtained by extrapolation

of TI to infinite dilution in a nonmagnetic solvent.

Plots of the log of T and of T1 as a function of
a 1 intra d 1 inter

1/T are linear over a wide temperature range. This linearity indicates

a single relaxation process which is exponentially dependent on tem-

perature. From these plots the energies of activation have been

obtained. In each case, T inter and T increase with increasing
1 inter 1 intra d












temperature which is consistent with BPP theory. Tsr decreases

with increasing temperature which is also the expected result.

The intramolecular dipolar contribution, T intra d follows
1 intra d'

the sequence o > m > p throughout the temperature range for the

chlorofluorobenzenes, consistent with BPP theory. This is not the

case for the fluoroiodobenzenes where the sequence is m > p > o.

The fact that the ortho molecule exhibits the smallest values for

T intra d at higher temperatures indicates that possibly an inter-

action between the quadrupolar moment of the iodine atom and the

nuclear magnetic moment of the fluorine is occurring.

The intermolecular dipolar contribution, T1 inter, follows
1 inter

the expected trend as predicted by BPP theory for the chlorofluoro-

benzenes. This result lends evidence to the fact that T1 is
1 inter

controlled by diffusional processes. There seems to be no simple

relationship between the viscosity and T inter for the fluoroiodo-
1 inter

benzenes.

The spin-rotation contribution follows the sequence o < m < p

over the entire temperature range for the chlorofludrobenzenes.

This result indicates that the position of the chlorine has a sig-

nificant effect on the molecular motion of the molecule. For a spher-

ical molecule Tsr should be inversely proportional, to a first

approximation, to the mean moment of inertia according to the Hubbard

theory. Instead, T1 sr was found to be inversely proportional to IA,

the moment of inertia about the axis in the plane of the ring coin-

cident with the C-F bond, for the chlorofluorobenzenes. The principal












part of the rotational motion seems to be about this axis. T1 sr for

the fluoroiodobenzenes lies in the sequence m < o < p. The low ortho

values indicate an additional intramolecular interaction to be present.

The most probable interaction for the ortho molecule would be that of

the quadrupolar moment of the iodine atom with the nuclear magnetic

moment of the fluorine atom.

The intramolecular and intermolecular energies of activation

for the chlorofluorobenzenes lie in the sequence o > m > p. This

result may be explained by the higher symmetry of the para molecule

and rotation about the IA axis. The intramolecular energies of acti-

vation lie in the sequence m > o > p for the fluoroiodobenzenes. The

intermolecular energies of activation lie in the sequence o,m > p.

Higher symmetry and a lower moment of inertia about the IA axis may be

used to explain the low vale of the para molecule. The ortho values

are not as large as expected, indicating another type of interaction

to possibly be present.

BPP theory predicts too efficient a relaxation mechanism for

both the chlorofluorobenzenes and the fluoroiodobenzenes. Calculations

based on the BPP theory predict the correct ordering in regard to

relative magnitudes for T intra d in the chlorofluorobenzenes but not
1 intra d

in the fluoroiodobenzenes. Calculations based on the Steele theory

for T in the chlorofluorobenzenes give values too large by
1 intra d
an order of magnitude. The theory is not known to be reliable for

polar molecules. However, it does predict an upper limit to T1 intra d
1 intra d












It is gratifying that the experimental T intra d values for the
1 intra d

chlorofluorobenzenes fall between the BPP and Steele theories.

The moduli of the spin-rotation tensors for the chlorofluoro-

benzenes have been calculated using the theory of Flygare and Chan.

These values are in good agreement with the value calculated by Chan

for fluorobenzene. The moduli of the spin-rotation tensors were also

determined experimentally using Hubbard's equations which apply to

spherical molecules. The experimental values are somewhat high com-

pared to those calculated from magnetic shielding data. If motion

about the axis in the plane of the ring coincident with the C-F bond

is considered only, and the experimental data is recalculated, much

better agreement is noted, especially in the para and meta molecules.

The Hubbard relationships do not seem applicable to nonspherical

molecules.

Some additional type of interaction seems present in the

fluoroiodobenzenes. The ortho values in each case seem inconsistent

with the expected values based on the trends observed in the chloro-

fluorobenzenes. It has already been suggested that there could be

a significant interaction due to the large quadrupolar moment of the

iodine atom.

The temperature dependence of T1 for the fluoroanilines was

measured. The same general temperature dependence of T1 is observed

as for the chlorofluorobenzenes and the fluoroiodobenzenes. The

quadrupolar moment of the nitrogen atom seems to have little effect

on T Also intramolecular hydrogen bonding between the amino group











and the fluorine atom which might be expected to occur in the ortho

position does not seem to be significant.

The temperature dependence of TI in o- and m-fluorophenol

has been measured. The plots of log T1 as a function of 1/T are

linear over a wide temperature range and somewhat less in magnitude

than the other fluorobenzenes investigated. These results may be

attributed to the intermolecular hydrogen bonding of the phenol.

Four hexafluorobenzene-hydrocarbon systems were investigated

to determine what specific interactions, if any, are present in

aromatic hydrocarbon-fluorocarbon systems.

The hexafluorobenzene-cyclohexane system was studied to

establish a reference system. The plot of (/ol ) T1 as a function of

hexafluorobenzene mole fraction and the proton chemical shift data

indicate that any specific fluorocarbon-hydrocarbon interaction is

extremely weak.

The hexafluorobenzene-benzene system gives results similar

to the cyclohexane system. No evidence of a specific fluorocarbon-

hydrocarbon interaction was obtained from the viscosity-corrected

spin-lattice relaxation times as a function of fluorocarbon concentra-

tion or from the proton chemical shifts.

A plot of (f/l ) T as a function of fluorocarbon concentra-
o 1
tion shows a weak maximum at 0.5 mole fraction in the hexafluorobenzene-

mesitylene system indicating a weak specific hydrocarbon-fluorocarbon

interaction. Thermodynamic measurements indicate a specific inter-

action to be present. The proton chemical shift evidence indicates














that in pure mesitylene the hydrocarbon-hydrocarbon interaction is

fairly strong.

The hexafluorobenzene-DMF system indicates that a specific

complex is formed. No new absorption band could be found in the

ultraviolet region which could be assigned to charge-transfer.

The proton chemical shifts indicate that the methyl groups are

positioned away from the ring. There is self-dissociation of DMF

with addition of hexafluorobenzene. The interaction between DMF

and hexafluorobenzene probably involves the carbonyl group of the DMF.

No direct evidence could be obtained for charge-transfer

interaction in these systems. Since methyl groups have a negative

inductive effect as compared to hydrogen atoms, mesitylene should

possess a somewhat larger r-quadrupolar moment than benzene.

Electrostatic or charge-transfer interactions would be enchanced in

mesitylene as compared to benzene. No conclusions can be drawn as to

the type of specific interactions occurring in the mesitylene and

DMF systems.

A plot of the viscosity-corrected spin-lattice relaxation time

as a function of TFE concentration in the ethanol-TFE system shows

a discontinuity at 0.42 mole fraction. This behavior has been

attributed to strong hydrogen bonding between TFE and ethanol involv-

ing the hydroxyl groups. At low TFE mole fraction the plot levels

off which indicates that hydrogen-fluorine hydrogen bonding is negli-

gible. The association constant for mixed dimer formation is probably

considerably larger than for TFE or ethanol self-association.







77



The n-perfluoroheptane-isooctane system is a typical aliphatic

perfluorocarbon-hydrocarbon system. Small-angle X-ray measurements

indicate cluster formation throughout the entire investigated concen-

tration range. No maximum or minimum is observed in the viscosity-

corrected T1 plot as a function of perfluorocarbon concentration.

Probably the isooctane molecules preferentially cluster segregating

the fluorocarbon molecules from solution. The hydrocarbon-hydrocarbon

interaction is probably stronger than either the fluorocarbon-

fluorocarbon or fluorocarbon-hydrocarbon interaction.







































APPENDIX




















TABLE 1

THE TEMPERATURE DEPENDENCE OF T IN
O-CHLOROFLUOROBENZENE



Temp. (sec) Temp. (sec)


1200C 14.7 22 C 16.6

108 15.9 10 15.2

99 16.5 0 12.8

89 17.0 -18 10.7

77 18.0 -30 8.4

62 18.2 -35 7.6

56 18.3 -42 6.4

51 17.6 -55 4.6

42 17.4 -61 3.4

30 16.8 -70 2.7




















TABLE 2

THE TEMPERATURE DEPENDENCE OF T1 IN
M-CHLOROFLUOROBENZENE


Temp. (sec) Temp. (sec)


1200C 16.9 230C 16.8

108 18.2 12 15.4

99 19.5 2 13.2

88 20.1 -14 11.8

79 20.8 -25 9.8

70 20.5 -30 8.8

62 20.4 -38 7.4

53 19.5 -45 6.4

44 18.6 -51 5.4

28 17.8 -70 3.2





















TABLE 3

THE TEMPERATURE DEPENDENCE OF T1 IN
P-CHLOROFLUOROBENZENE


Temp. (sec) Temp. (sec)


1220C 13.8 460C 17.8

109 15.3 31 16.9

101 16.4 22 16.6

89 17.4 12 15.0

78 17.7 5 14.2

72 18.4 1 12.9

61 18.3 -14 11.8

54 18.2 -23 10.1
















TABLE 4

THE TEMPERATURE DEPENDENCE OF T intra inter T sr'
1 intra' 1 inter 1 sr'
AND T1 intra d IN O-CHLOROFLUOROBENZENE



Tep. Tintra T inter T T1 intra d
1 intra 1 inter 1 sr 1 intra d


1200C

110

100

90

80

70

60
50

40

30

20

10

0

-10

-20

-30
-40

-50

-60


24.0 (sec)

24.8

25.6

26.1

26.0

27.7

28.9

29.5

29.8
29.6

29.2

28.3

27.1

25.5

23.4

20.9

17.8

14.4

8.5


(sec)


57.0

53.0

51.4

47.5

45.5
41.0

37.9

32.8

26.9

22.7
19.0

14.3

10.7

7.9


19.4 (sec)

21.0

23.7

25.5

28.5

32.2

36.0

41.0

46.8

55.0

63.0

76.0

89.0

156
370


(sec)






296

198

146

105

82.0

64.2

54.4

45.1

39.0

30.3

25.0
20.9

17.8

14.4

8.5
















TABLE 5

THE TEMPERATURE DEPENDENCE OF T intra T inter T s'
1 intra' 1 inter' 1 sr'
AND T intra d IN M-CHLOROFLUOROBENZENE
1 intra d


Temp. T intra 1 inter T sr T intrad


1200C

110

100

90

80

70

60

50
40

30
20

10

0

-10

-20

-30

-40

-50

-60


18.7 (sec)
20.6

21.5

22.5

23.8
24.7

25.4

25.7
26.0

25.8
25.4

24.4

23.0

21.2

18.7

17.2

14.4

11.4

8.2


(sec)


231

177

149

128

99.0

78.0

65.5

51.4

42.5

34.5

28.8

23.7

18.5
14.4

11.0

9.0


24.8 (sec)

28.0
33.0

36.5

40.0

46.5

53.0

60.0

69.0

80.0

92.0

103

119

189

232


(see)


61.5

58.6

58.9

52.7

48.8

45.0

41.8

38.0

35.1

32.0

28.5
23.8

20.2

17.2
14.4

11.4

8.2
















TABLE 6

THE TEMPERATURE DEPENDENCE OF T intra T inter T sr'
AND T intra d IN P-CHLOROFLUOROBENZENE



Temp. T1 intra T1 inter 1 sr 1 intra d


1000C 19.7 (sec) (sec) 34 (sec) 46.8 (sec)

90 20.7 41 41.7

80 21.5 51 36.6

70 22.8 98.0 66 34.2

60 24.0 80.8 81 34.2

50 25.2 65.5 102 33.3

40 25.5 57.8 135 31.4

30 25.2 52.3 177 29.8

20 24.0 49.8 350 25.5

10 23.1 43.8 23.1

0 22.2 35.7 22.2

-10 20.7 29.1 20.7

-20 19.1 24.3 19.1

-30 16.6 21.2 16.6



















TABLE 7

THE TEMPERATURE DEPENDENCE OF T
1 intra
IN O-CHLOROFLUOROBENZENE


Temp. T intra
1 intra

1250C 23.6 (sec)

112 24.8

100 25.6

88 24.8

78 26.8

70 27.1

62 28.5

53 29.5

42 28.8

29 29.3

2 27.7
-14 25.0

-32 20.0

-46 16.0

-58 11.1


















TABLE 8

THE TEMPERATURE DEPENDENCE OF T1
1 intra
IN M-CHLOROFLUOROBENZENE


Temp. T intra


126C 18.0 (sec)

116 19.6

100 21.5
94 22.5

81 23.5

72 24.6

63 24.4
54 25.3
44 25.5

29 25.5
- 4 22.1

-23 17.9

-33 16.0

-48 12.3

-60 8.2



















TABLE 9

THE TEMPERATURE DEPENDENCE OF T
1 intra
IN P-CHLOROFLUOROBENZENE


Temp. T1 intra


1000C 19.7 (sec)

91 20.7

82 21.5

73 22.4

60 24.0

53 25.0

44 25.3

30 25.2

7 22.8

- 6 21.5

-18 19.7

-35 14.8














TABLE 10

BOND DISTANCES AND MOMENTS OF INERTIA FOR
O-, M-, AND P-CHLOROFLUOROBENZENE


O- M- P-


Bond Distances

C-C 1.40 o 1.40 1 1.40 1

C-H 1.08 1.08 1.08

C-C1 1.72 1.71 1.71

C-F 1.31 1.30 1.30

Moments of Inertia in Amu-A

IA 173.4 147.6 87.8

IB 325.6 429.7 541.1

IC 499.2 577.3 629.2





TABLE 11

ENERGIES OF ACTIVATION FOR ROTATIONAL AND TRANSLATIONAL
MOTION IN 0-, M-, AND P-CHLOROFLUOROBENZENE


0- M- P-

Energies of Activation from the
Intramolecular Dipolar Interaction
(Rotation) in Kcal/Mole
2.7 .2 2.1 .2 1.2 .1

Energies of Activation from the
Intermolecular Dipolar Interaction
(Translation) in Kcal/Mole
2.8 .2 2.6 .2 2.2 .2



















TABLE 12

CALCULATED VALUES OF T intra d FROM BPP THEORY
1 intra d
AT VARIOUS TEMPERATURES FOR O-, M-,
AND P-CHLOROFLUOROBENZENE


Temp. 0- M- P-


1000C (sec) 30.9 (sec) 27.5 (sec)

90 27.8 25.5

80 41.5 25.2 22.8

70 37.4 22.2 20.4

60 33.3 18.7 18.4

50 29.0 16.4 16.1

40 25.5 14.5 14.2

30 22.2 12.6 12.5

20 19.0 11.0 10.8

10 16.1 9.4 9.3

0 13.6 8.0 7.9
-10 11.5



















TABLE 13

CALCULATED VALUES OF TI intra d FROM STEELE THEORY
AT VARIOUS TEMPERATURES FOR O-, M-,

AND P-CHLOROFLUOROBENZENE


Temp. O- M- P-


1000C 590 (sec) 311 (sec) 346 (sec)
90 583 307 342

80 575 303 337
70 566 298 332

60 558 294 328
50 549 289 322
40 542 285 318

30 532 281 313

20 524 276 308

10 515 271 302
0 506 266 298


















TABLE 14

THE TEMPERATURE DEPENDENCE OF T1 IN
0-FLUOROIODOBENZENE


Temp. (sec) Temp. (sec)


1480C 19.4 590C 14.8

132 19.8 48 14.2

120 20.2 32 11.8

107 20.3 29 10.9

96 19.8 6 10.4

85 18.4 1 7.7

75 17.0 -13 5.6

68 16.6 -27 4.3


















TABLE 15

THE TEMPERATURE DEPENDENCE OF T IN
M-FLUOROIODOBENZENE


Temp. (sec) Temp. (sec)


1450C 18.9 53C 14.7

130 19.1 47 13.6

117 19.7 30 11.8

104 19.3 15 10.1

90 18.4 2 7.4

80 17.5 -15 5.6

73 17.0 -27 4.2

63 15.9 -42 2.5




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