Title: Nuclear resonance in dispersed systems
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00099395/00001
 Material Information
Title: Nuclear resonance in dispersed systems
Physical Description: xiii, 167 leaves : ill. ; 28 cm.
Language: English
Creator: Yang, Koahsiung, 1947-
Copyright Date: 1977
Subject: Mesomerism   ( lcsh )
Emulsions   ( lcsh )
Liquid crystals   ( lcsh )
Physics thesis Ph. D
Dissertations, Academic -- Physics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by Koahsiung Yang.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 164-166.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00099395
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000205828
oclc - 04022125
notis - AAX2617


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To begin, I would like to thank Dr. Thomas A. Scott, the chairman

of my supervisory committee, for suggesting the study and providing a

very well equipped laboratory in which I could perform my work. Dr. Scott

gave not only academic help and financial support, but also spiritual

encouragement at the very time that I could concentrate most attention

to the work. Special appreciation is given Dr. William Derbyshire of

the University of Nottingham, England for his inspiring and tireless

advice on both experiment and theory. This project was proposed by

Dr. Derbyshire and initiated while he was visiting professor at the

University of Florida. Appreciation is also felt for the other members

of the supervisory committee: Drs. Raymond Pepinsky, Dinesh 0. Shah,

John W. Flowers and James W. Dufty.

I would also like to express my gratitude to Dr. Katherine Scott

for her great help in the high resolution NMR study. Many thanks are

extended to Mr. Paul C. Canepa for his electronic and technical

expertise during the course of experiment.

Finally, I wish to present the work in memory of my dear grandmother

who passed away on October 21, 1976. Because of many kinds of

difficulties, I was not able to fly home in the last days of her life.

Her kindness will be ever fresh to me in my whole life.



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

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

LE T OF FIGURES . . . . . . . ... . . v. ii

ABSTRACT . . . . . . . . . . .... . xii

CHAPTER I INTRODUCTION . . . . . . . . . 1

I.1 History and Significance of the Subject . . . . 1

1.2 The Microemulsions . . . . . . . . . 3

1.2.1 The Surfactant and Interfacial Tension . . 3

1.2.2 The Formation of Microemulsions . . . . 3

1.3 The Liquid Crystal Phase . . . . . . . 9

CHAPTER II BASIC THEORY . . . . . . . .. . . 16

11.1 Nuclear Magnetic Resonance . . . . . .. 16

11.2 Relaxation . . . . . . . . ... . . 19

11.3 Deuteron Relaxation in Water . . . . . ... .27

11.4 Bound Water Model for Microemulsions . . . ... 32

11.5 High Field Theory of Liquid Crystal Powder Pattern . 46


III.1 Sample Preparation . . . . . . . ... 53

III.1,1 Preparation of Chemicals . . . ... 53

1 .1.2 Sample Sealing . . . . . ... 54

111.2 Temperature Measurement and Controlling Apparatus . 55

III.2.1 Cryostat . . . . . . . ... 55

III.2.2 Thermometer . . . . . . . .

111.2.3 Feedback Regulator . . . . . .

III.3 Nuclear Resonance Measuring Apparatus . . . .

111.3.1 Circuit Description . . . . . .

II1.3.2 Electromagnet . . . . . . . .

111.3.3 Signal Generator and Frequency Synchronizer

111.3.4 Pulse Programmer and High Power Gated
Amplifier . . . . . . . . .

III.3.5 Sample Coil and Probe .. . . .....

111.3.6 Receiver . . . . .

111.3.7 Phase Sensitive Detector . ...

111.3.8 Diode Detector . . . . .

III.4 Continuous Wave Metnod . . . . . .....

III.4.1 Power Saturation and Line Width Broadening

III.4.2 Rate of Sweep and Magnetic Field
InhomogeneLty . . . . . . . .

III.5 Noise . . . . . . . .

III.6 T1 Measurement with I T T Pulse Sequence .

III.6.1 Disadvantage of Cross-Over Method .. ...

III.6.2 Ringing .. . . . . . . ....

III.7 T2 Measurement with T2 T it Pulse Sequence . .

III.8 Least Square Fit . . . . . . . . .

III.9 Visual Observation . . . . . . . . .


IV.1 The Microemulsions . . . . . . .. . .

IV.1.1 The Validity of Bound Water Model .. ...








---^ ^


IV.1.2 The Rotational Diffusion and Chemical
Exchange . . . . .... . . . 114

IV.2 The Liquid Crystals ... .. ... . . . . 129

IV.2.1 Explanation of Line Spectra and Relaxation . 129

IV.2.2 Motional Narrowing of the Quadrupole Splitting 143

IV.3 Comparison between Hexanol and Pentanol in
Water-Oil System . . . . ... . . .. 147

IV.3.1 Electrical Conductivity Difference ..... 147

IV.3.2 Experimental Evidence and Explanation . . 147

IV.4 Conclusions . ... . . . . . . . . 157

APPENDIX A . . . . . . . . . . . .

APPENDIX B . . . . . . . . . . . .

BIBLIOGRAPHY . . . . . . . . . . .

BIOGRAPHICAL SKETCH . . . . . . . . .

. . 162

S. . 164

. . 166


Table Page

(1) Effect of hexanol and potassium oleate on the average
volume of water drops in hexadecane . . . . . 7

(2) Effect of water contact on water droplet diameter in
the hexadecane system . . . . . . . 8

(3) Temperature dependence of various correlation times 29

(4) Components used for sample preparation . . . .. 53

(5) The thickness of the emotional restricted layer of the
microemulsions at different temperatures and various
radii . . . . . . . . ... .. . .. 111

(6) Temperature dependence of the OH peaks in the proton
spectrum of the hexanol microemulsion system .... .128

(7) The composition dependence of quadrupole splitting
and widths of the wide lines . . . .. . 143


Figure Page

(1) Schematic representation of the spontaneous development
of negative interfacial tension as a result of the
surfactants ..... . . . ............. 4

(2) The decrease of interfacial tension due to hexanol . 5

(3) The decrease of interfacial tension due to potassium
oleate . . . . . . . . . . ... 6

(4) Schematic representation of the structure of the
microemulsion . . . . . . . . 8

(5) Schematic representation of the structure of the
birefringent cylinders . . . . . . . 11

(6) Schematic representation of the structure of the
birefringent lamellae . . . . . . . . 12

(7) The changes in the viscosity of microemulsions and
liquid crystals with water/hexadecane ratio . . .13

(8) Disorientation and mutual entanglement results in higher
viscosity than that of the initially well oriented liquid
crystals ......... .. . . . . . 14

(9) The hydrogen bond association between carboxyl and
hydroxyl groups from adjacent droplets .......... 15

(10) The energy level splitting and population distribution
in equilibrium of nuclei in a static magnetic field . 17

(11) T1 measurement by TV t T pulse sequence . . .. .23

(12) The envelope of free induction decay of the 7T r t 2
sequence . . . . . . . . . . . 24

(13) The formation of an echo ...... . . . . 25

(14) The envelope of spin echoes of the 2 T U T1 pulse
sequence . . . . . . . . . . . 26

(15) T1 relaxation in pure D20 . . . . . . . 30

(16) Temperature dependence of the apparent activation energy 31

Figure Page

(17) The bound water model of microemulsions . . ... .35

(18) The relaxation time and population of the "bound" and
"free" phases influenced by exchange rate ...... .37

(19) The relationship between reorientation rate and
temperature . . . . .. . . . . . 38

(20) The relationship between reorientation rate of the
"bound" and "free" phases and temperature ...... .40

(21) The effect of exchange rate on (A) apparent reorientation
rates, (B) apparent relaxation rates, (C) apparent
populations of NMR in the "bound" and "free" phases . 41

(22) Change of relaxation time due to chemical exchange .45

(23) Geometry of the electric field gradient principal axes
at the deuteron nucleus and the laboratory frame in
the liquid crystal .... . . . . . . . 47

(24) Energy diagram for first order quadrupole perturbation
of the Zeeman effect of the deuteron nucleus .... .49

(25) The powder pattern resonance line for I = 1 . . .. 50

(26) The bound water model of lamellae structure . . .52

(27) Cryostat . . . . . . . . . . . 56

(28) Block diagram of Feed-Back Regulator for temperature
control of the sample . . . . . .... .. .60

(29) Simple block diagram for pulsed NMR experiment . . 62

(30) Block diagram of pulsed NMIR experiment with phase
sensitive detector . . . . .... . ... 64

(31) Block diagram of pulsed NMR experiment with diode
detector . . . . . . . . . . . 65

(32) Probe network . . . . . .. . . . 68

(33) Simple diagram for tuning of preamplifier ...... .69

(34) Phase detection . . . . . .. . . . . 73

(35) (a) Nonlinear characteristic of a diode, (b) modified
circuit for diode detection . .. ... . . . 74

(36) Diode detection . . . . . . . . . . 75


(37) The relation of the signal height to H, and H ..

(38) The relation between audio frequency f and line shape

(39) The affection of change of 11 upon H1 . .

(40) Line shapes of the cases: f > Af . . . . .
(41) Characteristic for different side bands . . . .

(42) Line shapes corresponding to different modulation
frequency f of signal composing both narrow and
wide line . . . . . .








(43) The effect of slow and fast sweep upon the spectrum. 86

(44) The distinction of line distortion due to magnetic
field inhomogeneity and rapid passage . . ... 87

(45) Magnetization flipped down by an angle 9 from initial
direction . . . . . . . . ... . . 91

(46) Comparison between first pulses of 6=- and S0r in
T1 measurements . . . . . . . . . 92

(47) The observed FID as displayed on the X-Y recorder . 94

(48) Effect of ringing on T1 measurements .... ..... 95

(49) Envelope of spin echoes of two typical liquid crystals 99

(50) Apparatus for visual observation . . . . .. 106

(51) Cryostat for visual observation . . . . .. 107

(52) The relation between line width and radius of the
microemulsions . . . . . . . . . 112

(53) Temperature dependence of the spin-spin relaxation
rate due to the bound water . . . . .... 113

(54) The temperature dependence of T1 of pure D20 and D20
in W/0=0.1 microemulsion . . . . . . .. 115

(55) The temperature dependence of relaxation times of
the hexanol microemulsion W/0=0.1 . . . ... .116

(56) The temperature dependence of relaxation times of
the hexanol microemulsion W/0=0.2 . . . ... .117

Figure Page

(57) The temperature dependence of relaxation times of
the hexanol microemulsion W/0=0.4 . . . ... 118

(58) The temperature dependence of relaxation times of
the hexanol microemulsion W/0=0.6 . . . ... 119

(59) The temperature dependence of spin-spin relaxation
time of the hexanol microemulsions above room
temperature . . . . . . . .... . 122

(60) High resolution NItR spectrum of the hexanol
microemulsion W/0=0.6 at 80C . . . . . . 123

(61) High resolution NMR spectrum of the hexancl
microemulsion W/0=0.6 at 230C . . . . .. 124

(62) High resolution IMR spectrum of the hexanol
microemulsion W/0=0.6 at 600C . . ... ..... 125

(63) High resolution NMR spectrum of the hexanol
microemulsion W/0=0.6 at 800C . . . ... ... 126

(64) High resolution NMR spectrum of the hexanol
microemulsion W/0=0.6 at 230C (30 minutes after 80C) 127

(65) Line shape variation of the liquid crystal W/0=1.4
obtained on cooling the sample from room temperature
to -190C . . . . . . . . ... . . 131

(66) Line shape variation of the liquid crystal W/0=1.4
obtained by heating the sample from room temperature
to 900C . . . . . . . . . . . 132

(67) The powder-pattern wide-line spectra in the derivative
mode and the corresponding absorption line shape . 133

(68) The wide-line spectrum of the hexanol liquid crystal
W/0=1.4 after shaking . . . . . . . 136

(69) The wide-line spectrum of the hexanol liquid crystal
W/0=1.0 after shaking . . . . . . ... 137

(70) The composition dependence of the relaxation times
of the hexanol system . . . . . . ... 138

(71) The temperature dependence of the relaxation times
of the hexanol liquid crystal W/O=1.0 . . ... 139

(72) The temperature dependence of the relaxation times
of the hexanol liquid crystal W/0=1.2 . . ... 140

Figure Page

(73) The temperature dependence of the relaxation times of
the hexanol liquid crystal W/0=1.4 . . . ... .141

(74) The coexisting two features of the spin echo in hexanol
liquid crystal W/0=1.2 . . . . . . ... 142

(75) (A) Electrical resistance of microemulsions containing
hexanol or pentanol as cosurfactant, (B) schematic
representation of cosolubilized and microemulsions
system . . . . . . . . ... . . 148

(76) Composition dependence of the relaxation times of the
pentanol dispersion system . . . . . ... 152

(77) Spin echoes from the pentanol emulsion W/0=0.6 at
3.720C and 16.80C . . . . . . . ... 153

(78) Temperature distribution of two features of the spin
echoes in the pentanol emulsion W/0=0.6 ...... 154

(79) The change of spin echoes of the pentanol emulsion
W/0=0.6 on cooling . . . . . . . . . 155

(80) The temperature dependence of the relaxation times of
the pentanol emulsion W/0=0.6 . . . . .... 156

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



Koahsiung Yang

December 1977

Chairman: Thomas A. Scott
Major Department: Physics

Continuous wave and pulse techniques have both been used to study

deuteron NMR lineshape, resonance frequencies, and relaxation times

T1 and T2 in oil-water dispersions as a function of temperature and

composition. The systems studied contain hexadecane, potassium oleate,

hexanol (or pentanol), and water. The water/oil ratio determines the

phases: W/O 5 0.6 for microemulsions, W/O = 1.0 for cylindrical rod

liquid crystal, and W/0 > 1.2 for lamellar liquid crystal. A model in

which the water molecules rapidly exchange between a "bound" state on

the surfactant interface and a "free" state in the bulk liquid is

highly successful in explaining many of the observations.

For the microemulsions the relaxation rate is proportional to the

reciprocal of the radius of the water droplet spheres dispersed in the

oil. The correlation time for both bound and free molecules is on the
order of 101 sec, which is fast compared with the reciprocal of the

resonance frequency(10-6 sec). The electric quadrupole interaction is

averaged to zero by the rapid interchange of water between the two

states and diffusion of "bound" molecules around the spherical surface

of the droplets. The high resolution data show that the chemical shift

difference at 230C between the two OH peaks of the hexanol and H20 is

approximately 0.045 ppm and therefore the lifetime of the OH is about

250 ms. The chemical exchange rate becomes rapid when the temperature

is raised to 600C and thus explains the anomaly in T2 occurring at 570C.

The cylindrical rod and lamellar liquid crystal phases exhibit a

static quadrupolar splitting of several hundred Hz, which was most

readily observed as a CW powder pattern spectrum. The observed

quadrupole splitting is approximately ten times smaller than is expected

from the two state bound-free model. The correlation time for slowest
tumbling of the bound water at room temperature, 0.32 x 10 sec, is

only slightly larger than the characteristic time of experiment,

approximately 0.15 x 10-6 sec. This explains the large degree of

motional averaging.

The pentanol emulsion has two coexisting features of the spin

echoes, one for isotropic microemulsion and the other for a liquid
crystalline structure with T2 = T2 = 0.72 ms. The portion having a

liquid crystal characteristic is temperature dependent and is presumed

to provide paths for charge carriers such as potassium ions, which

enhance the electrical conductivity.



I.1 History and Significance of the Subject

The membrane structure has been a major interest in biology

for a number of decades. For many years, biophysists and physical

chemists have used nuclear resonance techniques to study the

structure and mobility of the "head" group in lipid membranes.

This is basically a water-surfactant-lipid interface. The properties

of the lipid and surfactants separately are understood fairly well

from extensive studies of their chemical shift, mass spectroscopy, UV

and IR light absorption, etc. But upon addition of water the system

becomes much more complicated. The principal difficulty encountered

in the use of proton nuclear magnetic resonance lies in the extreme

difficulty of resolving the resultant multicomponent spectra into

assignable resonances[l],[2], especially when these individual

resonances occur over a wide frequency range(typically several kHz),

and overlap each other. Deuteron magnetic resonance(DMR) was first

used in 1971 to study the mobility of the hydrocarbon chains, in

isotopically enriched molecules by Oldfield, Chapman and Derbyshire.

As a simple model, they studied the modulation, by cholesterol, of

the quadrupole splitting in a synthetic di(perdeuterio)myristoyl-LA-

Lecithin, as a function of temperature. Subsequently, Finer[3],

Smith[4], Seelig[5] and their collaborators have performed many DMR

studies on the hydration of Lecithin and of the dynamics of the 2H

dispersions spin labelled lipids occurring in membranes and model

membranes. The kinetic properties of the hydratiar water in such

"liquid crystals" are gradually becoming clear to us.

The structure and physical properties of thermotropic liquid

crystals and lyotropic systems are also among the major interests

of the petroleum and pharmaceutical industry. They are intimately

related to the problems of oil recovery, and pollution, and the

mechanism of action of detergent, med cine, etc.

The microemulsion systems and liquid crystals studied in this

dissertation are composed of hexanol (pentanol), hexadecane,

potassium oleate and deuterium oxide(D20). To describe the properties

of the water we adopt a two state bound-free water model, which

assumes a layer of water near the surfactants having preferred

orientation and restricted motion while the rcmainings of water have

bulk-like isotropy in motion. The validity of the model can be checked

through DWR with both continuous wave and pulse techniques. The

correlation time of bound water, phase transitions, probability of

being bound, the isotropic rotational process of free water molecules

and anisotropic rotational process of bound water molecules are

expected to be deduced from the experiment.

A brief description of the microemulsion and liquid crystal

phases of the system are given in the following sections of this

chapter. An equally brief basic theory of nuclear resonance and its

application to this particular system are provided in chapter II.

Experimental method and procedure are described in chapter III.

Chapter IV gives results and conclusions.


1.2 The Microemulsions

1.2.1 The Surfactant and Interfacial Tension

Oil and water can be dispersed in each other at the microscopic

but not molecular level by introducing mixtures of surface-active

compounds as emulsifiers. The mixtures of surface-active compounds

are called surfactant and co-surfactant depending upon the degree of

interfacial tension obtained. The systems studied in this dissertation

are composed of hexadecane(oil), deuterated water, potassium oleate

(surfactant), and alcohol(co-surfactant). The alcohol used is hexanol/

or pentanol, but we put emphasis on the hexanol system.

The potassium oleate creates the interfacial film. The spontaneous

development of negative interfacial tension is caused by penetration

of hexanol through this film. A schematic representation is provided

in Fig.(1), Fig.(2) and Fig.(3)[6] on the next three pages to show

the hydrophilic and hydrophobic duality of potassium oleate and


1.2.2 The Formation of Microemulsions

Microemulsions are optically clear, thermodynamically stable

oil-water dispersions, obtained in low water/oil ratios. Phase

diagrams showing the regions of micropmulsion formation have been

obtained for a number of systems[7]. Studies of these systems by

light scattering[8], low-angle X-ray scattering[9], viscosity[10],

electron microscopy[11], ultra-centrifugation[12], nuclear magnetic

resonance[13][14] infrared spectroscopy[13] and electrical resistance

measurements[14] have been reported. Water-in-oil microemulsions


n n a 1 a n n 11 1 n OIL
o I i II I 0I II II O Il,
' 0 Q 0 'to f-,A


n ( n OIL

Yf 7

f < 0 IF To < "7

where 71 is the interfacial tension reduction due to
addition of hexanol

Fig.(1) A schematic representation of che spontaneous development of
negative interfacial tension as a result of penetration of an
interfacial film of potassium oleate by hexanol at the
hexadecane/water interface [6]




t 40



0 I I I

0 0.02 0.04 0.06 0.08 0.10

Fig. (2) The decrease of interfacial tension due to the surfactant
hexanol [6]




S40 -


H 30



0 -l_ ___ I___-----___[
0 0.02 0.04 0.06 0.08 0.1

Fig.(3) The decrease of interfacial tension due to the surfactant
potassium oleate [6]

have been shown to consist of water droplets from less than 100 A

to several hundred R in diameter surrounded by an interfacial film of

surfactant and co-surfactant as in Fig.(4).

The effect of hexanol and potassium oleate on tne average volume

of water droplets in hexadecane are shown in Table(l)[15] and Table(2)[16].

Table(l) Effect of Hexanol and Potassium Oleate on the Average Volume
of Water Drops in Hexadecane [15]

Interfacial Composition Average Drop-Volume
Hexadecane(oil) Water

No additive No additive 2.8x10-2ml
Hexanol No additive
0.2 ml/ml of oil No additive 6.0x10-3ml
0.4 ml/ml of oil No additive 5.0x10-3ml
0.6 ml/ml of oil No additive 5.0x10-3ml
No additive Potassium Oleate
No additive 0.02 gm/ml of water 8x10-4ml
No additive 0.06 gm/ml of water 8x10 ml
No additive 0.1 gm/ml of water 4.4x104ml
Hexanol Potassium Oleate
0.025 mi/mi of oi0.06 gm/ml of water 1xl0-4ml

0.05 ml/ml of oil 0.06 gm/ml of water 6.6x0-5ml
0.075 ml/ml of oil .06 gm/ml of water Volume <10-6ml

Table(2) Effect of Water Contact on Water Droplet Diameter in the
Hexadecane Systems [16]

Aggregate W/0 (*) Droplet Diameter

Inverted micelle 0.1 32
W/0 microemulsion 0.2 46
W/O microemulsion 0.4 56
W/O microemulsion 0.6 72

(*) Iml hexadecane was presented in system which contained 0.2 gm
potassium oleate and 0.4 ml hexanol.




r.W- -T c
r7 /^ -^~

Fig.(4) Schematic representation of the structure of
the microemulsions

1.3 The Liquid Crystal Phase

When the volume ratio of water to oil increases, the microemulsion

breaks down and a liquid crystal forms. For the composition W/O = 1.0,

a rod like structure [Fig.(5)] appears. Normally, the cylindrical

structure has a diameter roughly 100 A and a length of 1000 X. Water

is contained within the surfactant membrane. The membrane stability

has been discussed by Shah[17] who concludes that a surfactant

composition of 1 hexanol molecule to 3 potassium oleate molecules gives

the most stable association. It is speculated that potassium oleate

molecules occupy the corners and hexanol molecules occupy the centers

of hexagons. This is why we choose the system with potassium oleate/

hexadecane = 0.2 gm/cm3 and volume ratio of hexanol/hexadecane = 0.4.

As the water concentration is further increased, a lamellar

structure [Fig.(6a)] forms. Additional water merely increases the

gap between layers of surfactant [Fig.(6b)].

Figure(7)[18] shows the change in the viscosity of microemulsions

and liquid crystals (cylindrical and lamellar structures) upon

increasing the water/hexadecane ratio. The sharp increase of viscosity

after disorientation, such as violent shaking, is due to the mutual

entanglement of the liquid crystals [Fig.(8)]. After disorientation,

the cylindrical structure does not increase viscosity as much as

lamellar structure because of easier sliding due to circular cross

section. The lamellar structure results in more resistance among domains

after disorientation. Thus, the fact that the sample of W/O = 1.0 has

less viscosity than the sample of W/0 = 1.4 is well understood.

The gaps between liquid crystals of both cylindrical and lamellar

structure are similar to slits of a diffraction grating which cause


light (visible) interference. One therefore can observe colorful

birefringence through polarized plates.

Oil spheres are formed for water/oil ratio greater than 2.0.

In this case, oil is surrounded by a surfactant membrane. The hydrogen

bond association [Fig.(9)] between carboxyl and hydroxyl groups from

adjacent droplets causes an abrupt increase in viscosity [Fig.(8)].

This kind of electrostatic interaction is so strong that the viscosity

is much larger than that of liquid crystals. This region is not of

interest in the present dissertation study.

Fig. (5) Schematic representation of the structure of the
birefringent cylinders



(b) u u




T T ? T T F

Fig.(6) Schematic representation of the structure of the
birefringent lamellae

W/0(bv volume)

Fig.(7) The changes in the viscosity of microemulsions and liquid
crystals with water/hexadecane ratio [18]

Fig.(8) Disorientation and mutual entanglement results in higher
viscosity than that of the initially well oriented liquid


Schematic representation of the oil spheres suspended in water




Fig.(9) The hydrogen bond association between carboxyl and hydroxyl
groups from adjacent droplets causing an abrupt increase
in viscosity for water/hexadecane ratio of 2.0 to 3.5


II.1 Nuclear Magnetic Resonance

A nucleus with spin I has a nuclear magnetic moment ;= Yrl,

where Y is the nuclear magnetogyric ratio. If a magnetic field B is

applied, the interaction Hamiltonian is

= -+ A (II.1.1)

The nuclear moment processes about the applied magnetic field,

and the quantum mechanical equation of motion of the net magnetization

H of an ensemble of spins is identical with the classical Newtonian

law, namely the change of angular momentum is equal to the torque

applied. Therefore

= y1 xB (11.1.2)

where the macroscopic magnetization M is defined as a sum over

nuclear magnetic moments of all nuclei.

Since the nuclear spin I is space quantized, the allowed

eigenstates must be m = -I, -I+1, -1+2,....I-1, I. In thermal

equilibrium, the distribution of population on each energy level

is governed by the Boltzman factor exp(-yhB /kT) [see Fig.(10)]

to guarantee minimum internal energy.



/ g


H 0 0
o0 *H


" <-------- -rb


M -H

1 1 H
I ^
a .-i

N = N and m
m= and = exp(-yliB /kT) (II.1.3)
m=-I m+1

where N is the number of nuclei in the eigenstate designated by

magnetic quantum number m, N is the total number of nuclei of the

ensemble, and T is the temperature of the lattice.

The statistical description above strictly requires a large

number of nuclear moments but in practice N= 1020 so this is no

problem. Transition between states is induced by the applied rf

field with equal probability in both directions, but as the net

population of the lower states are higher than those of the higher

energy states there will be a net absorption of energy from the rf


A steady state nuclear resonance experiment can be interpreted

as the result of two competing processes, the relaxation which tends

to establish Boltzman inequalities after nuclei have been pumped to

higher energy levels and the driving electromagnetic field that tends

to destroy thermal equilibrium and to equalize the population of the

different energy levels. An alternative "classical" description is

that when disturbed from equilibrium the nuclear magnetic moment

process about the magnetic field that they experience. An applied rf

field,orthogonal to the main applied field,will interact with those

processing nuclei. An oscillatory field can be resolved into two

counter-rotating components. The interaction will be strongest with the

component rotating in the same direction as the processing nuclei and

will occur when the precessional frequency is the same as the rotation

frequency of the rf field. It is often convenient to discuss the

situation from a rotating frame of reference.

11.2 Relaxation

The macroscopic magnetization due to a spin system in a large

static magnetic field relaxes because of the coupling between the

microscopic magnetic moments of the nuclear spins and lattice motions.

As the molecules move about in space, they, of course, carry the

nuclear spins with them and the motions of the nuclear magnetic

moments generate fluctuating magnetic field which is experienced by

neighboring spins; this time varying field behaves in many respects

like the rf field generated in an NMR transmitter. The probability of

spontaneous transition is negligibly small at those low frequencies.

Transitions between different energy levels have,therefore,to be

induced. They may be induced by the experiments in the form of a rf

field or by the system itself by a random motion which produces an

oscillatory field of appropriate frequency.

Fluctuating local electric fields are produced also by molecular

motion and where the nuclei have an electric quadrupole moment, this

is an additional usually more potent source of relaxation. To describe

the return from non-equilibrium to equilibrium, we use a characteristic

time termed T1, the spin-lattice relaxation. T1 is often described as

a longitudinal relaxation time. After a disturbance the nuclear

magnetization may have a component at right angles to the applied

static field. However because of the presence of various local fields,

owing to the fact that the spins are actually not free but interact with

each other and with their surroundings, there is a progressive

dephasing giving rise to a transverse decay of the magnetization. We

use T2 to define this "spin-spin relaxation". T2 is also called transverse

relaxation time.

The Bloch equations are phenomenological equations developed to

describe the longitudinal and the transverse relaxation mechanisms

through the equation of motion(II.1.2) of the nuclear magnetization

for an ensemble of free spins. In a laboratory frame, this equation is

Mxi + M j M -M A
dM -r z o
yMxH- k (11.2.1)
dt T2 T1

where i,j,k are the unit vectors of the laboratory frame of reference.
Assume that the applied field is the sum of a d.c. field H =H = -
z o Y
and of an rf field H1 of amplitude HI= - rotating at a frequency

w in the neighbourhood of m This field will be the more effective

of the rotating components of an applied field Hx= 2H1cos-t,

linearly polarized along the OX axis of the laboratory frame. In the

frame rotating around H at the frequency there is an effective static

field. In the rotating frame the observed rate of nuclear precession equals

yBo0w and thus the effective field in the z direction=(yBo ')/Y
whereas the field in the i' direction= H1. Neglect of the counter-

rotating component gives

H =( o+ -)k' + H i (11.2.2)
eff 0 y 1

where i',J',k'=k are the unit vectors of the rotating frame. The

equation of motion of (11.2.1) can be rewritten as

M Mxi'+ M j M Mo
dM -* x v z o
S= y(1 x H )- k1
dt eff T2 T1

where M and H are the transverse components of M in the rotating
x y


frame. Therefore,

dM M

dt T2 + ( W-too) y

dM M
*= _

= + ( n
dt x T2 (11.2.3)

dMz M o
d -t- = lMy -

If a sufficiently long time has passed to allow transient effects

to decay away, we can obtain a steady state solution by setting

dM1 dM dM
= = = 0 (11.2.4)
dt dt dt


( o) HT2
2 2 22
x 1 12 T r (-)-w )+yT111T2

My 1 + T2( 2 -) 2 Y HTI 2 Mo (11.2.5)
2 o 1 2
1 + ( n-ro ) 12
z 1 +2 T ( 2 2H T 2 0
T2( n-no) +y H1T1T2

We can reconvert these values to tne laboratory frame by using

M + iMy = (M + In ) eiwt
x y x y

S* (11.2.6)
M = M cosutt M sinwt
x x y

M = M sinot + M cost (11.2.6)
y x y

The components of the magnetization in the laboratory frame are

functions of time and can induce in a coil a detectable voltage at

the frequency w. The power absorption of f =- d only occurs in

the transverse direction and has its maximum value at D= wo by

contribution of the term .
Various pulse techniques have been reported in the literature[19]

[20] for measuring the relaxation times T1 and T2. In this work the

TT'VIT-/2 pulse sequence was used to measure T1 and the 7/21 T 7T

pulse sequence to measure T2. For the measurement of T1 in high field,

the first pulse of time interval Atpulse tilts down the magnetization
pulse 1

Mo by T. As there is no transverse magnetization,only longitudinal

relaxation exists. After time T, the magnetization vector is tilted

back to the x-y plane by the second pulse( c At u = u T/2) so that
a pulse 2
the coil can pick up the signal. This pulse sequence and the

measurement of T1 are illustrated in Fig.(11), Fig.(12). The initial

amplitude of the free induction decay signal recorded after the r/2

pulse is a measure of the net component of the magnetization along

the z axis. In Fig. (13), the first -/2 pulse tilts the magnetization

Mo down to the x-y plane. In the rotating frame coherent with the

Larmor precession, the tilted magnetization spreads due to the

variations in H over the sample. The second pulse applied at t = T

rotates the magnetization by T and it is therefore still in the x-y

plane. The components of the magnetization that had processed more

rapidly by Aw=y AB and had developed a phase lead of A= Aa T now

lag the mean by A0. At t = 2T, the spread magnetization vectors


1,K 4, ---------- --

" Ni

4 1


o t


i, J

1 1

-1 1


Fig.(13) The formation of an echo. Initially the net magnetic moment
vector is in its equilibrium position (a) parallel to the
direction of the strong external field. The rf field H is
then applied. As viewed from the rotating frame of reference
the net magnetic moment appears (b) to rotate about H At
the end of a T/2 pulse the net magnetic moment is in the
equatorial plane (c). During the relatively long period of
time following the removal of Hl, the incremental moment
vectors begin to fan oun slowly (d). This is caused by the
variations in H over the sample. At time t=T the rf field
H is again applied. Again the moments (e) are rotated about
the direction of H This time H is applied just long enough
to satisfy the pulse condition. This implies that at the end
of the pulse all the incremental vectors begin to recluster
slowly (f). Because of the inverted relative positions
following the i pulse and because each incremental vector
continues to process with its former frequency, the
incremental vectors will perfectly reclustered (g) at t= 2T.
Thus the maximum signal is induced in the pickup coil at
t= 2T. This maximum signal, or echo, then begins to decay as
the incremental vectors again fan out (h).[From H. Y. Carr
and E. M. Purcell, Physical Review 94, p630 (1954)]

I.--- .

I (4


/ H

) / 0>

/ 4)
/ 0.

/ 0.

. I

4I -

I -I


overlap again and an "echo" occurs. The envelope of echoes generated

by a series of n rf pulses is governed by exp(-2t/T2) [Fig.(14) ],

that is if diffusion and other effects are ignored. ( Note: All the

pulse intervals are assumed much shorter than T1 and T2)

11.3 Deuteron Relaxation in Water

The standard Hamiltonian representing the electric quadrupole

interaction[21] is

t e q 13 2 -2 1 2 2 (11.3.1)
Q 41(21-1) 3 12z 2 +

where eQ=

The two parameters used to define the electric field gradient tensor


eq = V the z component of the field gradient

t1 = -V Y-_- the asymmetry parameter with V > IV > Vx[
V 2zz yy xx

The quadrupole interaction was first shown by Pound[22] to

dominate the spin lattice relaxation in water. The relaxation times

T1 and T2 are given by Bloembergen[23], calculated by standard

time-dependent perturbation theory applied to the quadrupole

interaction term (11.3.1). They are

S= Q 2 2TQ 8TQ 2
1 3 2 2 + ) ( 1 + ) (11.3.2)
T 80 1 + 2 2 1 2 2 3
1o Q 1 + T + o TQ

23 e2 521 2( 2
1= 3e 2 qQ)2 ( 3T + 5 )( I + ) (11.3.3)
T 80 h Q 2 2 2 2 2 3
2 1 + m T., 1 + 4 w) T.
o Q o Q

Intensive studies have been undertaken by Eisenberg[24] and

Hindman[25] on the quadruple relaxation in deuterated water. Even in

pure D20 anisotropic motion does exist at lower temperature, due to

cluster of hydrogen bonded molecules. The hydrogen bond influences the

activation energy and in turn the relaxation. In these systems the

quadrupolar relaxation mechanism is generally governed by two

processes[25] (I) a hydrogen bond(dipole-dipole pair) breaking

process and (II) a Brownian isotropic rotational diffusion process.

These two processes compete with each other. Process (I) dominates at

lower temperature and process (II) dominates at higher temperature;

each of them is subject to a different activation energy. The

relaxation time is a sum of two Arrhenius terms as shown in Fig.(15).

For simplicity, we only focus on two correlation times associated with

the processes mentioned. If exchange of D20 molecules between the

hydrogen bonded lattice and a isotropic rotational phase is rapid a

mean correlational frequency will result

T + IT (11.3.4)

and in turn influence the observed relaxation rate.

1 1 + 1 (II.3.4a)
1 T T
1 1

T and T are the T relaxation times corresponding to the correlation
times T and T .

For D20, the averaged quadrupole coupling constant h over a

wide temperature range is about 258.6 kHz[25]. Correlation times

extracted from Hindman's experimental result are given in Table(3).

Table (3) Temperature dependence of various correlation time[25]

t TQ T1 T (apparent)=-+ T+
Q-12 Q-12 Q -1
(C) ( x 10 sec) ( x 10 sec) ( x 10 sec)

5 1.93 2.76 4.70
20 0.75 2.03 2.79
40 0.24 1.41 1.66
60 0.091 1.03 1.12

From the values listed in Table(3), we obtain two correlation times
essentially having the same order of 10 12se in all cases and

therefore we can omit the quadratic term in the denominators of

formulae (II.3.2) and (11.3.3). In a NLR experiment of resonance

frequency 6.5 x 106 Hz. The simplified formula will become

-= 3 ( e )2 TQ when n = 0 (11.3.5)
T1,2 8 Q

Activation energies due to two different processes can be

calculated directly from Fig.(15) by the formula

S 2 d In T
Sexp d (11.3.6) ,R is the ideal gas constant.

For the convenience of comparison with experimental results on

microemulsions, Hindman's activation energy versus temperature graph

is included in Fig. (16). The figure indicates that the rotational motion

1.5 -----I I
/ /

-l.O = a exp(E /kT) + b exp(E /kT)-
1.05 /


-1.5 E = 10.2+0.3 kcal/mole

-2.0 E = 3.28+0.06 kcal/role
a = (1.7+1.0)10-
-2 0.5 (515+0.14)10
H II -

-3. /

Fig.(5) The contribution due to (I) hydrogen bond breaking

process and (II) isotropic rotational diffusion process
in T relaxation of pure D0[2 WERE
-1.5 / 7 i El- 10.2+0.3 kcal/mole

/ E 3.28+0.06 kcal/nole -

a = (1.7+1.0)10-8

4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2

Fig. (15) The contribution due to (I) hydrogen bond breaking
process and (II) isotropic rotational diffusion process
in T relaxation of pure D20[25]

-20 0 20 40 60 80 100 120 140 160


1 E, Ei
++ T constant [m (8) exp (--) + n(8)exp(- )]

180 200

Fig.(16) Plot of apparent activation energies, E (
versus temperature, for D20 water[25] exp.




for the D20 molecules relaxing in process (II) (high temperature path)

is isotropic and thus rules out the possibility that anisotropic

rotation is a factor in the relaxation process. The anisotropic rotation

will be reflected in differences in the apparent activation energies

for relaxation of geometrically non-equivalent quadrupolar nuclei in

the same molecule[26],[27].

In molecular terms water is normally considered as a mixture of

hydrogen bonded and non-hydrogen bonded species. The nature of the

mixture may be continuous or discrete, but in any event the ratio of

non-hydrogen bonded to hydrogen bonded will increase with increasing

temperature. The barriers to molecular rotation will differ between

the species, and hence so will the corresponding activation energies.

11.4 Bound Water Model for Microemulsions

Assume there are two types of water [Fig.(17)] in the small water

droplets, i.e. (a) free water, and (b) bound water, each subject to

different rates of molecular reorientation. The bound water molecules

have their preferred orientation determined by the polar groups of the

surfactants at the oil/water interface. If the radius of the water

droplet is r, with the thickness of the bound water layer Ar, the

weighting factor of bound water Pb is given by

rr Ar 3 Ar (.4.1)
b 4 3 r
-- Tr

Therefore, the weighting factor of free water is

3 Ar
P = 1 P = 1
f b r


If the exchange of molecules between bound and free water is rapid,

averaged physical observables < X > will be determined. These can be
1 1
the relaxation rate T' T or signal height, etc. and may be expressed
1 2
in the following form

< X > = Pb b + (1 Pb) X1 (11.4.3)

and for the microemulsions:

< X > = X + 3 Ar (X X) (11.4.4)

If the observable < X > is plotted against the reciprocal of

radius, i.e. the same experiment is repeated by replacing different

microemulsion samples, a constant slope is expected if the model is true.

This Xf can be obtained from the intercept of the line with the

ordinate, which also must be the same as given by a pure D20 data at

the same temperature.

When we measure the height of the free induction signal as the

temperature is varied an abrupt change of intensity will be noted

on crossing the freezing point. The loss of intensity below the

freezing point is caused by freezing of bulk water. The intrinsic
quadrupole constant e =258.6 kHz causes a very broad line; hence

the signal amplitude contributed by the solid D20 lattice is too

small to be detected at the spectrometer settings used. The remainder

of the signal observed is totally contributed by bound water. In fact

this is often used as a definition of bound water. The "bound" water

is that water whose molecular properties are modified by the proximity

of, or interactions with the surface to such an extent that the

structure of the water is not compatible with bulk ice and this

water remains unfrozen below the bulk freezing point. After freezing

the relaxation time of the bulk phase is reduced and exchange -.ith the

bound phase is reduced to such an extent that exchange between bound

water and bulk ice is slow or the new characteristic time scale and

separate signals are observable. The spectrometer settings can be

selected so that only one phase, i.e. the bound, is observed. The

indications are that the rate of molecular motion within the bound

phase is approximately the geometric mean of the bulk ice and bulk

water values. Nevertheless, the bound water will be "frozen"

eventually, when the temperature is further reduced and the rate of

molecular motion decreased. Therefore, the change of intensity at
3 Ar
the freezing point gives the weighting factor Pb of [ Fig. (17)

at that temperature.

Though the quadrupole interaction Hamiltonian is significant,

we do not expect to see line splitting by the continuous wave method.

The bond water molecules might be expected to have a preferred

orientation relative to the droplet surface. However the occurance of

a rapid exchange between bound and free water and the small size of

the droplets results in water molecules experiencing regions of the

bound phase at all orientation relative to the laboratory i.e. the

magnetic field on the NbR timescale thereby averaging out the

quadrupolar spectral features. The quadrupolar interactions are

manifested as relaxation mechanisms.

The exchange of nuclei or of molecules between two regions has

been discussed by two groups of workers. Anderson and Fryer[28] and

Zimmerman and Brittin[29]. Anderson and Fryer considered the transition



4 r sr 3Ar
b 4 3 r

3 -
Pf= i -Pb





_- Pf+Pb =1



Fig. (17) The bound water model of microemulsions

from slow to fast exchange where the exchange rate was compared with

the molecular reorientation rates in the two phases, whereas

Zimmerman and Brittin discussed the transition when the exchange

rate was compared with the intrinsic relaxation rates in the two phases.

At temperature to the high temperature side of the T1 minimum both

the spin lattice and spin-spin relaxation rates are inversely

proportional to the molecular reorientation rate v(= ) as in the

equations (11.3.2), (1.3.3) and (11.3.5) although the proportionality

relationship is more general than for relaxation by quadrupolar
1 1
interactions. It should be noted that and are very much less
1 2
than v or -. If the nuclei reside in the separate regions or phases

for times sufficiently long for relaxation to occur, separate

relaxations will be observed. If the residence lifetime is short

compared with the characteristic relaxation times, population weighted

average relaxation rates will be observed.

1 f Pb
+ (II.4.5)
T Tf Tb
f b

Hence a small fraction of bound phase having a greatly increased
relaxation rate can dominate the observed relaxation rate .

e.g. if T = 1 s, Tb= 1 ms, P = 0.99 and Pb= 0.01

1 0.99 0.01
S= .9+ .01 0.99 + 10 and T = 100 ms
T 1 10-3

Zimmerman and Brittin have developed expression relating the

apparent relaxation rates -, 1, and P and P to the exchange
b T

rate. These may be represented diagramatically as follows

(true value)

(true value)


p p
1 f Pb

-Af b


Fig. (18) The relaxation time and population of the "bound" and
"free" phases influenced by exchange rate

In developing this treatment it has been assumed that the exchange

process does not itself provide a relaxation mechanism. Because spin-

lattice and spin-spin relaxation times can have different values

exchange can be fast for one measurement and slow for the other. It

is possible to generalize the treatment to apply to a larger number

of discrete or to a continuous range of environments. Therefore fast

exchange in the Zimmnerman and Brittin sense means the observation of

averaged MIR relaxation rates but the concept of separate phases has

still some validity; many molecular rotations can occur in each phase

before exchange occurs.

Anderson and Fryer discuss the problem where the residence

lifetime in a phase becomes comparable to and ultimately exceeds the

molecular reorientation rates in that phase. The mathematical treatments

of the two models are formally similar but the physical consequences

differ. When exchange is slow in both models nuclei can reorientate

and relax in their separate environments before exchange occurs
1 1
and the separate environments are essentially uncoupled. As T

<< v for much of the range it is possible for exchange to be slow

in the Anderson and Fryer and fast in the Zimmernan-Brittin sense.




Fig.(19) The relationship between reorientation (or relaxation)
rate and temperature (logarithmic scale)

Measurements of reorientation rates e.g. by dielectric techniques

would still reveal separate phases but averaged relaxation rates will

be observed. As these are inversely proportional to the reorientation

rate the presence of a small fraction reorienting slowly will

dominate the relaxation as discussed earlier. If the exchange rate is

increased to become fast by the Anderson-Fryer criterion reorientation

will occur at a rate determined by the population weighted average

relaxation rate in the two phases.

S= P Vf + Pb Vb (11.4.6)

Using our previous values P = 0.99, P = 0.01, = 10- ,
a b o f

is completely dominated by the abundant rapidly reorientating a phase

and hence so is the recorded relaxation rate. This again assumes that

the exchange process does not itself provide a reorientation mechanism.

We can imagine a "thought experiment" where we increase the

exchange rate between two phases f and b (for convenience both may be

assumed to be to the high temperature side of their maximum spin lattice

relaxation rates), without at the same time modifying their intrinsic

relaxation and reorientation rates. In practice this is impossible

within a single system. An increase in exchange rate is normally

accomplished by a change in temperature which will affect the intrinsic





We are envisaging increasing the exchange rate along the line

Fig.(20) The relationship between reorientation (or relaxation) rate
of the "bound" and "free" phases and temperature (logarithmic
















& Brittin


-- - -



l/Tb /





E, \


Anderson & Fryer


Fig.(21) The effect of exchange rate on (A) apparent reorientation
rates, (B) apparent relaxation rates, (C) apparent
populations of NMR (or of reorientation) in the "bound"
and "free" phases

The core D20 has only isotropic rotational motion with rate k .

The bound D20 molecule has an anisotropic rotational rate k2. We

write the equilibrium

D20 (bound) 0 2 D20 (free) (11.4.7)

The value k3 is the exchange rate from free deuteron to bound deuteron.

The value k4 is the rate in the reverse direction. We are only concerned
2 2
with the situation w T <<1, which is true from the argument in the last

section. Two limiting cases to be considered are then: (1) the case

where the chemical or phase exchange is fast relative to the rotation

rate, and (2) the case where the chemical exchange is slow relative

to the rotation rate of the free water molecule, i.e., the relaxation

rate is limited by the rate of breaking polar bonds.

FAST EXCHANGE: k and k 4 ke and k2. This case has been fully

treated by Anderson and Fryer[28] with the result:

1 = Q'[(l + K)/(kK + k)], (11.4.8)

and if k2<< klK, which is a reasonable assumption,

1 1 1

S Q'( I- ) (11.4.9)
T1,2 k klK

where K = k /k3 and

Q'= [(3/40)(21 + 3)/12(21 1)][(1 + T2/3)(e2qQ/h2)].

We note that the assumption--- k2 << k1 is based on the premise that

the Debye-Stokes equation for the rotational correlation time,

T r 'a (II.4.10)
r 3kT

where r'= viscosity and a is a molecular radius, should be obeyed at

least approximately. If the relaxation were controled by molecular

motion of molecules in bound sites, i.e., k2>> klK,

= Q'1/k2 + K/k2) (II.4.11)

SLOW EXCHANGE: kI or k>> k3 and k4. Anderson and Fryer treated

tne case for k1 and k2>> k3 and k but a more general result is needed

here because, as noted above, k2 could be negligibly small. The more

general T1 equation is found to be

1 = Q'{[K/(l+K)](l+l/kl) + [1/(l+K)][l/(k,+k4)]
+k3/(kl-k2) (k2+k)} (II.4.12)

which for k1>> k2 reduces to

S= Q'{[K/(1+K)](1/k ) + [1/(l+K)][l/(k2+k)]
+k3/kl(k2+k )} (II.4.13)

The subcases are then, if k2<

1- = Q'[(K/k1 +l/k )/( + K) + l/Kk] (II.4.14)
1^ 2

and if k2>> k3 and k4 and K not <<1,

S= Q' [(K/k1 + 1/k2)/(l + K)] (11.4.15)

which is equivalent to the Anderson and Fryer result.

For K <<1

S= Q'/k2. (II.4.16)

The plotting of Fig.(22) by Anderson and Fryer is included for

future data analysis of the significant T2 change of the microemulsive

D20 droplets at 57C. This graph gives the change of relaxation time

due to chemical exchange of fast, intermediate and slow passages in

the presence of bound water.

100 -



70- 10

U 60

S50 -

\ \k

30 10


10 k
-4 = 10-4


0 0.2 0.4 0.6 0.8 1.0

Fig. (22) Change of relaxation time due to chemical exchange
of fast, intermediate and slow passages in the
presence of bound water [ Anderson and Fryer, J. Chem.
Phys. 50, 3785 (1969)]

11.5 High Field Theory of Liquid Crystal Powder Pattern

Though the layers of the liquid crystal are ordered within a

domain, these domains are distributed randomly throughout the sample.

Thus a powder pattern [30][31][32] is obtained. The quadrupole

interaction therefore must be weak for the line to be observable in

the presence of this broadening. Only first order splitting need be

considered in the present case.

X = +M Q where Q << gM (11.5.1)

i = Yi H I
M o z

The YQ is given in equation (11.3.1). Since the rotation of the D20
molecule is fast (about 1012 sec), the electric field gradient of the

OD bond is averaged around the molecular axis of symmetry, as seen

by the deuteron nucleus. For the isotropic water molecule, the

asymmetry parameter pr is zero, but is not for an anisotropic water

molecule. The anisotropic D 0 molecule has r about 0.1 [25]. This

small asymmetry parameter can be ignored in high field theory without

causing serious error because, n/2 appearing in the quadrupole

interaction Hamiltonian is much smaller than 1. The nuclear quadrupole

interaction Hamiltonian of (II.3.1) is then simplified to the following:

2 2
= A ( 3 I T2 ) (II.5.2)

where A is a constant of known value.

We choose xyz as the strong quantization frame (same as laboratory

frame) with the Oz axis parallel to the static field Ho and XYZ as the

principal axis frame of the electric field gradient. Since the system

is cylindrically symmetric, we can choose Oy, OY coincident. Now,

we can express IZ in terms of Ix, I and 8, the angle between the

static magnetic field H and the principal axis of the electric field

gradient of the molecule. This is shown in Fig.(23).

+ I cosO



Fig.(23) Geometry of the electric field gradient principal axes at
the deuteron nucleus and the laboratory frame in the liquid

I = IxsinO + I cos9


ly = I

Also, I and I can be replaced by ladder operators I and I
x y

Ix = ( + + I)/2

I = ( + I_)/2i
y + -


Substitute relation (II.5.3) and (II.5.4) into (II.5.2).

(in laboratory frame)= e _(2_) (3cos2 1)(312 2

+ sinecosO[Iz(I + I_) + (I+ + I_)Iz
2 zz

+ -sin2 (I + I2)] (11.5.5)
4 + -

The second and third terms do not contribute matrix elements of

the diagonal. The first order perturbation contributes only in the

case of m = 0, t1, therefore

E ()= yHom = h Lm with Larmor frequency \L 2=
m 0 L L -27

E(1)= < ml Im >

e= e2i) 1 (3Cos20 -1)(3m2- I(I + 1))
41(21-1) 2

=4 hvQ(3cos20 -)(m2- I(I + 1)/3) (11.5.6)
4 Q

where V = 3 e2qQ__
re Q 4 hI(I 1/2)

For the deuteron, I = 1, m = 1, 0

E = 8 (3cos20 1)

E(1)= e (3cos20 -1)
o 4

W(0,-l)= hv + --(3cos2O 1)

W(l,0)= hv (3cos 0 1)

+ 1

( Q = 0 ) ( 0Q 4 0 )

m Zeeman splitting after quadrupole perturbation

Fig.(24) Energy diagram for first order quadrupole perturbation of the
Zeeman effect of the deuteron nucleus

According to selection rules A m = 1, the transition energies

are given by

32 2
W(1,0) = y + 8 e qQ(3cos 1)
0 8
32 2
W(0,-l) = Th + 8 e qQ(3cos2 1)

Calculation of the spectral shape function, which is a product

of the transition probability by the density of transition at each

angle 0 requires the transition probabilities, which we obtain

directly from the matrix elements

< m I m+l > = [(I m)(I + m + 1)]

< m Ix m-1 > =- [(I + m)(I m + 1)]1/2
x [2




I= 1
3 e2qQ
x y- H0

1-2x l-x 1 l+x l+2x

Fig.(25) The powder pattern resonance line for I = 1, corresponding
to the transitions Am =1, in a strong magnetic field,
as a function of the transition energy. The ordinate unit
is arbitrary. The nuclear quadrupole interaction is treated
as a first-order perturbation of the NIR transitions. The
figure corresponds to a nuclear magnetic resonance
experiment in which the strong magnetic field is held
constant, while the oscillating frequency is swept through
the resonance.


P(1,0) 1< 1i -2Hlcostct Yt I 0> 2 =y2fi2H 2cos 2

P(O,-I)" l < 01 -2H1coswt h1 Ix -1 > 2 = 2y2 2H 2cos20t .

The value P is independent of 0. Thus, the shape function for the

transition depends on 0 only through the density of transition D at

angle 0. For an isotropic distribution all orientations are equally

probable and the number density of nuclei for a given orientation

varies as

d cos6
D(cos6) = d-s

dW -1
d cose

2 W yfiH 1
= e ( o + 1) 2 (11.5.11)
16 3 2
8e qQ

The signs in the parenthesis depend on which one of W(0,-l) and

W(1,0) is chosen for W. The final line shape is determined by

superposing the shape functions of both transitions.

The idealized shape shown in Fig.(25) by the dashed line has

certain striking features. For values of W corresponding to cosD = 0,

the denominator of the shape function vanishes and the line strength

becomes infinite. It is also to be noted that the outsides of the lines

are very sharp, while, on the inside, the lines merge. Observed spectra

shown by solid line, may be expected to be differ from this idealized

shape, because of various broadening mechanisms, such as lifetime and

dipolar broadening. In addition, the effect of second order quadrupole

perturbation terms, which were disregarded in our discussion of the

line shape-will distort the shape of the line and shift the positions

of the minimum-without, however, changing the distance between them.

The average quadrupole coupling constant of the deuteron nucleus

in D20 has the magnitude 258.6 k'z measured by Hindman[25].

The simple bound water model of lamellae structure is shown in

figure(26). If the water layer has a thickness d=100 Y and the bound

water a thickness with preferred orientation A=1.25 A, the observed

quadruple constant can be calculated from the relation

< eh >obs.= 258.6 kHz x Pb + 0 x (1 Pb) (II.5.12)

Only bound deuteron water contributes to the quadrupole splitting.
The weighting factor Pb for bound water [33], is equal to A/d = 1.25x10 .

The unbound deuteron water with fast tumbling frequency (on the order

of 1012Hz, is much faster than the Larmor frequency) has no contribution

due to quadrupole splitting. There numbers give

< e q > =3.23 kHz (II.5.13)
h obs.


SI I I I I I I I I I I IA A =1.25 R




Fig. (26) The bound water model of lamellae structure(bound water
has preferred orientation)


III.1 Sample Preparation

III.1.1 Preparation of Chemicals

The chemicals used in this research, their purities, molecular

weights, and the commercial source are listed below:

Table(4) Components used for sample preparation

Name of Component

Deuterium Oxide

Oleic Acid

Potassium Hydroxide









Molecular Weight








Stohler Isotope Chemicals

Fisher Scientific Co.

Fisher Scientific Co.

Fisher Scientific Co.

Fisher Scientific Co.

Fisher Scientific Co.

Potassium oleate is prepared by mixing equimolar amounts of

potassium hydroxide and oleic acid. Since solid potassium hydroxide

does not readily react with oleic acid, the latter is mixed with the

other three components(D20 hexanol and hexadecane) in the desired

ratio first and then with potassium hydroxide. The physical properties

of the dispersed system studied are highly sensitive to change of

potassium oleate.

Since potassium hydroxide rapidly absorbs water vapor and the

amount of it used is small, it was necessary to quickly and precisely

measure the weight so that negligible vapor is absorbed during weighing.
The resolution of the balance is about 10 gram.

The samples are labeled by W/0, the volume ratio of deuterium

oxide to hexadecane oil, and by S/0, the ratio of surfactant
potassium oleate in grams to hexadecane oil in cm All the samples

have a fixed ratio of the cosurfactant hexanol or pentanol to hexadecane

oil of 0.4 by volume.

The prepared samples are listed in the following:

Hexanol system (5/0= 0.2) W/0 = 0.1, 0.2,0.3, 0.4, 0.5, 0.6, 0.7, 0.8
1.0, 1.2, 1.4, 1.6, 1.8, 2.1
Pentanol system (S/0= 0.2) W/0= 0.1, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4

Other samples were prepared with changing surfactant/oil ratios and

a fixed W/0 ratio. Unfortunately most of them were not stable and had

a separation problem during tne time of the experiment. These samples

were all rejected.

III.1.2 Sample Sealing

Since the sample is a mixture of liquids, small amount of

dissolved oxygen molecules, which is a paramagnetic impurity having

a net magnetic moment arising from unpaired p electrons [34][35]

roughly 10 times larger than that of the deuteron, cause a

significant contribution to the relaxation process. In order to

exclude the oxygen molecules, standard freeze-pump-thaw method was

employed. Using the low solubility of the oxygen molecules at cold

temperature, we can freeze the sample with liquid nitrogen first and

then pump to evacuate. The next step is to thaw the sample to release

the remainder of the oxygen molecules. Repeat this method for two

cycles and then seal it. This procedure represents a compromise.

Prolonged freeze-pump thaw cycles may well cause composition changes.

The sample container is a Pyrex tube with an inner diameter of

1 cm and an outer diameter of 1.22 cm. The length of the sample tube

is about 3 cm. Before filling with sample, the tubes were cleaned by

aceytone and dried. Sample tubes were prepared by drawing to a narrow

neck and annealing with a moderate flame. During sealing, caution was

exercised to heat the sample, otherwise the chemicals may evaporate

or dissociate even though most of the sample tube was submerged in

liquid nitrogen.

111.2 Temperature Measurement and Controlling Apparatus

III.2.1 Cryostat

The cryostat is shown in Fig.(27). After locating the sample

in the rf coil, the inner copper and intermediate brass chambers

are sealed with an indium wire 0-Ring of 0.025" diameter. Helium

exchange gas of about 5 psi is admitted to both chambers. Though

the helium exchange gas in the brass chamber was latter pumped out,

it is important to do this to expell water vapor; otherwise the

water vapor attached on electric wire may cause current leaking

especially when the temperature was below ice point.





Fig.(27) Cryostat

S -1" -

I-1 --



For experiments below room temperature, a mixture of powdered

dry ice (solid CO2) and ethylalcohol is admitted to the outside

brass cylinder, Ethylalcohol guarantees good temperature uniformity

of the heat reservoir at -770C. Then, the helium gas between the

intermediate brass and inner copper chamber is pumped out to a pressure
of 10- torr or less by a two-stage vacuum pump. Even though the

pressure is low and brass is a poor thermal conductor, slow heat

exchange between the sample and environment is still possible. This

slow heat exchange facilitates proper cooling of the sample. The

copper chamber has excellent thermal conductivity, thus the rate of

heat exchange between heater and the sample is much faster than that

between environment and sample. The thermocouple and heater are

connected to the feed back regulator discussed in the following


III.2.2 Thermometer

A copper-constantan thermocouple was used as the thermometer, and

is located at the top of inner copper chamber [Fig.(27) ]. A mixture

of crushed ice and water was used as reference at 273.160K. Every 43 iv

thermovoltage corresponds to one degree of temperature difference

from the reference point. In order to obtain identical temperature

of the copper chamber and the sample, measurements should be made

during heating and cooling parts of any thermal cycle. The time needed

for temperature equilibrium and removal of the temperature gradient

across the sample varies from 5 to 30 minutes depending upon the

temperature difference between initial and the final states and the

rate of heat exchange between the sample and the environment.

111.2.3 Feedback Regulator

A feedback regulator is used for maintaining the sample at

constant temperature. Figure(28) shows the block diagram of the feedback

regulator. The three amplifiers in the system, namely the FLUKE 823 AR

DC-AC differential voltmeter, the DYMEC 2460 MI amplifier and the

Hewlett-Packard 467A power amplifier, give large multifold gain of
approximately 10 so that even a small difference between the

temperatures of the sample and control value is sensitive enough to

generate a considerable quantity of additional heat. The actual and

desired thermal potential difference between the sample and reference

ice-water mixture may be expressed as kAt and is compared with a

voltage Es. The value VB generated by KEPCO power supply (voltage

regulated) series with power amplifier HP 467A. The difference voltage

is amplified to produce an output A(Es- kAt). It is necessary to

operate the amplifier in a slightly unbalanced condition so that

positive and negative excursion of the sample temperature from the

desired value can be compensated by decreased or increased heater

power. If operated strictly a balance, positive and negative voltage

at the output would both produce heat in the sample.

The unbalance is produced by the insertion of a "DC" power supply

VB generated by the KEPCO in series with the balanced HP 467A. Even

so if the output of the amplifier is sufficiently negative the system

will become unstable, a high temperature will generate a greater

negative voltage (kAt V ), and a greater negative current will flow

through the heater. Insertion of a suitable diode prevents the negative

current flowing.

The value RH is the resistance of the sample heater. The

distinguishable temperature differentiation At is about 0.250C.

If E kAt > 0 The heater current turned on and the sample heated up.

E kAt < 0 The heater current is terminated by a diode between

the HP 467A and KEPCO, and the sample is cooled down.

The required value of VB is such that V 2 /R is larger than the

cooling rate between the sample and environment at the desired

temperature. The regulating procedure are listed below

(1) Set E a little larger than kAt, the real potential developed

in the thermocouple, then one will see current through ammeter.

(2) Increase the gain but not sufficiently that the current

exceeds the maximum current that the heater can tolerate.

(3) Adjust V to obtain a null current in ammeter, i.e. the

ammeter is balanced. This provides proper cut down current.

(4) Set E to the desired value, and the system will regulate.

61 W
ry) B




III.3 Nuclear Resonance Measuring Apparatus

III.3.1 Circuit Description

Figure(29) shows a block diagram of the probe and associated

major components. The output impedance of the transmitter is matched

to the transmission line and is equal to the input impedance of the

receiver. The impedance at resonance of the sample tank circuit is

also equal to that of the transmission line.

The operation of the system depends upon the nonlinear properties

of semiconductor diodes. During the application of a high-powered rf

pulse from the transmitter, both sets of crossed diodes in Fig.(29)

are conducting heavily and have low jipedarces. Thus, the rf pulse

passes through the diodes at A without appreciable attenuation, while

the diodes at B prevent the rf level at the receiver input from

rising above 1 v. Since point A is a quarter wavelength from B, the

effective short circuit at B appears as an open circuit at A and thus

does not affect the voltage at A.

Following the rf pulse and after the transients have decayed, the

diodes stop conducting and the series crossed diodes prevent a large

impedance at point A. The small NR signal voltage (typically about

1 my) is not enough to lower the impedance of the diodes, and thus

in the absence of an rf pulse the transmitter is isolated from the

system, while the receiver is matched to the sample tank circuit.

It should be observed that the length of the X/4 line between

points A and B is not specially critical, as the purpose of this line

is to allow the use of the diode short at B without presenting a low

impedance shunt at the sample coil. Thus, since the transformed


impedance of the diode short need only be large compared with 50 0,

within the bandwidth of the tuned sample coil, the cable need only be

of the order of X/4, and the use of the quarter wave cable does not

entail any significant narrow-banding of the system.

A more detailed block diagram is given in Fig.(30). The rf signal

generator (HP 606B) is stabilized by a HP 8708A synchronizer. High

voltage pulses are provided by an ARULAB PG-650C oscillator. A

programmed pulse generator (Wang Lab. 612AT) controls the width of

pulses and the delay time T between pulses. The resonance frequency,

pulse width, and the delay time can be checked using the model 729C

universal time counter. Transient signal picked up from the sample

coil after preamplification (the wide band amplifier serves as power

source for the preamplifier) is sufficient to feed the phase sensitive

detector (1-30 MHz F+H Instruments) about 0.5 v. However, in the case

of spin-echo measurement of T2 the stability of the electromagnet was

not adequate to use phase sensitive detection, and diode detection

was employed. This arrangement is shown in Fig.(31). Signals from

the phase sensitive detector were accumulated in a Fabritek 1062

signal average, whence the resultant could be plotted on an X-Y

recorder (Honeywell 550).

III.3.2 Electromagnet

This is a Varian V-3454, 9-inch diameter, Fieldial-regulated unit,

equipped with cooling system. The drift of the magnet is less than

240 parts per million of maximum field over one day when operated

continuously. In other words, this is the dominant source of error in

the maintainance of the resonance condition. The frequency stability

of the signal generator used is 2 x 10-6 per day.

Signal Generator HP606B

Synchronizer HP 8708A

Programmed Wang Lab ARULAB
Pulsed Oscillator
Pulse Generator 612A PG-650C

Model 729C
Universal Time Counter

Reference Sa Probe

Magnet Varian
__ --_ V-3454

Attenuatr RULAB Wide Band Amplifier
Attenuator Preamplifier PA-620 UL WA-600-E

1-30 Miz
Phase Sensitive Detector F+H Instruments

SSignal Averager Fabritek 1062
Trigger- -
Oscilloscope Tetronix RM 503

Honeywell 550 X-Y Recorder '

Oscilloscope Tetronix 547

Fig.(30) Block diagram of pulsed NMR experiment with phase sensitive

Programmed Wang Lab |,JF
Pulse Generator 612AT

Model 729C Universa
STime Counter

MaIgnet V-345 I4

Fig.( 31) Block diagram of pulsed NMR experiment with diode detector.

III.3.3 Signal Generator and Frequency Synchronizer

The signal generator is a Hewlett-Packard Model 606B unit,

which provides a signal adjustable from 0.1 microvolt to 3 volts and

which is applied to a 50 ohm resistive load.

The frequency synchronier is a Hewlett-Packard Model 8708A,

which is designed to phase-lock the HP 606B signal generator.

III.3.4 Pulse Programmer and High Power Gated Amplifier

The pulse generator is a Wang Model 612 AT transistorized

programmed pulse generator. This unit has two independent channels,

each capable of delivering twelve pulses which are collectively

adjustable in duration and timing as follows: the pulses in the

first direct channel can be programmed at any or all of the first

twelve equally spaced time marks established by an internal timing

source; the pulses in the second delay channel can likewise, except

that in addition the channel as a whole can be delayed with respect

to the timing source. Since the period of the timing source is

adjustable, a flexible pulse program is available. This unit has

several disadvantages: The change of delay time affects the pulsing

rate. There are only twelve delay pulses available for a Carr-Purcell

sequence. Finally, the output impedance is fairly high, and the output

voltage level of 10 volts maximum is marginal for the requirements of

the transmitter. The last disadvantage is overcome by inserting a

high power rf amplifier.

The high power rf amplifier is a Arenberg Ultrasonics Laboratories

Instrument Company Model PG 650-C pulsed oscillator. The unit receives

the rf signal from the rf signal generator, together with gate

rectangular pulses from the pulser. The transmitter delivers a maximum

rf amplitude of about 300 volts into 50 ohms.

III.3.5 Sample Coil and Probe

The sample coil consists of 16 turns of No.22 double cotton

copper wire with a total inductance of 17ph.

The probe (including sample coil) serves as part impedance

matching network to the transmitter and receiver. The capacitors of

the probe, C1, C2, and C, are tuned so as to maximize the observed

signal. The circuit diagram is given in Fig.(32).

III.3.6 Receiver

The preamplifier used is an ARULAB Model PA-620-L. This is a

tuned amplifier, which provides voltage gain of approximately 60 db

with a low noise figure. The output and input stages each has nine

tuning coil caps. These are used to balance the capacitance existing

between grid and plate of the vacuum tubes and thus limit the

recovery time and optimize the system [Fig.(33)]. The frequency

selectors must obviously be set in the proper range for sample

resonance. The bandwidth selector can be used to adjust the resistance

between grid and ground so that high gain with narrow bandwidth or low

gain with broad width can be obtained depending on the frequency

distribution of the sample signal. The well tuned narrowest bandwidth

is about 200 kHz, which is wide enough for the quadrupole perturbation

frequency range found in these studies.








SL ib;-----. _ l


II u


S I,
I 1

An ARULAB Model WA 600 E Wide Band Amplifier follows the

preamplifier PA-620-L. This unit has an rf gain of about 60-65 db,

flat to within +3db from 2 to 65 MHz.
The dead time is about 1.5 x 10 sec. The gain of the preamplifier

is about 180 and the total rf gain of the receiver is about 105

III.3.7 Phase Sensitive Detector

The following is a qualitative description of the ring diode

phase sensitive detector. For a more rigorous treatment reference

should be made to Arundell,L.,Clarendon Laboratory, Oxford memo.

The assumption is made that VR > Vs and that the diodes when

forward biassed have a resistance R and when reverse biassed have an

infinite impedance.

Following the nomenclature of Fig.(34) in the half cycle when

VB > V the circuit becomes


+ Ii

vRVRsinwt C
vR R


L Vs + )

v s= Vssin(wt 1-)

Applying Kirchoff's Laws,

2 v = I1R + (I1 + IL) R = 2 I R + I R (III.3.7.1)

vR vs = LRL + (I1 +IL) R = 11R + 2 ILR (III.3.7.2)

2 v
.- 2 v = 3 ILR or ILR 3 (

In the other half cycle

1 + IL R L

V = VRsin(t A
vR R

+ D

v = V sin(wt + 1)
s s

As before

2 vR = IR + (I1 + I ) R = 2 I R + I R (III.3.7.4)
R 1 1 L 1 L

vR Vs = 1 + (I L + = I1R + 2 ILR (III.3.7.5)

and 2 v = 3 I R or I R = (III.3.7.6)
s L L 3

vR: solid line

v : dashed line

S Ov

Output = ILRL

I / ' /
.. I. I /

/ I

If the assumption is made that the switching is done by v' the

putput is proportional to

1 V T sin(6 + i) dG
T s o

= [ cosa / sinG d6 + siny f'cosd de ]
IT o o

= Vs cos
r s


There may be a portion of the cycle when vs exceeds vR and at that

time diodes CB and BA may conduct whilst CD and DA are switched off or

vice versa depending upon the sign of v The treatment is also

neglecting non-linearities in the diode characteristic.


Q< ------ >0 ---- >


0 0
0 H*

> zO




1 VAB + VBC = 0.3 v

R 2

O. V = 0.3 v + A V

Fig.(35) (a) Nonlinear characteristic of a diode
(b) Modified circuit for diode detector


0.3 v

111.3.8 Diode Detector

The idea of amplification of diode detector comes from linear

part of the diode characteristic of the current-voltage relation in

a semiconductor.

The input signal V. and output signal V characteristic of a
1 O

diode is shown in Fig.(35a). In the case of small V., V the

amplification V /V. is reduced. This causes distortion on small spin

echoes and gives a smaller 12 than the true value. The modification

of the diode detector is given in Fig.(35b).

For the system used in this dissertation study, an additional

0.3 volt reverse bias is applied to push the characteristic toward

the left so that a linear amplification is obtained.

Since the diode has rectification property, the information

collected gives only the magnitude. Thus the signal average

(Fabritek 1062) only accumulates positive input and fails to average

out random noise. In Fig.(36), the basic structure of a diode detector

is shown. The voltage V is used to shift the signal level.




Fig.(36) Diode detection

A diode detector is also inferior in tuning. The resonant

frequency is determined by mixing a reference signal (from the pulse

generator) through an attenuator with the nuclear signal. The attenuator

is used to shift the level of the signal to reduce the base line offset.

When tuned off resonance, there are beats on the free induction decay.

One can tune either field or rf frequency to remove this ripple thereby

ensuring that the resonance condition is fulfilled. When making the

measurements, reference signal is removed.

In diode detection, the requirement of stabilities for field

and rf source are not as critical. Spin-spin relaxation times obtained

from diode detection was generally smaller by about 30 % than that

obtained from Gill-Meiboom-Carr-Purcell[36] pulse sequence phase


III.4 Continuous Wave Method

A Varian DP-60 Wide Line spectrometer was used to record the

narrow line of the liquid crystals and microemulsions. The wide line

of the liquid crystals contributed by the deuteron quadrupolar

splitting of the bound D20 was also recorded by saturating the

central narrow line.

111.4.1 Power Saturation and Line Width Broadening

Figure(37) shows the relation of signal to H (magnitude of rf

field) and H (magnitude of audio modulation field). We will see diagram

(a) and (b) being both similar. At low H1 and H values the signal

height is proportional to H1 and Hm, but at high values saturation

occurs followed by a decrease in signal amplitude.The corresponding line

width is no longer a constant, being broadened by instrumental reasons.

To avoid such saturation problem, one should check the magnitude of

saturation field before running each sample and set both rf and audio

field magnitude by 50 % below. When phase detected at the modulation

frequency, the familiar derivative spectrum is observed. This applies

to the frequency am is less than the linewidth expressed in frequency


In the severe saturation a series of sidebands are produced at

a m u 2m etc.[Fig.(38)]. The effective H at the sideband

frequencies is affected by 1m and can be expressed as H1 multiplied

by a scaling factor. The scaling factor is a Bessel function of parameter
( B = -m)37]. Figure (35) shows that increasing Hm requires higher H1
to obtain the same signal height. In other words, smaller signal height

is obtained if H is increased and H1 is kept fixed.(Note: This is

true for the central band but not for the sidebands, which will be

discussed in next section.)

For the first sideband detected at the modulation frequency

Effective= J B)

n B \ effective ", m .2
when S is small: J( ) = and Hffective=
1 m1(

Change of H is basically equal to change of H In practice,

H is selected at some suitable (linear region) value and final

adjustment are made using H1.

Thus the frequency of audio modulation fm determines whether the

line shape is in derivative or absorption mode. For the convenience















M -4

H g





of comparison, we can convert the spectral line width (half height

width of spectral line) to corresponding Af. When phase detected at

the field modulation frequency, the familiar derivative spectrum is

obtained. The discussion thus far applies to the situation where the

modulation frequency u is less than the linewidth expressed in

frequency units. In the phase angle $ between the audio output and

reference is adjusted to the largest central peak is expected

[graph(a) of Fig.(40)]. The change of polarity of the central peak in

this graph is not a 'derivative' case; this must be noted during data

analysing. Graph(b) of Fig.(40) shows the correct audio phasing at (=00

removes the central narrow line and obtains prominent side bands if

the effective H1 is large enough. Under this condition the first

sidebands are the undifferentiated absorption spectra, which are
subject to saturation by H, e in the usual manner. The line

width and signal height of each side-band depend on different

characteristic curves shown in Fig. (41).

Suppose spectrum is more complex as shown in graph(a) of Fig.(42).

If fm is much larger either Afl or Af2, we expect to see both line

shapes are in absorption mode as shown in graph(b). If fm is smaller

than Af2, we will see both in derivative mode as shown in graph(c).

If fm is between Afi and Af2, then the narrow line is in absorption

mode and the wide line is in derivative mode; the spectrum is expected

as shown in graph(d), and the frequency between the two narrow lines

is still 2f Graph(e) shows that misphasing of the third case can

cause other sidebands besides the first sidebands and each of them

with same width in the case of no saturation.

2 f !>--A f 2
( a.) >A>, T= 0

-- f --- -- 2 f -- -- f -->
m m m

( b ) f LAf, 9= 0

m m m f

Fig. ( 0) Line shaps of the case : fm

k- f --> f < f _1<__ f j
I m I m m

Fig. (40) Line shapes of the case :f >4f







U I'


L Afl

( b ) CASE 1

( c) CASE 2
f m


Af 2

(d ) CASE 3
Af2< f

2 f

( e ) MISPLu

A; ------

;E 3

fm m

Fig. (42) Line shapes corresponding to different modulation frequency
f of signal composing both narrow and wide line

"" ^



III.4.2 Rate of Sweep and Magnetic Field Inhomogeneity

The line shape' also depends upon the time taken to sweep through

AH is the line width in magnetic field units and the sweep speed.
Figure(43) shows how th sweep rate affects the line shape. In case(I),

we obtain normal derivative spectra when AT is much larger than the

time constant, and distortion of spectra when AT is close to the time

constant. In case (II), we obtain further distortion of spectra when

AT is smaller than the time constant. The symptom will also be observed

if AT is smaller than the spin lattice relaxation time TI. Thus the

sweep rate has to be sufficiently slow that AT is slightly in excess

of the time constant or T1 whichever is the larger, whereas the noise

is inversely proportional to the square root of the time constant.

For optimum performance the time constant should not be less than T1.

Noise can be reduced by increasing the time constant and scanning more

slowly or by making the two times comparable, scanning as rapidly as

possible, and signal averaging.

Complication also arises from magnetic field inhomogeneity.

Figure(44) shows that distortion due to magnetic field inhomogeneity

may have a similar symptom e.g.,if the field has a quadrupole component

which produces an asymmetric line shape. We can distinguish this by

checking the scan in both directions. If the polarity of the spectra

does not change,this is due to magnetic field inhomogeneity. If only

polarity change and distortion is in the same side as before, this is

due to rapid passage.

The CW measurements recorded in this dissertation employed only

slow passage conditions. Though the fast passage condition is not


(a) TT >>TIME

(b) AT TiME

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