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Application of time domain reflectometry to solution processes

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Application of time domain reflectometry to solution processes
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Wong, Ngai M., 1961-
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English
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x, 144 leaves : ill. ; 29 cm.

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Subjects / Keywords:
Butanols ( jstor )
Conductivity ( jstor )
Critical frequencies ( jstor )
Dielectric materials ( jstor )
Electric fields ( jstor )
Micelles ( jstor )
Molecules ( jstor )
Permittivity ( jstor )
Pyridines ( jstor )
Solvents ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1990.
Bibliography:
Includes bibliographical references (leaves 138-143).
Additional Physical Form:
Also available online.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Ngai M. Wong.

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University of Florida
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Full Text











APPLICATION OF TIME DOMAIN REFLECTOMETRY
TO SOLUTION PROCESSES
















By

NGAI M. WONG















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1990














ACKNOWLEDGEMENTS



I would like to give my greatest appreciation to my

research director, Dr. Russell S. Drago, for his skillful leadership and scientific wisdom and to his wife Ruth, for her caring and heartwarming get-togethers.

I would like to thank the Drago Group members, both past and present, for their suggestions. In particular, I would like to thank Curtis Barnes, Mark Barnes, Larry Chamusco, Peter Doan, Jerry Grunewald, and Richard Riley for their helpful discussions concerning chemistry and other important matters.

Special thanks go to my father, Mr. Wai Woon Wong, my mother, Mrs. Kuen Suen Wong, my brother, Mr. Edward Wong, and my sister, Ms. Yin Wa Wong, whose continued understanding and support made this effort possible.















ii















TABLE OF CONTENTS



ACKNOWLEDGEMENTS ............... . ii

LISTS OF TABLES . . . . . . . . . v

LISTS OF FIGURES . . . . . . . . . vi

ABSTRACT ...... ............... ix

INTRODUCTION .................. . 1

BACKGROUND .................. . 3

Dielectric Theory ..... ......... . 3
Time Domain Reflectometry .......... . 13
Solution Systems to be Studied ......... 16

EXPERIMENTAL .............. . . 37

Time Domain Reflectometry . . . . . . 37
Nuclear Magnetic Resonance ......... . 52
Chemicals . . . . ...... ... . 53

RESULTS AND DISCUSSION . . . . . . . 54

Alipliatic Alcohols . . ......... . 54
Binary System of Carbon Tetrachloride
and n-Butanol ........... .. . 54
Binary System of n-Propanol and n-Hexanol . . 60 Binary System of n-Butanol and Pyridine ... . 66
Ternary System of Carbon Tetrachloride,
n-Butanol, and Pyridine .......... 71

Surfactant Systems . . . . .. . . .. 72
Binary System of n-Butanol and Aliquat 336 . 72
Ternary System of Carbon Tetrachloride,
n-Butanol, and Aliquat 336 ..... .. . 81
Binary System of n-Butanol and Water ..... 87
Ternary System of Water, n-Butanol,
and Aliquat 336 ............... 92

TDR SYSTEM ENHANCEMENTS AND MODIFICATIONS ... . 98


iii









CONCLUSIONS . . . . . . . . . . 103

APPENDIX ..... .. ..... ...... .. 106

REFERENCES . . . . . . . . . . 138

BIOGRAPHICAL SKETCH .............. 144



















































iv















LISTS OF TABLES



1. Energy of Activation for Bromide Ion Quadrupole
Relaxation in Surfactant Systems. ....... 34 2. Butanol in Carbon Tetrachloride ... .... 61 3. Primary Alcohols ............. ... 62

4. n-Hexanol and n-Propanol .... ... . . 65

5. Pyridine and Butanol Systems ...... . 69

6. Aliquat 336 in n-Butanol ..... ..... . 79

7. Ternary System of Aliquat 336, n-Butanol, and
Carbon Tetrachloride ............. . 85

8. Water in n-Butanol .............. 90

9. Water in a Solution of 10% Aliquat 336 in
n-Butanol .................. 96














LISTS OF FIGURES



1. Dielectric material filled parallel plate capacitor experiment ............. 4

2. Three mechanisms for describing dielectric relaxation . . . . . . . . . 7

3. Plot of the frequency dependent complex dielectric function; real and imaginary
components . . ... .. .. . . . 10

4. Plot of the imaginary versus the real component of the complex dielectric constant, Cole-Cole
plot ................... ... 12

5. 79Br relaxation rates (from line widths) at 30'C for 0.500M aqueous solutions of alkylammonium
bromides . . . . . . . . .. 25

6. Phase diagram of a ternary system composing of hexadecyltrimethylammonium bromide (CTAB),
hexanol, and water ............. 27

7. 79Br relaxation rates (from line widths) at 30*C for aqueous solutions of monoalkylammonium
bromide solutions ......... ..... 29

8. 35C1 relaxation rates (from line widths) as a function of the inverse concentration of
octyltrimethylammonium chloride and octylammonium
chloride at 28C ..... . . ... . 31

9. Observed 81Br relaxation rates (from line widths) divided by that at infinite dilution in water for
solutions of hexadecyltrimethylammonium bromide
(CTAB) and water in hexanol ......... . 32

10. 79Br- transverse relaxation rates (from line
widths) in non-aqueous and mixed solvent systems
as a function of electrolyte concentration . 36

11. Block diagram of TDR setup ....... ... 38


vi









12. Complete waveform obtained from the TDR ... 41

13. Process is observed in approximately half the
time window with the correct time window
setting .................... . 42

14. Raw time domain data for an air reference and a
sample of n-butanol ...... . ...... 48

15. DIF and SUM time domain spectra for n-butanol . 49

16. Fourier transformed n-butanol spectra ..... 51

17. Frequency dependent imaginary component of the
observed complex dielectric constant for solutions
of n-butanol and carbon tetrachloride ..... 55

18. Concentration dependence of the observed static
dielectric constant for solutions of n-butanol
and carbon tetrachloride .......... .. . 57

19. Theoretical fit of the observed real component
spectra for solutions of n-butanol and carbon
tetrachloride ................. 58

20. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and carbon tetrachloride ... .. ..... 59

21. Frequency dependent imaginary component of the
observed complex dielectric constant for solutions
of n-propanol and n-hexanol ...... .... 64

22. Theoretical fit of the observed real component
spectra for solutions of n-butanol and pyridine 67

23. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and pyridine ................. 68

24. Comparison of the critical frequencies obtained
for the pyridine and carbon tetrachloride
systems ...... ............ .. 70

25. Concentration dependence of the observed DC
conductivity for solutions of Aliquat 336 in
n-Butanol. .. .... . . .. . . 73

26. 35C1 NMR line widths obtained for solutions of
Aliquat 336 in n-Butanol ........... 75



vii









27. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336 and
n-butanol ............... .... .. 77

28. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336
and n-butanol ..... ....... .. . . 78

29. Concentration dependence of the observed static
dielectric constant for solutions of Aliquat 336
and n-butanol ....... .......... 80

30. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and carbon tetrachloride .... .... . 83

31. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and carbon tetrachloride ...... 84

32. Theoretical fit of the observed real component
spectra for solutions of n-butanol and water . 88

33. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and water ... .................. . 89

34. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and water ....... . .. ..... . 93

35. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and water .... ........ . 94


















viii














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

APPLICATION OF TIME DOMAIN REFLECTOMETRY TO SOLUTION PROCESSES

By

Ngai M. Wong

December 1990

Chairman: Professor Russell S. Drago Major Department: Chemistry

The aggregation of alipliatic alcohols and Aliquat 336 is studied by using time domain reflectometry, TDR. The aggregation of the alcohol leads to the formation of a three-dimensional dynamic network through the coordination of the two lone pairs on the oxygen and the OH hydrogen. Molecular size and adduct bond strength play an important role in the formation of this dynamic structure. The formation of an adduct tends to shift the aggregate size distribution of the alcohol to smaller species. The aggregate size remains fairly constant with systems of similar adduct strengths. In the absence of adduct formation, the aggregate size remains fairly constant at low dilution. The shift to the smaller species occurs at a slower rate than that observed for systems with adduct formation.

ix








The formation of micelles can be observed in dielectric spectra. The critical micelle concentration can be determined from solution DC conductivity and the static dielectric constant obtained from TDR dielectric spectra. The study of Aliquat 336 has shown that solvents like n-butanol prefer the hydrophobic region of the quaternary ammonium salt in neat solvent. The addition of a nonpolar solvent like CC14 to a solution of Aliquat in n-butanol causes the butanol to leave the hydrophobic sites and interact with the hydrophilic sites of Aliquat. In contrast, the addition of water does not influence the observed interactions of butanol. These effects are manifested in the intensity of the dielectric constant and in the critical frequency of the dielectric spectra.
























x














INTRODUCTION


Time Domain Reflectometry, TDR, is a technique used to study the time-dependent response of a sample to a timedependent electromagnetic field. This response depends upon the dielectric properties of the sample. Practical application of this technique became available with the introduction of the tunnel diode as a voltage pulse generator which is used as an excitation source. This technological development allows systems that have processes as fast as 1 psec (2 X 1011 Hz) to be studied by TDR. A multitude of systems including pure liquids,1 mixed valent systems,2 biological systems,3-5 and polymers in solution6 have been studied by this technique.

The current state of the art time domain reflectometer is in the infancy stages. The potential of TDR lies in its ability to collect dielectric data in a very short time (minutes for a typical frequency range of 106 Hz to 109 Hz) compared to the standard method which is a long and tedious task of point by point data collection. Typical studies using TDR involve systems that have only one or two processes of interest. In this way, fundamental information about these processes is fairly easy to obtain. Systems


1








2

with multiple processes are more difficult to study because of the problem in assigning the TDR response to the correct process. The inability of this technique to provide structural information about a given process requires the correlation of observed dielectric changes with structural information from other techniques like nuclear magnetic resonance (NMR).

Emulsion and micelle systems are good test cases to

illustrate the complementary nature of TDR spectra to other structural techniques. These systems, of increasing interest since the 1950's, exhibit fascinating properties with numerous applications. The unique properties of these systems can be related to the amphiphilic nature of components. An amphiphilic substance is a general classification of molecules that contain both polar and nonpolar ends. There are many different substances that can be classified as amphiphilic, ranging from molecules like sodium n-dodecylsulfate (ionic), to N-n-dodecyl-N-,Ndimethylbetaine (amphoteric), to dimethyln-dodecylamineoxide (nonionic). The unique properties of these substances can be attributed to the tendency of the nonpolar group to avoid contact with a polar solvent like water while the polar end tends to be strongly solvated by water. These systems should give some very interesting TDR spectra and bring additional insight into the dynamics of these systems.














BACKGROUND


Dielectric Theory

A perfect dielectric material is an insulator. The internal charges are so closely bound that no electric current may be conducted through it. The atoms are fixed in its lattice and are not free to move through the material. In reality, there are no perfect dielectric materials because atoms are free to shift around their fixed positions when an external field, Eo, is applied to the material. A parallel plate capacitor can be used to generate this external field.7 The dielectric material is placed between the plates as shown in Figure la. The capacitor is charged so that one plate is positively charged and the other is negatively charged. The dielectric material's response to this external field is to set up its own electric field (induced field, E1) to counter the field from the capacitor. The induced field is produced by the realignment of the dipoles in the dielectric material. This sets up a surface charge that is opposite of that for each of the plates in the capacitor as shown in Figure lb. Typically, the induced field from dielectric material is less than the external field. The observed or resultant field, E2, for dielectric


3








4















I

(a)





+00
+










go
I




(b)


Figure 1: Dielectric material filled parallel plate
capacitor experiment.
a) Random dipole motion with no external field.
b) Alignment of dipoles to an external field.








5

material filled capacitor which is the summation of the external and induced fields. Since the induced field is opposite in direction of the external field, the resultant field is always less than the external field. The ratio of the external field to the resultant field is the dielectric constant of the material. The official definition of the dielectric constant,8 E, is



Q Q'
F r2 (1)


where F is the force of attraction between the two charges Q and Q' separated by the distance r in a uniform medium. A more convenient definition is the relative permittivity which is the ratio of the electric fields in the gap between the plates of a capacitor when the plates are separated by vacuum and by a dielectric material. A more intuitive feel for the dielectric constant is the material's ability to store electrical energy (i.e. the greater the charges ([Q and Q']) the larger the dielectric constant as expressed in the official definition).

The induced field from the dielectric material occurs through processes best described as "dielectric relaxations." Consider a system containing a dipole moment which responds to the application of an external field. The nature of the dipole moment may be permanent or induced by








6

the external field. The field is then turned off and the perturbed system is allowed to relax back to an equilibrium state. This relaxation process is referred to as "dielectric relaxation." Three basic mechanisms are involved in this relaxation process: electronic polarization, atomic polarization, and dipole reorientation.7 Electronic polarization is the rearrangement of the electron density around a nucleus. Atomic polarization results from the movement of latticebound atoms or molecules. Dipole reorientation involves the movement of polar molecules in space. Typical frequencies for these processes in polar liquids9 are 1017, 1014, and 108 1012 Hz, respectively (Figure 2).

In a static experiment similar to that described for the parallel plate capacitor, all three mechanisms are operative and contribute to the induced field from the dielectric material. The dielectric constant from this type of experiment is termed the "static" dielectric constant, Es. This quantity is typically reported in literature for a wide range of substances as the dielectric constant. Alternating the polarity of the applied field will modify the parallel plate capacitor experiment to allow each of the three processes to be isolated. The contribution from a particular process can be eliminated when the speed of the alternating field exceeds the rate of relaxation of process. For example, a long chain molecule that can rotate at a rate








7
DIPOLE ELECTRONIC ORIENTATION POLARIZATION ATOMIC
POLARIZATION







$







8 10 12 14 16 18 Log Frequency (Hz)






6'(J) FREQUENCY DEPENDENT DIELECTRIC CONSTANT E"((J) LOSS FACTOR






Figure 2: Three mechanisms for describing dielectric
relaxation.








8

of 1800 per second will move only 0.20 in a field that is alternating at a rate of 1000 cycles per second. In essence the molecule appears to be frozen in place.

The time scale for the electronic and atomic

polarization is so fast that they appear to be instantaneous on current instrumentation that is used to measure dielectric relaxation processes. Consequently, the only processes that can be studied occur through the dipole reorientation mechanism. The "high frequency" dielectric constant, e, is used to describe the contribution from the electronic and atomic polarizations.

The first theoretical model for describing the dipole

reorientation in molecular systems was given by Debye.10 It is assumed that the dipole moment of a molecule moves under the influence of a torque with full orientational freedom. The dipolar motion is hindered by internal friction that is related to the viscosity of the medium. Brownian motion acts as the randomizing factor which causes the breakdown of the dipole realignment. The resulting steady-state equation for a single process in terms of a complex dielectric function, e (iw), is given by



S E
(iw) = e + (2)
1 + i
where w is the angular frequency with 2 = 2rf, f is the frequency in Hz, r is the process time constant for the








9

molecular realignment or response in seconds, Es is the static dielectric constant measured in the frequency range in which wr << 1, and E. is the high frequency dielectric constant measured in the frequency range in which wT >> 1. The switching frequency of the external field is much lower than the frequency of the observed molecular process when Wr << 1. In the regime of wr >> 1, the observed molecular process has the lower frequency.

The complex dielectric function, equation (2), can be rearranged into its real and imaginary components



e*(i,) = E'(iw) iE"(iw) (3) where

E --E
E'(i) =E + (4)
1 + ((4)r)

s E
E"(i(w) = 2 W7 (5)
1 + (wr)


The frequency functionality, iw of the real component, e', and the imaginary component, el, is left out and will be implied in the remainder of this dissertation. Plots of e' and e" versus logl0w show the relationships between the functions in Figure 3.

The real component (absorption mode) is the frequency dependent dielectric constant measured in the alternating polarity parallel plate experiment. The imaginary component








10







63 e'(J) Debye Theory --.. --- Broader curves often
s Iseen in experiments.












-1






log (Wd) or log (f)









Figure 3: Plot of the frequency dependent complex
dielectric function; real and imaginary
components. Dash lines show typical systems that
deviate from Debye theory.
\4
%s



























deviate from Debye theory.








11

(dispersion mode) is called the dielectric loss function which refers to the power lost through the dielectric material. The energy absorbed from the applied electric field (the real component) is dissipated by the "friction" (the imaginary component) created by the dipole attempting to align itself to the field. The maximum loss value occurs at the critical frequency, fc, which is the same point as the inflection point seen in the real component where wr = 1 and describes the frequency of the observed process. The imaginary component is symmetric in the log of frequency around the maximum loss value covering a broad range of frequencies. A plot of E" versus e', Cole-Cole plot,9 for a Debye dielectric yields a semicircle as shown in Figure 4. The maximum loss value is equal to (es 0,)/2. Materials that obey the complex dielectric function, equation (2), are termed Debye dielectrics. The Debye model can be extended to describe multiple processes10 where equations (3) and (4) become



n

S= + i i6) i= 1 + (i)2 ()


n
\,, =i-1 i
El 2 7. (7)
1 + (w)









12









































Figure 4: Plot of the imaginary versus the real component
of the complex dielectric constant, Cole-Cole
plot.








13

for n processes with ei-1 and ei for each process equivalent to Es and E. for a single process.

Many systems (mainly solids and highly viscous liquids) show Debye type relaxation effects, but do not fit Debye's assumption that a dipolar process leading to the dipole moment change must have full orientational freedom. A rate theory model was suggested by Kauzmann11 to overcome this problem. The model involves a potential surface with an arbitrary number of wells of equal depth in the absence of an applied field. As the applied field changes the orientation of the dipole, the dipole moves from one well to another thus assuming a discrete set of orientations with respect to a fixed axis.

This work uses liquid systems which fit the Debye model. Accordingly, further discussion of the Kauzmann model will not be presented.



Time Domain Reflectometry

The complex dielectric function for a wide range of

substances has been measured by fixed frequency methods for many years. This process of collecting data is a slow and tedious ordeal due to the order of magnitude ranges of the frequencies involved in the frequency dependent dielectric process. Recently, a time-dependent technique called time domain reflectometry has been used to collect these data.12 TDR can greatly reduce the number of required measurements








14

and time required for frequency dependent dielectric measurements. This technique uses real time measurements to observe the properties of a system excited by a voltage pulse. As in any pulse technique, the characteristics of the voltage pulse define the theoretical limits of the range of observable frequencies. The pulse risetime describes the high frequency limit and the pulse width describes the low frequency limit.

The basic experiment compares the charging of a parallel plate capacitor containing the dielectric material to the charging of a parallel plate capacitor containing air. The charging function for the parallel plate capacitor changes due to the difference in the impedance (dielectric properties) between the sample cell and the dielectric material. Analysis of this time dependent charging function gives the characteristic constants (Es' ew, and r) for the complex dielectric function. The three basic TDR termination schemes will be covered briefly here because the derivation of the equations describing the complex dielectric function for each scheme have been discussed in previous work.9,13-15

The direct reflectance method9 analyzes only the first reflection which comes from the surface of the sample and requires that the sample length be long, usually 10 cm or longer, and the sample cell be terminated by an electrical short. The length of the cell is used to separate the first








15

reflection from the others. This results in a narrow range of observable frequencies. For example, a system with a pulse risetime of 25 psec and a cell length of 10 cm has an upper limit of 5 X 1010 Hz and a lower limit of 1 X 109 Hz.

The limitation of the sample cell length is removed in the multiple or total reflection methods.13-15 All reflections are resolved, eliminating the need to separate the reflections through the use of the sample cell length. A pulse width of about 100 nsec gives a lower frequency limit of 1 X 107 Hz for total reflection methods. Two forms of the total reflection technique are used: matched and open termination. The matched termination methodl3-15 requires that the cell be shorted with an impedance matched to that of the coaxial cable. As the voltage pulse reaches the sample cell/sample interface, part of the pulse is reflected back to the detector with the remainder being absorbed by the sample cell. The reflections due to this impedance mismatch between the dielectric material and the sample cell contain information only about the sample. Unfortunately, matching the impedance of the cable and the cell is not as simple as it appears. The sample cell, the coaxial cables, the connects, and various other components of the TDR have their own individual characteristic impedances. In addition, the equations that describe the reflected pulses can not be solved in closed form and require an iterative numerical solution such as the Newton-Raphson method.14








16

Iterative solutions are slow, tedious, and frequently converge on the wrong solution.

Open termination15 uses an open circuit with all of the voltage pulse reflected back to the detector, providing information about the entire system: the sample, the sample cell, the coaxial cables, etc. This method is the simplest in terms of equipment but the most complex for the analysis of the complex dielectric function. The use of an air reference is crucial in factoring out the dielectric properties from the TDR system itself. The analysis of the equations for the open termination method require an iterative numerical solution as in the matched termination method. Cole15 solved this problem by developing an approximate solution for the complex dielectric function using a Taylor series expansion for this termination scheme.


Solution Systems to be Studied

Donor-acceptor interactions in protic solvents are complex systems in which the self-association of the solvent, the hydrogen bonding of the solvent, and the adduct and Born type non-specific solvation effects all contribute to the position of the equilibrium and the enthalpy of complexation. In order to investigate the donor-acceptor bonding, component studies of the enthalpy of complexation of various bases to alipliatic alcohols in CCl4 solvent have been reported.16,17 Information about the extent of








17

aggregation of the alcohol is absent. Often it is assumed that monomeric species are involved. Similar assumptions are made in studies of the change in O-H stretching frequencies for alcohol-base adducts in dilute CC14 solution.18 In a recent analysis of the "anomalous basicity of amines,"19 it was shown that the acidity of hydrated proton species as well as the relative importance of covalent and electrostatic bonding contributions changed appreciably with the extent of hydration, i.e. the n value of H(H20)n. Similar changes in the acidity or basicity of (ROH)n molecules may be anticipated as n varies. As a result, gas phase studies of monomers and solution studies in inert solvents may determine properties of species that do not exist in pure solvents. Such information is relevant to understanding the chemistry in pure protic solvents and in mixed solvent systems.

Frequency dependent studies of the dielectric constant show dielectric relaxation corresponding to the making and breaking of hydrogen bonds in alcohol clusters.20 Three different relaxation times have been found for each of the 10 primary alcohols from propyl to dodecyl. Sixteen wavelengths of measurement were used spanning 30,000 to

0.22 cm. The long relaxation occurs over ranges of 1 to 22 X 10-10 sec and corresponds to breaking hydrogen bonds of terminal OH groups in a cluster concurrent with rotation of the alcohol as it forms a new hydrogen bond in the same








18

cluster. The rotation gives rise to the mechanism for dielectric relaxation. The relaxation times increase regularly with increasing chain length. The activation energy for this process range from 5 to 8 kcal mole-1 increasing in a regular fashion with chain length. This is of the order of magnitude expected for breaking a hydrogen bond and rules out rotational mechanisms that require the breaking of two hydrogen bonds. Accordingly, the molecular motion involves the terminal groups of the three dimensional structures. Since the hydrogen bond dissociation energies are not expected to increase with increasing length of the alkyl group, the size of the group involved in the molecular rotation is proposed to contribute to the observed activation enthalpy and entropy. In the neat alcohol, one expects a distribution of cluster sizes and hence a distribution of relaxation times. Since this is not observed, the energetics of the processes described must not differ enough with cluster size to be resolved. Failure to observe a distribution of relaxations is taken as evidence to rule out the reorientation of the whole cluster as the relaxation mechanism.

The other two relaxations correspond to rotation of
monomeric molecules (1.7 to 5 X 10-11 sec) and to rotation of the OH group around the C-O bond (1.7 to 4 X 10-12 sec). The time scale for these two relaxations are beyond the








19

range of our current TDR system. Accordingly, no further discussion of these processes will be presented.

Metals like gold, iridium, manganese, mercury,

molybdenum, nickel, niobium, palladium, platinum, tungsten, and zirconium have been extracted or separated using Aliquat 336 (trioctylmethylammonium chloride).21-28 This quaternary ammonium salt is widely used as a phase transfer catalyst and as a mobile phase catalyst. The better known systems involve quaternary ammonium salts with large alkyl groups. In general, little is known about the dynamics of this class of compounds in solution or in moving substances in and out of the different phases. The majority of the physical characterization studies have been done using nuclear magnetic resonance to study the quadrupolar relaxation of chlorine, bromine, and iodine.

Nuclear magnetic quadrupole relaxation29 arises from the interaction of a quadrupolar nucleus with a time-dependent electric field gradient. This field gradient depends on two properties: the molecular motion of the quadrupolar nuclei and the surrounding species' dielectric properties. The magnitude of the field gradient, influenced by the surrounding species, is the major contribution in the relaxation of halide ions in solution. The molecular motion of the quadrupolar nuclei alters the direction of the field gradient, providing the major contribution to the relaxation mechanism of covalently bonded halides.








20

There are many models proposed for molecular motion

(described by the correlation time, rc) in liquids and it is beyond the scope of this dissertation to give a detailed discussion of each. Only two fundamental ones will be briefly described. Mechanistically, the theory of rotation can be broken down into two simple models: "classical" and "jump" reorientation models.30,31 Classical reorientation (Debye-Stokes-Einstein relationship) describes the rotation of a molecule in a liquid as a solid body moving in a fluid continuum. This simple model works well for macromolecules in low molecular weight solvents but is not very realistic for molecular motion in neat liquids. Gierer and Wirtz32 proposed that the discontinuous nature of liquids can be explained by the addition of a "microviscosity" factor to the classical model to describe a local environment around each molecule in neat liquids, whereas Gordon33 proposed that the molecules are freely rotating between randomly occurring collisions. The collisions change the angular momentum, but not the orientation of the molecules. The change in the angular momentum of Gordon's classical model can be further broken down into two cases. The J-diffusion model states that the direction and magnitude of the angular momentum is completely randomized by the collision with no correlation between the momentum just before and after the collision. The M-diffusion model randomizes only the








21

direction of the angular momentum and leaves the magnitude unaffected.

The jump reorientation model looks at the liquid with

activation barriers to rotation or the migration of lattice defects or holes. Application of this model to the experimental data presents some difficulties due to the lack of information about several of the parameters needed in the analysis. These parameters include the geometry of the lattice, the energy barriers, the number of vacancies or defects, etc. A quasilattice random flight model was proposed by O'Reilly.34,35 The model assumes that the first solvation shell can be approximated by a lattice and describes large changes in angular rotation by small-steps of angular rotation. O'Reilly's model addressed some of the problems like vacancies and translational diffusion by vacancy migration, but still require several other parameters that are lacking for a complete analysis.

The quadrupolar relaxation of halide ions is

intermolecular in nature and result from the interaction with other ions or dipoles in solution. Two models have been proposed for the origin of the change in the magnitude of the field gradient at the nuclei; electrostatic and electron distortion models. Experimental discrimination between these two models is difficult due to limited literature comparison on the merits of each model. The electrostatic mode136-43 looks at the distribution of








22

charges from other ions and solvent molecules around the relaxing ion. The change in the field gradient is caused by the molecular motion of the surrounding species. Hertz36-38 and Valiev39-43 have both studied this problem using the electrostatic model with different approaches and varying degrees of completeness. The most recent work by Hertz,38 being the most elaborate for halides at infinite dilution in water, calculated I/T1 using the electrostatic model for 35C1, 81Br, and 127I to be 40, 1350, and 5650 sec-1 compared to the observed values of 42, 1050, and 5270 sec-1 respectively.

The electronic distortion model was first proposed by

Itoh and Yamagata.44 The model suggests that the relaxation is produced by the deformation of the ion's electron cloud caused by the collision of the relaxing nuclei with other species in solution. Comparison of the experimental results with electronic distortion theory is difficult since some of the important quantities (correlation time, excitation energy, field gradient, and nuclear magnetic shielding) are very difficult to estimate.

Covalently bonded halides have been used to study molecular motion through the correlation time of the molecule.45-48 Estimates of the correlation time have been obtained mainly from NMR line widths for various molecules. The theoretical models that describe the changes in the field gradient that affect quadrupolar relaxation are








23

important in helping to understand these processes, but are of limited utility since the body of experimental data is small, limiting the application of these models. Comparison of the experimental results with different theories has led to the preferred use of the extended J-diffusion classical model over others.49-51 A number of people have studied alkali halides in aqueous solution: Itoh and Yamagata,44 Hertz,36,37,52-56 Richards and co-workers,57-62 Arnold and Packer,63 and Bryant.64 The concentration dependence studies of alkali halides in aqueous solution can be summarized with the following observations. The relaxation rate increases with an increase in concentration. The relative magnitude of the change depends on the size of the halide ion. The mechanism for the relaxation rate depends upon a complex interaction involving the alkali halide concentration as well as the size of the alkali metal ion. The order of increasing effect on the Cl- and Br- relaxation is K+ < Na+ < Rb+ < Li+ < Cs+ with I-, the position of Na+ and Rb+ are reversed.

Studies involving other inorganic halides like hydrogen halides,48,57,65,66 ammonium halides,36,55 and alkaline earth halides36,57,58,67,68 have yielded little additional information. The observed effects were similar to those seen for the alkali halides. In the case of hydrogen and ammonium, similar results to those from the smaller sized alkali ions were obtained. The alkaline earth ions proved








24

to have a much stronger effect on the relaxation rate, but show the same trend in the family with size as that observed for the alkali ions.

Aqueous solutions of tetraalkylammonium halides69-75 are much more effective at quadrupolar relaxation than even those of alkali or alkaline earth halides. Figure 5 shows how the length of the alkyl group on the ammonium ion influences the relaxation rate of the halide ion. The nonpolar groups on the cation can exert a strong structurestabilizing effect on the water lattice.76 The formation of crystalline hydrates found in tetraalkylammonium halides suggests that the hydrogen bonded water molecules form large clathrates in which the hydrophobic cations are enclosed with some of the halide ions replacing the water molecules in the clathrate lattice.77,78 This stabilization effect is manifested in the slowing down of the water's rotational and translational motions as observed in the change in the quadrupolar relaxation rate of the halide.79,80

These observations imply that all nonpolar solutes can cause enhanced relaxations as shown with the tetraalkylammonium halides and that the mechanism for this enhancement is similar in all cases.81 The possible mechanisms involved in the rapid relaxation of the substituted ammonium halides are direct anion-cation interactions which results in ion pair formation or modification of the anion-solvent interaction by the








25







310'








2. 10'








10'








0 1 2 3 4 5
Nurnoer of carbon atoms in the alkyl group




Figure 5: 79Br relaxation rates (from line widths) at 30C
for 0.500M aqueous solutions of alkylammonium
bromides. The different curves correspond from the top to tetra, tri, di, and mono substituted
alkylammonium bromides. The y-intercept
corresponds to ammonium bromide. This figure was
obtained from reference 71.








26

hydrophobic cation. The observations tend to exclude direct ion-ion interactions on the grounds that the change in the relaxation rate is related to the change in the number and length of the substituted alkyl groups, the lack of a competition effect between differing halide ions, and the presence of relaxation enhancement in uncharged solutes. In addition, modelling studies of tetraalkylammonium systems using an ion-ion interaction model failed to produce reasonable results.69-71,76 With these considerations, it is proposed that the mechanism for quadrupolar relaxation in tetraalkylammonium halide systems is indirectly influenced by the hydrophobic cation.

A natural extension of the substituted alkyl ammonium halides studies is to look at micelle type systems, since many of the substituted alkyl ammonium salts can form micelles. Some of the major problems associated with studying micelle systems are the drastic changes in phase equilibria and the different micellar shapes that may accompany the various composition of the micelle system as shown in Figure 6. These problems result from the nature of these amphiphilic substances (surfactants) which consists of a hydrophilic part that is either charged or highly polar and a hydrophobic part that is neutral, nonpolar, and typically a long alkyl chains.82-84

The surfactants behaves as ordinary electrolytes at low concentrations, but as the concentration increases they








27







Hexanol





0/









20 3 0 50 60 70 80 90
Water CTAB














Figure 6: Phase diagram of a ternary system composing of
hexadecyltrimethylammonium bromide (CTAB),
hexanol, and water, reference 84. L1 denotes a
region with water rich solutions; L a region
with hexanol rich solutions; D and are lamellar
and hexagonal liquid crystalline phases,
respectively. In the figure are also
schematically indicated the structures of normal
(L1 region) and reversed (L2) micelles as well as
liquid crystalline phases.








28

first form small complexes (dimers, trimers, etc.), then form larger aggregates which are termed micelles and are of colloidal dimensions. Micelle formation of long-chain amphiphiles starts abruptly and is well defined by a given concentration, the critical micelle concentration (cmc). Concentrations that are well above the cmc often lead to a transformation of the first formed micelle, approximately spherical in shape to a very long rod shaped micelle. The shape changes continue as the concentration reaches the solubility limit for the surfactant. The possible formation of liquid crystals can occur with different structures depending on the composition of the system or the formation of reversed micelles, aggregates with the polar phase as the core and the nonpolar phase as the continuous environment.

Detailed studies of halide ion relaxation have been done with micelle, reversed micelle, and liquid crystal solutions.73,85-93 The results shown in Figure 7 are typical of micellar solutions. Theoretical modelling of the concentration dependence of the quadrupole relaxation for these systems have been fit to a two site model.82,89,94 The model assumes that the halide appears in two forms, free and attached to the micelle, the ratio between the counterions and surfactant ions in the micelles is independent of the concentration, and that the pseudo-phase separation model of micelle formation applies. This separation model treats the micelle formation as a phase








29








7.103- 1.5.10 5


S5.103 - 105


3.103 ,
5-104
10510



0 1 2 3 5 6 7 8 9 10 11 12
Number of carbon atoms in the cation
















Figure 7: 79Br relaxation rates (from line widths) at 30C
for aqueous solutions of monoalkylammonium
bromide; o, 0.100M solutions; X, 0.500M
solutions. The upper two curves are an expanded view of the lower two curves. The left vertical axis belongs to the upper two curves. The scale
on the right vertical axis belongs to the lower
two curves (reference 71).








30

separation, with the cmc as the saturation concentration. This two site model works well for a number of systems:86-88 C8H17NH3C1, C8H17N(CH3)3C1, C16H33N(CH3)3C1, C9H19NH3Br, C10H21NH3Br, C9H19N(CH3)3Br, C10H21N(CH3)3Br, C14H29N(CH3)3Br, C16H33N(CH3)3Br, and decylpyridinium bromide. Plots of the relaxation data versus the inverse of the concentration give two straight lines like that shown in Figure 8 with the intersection at the cmc for the system. This value has been found to compare well with other methods of determining the cmc.87 The model breaks down at high concentrations of the surfactant. This deviation is attributed to the transition of the micelle shape from spherical to the rod shaped88 which leads to a much larger surface area and alteration in the interactions that affect the quadrupolar relaxation.

Reversed micelle studies show similar results to those observed in the micelle studies as seen in the cetyltrimethyl ammonium bromide, hexanol, and water system.86,88,91,92 The halide relaxation rate is observed to be independent of the hexanol concentration below a critical value. As the concentration exceeds this value, the relaxation rate increases at a greatly enhanced rate as seen in Figure 9. It is believed that the halide ions resides at the core of the micelle where they are highly hydrated. The environment around the halide remains fairly constant while the hexanol concentration is below this








31













400


300


200

OTAC 100 O oAC

I I I I
0 2 4 6 8 10 12 14 16 18
-I









Figure 8: 35C1 relaxation rates (from line widths) as a
function of the inverse concentrations of
octyltrimethylammonium chloride (o) and
octylammonium chloride (.) at 280C, reference 87.








32











120
-\ -20
100

._-80 15
80- \


60 -10


40
.O"W- 5 20L I I 1 20
40 60 80 130 Weight per cent hexanol







Figure 9: Observed 81Br relaxation rates (from line widths)
divided by that at infinite dilution in water for
solutions of hexadecyltrimethylammonium bromide
(CTAB) and water in hexanol (region L of the
phase diagram in Figure 6). The weigt ratio of CTAB to water was kept constant at 1.04 and 270C.
As a comparison the viscosity (q) at 25C
relative to that of pure water (no) is shown (X),
reference 91.








33

critical value. Above this value, the increase in the relaxation rate corresponds to the disappearance of the reversed micelles and can be attributed to ion pair formation.

To be consistent with the micelle and reverse micelle

modelling studies, the liquid crystal systems also use a two site model in attempting to analyze the data.86,93 Liquid crystal systems are more complex, but can also be broken down to a two step process. The faster process corresponds to local interactions inside the liquid crystalline phase. The slower process spans the dimensions of the aggregates and may be from micellar rotation, counterion or amphiphile diffusion along the micellar surface, or intermicellar counterion exchange. Studies to separate the contributions of these two steps to the relaxation,71,86-88,91-96 all tend to show that the slower process gives only a small and mostly undetectable contribution. Different motional processes should have different energies of activation, therefore the similar activation energies shown in Table 1 for the various phases suggest that the same type of motion is responsible for the relaxation found in all phases. In support of this, a number of cases have shown that the relaxations are frequency independent and intensity consideration gives a correlation time describing the major part of the relaxation at 7c << 10-8s (2 X 107 Hz).









34

Table 1

Energy of Activation for Bromide
Ion Quadrupole Relaxation in Surfactant Systems


Sample composition percent by weight
Act. Energy C16H33N(CH3)3Br H20 C6H130H Phase kcal/mol


6.0 94.0 micellar 6.5 solution

24.0 76.0 micellar 6.5 solution

62.3 20.0 17.7 lamellar 6.5 mesophase

reversed 24.4 45.0 30.6 micellar 7.5 solution

reversed 40.0 10.0 50.0 micellar 6.8 solution

reversed 10.2 9.8 80.0 micellar 6.5 solution








35

The next logical step in the natural progression of determining what influences quadrupolar relaxation is to move from aqueous to mixed solvents and non-aqueous media. This next step allows for changes in the solvent's dipole moment, molecular size, dielectric constant, solvation number, etc. to study the effects of ion pair formation, ion solvation, complex formation, etc. Studies of alkali halides show that the relaxation is mainly determined by ion-solvent interactions where the correlation time of the solvent plays an important role. In aqueous systems, the relaxation is due to the motion of randomly oriented and distributed point dipoles.97 For methanol systems,57,58,69,98,99 the relaxation can be modelled to a tightly packed first solvation sphere with radially oriented dipoles. Modelling Br- in dimethyl sulfoxide70,100 using a distinct solvation sphere approximation gives results that are higher than the experimental ones, suggesting that the differences in the ion solvation from various solvents should be of great interest in elucidating solvation phenomena. The methanol and dimethyl sulfoxide studies also suggest that ion pair formation gives a significant contribution to relaxation, but in the dimethyl sulfoxide case this effect does not explain the trend of the cations as shown in Figure 10.









36

10 *


41
610

0NH4 Br (DMSO) 410
/4 H)4 NBr(DO*H20)
310
3NaBr (CH30t)










Na 8 r(DO*H20) 6-10 / / (C4Hg)4 NBr(DMSO)


4*10 3.10

210

0 0.1 0.5 1.0 concentration,M


Figure 10: 79Br transverse relaxation rates (from line
widths) in non-aqueous and mixed solvent systems
as a function of electrolyte concentration
(reference 100).















EXPERIMENTAL



Time Domain Reflectometry

A block diagram of the TDR setup is shown in Figure 11. The TDR setup is composed of a Tektronix 7854 mainframe oscilloscope with a waveform calculator, a 7S12 time domain module, a S-52 pulse generator, and a S6 sampling head. The sample cell is made from a 7 mm SMA male rebuild kit model 2542 from Midwest Microwave with the center post 1.5 mm in length. The TDR is connected to the sample cell through matched low loss 50 ohm impedance coaxial cables from W. L. Gore models G3S0101078.0 and G3S0101072.0 which are 78.0 and 72.0 inches long, respectively. Communication with the TDR is done through an IEEE-488 interface on the scope to a RS232 interface on an IBM PC/AT using a Black Box model 232-488 interface converter.

The power-up sequence of the equipment is very

important. The Black Box converter unit must be turned on last to eliminate communication handshake problems. Once this protocol problem occurs, the Black Box converter and the Tektronix scope must be shut down and powered up again. The Black Box converter unit is the key to this problem, the converter on power-up sends a request for service signal to 37









38






















S-52 VOLTAGE S712 S-6 1 t. PULSE GENERATOR COAXIAL SAMPLER Tr < 25 psec Tr < 30psec TEKTRONIX 7854 SAMPLE












Figure 11: Block diagram of TDR setup.








39

the scope and waits for an answer, the scope when powered up waits for a request for service signal and does nothing until it receives this request. This mismatching of communication protocol can be avoided as long as the Black Box unit is the last piece of equipment to be turned on.

The scope needs to be powered up for at least six to

eight hours to ensure thermal stability of the electronics (at least 24 hours if the system is moved or powered down for more than three or four hours). Any control changes other than calling up a cursor or using the waveform calculator function will require the scope to sit idle and equilibrate for a minimum of one hour. The system should remain stable for at least one to one and a half hour before any electronic drift can be detected after thermal equilibrium is reached. Power fluctuations can introduce random noise into the data lines between the scope and the IBM PC/AT when the system is at idle. This noise is introduced through the Black Box converter unit and can be eliminated by keeping the Black Box unit powered down until the system is ready for use. The remaining units should be left powered up to minimize the system's required stabilization time.

The theoretical limits of this TDR using the open

termination method are governed by the pulse generator in this setup. The S-52 pulse generator has a risetime of 25 psec (time for the "half-life" of raising the voltage to








40

the rated value), a pulse size of 250 mV, a pulse width of 700 nsec, and a repetition frequency of 50 kHz. This gives our TDR setup a theoretical upper and lower limit of
5 X 1010 Hz and 1 X 106 Hz from the risetime and pulse width, respectively.

The actual use of the TDR starts with the adjustments of the time-distance control. This control allows the positioning of the window to be shifted to any portion of the waveform (from the beginning just prior to the voltage pulse being emitted to the end where the pulse potential returns to ground). As one moves through the entire waveform, four transitions are seen (Figure 12). The first and second transitions are the incident and reflected steps of the voltage pulse, respectively. The third and fourth transitions are due to the voltage pulse returning to ground. The part of the waveform (reflected step) that contains the second transition through just before the third transition contains all the information about the properties of the sample. The time-distance control is set to observe only the second transition with a small amount of the baseline before the transition (typically 10% of the time window).

The time window of choice is one where the second

transition takes up approximately half of the time window as shown in Figure 13. This is easily accomplished by adjusting the time/division control until the process fills








41












2Vo

Step 2 Step 3


o Vo
0
Step 1 Step 4

0



Time






Figure 12: Complete waveform obtained from the TDR. Step 1
is the incident pulse. Step 2 is the reflected
pulse. Step 3 is the incident pulse returning to ground. Step 4 is the reflected pulse returning
to ground.








42










2Vo












Vo

0 50 100 Time





Figure 13: Process is observed in approximately half the
time window with the correct time window setting.








43

half the window. It is best to start with 50 nsec/division (500 nsec window) and work towards 1 nsec/division (10 nsec window) for new systems.

The use of time windows less than 5 nsec tends to have problems in the Fourier transform routine. Temperature instability of the various components causes timing and electronic drift problems which leads to large errors in the Fourier transform routines, imposing a practical upper limit of 3 X 109 Hz on the system. A practical lower limit of

1.5 X 107 Hz is dictated by the manner in which the scope collects data. This system is capable of collecting a maximum of 1024 points with its largest window being 500 nsec. This gives spectral data in the range of 15 to 400 X 106 Hz for the 500 nsec window. This limited range is determined by the width of the time window and the resolution of data used in the Fourier transform. Several windows are needed to cover the entire spectral range with each overlapping window spanning a frequency range of approximately 1.5 order of magnitude. A single time window covering the frequency range of 1.5 X 107 to 3 X 109 Hz can be obtained if the resolution of the collected data in this 500 nsec window is increased by at least one order of magnitude (a minimum of 10,000 data points).

The voltage/division control setting is determined by the size of the voltage pulse used. A setting of 50 mV/division is required for the 250 mV pulse outputted by








44
the S-52 pulse generator. For an empty sample cell, the reflected pulse will have its greatest amplitude. The reflected pulse for a perfect system (no loss) has an amplitude that is twice the original inputted pulse. Our TDR setup has a loss of approximately 10% through the electronics and cables in the form of heat. The amplitude of the reflected pulse also decreases when a sample is introduced into the sample cell. The decrease in amplitude is proportional to the DC conductivity of the sample.

Samples with DC conductivities greater than 0.01 mho/cm will short circuit the TDR sample cell. Conductivities of the samples can be obtained from the time domain data collected on the TDR. The lower limit of the conductivity that can be measured is 1 X 10-6 mho/cm. Conductivities of less than 1 X 10-5 mho/cm have little effect on the spectral data for the sample. Larger conductivities behave like relaxation processes and need to be corrected for in the imaginary component of the complex dielectric constant. The real component of the dielectric constant is not affected by DC conductivity.

Other problems that exist are the size of the static
dielectric constant, the ability to pack solid samples, the volatility of liquid samples, and fringing effects. Samples with static dielectric constants less than three have large errors associated in their spectral data. Solids are a problem because of the variability in packing of the sample








45
cell. The difference in the packing leads to irreproducible values of the dielectric constant, but the frequency of the various processes is not affected and can be reliably obtained. In order to pack the cell properly, the solid must be in the form of a fine powder with the particle size in the micron range. Volatile samples have to be watched carefully since heat is produced in the sample cell from the power loss. The sample must cover the center post in the sample cell because fringing effects can give some very interesting looking distorted spectra. This effect can be eliminated by burying the center post to a depth of at least half the cell diameter.

The process of collecting the spectral data is simple once the proper settings have been established for the TDR setup. All waveforms are collected using signal averaging to help reduce the random noise and drift problems. It has been determined by trial and error that 100 signal averages are reasonable for this TDR setup. Averages in excess of 100 help to reduce the random noise, but is offset by drift problems. Waveforms of 1024 points in size should only be collected for time windows greater than 50 nsec. Time windows less than 50 nsec give distortion of the spectral data when 1024 points are used. The drift problems show up in the higher resolution spectra for the shorter time windows. It has been determined that 512 points are normally adequate to describe most samples in time windows








46

of 5 nsec and larger. The use of time windows less than 5 nsec is discouraged because the drift problems are highly evident in such small time windows. The poor alignment between the reference and sample gives irreproducible distorted spectra.

A reference waveform is collected using the scope's

waveform calculator signal averaging function to establish that the TDR is stable and to provide the Fourier transform routine with a reference point. The reference waveform is collected every five minutes until the difference between the waveforms is less than 4 mV for the largest difference. Sample waveforms are collected in a similar manner using the same settings as the reference waveform. The sample needs to equilibrate, typically one to three minutes, in the sample cell after being introduced. This enables the sample to reach equilibrium under the conditions of repetitive excitation by the voltage pulse. The equilibrated sample waveform can then be stored in one of the TDR's memory. The TDR memory can hold nine waveforms of 512 points or three waveforms of 1024 points.

Liquid samples are the easiest to handle and typically take 15 to 20 minutes to collect data for seven different samples using the same TDR settings. The reference waveform is first taken then each of the samples is introduced into the sample cell and their waveforms collected. Once the reference waveform is taken, care must be used as not to








47

disrupt any of the connections between the cell and the TDR. Disruption of these connections will invalidate the reference waveform and sample data collected afterward will be meaningless. Figure 14 shows a typical set of collected raw data.

Solid samples take 30 to 40 minutes to collect data for seven samples. The sample should be powdered (best if particle size is 100 microns or less) to help eliminate the nonuniformity in the packing when it is introduced into the cell. There is a greater chance in disrupting the connections in the setup during the sample removal process especially when working with solids. It is best to take a reference waveform for each solid sample to help minimize the difference due to the disruption in the connections. Tests with removing and reconnecting the sample cell to the TDR setup shows significant shifts in the reference waveform from one set of removing and reconnecting to the next set.

The collected data are then transferred to an IBM PC/AT via a communication program listed in the Appendix. The communication program is interactive and handles everything from automated data collection to transferring the data to the computer and setting up the data for use in the Fourier transform routine. The transform routine is listed in the Appendix and requires two files; the DIF file contains the difference data between the reference and sample waveforms while the SUM file contains the summed data (Figure 15).








48










Air Reference




n-Butanol O0







Time Figure 14: Raw time domain data for an air reference and a
sample of n-butanol.









49










SUM











c-)
o


DIF



Time








Figure 15: DIF and SUM time domain spectra for n-butanol.








50

The Fourier program takes these two time-domain files and transforms them into a frequency-dependent complex dielectric constant, as shown in Figure 16. The program automatically handles all baseline corrections and data smoothing.

The DIF and SUM files are used to obtain the DC

conductivity of the sample. The ratio of the values of the tail for these two spectra after baseline correction, as shown in Figure 15, is proportional to the value of the conductivity, ao (in esu units),101 according to


c P
= (8) 4Rd QOO



where c is the speed of light (3 X 1011 mm/sec), d is the length of the center conductor of the sample cell in millimeters, P, and Q, are the difference between the tail end value and the baseline for the DIF and SUM data, respectively. The specific conductance, K is equal to ao/9 X 1011 which is the DC conductivity with units of mho/cm, a more appropriate set of units for comparison to literature. DC conductivity determined from the time-domain data is within five percent of the value obtained from a commercially available conductance meter (a YSI model 35 conductance meter with a YSI model 3403 conductivity cell). The DC conductivity is then used to calculate the frequency








51










20 18 Real 16 c14
0
c12
o
010 t8




24
2 Imaginary
0 I I
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 16: Fourier transformed n-butanol spectra.








52

dependent conductivity correction values for the imaginary component of the complex dielectric constant, as shown in Figure 16, with




corr = o



where Ecorr and e" are the conductance corrected and uncorrected imaginary components of the dielectric constant at the angular frequency w, respectively.



Nuclear Magnetic Resonance
35Cl Nuclear magnetic resonance (NMR) spectroscopy was

done on a Varian VXR300 (300 MHz) spectrometer. The NMR was tuned to the 35C1 nucleus. The solvated chloride ion from a 5 M aqueous solution of sodium chloride with a trace of D20 was used as the external reference for all 35C1 NMR spectra. The NMR was setup for the majority of the Aliquat studies using observation parameters of nucleus 35, frequency 29 MHz, spectral width 100 kHz, offset 400 Hz, acquisition time

0.005 sec, delay 0, pulse width 30 Asec, and transients 10,000, decouple parameters of nucleus 1.5, offset 584.7 Hz, mode NNN, power 3 db, modulation mode S, frequency 9.9 kHz, and pulse width 22.5 psec, processing parameters of FN 64K, line broaden 10 Hz and width 100 kHz, and the standard 13C pulse sequence. Studies with large amounts of water used the above parameters with these differences in the








53
observation parameters, acquisition time 0.15 sec, pulse width 36 psec, and transients 5000. The viscosity and linewidth of the samples required the majority of spectra to be manually phased.


Chemicals
Aliquat 336 (trioctylmethylammonium chloride) was purchased from Aldrich and used without further purification. Water with a resistivity of 15 megaohm/cm was obtained from a Barnstead NANOpure filtration setup. All other chemicals are of reagent grade and used without further treatment. All solution concentrations are given in mole fraction units.














RESULTS AND DISCUSSION


Alipliatic Alcohols


Binary System of Carbon Tetrachloride and n-Butanol

Carbon tetrachloride is a poorly coordinating, nonpolar solvent with no permanent dipole moment. This solvent does not give a dielectric spectrum in the frequency range of

2 X 107 Hz to 2 X 109 Hz. A constant complex dielectric of one is observed for the real component and zero for the imaginary component. The dielectric spectra of the binary system of CCl4 and butanol are shown in Figure 17. The critical frequency, fc', for the dielectric relaxation of the various solutions appears to remain constant at the fc normally observed for neat butanol. The possible interactions involved are CCl4/CC14, butanol/CCl4, and butanol/butanol. The former two CCl4 interactions will not influence the observed dielectric relaxation directly. The main influence of dilution in CC14 is to decrease the average size of the aggregate by shifting the equilibrium:


(C4H9OH)n -- > (C4H9OH)n-1 ..... > C4H90OH (10) toward the smaller species.

54








55







Butanol
S- 95.4 mole 7.
89.7 mole % 10 84.9 mole Z 9- 70.1 mole %
- 49.9 mole 7.
8 - 39.4 mole Z 0 .. 28.9 mole 7 o 7 Butanol in CC14

- 6

45


) 3

C 2


0 -,r
0 r ........ I
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)




Figure 17: Frequency dependent imaginary component of the
observed complex dielectric constant for
solutions of n-butanol and carbon tetrachloride.








56
The static dielectric constant of a mixture of noninteracting systems is given by:102


Es = NA sA + NBEsB (11)


Over the concentration range 0 to 100 mole percent butanol in CC14, our results show that the intensity of the static dielectric is not obeying this relationship (Figure 18). The observed behavior suggests that the average molecular weight of the aggregates is staying about the same over the concentration range 70 to 100% butanol. At lower concentrations of butanol, the deviation is that expected for an increase in the concentration of the smaller aggregates.

The frequency dependence of the real and imaginary

components of the dielectric constant is plotted versus the log frequency in Figures 19 and 20. The data can be fit to within experimental error with one average process to equations (6) and (7) using a Simplex routine program listed in the Appendix. The critical frequency is constant for the range of 70 to 100% butanol. At higher dilutions, the process becomes faster.

Neat butanol has a critical frequency of 3.4 X 108 Hz with the peak spanning the range of 6 X 107 to 2 X 109 Hz. This frequency range represents an overlap of the dynamic process on a large number of aggregates in a three-








57









20

18 216
c(14 012

-10 T 8 S6


2 0
0 10 20 30 40 50 60 70 80 90 100 Mole 7. n-Butanol in CCI4






Figure 18: Concentration dependence of the observed static
dielectric constant for solutions of n-butanol
and carbon tetrachloride. Equation (11) is
represented by the line for this system.








58









20
C :* Butanol .1 8 U 95.4 mole Z C 89.7 mole Z 01 6 A 84.9 mole Z o 0 70.1 mole Z S14 49.9 mole % 12 0 39.4 mole Z ,1 A 28.9 mole % 10 O -1 0Theoretical o Butanol in CC14
8
0
S6

0 2
2

7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 19: Theoretical fit of the observed real component
spectra for solutions of n-butanol and carbon
tetrachloride.








59






Butanol
0 95.4 mole %
89.7 mole Z A 84.9 mole % 10 0 70.1 mole Z l 49.9 mole Z
9
9 39.4 mole % 8 _A 28.9 mole % o- Theoretical 'z 7 Butanol in CCl4
C
LL_ 6

o 5

-


2 El D
0 E"


7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 20: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
carbon tetrachloride.









60

dimensional dynamic network. The critical frequency obtained is a complex average of the frequencies of all the individual aggregates exchanging with each other. A summary of the results of the fit of the complex components of the frequency dependent dielectric constant is given in Table 2. Both the average dielectric constant and analysis of the frequency dependence of the complex dielectric constant indicate that this distribution does not change appreciably over the concentration range of 70 to 100% n-butanol in CC14. In more dilute solutions, dissociation to produce smaller aggregates results. The rate of butanol relaxation in the smaller cluster is faster and the dipole moment change is smaller. The latter effect leads to a nonlinearity in the intensity of the entire complex dielectric constant as shown for the static component in Figure 18.



Binary System of n-Propanol and n-Hexanol

This system was selected for study in order to

illustrate the influence that changes in the average molecular weight of the mixed alcohol system have on the frequency of the dielectric relaxation. The reported static dielectric constants, the values obtained by us and the observed critical frequencies for relaxation are summarized in Table 3 for a variety of alcohols. The critical frequency describes the rate at which the alcohol "tumbles" in solution in the process of making and breaking hydrogen









61

Table 2

Butanol in Carbon Tetrachloride



% Butanol is 0 r x 10-6 Hz

100.0 18.6 2.2 340

95.4 17.6 2.4 344 89.7 16.8 2.7 335 84.9 15.8 2.7 335 70.1 12.6 2.8 340 49.9 7.2 2.5 414 39.4 4.8 2.1 504 28.9 3.6 2.5 698








62

Table 3

Primary Alcohols



Static Dielectric Constant

Alcohol um Lit. x 10-6 Hz Methanol* 33.2 32.7 --Ethanol* 25.5 24.3 980 1-Propanol 21.8 20.1 490 1-Butanol 18.6 17.6 340 1-Hexanol 11.3 13.3 260 1-Octanol* 9.5 9.6 130 l-Decanol* 7.6 7.7 66 1-Dodecanol* 5.7 5.4 56




*Reference 103.








63

bonds. With comparable hydrogen bond strengths expected for the alcohols listed (e.g. the -AH of hydrogen bonding of ethanol and octanol to pyridine in CC14 are the same within the 0.2 kcal mole-1 experimental errorl6,17), the frequency differences are seen to be related to the average composition of the solution.

In propanol-hexanol mixtures, the major interactions involved are propanol/propanol, propanol/hexanol, hexanol/hexanol. The frequency dependence of the imaginary component (Figure 21) shows the change in the critical frequency and the intensity of solutions for various mole fractions of n-hexanol in n-propanol. The static dielectric constant obeys Equation (11). The frequency dependence of the real and complex dielectric constants obey Equations (6) and (7) using two relaxation processes whose frequencies are unchanged over the entire concentration range. When this is the case, the intensity and critical frequency are mole fraction averages of the pure components:



fc = xAfcA + xBfcB (12)


The critical frequencies for the neat alcohols and the various alcoholic mixtures are summarized in Table 4. These results indicate that the clusters are composed of a mixture of alcohols and the rate of rearrangement of propanol on a mixed cluster is the same as the rate on a propanol cluster








64









10 Proponol 31 mole%
9 - 55 mole Z
80 mole % c 8 ..... Hexanol
0 _,

6

o 5


3, 4

2


0
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 21: Frequency dependent imaginary component of the
observed complex dielectric constant for
solutions of n-propanol and n-hexanol.









65

Table 4

n-Hexanol and n-Propanol



Hexanol s ~r x 10-6 Hz

0 21.8 2.2 493 31 18.5 2.2 431 55 15.8 2.2 345 80 13.8 2.2 315 100 11.3 1.8 263








66

and that of hexanol on the mixed and pure clusters is the same. This is consistent with the hydrogen bond strengths being similar and the dynamic process being dominated by the molecular size of the moving group with the average size of the aggregates being comparable to the average size in the neat liquids.


Binary System of n-Butanol and Pyridine

This system provides the opportunity to examine the

perturbation made on butanol aggregation by the addition of strong donor molecules. Pyridine has a relaxation frequency that is faster than can be observed in our apparatus. Thus, the main interactions that will influence the spectrum are butanol/pyridine and butanol/butanol.

The dielectric spectra of various solutions of butanol and pyridine are shown in Figures 22 and 23. The critical frequency of these solutions shifts to higher frequencies as the mole fraction of the pyridine is increased. The data are fitted to Equations (6) and (7) with a single 7 value that increases with pyridine concentration, summarized in Table 5. The greater influence of pyridine compared to CCl4 is shown in Figure 24. The single peak indicates that the distribution of processes occurring is shifted toward faster rates of relaxation with a decrease in the intensity of the response. The direction and non-linear behavior of the static dielectric constant and the critical frequency








67










20

,18
C
016 ,

14

-12
0 5.0 mole 10
o N 9.9 mole Z
8 A 15.1 mole 7 o 30.4 mole 7. 6 49.5 mole 7 o O Pyridine S4 Theoretical

S2 Pyridine in Butanol
o

0I
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 22: Theoretical fit of the observed real component
spectra for solutions of n-butanol and pyridine.








68





5.0 mole Z 0 9.9 mole %
A 15.1 mole Z
30.4 mole 7
10 : I 49.5 mole 7
O Pyridine
9 Theoretical
c 8 Pyridine in Butonol S7

G_ 6

_(I
o 5

4 e


S2
0
1 0

7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 23: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
pyridine.









69

Table 5

Pyridine and Butanol Systems



BuOH/py
.C14 Y % BuOH ratio Is go r x 10-6 Hz

--- 5.0 95.0 20 18.2 2.6 407 58.0 1.9 40.1 20 5.0 1.4 524



--- 9.9 90.9 10 17.5 3.6 546 55.8 4.0 40.2 10 5.2 1.2 630



--- 15.1 84.9 6 17.3 3.4 716 54.2 6.8 39.0 6 6.4 1.8 778



--- 30.4 69.6 2 16.5 4.2 1364 43.3 16.9 39.8 2 8.3 2.4 1245



--- 49.5 50.5 1 15.7 4.7 2624 20.6 39.8 39.6 1 11.9 3.5 2845








70









3000
2 IPyridine 2700 A CC14 z 2400
2100 x 1 800 c 1500 r 1200

- 900 S600 300

0 10 20 30 40 50 60 70 80 90 100 Mole 7. Solute in n-Butanol






Figure 24: Comparison of the critical frequencies obtained
for the pyridine and carbon tetrachloride
systems.








71

suggest a decrease in aggregate size as pyridine is added to butanol. The initial increments of added pyridine hydrogen bond to terminal OH groups of butanol aggregates with only minor changes in the dielectric spectrum. As the mole fraction of pyridine increases, clusters must be broken in order to provide hydrogen coordination sites for pyridine causing the average fc to shift to a higher frequency. One can view the three dimensional nature of the alcohol adducts as arising from the fact that two oxygen lone pairs of a given molecule function as coordination positions for protons of other molecules, while its hydrogen functions as an acid site to another alcohol. The system is one hydrogen short (as a consequence of the R group) of the tetrahedral nature of a water molecule in a water structure and the aggregate is not as stable. When a base coordinates to the acid site of an alcohol molecule, one additional site for chain growth is removed and the tendency to form a 3-D structure is decreased.


Ternary System of Carbon Tetrachloride. n-Butanol. and
Pyridine
The relaxation processes are investigated for solutions of -40% butanol in CCl4 to which pyridine is added. A similar trend in the frequency with increased concentration is observed as shown in Table 5. The 50% composition which would correspond to the 1:1 adduct shows similar behavior in neat butanol and in CCl4. Taking the dilution factor into








72

consideration, the static dielectric constant gives a comparable value for the adduct in CC14 and that made in neat butanol. No new relaxation processes are observed in CC14 and the behavior is similar to that for neat butanol. The variation in cluster size when butanol is diluted in CCl4 is small compared to pyridine addition as seen in Figure 24.



Surfactant Systems


Binary System of n-Butanol and Aliquat 336

The conductivity of the Aliquat solutions (Figure 25) increase as the concentration of the Aliquat is increased. The maximum conductivity of this system is found at 10.0% Aliquat followed by a steady decrease at the higher concentrations of Aliquat. The conductivity levels off at about 50.0% Aliquat to the value observed for neat Aliquat. The increase in the conductivity at low Aliquat concentrations is that expected for a simple salt being dissolved. The conductivity of dissolved salts increase with concentration and then level off as the solubility limit is reached. The deviation from this behavior suggest that the Aliquat is ion-paired with aggregation taking place at the higher concentrations. This effect is even more dramatic in solvents like methanol and water, where the conductivity of the dilute Aliquat solution is 25 times








73










80 70

S60
E
50
o

>40

t.1:3

8c 20 010

0
0 10 20 30 40 50 60 70 80 90 100 Mole 7Z Aliquat 336 in n-Butanol






Figure 25: Concentration dependence of the observed DC
conductivity for solutions of Aliquat 336 in
n-Butanol.








74

larger than in butanol. Sodium chloride in these solvents has a five fold difference in solution conductivity. The conductivity of aqueous sodium chloride solutions is attributed to the migration of ions that are formed in a 1:1 ionic system. The observed lower conductivity of sodium chloride in butanol suggests that the sodium chloride is ion-paired. The difference in the solution conductivity of the various solvents indicates that Aliquat becomes highly ion-paired in solvents like butanol with the solution conductivity arising from Aliquat's ability to migrate in solution. At low concentrations, the number of Aliquat molecules determines the solution conductivity. At approximately 10% Aliquat, aggregation begins to occur, lowering Aliquat's mobility by increasing the aggregate size and decreasing the total number of mobile aggregates found in solution.

The 35C1 NMR line width, full width at half height, of Aliquat/butanol solutions are shown in Figure 26. The line width remains constant for solutions with less than 5.0% Aliquat. At higher concentrations of Aliquat, the line width increases with increasing concentration. This type of behavior is indicative of systems that form micelles. The break point in the 35C1 NMR line width is the critical micelle concentration, cmc,87 where a transition in structure is made from simple monomeric and dimeric ionpairs to higher order aggregates. The cmc for Aliquat in








75









8000 7000 ,6000
N
c5000 E 4000

3000 z 2000

1000

0
0 20 40 60 80 100 120 140 160 180 200 Mole Ratio of n-Butanol to Aliquat 336






Figure 26: 35C1 NMR line widths obtained for solutions of
Aliquat 336 in n-Butanol.








76

butanol is about 10% which corresponds well with the conductivity studies.

The dielectric spectra for the Aliquat/butanol system shown in Figures 27 and 28 can be fit to equations (6) and

(7) with a single process (Table 6). The intensity of the static dielectric constant shows a similar trend to that observed in the 35CI1 NMR studies (Figure 29) with the cmc at about 15% Aliquat. The spectra show that virtually all the processes in our time window are nonexistent when the concentration of the Aliquat exceed 15%. The critical frequency remains fairly constant over the concentration range of 0 to 15% Aliquat. Lindman et al.94 has proposed that the solvent molecules exists in two states: bulk solvent molecules and micelle incorporated solvent molecules. These results support the proposal that the Aliquat is coordinating to butanol and removing it out of the bulk solvent leading to a decrease in the intensity of the static dielectric constant. The presence of the Aliquat does not influence the bulk solvent, thus the aggregate size distribution is similar to that observed in neat butanol leading to a constant value for the critical frequency over the 0 to 15% Aliquat concentration range.

Butanol has three possible coordination sites: two lone pairs on the oxygen and the hydrogen on the OH group. Pyridine coordinates through the OH hydrogen leaving the two lone pair sites available, limiting butanol's ability to








77







S 1.0 mole 7 0 5.0 mole Z 20 A 7.5 mole 7. c 10.0 mole ,18 O 15.0moe% c 3015.0 mole % 1 6 5 30.0 mole 7.

0
7)12
,12 Aliquat in n-Butanol

0
8
0
C: 6 AAAA AA

4
o



0
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 27: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336 and
n-butanol.








78





1.0 mole 7.
5.0 mole 7. A 7.5 mole 7.
10.0 mole 7. O 15.0 mole % 10 ] 30.0 mole 7.
A 50.0 mole % <> Aliquat 336 c 8 Theoretical o Aliquat in n-Butanol a 7
C
L 6

o 5-a

U U



1 El-El E] El E [E

0
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 28: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336
and n-butanol.









79

Table 6

Aliquat 336 in n-Butanol



% Aliquat fs fm 7 X 10-6 Hz

0.5 19.4 3.8 330 1.0 20.0 5.1 313 2.5 19.8 6.1 284 5.0 16.8 6.4 287 7.5 14.2 6.5 312 10.0 12.8 6.9 350 15.0 7.9 3.5 365 20.0 7.8 4.3 --30.0 7.0 5.1 --50.0 6.4 4.8 --100 3.0 3.0 ---








80










20

18

-16 0O
514
0
012







2 0
-4-,





0 I
0 10 20 30 40 50 60 70 80 90 100 Mole 7. Aliquot 336 in n-Butanol






Figure 29: Concentration dependence of the observed static
dielectric constant for solutions of Aliquat 336
and n-butanol.








81

form large three-dimensional dynamic network type structures normally found in neat butanol. The average size of the butanol cluster decreases with pyridine concentration. This is manifested in the change of the observed critical frequency; increased critical frequency with increased concentration of the pyridine. In comparison, Aliquat and butanol show no change in the observed critical frequency suggesting that the aggregate size for butanol remains fairly constant. We propose that Aliquat is extracting butanol from the bulk phase without modifying the properties of the remaining bulk butanol phase. This literately removes the entire butanol molecule out of the bulk solvent and has no influence on the aggregation of the bulk butanol. The model can be simplistically described as consisting of two separate non-interacting microscopic phases. The butanol in the Aliquat phase has its relaxation modified, so it is no longer observed in our time window; i.e., the critical frequency is either decreased or increased.


Ternary System of Carbon Tetrachloride. n-Butanol, and
Aliquat 336
The relaxation processes observed in the binary system of Aliquat and butanol are investigated in the ternary system formed by the addition of CC14. Carbon tetrachloride, a nonpolar, poorly coordinating solvent can bring about some interesting modifications in the butanolAliquat interactions. It will dilute the system and lower








82

the intensity of the butanol/butanol interactions enabling us to detect other processes. Furthermore, one can compare the competition between CCl4 and butanol for the hydrophobic region of Aliquat. The dielectric spectra for various solutions of approximately 40% butanol in CCl4 are shown in Figures 30 and 31. The spectral data can be fit to a single process for mole ratio greater than 100/1 butanol to Aliquat. This single process is that normally observed for a binary system of butanol and CC14, summarized in Table 7. The aggregate size of the diluted butanol is smaller than that normally found in neat butanol; correspondingly, a larger value is observed for the critical frequency. Two processes are required to fit the observed spectra for mole ratios ranging from 13/1 to 100/1 (Table 7) with the fast process' critical frequency remaining fairly constant. The intensity of the slower process increases with increasing Aliquat with the critical frequency remaining constant. The spectral data shows that the tail end of the slower process is just appearing inside the lower frequency range of our time window, the values obtained for this process are the upper limit for the critical frequency and the lower limit for the static dielectric constant. We can only estimate this slower process from the perturbation made on the butanol spectrum. When the butanol relaxation disappears, we lose our probe for estimating the slower process's critical frequency and static dielectric constant. At high








83








No Aliquat
7 1,30/1
A7.5 80/1 D 40/1 O 20/1 c ] 13/1 0 A 5.7/1 o. Theoretical
SButanol/Aliquat Ratio
2 4.5

S4

-0 3.0
0
C
0
S1.5
O
CL
(0

0.0
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 30: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and carbon tetrachloride.








84






No Aliquat
130/1 A 80/1 3.0 40/1 o 20/1
[ 13/1
2.5 5.7/1
2.5 Theoretical
2.0 E Butanol/Aliquat Ratio cc2.0 El


o 1.5





0.5
-a




0.0
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 31: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and carbon tetrachloride.









85

Table 7

Ternary System of
Aliquat 336, n-Butanol, and Carbon Tetrachloride



% Composition BuOH/Aliq X 10-6 Hz Aliq/BuOH/CCl4 ratio es 1 1 12

0.0/40.0/60.0 --- 4.4 --- 1.4 --- 409

0.1/40.1/59.8 400 4.6 --- 1.3 --- 410

0.3/40.2/59.5 130 4.6 --- 1.3 --- 382

0.5/40.0/59.5 80 5.8 4.0 1.3 71 488 1.0/40.4/58.6 40 6.5 4.1 1.5 77 459 2.0/39.5/58.6 20 7.2 4.0 1.6 75 451 3.1/39.9/57.0 13 8.0 4.1 1.9 62 459 4.0/39.8/56.2 10 --- --- 2.2 --- --7.1/40.2/52.7 6 --- --- 2.3 --- --16.9/40.3/42.8 2 --- --- 2.4 --- --39.7/40.5/19.8 1 --- --- 2.3 --- ...








86
concentrations of Aliquat, mole ratios less than 10/1, we can only observe the tail end of this slow process in our time window. The spectra show only a sloping baseline with no discernible features.

The intensity and critical frequency of the fast process are constant over the butanol/Aliquat mole ratio range of 13/1 to no Aliquat. In neat butanol, Aliquat can extract butanol molecules out of the bulk phase without influencing the properties of the bulk phase. A constant critical frequency and decreasing intensity of the butanol relaxation occur with increasing Aliquat concentration. The observed trends of this ternary system suggest that the concentration and aggregate size of the butanol species in CC14 are not influenced by the addition of Aliquat. The constant intensity of the butanol relaxation results from the CC14 interfering with the extraction of butanol by Aliquat. This implies that the butanol is extracted into the hydrophobic region of Aliquat in neat butanol solutions. Since CCl4 is normally preferred over butanol in hydrophobic interactions, the butanol in this ternary system is left in the bulk and is unaffected by the addition of Aliquat. The presence of the slow process suggests that butanol is coordinating to the hydrophilic region of Aliquat at mole ratios of butanol to Aliquat less than 100/1. The intensity of the slow process increases with increasing Aliquat concentration indicating a large change in the dipole moment. The simple








87

addition of butanol to Aliquat should produce a species that has a larger dipole moment. The increasing intensity of the slow process corresponds to this increase in dipole moment. At present, no further conclusions can be drawn on this slower process.



Binary System of n-Butanol and Water

Mixed solvent systems have many uses, their applications range from solubility enhancement, product or impurity extraction, to reactions occurring at the interface between two immiscible solvents. The system of butanol and water is studied in order to obtain a fundamental understanding of the processes found in a mixed solvent system. All solutions less than 40% water are homogeneous. A brief period of cloudiness was observed during the preparation of the 40% water solution. The 50% water solution remains cloudy for several hours after being agitated. Solutions in excess of 50% water separate into a distinct two phase system. The dielectric spectra of these various solutions of butanol and water are shown in Figures 32 and 33. The intensity of the static dielectric constant and the critical frequency increase with increasing water concentration. The butanol phase of the solutions with greater than 50% water show no additional changes in the dielectric spectra. The spectra can be fitted to a single process, summarized in Table 8. The observed results at low water concentration








88






10.0 mole .
25.1 mole 7. A 37.7 mole 7. 35 50.6 mole 7 .35 V 60.1 mole % S~- Theoretical ~ 30 V V V H20 in Butonol




o
0


Qi)
e320
V5

0




rc,


7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 32: Theoretical fit of the observed real component
spectra for solutions of n-butanol and water.








89







10.0 mole 7.
W 25.1 mole 7.
10 r 37.7 mole % S50.6 mole% V
V 60.1 mole 7%
S8 Theoretical 0 8 H20 in Butonol
7
G6

o 5


3a



1

0
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)






Figure 33: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
water.








90

Table 8

Water in n-Butanol


% Water s A T X 10-6 Hz

10.0 18.3 2.2 423 25.1 19.1 3.1 669 37.7 20.4 4.1" 912 50.6 23.0 5.3* 1271 60.1 30.6 10.4* 1478






High values of e., indicate that a faster process exist outside of our time window. This value of E, is not the value normally observed for a single process system.




Full Text
iii2SL?.^or,da
3 25 o eS1!"11
162 08554 8708


47
disrupt any of the connections between the cell and the TDR.
Disruption of these connections will invalidate the
reference waveform and sample data collected afterward will
be meaningless. Figure 14 shows a typical set of collected
raw data.
Solid samples take 30 to 40 minutes to collect data for
seven samples. The sample should be powdered (best if
particle size is 100 microns or less) to help eliminate the
nonuniformity in the packing when it is introduced into the
cell. There is a greater chance in disrupting the
connections in the setup during the sample removal process
especially when working with solids. It is best to take a
reference waveform for each solid sample to help minimize
the difference due to the disruption in the connections.
Tests with removing and reconnecting the sample cell to the
TDR setup shows significant shifts in the reference waveform
from one set of removing and reconnecting to the next set.
The collected data are then transferred to an IBM PC/AT
via a communication program listed in the Appendix. The
communication program is interactive and handles everything
from automated data collection to transferring the data to
the computer and setting up the data for use in the Fourier
transform routine. The transform routine is listed in the
Appendix and requires two files; the DIF file contains the
difference data between the reference and sample waveforms
while the SUM file contains the summed data (Figure 15).


132
RESTORE
CLS
DIM D(13), RI(14) S(13, 14), TT(13), E(13)
DIM SUOLD(13), DCR(250), DCI(250), FREQ(250)
DIM AR(6, 250), AI (6, 250)
DEF FNAN$
1 AZ$ = UCASE$(INKEY$)
IF AZ$ = "" GOTO 1
FNAN$ = AZ$
END DEF
DEF FNFUNK
FUNK = 0!
FOR ISS = 1 TO NH
FUNCTR = E(2 NPROC + 1)
FUNCTI = 0!
FOR JS = 1 TO NPROC
WT = (10 A (FREQ(ISS))) / E(JS)
DCAMP = E(NPROC + JS) E(NPROC + JS + 1)
FUNCTR = FUNCTR + DCAMP / (1 + WT A 2)
FUNCTI = FUNCTI + DCAMP WT / (1 + WT A 2)
NEXT JS
FUNK = FUNK+((DCR(ISS)-FUNCTR)A2)+((DCI(ISS)-FUNCTI)A2)
NEXT ISS
FNFUNK = SQR(FUNK / (2 NH 1))
END DEF
EP = .1
INPUT "Name of input DATA FILE is"; INPT$
30 INPUT "Number of processes to fit DATA is"; NPROC
IF NPROC < 1 THEN NPROC = 1
IF NPROC > 6 THEN NPROC = 6
INPUT "Static Dielectric Constant is"; E(NPROC+l),D(NPROC+l)
IF E(NPROC + 1) < 1 THEN E(NPROC + 1) = 10
IF E(NPROC + 1) > 100 THEN E(NPROC + 1) = 100
HFREQ = 2 NPROC + 1
INPUT "High Freq. Dielectric Const, is"; E(HFREQ),D(HFREQ)
IF E(2 NPROC + 1) < 1 THEN E(2 NPROC + 1) = 1
IF E(2 NPROC + 1) > E(NPROC + 1) THEN E(2 NPROC + 1) = 1
FOR I = 1 TO NPROC
PRINT USING "Rate Process ## has a FREQ, of (MHz) "; I;
INPUT E(I), D(I)
E(I) = E(I) 1000000!
NEXT I
INPUT "Max number of LOOPS (DEFAULT is 250)"; KX
IF KX < 250 THEN KX = 250
IF KX > 5000 THEN KX = 5000
OPEN INPT$ FOR INPUT AS #1
NH = 0
DO UNTIL EOF(1)
NH = NH + 1
INPUT #1, FREQ(NH), DCR(NH), DCI(NH)
LOOP
CLOSE #1


116
ELSE
IF 2 <> INSTR(PATHH$, AND 1 O INSTR(PATHH$, "\
PATHH$ = "\" + PATHH$
END IF
IF "\" = MID$(PATHH$, PLEN, 1) THEN
PATHH$ = MID$(PATHH$, 1, PLEN 1)
END IF
END IF
LOCATE 9, 26
PRINT BLK$
LOCATE 9, 26
PRINT PATHH$
LOCATE 11, 4
PRINT "Root Name to save acquired files to?"
150 LOCATE 11, 41
PRINT "
LOCATE 11, 41
LL$ = FNINP$
IF LEN(LL$) > 5 OR SPACE$(LEN(LL$)) = LL$ GOTO 150
IF LEN(LL$) < 1 GOTO 150
ROOT$ = LL$
160 LOCATE 13, 4
PRINT "Time interval: HOURS ; MINS. ; SECS.
162 LOCATE 13, 27
PRINT "
LOCATE 13, 27
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 162
HRS = VAL(LL$)
LOCATE 13, 27
PRINT USING HRS
164 LOCATE 13, 40
PRINT "
LOCATE 13, 40
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 164
MINS = VAL(LL$)
LOCATE 13, 40
PRINT USING MINS
166 LOCATE 13, 53
PRINT "
LOCATE 13, 53
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 166
SECS = VAL(LL$)
LOCATE 13, 53
PRINT USING SECS
TINTERVAL = 3600 HRS + 60 MINS + SECS
IF TINTERVAL < 180 THEN
LOCATE 15, 10
PRINT "Time interval is too short 3 minute minimumI"
GOTO 160
) THEN
II


87
addition of butanol to Aliquat should produce a species that
has a larger dipole moment. The increasing intensity of the
slow process corresponds to this increase in dipole moment.
At present, no further conclusions can be drawn on this
slower process.
Binary System of n-gutanoj and Water
Mixed solvent systems have many uses, their applications
range from solubility enhancement, product or impurity
extraction, to reactions occurring at the interface between
two immiscible solvents. The system of butanol and water is
studied in order to obtain a fundamental understanding of
the processes found in a mixed solvent system. All
solutions less than 40% water are homogeneous. A brief
period of cloudiness was observed during the preparation of
the 40% water solution. The 50% water solution remains
cloudy for several hours after being agitated. Solutions in
excess of 50% water separate into a distinct two phase
system. The dielectric spectra of these various solutions
of butanol and water are shown in Figures 32 and 33. The
intensity of the static dielectric constant and the critical
frequency increase with increasing water concentration. The
butanol phase of the solutions with greater than 50% water
show no additional changes in the dielectric spectra. The
spectra can be fitted to a single process, summarized in
Table 8. The observed results at low water concentration


128
for( i = 2; i < ni; i++) {
sum = x[i + 2] x3;
sum2 = x[i + 1] x2;
x[i] = factorl sum factor2 sum2;
x3 = x2;
x2 = xl;
xl = x[i + 1];
}
x[n 2] = x[n 1] x[n 2];
x[n 1] = 0.0;
for(i = 0; i < k; i++)
x[i] = 0.0;
}
y* ******************************************************** *y
float *zero_fill(n,x)
int n;
float *x;
{
int i,j,n2;
float *xnew,*xhold,*xnhold, y;
void apodize();
xhold = x;
n2 = n 2;
xnew = (float *)malloc(n2 sizeof(y));
xnhold = xnew;
for( i = 0; i < n; i++) {
/* fill the new pointer with the old */
*xnew = *x; /* old points */
xnew++;
x++;
}
free(xhold); /* frees the earlier spectrum block */
for(i = 0; i < n; i++) {
*xnew = 0.0;
xnew++;
}
xnew = xnhold;
apodize(n,xnew);
n = n2;
return(xnhold);
} /* end of zero fill routine */
/* ******************************************************** *y
void apodize(n,x)
int n; /* n is the number of experimental points */


18
cluster. The rotation gives rise to the mechanism for
dielectric relaxation. The relaxation times increase
regularly with increasing chain length. The activation
energy for this process range from 5 to 8 kcal mole-1
increasing in a regular fashion with chain length. This is
of the order of magnitude expected for breaking a hydrogen
bond and rules out rotational mechanisms that require the
breaking of two hydrogen bonds. Accordingly, the molecular
motion involves the terminal groups of the three dimensional
structures. Since the hydrogen bond dissociation energies
are not expected to increase with increasing length of the
alkyl group, the size of the group involved in the molecular
rotation is proposed to contribute to the observed
activation enthalpy and entropy. In the neat alcohol, one
expects a distribution of cluster sizes and hence a
distribution of relaxation times. Since this is not
observed, the energetics of the processes described must not
differ enough with cluster size to be resolved. Failure to
observe a distribution of relaxations is taken as evidence
to rule out the reorientation of the whole cluster as the
relaxation mechanism.
The other two relaxations correspond to rotation of
monomeric molecules (1.7 to 5 X 10-11 sec) and to rotation
of the OH group around the C-0 bond (1.7 to 4 X 10-12 sec).
The time scale for these two relaxations are beyond the


12

£
Figure 4:
Plot of the imaginary versus the real component
of the complex dielectric constant, Cole-Cole
plot.


109
XYZ = FNWAIT(2)
PRINT #1, "RQSOFF"
XYZ = FNWAIT(1)
CLOSE
LOCATE 9, 3: PRINT BLK$
LOCATE 9, 3: PRINT COM$
RETURN
DIR:
CLS
LOCATE 8, 25
PRINT "Please specify directory?"
LOCATE 10, 25
PRINT "Default is current directory"
LOCATE 14, 25
LDR$ = FNINP$
CLS
FILES LDR$
LOCATE 23, 30
PRINT "Any key to continue"
ANY$ = FNAN$
RETURN
HELP:
CLS
LOCATE 2, 2
PRINT "DIR Listing of files in a directory"
LOCATE 4, 2
PRINT "SERIES Routinue to retrieve a series of files"
LOCATE 5, 2
PRINT for the FFT program."
LOCATE 7, 2
PRINT "TIMED Routinue to automate data acquisition over"
LOCATE 8, 2
PRINT a long time period at a fixed time interval."
LOCATE 10, 2
PRINT "HELP This listing"
LOCATE 12, 2
PRINT "EXIT or QUIT Terminate this program"
LOCATE 23, 30
PRINT "Any key to continue"
ANY$ = FNAN$
RETURN
MAINSCREEN:
CLS


123
puts("transforming dif spectrum \n");
/* puts result in fr_dif */
slow_ft(npd,nf,dif_spec,frequency,dtd,fr_dif);
if(RAW_OUT == 1)
disk_out("a:dif_puls.dat",nf,frequency,fr_dif);
free(dif_spec); /* deallocate time domain block now */
renorm(nf,fr_dif,frequency);
/* as the d(dif)/dt, it must be */
/* corrected back to true FT by */
/* the derivative formula */
puts("transforming d(sum)/dt ");
slow_ft(nps,nf,sum_spec,frequency,dts,fr_sum);
if(RAW_OUT == 1)
disk_out("a rpulse.dat",nf,frequency,fr_sum);
free(sum_spec); /* deallocate block */
puts("taking ratio of dif to sum");
ratio(nf,fr_dif,fr_sum,depth);
diel_spec = fr_dif; /* rename the block */
puts("creating complex impedence function");
trans_to_diel(nf, depth, frequency, diel_spec,diel_spec);
while ((outfile = fopen(argv[3],"w")) == NULL) {
puts("error in opening output file");
puts("input file name ");
scanf("%s",argv[3]);
)
fprintf(outfile,"%d\n",nf);
for( i = 0; i < nf; i++) {
fprintf(outfile,"%f %f %f\n",*frequency,
-diel_spec->real,diel_spec->imag);
frequency++;
diel_spec++;
}
fclose(outfile);
exit(0);
}
void output(n,w,x)


4
12*
Figure 1: Dielectric material filled parallel plate
capacitor experiment.
a) Random dipole motion with no external field.
b) Alignment of dipoles to an external field.


42
Figure 13: Process is observed in approximately half the
time window with the correct time window setting.


76
butanol is about 10% which corresponds well with the
conductivity studies.
The dielectric spectra for the Aliquat/butanol system
shown in Figures 27 and 28 can be fit to equations (6) and
(7) with a single process (Table 6). The intensity of the
static dielectric constant shows a similar trend to that
observed in the 35C1 NMR studies (Figure 29) with the cmc at
about 15% Aliquat. The spectra show that virtually all the
processes in our time window are nonexistent when the
concentration of the Aliquat exceed 15%. The critical
frequency remains fairly constant over the concentration
range of 0 to 15% Aliquat. Lindman et al.94 has proposed
that the solvent molecules exists in two states: bulk
solvent molecules and micelle incorporated solvent
molecules. These results support the proposal that the
Aliquat is coordinating to butanol and removing it out of
the bulk solvent leading to a decrease in the intensity of
the static dielectric constant. The presence of the Aliquat
does not influence the bulk solvent, thus the aggregate size
distribution is similar to that observed in neat butanol
leading to a constant value for the critical frequency over
the 0 to 15% Aliquat concentration range.
Butanol has three possible coordination sites: two lone
pairs on the oxygen and the hydrogen on the OH group.
Pyridine coordinates through the OH hydrogen leaving the two
lone pair sites available, limiting butanol's ability to


85
Table 7
Ternary System of
Aliquat 336, n-Butanol, and Carbon Tetrachloride
% Composition
Alia/BuOH/CCl4
BuOH/Aliq
ratio
S
1
X 10"6
^1
HZ
2
0.0/40.0/60.0

4.4

1.4

409
0.1/40.1/59.8
400
4.6

1.3

410
0.3/40.2/59.5
130
4.6

1.3

382
0.5/40.0/59.5
80
5.8
4.0
1.3
71
488
1.0/40.4/58.6
40
6.5
4.1
1.5
77
459
2.0/39.5/58.6
20
7.2
4.0
1.6
75
451
3.1/39.9/57.0
13
8.0
4.1
1.9
62
459
4.0/39.8/56.2
10


2.2


7.1/40.2/52.7
6


2.3


16.9/40.3/42.8
2


2.4


39.7/40.5/19.8
1


2.3




105
the hydrophilic region and leaves the butanol alone in the
hydrophobic region.
These studies have shown some of the limitations of our
current TDR setup. The most cost effective modification is
to change the smoothing and baseline routines in the Fourier
analysis. This should increase the sensitivity of the
instrumentation and allow systems with low static dielectric
constants like polymer solutions to be studied. The next
most important change is to extend the frequency range of
the instrument. This is a high cost type modification and
involves the acquisition of real time modules for the
Tektronix oscilloscope. In addition to these modules, a new
delay line is required. A low loss coaxial cable is
essential since the cable length needs to be in the 1000
feet range. Signal loss through such a length would be
tremendous, requiring extreme care in the selection of the
cable. With these enhancements, the studies involving
Aliquat, butanol, and water should be repeated. The
combination of a lower detection limit and wider frequency
range can enhance the fundamental understanding of the
interactions of butanol in the hydrophobic region of
Aliquat. Extension of these studies to longer alipliatic
alcohols and nonpolar solvents like hexane and cyclohexane
can be beneficial in the understanding of the fundamental
chemistry of micellar systems.


94
7.5 7.7 7.9 8.1
8.3 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.3 9.5
Figure 35: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and water.


131
Program DEBYE.BAS
This program was written in Microsoft's QuickBasic
version 4.5. The program fits experimental complex
dielectric spectra obtained from the TDR system after being
Fourier transformed and DC conductivity corrected to a
modified form of the Debye model, eguations (6) and (7). A
Simplex routine is use to fit the equations to the
experimental data. The program requires the input of
estimates for each process time constant, the overall static
dielectric constant, and the overall high frequency
dielectric constant. Each of the guesses can be allowed to
float or be fix if the value is known. The program gives
output in two forms, graphics on a VGA monitor for comparing
the experimental results to the theoretical and output to a
data files for storage.


Absorption Mode of Dielectric Constant
67
20
0 11* *-
7.5 7.7 7.9
1.1I i I i I
8.1 8.3 8.5 8.7 8.9
Log Frequency(Hz)
9.1
9.3 9.5
Figure 22: Theoretical fit of the observed real component
spectra for solutions of n-butanol and pyridine.


Absorption Mode of Dielectric Constant
93
Log Frequency (Hz)
Figure 34: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and water.


59
c
o
o
c
D

co
O
o
o
_a>
a>
b
.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5

Butanol

95.4 mole 7.

89.7 mole 7.
A
84.9 mole 7.
O
70.1 mole 7.

49.9 mole 7.
O
39.4 mole 7.
A
28.9 mole 7.
Theoretical
Butanol in CCU
Log Frequency (Hz)
Figure 20: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
carbon tetrachloride.


135
END
REM* ***************************************************
REM SUBROUTINE SIMPLEX
REM* ***************************************************
SIMPLEX:
GOSUB PARMAT
IF NH = 0 OR RI(1) =0 GOTO 1100
KI = 1
KII = 1
1010 IF BR = 0 OR BR >= EP GOTO 1020
EP = EP / 10
GOTO 1010
1020 WR = RI(1)
BR = WR
JW = 1
JB = 1
FOR I = 2 TO 2 NPROC + 2
IF RI(I) >= WR THEN WR = RI(I)
IF RI(I) >= WR THEN JW = I
IF RI(I) < BR THEN BR = RI(I)
IF RI(I) < BR THEN JB = I
NEXT I
IF KII = 5 THEN
LOCATE 12, 33: PRINT USING "ITERATION #### "; KI
LOCATE 14, 27: PRINT USING "REDUCED CHI IS ####.#####; BR
KII = 0
END IF
IF KI > KX THEN
CLS : LOCATE 12, 25
PRINT "MAXIMUM NUMBER OF LOOPS REACHED"
LOCATE 23, 30: PRINT "Any key to continue"
ANDDD$ = FNAN$
RETURN
END IF
IF BR < EP THEN
CLS : LOCATE 12, 26
PRINT "CONVERGENCE CRITERIA REACHED"
LOCATE 23, 30: PRINT "Any key to continue"
ANDDD$ = FNAN$
RETURN
END IF
IF WR BR < EP / 100 THEN
CLS : LOCATE 12, 32
PRINT "BEST FIT REACHED"
LOCATE 23, 30: PRINT "Any key to continue"
ANDDD$ = FNAN$
RETURN
END IF
KI = KI + 1
KII = KII + 1
IF BR <> PR THEN PR = BR
F = 1


13
for n processes with and for each process equivalent
to es and for a single process.
Many systems (mainly solids and highly viscous liquids)
show Debye type relaxation effects, but do not fit Debye's
assumption that a dipolar process leading to the dipole
moment change must have full orientational freedom. A rate
theory model was suggested by Kauzmann11 to overcome this
problem. The model involves a potential surface with an
arbitrary number of wells of equal depth in the absence of
an applied field. As the applied field changes the
orientation of the dipole, the dipole moves from one well to
another thus assuming a discrete set of orientations with
respect to a fixed axis.
This work uses liquid systems which fit the Debye model.
Accordingly, further discussion of the Kauzmann model will
not be presented.
Time Domain Reflectometrv
The complex dielectric function for a wide range of
substances has been measured by fixed frequency methods for
many years. This process of collecting data is a slow and
tedious ordeal due to the order of magnitude ranges of the
frequencies involved in the frequency dependent dielectric
process. Recently, a time-dependent technique called time
domain reflectometry has been used to collect these data.12
TDR can greatly reduce the number of required measurements


Dielectric Constant
51
Figure 16: Fourier transformed n-butanol spectra.


Absorption Mode of Dielectric Constant
77
20 r
18
1 6 h
1 4
1 2
10
8 h
6
4
2
0
B § Q

1.0 mole 7.

5.0 mole 7.
A
7.5 mole %

1 0.0 mole %
O
1 5.0 mole %

30.0 mole 7
A
50.0 mole %
o
Aliquat 336
Theoretical
Aliquat in n-Butanol
oooooooooooooooooooo
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)
Figure 27: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336 and
n-butanol.


46
of 5 nsec and larger. The use of time windows less than 5
nsec is discouraged because the drift problems are highly
evident in such small time windows. The poor alignment
between the reference and sample gives irreproducible
distorted spectra.
A reference waveform is collected using the scope's
waveform calculator signal averaging function to establish
that the TDR is stable and to provide the Fourier transform
routine with a reference point. The reference waveform is
collected every five minutes until the difference between
the waveforms is less than 4 mV for the largest difference.
Sample waveforms are collected in a similar manner using the
same settings as the reference waveform. The sample needs
to equilibrate, typically one to three minutes, in the
sample cell after being introduced. This enables the sample
to reach equilibrium under the conditions of repetitive
excitation by the voltage pulse. The equilibrated sample
waveform can then be stored in one of the TDR's memory. The
TDR memory can hold nine waveforms of 512 points or three
waveforms of 1024 points.
Liquid samples are the easiest to handle and typically
take 15 to 20 minutes to collect data for seven different
samples using the same TDR settings. The reference waveform
is first taken then each of the samples is introduced into
the sample cell and their waveforms collected. Once the
reference waveform is taken, care must be used as not to


Ill
XYZ = FNWAIT(l)
30 PRINT #1, COM$
NPT = 0
TIMEINT = 0
VOLTINT = 0
XYZ = FNWAIT(l)
IF LOC(l) = 0 GOTO 30
1 = 0
DO UNTIL LOC(l) = 0
1 = 1 + 1
INPUT #1, HEAD$(I)
LOOP
NPT = VAL(MID$(HEAD$(2) INSTR(HEAD$(2), ":") + 1))
TIMEINT = VAL(MID$(HEAD$(5) INSTR(HEAD$(5) "s") + 1))
VOLTINT = VAL(MID$(HEAD$(8), INSTR(HEAD$(8), + 1))
IF NPT = 0 THEN
XYZ = FNWAIT(l)
PRINT #1, ""
XYZ = FNWAIT(l)
DO UNTIL LOC(l) = 0
LINE INPUT #1, LLL$
LOOP
XYZ = FNWAIT(l)
GOTO 30
END IF
LOCATE 19, 48
PRINT USING "Points ####",* NPT
LOCATE 20, 48
PRINT USING "Time/Div ##.###AAAA"; TIMEINT
LOCATE 21, 48
PRINT USING "mV/Div ###.###"; VOLTINT 1000
OPEN NAME$ FOR OUTPUT AS 2
PRINT #2, NPT
PRINT #2, TIMEINT
XYZ = FNWAIT(l)
PRINT #1, ""
XYZ = FNWAIT(3)
1 = 0
LOCATE 21, 13: PRINT "Receiving"
DO UNTIL LOC(l) = 0
INPUT #1, WNUM
IF I >= 1 AND I <= NPT THEN
LOCATE 18, 5
PRINT BLK$
LOCATE 18, 8
PRINT USING "####"; I
LOCATE 18, 18
PRINT WNUM VOLTINT 1000
PRINT #2, WNUM VOLTINT 1000
END IF
1 = 1 + 1
LOOP


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Michael D. Sacks
Associate Professor, Materials
Science and Engineering
This dissertation was submitted to the Graduate Faculty
of the Department of Chemistry in the College of Liberal
Arts and Sciences and to the Graduate School and was
accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
December 1990
Dean, Graduate School


ACKNOWLEDGEMENTS
I would like to give my greatest appreciation to my
research director, Dr. Russell S. Drago, for his skillful
leadership and scientific wisdom and to his wife Ruth, for
her caring and heartwarming get-togethers.
I would like to thank the Drago Group members, both past
and present, for their suggestions. In particular, I would
like to thank Curtis Barnes, Mark Barnes, Larry Chamusco,
Peter Doan, Jerry Grnewald, and Richard Riley for their
helpful discussions concerning chemistry and other important
matters.
Special thanks go to my father, Mr. Wai Woon Wong, my
mother, Mrs. Kuen Suen Wong, my brother, Mr. Edward Wong,
and my sister, Ms. Yin Wa Wong, whose continued
understanding and support made this effort possible.
ii


50
The Fourier program takes these two time-domain files and
transforms them into a frequency-dependent complex
dielectric constant, as shown in Figure 16. The program
automatically handles all baseline corrections and data
smoothing.
The DIF and SUM files are used to obtain the DC
conductivity of the sample. The ratio of the values of the
tail for these two spectra after baseline correction, as
shown in Figure 15, is proportional to the value of the
101
conductivity, aQ (in esu units), UJ- according to
a
o
c
4nd
(8)
where c is the speed of light (3 X 1011 mm/sec), d is the
length of the center conductor of the sample cell in
millimeters, and are the difference between the tail
end value and the baseline for the DIF and SUM data,
respectively. The specific conductance, k is equal to
aQ/9 X 1011 which is the DC conductivity with units of
mho/cm, a more appropriate set of units for comparison to
literature. DC conductivity determined from the time-domain
data is within five percent of the value obtained from a
commercially available conductance meter (a YSI model 35
conductance meter with a YSI model 3403 conductivity cell).
The DC conductivity is then used to calculate the frequency


RESULTS AND DISCUSSION
Alipliatic Alcohols
Binary System of Carbon Tetrachloride and n-Butanol
Carbon tetrachloride is a poorly coordinating, nonpolar
solvent with no permanent dipole moment. This solvent does
not give a dielectric spectrum in the frequency range of
2 X 107 Hz to 2 X 109 Hz. A constant complex dielectric of
one is observed for the real component and zero for the
imaginary component. The dielectric spectra of the binary
system of CC14 and butanol are shown in Figure 17. The
critical frequency, fc, for the dielectric relaxation of the
various solutions appears to remain constant at the fc
normally observed for neat butanol. The possible
interactions involved are CC14/CC14, butanol/CCl4, and
butanol/butanol. The former two CC14 interactions will not
influence the observed dielectric relaxation directly. The
main influence of dilution in CC14 is to decrease the
average size of the aggregate by shifting the equilibrium:
(C4H9OH)n > (C4H9OH)n_1 > C4H9OH (10)
toward the smaller species.
54


20
There are many models proposed for molecular motion
(described by the correlation time, tc) in liquids and it is
beyond the scope of this dissertation to give a detailed
discussion of each. Only two fundamental ones will be
briefly described. Mechanistically, the theory of rotation
can be broken down into two simple models: "classical" and
"jump" reorientation models.30'31 Classical reorientation
(Debye-Stokes-Einstein relationship) describes the rotation
of a molecule in a liquid as a solid body moving in a fluid
continuum. This simple model works well for macromolecules
in low molecular weight solvents but is not very realistic
for molecular motion in neat liquids. Gierer and Wirtz32
proposed that the discontinuous nature of liquids can be
explained by the addition of a "microviscosity" factor to
the classical model to describe a local environment around
each molecule in neat liquids, whereas Gordon33 proposed
that the molecules are freely rotating between randomly
occurring collisions. The collisions change the angular
momentum, but not the orientation of the molecules. The
change in the angular momentum of Gordon's classical model
can be further broken down into two cases. The J-diffusion
model states that the direction and magnitude of the angular
momentum is completely randomized by the collision with no
correlation between the momentum just before and after the
collision. The M-diffusion model randomizes only the


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INGEST IEID E1G4FW6V8_D8N5S3 INGEST_TIME 2015-04-06T18:38:52Z PACKAGE AA00029749_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


124
int n;
float w[];
struct complex x[];
{
int i;
for(i = 0; i < n; i++)
printf(M%f %f %f \n",w[i],x[i].real,x[i].imag);
}
void disk_out(name,n,x,y)
char *name;
int n;
float x[];
struct complex y[];
{
int i;
FILE *outfile;
outfile = fopen(name,"w");
for(i =0; i < n; i++)
fprintf(outfile,"%f %f %f\n",x[i],y[i],real,y[i].imag);
fclose(outfile);
void renorm(n,y,x)
int n;
float x[];
struct complex y[];
{
int i;
struct complex c[50];
for(i =0; i < n; i++)
c[i] = Cmplx(0.0, x[i]);
for(i =0; i < n; i++)
y[i] = Cdiv(y[i],c[i]);


137
REM
REM End subroutine Parmat
REM
REM* *******************************************************
REM SUBROUTINE VERTIX
REM* *******************************************************
VERTIX:
FOR I = 1 TO 2 NPROC + 1
SU = 0
IF F <> 1 GOTO 1230
FOR J = 1 TO 2 NPROC + 2
IF J O JW THEN SU = SU + S(I, J)
NEXT J
SUOLD(I) = SU / (2 NPROC + 1)
1230 E(I) = SUOLD(I) (1 + F) F S(I, JW)
NEXT I
R = FNFUNK
RETURN
REM
REM End subroutine Vertix
REM


130
sreal = sreal + cwt x[j];
simag = simag + swt x[jj;
cwtemp = cwt;
cwt = cwt cwi swt swi;
swt = cwtemp swi + swt cwi;
}
trans[i].real = sreal;
trans[i].imag = simag;
}
}
/* *************************************************** */
float *gen_freq(nf,ttot,fmax, np)
int nf;
float ttot,fmax;
{
int i;
float dw, *w, *whold, true_max, true_min;
float PI = 3.1415926536;
w = (float *)malloc(nf sizeof(float));
whold = w;
true_min = 2 PI / ttot; /* sampling theorem limit */
true_max = np true_min / 2; /* sampling theorem limit */
if( fmax > true_max) fmax = true_max;
dw = log(fmax/true_min) / (float ) nf;
/* gives equally spaced */
dw = exp(dw); /* points in log of w */
*w = true_min;
for( i = 1; i < nf; i++) {
w++;
*w = *(w 1) dw;
}
return(whold);
}


141
55. Hertz, H. G.; Holz, M.; Klute, R.; Stalidis, G.;
Versxnold, H. Ber. Bunsenaes. Phys. Chem. 1974, 78, 24
56. Hertz, H. G.; Holz, M.; Keller, G.; Versmold, H.; Yoon
C. Ber. Bunsenqes. Phys. Chem., 1974, 78, 493.
57. Richards, R. E.; York, B. A. Mol. Phys.. 1963, 6, 289.
58. Deverell, C.; Frost, D. J.; Richards, R. E. Mol. Phys.
1965, 9, 565.
59. Deverell, C. Mol. Phvs.. 1969, 16, 491.
60. Deverell, C. Progr. NMR Spectroscopy. 1969, 4, 235.
61. Richards, R. E. Mol. Phys.. 1964, 7, 500.
62. Hall, C.; Richards, R. E.; Schulz, G. N.; Sharp, R. R.
Mol. Phvs.. 1969, 16, 529.
63. Arnold, M. St. J. ; Packer, K. J. Mol. Phys. 1968, 14.,
241.
64. Bryant, R. G. J. Phvs. Chem.. 1969, 73, 1153.
65. Proctor, W. G.; Yu, F. C. Phys. Rev.. 1951, 81, 20.
66. Masuda, Y.; Kanda, T. J. Phys. Soc. Japan. 1954, 9, 82
67. Valiev, K. A.; Emel'yanov, M. I. J. Struct. Chem..
1964, 5, 625.
68. Hertz, H. G. Progress NMR Spectroscopy. 1967, 3, 159.
69. Lindman, B.; Forsen, S.; Forslind, E. J. Phys. Chem..
1968, 72, 2805.
70. Wennerstrom, H.; Lindman, B.; Forsen, S. J. Phys.
Chem.. 1971, 75, 2936.
71. Lindman, B.; Wennerstrom, H.; Forsen, S. J. Phys.
Chem., 1970, 71, 754.
72. Lindman, B. "Applications of Nuclear Quadrupole
Relaxation to the Study of Ion Binding in Solution,"
Thesis, Lund Inst. Technol., 1971.
73. Hertz, H. G.; Holz, M. J. Phys. Chem. 1974 23, 1002.
74. Holz, M. "Magnetische Relaxation von Ionenkernen und
hydrophobe Hydratation," Thesis, Univ. of Karlsruhe,
1973.


10
Figure 3: Plot of the frequency dependent complex
dielectric function; real and imaginary
components. Dash lines show typical systems that
deviate from Debye theory.


127
trans_to_diel(n, d, x, a, e)
int n;
float x[],d;
struct complex a[],e[];
{
int i, j;
float y, dl, tolerance;
struct complex tl,t2;
struct complex C_ONE = Cmplx(1.0,0.0);
tolerance = 1.0e-4;
/* the first round correction uses only the first two terms */
/* in the expansion of xcotx, to the linear term in (EPS* + 1)*/
/* EPS* = {a[i](1 y[i]) + 1} / (1 + y a[i]) */
/* where y = 1/3 (wd/c)A2 */
dl = d / C;
for( i = 0; i < n; i++) {
y = x[i] dl;
tl = escalar(a[i],(y y / 3.))?
t2 = Csub(a[i],tl);
t2 = Cadd(t2,C_0NE);
tl = Cadd(C_ONE, tl);
e[i] = Cdiv(t2,tl);
}
}
/* *************************************************** */
/* */
void derivative(n,k,x)
int n,k;
float x[];
{
int i, nl;
float xl, x2, x3;
float factorl, factor2, suml, sum2;
factorl = 1. / 12.;
factor2 = 8. / 12.;
nl = n 2; /* the derivative is based on a 4th order */
x3 = x[0]; /* polynomial approximation to the curves */
x2 = x[l]; /* this has a tendency to smooth high freq. */
xl = x[2]; /* instability, producing a smoother curve */


#include
#include
126
float C = 29.9772; /* (units of cm/nsec) */
/* ****************************************************** */
/* SUBROUTINE SMOOTH*/
/* */
/* This subroutine smooths the spectrum of n points which */
/* is pointed to by the x pointer. The routine uses a */
/* 3 point binomial smooth: */
/* x[i](new) = .25 (x[i 1] + x[i +1] ) + .5 x[i] */
/* */
/* This routine can be iterated k times to produce a 2k + 1 */
/* binomial smooth*/
void smooth(n,x,k)
int n,k;
float x[];
{
int i,j, nl;
float sum,xl/x2;
nl = n 1;
for(j = 0; j < k; j++) { /* outer loop */
xl = x[0];
x2 = x[1 ] ;
sum = .25 (xl + x[2]) + .5 x2;
for( i = 1; i < nl; i++) { /* smoothing loop */
x[i] = sum;
sum = sum + .25 (x[i+l] + x[i+2] xl x2);
xl = x2;
x2 = x[i+1];
}
/* ********************************************************* j
/* SUBROUTINE trans_to_diel
*/
/* */
/* This subroutine takes the converts the ratios of the */
/* dif and d(sum)/dt arrays and converts them to the complex */
/* dielectric response by using the transmission coefficient */


Voltage
49
SUM
Figure 15: DIF and SUM time domain spectra for n-butanol.


12. Complete waveform obtained from the TDR 41
13. Process is observed in approximately half the
time window with the correct time window
setting 42
14. Raw time domain data for an air reference and a
sample of n-butanol 48
15. DIF and SUM time domain spectra for n-butanol 49
16. Fourier transformed n-butanol spectra 51
17. Frequency dependent imaginary component of the
observed complex dielectric constant for solutions
of n-butanol and carbon tetrachloride 55
18. Concentration dependence of the observed static
dielectric constant for solutions of n-butanol
and carbon tetrachloride 57
19. Theoretical fit of the observed real component
spectra for solutions of n-butanol and carbon
tetrachloride 58
20. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and carbon tetrachloride 59
21. Frequency dependent imaginary component of the
observed complex dielectric constant for solutions
of n-propanol and n-hexanol 64
22. Theoretical fit of the observed real component
spectra for solutions of n-butanol and pyridine 67
23. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and pyridine 68
24. Comparison of the critical frequencies obtained
for the pyridine and carbon tetrachloride
systems 70
25. Concentration dependence of the observed DC
conductivity for solutions of Aliquat 336 in
n-Butanol 73
26. 35C1 NMR line widths obtained for solutions of
Aliquat 336 in n-Butanol 75
vii


55
Log Frequency (Hz)
Figure 17: Frequency dependent imaginary component of the
observed complex dielectric constant for
solutions of n-butanol and carbon tetrachloride.


14
and time required for frequency dependent dielectric
measurements. This technique uses real time measurements to
observe the properties of a system excited by a voltaqe
pulse. As in any pulse technique, the characteristics of
the voltage pulse define the theoretical limits of the range
of observable frequencies. The pulse risetime describes the
high frequency limit and the pulse width describes the low
frequency limit.
The basic experiment compares the charging of a parallel
plate capacitor containing the dielectric material to the
charging of a parallel plate capacitor containing air. The
charging function for the parallel plate capacitor changes
due to the difference in the impedance (dielectric
properties) between the sample cell and the dielectric
material. Analysis of this time dependent charging function
gives the characteristic constants (eg, and r) for the
complex dielectric function. The three basic TDR
termination schemes will be covered briefly here because the
derivation of the equations describing the complex
dielectric function for each scheme have been discussed in
previous work.9'13-15
The direct reflectance method9 analyzes only the first
reflection which comes from the surface of the sample and
requires that the sample length be long, usually 10 cm or
longer, and the sample cell be terminated by an electrical
short. The length of the cell is used to separate the first


44
the S-52 pulse generator. For an empty sample cell, the
reflected pulse will have its greatest amplitude. The
reflected pulse for a perfect system (no loss) has an
amplitude that is twice the original inputted pulse. Our
TDR setup has a loss of approximately 10% through the
electronics and cables in the form of heat. The amplitude
of the reflected pulse also decreases when a sample is
introduced into the sample cell. The decrease in amplitude
is proportional to the DC conductivity of the sample.
Samples with DC conductivities greater than 0.01 mho/cm
will short circuit the TDR sample cell. Conductivities of
the samples can be obtained from the time domain data
collected on the TDR. The lower limit of the conductivity
that can be measured is 1 X 10-6 mho/cm. Conductivities of
less than 1 X 10-5 mho/cm have little effect on the spectral
data for the sample. Larger conductivities behave like
relaxation processes and need to be corrected for in the
imaginary component of the complex dielectric constant. The
real component of the dielectric constant is not affected by
DC conductivity.
Other problems that exist are the size of the static
dielectric constant, the ability to pack solid samples, the
volatility of liquid samples, and fringing effects. Samples
with static dielectric constants less than three have large
errors associated in their spectral data. Solids are a
problem because of the variability in packing of the sample


110
FOR IMS = 3 TO 22
LOCATE IMS, 40
PRINT CHR$(186)
NEXT IMS
FOR IMS = 5 TO 75
LOCATE 13, IMS
PRINT CHR$(205)
NEXT IMS
LOCATE 13, 40
PRINT CHR$(206)
LOCATE 3, 45
PRINT "Special Program Commands"
LOCATE 6, 52
PRINT "SERIES"
LOCATE 5, 52
PRINT "DIR"
LOCATE 7, 52
PRINT "TIMED"
LOCATE 9, 52
PRINT "HELP"
LOCATE 10, 52
PRINT "EXIT or QUIT"
LOCATE 3, 2
PRINT "Enter command for TDR"
LOCATE 7, 2
PRINT "Last command sent to TDR"
LOCATE 9, 3
PRINT LCOM$
LOCATE 14, 8
PRINT "Data transmission"
LOCATE 16, 8
PRINT "Point"
LOCATE 16, 19
PRINT "mVolts"
LOCATE 15, 45
PRINT "Sending file to:"
RETURN
SENDTDR:
OPEN "COMI:9600,N,8,1,RB10000" FOR RANDOM AS 1
IF LOC(l) <> 0 THEN
DO UNTIL LOC(l) = 0
LINE INPUT #1, LLLL$
LOOP
END IF
LOCATE 17, 45
PRINT NAME$
LOCATE 5, 3
PRINT "Receiving data from TDR"
PRINT #1, "RQSON"


16
Iterative solutions are slow, tedious, and frequently
converge on the wrong solution.
Open termination15 uses an open circuit with all of the
voltage pulse reflected back to the detector, providing
information about the entire system: the sample, the sample
cell, the coaxial cables, etc. This method is the simplest
in terras of equipment but the most complex for the analysis
of the complex dielectric function. The use of an air
reference is crucial in factoring out the dielectric
properties from the TDR system itself. The analysis of the
equations for the open termination method require an
iterative numerical solution as in the matched termination
method. Cole15 solved this problem by developing an
approximate solution for the complex dielectric function
using a Taylor series expansion for this termination scheme.
Solution Systems to be Studied
Donor-acceptor interactions in protic solvents are
complex systems in which the self-association of the
solvent, the hydrogen bonding of the solvent, and the adduct
and Born type non-specific solvation effects all contribute
to the position of the equilibrium and the enthalpy of
complexation. In order to investigate the donor-acceptor
bonding, component studies of the enthalpy of complexation
of various bases to alipliatic alcohols in CC14 solvent have
been reported.16'17
Information about the extent of


89
c
O
o
c
D
Li
en
en
O
_i
ej
<
0)
b
10
9
8
7
6
5
4
3
2
1
0

1 0.0 mole 7.

25.1 mole 7.

37.7 mole 7.

50.6 mole 7.

60.1 mole %
Theoretical
H2O in Butanol
7.5 7.7 7.9 8.1
8.3 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.3 9.5
Figure 33: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
water.


Voltage
48
Figure 14: Raw time domain data for an air reference and a
sample of n-butanol.


REFERENCES
1. Cole, R. H. Annu. Rev. Phvs. Chem.. 1977, 28, 283.
2. Stine, E. "The Study of Mixed Valence Compounds by Time
Pojnain Ref lectometry," Ph.D. Dissertation, University
of Florida, 1985.
3. Bone, S. Biochim. Biophvs. Act?.. 1987, 916, 128.
4. Imamatsu, K.; Nozaki, R.; Yagihara, S.; Mashimo, S.;
Hashimoto, M. J. Chem. Phys.. 1986, 84/ 6511.
5. Bose, T. K.; Bottreau, A. M.; Chahine, R. IEEE Trans.
Instrum. Meas., 1986, IM-35. 56.
6. Nakamura, H.; Mashimo, S.; Wada, A. Jpn. J. Appl.
Phvs.. Part 1, 1982, 21, 467.
7. Hill, N.; Vaughan, W.; Price, A.; Davies, M.
"Dielectric Properties and Molecular Behavior," Van
Nostrand Reinhold Company Ltd., London, 1969.
8. "Handbook of Chemistry and Physics," Weast, Robert C.,
ed., CRC Press, Cleveland, 1975, F95.
9. Cole, K. S.; Cole, R. H. J. Chem. Phys.. 1941, 2, 341.
10. Rao, G. V. S.; Wanklyn, B. M.; Rao, C. N. R. Phys.
Chem. Solids. 1971, 22, 345.
11. Kauzmann, R. Rev. Mod Phys.. 1942, 14, 12.
12. Cole, R. H.; Windsor, P. "Fourier, Hadamond and Hilbert
Transforms in Chemistry," Marshall, A., ed., Plenum
Press, New York, 1982, 183-206.
13. Clark, A. H.; Quickenden, P. A.; Suggett, A. J. Chem.
Soc. Faraday II. 1974, 70, 1847.
14. Classen, T. A. C. M.; van Gemert, M. J. C. J. Chem.
Phvs.. 1975, 63, 68.
15. Cole, R. H. J. Phvs. Chem.. 1975, 22, 1459; 1469.
138


APPENDIX
COMPUTER PROGRAMS
Program TDR.BAS
This program was written using Microsoft QuickBasic
version 4.5. The program is designed to run interactively
using a character based interface. This program is used to
interface the Tektronix 7854 oscilloscope to an IBM
compatible personal computer for the purpose of downloading
data collected from the TDR system. The program can
automatically collect and form data files for the Fourier
transform routine.
106


6
the external field. The field is then turned off and the
perturbed system is allowed to relax back to an equilibrium
state. This relaxation process is referred to as
"dielectric relaxation." Three basic mechanisms are
involved in this relaxation process: electronic
polarization, atomic polarization, and dipole
reorientation.7 Electronic polarization is the
rearrangement of the electron density around a nucleus.
Atomic polarization results from the movement of lattice-
bound atoms or molecules. Dipole reorientation involves the
movement of polar molecules in space. Typical frequencies
for these processes in polar liquids9 are 1017, 1014, and
108 1012 Hz, respectively (Figure 2).
In a static experiment similar to that described for the
parallel plate capacitor, all three mechanisms are operative
and contribute to the induced field from the dielectric
material. The dielectric constant from this type of
experiment is termed the "static" dielectric constant, e .
o
This quantity is typically reported in literature for a wide
range of substances as the dielectric constant. Alternating
the polarity of the applied field will modify the parallel
plate capacitor experiment to allow each of the three
processes to be isolated. The contribution from a
particular process can be eliminated when the speed of the
alternating field exceeds the rate of relaxation of process.
For example, a long chain molecule that can rotate at a rate


TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS
LISTS OF TABLES V
LISTS OF FIGURES vi
ABSTRACT ix
INTRODUCTION 1
BACKGROUND 3
Dielectric Theory 3
Time Domain Reflectometry 13
Solution Systems to be Studied 16
EXPERIMENTAL 37
Time Domain Reflectometry 37
Nuclear Magnetic Resonance 52
Chemicals 53
RESULTS AND DISCUSSION 54
Alipliatic Alcohols 54
Binary System of Carbon Tetrachloride
and n-Butanol 54
Binary System of n-Propanol and n-Hexanol .... 60
Binary System of n-Butanol and Pyridine 66
Ternary System of Carbon Tetrachloride,
n-Butanol, and Pyridine 71
Surfactant Systems 72
Binary System of n-Butanol and Aliquat 336 ... 72
Ternary System of Carbon Tetrachloride,
n-Butanol, and Aliquat 336 81
Binary System of n-Butanol and Water 87
Ternary System of Water, n-Butanol,
and Aliquat 336 92
TDR SYSTEM ENHANCEMENTS AND MODIFICATIONS 98
iii


LISTS OF TABLES
page
1. Energy of Activation for Bromide Ion Quadrupole
Relaxation in Surfactant Systems 34
2. Butanol in Carbon Tetrachloride 61
3. Primary Alcohols 62
4. n-Hexanol and n-Propanol 65
5. Pyridine and Butanol Systems 69
6. Aliquat 336 in n-Butanol 79
7. Ternary System of Aliquat 336, n-Butanol, and
Carbon Tetrachloride 85
8. Water in n-Butanol 90
9. Water in a Solution of 10% Aliquat 336 in
n-Butanol 96
v


52
dependent conductivity correction values for the imaginary
component of the complex dielectric constant, as shown in
Figure 16, with
It
ecorr
ii
e
47T
a
w o
(9)
n
where ecorr and e" are the conductance corrected and
uncorrected imaginary components of the dielectric constant
at the angular frequency w, respectively.
Nuclear Magnetic Resonance
35C1 Nuclear magnetic resonance (NMR) spectroscopy was
done on a Varian VXR300 (300 MHz) spectrometer. The NMR was
tuned to the 35C1 nucleus. The solvated chloride ion from a
5 M aqueous solution of sodium chloride with a trace of D20
was used as the external reference for all 35C1 NMR spectra.
The NMR was setup for the majority of the Aliquat studies
using observation parameters of nucleus 35, frequency 29
MHz, spectral width 100 kHz, offset 400 Hz, acquisition time
0.005 sec, delay 0, pulse width 30 /isec, and transients
10,000, decouple parameters of nucleus 1.5, offset 584.7 Hz,
mode NNN, power 3 db, modulation mode S, frequency 9.9 kHz,
and pulse width 22.5 tsec, processing parameters of FN 64K,
line broaden 10 Hz and width 100 kHz, and the standard 13C
pulse sequence. Studies with large amounts of water used
the above parameters with these differences in the


68
10 r
9
c
o
'-t'
o
c
3
Li-
CO
CO
O
O
a>
b

5.0 mole 7.

9.9 mole 7.
A
1 5.1 mole 7.

50.4 mole 7.
X
49.5 mole 7.
O
Pyridine
Theoretical
Pyridine in Butanol
1
0
7.5 7.7 7.9 8.1
8.5 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.5 9.5
Figure 23: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
pyridine.


96
Table 9
Water in a Solution of 10% Aliquat 336 in n-Butanol
% Water
1
X 10
*1
6 Hz
2
0.0
8.9

2.8
295

10.3
9.3
4.7
2.0
234
1047
21.5
10.8
6.6
2.5
213
1061
30.2
12.1
8.0
3.0
216
1088
40.0
13.7
8.6
3.3
343
1688
51.2
16.9
10.6
3.6
356
2223


28
first form small complexes (dimers, trimers, etc.) then
form larger aggregates which are termed micelles and are of
colloidal dimensions. Micelle formation of long-chain
amphiphiles starts abruptly and is well defined by a given
concentration, the critical micelle concentration (cmc).
Concentrations that are well above the cmc often lead to a
transformation of the first formed micelle, approximately
spherical in shape to a very long rod shaped micelle. The
shape changes continue as the concentration reaches the
solubility limit for the surfactant. The possible formation
of liquid crystals can occur with different structures
depending on the composition of the system or the formation
of reversed micelles, aggregates with the polar phase as the
core and the nonpolar phase as the continuous environment.
Detailed studies of halide ion relaxation have been done
with micelle, reversed micelle, and liquid crystal
solutions.73'85-93 The results shown in Figure 7 are
typical of micellar solutions. Theoretical modelling of the
concentration dependence of the quadrupole relaxation for
these systems have been fit to a two site model.82'89'94
The model assumes that the halide appears in two forms, free
and attached to the micelle, the ratio between the
counterions and surfactant ions in the micelles is
independent of the concentration, and that the pseudo-phase
separation model of micelle formation applies. This
separation model treats the micelle formation as a phase


32
Weight per cent hexanol
Figure 9: Observed 81Br relaxation rates (from line widths)
divided by that at infinite dilution in water for
solutions of hexadecyltrimethylammonium bromide
(CTAB) and water in hexanol (region L2 of the
phase diagram in Figure 6). The weight ratio of
CTAB to water was kept constant at 1.04 and 27C.
As a comparison the viscosity (r\) at 25"C
relative to that of pure water (r¡0) is shown (X),
reference 91.


63
bonds. With comparable hydrogen bond strengths expected for
the alcohols listed (e.g. the -AH of hydrogen bonding of
ethanol and octanol to pyridine in CC14 are the same within
the 0.2 kcal mole-1 experimental error16'17), the frequency
differences are seen to be related to the average
composition of the solution.
In propanol-hexanol mixtures, the major interactions
involved are propanol/propanol, propanol/hexanol,
hexanol/hexanol. The frequency dependence of the imaginary
component (Figure 21) shows the change in the critical
frequency and the intensity of solutions for various mole
fractions of n-hexanol in n-propanol. The static dielectric
constant obeys Equation (11). The frequency dependence of
the real and complex dielectric constants obey Equations (6)
and (7) using two relaxation processes whose frequencies are
unchanged over the entire concentration range. When this is
the case, the intensity and critical frequency are mole
fraction averages of the pure components:
fc = xAfcA + xBfcB <12)
The critical frequencies for the neat alcohols and the
various alcoholic mixtures are summarized in Table 4. These
results indicate that the clusters are composed of a mixture
of alcohols and the rate of rearrangement of propanol on a
mixed cluster is the same as the rate on a propanol cluster


33
critical value. Above this value, the increase in the
relaxation rate corresponds to the disappearance of the
reversed micelles and can be attributed to ion pair
formation.
To be consistent with the micelle and reverse micelle
modelling studies, the liquid crystal systems also use a two
site model in attempting to analyze the data.86'93 Liquid
crystal systems are more complex, but can also be broken
down to a two step process. The faster process corresponds
to local interactions inside the liquid crystalline phase.
The slower process spans the dimensions of the aggregates
and may be from micellar rotation, counterion or amphiphile
diffusion along the micellar surface, or intermicellar
counterion exchange. Studies to separate the contributions
of these two steps to the relaxation,71'86-88/91-96 all tend
to show that the slower process gives only a small and
mostly undetectable contribution. Different motional
processes should have different energies of activation,
therefore the similar activation energies shown in Table 1
for the various phases suggest that the same type of motion
is responsible for the relaxation found in all phases. In
support of this, a number of cases have shown that the
relaxations are frequency independent and intensity
consideration gives a correlation time describing the major
part of the relaxation at tc 10-8s (2 X 107 Hz).


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Javid E. Richardson
Associate Professor, Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Robert C. StouJ
Associate Professor, Chemistry


15
reflection from the others. This results in a narrow range
of observable frequencies. For example, a system with a
pulse risetime of 25 psec and a cell length of 10 cm has an
upper limit of 5 X 1010 Hz and a lower limit of 1 X 109 Hz.
The limitation of the sample cell length is removed in
the multiple or total reflection methods.13-15 All
reflections are resolved, eliminating the need to separate
the reflections through the use of the sample cell length.
A pulse width of about 100 nsec gives a lower frequency
limit of 1 X 107 Hz for total reflection methods. Two forms
of the total reflection technique are used: matched and open
termination. The matched termination method13-15 requires
that the cell be shorted with an impedance matched to that
of the coaxial cable. As the voltage pulse reaches the
sample cell/sample interface, part of the pulse is reflected
back to the detector with the remainder being absorbed by
the sample cell. The reflections due to this impedance
mismatch between the dielectric material and the sample cell
contain information only about the sample. Unfortunately,
matching the impedance of the cable and the cell is not as
simple as it appears. The sample cell, the coaxial cables,
the connects, and various other components of the TDR have
their own individual characteristic impedances. In
addition, the equations that describe the reflected pulses
can not be solved in closed form and require an iterative
numerical solution such as the Newton-Raphson method.14


24
to have a much stronger effect on the relaxation rate, but
show the same trend in the family with size as that observed
for the alkali ions.
Aqueous solutions of tetraalkylammonium halides69-75 are
much more effective at quadrupolar relaxation than even
those of alkali or alkaline earth halides. Figure 5 shows
how the length of the alkyl group on the ammonium ion
influences the relaxation rate of the halide ion. The
nonpolar groups on the cation can exert a strong structure-
stabilizing effect on the water lattice.76 The formation of
crystalline hydrates found in tetraalkylammonium halides
suggests that the hydrogen bonded water molecules form large
clathrates in which the hydrophobic cations are enclosed
with some of the halide ions replacing the water molecules
in the clathrate lattice.77,78 This stabilization effect is
manifested in the slowing down of the water's rotational and
translational motions as observed in the change in the
quadrupolar relaxation rate of the halide.79'80
These observations imply that all nonpolar solutes can
cause enhanced relaxations as shown with the
tetraalkylammonium halides and that the mechanism for this
enhancement is similar in all cases.81 The possible
mechanisms involved in the rapid relaxation of the
substituted ammonium halides are direct anion-cation
interactions which results in ion pair formation or
modification of the anion-solvent interaction by the


71
suggest a decrease in aggregate size as pyridine is added to
butanol. The initial increments of added pyridine hydrogen
bond to terminal OH groups of butanol aggregates with only
minor changes in the dielectric spectrum. As the mole
fraction of pyridine increases, clusters must be broken in
order to provide hydrogen coordination sites for pyridine
causing the average f_ to shift to a higher frequency. One
can view the three dimensional nature of the alcohol adducts
as arising from the fact that two oxygen lone pairs of a
given molecule function as coordination positions for
protons of other molecules, while its hydrogen functions as
an acid site to another alcohol. The system is one hydrogen
short (as a consequence of the R group) of the tetrahedral
nature of a water molecule in a water structure and the
aggregate is not as stable. When a base coordinates to the
acid site of an alcohol molecule, one additional site for
chain growth is removed and the tendency to form a 3-D
structure is decreased.
Ternary System of Carbon Tetrachloride. n-Butanol. and
Pyridine
The relaxation processes are investigated for solutions
of -40% butanol in CC14 to which pyridine is added. A
similar trend in the frequency with increased concentration
is observed as shown in Table 5. The 50% composition which
would correspond to the 1:1 adduct shows similar behavior in
neat butanol and in CC14. Taking the dilution factor into


2
with multiple processes are more difficult to study because
of the problem in assigning the TDR response to the correct
process. The inability of this technique to provide
structural information about a given process requires the
correlation of observed dielectric changes with structural
information from other techniques like nuclear magnetic
resonance (NMR).
Emulsion and micelle systems are good test cases to
illustrate the complementary nature of TDR spectra to other
structural techniques. These systems, of increasing
interest since the 1950's, exhibit fascinating properties
with numerous applications. The unique properties of these
systems can be related to the amphiphilic nature of
components. An amphiphilic substance is a general
classification of molecules that contain both polar and
nonpolar ends. There are many different substances that can
be classified as amphiphilic, ranging from molecules like
sodium n-dodecylsulfate (ionic), to N-n-dodecyl-N-,N-
dimethylbetaine (amphoteric), to dimethyl-
n-dodecylamineoxide (nonionic). The unique properties of
these substances can be attributed to the tendency of the
nonpolar group to avoid contact with a polar solvent like
water while the polar end tends to be strongly solvated by
water. These systems should give some very interesting TDR
spectra and bring additional insight into the dynamics of
these systems.


i/l
25
Numoer of carbon atoms in the alkyl group
Figure 5: 79Br relaxation rates (from line widths) at 30C
for 0.500M aqueous solutions of alkylammonium
bromides. The different curves correspond from
the top to tetra, tri, di, and mono substituted
alkylammonium bromides. The y-intercept
corresponds to ammonium bromide. This figure was
obtained from reference 71.


121
depth = 0.15;
nf = 50;
fmax = 70.;
RAW_OUT = 1;
/* sizeof(complex) = 2 sizeof(float) */
fr_dif = (struct complex *)malloc(2 nf sizeof(float));
fr_sum = (struct complex *)malloc(2 nf sizeof(float));
/* ********************************************************* */
/* get data */
/* */
while((dif = fopen(argv[1],"r")) == NULL) {
puts("error in opening difference file...\n");
puts("input file name for difference file ");
gets(argv[1]);
}
fscanf(dif,"%d",&npd);
printf("%d\n", npd);
fscanf(dif,"%e",&dtd);
printf("%e\n",dtd);
dif_spec = (float *) malloc(npd sizeof(dts));
dhold = dif_spec;
for(i = 0; i < npd; i++) {
fscanf(dif,"%f",dif_spec);
dif_spec++;
)
fclose(dif);
dif_spec = dhold;
while ((sum = fopen(argv[2],"r")) == NULL) (
puts("error in opening sum file....\n");
puts("input sum file name ");
gets(argv[2]);
}
fscanf(sum,"%d",&nps);
printf("%d\n",nps);
if( nps != npd) (
puts("sum and dif files do not match...npoints differ\n");
exit(0);
}
fscanf(sum,"%e",&dts);
printf("%e\n",dts);
dtd = dtd le9;
/* convert to nsec to format */


118
MID$(C0M1$, 13, 1) =
COM$ = C0M1$
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NUMB$ = MID$(STR$(III), 2, LEN(STR$(III)) 1)
SELECT CASE LEN(NUMB$)
CASE 1
NUMB$ = "00" + NUMB$
CASE 2
NUMB$ = "0" + NUMB$
END SELECT
NAME$ = PATHH$ + "\" + ROOT$ + NUMB$ + ".DIF"
XYZ = FNWAIT(5)
GOSUB SENDTDR
MID$(C0M1$, 13, 1) = "+"
COM$ = C0M1$
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NAME$ = PATHH$ + "\" + ROOT$ + NUMB$ + ".SUM"
XYZ = FNWAIT(5)
GOSUB SENDTDR
FINSH = TIMER
IF FINSH < START1 THEN
DIFFER = 86400 START1 + FINSH
ELSE
DIFFER = FINSH START1
END IF
III = III + 1
IF III > NSAMP GOTO 199
IF III > 25 THEN SCN = 25
IF III > 50 THEN SCN = 50
IF III > 75 THEN SCN = 75
CLS : LOCATE III SCN, 10
PRINT "Running a TDR experiment please do not disturb."
IF DIFFER > TINTERVAL GOTO 180
XYZ = FNWAIT(TINTERVAL DIFFER)
GOTO 180
199 RETURN


Absorption Mode of Dielectric Constant
83
7.5
6.0
4.5
3.0
1 .5
0.0


No Aliquat

130/1
A
80/1

40/1
O
20/1

13/1
A
5.7/1
Theoretical
Butanol/Aliquat Ratio
7.5 7.7 7.9 8.1
8.3 8.5 8.7 8.9
Log Frequency (Hz)
9.1
9.3 9.5
Figure 30: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and carbon tetrachloride.


39
the scope and waits for an answer, the scope when powered up
waits for a request for service signal and does nothing
until it receives this request. This mismatching of
communication protocol can be avoided as long as the Black
Box unit is the last piece of equipment to be turned on.
The scope needs to be powered up for at least six to
eight hours to ensure thermal stability of the electronics
(at least 24 hours if the system is moved or powered down
for more than three or four hours). Any control changes
other than calling up a cursor or using the waveform
calculator function will require the scope to sit idle and
equilibrate for a minimum of one hour. The system should
remain stable for at least one to one and a half hour before
any electronic drift can be detected after thermal
equilibrium is reached. Power fluctuations can introduce
random noise into the data lines between the scope and the
IBM PC/AT when the system is at idle. This noise is
introduced through the Black Box converter unit and can be
eliminated by keeping the Black Box unit powered down until
the system is ready for use. The remaining units should be
left powered up to minimize the system's required
stabilization time.
The theoretical limits of this TDR using the open
termination method are governed by the pulse generator in
this setup. The S-52 pulse generator has a risetime of
25 psec (time for the "half-life" of raising the voltage to


119
Program TDRDRIVE.C
This program was written in Borland's Turbo C version
1.5 by Dr. Peter Doan. This program is required in the
analysis of the TDR data. Two program modules are required
for the Fourier transform analysis, the second module is
TDRUTIL.C. The Fourier routines require two files from the
TDR.BAS program. Included in these two modules are data
baseline correction and smoothing routines, their functions
are all automated.


140
34. O'Reilly, D. E.; Schacher, G. E. J. Chem. Phys.. 1963,
39, 1768.
35. O'Reilly, D. E. J. Chem. Phys.. 1968, 49, 5416.
36. Hertz, H. G. Z. Elektrochem.. 1961, £5, 20.
37. Hertz, H. G.; Stalidis, G.; Versmold, H. J. Chim. Phys.
pftysjcochiro. Biol., Numero special, Oct. 1966, 177.
38. Hertz, H. G. Ber. Bunsenaes. Phys. Chem.. 1973, 22,
531.
39. Valiev, K. A. Soviet Phvs. JETP.. 1960, 10, 77.
40. Valiev, K. A. Soviet Phys. JETP.. 1960, 11, 883.
41. Valiev, K. A.; Khabibullin, B. M. Russ. J. Phys. Chem.f
1961, 35, 1118.
42. Valiev, K. A. J. Struct. Chem.. 1962, 1, 630.
43. Valiev, K. A. J. Struct. Chem.. 1964, £, 477.
44. Itoh, J.; Yamagata, Y. J. Phys. Soc. Japan, 1958, 13,
1182.
45. Wertz, J. E. J. Phys. Chem.. 1957, 61, 51.
46. Pound, R. V. Phvs. Rev.. 1947, 72, 1273.
47. Pound, R. V. Phvs. Rev.. 1948, 72, 1247.
48. Proctor, W. G.; Yu, F. C. Phys. Rev.. 1950, 27, 716.
49. Sunder, S.; McClung, R. E. D. Chem. Phys.f 1973, 2/
467.
50. Bull, T. E. J. Chem. Phvs.. 1975, 62, 222.
51. Lindman, B.; Forsen, S. "Chlorine, Bromine, and Iodine
NMR," Springer-Verlag, Berlin, 1976, 55.
52. Hertz, H. G. Ber. Bunsenqes, Phys. Chem., 1963, 67.
311.
53. Hertz, H. G. "Theorie der Elektrolyte," Falkenhagen,
H., ed., Hirzel, Leipzig, 1971.
54. Hertz, H. G. Ber. Bunsenqes. Phvs. Chem.. 1977, 22,
688.


81
form large three-dimensional dynamic network type structures
normally found in neat butanol. The average size of the
butanol cluster decreases with pyridine concentration. This
is manifested in the change of the observed critical
freguency; increased critical freguency with increased
concentration of the pyridine. In comparison, Aliquat and
butanol show no change in the observed critical frequency
suggesting that the aggregate size for butanol remains
fairly constant. We propose that Aliquat is extracting
butanol from the bulk phase without modifying the properties
of the remaining bulk butanol phase. This literately
removes the entire butanol molecule out of the bulk solvent
and has no influence on the aggregation of the bulk butanol.
The model can be simplistically described as consisting of
two separate non-interacting microscopic phases. The
butanol in the Aliquat phase has its relaxation modified, so
it is no longer observed in our time window; i.e., the
critical frequency is either decreased or increased.
Ternary System of Carbon Tetrachloride. n-Butanol, and
Aliauat 336
The relaxation processes observed in the binary system
of Aliquat and butanol are investigated in the ternary
system formed by the addition of CC14. Carbon
tetrachloride, a nonpolar, poorly coordinating solvent can
bring about some interesting modifications in the butanol-
Aliquat interactions. It will dilute the system and lower


9
molecular realignment or response in seconds, eg is the
static dielectric constant measured in the frequency range
in which wr 1, and is the high frequency dielectric
constant measured in the frequency range in which wt 1.
The switching frequency of the external field is much lower
than the frequency of the observed molecular process when
wt 1. In the regime of ut 1, the observed molecular
process has the lower frequency.
The complex dielectric function, equation (2), can be
rearranged into its real and imaginary components
e*(iw) = e'(iw) ie"(ia>) (3)
where
e'(i) = £ + (4>
1 + (urr
es eoo
e"(iw) = = ut (5)
i + (wT-r
The frequency functionality, iw of the real component, e',
and the imaginary component, e", is left out and will be
implied in the remainder of this dissertation. Plots of t'
and e" versus log1Qw show the relationships between the
functions in Figure 3.
The real component (absorption mode) is the frequency
dependent dielectric constant measured in the alternating
polarity parallel plate experiment. The imaginary component


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy
APPLICATION OF TIME DOMAIN REFLECTOMETRY
TO SOLUTION PROCESSES
By
Ngai M. Wong
December 1990
Chairman: Professor Russell S. Drago
Major Department: Chemistry
The aggregation of alipliatic alcohols and Aliquat 336
is studied by using time domain reflectometry, TDR. The
aggregation of the alcohol leads to the formation of a
three-dimensional dynamic network through the coordination
of the two lone pairs on the oxygen and the OH hydrogen.
Molecular size and adduct bond strength play an important
role in the formation of this dynamic structure. The
formation of an adduct tends to shift the aggregate size
distribution of the alcohol to smaller species. The
aggregate size remains fairly constant with systems of
similar adduct strengths. In the absence of adduct
formation, the aggregate size remains fairly constant at low
dilution. The shift to the smaller species occurs at a
slower rate than that observed for systems with adduct
formation.
IX


DC Conductivity X1 05 mho/cm
73
Figure 25: Concentration dependence of the observed DC
conductivity for solutions of Aliquat 336 in
n-Butanol.


APPLICATION OF TIME DOMAIN REFLECTOMETRY
TO SOLUTION PROCESSES
By
NGAI M. WONG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1990

ACKNOWLEDGEMENTS
I would like to give my greatest appreciation to my
research director, Dr. Russell S. Drago, for his skillful
leadership and scientific wisdom and to his wife Ruth, for
her caring and heartwarming get-togethers.
I would like to thank the Drago Group members, both past
and present, for their suggestions. In particular, I would
like to thank Curtis Barnes, Mark Barnes, Larry Chamusco,
Peter Doan, Jerry Grnewald, and Richard Riley for their
helpful discussions concerning chemistry and other important
matters.
Special thanks go to my father, Mr. Wai Woon Wong, my
mother, Mrs. Kuen Suen Wong, my brother, Mr. Edward Wong,
and my sister, Ms. Yin Wa Wong, whose continued
understanding and support made this effort possible.
ii

TABLE OF CONTENTS
page
ACKNOWLEDGEMENTS
LISTS OF TABLES V
LISTS OF FIGURES vi
ABSTRACT ix
INTRODUCTION 1
BACKGROUND 3
Dielectric Theory 3
Time Domain Reflectometry 13
Solution Systems to be Studied 16
EXPERIMENTAL 37
Time Domain Reflectometry 37
Nuclear Magnetic Resonance 52
Chemicals 53
RESULTS AND DISCUSSION 54
Alipliatic Alcohols 54
Binary System of Carbon Tetrachloride
and n-Butanol 54
Binary System of n-Propanol and n-Hexanol .... 60
Binary System of n-Butanol and Pyridine 66
Ternary System of Carbon Tetrachloride,
n-Butanol, and Pyridine 71
Surfactant Systems 72
Binary System of n-Butanol and Aliquat 336 ... 72
Ternary System of Carbon Tetrachloride,
n-Butanol, and Aliquat 336 81
Binary System of n-Butanol and Water 87
Ternary System of Water, n-Butanol,
and Aliquat 336 92
TDR SYSTEM ENHANCEMENTS AND MODIFICATIONS 98
iii

CONCLUSIONS
103
APPENDIX 106
REFERENCES 138
BIOGRAPHICAL SKETCH 144
iv

LISTS OF TABLES
page
1. Energy of Activation for Bromide Ion Quadrupole
Relaxation in Surfactant Systems 34
2. Butanol in Carbon Tetrachloride 61
3. Primary Alcohols 62
4. n-Hexanol and n-Propanol 65
5. Pyridine and Butanol Systems 69
6. Aliquat 336 in n-Butanol 79
7. Ternary System of Aliquat 336, n-Butanol, and
Carbon Tetrachloride 85
8. Water in n-Butanol 90
9. Water in a Solution of 10% Aliquat 336 in
n-Butanol 96
v

LISTS OF FIGURES
page
1. Dielectric material filled parallel plate
capacitor experiment 4
2. Three mechanisms for describing dielectric
relaxation 7
3. Plot of the frequency dependent complex
dielectric function; real and imaginary
components 10
4. Plot of the imaginary versus the real component
of the complex dielectric constant, Cole-Cole
plot 12
5. 79Br relaxation rates (from line widths) at 30C
for 0.500M aqueous solutions of alkylammonium
bromides 25
6. Phase diagram of a ternary system composing of
hexadecyltrimethylammonium bromide (CTAB),
hexanol, and water 27
7. 79Br relaxation rates (from line widths) at 30"C
for aqueous solutions of monoalkylammonium
bromide solutions 29
8. 35C1 relaxation rates (from line widths) as a
function of the inverse concentration of
octyltrimethylammonium chloride and octylammonium
chloride at 28C 31
9. Observed 81Br relaxation rates (from line widths)
divided by that at infinite dilution in water for
solutions of hexadecyltrimethylammonium bromide
(CTAB) and water in hexanol 32
10. ^Br transverse relaxation rates (from line
widths) in non-aqueous and mixed solvent systems
as a function of electrolyte concentration ... 36
11. Block diagram of TDR setup 38
vi

12. Complete waveform obtained from the TDR 41
13. Process is observed in approximately half the
time window with the correct time window
setting 42
14. Raw time domain data for an air reference and a
sample of n-butanol 48
15. DIF and SUM time domain spectra for n-butanol 49
16. Fourier transformed n-butanol spectra 51
17. Frequency dependent imaginary component of the
observed complex dielectric constant for solutions
of n-butanol and carbon tetrachloride 55
18. Concentration dependence of the observed static
dielectric constant for solutions of n-butanol
and carbon tetrachloride 57
19. Theoretical fit of the observed real component
spectra for solutions of n-butanol and carbon
tetrachloride 58
20. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and carbon tetrachloride 59
21. Frequency dependent imaginary component of the
observed complex dielectric constant for solutions
of n-propanol and n-hexanol 64
22. Theoretical fit of the observed real component
spectra for solutions of n-butanol and pyridine 67
23. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and pyridine 68
24. Comparison of the critical frequencies obtained
for the pyridine and carbon tetrachloride
systems 70
25. Concentration dependence of the observed DC
conductivity for solutions of Aliquat 336 in
n-Butanol 73
26. 35C1 NMR line widths obtained for solutions of
Aliquat 336 in n-Butanol 75
vii

27. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336 and
n-butanol 77
28. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336
and n-butanol 78
29. Concentration dependence of the observed static
dielectric constant for solutions of Aliquat 336
and n-butanol 80
30. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and carbon tetrachloride 83
31. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and carbon tetrachloride 84
32. Theoretical fit of the observed real component
spectra for solutions of n-butanol and water 88
33. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and water 89
34. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and water 93
35. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and water 94
viii

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment
of the Requirements for the Degree of
Doctor of Philosophy
APPLICATION OF TIME DOMAIN REFLECTOMETRY
TO SOLUTION PROCESSES
By
Ngai M. Wong
December 1990
Chairman: Professor Russell S. Drago
Major Department: Chemistry
The aggregation of alipliatic alcohols and Aliquat 336
is studied by using time domain reflectometry, TDR. The
aggregation of the alcohol leads to the formation of a
three-dimensional dynamic network through the coordination
of the two lone pairs on the oxygen and the OH hydrogen.
Molecular size and adduct bond strength play an important
role in the formation of this dynamic structure. The
formation of an adduct tends to shift the aggregate size
distribution of the alcohol to smaller species. The
aggregate size remains fairly constant with systems of
similar adduct strengths. In the absence of adduct
formation, the aggregate size remains fairly constant at low
dilution. The shift to the smaller species occurs at a
slower rate than that observed for systems with adduct
formation.
IX

The formation of micelles can be observed in dielectric
spectra. The critical micelle concentration can be
determined from solution DC conductivity and the static
dielectric constant obtained from TDR dielectric spectra.
The study of Aliquat 336 has shown that solvents like
n-butanol prefer the hydrophobic region of the quaternary
ammonium salt in neat solvent. The addition of a nonpolar
solvent like CC14 to a solution of Aliquat in n-butanol
causes the butanol to leave the hydrophobic sites and
interact with the hydrophilic sites of Aliquat. In
contrast, the addition of water does not influence the
observed interactions of butanol. These effects are
manifested in the intensity of the dielectric constant and
in the critical frequency of the dielectric spectra.
x

INTRODUCTION
Time Domain Reflectometry, TDR, is a technique used to
study the time-dependent response of a sample to a time-
dependent electromagnetic field. This response depends upon
the dielectric properties of the sample. Practical
application of this technique became available with the
introduction of the tunnel diode as a voltage pulse
generator which is used as an excitation source. This
technological development allows systems that have processes
as fast as 1 psec (2 X 1011 Hz) to be studied by TDR. A
multitude of systems including pure liquids,1 mixed valent
systems,2 biological systems,3-5 and polymers in solution6
4
have been studied by this technique.
The current state of the art time domain reflectometer
is in the infancy stages. The potential of TDR lies in its
ability to collect dielectric data in a very short time
(minutes for a typical frequency range of 106 Hz to 109 Hz)
compared to the standard method which is a long and tedious
task of point by point data collection. Typical studies
using TDR involve systems that have only one or two
processes of interest. In this way, fundamental information
about these processes is fairly easy to obtain. Systems
1

2
with multiple processes are more difficult to study because
of the problem in assigning the TDR response to the correct
process. The inability of this technique to provide
structural information about a given process requires the
correlation of observed dielectric changes with structural
information from other techniques like nuclear magnetic
resonance (NMR).
Emulsion and micelle systems are good test cases to
illustrate the complementary nature of TDR spectra to other
structural techniques. These systems, of increasing
interest since the 1950's, exhibit fascinating properties
with numerous applications. The unique properties of these
systems can be related to the amphiphilic nature of
components. An amphiphilic substance is a general
classification of molecules that contain both polar and
nonpolar ends. There are many different substances that can
be classified as amphiphilic, ranging from molecules like
sodium n-dodecylsulfate (ionic), to N-n-dodecyl-N-,N-
dimethylbetaine (amphoteric), to dimethyl-
n-dodecylamineoxide (nonionic). The unique properties of
these substances can be attributed to the tendency of the
nonpolar group to avoid contact with a polar solvent like
water while the polar end tends to be strongly solvated by
water. These systems should give some very interesting TDR
spectra and bring additional insight into the dynamics of
these systems.

BACKGROUND
Dielectric Theory
A perfect dielectric material is an insulator. The
internal charges are so closely bound that no electric
current may be conducted through it. The atoms are fixed in
its lattice and are not free to move through the material.
In reality, there are no perfect dielectric materials
because atoms are free to shift around their fixed positions
when an external field, EQ, is applied to the material. A
parallel plate capacitor can be used to generate this
external field.7 The dielectric material is placed between
the plates as shown in Figure la. The capacitor is charged
so that one plate is positively charged and the other is
negatively charged. The dielectric material's response to
this external field is to set up its own electric field
(induced field, E-^) to counter the field from the capacitor.
The induced field is produced by the realignment of the
dipoles in the dielectric material. This sets up a surface
charge that is opposite of that for each of the plates in
the capacitor as shown in Figure lb. Typically, the induced
field from dielectric material is less than the external
field. The observed or resultant field, E2, for dielectric
3

4
12*
Figure 1: Dielectric material filled parallel plate
capacitor experiment.
a) Random dipole motion with no external field.
b) Alignment of dipoles to an external field.

5
material filled capacitor which is the summation of the
external and induced fields. Since the induced field is
opposite in direction of the external field, the resultant
field is always less than the external field. The ratio of
the external field to the resultant field is the dielectric
constant of the material. The official definition of the
dielectric constant,8 e, is
Q Q'
e = 5 (1)
F r
where F is the force of attraction between the two charges Q
and Q' separated by the distance r in a uniform medium. A
more convenient definition is the relative permittivity
which is the ratio of the electric fields in the gap between
the plates of a capacitor when the plates are separated by
vacuum and by a dielectric material. A more intuitive feel
for the dielectric constant is the material's ability to
store electrical energy (i.e. the greater the charges ([Q
and Q']) the larger the dielectric constant as expressed in
the official definition).
The induced field from the dielectric material occurs
through processes best described as "dielectric
relaxations." Consider a system containing a dipole moment
which responds to the application of an external field. The
nature of the dipole moment may be permanent or induced by

6
the external field. The field is then turned off and the
perturbed system is allowed to relax back to an equilibrium
state. This relaxation process is referred to as
"dielectric relaxation." Three basic mechanisms are
involved in this relaxation process: electronic
polarization, atomic polarization, and dipole
reorientation.7 Electronic polarization is the
rearrangement of the electron density around a nucleus.
Atomic polarization results from the movement of lattice-
bound atoms or molecules. Dipole reorientation involves the
movement of polar molecules in space. Typical frequencies
for these processes in polar liquids9 are 1017, 1014, and
108 1012 Hz, respectively (Figure 2).
In a static experiment similar to that described for the
parallel plate capacitor, all three mechanisms are operative
and contribute to the induced field from the dielectric
material. The dielectric constant from this type of
experiment is termed the "static" dielectric constant, e .
o
This quantity is typically reported in literature for a wide
range of substances as the dielectric constant. Alternating
the polarity of the applied field will modify the parallel
plate capacitor experiment to allow each of the three
processes to be isolated. The contribution from a
particular process can be eliminated when the speed of the
alternating field exceeds the rate of relaxation of process.
For example, a long chain molecule that can rotate at a rate

DIPOLE
ORIENTATION
7
ELECTRONIC
POLARIZATION
E'(U) FREQUENCY DEPENDENT
DIELECTRIC CONSTANT
£*(0) LOSS FACTOR
Figure 2: Three mechanisms for describing dielectric
relaxation.

8
of 180 per second will move only 0.2 in a field that is
alternating at a rate of 1000 cycles per second. In essence
the molecule appears to be frozen in place.
The time scale for the electronic and atomic
polarization is so fast that they appear to be instantaneous
on current instrumentation that is used to measure
dielectric relaxation processes. Consequently, the only
processes that can be studied occur through the dipole
reorientation mechanism. The "high frequency" dielectric
constant, e^, is used to describe the contribution from the
electronic and atomic polarizations.
The first theoretical model for describing the dipole
reorientation in molecular systems was given by Debye.10 It
is assumed that the dipole moment of a molecule moves under
the influence of a torque with full orientational freedom.
The dipolar motion is hindered by internal friction that is
related to the viscosity of the medium. Brownian motion
acts as the randomizing factor which causes the breakdown of
the dipole realignment. The resulting steady-state equation
for a single process in terms of a complex dielectric
function, e*(iw), is given by
e*U) = i. + (2)
1 + WT
where w is the angular frequency with w = 2?rf, f is the
frequency in Hz, t is the process time constant for the

9
molecular realignment or response in seconds, eg is the
static dielectric constant measured in the frequency range
in which wr 1, and is the high frequency dielectric
constant measured in the frequency range in which wt 1.
The switching frequency of the external field is much lower
than the frequency of the observed molecular process when
wt 1. In the regime of ut 1, the observed molecular
process has the lower frequency.
The complex dielectric function, equation (2), can be
rearranged into its real and imaginary components
e*(iw) = e'(iw) ie"(ia>) (3)
where
e'(i) = £ + (4>
1 + (urr
es eoo
e"(iw) = = ut (5)
i + (wT-r
The frequency functionality, iw of the real component, e',
and the imaginary component, e", is left out and will be
implied in the remainder of this dissertation. Plots of t'
and e" versus log1Qw show the relationships between the
functions in Figure 3.
The real component (absorption mode) is the frequency
dependent dielectric constant measured in the alternating
polarity parallel plate experiment. The imaginary component

10
Figure 3: Plot of the frequency dependent complex
dielectric function; real and imaginary
components. Dash lines show typical systems that
deviate from Debye theory.

11
(dispersion mode) is called the dielectric loss function
which refers to the power lost through the dielectric
material. The energy absorbed from the applied electric
field (the real component) is dissipated by the "friction"
(the imaginary component) created by the dipole attempting
to align itself to the field. The maximum loss value occurs
at the critical frequency, fc, which is the same point as
the inflection point seen in the real component where ut = 1
and describes the frequency of the observed process. The
imaginary component is symmetric in the log of frequency
around the maximum loss value covering a broad range of
frequencies. A plot of e" versus e', Cole-Cole plot,9 for a
Debye dielectric yields a semicircle as shown in Figure 4.
The maximum loss value is equal to (es e^/2. Materials
that obey the complex dielectric function, equation (2), are
termed Debye dielectrics. The Debye model can be extended
to describe multiple processes10 where equations (3) and (4)
become
n
i
(6)
i=l
n
i=l
(7)

12

£
Figure 4:
Plot of the imaginary versus the real component
of the complex dielectric constant, Cole-Cole
plot.

13
for n processes with and for each process equivalent
to es and for a single process.
Many systems (mainly solids and highly viscous liquids)
show Debye type relaxation effects, but do not fit Debye's
assumption that a dipolar process leading to the dipole
moment change must have full orientational freedom. A rate
theory model was suggested by Kauzmann11 to overcome this
problem. The model involves a potential surface with an
arbitrary number of wells of equal depth in the absence of
an applied field. As the applied field changes the
orientation of the dipole, the dipole moves from one well to
another thus assuming a discrete set of orientations with
respect to a fixed axis.
This work uses liquid systems which fit the Debye model.
Accordingly, further discussion of the Kauzmann model will
not be presented.
Time Domain Reflectometrv
The complex dielectric function for a wide range of
substances has been measured by fixed frequency methods for
many years. This process of collecting data is a slow and
tedious ordeal due to the order of magnitude ranges of the
frequencies involved in the frequency dependent dielectric
process. Recently, a time-dependent technique called time
domain reflectometry has been used to collect these data.12
TDR can greatly reduce the number of required measurements

14
and time required for frequency dependent dielectric
measurements. This technique uses real time measurements to
observe the properties of a system excited by a voltaqe
pulse. As in any pulse technique, the characteristics of
the voltage pulse define the theoretical limits of the range
of observable frequencies. The pulse risetime describes the
high frequency limit and the pulse width describes the low
frequency limit.
The basic experiment compares the charging of a parallel
plate capacitor containing the dielectric material to the
charging of a parallel plate capacitor containing air. The
charging function for the parallel plate capacitor changes
due to the difference in the impedance (dielectric
properties) between the sample cell and the dielectric
material. Analysis of this time dependent charging function
gives the characteristic constants (eg, and r) for the
complex dielectric function. The three basic TDR
termination schemes will be covered briefly here because the
derivation of the equations describing the complex
dielectric function for each scheme have been discussed in
previous work.9'13-15
The direct reflectance method9 analyzes only the first
reflection which comes from the surface of the sample and
requires that the sample length be long, usually 10 cm or
longer, and the sample cell be terminated by an electrical
short. The length of the cell is used to separate the first

15
reflection from the others. This results in a narrow range
of observable frequencies. For example, a system with a
pulse risetime of 25 psec and a cell length of 10 cm has an
upper limit of 5 X 1010 Hz and a lower limit of 1 X 109 Hz.
The limitation of the sample cell length is removed in
the multiple or total reflection methods.13-15 All
reflections are resolved, eliminating the need to separate
the reflections through the use of the sample cell length.
A pulse width of about 100 nsec gives a lower frequency
limit of 1 X 107 Hz for total reflection methods. Two forms
of the total reflection technique are used: matched and open
termination. The matched termination method13-15 requires
that the cell be shorted with an impedance matched to that
of the coaxial cable. As the voltage pulse reaches the
sample cell/sample interface, part of the pulse is reflected
back to the detector with the remainder being absorbed by
the sample cell. The reflections due to this impedance
mismatch between the dielectric material and the sample cell
contain information only about the sample. Unfortunately,
matching the impedance of the cable and the cell is not as
simple as it appears. The sample cell, the coaxial cables,
the connects, and various other components of the TDR have
their own individual characteristic impedances. In
addition, the equations that describe the reflected pulses
can not be solved in closed form and require an iterative
numerical solution such as the Newton-Raphson method.14

16
Iterative solutions are slow, tedious, and frequently
converge on the wrong solution.
Open termination15 uses an open circuit with all of the
voltage pulse reflected back to the detector, providing
information about the entire system: the sample, the sample
cell, the coaxial cables, etc. This method is the simplest
in terras of equipment but the most complex for the analysis
of the complex dielectric function. The use of an air
reference is crucial in factoring out the dielectric
properties from the TDR system itself. The analysis of the
equations for the open termination method require an
iterative numerical solution as in the matched termination
method. Cole15 solved this problem by developing an
approximate solution for the complex dielectric function
using a Taylor series expansion for this termination scheme.
Solution Systems to be Studied
Donor-acceptor interactions in protic solvents are
complex systems in which the self-association of the
solvent, the hydrogen bonding of the solvent, and the adduct
and Born type non-specific solvation effects all contribute
to the position of the equilibrium and the enthalpy of
complexation. In order to investigate the donor-acceptor
bonding, component studies of the enthalpy of complexation
of various bases to alipliatic alcohols in CC14 solvent have
been reported.16'17
Information about the extent of

17
aggregation of the alcohol is absent. Often it is assumed
that monomeric species are involved. Similar assumptions
are made in studies of the change in 0-H stretching
freguencies for alcohol-base adducts in dilute CC14
solution.18 In a recent analysis of the "anomalous basicity
of amines,"19 it was shown that the acidity of hydrated
proton species as well as the relative importance of
covalent and electrostatic bonding contributions changed
appreciably with the extent of hydration, i.e. the n value
of H(H20)n+. Similar changes in the acidity or basicity of
(ROH)n molecules may be anticipated as n varies. As a
result, gas phase studies of monomers and solution studies
in inert solvents may determine properties of species that
do not exist in pure solvents. Such information is relevant
to understanding the chemistry in pure protic solvents and
in mixed solvent systems.
Frequency dependent studies of the dielectric constant
show dielectric relaxation corresponding to the making and
breaking of hydrogen bonds in alcohol clusters.20 Three
different relaxation times have been found for each of the
10 primary alcohols from propyl to dodecyl. Sixteen
wavelengths of measurement were used spanning 30,000 to
0.22 cm. The long relaxation occurs over ranges of 1 to
22 X 10-10 sec and corresponds to breaking hydrogen bonds of
terminal OH groups in a cluster concurrent with rotation of
the alcohol as it forms a new hydrogen bond in the same

18
cluster. The rotation gives rise to the mechanism for
dielectric relaxation. The relaxation times increase
regularly with increasing chain length. The activation
energy for this process range from 5 to 8 kcal mole-1
increasing in a regular fashion with chain length. This is
of the order of magnitude expected for breaking a hydrogen
bond and rules out rotational mechanisms that require the
breaking of two hydrogen bonds. Accordingly, the molecular
motion involves the terminal groups of the three dimensional
structures. Since the hydrogen bond dissociation energies
are not expected to increase with increasing length of the
alkyl group, the size of the group involved in the molecular
rotation is proposed to contribute to the observed
activation enthalpy and entropy. In the neat alcohol, one
expects a distribution of cluster sizes and hence a
distribution of relaxation times. Since this is not
observed, the energetics of the processes described must not
differ enough with cluster size to be resolved. Failure to
observe a distribution of relaxations is taken as evidence
to rule out the reorientation of the whole cluster as the
relaxation mechanism.
The other two relaxations correspond to rotation of
monomeric molecules (1.7 to 5 X 10-11 sec) and to rotation
of the OH group around the C-0 bond (1.7 to 4 X 10-12 sec).
The time scale for these two relaxations are beyond the

19
range of our current TDR system. Accordingly, no further
discussion of these processes will be presented.
Metals like gold, iridium, manganese, mercury,
molybdenum, nickel, niobium, palladium, platinum, tungsten,
and zirconium have been extracted or separated using
Aliquat 336 (trioctylmethylammonium chloride).21-28 This
quaternary ammonium salt is widely used as a phase transfer
catalyst and as a mobile phase catalyst. The better known
systems involve quaternary ammonium salts with large alkyl
groups. In general, little is known about the dynamics of
this class of compounds in solution or in moving substances
in and out of the different phases. The majority of the
physical characterization studies have been done using
nuclear magnetic resonance to study the quadrupolar
relaxation of chlorine, bromine, and iodine.
Nuclear magnetic quadrupole relaxation29 arises from the
interaction of a quadrupolar nucleus with a time-dependent
electric field gradient. This field gradient depends on two
properties: the molecular motion of the quadrupolar nuclei
and the surrounding species' dielectric properties. The
magnitude of the field gradient, influenced by the
surrounding species, is the major contribution in the
relaxation of halide ions in solution. The molecular motion
of the quadrupolar nuclei alters the direction of the field
gradient, providing the major contribution to the relaxation
mechanism of covalently bonded halides.

20
There are many models proposed for molecular motion
(described by the correlation time, tc) in liquids and it is
beyond the scope of this dissertation to give a detailed
discussion of each. Only two fundamental ones will be
briefly described. Mechanistically, the theory of rotation
can be broken down into two simple models: "classical" and
"jump" reorientation models.30'31 Classical reorientation
(Debye-Stokes-Einstein relationship) describes the rotation
of a molecule in a liquid as a solid body moving in a fluid
continuum. This simple model works well for macromolecules
in low molecular weight solvents but is not very realistic
for molecular motion in neat liquids. Gierer and Wirtz32
proposed that the discontinuous nature of liquids can be
explained by the addition of a "microviscosity" factor to
the classical model to describe a local environment around
each molecule in neat liquids, whereas Gordon33 proposed
that the molecules are freely rotating between randomly
occurring collisions. The collisions change the angular
momentum, but not the orientation of the molecules. The
change in the angular momentum of Gordon's classical model
can be further broken down into two cases. The J-diffusion
model states that the direction and magnitude of the angular
momentum is completely randomized by the collision with no
correlation between the momentum just before and after the
collision. The M-diffusion model randomizes only the

21
direction of the angular momentum and leaves the magnitude
unaffected.
The jump reorientation model looks at the liquid with
activation barriers to rotation or the migration of lattice
defects or holes. Application of this model to the
experimental data presents some difficulties due to the lack
of information about several of the parameters needed in the
analysis. These parameters include the geometry of the
lattice, the energy barriers, the number of vacancies or
defects, etc. A quasilattice random flight model was
proposed by O'Reilly.34'35 The model assumes that the first
solvation shell can be approximated by a lattice and
describes large changes in angular rotation by small-steps
of angular rotation. O'Reilly's model addressed some of the
problems like vacancies and translational diffusion by
vacancy migration, but still require several other
parameters that are lacking for a complete analysis.
The quadrupolar relaxation of halide ions is
intermolecular in nature and result from the interaction
with other ions or dipoles in solution. Two models have
been proposed for the origin of the change in the magnitude
of the field gradient at the nuclei; electrostatic and
electron distortion models. Experimental discrimination
between these two models is difficult due to limited
literature comparison on the merits of each model. The
electrostatic model36-43 looks at the distribution of

22
charges from other ions and solvent molecules around the
relaxing ion. The change in the field gradient is caused by
the molecular motion of the surrounding species. Hertz36-38
and Valiev39-43 have both studied this problem using the
electrostatic model with different approaches and varying
degrees of completeness. The most recent work by Hertz,38
being the most elaborate for halides at infinite dilution in
water, calculated 1/T1 using the electrostatic model for
35C1, 81Br, and 127I to be 40, 1350, and 5650 sec-1 compared
to the observed values of 42, 1050, and 5270 sec-1,
respectively.
The electronic distortion model was first proposed by
Itoh and Yamagata.44 The model suggests that the relaxation
is produced by the deformation of the ion's electron cloud
caused by the collision of the relaxing nuclei with other
species in solution. Comparison of the experimental results
with electronic distortion theory is difficult since some of
the important quantities (correlation time, excitation
energy, field gradient, and nuclear magnetic shielding) are
very difficult to estimate.
Covalently bonded halides have been used to study
molecular motion through the correlation time of the
molecule.45-48 Estimates of the correlation time have been
obtained mainly from NMR line widths for various molecules.
The theoretical models that describe the changes in the
field gradient that affect quadrupolar relaxation are

23
important in helping to understand these processes, but are
of limited utility since the body of experimental data is
small, limiting the application of these models. Comparison
of the experimental results with different theories has led
to the preferred use of the extended J-diffusion classical
model over others.49-51 A number of people have studied
alkali halides in aqueous solution: Itoh and Yamagata,44
Hertz,36'37'52-56 Richards and co-workers,57-62 Arnold and
Packer,63 and Bryant.64 The concentration dependence
studies of alkali halides in aqueous solution can be
summarized with the following observations. The relaxation
rate increases with an increase in concentration. The
relative magnitude of the change depends on the size of the
halide ion. The mechanism for the relaxation rate depends
upon a complex interaction involving the alkali halide
concentration as well as the size of the alkali metal ion.
The order of increasing effect on the Cl- and Br relaxation
is K+ < Na+ < Rb+ < Li+ < Cs+ with I-, the position of Na+
and Rb+ are reversed.
Studies involving other inorganic halides like hydrogen
halides,48'57'65'66 ammonium halides,36'55 and alkaline
earth halides36'57'58'67'68 have yielded little additional
information. The observed effects were similar to those
seen for the alkali halides. In the case of hydrogen and
ammonium, similar results to those from the smaller sized
alkali ions were obtained. The alkaline earth ions proved

24
to have a much stronger effect on the relaxation rate, but
show the same trend in the family with size as that observed
for the alkali ions.
Aqueous solutions of tetraalkylammonium halides69-75 are
much more effective at quadrupolar relaxation than even
those of alkali or alkaline earth halides. Figure 5 shows
how the length of the alkyl group on the ammonium ion
influences the relaxation rate of the halide ion. The
nonpolar groups on the cation can exert a strong structure-
stabilizing effect on the water lattice.76 The formation of
crystalline hydrates found in tetraalkylammonium halides
suggests that the hydrogen bonded water molecules form large
clathrates in which the hydrophobic cations are enclosed
with some of the halide ions replacing the water molecules
in the clathrate lattice.77,78 This stabilization effect is
manifested in the slowing down of the water's rotational and
translational motions as observed in the change in the
quadrupolar relaxation rate of the halide.79'80
These observations imply that all nonpolar solutes can
cause enhanced relaxations as shown with the
tetraalkylammonium halides and that the mechanism for this
enhancement is similar in all cases.81 The possible
mechanisms involved in the rapid relaxation of the
substituted ammonium halides are direct anion-cation
interactions which results in ion pair formation or
modification of the anion-solvent interaction by the

i/l
25
Numoer of carbon atoms in the alkyl group
Figure 5: 79Br relaxation rates (from line widths) at 30C
for 0.500M aqueous solutions of alkylammonium
bromides. The different curves correspond from
the top to tetra, tri, di, and mono substituted
alkylammonium bromides. The y-intercept
corresponds to ammonium bromide. This figure was
obtained from reference 71.

26
hydrophobic cation. The observations tend to exclude direct
ion-ion interactions on the grounds that the change in the
relaxation rate is related to the change in the number and
length of the substituted alkyl groups, the lack of a
competition effect between differing halide ions, and the
presence of relaxation enhancement in uncharged solutes. In
addition, modelling studies of tetraalkylammonium systems
using an ion-ion interaction model failed to produce
reasonable results.69-71'76 With these considerations, it
is proposed that the mechanism for quadrupolar relaxation in
tetraalkylammonium halide systems is indirectly influenced
by the hydrophobic cation.
A natural extension of the substituted alkyl ammonium
halides studies is to look at micelle type systems, since
many of the substituted alkyl ammonium salts can form
micelles. Some of the major problems associated with
studying micelle systems are the drastic changes in phase
equilibria and the different micellar shapes that may
accompany the various composition of the micelle system as
shown in Figure 6. These problems result from the nature of
these amphiphilic substances (surfactants) which consists of
a hydrophilic part that is either charged or highly polar
and a hydrophobic part that is neutral, nonpolar, and
typically a long alkyl chains.82-84
The surfactants behaves as ordinary electrolytes at low
concentrations, but as the concentration increases they

27
Figure 6: Phase diagram of a ternary system composing of
hexadecyltrimethylammonium bromide (CTAB),
hexanol, and water, reference 84. L1 denotes a
region with water rich solutions; L2 a region
with hexanol rich solutions; D and E are lamellar
and hexagonal liguid crystalline phases,
respectively. In the figure are also
schematically indicated the structures of normal
(region) and reversed (L2) micelles as well as
liquid crystalline phases.

28
first form small complexes (dimers, trimers, etc.) then
form larger aggregates which are termed micelles and are of
colloidal dimensions. Micelle formation of long-chain
amphiphiles starts abruptly and is well defined by a given
concentration, the critical micelle concentration (cmc).
Concentrations that are well above the cmc often lead to a
transformation of the first formed micelle, approximately
spherical in shape to a very long rod shaped micelle. The
shape changes continue as the concentration reaches the
solubility limit for the surfactant. The possible formation
of liquid crystals can occur with different structures
depending on the composition of the system or the formation
of reversed micelles, aggregates with the polar phase as the
core and the nonpolar phase as the continuous environment.
Detailed studies of halide ion relaxation have been done
with micelle, reversed micelle, and liquid crystal
solutions.73'85-93 The results shown in Figure 7 are
typical of micellar solutions. Theoretical modelling of the
concentration dependence of the quadrupole relaxation for
these systems have been fit to a two site model.82'89'94
The model assumes that the halide appears in two forms, free
and attached to the micelle, the ratio between the
counterions and surfactant ions in the micelles is
independent of the concentration, and that the pseudo-phase
separation model of micelle formation applies. This
separation model treats the micelle formation as a phase

i/t2,
29
Figure 7: 79Br relaxation rates (from line widths) at 30C
for aqueous solutions of monoalkylammonium
bromide; o, 0.100M solutions; X, 0.500M
solutions. The upper two curves are an expanded
view of the lower two curves. The left vertical
axis belongs to the upper two curves. The scale
on the right vertical axis belongs to the lower
two curves (reference 71).

30
separation, with the cmc as the saturation concentration.
This two site model works well for a number of systems:86-88
CgH17NH3Cl, C8H17N(CH3)3C1, C16H33N(CH3) 3C1, CgH-^Nf^Br,
C10H21NH3Br' C9H19N(CH3)3Br, C10H21N(CH3)3Br,
C14H29N(CH3)3Br' C16H33N(CH3)3Br/ and decylpyridinium
bromide. Plots of the relaxation data versus the inverse of
the concentration give two straight lines like that shown in
Figure 8 with the intersection at the cmc for the system.
This value has been found to compare well with other methods
of determining the cmc.87 The model breaks down at high
concentrations of the surfactant. This deviation is
attributed to the transition of the micelle shape from
spherical to the rod shaped88 which leads to a much larger
surface area and alteration in the interactions that affect
the quadrupolar relaxation.
Reversed micelle studies show similar results to those
observed in the micelle studies as seen in the
cetyltrimethyl ammonium bromide, hexanol, and water
system.86,88'91'92 The halide relaxation rate is observed
to be independent of the hexanol concentration below a
critical value. As the concentration exceeds this value,
the relaxation rate increases at a greatly enhanced rate as
seen in Figure 9. It is believed that the halide ions
resides at the core of the micelle where they are highly
hydrated. The environment around the halide remains fairly
constant while the hexanol concentration is below this

31
35C1 relaxation rates (from line widths) as a
function of the inverse concentrations of
octyltrimethylammonium chloride (o) and
octylammonium chloride () at 28C, reference 87.
Figure 8:

32
Weight per cent hexanol
Figure 9: Observed 81Br relaxation rates (from line widths)
divided by that at infinite dilution in water for
solutions of hexadecyltrimethylammonium bromide
(CTAB) and water in hexanol (region L2 of the
phase diagram in Figure 6). The weight ratio of
CTAB to water was kept constant at 1.04 and 27C.
As a comparison the viscosity (r\) at 25"C
relative to that of pure water (r¡0) is shown (X),
reference 91.

33
critical value. Above this value, the increase in the
relaxation rate corresponds to the disappearance of the
reversed micelles and can be attributed to ion pair
formation.
To be consistent with the micelle and reverse micelle
modelling studies, the liquid crystal systems also use a two
site model in attempting to analyze the data.86'93 Liquid
crystal systems are more complex, but can also be broken
down to a two step process. The faster process corresponds
to local interactions inside the liquid crystalline phase.
The slower process spans the dimensions of the aggregates
and may be from micellar rotation, counterion or amphiphile
diffusion along the micellar surface, or intermicellar
counterion exchange. Studies to separate the contributions
of these two steps to the relaxation,71'86-88/91-96 all tend
to show that the slower process gives only a small and
mostly undetectable contribution. Different motional
processes should have different energies of activation,
therefore the similar activation energies shown in Table 1
for the various phases suggest that the same type of motion
is responsible for the relaxation found in all phases. In
support of this, a number of cases have shown that the
relaxations are frequency independent and intensity
consideration gives a correlation time describing the major
part of the relaxation at tc 10-8s (2 X 107 Hz).

34
Table 1
Energy of Activation for Bromide
Ion Quadrupole Relaxation in Surfactant Systems
Sample composition
percent by weight
Act. Energy
C16H33N(CH3)3Br H2 C6H13OH Phase kcal/mol
6.0
94.0
micellar
solution
6.5
24.0
76.0

micellar
solution
6.5
62.3
20.0
17.7
lamellar
mesophase
6.5
24.4
45.0
30.6
reversed
micellar
solution
7.5
40.0
10.0
50.0
reversed
micellar
solution
6.8
10.2
9.8
80.0
reversed
micellar
solution
6.5

35
The next logical step in the natural progression of
determining what influences quadrupolar relaxation is to
move from aqueous to mixed solvents and non-aqueous media.
This next step allows for changes in the solvent's dipole
moment, molecular size, dielectric constant, solvation
number, etc. to study the effects of ion pair formation, ion
solvation, complex formation, etc. Studies of alkali
halides show that the relaxation is mainly determined by
ion-solvent interactions where the correlation time of the
solvent plays an important role. In aqueous systems, the
relaxation is due to the motion of randomly oriented and
distributed point dipoles.97 For methanol
systems,57'58'69'98'99 the relaxation can be modelled to a
tightly packed first solvation sphere with radially oriented
dipoles. Modelling Br_ in dimethyl sulfoxide70'100 using a
distinct solvation sphere approximation gives results that
are higher than the experimental ones, suggesting that the
differences in the ion solvation from various solvents
should be of great interest in elucidating solvation
phenomena. The methanol and dimethyl sulfoxide studies also
suggest that ion pair formation gives a significant
contribution to relaxation, but in the dimethyl sulfoxide
case this effect does not explain the trend of the cations
as shown in Figure 10.

36
Figure 10: 79Br transverse relaxation rates (from line
widths) in non-aqueous and mixed solvent systems
as a function of electrolyte concentration
(reference 100).

EXPERIMENTAL
Time Domain Reflectometrv
A block diagram of the TDR setup is shown in Figure 11.
The TDR setup is composed of a Tektronix 7854 mainframe
oscilloscope with a waveform calculator, a 7S12 time domain
module, a S-52 pulse generator, and a S6 sampling head. The
sample cell is made from a 7 mm SMA male rebuild kit model
2542 from Midwest Microwave with the center post 1.5 mm in
length. The TDR is connected to the sample cell through
matched low loss 50 ohm impedance coaxial cables from W. L.
Gore models G3S0101078.0 and G3S0101072.0 which are 78.0 and
72.0 inches long, respectively. Communication with the TDR
is done through an IEEE-488 interface on the scope to a
RS232 interface on an IBM PC/AT using a Black Box model
232-488 interface converter.
The power-up sequence of the equipment is very
important. The Black Box converter unit must be turned on
last to eliminate communication handshake problems. Once
this protocol problem occurs, the Black Box converter and
the Tektronix scope must be shut down and powered up again.
The Black Box converter unit is the key to this problem, the
converter on power-up sends a request for service signal to
37

38
Figure 11: Block diagram of TDR setup.

39
the scope and waits for an answer, the scope when powered up
waits for a request for service signal and does nothing
until it receives this request. This mismatching of
communication protocol can be avoided as long as the Black
Box unit is the last piece of equipment to be turned on.
The scope needs to be powered up for at least six to
eight hours to ensure thermal stability of the electronics
(at least 24 hours if the system is moved or powered down
for more than three or four hours). Any control changes
other than calling up a cursor or using the waveform
calculator function will require the scope to sit idle and
equilibrate for a minimum of one hour. The system should
remain stable for at least one to one and a half hour before
any electronic drift can be detected after thermal
equilibrium is reached. Power fluctuations can introduce
random noise into the data lines between the scope and the
IBM PC/AT when the system is at idle. This noise is
introduced through the Black Box converter unit and can be
eliminated by keeping the Black Box unit powered down until
the system is ready for use. The remaining units should be
left powered up to minimize the system's required
stabilization time.
The theoretical limits of this TDR using the open
termination method are governed by the pulse generator in
this setup. The S-52 pulse generator has a risetime of
25 psec (time for the "half-life" of raising the voltage to

40
the rated value), a pulse size of 250 mV, a pulse width of
700 nsec, and a repetition frequency of 50 kHz. This gives
our TDR setup a theoretical upper and lower limit of
5 X 1010 Hz and 1 X 106 Hz from the risetime and pulse
width, respectively.
The actual use of the TDR starts with the adjustments of
the time-distance control. This control allows the
positioning of the window to be shifted to any portion of
the waveform (from the beginning just prior to the voltage
pulse being emitted to the end where the pulse potential
returns to ground). As one moves through the entire
waveform, four transitions are seen (Figure 12). The first
and second transitions are the incident and reflected steps
of the voltage pulse, respectively. The third and fourth
transitions are due to the voltage pulse returning to
ground. The part of the waveform (reflected step) that
contains the second transition through just before the third
transition contains all the information about the properties
of the sample. The time-distance control is set to observe
only the second transition with a small amount of the
baseline before the transition (typically 10% of the time
window).
The time window of choice is one where the second
transition takes up approximately half of the time window as
shown in Figure 13. This is easily accomplished by
adjusting the time/division control until the process fills

Voltage
41
Figure 12: Complete waveform obtained from the TDR. Step 1
is the incident pulse. Step 2 is the reflected
pulse. Step 3 is the incident pulse returning to
ground. Step 4 is the reflected pulse returning
to ground.

42
Figure 13: Process is observed in approximately half the
time window with the correct time window setting.

43
half the window. It is best to start with 50 nsec/division
(500 nsec window) and work towards 1 nsec/division (10 nsec
window) for new systems.
The use of time windows less than 5 nsec tends to have
problems in the Fourier transform routine. Temperature
instability of the various components causes timing and
electronic drift problems which leads to large errors in the
Fourier transform routines, imposing a practical upper limit
of 3 X 109 Hz on the system. A practical lower limit of
1.5 X 107 Hz is dictated by the manner in which the scope
collects data. This system is capable of collecting a
maximum of 1024 points with its largest window being
500 nsec. This gives spectral data in the range of
15 to 400 X 106 Hz for the 500 nsec window. This limited
range is determined by the width of the time window and the
resolution of data used in the Fourier transform. Several
windows are needed to cover the entire spectral range with
each overlapping window spanning a frequency range of
approximately 1.5 order of magnitude. A single time window
covering the frequency range of 1.5 X 107 to 3 X 109 Hz can
be obtained if the resolution of the collected data in this
500 nsec window is increased by at least one order of
magnitude (a minimum of 10,000 data points).
The voltage/division control setting is determined by
the size of the voltage pulse used. A setting of
50 mV/division is required for the 250 mV pulse outputted by

44
the S-52 pulse generator. For an empty sample cell, the
reflected pulse will have its greatest amplitude. The
reflected pulse for a perfect system (no loss) has an
amplitude that is twice the original inputted pulse. Our
TDR setup has a loss of approximately 10% through the
electronics and cables in the form of heat. The amplitude
of the reflected pulse also decreases when a sample is
introduced into the sample cell. The decrease in amplitude
is proportional to the DC conductivity of the sample.
Samples with DC conductivities greater than 0.01 mho/cm
will short circuit the TDR sample cell. Conductivities of
the samples can be obtained from the time domain data
collected on the TDR. The lower limit of the conductivity
that can be measured is 1 X 10-6 mho/cm. Conductivities of
less than 1 X 10-5 mho/cm have little effect on the spectral
data for the sample. Larger conductivities behave like
relaxation processes and need to be corrected for in the
imaginary component of the complex dielectric constant. The
real component of the dielectric constant is not affected by
DC conductivity.
Other problems that exist are the size of the static
dielectric constant, the ability to pack solid samples, the
volatility of liquid samples, and fringing effects. Samples
with static dielectric constants less than three have large
errors associated in their spectral data. Solids are a
problem because of the variability in packing of the sample

45
cell. The difference in the packing leads to irreproducible
values of the dielectric constant, but the frequency of the
various processes is not affected and can be reliably
obtained. In order to pack the cell properly, the solid
must be in the form of a fine powder with the particle size
in the micron range. Volatile samples have to be watched
carefully since heat is produced in the sample cell from the
power loss. The sample must cover the center post in the
sample cell because fringing effects can give some very
interesting looking distorted spectra. This effect can be
eliminated by burying the center post to a depth of at least
half the cell diameter.
The process of collecting the spectral data is simple
once the proper settings have been established for the TDR
setup. All waveforms are collected using signal averaging
to help reduce the random noise and drift problems. It has
been determined by trial and error that 100 signal averages
are reasonable for this TDR setup. Averages in excess of
100 help to reduce the random noise, but is offset by drift
problems. Waveforms of 1024 points in size should only be
collected for time windows greater than 50 nsec. Time
windows less than 50 nsec give distortion of the spectral
data when 1024 points are used. The drift problems show up
in the higher resolution spectra for the shorter time
windows. It has been determined that 512 points are
normally adequate to describe most samples in time windows

46
of 5 nsec and larger. The use of time windows less than 5
nsec is discouraged because the drift problems are highly
evident in such small time windows. The poor alignment
between the reference and sample gives irreproducible
distorted spectra.
A reference waveform is collected using the scope's
waveform calculator signal averaging function to establish
that the TDR is stable and to provide the Fourier transform
routine with a reference point. The reference waveform is
collected every five minutes until the difference between
the waveforms is less than 4 mV for the largest difference.
Sample waveforms are collected in a similar manner using the
same settings as the reference waveform. The sample needs
to equilibrate, typically one to three minutes, in the
sample cell after being introduced. This enables the sample
to reach equilibrium under the conditions of repetitive
excitation by the voltage pulse. The equilibrated sample
waveform can then be stored in one of the TDR's memory. The
TDR memory can hold nine waveforms of 512 points or three
waveforms of 1024 points.
Liquid samples are the easiest to handle and typically
take 15 to 20 minutes to collect data for seven different
samples using the same TDR settings. The reference waveform
is first taken then each of the samples is introduced into
the sample cell and their waveforms collected. Once the
reference waveform is taken, care must be used as not to

47
disrupt any of the connections between the cell and the TDR.
Disruption of these connections will invalidate the
reference waveform and sample data collected afterward will
be meaningless. Figure 14 shows a typical set of collected
raw data.
Solid samples take 30 to 40 minutes to collect data for
seven samples. The sample should be powdered (best if
particle size is 100 microns or less) to help eliminate the
nonuniformity in the packing when it is introduced into the
cell. There is a greater chance in disrupting the
connections in the setup during the sample removal process
especially when working with solids. It is best to take a
reference waveform for each solid sample to help minimize
the difference due to the disruption in the connections.
Tests with removing and reconnecting the sample cell to the
TDR setup shows significant shifts in the reference waveform
from one set of removing and reconnecting to the next set.
The collected data are then transferred to an IBM PC/AT
via a communication program listed in the Appendix. The
communication program is interactive and handles everything
from automated data collection to transferring the data to
the computer and setting up the data for use in the Fourier
transform routine. The transform routine is listed in the
Appendix and requires two files; the DIF file contains the
difference data between the reference and sample waveforms
while the SUM file contains the summed data (Figure 15).

Voltage
48
Figure 14: Raw time domain data for an air reference and a
sample of n-butanol.

Voltage
49
SUM
Figure 15: DIF and SUM time domain spectra for n-butanol.

50
The Fourier program takes these two time-domain files and
transforms them into a frequency-dependent complex
dielectric constant, as shown in Figure 16. The program
automatically handles all baseline corrections and data
smoothing.
The DIF and SUM files are used to obtain the DC
conductivity of the sample. The ratio of the values of the
tail for these two spectra after baseline correction, as
shown in Figure 15, is proportional to the value of the
101
conductivity, aQ (in esu units), UJ- according to
a
o
c
4nd
(8)
where c is the speed of light (3 X 1011 mm/sec), d is the
length of the center conductor of the sample cell in
millimeters, and are the difference between the tail
end value and the baseline for the DIF and SUM data,
respectively. The specific conductance, k is equal to
aQ/9 X 1011 which is the DC conductivity with units of
mho/cm, a more appropriate set of units for comparison to
literature. DC conductivity determined from the time-domain
data is within five percent of the value obtained from a
commercially available conductance meter (a YSI model 35
conductance meter with a YSI model 3403 conductivity cell).
The DC conductivity is then used to calculate the frequency

Dielectric Constant
51
Figure 16: Fourier transformed n-butanol spectra.

52
dependent conductivity correction values for the imaginary
component of the complex dielectric constant, as shown in
Figure 16, with
It
ecorr
ii
e
47T
a
w o
(9)
n
where ecorr and e" are the conductance corrected and
uncorrected imaginary components of the dielectric constant
at the angular frequency w, respectively.
Nuclear Magnetic Resonance
35C1 Nuclear magnetic resonance (NMR) spectroscopy was
done on a Varian VXR300 (300 MHz) spectrometer. The NMR was
tuned to the 35C1 nucleus. The solvated chloride ion from a
5 M aqueous solution of sodium chloride with a trace of D20
was used as the external reference for all 35C1 NMR spectra.
The NMR was setup for the majority of the Aliquat studies
using observation parameters of nucleus 35, frequency 29
MHz, spectral width 100 kHz, offset 400 Hz, acquisition time
0.005 sec, delay 0, pulse width 30 /isec, and transients
10,000, decouple parameters of nucleus 1.5, offset 584.7 Hz,
mode NNN, power 3 db, modulation mode S, frequency 9.9 kHz,
and pulse width 22.5 tsec, processing parameters of FN 64K,
line broaden 10 Hz and width 100 kHz, and the standard 13C
pulse sequence. Studies with large amounts of water used
the above parameters with these differences in the

53
observation parameters, acquisition time 0.15 sec, pulse
width 36 nsec, and transients 5000. The viscosity and
linewidth of the samples required the majority of spectra to
be manually phased.
Chemicals
Aliquat 336 (trioctylmethylammonium chloride) was
purchased from Aldrich and used without further
purification. Water with a resistivity of 15 megaohm/cm was
obtained from a Barnstead NANOpure filtration setup. All
other chemicals are of reagent grade and used without
further treatment. All solution concentrations are given in
mole fraction units.

RESULTS AND DISCUSSION
Alipliatic Alcohols
Binary System of Carbon Tetrachloride and n-Butanol
Carbon tetrachloride is a poorly coordinating, nonpolar
solvent with no permanent dipole moment. This solvent does
not give a dielectric spectrum in the frequency range of
2 X 107 Hz to 2 X 109 Hz. A constant complex dielectric of
one is observed for the real component and zero for the
imaginary component. The dielectric spectra of the binary
system of CC14 and butanol are shown in Figure 17. The
critical frequency, fc, for the dielectric relaxation of the
various solutions appears to remain constant at the fc
normally observed for neat butanol. The possible
interactions involved are CC14/CC14, butanol/CCl4, and
butanol/butanol. The former two CC14 interactions will not
influence the observed dielectric relaxation directly. The
main influence of dilution in CC14 is to decrease the
average size of the aggregate by shifting the equilibrium:
(C4H9OH)n > (C4H9OH)n_1 > C4H9OH (10)
toward the smaller species.
54

55
Log Frequency (Hz)
Figure 17: Frequency dependent imaginary component of the
observed complex dielectric constant for
solutions of n-butanol and carbon tetrachloride.

56
The static dielectric constant of a mixture of non
interacting systems is given by:102
es = NAesA + NBesB
(ID
Over the concentration range 0 to 100 mole percent butanol
in CC14, our results show that the intensity of the static
dielectric is not obeying this relationship (Figure 18).
The observed behavior suggests that the average molecular
weight of the aggregates is staying about the same over the
concentration range 70 to 100% butanol. At lower
concentrations of butanol, the deviation is that expected
for an increase in the concentration of the smaller
aggregates.
The frequency dependence of the real and imaginary
components of the dielectric constant is plotted versus the
log frequency in Figures 19 and 20. The data can be fit to
within experimental error with one average process to
equations (6) and (7) using a Simplex routine program listed
in the Appendix. The critical frequency is constant for the
range of 70 to 100% butanol. At higher dilutions, the
process becomes faster.
Neat butanol has a critical frequency of 3.4 X 108 Hz
with the peak spanning the range of 6 X 107 to 2 X 109 Hz.
This frequency range represents an overlap of the dynamic
process on a large number of aggregates in a three-

Static Dielectric Constant
57
Figure 18: Concentration dependence of the observed static
dielectric constant for solutions of n-butanol
and carbon tetrachloride. Equation (11) is
represented by the line for this system.

Absorption Mode of Dielectric Constant
58
20
18
1 6
1 4
12
10
8
6
4
2
0
i 1
7.5 7.7 7.9
8.1 8.3 8.5 8.7 8.9
Log Frequency (Hz)
9.1 9.3 9.5

Butanol

95.4 mole 7.

89.7 mole 7.

84.9 mole 7.
o
70.1 mole 7.

49.9 mole 7.
O
39.4 mole 7.
A
28.9 mole 7.
Theoretical
Butanol in CCU
Figure 19: Theoretical fit of the observed real component
spectra for solutions of n-butanol and carbon
tetrachloride.

59
c
o
o
c
D

co
O
o
o
_a>
a>
b
.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5

Butanol

95.4 mole 7.

89.7 mole 7.
A
84.9 mole 7.
O
70.1 mole 7.

49.9 mole 7.
O
39.4 mole 7.
A
28.9 mole 7.
Theoretical
Butanol in CCU
Log Frequency (Hz)
Figure 20: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
carbon tetrachloride.

60
dimensional dynamic network. The critical frequency
obtained is a complex average of the frequencies of all the
individual aggregates exchanging with each other. A summary
of the results of the fit of the complex components of the
frequency dependent dielectric constant is given in Table 2.
Both the average dielectric constant and analysis of the
frequency dependence of the complex dielectric constant
indicate that this distribution does not change appreciably
over the concentration range of 70 to 100% n-butanol in
CC14. In more dilute solutions, dissociation to produce
smaller aggregates results. The rate of butanol relaxation
in the smaller cluster is faster and the dipole moment
change is smaller. The latter effect leads to a non
linearity in the intensity of the entire complex dielectric
constant as shown for the static component in Figure 18.
Binary System of n-Propanol and n-Hexanol
This system was selected for study in order to
illustrate the influence that changes in the average
molecular weight of the mixed alcohol system have on the
frequency of the dielectric relaxation. The reported static
dielectric constants, the values obtained by us and the
observed critical frequencies for relaxation are summarized
in Table 3 for a variety of alcohols. The critical
frequency describes the rate at which the alcohol "tumbles"
in solution in the process of making and breaking hydrogen

61
Table 2
Butanol in Carbon Tetrachloride
Butanol
£<=
r x 10"6
100.0
s
18.6
2.2
340
95.4
17.6
2.4
344
89.7
16.8
2.7
335
84.9
15.8
2.7
335
70.1
12.6
2.8
340
49.9
7.2
2.5
414
39.4
4.8
2.1
504
28.9
3.6
2.5
698

62
Table 3
Primary Alcohols
Static Dielectric Constant
Alcohol
TDR
Lit.
fc x 10
Methanol*
33.2
32.7
Ethanol*
25.5
24.3
980
1-Propanol
21.8
20.1
490
1-Butanol
18.6
17.6
340
1-Hexanol
11.3
13.3
260
1-Octanol*
9.5
9.6
130
1-Decanol*
7.6
7.7
66
1-Dodecanol*
5.7
5.4
56
*Reference 103.

63
bonds. With comparable hydrogen bond strengths expected for
the alcohols listed (e.g. the -AH of hydrogen bonding of
ethanol and octanol to pyridine in CC14 are the same within
the 0.2 kcal mole-1 experimental error16'17), the frequency
differences are seen to be related to the average
composition of the solution.
In propanol-hexanol mixtures, the major interactions
involved are propanol/propanol, propanol/hexanol,
hexanol/hexanol. The frequency dependence of the imaginary
component (Figure 21) shows the change in the critical
frequency and the intensity of solutions for various mole
fractions of n-hexanol in n-propanol. The static dielectric
constant obeys Equation (11). The frequency dependence of
the real and complex dielectric constants obey Equations (6)
and (7) using two relaxation processes whose frequencies are
unchanged over the entire concentration range. When this is
the case, the intensity and critical frequency are mole
fraction averages of the pure components:
fc = xAfcA + xBfcB <12)
The critical frequencies for the neat alcohols and the
various alcoholic mixtures are summarized in Table 4. These
results indicate that the clusters are composed of a mixture
of alcohols and the rate of rearrangement of propanol on a
mixed cluster is the same as the rate on a propanol cluster

64
Log Frequency (Hz)
Figure 21: Frequency dependent imaginary component of the
observed complex dielectric constant for
solutions of n-propanol and n-hexanol.

65
Table 4
n-Hexanol and n-Propanol
Hexanol
CM
CM
r x 10
0
s
21.8
493
31
18.5
2.2
431
55
15.8
2.2
345
80
13.8
2.2
315
100
11.3
1.8
263

66
and that of hexanol on the mixed and pure clusters is the
same. This is consistent with the hydrogen bond strengths
being similar and the dynamic process being dominated by the
molecular size of the moving group with the average size of
the aggregates being comparable to the average size in the
neat liquids.
Binary System of n-Butanol and Pyridine
This system provides the opportunity to examine the
perturbation made on butanol aggregation by the addition of
strong donor molecules. Pyridine has a relaxation frequency
that is faster than can be observed in our apparatus. Thus,
the main interactions that will influence the spectrum are
butanol/pyridine and butanol/butanol.
The dielectric spectra of various solutions of butanol
and pyridine are shown in Figures 22 and 23. The critical
frequency of these solutions shifts to higher frequencies as
the mole fraction of the pyridine is increased. The data
are fitted to Equations (6) and (7) with a single r value
that increases with pyridine concentration, summarized in
Table 5. The greater influence of pyridine compared to CC14
is shown in Figure 24. The single peak indicates that the
distribution of processes occurring is shifted toward faster
rates of relaxation with a decrease in the intensity of the
response. The direction and non-linear behavior of the
static dielectric constant and the critical frequency

Absorption Mode of Dielectric Constant
67
20
0 11* *-
7.5 7.7 7.9
1.1I i I i I
8.1 8.3 8.5 8.7 8.9
Log Frequency(Hz)
9.1
9.3 9.5
Figure 22: Theoretical fit of the observed real component
spectra for solutions of n-butanol and pyridine.

68
10 r
9
c
o
'-t'
o
c
3
Li-
CO
CO
O
O
a>
b

5.0 mole 7.

9.9 mole 7.
A
1 5.1 mole 7.

50.4 mole 7.
X
49.5 mole 7.
O
Pyridine
Theoretical
Pyridine in Butanol
1
0
7.5 7.7 7.9 8.1
8.5 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.5 9.5
Figure 23: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
pyridine.

69
Table 5
Pyridine and Butanol Systems
BuOH/py
%CC14
%Pv
3l Buon
ratio

5.0
95.0
20
58.0
1.9
40.1
20

9.9
90.9
10
55.8
4.0
40.2
10

15.1
84.9
6
54.2
6.8
39.0
6

30.4
69.6
2
43.3
16.9
39.8
2

49.5
50.5
1
20.6
39.8
39.6
1
s
£<*>
T X 10~6 Hz
18.2
2.6
407
5.0
1.4
524
17.5
3.6
546
5.2
1.2
630
17.3
3.4
716
6.4
1.8
778
16.5
4.2
1364
8.3
2.4
1245
15.7
4.7
2624
11.9
3.5
2845

Critical Frequency X 1 0-6 Hz
70
Mole 7. Solute in n-Butanol
Figure 24: Comparison of the critical frequencies obtained
for the pyridine and carbon tetrachloride
systems.

71
suggest a decrease in aggregate size as pyridine is added to
butanol. The initial increments of added pyridine hydrogen
bond to terminal OH groups of butanol aggregates with only
minor changes in the dielectric spectrum. As the mole
fraction of pyridine increases, clusters must be broken in
order to provide hydrogen coordination sites for pyridine
causing the average f_ to shift to a higher frequency. One
can view the three dimensional nature of the alcohol adducts
as arising from the fact that two oxygen lone pairs of a
given molecule function as coordination positions for
protons of other molecules, while its hydrogen functions as
an acid site to another alcohol. The system is one hydrogen
short (as a consequence of the R group) of the tetrahedral
nature of a water molecule in a water structure and the
aggregate is not as stable. When a base coordinates to the
acid site of an alcohol molecule, one additional site for
chain growth is removed and the tendency to form a 3-D
structure is decreased.
Ternary System of Carbon Tetrachloride. n-Butanol. and
Pyridine
The relaxation processes are investigated for solutions
of -40% butanol in CC14 to which pyridine is added. A
similar trend in the frequency with increased concentration
is observed as shown in Table 5. The 50% composition which
would correspond to the 1:1 adduct shows similar behavior in
neat butanol and in CC14. Taking the dilution factor into

72
consideration, the static dielectric constant gives a
comparable value for the adduct in CC14 and that made in
neat butanol. No new relaxation processes are observed in
CC14 and the behavior is similar to that for neat butanol.
The variation in cluster size when butanol is diluted in
CC14 is small compared to pyridine addition as seen in
Figure 24.
Surfactant Systems
Binary. System of n-Butanol apd Aliguat 336
The conductivity of the Aliquat solutions (Figure 25)
increase as the concentration of the Aliquat is increased.
The maximum conductivity of this system is found at 10.0%
Aliquat followed by a steady decrease at the higher
concentrations of Aliquat. The conductivity levels off at
about 50.0% Aliquat to the value observed for neat Aliquat.
The increase in the conductivity at low Aliquat
concentrations is that expected for a simple salt being
dissolved. The conductivity of dissolved salts increase
with concentration and then level off as the solubility
limit is reached. The deviation from this behavior suggest
that the Aliquat is ion-paired with aggregation taking place
at the higher concentrations. This effect is even more
dramatic in solvents like methanol and water, where the
conductivity of the dilute Aliquat solution is 25 times

DC Conductivity X1 05 mho/cm
73
Figure 25: Concentration dependence of the observed DC
conductivity for solutions of Aliquat 336 in
n-Butanol.

74
larger than in butanol. Sodium chloride in these solvents
has a five fold difference in solution conductivity. The
conductivity of aqueous sodium chloride solutions is
attributed to the migration of ions that are formed in a 1:1
ionic system. The observed lower conductivity of sodium
chloride in butanol suggests that the sodium chloride is
ion-paired. The difference in the solution conductivity of
the various solvents indicates that Aliquat becomes highly
ion-paired in solvents like butanol with the solution
conductivity arising from Aliquat's ability to migrate in
solution. At low concentrations, the number of Aliquat
molecules determines the solution conductivity. At
approximately 10% Aliquat, aggregation begins to occur,
lowering Aliquat's mobility by increasing the aggregate size
and decreasing the total number of mobile aggregates found
in solution.
The 35C1 NMR line width, full width at half height, of
Aliquat/butanol solutions are shown in Figure 26. The line
width remains constant for solutions with less than 5.0%
Aliquat. At higher concentrations of Aliquat, the line
width increases with increasing concentration. This type of
behavior is indicative of systems that form micelles. The
break point in the 35C1 NMR line width is the critical
micelle concentration, cmc,87 where a transition in
structure is made from simple monomeric and dimeric ion-
pairs to higher order aggregates. The cmc for Aliquat in

NMR Line Width (Hz)
75
Figure 26: 35C1 NMR line widths obtained for solutions of
Aliquat 336 in n-Butanol.

76
butanol is about 10% which corresponds well with the
conductivity studies.
The dielectric spectra for the Aliquat/butanol system
shown in Figures 27 and 28 can be fit to equations (6) and
(7) with a single process (Table 6). The intensity of the
static dielectric constant shows a similar trend to that
observed in the 35C1 NMR studies (Figure 29) with the cmc at
about 15% Aliquat. The spectra show that virtually all the
processes in our time window are nonexistent when the
concentration of the Aliquat exceed 15%. The critical
frequency remains fairly constant over the concentration
range of 0 to 15% Aliquat. Lindman et al.94 has proposed
that the solvent molecules exists in two states: bulk
solvent molecules and micelle incorporated solvent
molecules. These results support the proposal that the
Aliquat is coordinating to butanol and removing it out of
the bulk solvent leading to a decrease in the intensity of
the static dielectric constant. The presence of the Aliquat
does not influence the bulk solvent, thus the aggregate size
distribution is similar to that observed in neat butanol
leading to a constant value for the critical frequency over
the 0 to 15% Aliquat concentration range.
Butanol has three possible coordination sites: two lone
pairs on the oxygen and the hydrogen on the OH group.
Pyridine coordinates through the OH hydrogen leaving the two
lone pair sites available, limiting butanol's ability to

Absorption Mode of Dielectric Constant
77
20 r
18
1 6 h
1 4
1 2
10
8 h
6
4
2
0
B § Q

1.0 mole 7.

5.0 mole 7.
A
7.5 mole %

1 0.0 mole %
O
1 5.0 mole %

30.0 mole 7
A
50.0 mole %
o
Aliquat 336
Theoretical
Aliquat in n-Butanol
oooooooooooooooooooo
7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)
Figure 27: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336 and
n-butanol.

78
10
9
c
o
o
c
D
en
en
o
8
7
6
5
o
*i_
A->
<_>
_CL>
QJ
h
4
3
2
1
0 -
7.5

1.0 mole 7.

5.0 mole 7.

7.5 mole 7.

1 0.0 mole %
o
1 5.0 mole %

30.0 mole %
A
50.0 mole 7.
o
Aliquat 336
Theoretical
Aliquat in n Butanol
7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)
Figure 28: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336
and n-butanol.

79
Table 6
Aliquat 336 in n-Butanol
% Alicmat
e_
r X 10"
0.5
S
19.4
3.8
330
1.0
20.0
5.1
313
2.5
19.8
6.1
284
5.0
16.8
6.4
287
7.5
14.2
6.5
312
10.0
12.8
6.9
350
15.0
7.9
3.5
365
20.0
7.8
4.3

30.0
7.0
5.1

50.0
6.4
4.8

100
3.0
3.0
_ _

Static Dielectric Constant
80
Mole 7. Aliquot 336 in n-Butanol
Figure 29: Concentration dependence of the observed static
dielectric constant for solutions of Aliquat 336
and n-butanol.

81
form large three-dimensional dynamic network type structures
normally found in neat butanol. The average size of the
butanol cluster decreases with pyridine concentration. This
is manifested in the change of the observed critical
freguency; increased critical freguency with increased
concentration of the pyridine. In comparison, Aliquat and
butanol show no change in the observed critical frequency
suggesting that the aggregate size for butanol remains
fairly constant. We propose that Aliquat is extracting
butanol from the bulk phase without modifying the properties
of the remaining bulk butanol phase. This literately
removes the entire butanol molecule out of the bulk solvent
and has no influence on the aggregation of the bulk butanol.
The model can be simplistically described as consisting of
two separate non-interacting microscopic phases. The
butanol in the Aliquat phase has its relaxation modified, so
it is no longer observed in our time window; i.e., the
critical frequency is either decreased or increased.
Ternary System of Carbon Tetrachloride. n-Butanol, and
Aliauat 336
The relaxation processes observed in the binary system
of Aliquat and butanol are investigated in the ternary
system formed by the addition of CC14. Carbon
tetrachloride, a nonpolar, poorly coordinating solvent can
bring about some interesting modifications in the butanol-
Aliquat interactions. It will dilute the system and lower

82
the intensity of the butanol/butanol interactions enabling
us to detect other processes. Furthermore, one can compare
the competition between CC14 and butanol for the hydrophobic
region of Aliguat. The dielectric spectra for various
solutions of approximately 40% butanol in CC14 are shown in
Figures 30 and 31. The spectral data can be fit to a single
process for mole ratio greater than 100/1 butanol to
Aliguat. This single process is that normally observed for
a binary system of butanol and CC14, summarized in Table 7.
The aggregate size of the diluted butanol is smaller than
that normally found in neat butanol; correspondingly, a
larger value is observed for the critical freguency. Two
processes are required to fit the observed spectra for mole
ratios ranging from 13/1 to 100/1 (Table 7) with the fast
process7 critical frequency remaining fairly constant. The
intensity of the slower process increases with increasing
Aliquat with the critical frequency remaining constant. The
spectral data shows that the tail end of the slower process
is just appearing inside the lower frequency range of our
time window, the values obtained for this process are the
upper limit for the critical frequency and the lower limit
for the static dielectric constant. We can only estimate
this slower process from the perturbation made on the
butanol spectrum. When the butanol relaxation disappears,
we lose our probe for estimating the slower process's
critical frequency and static dielectric constant. At high

Absorption Mode of Dielectric Constant
83
7.5
6.0
4.5
3.0
1 .5
0.0


No Aliquat

130/1
A
80/1

40/1
O
20/1

13/1
A
5.7/1
Theoretical
Butanol/Aliquat Ratio
7.5 7.7 7.9 8.1
8.3 8.5 8.7 8.9
Log Frequency (Hz)
9.1
9.3 9.5
Figure 30: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and carbon tetrachloride.

Dielectric Loss Function
84
0.0

No Aliquat

130/1

80/1

40/1
0
20/1

13/1
A
5.7/1
Theoretical
Butanol/Aliquat Ratio
7.5 7.7 7.9
8.1 8.3 8.5 8.7 8.9
Log Frequency (Hz)
9.1 9.3 9.5
Figure 31: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and carbon tetrachloride.

85
Table 7
Ternary System of
Aliquat 336, n-Butanol, and Carbon Tetrachloride
% Composition
Alia/BuOH/CCl4
BuOH/Aliq
ratio
S
1
X 10"6
^1
HZ
2
0.0/40.0/60.0

4.4

1.4

409
0.1/40.1/59.8
400
4.6

1.3

410
0.3/40.2/59.5
130
4.6

1.3

382
0.5/40.0/59.5
80
5.8
4.0
1.3
71
488
1.0/40.4/58.6
40
6.5
4.1
1.5
77
459
2.0/39.5/58.6
20
7.2
4.0
1.6
75
451
3.1/39.9/57.0
13
8.0
4.1
1.9
62
459
4.0/39.8/56.2
10


2.2


7.1/40.2/52.7
6


2.3


16.9/40.3/42.8
2


2.4


39.7/40.5/19.8
1


2.3



86
concentrations of Aliquat, mole ratios less than 10/1, we
can only observe the tail end of this slow process in our
time window. The spectra show only a sloping baseline with
no discernible features.
The intensity and critical frequency of the fast process
are constant over the butanol/Aliquat mole ratio range of
13/1 to no Aliquat. In neat butanol, Aliquat can extract
butanol molecules out of the bulk phase without influencing
the properties of the bulk phase. A constant critical
frequency and decreasing intensity of the butanol relaxation
occur with increasing Aliquat concentration. The observed
trends of this ternary system suggest that the concentration
and aggregate size of the butanol species in CC14 are not
influenced by the addition of Aliquat. The constant
intensity of the butanol relaxation results from the CC14
interfering with the extraction of butanol by Aliquat. This
implies that the butanol is extracted into the hydrophobic
region of Aliquat in neat butanol solutions. Since CC14 is
normally preferred over butanol in hydrophobic interactions,
the butanol in this ternary system is left in the bulk and
is unaffected by the addition of Aliquat. The presence of
the slow process suggests that butanol is coordinating to
the hydrophilic region of Aliquat at mole ratios of butanol
to Aliquat less than 100/1. The intensity of the slow
process increases with increasing Aliquat concentration
indicating a large change in the dipole moment. The simple

87
addition of butanol to Aliquat should produce a species that
has a larger dipole moment. The increasing intensity of the
slow process corresponds to this increase in dipole moment.
At present, no further conclusions can be drawn on this
slower process.
Binary System of n-gutanoj and Water
Mixed solvent systems have many uses, their applications
range from solubility enhancement, product or impurity
extraction, to reactions occurring at the interface between
two immiscible solvents. The system of butanol and water is
studied in order to obtain a fundamental understanding of
the processes found in a mixed solvent system. All
solutions less than 40% water are homogeneous. A brief
period of cloudiness was observed during the preparation of
the 40% water solution. The 50% water solution remains
cloudy for several hours after being agitated. Solutions in
excess of 50% water separate into a distinct two phase
system. The dielectric spectra of these various solutions
of butanol and water are shown in Figures 32 and 33. The
intensity of the static dielectric constant and the critical
frequency increase with increasing water concentration. The
butanol phase of the solutions with greater than 50% water
show no additional changes in the dielectric spectra. The
spectra can be fitted to a single process, summarized in
Table 8. The observed results at low water concentration

Absorption Mode of Dielectric Constant
88
35
30
25
20
1 5
10
0
7.5 7.7 7.9 8.1
8.3 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.3 9.5
Figure 32: Theoretical fit of the observed real component
spectra for solutions of n-butanol and water.

89
c
O
o
c
D
Li
en
en
O
_i
ej
<
0)
b
10
9
8
7
6
5
4
3
2
1
0

1 0.0 mole 7.

25.1 mole 7.

37.7 mole 7.

50.6 mole 7.

60.1 mole %
Theoretical
H2O in Butanol
7.5 7.7 7.9 8.1
8.3 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.3 9.5
Figure 33: Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol and
water.

90
Table 8
Water in n-Butanol
% Water es r X 10~6 Hz
10.0
18.3
2.2
423
25.1
19.1
3.1
669
37.7
20.4
4.1*
912
50.6
23.0
5.3*
1271
60.1
30.6
10.4*
1478
High values of indicate that a faster process exist
outside of our time window. This value of is not the
value normally observed for a single process system.

91
show the same trends as that observed in the pyridine-
butanol system. The aggregates of butanol are broken apart
by the coordination to pyridine. As the concentration of
pyridine is increased, the system's behavior moves from the
characteristics of neat butanol to neat pyridine indicated
by the changes in the intensity of the static dielectric
constant and the critical freguency. At high water
concentrations, the system deviates in behavior to that
observed for the pyridine system. The change in the static
dielectric constant is similar to that found for pyridine,
but the change in the critical freguency is much less than
expected. An obvious difference between pyridine and water
is that a two phase system is observed for water, but not
for pyridine. The structure for neat pyridine is different
to that observed for neat butanol or water. Pyridine forms
a stacked structure through the interaction of the rings.
Both butanol and water form three-dimensional dynamic
network structures through H-bonding of the hydrogen on the
OH group to the lone pairs on the oxygen. Water is more
efficient at forming this dynamic structure because of the
tetrahedral geometry that the water molecule can assume in
this network structure compared to butanol which is short
one hydrogen (as a conseguence of the R group) to form the
tetrahedral geometry. At low concentrations of water, the
overall dynamic structure of the butanol is maintained and
results in a homogeneous system. As the concentration of

92
water increases, the composition of the aggregate changes
from pure butanol to a 1:1 butanol/water aggregate. This
1:1 aggregate is manifested in a constant dielectric spectra
observed for the butanol phase for solutions with water
greater than 50%. The addition of water beyond the 50%
water region forces the formation of water aggregates,
leading to the formation of the second phase.
Ternary System of Water, n-Butanol. and Aliquat 336
Many practical applications of Aliguat 336 have involved
the use of agueous media. In general, little is known about
the interactions that occur with phase transfer agents like
Aliguat 336. Many of the applications are optimized through
trial and error type technigues. A fundamental
understanding of the competition and interactions of water
and butanol for the various sites on Aliguat can enhance and
widen the applicability of this class of compounds. The
relaxation processes of a 10% Aliguat in n-butanol solution
with varying amounts of water added are investigated. The
solutions are homogeneous up to 50% water. The 50% water
solution shows two phases with a third observed for
solutions of higher water concentration. The two phase
system is the separation of the water and butanol phases.
The third phase (a precipitate) shows up in solution with
water greater than 50% is Aliquat. The dielectric spectra
for these solutions are shown in Figures 34 and 35. The

Absorption Mode of Dielectric Constant
93
Log Frequency (Hz)
Figure 34: Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and water.

94
7.5 7.7 7.9 8.1
8.3 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.3 9.5
Figure 35: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and water.

95
spectra data can be fitted to two processes, summarized in
Table 9. The observed critical frequency for the two
processes are fairly constant for solution less than 40%
water. The faster process's dielectric intensity (e-j^ ew)
increases with increasing water concentration. The slow
process has a lower critical frequency than that found for
Aliquat in neat butanol with a constant dielectric intensity
(eg e-j^). As water concentrations increase, above 40%, the
critical frequency for both processes increase with the slow
process increasing at a slower rate. The butanol phase of
solutions that is in excess of 80% water gives dielectric
spectra similar to those observed in the greater than 50%
water in neat butanol. This behavior suggests two possible
sites: a hydrophobic site for the butanol and a hydrophilic
site for the water. The slow process describing the butanol
aggregate suggests that the concentration and aggregate size
of the butanol is remaining constant in the hydrophobic
region of Aliquat and does not compete with water for the
hydrophilic region. The fast process's critical frequency
is similar to that observed for a solution of 40% water in
neat butanol suggesting that the water aggregate size is
approximately that observed in the butanol/water system.
The change in the fast process's intensity indicates that
the change in dipole moment in this ternary system is much
smaller than that of the butanol/water system. High
concentrations of water causes Aliquat to undergo a

96
Table 9
Water in a Solution of 10% Aliquat 336 in n-Butanol
% Water
1
X 10
*1
6 Hz
2
0.0
8.9

2.8
295

10.3
9.3
4.7
2.0
234
1047
21.5
10.8
6.6
2.5
213
1061
30.2
12.1
8.0
3.0
216
1088
40.0
13.7
8.6
3.3
343
1688
51.2
16.9
10.6
3.6
356
2223

97
structural transition from micelles to some other aggregate
form that is insoluble in this system. The Aliquat is
stripped from solution, converting this ternary system into
a binary butanol/water system. This transformation changes
the concentration of Aliquat found in the butanol phase as
indicated in the increase of the critical frequencies of the
two observed processes.

TDR SYSTEM ENHANCEMENTS AND MODIFICATIONS
Studies of various systems have indicated two
limitations of the current TDR setup. The frequency range
and the detection limit need to be addressed to enhance the
usefulness of TDR. The frequency range limits the TDR to
studying systems which have processes with rates similar to
those found in polar liquids. The detection limit of the
TDR require that the system's static dielectric constant be
greater than 3. There are many other interesting systems
like polymers and micelles that do not fit these
requirements.
The detection limit arises from the size of the voltage
pulse, the noise level of the signal, and the manner in
which the data is handled in the Fourier analysis. The
sensitivity can be increased by increasing the size of the
voltage pulse to obtain larger responses through a larger
excitation source. The present size of the voltage pulse is
0.25 V and can be increased to 0.5 V without any
difficulties. Large voltage pulses can cause the sample to
experience a phenomena called dielectric breakdown. This is
the decomposition of the sample through oxidation/reduction
type pathways. The commercial availability of pulse
98

99
generators that have larger than 0.25 V potential is limited
to generators that have risetimes in the nanosecond range,
reducing the upper frequency limit to about 108 Hz. The
fast risetime pulse generators (faster than 25 psec) are
typically custom designed components and must be
specifically designed for a system (commercial availability
is questionable).
The minimal noise level for the current TDR setup is
2 mV with a typical noise level of 5 to 10 mV. A pulse size
of 0.25 V gives a signal to noise ratio (S/N) of about
100/1. The noise comes from several sources: a glitch in
the power supply, electronic drift, reflections from
impedance mismatches in the connectors, loose connections,
temperature variations, etc. Samples with a large static
dielectric constant show little effect from these noise
sources due to the large response of the sample to the
voltage pulse. The problem arises in samples with a
dielectric constant below 3, where the response is about
30 mV in size with noise in the 10 mV range. The obvious
solution is to eliminate as many of the noise sources as
possible, but one can only go so far in this regard. There
is not much that can be done about the electronic drift, the
temperature variations inside the oscilloscope, the
impedance mismatches in the internal circuits, etc.
Attempts at using a two channel system to help offset some
of these problems has lead to the appearance of artifacts in

100
the spectral data. These artifacts arise from the power
splitter that is used to send the voltage pulse to two
separate cells (one reference, one sample). The splitter
has a tendency to set up a resonance feedback from the
repetitive excitation of the voltage pulse. This feedback
creates artifacts in the high frequency end of the TDR and
distorts the remaining portions of the spectra. The
required specifications for this power splitter limits the
availability of this device from alternative sources.
Several difference units have been tried with similar
results.
The best solution for handling this noise problem is in
the software manipulation of the data. The smoothing and
baseline correction routines used in the Fourier analysis
play an important role in this sensitivity problem. These
routines are used to distinguish between the noise in the
baseline and the observed processes. Systems with small
static dielectric constants are significantly affect by
these smoothing and baseline correction routines. The
spikes and discontinuities in the baseline can be mistaken
for processes, resulting in greatly distorted frequency
domain spectral data. The spikes can be handled by most
smoothing routine with a minimal amount of problems. The
discontinuities in the baseline are more difficult to
handle. The current routines used for the data smoothing
and baseline correction do not contain algorithms to handle

101
this type of noise. The addition of a manual baseline
correction routine would be the easiest and most versatile
in correcting this discontinuity problem. The manual
correction routine should allow the study of systems with
static dielectric constant as low as 1.5 with the current
TDR setup.
The maximum frequency range of the TDR is determined by
the pulse generator in the system. Two pulse generator
characteristics govern the frequency range of the system,
the risetime and the pulse width. The risetime determines
the upper limit, while the pulse width determines the lower
limit. Current commercial technology can produce a pulse
generator with a risetime of about 1 psec, which gives a
realistic upper limit of 8 X 1010 Hz. The pulse width can
be set to virtually any value, thus removing the lower
limit. In generally, the lower limit of the pulse generator
is matched to the ability of the sampling device.
Commercially available pulse generators are broken down into
two categories: 1 to 100 psec and 1 to 5 nsec risetime pulse
generators. The fast risetime generators typically have
fixed pulse widths of a microsecond or shorter. The slow
pulse generators have variable pulse widths that can be set
from microseconds to seconds.
The Tektronix TDR setup is designed to use the fast
risetime pulse generators. The acquisition of real time
modules is required to use pulse generators with wider pulse

102
widths. The delay lines used in the current setup will be
inadequate for wider time windows. The delay line is used
to offset the incident and reflected steps observed for the
voltage pulse. Assuming that the speed of light in a
coaxial cable is 3 X 108 m/sec and a time window wide enough
to see a process with a fc of 1 X 104 Hz will require a
cable of 1,640 feet in length to offset the incident and
reflected pulse by 5% of the time window. This offset is
important, it is used as the baseline for the observed
waveform.

CONCLUSIONS
Time domain reflectometry is a useful technique in
understanding the fundamental interactions found in
solvation processes. Molecular size and adduct bond
strength have been seen to play important roles in solvation
processes. The mixed alcohol studies help to define the
dependence of the relaxation processes to the size of the
molecules. The statistically weighed averaging of the pure
alcohol critical frequencies and peak intensities allows the
prediction of these characteristics for any binary and
ternary alcohol systems using any primary alcohol from
ethanol to octanol. The pyridine, water, and carbon
tetrachloride in n-butanol studies have shown how the adduct
formation can affect the solvation process. In the case of
pyridine, the butanol aggregates are broken apart by the
coordination of the pyridine. The water which has a similar
dynamic structure to that observed for butanol does not
significantly affect the behavior of butanol at low
concentrations. Higher concentrations of water produce
behavior that is vastly different to that observed for
pyridine. In addition, the behavior does not resemble that
of neat butanol or water suggesting that both the butanol
103

104
and water take on new properties in the formation of this
butanol/water adduct. These new properties do not change
even under the conditions where phase separation of the
butanol and water take place. With carbon tetrachloride,
virtually no interactions are observed compared to the other
systems studied here. The only effect seen is the buffering
ability of the individual CC14 molecules to separate the
other interacting centers apart, lowering the butanol
concentration to prevent the formation of large aggregates.
Combining halide guadrupole NMR studies with TDR
observations have led to a better understanding of the
fundamental interactions found in solutions of Aliquat 336.
The Aliquat molecule is found to be highly ion-paired even
in a polar solvent like n-butanol. The mobility of Aliquat
in butanol is unhindered at low concentrations but at a mole
fraction of 0.10, Aliquat begins to form aggregates.
Different forms of these aggregates are seen under the
various conditions of mixed solvents with differing
properties. Various solvents are observed to interact at
different sites found in Aliquat. Alcohols like n-butanol
can interact with both the hydrophobic and hydrophilic sites
but prefer the hydrophobic site in neat solvent. The
introduction of a nonpolar solvent like CC14 forces the
butanol out of the hydrophobic region and into the
hydrophilic region of Aliquat, whereas water interacts with

105
the hydrophilic region and leaves the butanol alone in the
hydrophobic region.
These studies have shown some of the limitations of our
current TDR setup. The most cost effective modification is
to change the smoothing and baseline routines in the Fourier
analysis. This should increase the sensitivity of the
instrumentation and allow systems with low static dielectric
constants like polymer solutions to be studied. The next
most important change is to extend the frequency range of
the instrument. This is a high cost type modification and
involves the acquisition of real time modules for the
Tektronix oscilloscope. In addition to these modules, a new
delay line is required. A low loss coaxial cable is
essential since the cable length needs to be in the 1000
feet range. Signal loss through such a length would be
tremendous, requiring extreme care in the selection of the
cable. With these enhancements, the studies involving
Aliquat, butanol, and water should be repeated. The
combination of a lower detection limit and wider frequency
range can enhance the fundamental understanding of the
interactions of butanol in the hydrophobic region of
Aliquat. Extension of these studies to longer alipliatic
alcohols and nonpolar solvents like hexane and cyclohexane
can be beneficial in the understanding of the fundamental
chemistry of micellar systems.

APPENDIX
COMPUTER PROGRAMS
Program TDR.BAS
This program was written using Microsoft QuickBasic
version 4.5. The program is designed to run interactively
using a character based interface. This program is used to
interface the Tektronix 7854 oscilloscope to an IBM
compatible personal computer for the purpose of downloading
data collected from the TDR system. The program can
automatically collect and form data files for the Fourier
transform routine.
106

107
DEF FNAN$
1 AZ$ = UCASE$(INKEY$)
IF AZ$ = "" GOTO 1
FNAN$ = AZ$
END DEF
DEF FNINP$
LINE INPUT L$
FNINP$ = UCASE$(L$)
END DEF
DEF FNWAIT (SEC)
STARTING! = TIMER
FINISH! = STARTING! + SEC
IF FINISH! > 86400 THEN
DO UNTIL TIMER = .1
LOOP
FINISH! = STARTING! + SEC 86400
END IF
DO UNTIL TIMER > FINISH!
LOOP
FNWAIT = 1
END DEF
DIM FILENAME$(10), SAMP(10), HEAD$(25)
BLK$ = SPACE$(35)
COM$ = ""
LCOM$ = ""
GOSUB MAINSCREEN
10 LOCATE 5, 3
COM$ = FNINP$
LOCATE 5, 3
PRINT BLK$
LINLEN = LEN(COM$)
IF LINLEN < 2 GOTO 10
IF LINLEN >35 THEN
LOCATE 5, 3
PRINT BLK$
LOCATE 5, 3
PRINT "TOO MANY COMMANDS"
LOCATE 23, 35
PRINT "Any key to continue"
ANY$ = FNAN$
GOSUB MAINSCREEN
GOTO 10
END IF
LCOM$ = COM$
IF COM$ = "DIR" THEN
GOSUB DIR
GOSUB MAINSCREEN
GOTO 10
END IF
IF COM$ = "EXIT" OR COM$ = "QUIT" GOTO 9999
IF COM$ = "HELP" THEN
GOSUB HELP

108
GOSUB MAINSCREEN
GOTO 10
END IF
IF COM$ = "SERIES" THEN
GOSUB SERIES
LCOM$ = "SERIES completed"
GOSUB MAINSCREEN
GOTO 10
END IF
IF COM$ = "TIMED" THEN
GOSUB TIMED
LCOM$ = "TIMED SERIES completed"
GOSUB MAINSCREEN
IF ENDD$ = "Y" THEN GOTO 9999 ELSE GOTO 10
END IF
FOR I = 1 TO LINLEN 4
IF INSTR(COM$, "SENDX") > 0 THEN
CLS
LOCATE 10, 2
PRINT "Filename to save data in?"
LOCATE 10, 30
NAME$ = FNINP$
NLEN = LEN(NAME$)
IF NLEN = 0 OR SPACE$(NLEN) = NAME$ THEN
LOCATE 10, 30
PRINT BLK$
GOTO 90
END IF
GOSUB MAINSCREEN
GOSUB SENDTDR
LOCATE 9, 3
PRINT BLK$
LOCATE 9, 3
PRINT LCOM$ + completed"
GOTO 10
END IF
NEXT I
GOSUB COMTDR
LOCATE 9, 3
PRINT BLK$
LOCATE 9, 3
PRINT COM$ + was sent"
GOTO 10
9999 END
COMTDR:
OPEN "COMI:9600,N,8,1,RB10000" FOR RANDOM AS 1
PRINT #1, "RQSON"
XYZ = FNWAIT(l)
PRINT #1, COM$

109
XYZ = FNWAIT(2)
PRINT #1, "RQSOFF"
XYZ = FNWAIT(1)
CLOSE
LOCATE 9, 3: PRINT BLK$
LOCATE 9, 3: PRINT COM$
RETURN
DIR:
CLS
LOCATE 8, 25
PRINT "Please specify directory?"
LOCATE 10, 25
PRINT "Default is current directory"
LOCATE 14, 25
LDR$ = FNINP$
CLS
FILES LDR$
LOCATE 23, 30
PRINT "Any key to continue"
ANY$ = FNAN$
RETURN
HELP:
CLS
LOCATE 2, 2
PRINT "DIR Listing of files in a directory"
LOCATE 4, 2
PRINT "SERIES Routinue to retrieve a series of files"
LOCATE 5, 2
PRINT for the FFT program."
LOCATE 7, 2
PRINT "TIMED Routinue to automate data acquisition over"
LOCATE 8, 2
PRINT a long time period at a fixed time interval."
LOCATE 10, 2
PRINT "HELP This listing"
LOCATE 12, 2
PRINT "EXIT or QUIT Terminate this program"
LOCATE 23, 30
PRINT "Any key to continue"
ANY$ = FNAN$
RETURN
MAINSCREEN:
CLS

110
FOR IMS = 3 TO 22
LOCATE IMS, 40
PRINT CHR$(186)
NEXT IMS
FOR IMS = 5 TO 75
LOCATE 13, IMS
PRINT CHR$(205)
NEXT IMS
LOCATE 13, 40
PRINT CHR$(206)
LOCATE 3, 45
PRINT "Special Program Commands"
LOCATE 6, 52
PRINT "SERIES"
LOCATE 5, 52
PRINT "DIR"
LOCATE 7, 52
PRINT "TIMED"
LOCATE 9, 52
PRINT "HELP"
LOCATE 10, 52
PRINT "EXIT or QUIT"
LOCATE 3, 2
PRINT "Enter command for TDR"
LOCATE 7, 2
PRINT "Last command sent to TDR"
LOCATE 9, 3
PRINT LCOM$
LOCATE 14, 8
PRINT "Data transmission"
LOCATE 16, 8
PRINT "Point"
LOCATE 16, 19
PRINT "mVolts"
LOCATE 15, 45
PRINT "Sending file to:"
RETURN
SENDTDR:
OPEN "COMI:9600,N,8,1,RB10000" FOR RANDOM AS 1
IF LOC(l) <> 0 THEN
DO UNTIL LOC(l) = 0
LINE INPUT #1, LLLL$
LOOP
END IF
LOCATE 17, 45
PRINT NAME$
LOCATE 5, 3
PRINT "Receiving data from TDR"
PRINT #1, "RQSON"

Ill
XYZ = FNWAIT(l)
30 PRINT #1, COM$
NPT = 0
TIMEINT = 0
VOLTINT = 0
XYZ = FNWAIT(l)
IF LOC(l) = 0 GOTO 30
1 = 0
DO UNTIL LOC(l) = 0
1 = 1 + 1
INPUT #1, HEAD$(I)
LOOP
NPT = VAL(MID$(HEAD$(2) INSTR(HEAD$(2), ":") + 1))
TIMEINT = VAL(MID$(HEAD$(5) INSTR(HEAD$(5) "s") + 1))
VOLTINT = VAL(MID$(HEAD$(8), INSTR(HEAD$(8), + 1))
IF NPT = 0 THEN
XYZ = FNWAIT(l)
PRINT #1, ""
XYZ = FNWAIT(l)
DO UNTIL LOC(l) = 0
LINE INPUT #1, LLL$
LOOP
XYZ = FNWAIT(l)
GOTO 30
END IF
LOCATE 19, 48
PRINT USING "Points ####",* NPT
LOCATE 20, 48
PRINT USING "Time/Div ##.###AAAA"; TIMEINT
LOCATE 21, 48
PRINT USING "mV/Div ###.###"; VOLTINT 1000
OPEN NAME$ FOR OUTPUT AS 2
PRINT #2, NPT
PRINT #2, TIMEINT
XYZ = FNWAIT(l)
PRINT #1, ""
XYZ = FNWAIT(3)
1 = 0
LOCATE 21, 13: PRINT "Receiving"
DO UNTIL LOC(l) = 0
INPUT #1, WNUM
IF I >= 1 AND I <= NPT THEN
LOCATE 18, 5
PRINT BLK$
LOCATE 18, 8
PRINT USING "####"; I
LOCATE 18, 18
PRINT WNUM VOLTINT 1000
PRINT #2, WNUM VOLTINT 1000
END IF
1 = 1 + 1
LOOP

112
XYZ =
PRINT
CLOSE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
RETURN
FNWAIT(l)
#1, "RQSOFF"
5, 3: PRINT BLK$
9, 3: PRINT BLK$
9, 3: PRINT COM$
17, 42: PRINT BLK$
18, 2: PRINT BLK$
19, 42: PRINT BLK$
20, 42: PRINT BLK$
21, 2: PRINT BLK$
21, 42: PRINT BLK$
SERIES:
90 CLS
LOCATE 3, 4
PRINT "How many samples do you need to retrieve?"
40 LOCATE 3, 46
LL$ = FNINP$
IF LEN(LL$) > 1 THEN
LOCATE 3, 46
PRINT SPACE$(LEN(LL$))
GOTO 40
END IF
IF LL$ = "E" GOTO 99
NSAMP = VAL(LL$)
IF NSAMP < 1 OR NSAMP > 8 THEN
LOCATE 3, 46
PRINT "
GOTO 40
END IF
LOCATE 5, 4
PRINT "Reference Waveform Number "
50 LOCATE 5, 32
LINE INPUT LL$
IF LEN(LL$) > 1 THEN
LOCATE 5, 32
PRINT SPACE$(LEN(LL$))
GOTO 50
END IF
REFF = VAL(LL$)
IF REFF < 1 OR REFF > 9 THEN
LOCATE 5, 32
PRINT BLK$
GOTO 50
END IF
LOCATE 7, 4
PRINT "Path to send files to "
LOCATE 7, 26

113
PATHH$ = FNINP$
PLEN = LEN(PATHH$)
IF PLEN = 0 OR SPACE$(PLEN) = PATHH$ THEN
PATHH$ = ""
ELSE
IF 2 <> INSTR(PATHH$, AND 1 <> INSTR(PATHH$, "\") THEN
PATHH$ = "\" + PATHH$
END IF
IF "\" = MID$(PATHH$, PLEN, 1) THEN
PATHH$ = MID$(PATHH$, 1, PLEN 1)
END IF
END IF
LOCATE 7, 26
PRINT BLK$
LOCATE 7, 26
PRINT PATHH$
LOCATE 9, 20
PRINT "Waveform"
LOCATE 9, 30
PRINT "Filename"
FOR ISS = 1 TO NSAMP
LOCATE 9 + ISS, 4
PRINT USING "Sample # is in"; ISS
60 LOCATE 9 + ISS, 24
PRINT
LOCATE 9 + ISS, 24
LL$ = FNINP$
IF LEN(LL$) O 1 OR VAL(LL$) < 1 OR VAL(LL$) > 9 THEN
LOCATE 9 + ISS, 18
PRINT BLK$
GOTO 60
END IF
SAMP(ISS) = VAL(LL$)
IF SAMP(ISS) = REFF THEN
LOCATE 9 + ISS, 24
PRINT BLK$
GOTO 60
END IF
IF ISS <> 1 THEN
FOR ISI = 1 TO ISS 1
IF SAMP(ISS) = SAMP(ISI) THEN
LOCATE 9 + ISS, 24
PRINT BLK$
GOTO 60
END IF
NEXT ISI
END IF
70 LOCATE 9 + ISS, 30
PRINT "
LOCATE 9 + ISS, 30
FILENAME$(ISS) = FNINP$
LLEN = LEN(FILENAME$(ISS))

114
IF LLEN = 0 GOTO 70
IF LLEN > 8 OR SPACE$(LLEN) = FILENAME$(ISS) THEN
LOCATE 9 + ISS, 30
PRINT BLK$
GOTO 70
END IF
IF ISS O 1 THEN
FOR ISI = 1 TO ISS 1
IF FILENAMES(ISS) = FILENAMES(ISI) THEN
LOCATE 9 + ISS, 30
PRINT BLK$
GOTO 70
END IF
NEXT ISI
END IF
NEXT ISS
LOCATE 23, 20
PRINT "Is this correct? Y/N"
LOCATE 23, 41
ANS$ = FNAN$
IF ANS$ <> "Y" GOTO 90
COM1S = WFM WFM "
MID$(C0M1$, 1, 1) = CHR$(48 + REFF)
GOSUB MAINSCREEN
FOR III = 1 TO NSAMP
MID$(C0M1$, 7, 1) = CHR$(48 + SAMP(III))
MID$(C0M1$, 13, 1) =
COM$ = C0M1$
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NAMES = PATHH$ + "\" + FILENAMES(III) + ".DIF"
XYZ = FNWAIT(5)
GOSUB SENDTDR
MID$(C0M1$, 13, 1) = "+"
COM$ = COM1S
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NAMES = PATHHS + "\" + FILENAMES(III) + ".SUM"
XYZ = FNWAIT(5)
GOSUB SENDTDR
NEXT III
99 RETURN
TIMED:
110 CLS
III = 1
LOCATE 3, 4
PRINT "How many samples do you wish to take? (999 max.)"
120 LOCATE 3, 42
LL$ = FNINPS

115
IF LEN(LL$) > 2 THEN
LOCATE 3, 42
PRINT SPACE$(LEN(LL$))
GOTO 120
END IF
IF LL$ = "E" GOTO 199
NSAMP = VAL(LL$)
IF NSAMP < 1 OR NSAMP > 999 THEN
LOCATE 3, 42
PRINT "
GOTO 120
END IF
LOCATE 5, 4
PRINT "Reference Waveform Number "
130 LOCATE 5, 32
LL$ = FNINP$
IF LEN(LL$) > 1 THEN
LOCATE 5, 32
PRINT SPACE$(LEN(LL$))
GOTO 130
END IF
REFF = VAL(LL$)
IF REFF < 1 OR REFF > 9 THEN
LOCATE 5, 32
PRINT BLK$
GOTO 130
END IF
LOCATE 7, 4
PRINT "Sample Waveform Number "
140 LOCATE 7, 29
LL$ = FNINP$
IF LEN(LL$) > 1 THEN
LOCATE 7, 29
PRINT SPACE$(LEN(LL$))
GOTO 140
END IF
SSAMP = VAL(LL$)
IF SSAMP < 1 OR SSAMP > 9 OR SSAMP = REFF THEN
LOCATE 7, 29
PRINT "
GOTO 140
END IF
C0M1$ = WFM WFM "
MID$(C0M1$, 1,1)= CHR$(48 + REFF)
MID$(C0M1$, 7, 1) = CHR$(48 + SSAMP)
LOCATE 9, 4
PRINT "Path to send files to "
LOCATE 9, 26
PATHH$ = FNINP$
PLEN = LEN(PATHH$)
IF PLEN = 0 OR SPACE$(PLEN) = PATHH$ THEN
PATHH$ = ""

116
ELSE
IF 2 <> INSTR(PATHH$, AND 1 O INSTR(PATHH$, "\
PATHH$ = "\" + PATHH$
END IF
IF "\" = MID$(PATHH$, PLEN, 1) THEN
PATHH$ = MID$(PATHH$, 1, PLEN 1)
END IF
END IF
LOCATE 9, 26
PRINT BLK$
LOCATE 9, 26
PRINT PATHH$
LOCATE 11, 4
PRINT "Root Name to save acquired files to?"
150 LOCATE 11, 41
PRINT "
LOCATE 11, 41
LL$ = FNINP$
IF LEN(LL$) > 5 OR SPACE$(LEN(LL$)) = LL$ GOTO 150
IF LEN(LL$) < 1 GOTO 150
ROOT$ = LL$
160 LOCATE 13, 4
PRINT "Time interval: HOURS ; MINS. ; SECS.
162 LOCATE 13, 27
PRINT "
LOCATE 13, 27
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 162
HRS = VAL(LL$)
LOCATE 13, 27
PRINT USING HRS
164 LOCATE 13, 40
PRINT "
LOCATE 13, 40
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 164
MINS = VAL(LL$)
LOCATE 13, 40
PRINT USING MINS
166 LOCATE 13, 53
PRINT "
LOCATE 13, 53
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 166
SECS = VAL(LL$)
LOCATE 13, 53
PRINT USING SECS
TINTERVAL = 3600 HRS + 60 MINS + SECS
IF TINTERVAL < 180 THEN
LOCATE 15, 10
PRINT "Time interval is too short 3 minute minimumI"
GOTO 160
) THEN
II

117
END IF
LOCATE 15, 4
PRINT "Delay time: HOURS ; MINS. ; SECS. -
170 LOCATE 15, 24
PRINT "
LOCATE 15, 24
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 170
HRS = VAL(LL$)
LOCATE 15, 24
PRINT USING HRS
172 LOCATE 15, 37
PRINT "
LOCATE 15, 37
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 172
MINS = VAL(LL$)
LOCATE 15, 37
PRINT USING "##; MINS
174 LOCATE 15, 50
PRINT "
LOCATE 15, 50
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 174
SECS = VAL(LL$)
LOCATE 15, 50
PRINT USING SECS
TDELAY = 3600 HRS + 60 MINS + SECS
LOCATE 17, 4
PRINT "Quit when the intervals are completed? Y/N"
176 LOCATE 17, 60
PRINT "
ENDD$ = FNAN$
LOCATE 17, 60
IF ENDD$ <> "Y" AND ENDD$ <> "N" GOTO 176
IF ENDD$ = "Y" THEN PRINT "Yes" ELSE PRINT "No"
LOCATE 23, 20
PRINT "Is this correct? Y/N"
LOCATE 23, 41
ANS$ = FNAN$
IF ANS$ <> "Y" GOTO 110
CLS : LOCATE 12, 4
PRINT "Running a TDR experiment please do not disturb."
XYZ = FNWAIT(TDELAY)
180 GOSUB MAINSCREEN
START1 = TIMER
COM$ = "AVG100"
GOSUB COMTDR
XYZ = FNWAIT(20)
COM$ = "0 WFM + CHR$(48 + SSAMP) + >WFM"
GOSUB COMTDR
XYZ = FNWAIT(5)

118
MID$(C0M1$, 13, 1) =
COM$ = C0M1$
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NUMB$ = MID$(STR$(III), 2, LEN(STR$(III)) 1)
SELECT CASE LEN(NUMB$)
CASE 1
NUMB$ = "00" + NUMB$
CASE 2
NUMB$ = "0" + NUMB$
END SELECT
NAME$ = PATHH$ + "\" + ROOT$ + NUMB$ + ".DIF"
XYZ = FNWAIT(5)
GOSUB SENDTDR
MID$(C0M1$, 13, 1) = "+"
COM$ = C0M1$
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NAME$ = PATHH$ + "\" + ROOT$ + NUMB$ + ".SUM"
XYZ = FNWAIT(5)
GOSUB SENDTDR
FINSH = TIMER
IF FINSH < START1 THEN
DIFFER = 86400 START1 + FINSH
ELSE
DIFFER = FINSH START1
END IF
III = III + 1
IF III > NSAMP GOTO 199
IF III > 25 THEN SCN = 25
IF III > 50 THEN SCN = 50
IF III > 75 THEN SCN = 75
CLS : LOCATE III SCN, 10
PRINT "Running a TDR experiment please do not disturb."
IF DIFFER > TINTERVAL GOTO 180
XYZ = FNWAIT(TINTERVAL DIFFER)
GOTO 180
199 RETURN

119
Program TDRDRIVE.C
This program was written in Borland's Turbo C version
1.5 by Dr. Peter Doan. This program is required in the
analysis of the TDR data. Two program modules are required
for the Fourier transform analysis, the second module is
TDRUTIL.C. The Fourier routines require two files from the
TDR.BAS program. Included in these two modules are data
baseline correction and smoothing routines, their functions
are all automated.

#include
#include
#include
120
void baseline();
void trans_to_diel();
void smooth();
float *zero_fill();
void ratio();
void slow_ft();
float *gen_freq();
void renorm();
main(argc,argv)
int argc;
char *argv[];
{
int i,j,k, npd,nps,nskip, nf, DER_DIF, RAW_OUT;
float *dif_spec,*sum_spec, dtd, dts, *dhold, *shold;
float *frequency, depth, fmax, x;
struct complex *fr_dif, *fr_sum, *diel_spec, rrr,qqq,sss;
FILE *dif, *sum, *outfile, *config;
void output();
void disk_out();
/* the configuration file is a flat ASCII file with the */
/* following format the (A,B) notation refers to a choice */
/* of A or B *is default */
/*
Explanations:
NF No zero Fill
*ZF Zero Fill to 2t
SR Sample and Reference spectra
*SD sum and difference spectra
*DR Transform as derivatives both sum and dif
ND Transform dif as natural function
*NC No Conductivity
CO Conductivity correction if warrented
filenamel Difference spectrum (SD) or
Sample spectrum (SR)
filename2 Sum spectrum (SD) or
Reference spectrum (SR)
filename3 name for output of raw transform data
CARD 1 (NF,ZF) (SR,DS) (DR,ND) (NC,CO)
CARD 2 sample depth (in cm)
CARD 3 NSMOOTH NSKIP
CARD 3 filenamel filename2 filename3
CARD 4..EOF comments on the experiment
*/

121
depth = 0.15;
nf = 50;
fmax = 70.;
RAW_OUT = 1;
/* sizeof(complex) = 2 sizeof(float) */
fr_dif = (struct complex *)malloc(2 nf sizeof(float));
fr_sum = (struct complex *)malloc(2 nf sizeof(float));
/* ********************************************************* */
/* get data */
/* */
while((dif = fopen(argv[1],"r")) == NULL) {
puts("error in opening difference file...\n");
puts("input file name for difference file ");
gets(argv[1]);
}
fscanf(dif,"%d",&npd);
printf("%d\n", npd);
fscanf(dif,"%e",&dtd);
printf("%e\n",dtd);
dif_spec = (float *) malloc(npd sizeof(dts));
dhold = dif_spec;
for(i = 0; i < npd; i++) {
fscanf(dif,"%f",dif_spec);
dif_spec++;
)
fclose(dif);
dif_spec = dhold;
while ((sum = fopen(argv[2],"r")) == NULL) (
puts("error in opening sum file....\n");
puts("input sum file name ");
gets(argv[2]);
}
fscanf(sum,"%d",&nps);
printf("%d\n",nps);
if( nps != npd) (
puts("sum and dif files do not match...npoints differ\n");
exit(0);
}
fscanf(sum,"%e",&dts);
printf("%e\n",dts);
dtd = dtd le9;
/* convert to nsec to format */

122
dts = dts le9;
if(dts != dtd) {
puts("sum and dif files do not match...time inc differ\n");
exit(O);
}
sum_spec = (float *) malloc(nps sizeof(dts));
shold = sum_spec;
for(i =0; i < npd; i++) {
fscanf(sum,"%f",sum_spec);
sum_spec++;
}
fclose(sum);
sum_spec = shold;
********************************************************** */
/* MASSAGE DATA BEFORE TRANSFORM */
/* */
nskip = 30;
puts("baseline correct dif\n");
DER_DIF = 0;
baseline(npd,nskip,dif_spec,1,1);
puts("baseline correct sum\n");
baseline(nps,nskip,sum_spec,1,1);
puts("smoothing dif\n");
smooth(npd,dif_spec,2);
puts("smoothing sum\n");
smooth(nps,sum_spec,2);
puts("zero filling dif\n");
dif_spec = zero_fill(npd,dif_spec);
dhold = dif_spec;
npd = npd 2;
puts("zero filling sum \n");
sum_spec = zero_fill(nps,sum_spec);
shold = sum_spec;
nps = nps 2;
/* ********************************************************** */
/* SET UP AND PERFORM FT */
puts("generating freguency points ");
freguency = gen_freg(nf,nps dts,fmax,nps);
dhold = freguency;

123
puts("transforming dif spectrum \n");
/* puts result in fr_dif */
slow_ft(npd,nf,dif_spec,frequency,dtd,fr_dif);
if(RAW_OUT == 1)
disk_out("a:dif_puls.dat",nf,frequency,fr_dif);
free(dif_spec); /* deallocate time domain block now */
renorm(nf,fr_dif,frequency);
/* as the d(dif)/dt, it must be */
/* corrected back to true FT by */
/* the derivative formula */
puts("transforming d(sum)/dt ");
slow_ft(nps,nf,sum_spec,frequency,dts,fr_sum);
if(RAW_OUT == 1)
disk_out("a rpulse.dat",nf,frequency,fr_sum);
free(sum_spec); /* deallocate block */
puts("taking ratio of dif to sum");
ratio(nf,fr_dif,fr_sum,depth);
diel_spec = fr_dif; /* rename the block */
puts("creating complex impedence function");
trans_to_diel(nf, depth, frequency, diel_spec,diel_spec);
while ((outfile = fopen(argv[3],"w")) == NULL) {
puts("error in opening output file");
puts("input file name ");
scanf("%s",argv[3]);
)
fprintf(outfile,"%d\n",nf);
for( i = 0; i < nf; i++) {
fprintf(outfile,"%f %f %f\n",*frequency,
-diel_spec->real,diel_spec->imag);
frequency++;
diel_spec++;
}
fclose(outfile);
exit(0);
}
void output(n,w,x)

124
int n;
float w[];
struct complex x[];
{
int i;
for(i = 0; i < n; i++)
printf(M%f %f %f \n",w[i],x[i].real,x[i].imag);
}
void disk_out(name,n,x,y)
char *name;
int n;
float x[];
struct complex y[];
{
int i;
FILE *outfile;
outfile = fopen(name,"w");
for(i =0; i < n; i++)
fprintf(outfile,"%f %f %f\n",x[i],y[i],real,y[i].imag);
fclose(outfile);
void renorm(n,y,x)
int n;
float x[];
struct complex y[];
{
int i;
struct complex c[50];
for(i =0; i < n; i++)
c[i] = Cmplx(0.0, x[i]);
for(i =0; i < n; i++)
y[i] = Cdiv(y[i],c[i]);

125
Program TDRUTIL.C
This is the second module required for the Fourier
routines, please refer to TDRDRIVE.C for description of
these routines.

#include
#include
126
float C = 29.9772; /* (units of cm/nsec) */
/* ****************************************************** */
/* SUBROUTINE SMOOTH*/
/* */
/* This subroutine smooths the spectrum of n points which */
/* is pointed to by the x pointer. The routine uses a */
/* 3 point binomial smooth: */
/* x[i](new) = .25 (x[i 1] + x[i +1] ) + .5 x[i] */
/* */
/* This routine can be iterated k times to produce a 2k + 1 */
/* binomial smooth*/
void smooth(n,x,k)
int n,k;
float x[];
{
int i,j, nl;
float sum,xl/x2;
nl = n 1;
for(j = 0; j < k; j++) { /* outer loop */
xl = x[0];
x2 = x[1 ] ;
sum = .25 (xl + x[2]) + .5 x2;
for( i = 1; i < nl; i++) { /* smoothing loop */
x[i] = sum;
sum = sum + .25 (x[i+l] + x[i+2] xl x2);
xl = x2;
x2 = x[i+1];
}
/* ********************************************************* j
/* SUBROUTINE trans_to_diel
*/
/* */
/* This subroutine takes the converts the ratios of the */
/* dif and d(sum)/dt arrays and converts them to the complex */
/* dielectric response by using the transmission coefficient */

127
trans_to_diel(n, d, x, a, e)
int n;
float x[],d;
struct complex a[],e[];
{
int i, j;
float y, dl, tolerance;
struct complex tl,t2;
struct complex C_ONE = Cmplx(1.0,0.0);
tolerance = 1.0e-4;
/* the first round correction uses only the first two terms */
/* in the expansion of xcotx, to the linear term in (EPS* + 1)*/
/* EPS* = {a[i](1 y[i]) + 1} / (1 + y a[i]) */
/* where y = 1/3 (wd/c)A2 */
dl = d / C;
for( i = 0; i < n; i++) {
y = x[i] dl;
tl = escalar(a[i],(y y / 3.))?
t2 = Csub(a[i],tl);
t2 = Cadd(t2,C_0NE);
tl = Cadd(C_ONE, tl);
e[i] = Cdiv(t2,tl);
}
}
/* *************************************************** */
/* */
void derivative(n,k,x)
int n,k;
float x[];
{
int i, nl;
float xl, x2, x3;
float factorl, factor2, suml, sum2;
factorl = 1. / 12.;
factor2 = 8. / 12.;
nl = n 2; /* the derivative is based on a 4th order */
x3 = x[0]; /* polynomial approximation to the curves */
x2 = x[l]; /* this has a tendency to smooth high freq. */
xl = x[2]; /* instability, producing a smoother curve */

128
for( i = 2; i < ni; i++) {
sum = x[i + 2] x3;
sum2 = x[i + 1] x2;
x[i] = factorl sum factor2 sum2;
x3 = x2;
x2 = xl;
xl = x[i + 1];
}
x[n 2] = x[n 1] x[n 2];
x[n 1] = 0.0;
for(i = 0; i < k; i++)
x[i] = 0.0;
}
y* ******************************************************** *y
float *zero_fill(n,x)
int n;
float *x;
{
int i,j,n2;
float *xnew,*xhold,*xnhold, y;
void apodize();
xhold = x;
n2 = n 2;
xnew = (float *)malloc(n2 sizeof(y));
xnhold = xnew;
for( i = 0; i < n; i++) {
/* fill the new pointer with the old */
*xnew = *x; /* old points */
xnew++;
x++;
}
free(xhold); /* frees the earlier spectrum block */
for(i = 0; i < n; i++) {
*xnew = 0.0;
xnew++;
}
xnew = xnhold;
apodize(n,xnew);
n = n2;
return(xnhold);
} /* end of zero fill routine */
/* ******************************************************** *y
void apodize(n,x)
int n; /* n is the number of experimental points */

129
float x[];
{
int i,j,l, nstart, ntot;
float xl, x2, sum;
nstart = n 48;
ntot =64;
for( j = 0; j < 3; j++) {
smooth(ntot,&x[nstart], 2);
nstart = nstart + 16;
}
}
/* ********************************************************* */
void ratio(n,top,bottom,depth) /* returns ratio in top
*/
int n;
float depth;
struct complex top[], bottom[];
{
int i;
float depthl;
depthl = C / depth; /* c / d is factor */
for( i = 0; i < n; i++)
top[i] = escalar(Cdiv(top[i],bottom[i]),depthl);
}
/* ********************************************************* y
/* ******************************************************** */
void slow_ft(nx,nf,x,f,dt,trans)
int nx,nf;
float x[],f[],dt;
struct complex trans[];
{
int i,j;
float sreal,simag, dwt;
double swt, swi, cwt, ewi, cwtemp;
for(i = 0; i < nf; i++)
dwt = dt f[i];
sreal = x[0];
simag = 0.0;
swi = sin(dwt);
ewi = cos(dwt);
swt = swi;
cwt = ewi;
for(j =1; j < nx
/* the sine and cosine functions are */
/* calculated incrementally by the */
/* angle addition formula rather than */
/* repeated calls to sin and cos */
' j++) {

130
sreal = sreal + cwt x[j];
simag = simag + swt x[jj;
cwtemp = cwt;
cwt = cwt cwi swt swi;
swt = cwtemp swi + swt cwi;
}
trans[i].real = sreal;
trans[i].imag = simag;
}
}
/* *************************************************** */
float *gen_freq(nf,ttot,fmax, np)
int nf;
float ttot,fmax;
{
int i;
float dw, *w, *whold, true_max, true_min;
float PI = 3.1415926536;
w = (float *)malloc(nf sizeof(float));
whold = w;
true_min = 2 PI / ttot; /* sampling theorem limit */
true_max = np true_min / 2; /* sampling theorem limit */
if( fmax > true_max) fmax = true_max;
dw = log(fmax/true_min) / (float ) nf;
/* gives equally spaced */
dw = exp(dw); /* points in log of w */
*w = true_min;
for( i = 1; i < nf; i++) {
w++;
*w = *(w 1) dw;
}
return(whold);
}

131
Program DEBYE.BAS
This program was written in Microsoft's QuickBasic
version 4.5. The program fits experimental complex
dielectric spectra obtained from the TDR system after being
Fourier transformed and DC conductivity corrected to a
modified form of the Debye model, eguations (6) and (7). A
Simplex routine is use to fit the equations to the
experimental data. The program requires the input of
estimates for each process time constant, the overall static
dielectric constant, and the overall high frequency
dielectric constant. Each of the guesses can be allowed to
float or be fix if the value is known. The program gives
output in two forms, graphics on a VGA monitor for comparing
the experimental results to the theoretical and output to a
data files for storage.

132
RESTORE
CLS
DIM D(13), RI(14) S(13, 14), TT(13), E(13)
DIM SUOLD(13), DCR(250), DCI(250), FREQ(250)
DIM AR(6, 250), AI (6, 250)
DEF FNAN$
1 AZ$ = UCASE$(INKEY$)
IF AZ$ = "" GOTO 1
FNAN$ = AZ$
END DEF
DEF FNFUNK
FUNK = 0!
FOR ISS = 1 TO NH
FUNCTR = E(2 NPROC + 1)
FUNCTI = 0!
FOR JS = 1 TO NPROC
WT = (10 A (FREQ(ISS))) / E(JS)
DCAMP = E(NPROC + JS) E(NPROC + JS + 1)
FUNCTR = FUNCTR + DCAMP / (1 + WT A 2)
FUNCTI = FUNCTI + DCAMP WT / (1 + WT A 2)
NEXT JS
FUNK = FUNK+((DCR(ISS)-FUNCTR)A2)+((DCI(ISS)-FUNCTI)A2)
NEXT ISS
FNFUNK = SQR(FUNK / (2 NH 1))
END DEF
EP = .1
INPUT "Name of input DATA FILE is"; INPT$
30 INPUT "Number of processes to fit DATA is"; NPROC
IF NPROC < 1 THEN NPROC = 1
IF NPROC > 6 THEN NPROC = 6
INPUT "Static Dielectric Constant is"; E(NPROC+l),D(NPROC+l)
IF E(NPROC + 1) < 1 THEN E(NPROC + 1) = 10
IF E(NPROC + 1) > 100 THEN E(NPROC + 1) = 100
HFREQ = 2 NPROC + 1
INPUT "High Freq. Dielectric Const, is"; E(HFREQ),D(HFREQ)
IF E(2 NPROC + 1) < 1 THEN E(2 NPROC + 1) = 1
IF E(2 NPROC + 1) > E(NPROC + 1) THEN E(2 NPROC + 1) = 1
FOR I = 1 TO NPROC
PRINT USING "Rate Process ## has a FREQ, of (MHz) "; I;
INPUT E(I), D(I)
E(I) = E(I) 1000000!
NEXT I
INPUT "Max number of LOOPS (DEFAULT is 250)"; KX
IF KX < 250 THEN KX = 250
IF KX > 5000 THEN KX = 5000
OPEN INPT$ FOR INPUT AS #1
NH = 0
DO UNTIL EOF(1)
NH = NH + 1
INPUT #1, FREQ(NH), DCR(NH), DCI(NH)
LOOP
CLOSE #1

133
40 CLS
FOR I = 2 TO NPROC
E(NPROC+I) = E(NPROC+I-1)-(E(NPROC+1)-E(2*NPROC+l))/NPROC
D(NPROC + I) = 1
NEXT I
FOR I = 1 TO 2 NPROC + 1
IF D(I) <> 0 THEN D(I) = E(I) .1
NEXT I
GOSUB SIMPLEX
CLS
AFIX$ = "Rate ## has a fixed freq. of #####.# MHz"
AFLT$ = "Rate ## has a freq. of #####.# MHz"
FOR I = 1 TO 2 NPROC + 1
IF I <= NPROC THEN
IF D(I) = 0 THEN
PRINT USING AFIX$; I; E(I) / 1000000!
ELSE
PRINT USING AFLT$; I; E(I) / 1000000!
END IF
END IF
DCFIX$ = "Dielectric Constant ## is fixed at ###.###"
DCFLT$ = "Dielectric Constant ## is ###.###"
IF I = NPROC THEN PRINT
IF I > NPROC THEN
IF D(I) = 0 THEN
PRINT USING DCFIX$; I NPROC; E(I)
ELSE
PRINT USING DCFLT$; I NPROC; E(I)
END IF
END IF
NEXT I
PRINT
PRINT USING "Reduced CHI squared is ###.#####; BR
PRINT : PRINT
FOR I = 1 TO NH
FOR J = 1 TO NPROC
WT = (10 A (FREQ(I))) / E(J)
DCAMP = E(NPROC + J) E(NPROC + J + 1)
AR(J, I) = DCAMP / (1 + WT A 2)
AI(J, I) = DCAMP WT / (1 + WT A 2)
NEXT J
NEXT I
PRINT "Do you wish to see graphics? Y/N"
11 AN$ = FNAN$
IF AN$ = "N" THEN GOTO 10
IF AN$ <> "Y" THEN GOTO 11
SCREEN 12
VIEW (20, 15)(619, 464), 7
WINDOW (FREQ(1), -.5)-(FREQ(NH), E(NPROC + 1) + 1)
FOR I = 1 TO NH
X = FREQ(I)
Y = DCR(I)

134
CIRCLE (X, Y), .015, 1
PAINT (X, Y), 1
Y = DCI(I)
CIRCLE (X, Y), .015, 4
PAINT (X, Y), 4
IF I < NH THEN
YRT1 = E(2
*
NPROC
+
1)
YRT2 = E(2
*
NPROC
+
1)
YIT1 = 0
YIT2 = 0
FOR J = 1 '
ro
NPROC
Y1 = E(2
*
NPROC
+
1)
+ AR(J,
I)
Y2 = E(2
*
NPROC
+
1)
+ AR(J,
I +
LINE (FREQ(I), Y1)-(FREQ(I + 1), Y2), 8 + J
LINE (FREQ(I), AI(J, I))-(FREQ(1+1), AI(J, 1+1)), 8+J
YRT1 = YRT1 + AR(J, I)
YRT2 = YRT2 + AR(J, I + 1)
YIT1 = YIT1 + AI(J, I)
YIT2 = YIT2 + AI(J, I + 1)
NEXT J
LINE (FREQ(I), YRT1)-(FREQ(I +1), YRT2), 15
LINE (FREQ(I), YIT1)-(FREQ(I +1), YIT2), 15
END IF
NEXT I
AN$ = FNAN$
SCREEN 0
10 PRINT "Do you wish to save this data? Y/N"
21 AN$ = FNAN$
IF AN$ = "N" THEN GOTO 20
IF AN$ <> "Y" THEN GOTO 21
INPUT "Name of OUTPUT DATA FILE"; OUTPT$
OPEN OUTPT$ FOR OUTPUT AS #2
AA$ = "#.##### ###.### ###.### ###.### ###.###"
FOR I = 1 TO NH
CALR = E(2 NPROC + 1)
CALI = 0
FOR J = 1 TO NPROC
CALR = CALR + AR(J, I)
CALI = CALI + AI(J, I)
NEXT J
PRINT #2, USING AA$; FREQ(I); DCR(I); CALR; DCI(I); CALI
NEXT I
CLOSE #2
20 PRINT "Do you wish to run again? Y/N"
25 AN$ = FNAN$
IF AN$ = "N" THEN END
IF AN$ <> "Y" THEN GOTO 25
PRINT "Wish to use the OUTPUT as the NEW ESTIMATES? Y/N"
31 AN$ = FNAN$
IF AN$ = "Y" THEN GOTO 40
IF AN$ <> "N" THEN GOTO 31
GOTO 30

135
END
REM* ***************************************************
REM SUBROUTINE SIMPLEX
REM* ***************************************************
SIMPLEX:
GOSUB PARMAT
IF NH = 0 OR RI(1) =0 GOTO 1100
KI = 1
KII = 1
1010 IF BR = 0 OR BR >= EP GOTO 1020
EP = EP / 10
GOTO 1010
1020 WR = RI(1)
BR = WR
JW = 1
JB = 1
FOR I = 2 TO 2 NPROC + 2
IF RI(I) >= WR THEN WR = RI(I)
IF RI(I) >= WR THEN JW = I
IF RI(I) < BR THEN BR = RI(I)
IF RI(I) < BR THEN JB = I
NEXT I
IF KII = 5 THEN
LOCATE 12, 33: PRINT USING "ITERATION #### "; KI
LOCATE 14, 27: PRINT USING "REDUCED CHI IS ####.#####; BR
KII = 0
END IF
IF KI > KX THEN
CLS : LOCATE 12, 25
PRINT "MAXIMUM NUMBER OF LOOPS REACHED"
LOCATE 23, 30: PRINT "Any key to continue"
ANDDD$ = FNAN$
RETURN
END IF
IF BR < EP THEN
CLS : LOCATE 12, 26
PRINT "CONVERGENCE CRITERIA REACHED"
LOCATE 23, 30: PRINT "Any key to continue"
ANDDD$ = FNAN$
RETURN
END IF
IF WR BR < EP / 100 THEN
CLS : LOCATE 12, 32
PRINT "BEST FIT REACHED"
LOCATE 23, 30: PRINT "Any key to continue"
ANDDD$ = FNAN$
RETURN
END IF
KI = KI + 1
KII = KII + 1
IF BR <> PR THEN PR = BR
F = 1

136
* NPROC + 1
1050
* NPROC
+ 1
GOSUB VERTIX
IF R > BR GOTO 1030
RT = R
FOR I = 1 TO 2
TT(I) = E(I)
NEXT I
F = 2
GOSUB VERTIX
IF R > RT GOTO
1080 FOR I = 1 TO 2
S(I, JW) = E(I)
NEXT I
RI(JW) = R
GOTO 1020
1050 R = RT
FOR I = 1 TO 2
E(I) = TT(I)
NEXT I
GOTO 1080
1030 IF R <= WR GOTO 1080
F = -.5
GOSUB VERTIX
IF R <= WR GOTO 1080
FOR I = 1 TO 2 NPROC + 1
FOR J = 1 TO 2 NPROC + 2
IF J <> JB THEN S(I, J) = (S(I,
NEXT J
NEXT I
GOTO 1020
RETURN
* NPROC + 1
JB) + S(I, J)) / 2
End subroutine Simplex
1100
REM
REM
REM
REM* ****************************************************
REM Set up of parameter matrix
REM*****************************************************
PARMAT:
FOR I = 1 TO 2 NPROC + 1
FOR J = 1 TO 2 NPROC + 2
AI = 0
IF I >= J THEN AI = -1!
S(I, J) = E( I) D( I) AI D( I) / 2
NEXT J
NEXT I
FOR I = 1 TO 2 NPROC + 2
FOR J = 1 TO 2 NPROC + 1
E(J) = S(J, I)
NEXT J
R = FNFUNK
RI(I) = R
NEXT I
RETURN

137
REM
REM End subroutine Parmat
REM
REM* *******************************************************
REM SUBROUTINE VERTIX
REM* *******************************************************
VERTIX:
FOR I = 1 TO 2 NPROC + 1
SU = 0
IF F <> 1 GOTO 1230
FOR J = 1 TO 2 NPROC + 2
IF J O JW THEN SU = SU + S(I, J)
NEXT J
SUOLD(I) = SU / (2 NPROC + 1)
1230 E(I) = SUOLD(I) (1 + F) F S(I, JW)
NEXT I
R = FNFUNK
RETURN
REM
REM End subroutine Vertix
REM

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T. "Colloidal Surfactants," Academic Press, New York,
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143
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Interface Sci.. 1970, 34, 262.
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NMR," Springer-Verlag, Berlin, 1976, 106.
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1974, 21, 56.
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1985, EI-20. 927.

BIOGRAPHICAL SKETCH
Ngai M. Wong was born on May 8, 1961, in Hong Kong. He
immigrated to the United States in September of 1966.
Upon graduation from Brooklyn Technical High School in
New York, he entered a 3:2 program in chemistry and chemical
engineering at Ithaca College and Cornell University,
respectively. He received a dual degree in chemistry (B.A.)
and chemical engineering (B.S.) in May of 1984.
In August of 1984, he entered the graduate program at
the University of Florida and began working with Dr. Russell
S. Drago. He received a Master of Science degree in August
of 1986 from the University of Florida with a thesis
entitled Extension and Application of the E and C Equation.
144

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Javid E. Richardson
Associate Professor, Chemistry
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Robert C. StouJ
Associate Professor, Chemistry

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Michael D. Sacks
Associate Professor, Materials
Science and Engineering
This dissertation was submitted to the Graduate Faculty
of the Department of Chemistry in the College of Liberal
Arts and Sciences and to the Graduate School and was
accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
December 1990
Dean, Graduate School

iii2SL?.^or,da
3 25 o eS1!"11
162 08554 8708



69
Table 5
Pyridine and Butanol Systems
BuOH/py
%CC14
%Pv
3l Buon
ratio

5.0
95.0
20
58.0
1.9
40.1
20

9.9
90.9
10
55.8
4.0
40.2
10

15.1
84.9
6
54.2
6.8
39.0
6

30.4
69.6
2
43.3
16.9
39.8
2

49.5
50.5
1
20.6
39.8
39.6
1
s
£<*>
T X 10~6 Hz
18.2
2.6
407
5.0
1.4
524
17.5
3.6
546
5.2
1.2
630
17.3
3.4
716
6.4
1.8
778
16.5
4.2
1364
8.3
2.4
1245
15.7
4.7
2624
11.9
3.5
2845


143
91. Lindblom, G.; Lindman, B.; Mandell, L. J. Colloid
Interface Sci.. 1970, 34, 262.
92. Friberg, S.; Rydhag, L.; Lindman, B. J. Phys. Chem..
1973, 22, 1280.
93. Lindblom, G.; Lindman, B. Mol. Cryst. Liquid Cryst..
1971, 14, 49.
94. Wennerstrom, H.; Lindblom, G.; Lindman, B. Chem. Scr..
1974, 6, 97.
95. Gustavsson, H.; Lindman, B. J. Am. Chem. Soc.. 1975,
92, 3923.
96. Gustavsson, H.; Lindman, B. "Proc. Int. Conf. on
Colloid and Surface Science," Wolfram, E., ed., Vol. 1,
Akademiai Kiado, Budapest, 1975, 625.
97. Lindman, B.; Forsen, S. "Chlorine, Bromine, and Iodine
NMR," Springer-Verlag, Berlin, 1976, 106.
98. Hall, C.; Haller, G. L.,; Richards, R. E. Mol. Phys.f
1969, 16, 377.
99. Neggia, P.; Holz, M.; Hertz, H. G. J. Chim. Phys..
1974, 21, 56.
100. Lindman, B. Acta Chem. Scand.. 1975, A 29. 935.
101. Winsor, IV, P.; Cole, R. J. Phys. Chem.. 1982, 86,
2486.
102. Forest, E.; Smyth, C. P. J. Phys. Chem.. 1965, 69.
1302.
103. Barker, R. E. Jr.; Huang, C. IEEE Trans. Elect. Ins..
1985, EI-20. 927.


35
The next logical step in the natural progression of
determining what influences quadrupolar relaxation is to
move from aqueous to mixed solvents and non-aqueous media.
This next step allows for changes in the solvent's dipole
moment, molecular size, dielectric constant, solvation
number, etc. to study the effects of ion pair formation, ion
solvation, complex formation, etc. Studies of alkali
halides show that the relaxation is mainly determined by
ion-solvent interactions where the correlation time of the
solvent plays an important role. In aqueous systems, the
relaxation is due to the motion of randomly oriented and
distributed point dipoles.97 For methanol
systems,57'58'69'98'99 the relaxation can be modelled to a
tightly packed first solvation sphere with radially oriented
dipoles. Modelling Br_ in dimethyl sulfoxide70'100 using a
distinct solvation sphere approximation gives results that
are higher than the experimental ones, suggesting that the
differences in the ion solvation from various solvents
should be of great interest in elucidating solvation
phenomena. The methanol and dimethyl sulfoxide studies also
suggest that ion pair formation gives a significant
contribution to relaxation, but in the dimethyl sulfoxide
case this effect does not explain the trend of the cations
as shown in Figure 10.


Static Dielectric Constant
57
Figure 18: Concentration dependence of the observed static
dielectric constant for solutions of n-butanol
and carbon tetrachloride. Equation (11) is
represented by the line for this system.


60
dimensional dynamic network. The critical frequency
obtained is a complex average of the frequencies of all the
individual aggregates exchanging with each other. A summary
of the results of the fit of the complex components of the
frequency dependent dielectric constant is given in Table 2.
Both the average dielectric constant and analysis of the
frequency dependence of the complex dielectric constant
indicate that this distribution does not change appreciably
over the concentration range of 70 to 100% n-butanol in
CC14. In more dilute solutions, dissociation to produce
smaller aggregates results. The rate of butanol relaxation
in the smaller cluster is faster and the dipole moment
change is smaller. The latter effect leads to a non
linearity in the intensity of the entire complex dielectric
constant as shown for the static component in Figure 18.
Binary System of n-Propanol and n-Hexanol
This system was selected for study in order to
illustrate the influence that changes in the average
molecular weight of the mixed alcohol system have on the
frequency of the dielectric relaxation. The reported static
dielectric constants, the values obtained by us and the
observed critical frequencies for relaxation are summarized
in Table 3 for a variety of alcohols. The critical
frequency describes the rate at which the alcohol "tumbles"
in solution in the process of making and breaking hydrogen


122
dts = dts le9;
if(dts != dtd) {
puts("sum and dif files do not match...time inc differ\n");
exit(O);
}
sum_spec = (float *) malloc(nps sizeof(dts));
shold = sum_spec;
for(i =0; i < npd; i++) {
fscanf(sum,"%f",sum_spec);
sum_spec++;
}
fclose(sum);
sum_spec = shold;
********************************************************** */
/* MASSAGE DATA BEFORE TRANSFORM */
/* */
nskip = 30;
puts("baseline correct dif\n");
DER_DIF = 0;
baseline(npd,nskip,dif_spec,1,1);
puts("baseline correct sum\n");
baseline(nps,nskip,sum_spec,1,1);
puts("smoothing dif\n");
smooth(npd,dif_spec,2);
puts("smoothing sum\n");
smooth(nps,sum_spec,2);
puts("zero filling dif\n");
dif_spec = zero_fill(npd,dif_spec);
dhold = dif_spec;
npd = npd 2;
puts("zero filling sum \n");
sum_spec = zero_fill(nps,sum_spec);
shold = sum_spec;
nps = nps 2;
/* ********************************************************** */
/* SET UP AND PERFORM FT */
puts("generating freguency points ");
freguency = gen_freg(nf,nps dts,fmax,nps);
dhold = freguency;


Dielectric Loss Function
84
0.0

No Aliquat

130/1

80/1

40/1
0
20/1

13/1
A
5.7/1
Theoretical
Butanol/Aliquat Ratio
7.5 7.7 7.9
8.1 8.3 8.5 8.7 8.9
Log Frequency (Hz)
9.1 9.3 9.5
Figure 31: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and carbon tetrachloride.


104
and water take on new properties in the formation of this
butanol/water adduct. These new properties do not change
even under the conditions where phase separation of the
butanol and water take place. With carbon tetrachloride,
virtually no interactions are observed compared to the other
systems studied here. The only effect seen is the buffering
ability of the individual CC14 molecules to separate the
other interacting centers apart, lowering the butanol
concentration to prevent the formation of large aggregates.
Combining halide guadrupole NMR studies with TDR
observations have led to a better understanding of the
fundamental interactions found in solutions of Aliquat 336.
The Aliquat molecule is found to be highly ion-paired even
in a polar solvent like n-butanol. The mobility of Aliquat
in butanol is unhindered at low concentrations but at a mole
fraction of 0.10, Aliquat begins to form aggregates.
Different forms of these aggregates are seen under the
various conditions of mixed solvents with differing
properties. Various solvents are observed to interact at
different sites found in Aliquat. Alcohols like n-butanol
can interact with both the hydrophobic and hydrophilic sites
but prefer the hydrophobic site in neat solvent. The
introduction of a nonpolar solvent like CC14 forces the
butanol out of the hydrophobic region and into the
hydrophilic region of Aliquat, whereas water interacts with


79
Table 6
Aliquat 336 in n-Butanol
% Alicmat
e_
r X 10"
0.5
S
19.4
3.8
330
1.0
20.0
5.1
313
2.5
19.8
6.1
284
5.0
16.8
6.4
287
7.5
14.2
6.5
312
10.0
12.8
6.9
350
15.0
7.9
3.5
365
20.0
7.8
4.3

30.0
7.0
5.1

50.0
6.4
4.8

100
3.0
3.0
_ _


45
cell. The difference in the packing leads to irreproducible
values of the dielectric constant, but the frequency of the
various processes is not affected and can be reliably
obtained. In order to pack the cell properly, the solid
must be in the form of a fine powder with the particle size
in the micron range. Volatile samples have to be watched
carefully since heat is produced in the sample cell from the
power loss. The sample must cover the center post in the
sample cell because fringing effects can give some very
interesting looking distorted spectra. This effect can be
eliminated by burying the center post to a depth of at least
half the cell diameter.
The process of collecting the spectral data is simple
once the proper settings have been established for the TDR
setup. All waveforms are collected using signal averaging
to help reduce the random noise and drift problems. It has
been determined by trial and error that 100 signal averages
are reasonable for this TDR setup. Averages in excess of
100 help to reduce the random noise, but is offset by drift
problems. Waveforms of 1024 points in size should only be
collected for time windows greater than 50 nsec. Time
windows less than 50 nsec give distortion of the spectral
data when 1024 points are used. The drift problems show up
in the higher resolution spectra for the shorter time
windows. It has been determined that 512 points are
normally adequate to describe most samples in time windows


INTRODUCTION
Time Domain Reflectometry, TDR, is a technique used to
study the time-dependent response of a sample to a time-
dependent electromagnetic field. This response depends upon
the dielectric properties of the sample. Practical
application of this technique became available with the
introduction of the tunnel diode as a voltage pulse
generator which is used as an excitation source. This
technological development allows systems that have processes
as fast as 1 psec (2 X 1011 Hz) to be studied by TDR. A
multitude of systems including pure liquids,1 mixed valent
systems,2 biological systems,3-5 and polymers in solution6
4
have been studied by this technique.
The current state of the art time domain reflectometer
is in the infancy stages. The potential of TDR lies in its
ability to collect dielectric data in a very short time
(minutes for a typical frequency range of 106 Hz to 109 Hz)
compared to the standard method which is a long and tedious
task of point by point data collection. Typical studies
using TDR involve systems that have only one or two
processes of interest. In this way, fundamental information
about these processes is fairly easy to obtain. Systems
1


38
Figure 11: Block diagram of TDR setup.


64
Log Frequency (Hz)
Figure 21: Frequency dependent imaginary component of the
observed complex dielectric constant for
solutions of n-propanol and n-hexanol.


90
Table 8
Water in n-Butanol
% Water es r X 10~6 Hz
10.0
18.3
2.2
423
25.1
19.1
3.1
669
37.7
20.4
4.1*
912
50.6
23.0
5.3*
1271
60.1
30.6
10.4*
1478
High values of indicate that a faster process exist
outside of our time window. This value of is not the
value normally observed for a single process system.


117
END IF
LOCATE 15, 4
PRINT "Delay time: HOURS ; MINS. ; SECS. -
170 LOCATE 15, 24
PRINT "
LOCATE 15, 24
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 170
HRS = VAL(LL$)
LOCATE 15, 24
PRINT USING HRS
172 LOCATE 15, 37
PRINT "
LOCATE 15, 37
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 172
MINS = VAL(LL$)
LOCATE 15, 37
PRINT USING "##; MINS
174 LOCATE 15, 50
PRINT "
LOCATE 15, 50
LL$ = FNINP$
IF LEN(LL$) > 2 GOTO 174
SECS = VAL(LL$)
LOCATE 15, 50
PRINT USING SECS
TDELAY = 3600 HRS + 60 MINS + SECS
LOCATE 17, 4
PRINT "Quit when the intervals are completed? Y/N"
176 LOCATE 17, 60
PRINT "
ENDD$ = FNAN$
LOCATE 17, 60
IF ENDD$ <> "Y" AND ENDD$ <> "N" GOTO 176
IF ENDD$ = "Y" THEN PRINT "Yes" ELSE PRINT "No"
LOCATE 23, 20
PRINT "Is this correct? Y/N"
LOCATE 23, 41
ANS$ = FNAN$
IF ANS$ <> "Y" GOTO 110
CLS : LOCATE 12, 4
PRINT "Running a TDR experiment please do not disturb."
XYZ = FNWAIT(TDELAY)
180 GOSUB MAINSCREEN
START1 = TIMER
COM$ = "AVG100"
GOSUB COMTDR
XYZ = FNWAIT(20)
COM$ = "0 WFM + CHR$(48 + SSAMP) + >WFM"
GOSUB COMTDR
XYZ = FNWAIT(5)


CONCLUSIONS
103
APPENDIX 106
REFERENCES 138
BIOGRAPHICAL SKETCH 144
iv


DIPOLE
ORIENTATION
7
ELECTRONIC
POLARIZATION
E'(U) FREQUENCY DEPENDENT
DIELECTRIC CONSTANT
£*(0) LOSS FACTOR
Figure 2: Three mechanisms for describing dielectric
relaxation.


APPLICATION OF TIME DOMAIN REFLECTOMETRY
TO SOLUTION PROCESSES
By
NGAI M. WONG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1990


129
float x[];
{
int i,j,l, nstart, ntot;
float xl, x2, sum;
nstart = n 48;
ntot =64;
for( j = 0; j < 3; j++) {
smooth(ntot,&x[nstart], 2);
nstart = nstart + 16;
}
}
/* ********************************************************* */
void ratio(n,top,bottom,depth) /* returns ratio in top
*/
int n;
float depth;
struct complex top[], bottom[];
{
int i;
float depthl;
depthl = C / depth; /* c / d is factor */
for( i = 0; i < n; i++)
top[i] = escalar(Cdiv(top[i],bottom[i]),depthl);
}
/* ********************************************************* y
/* ******************************************************** */
void slow_ft(nx,nf,x,f,dt,trans)
int nx,nf;
float x[],f[],dt;
struct complex trans[];
{
int i,j;
float sreal,simag, dwt;
double swt, swi, cwt, ewi, cwtemp;
for(i = 0; i < nf; i++)
dwt = dt f[i];
sreal = x[0];
simag = 0.0;
swi = sin(dwt);
ewi = cos(dwt);
swt = swi;
cwt = ewi;
for(j =1; j < nx
/* the sine and cosine functions are */
/* calculated incrementally by the */
/* angle addition formula rather than */
/* repeated calls to sin and cos */
' j++) {


74
larger than in butanol. Sodium chloride in these solvents
has a five fold difference in solution conductivity. The
conductivity of aqueous sodium chloride solutions is
attributed to the migration of ions that are formed in a 1:1
ionic system. The observed lower conductivity of sodium
chloride in butanol suggests that the sodium chloride is
ion-paired. The difference in the solution conductivity of
the various solvents indicates that Aliquat becomes highly
ion-paired in solvents like butanol with the solution
conductivity arising from Aliquat's ability to migrate in
solution. At low concentrations, the number of Aliquat
molecules determines the solution conductivity. At
approximately 10% Aliquat, aggregation begins to occur,
lowering Aliquat's mobility by increasing the aggregate size
and decreasing the total number of mobile aggregates found
in solution.
The 35C1 NMR line width, full width at half height, of
Aliquat/butanol solutions are shown in Figure 26. The line
width remains constant for solutions with less than 5.0%
Aliquat. At higher concentrations of Aliquat, the line
width increases with increasing concentration. This type of
behavior is indicative of systems that form micelles. The
break point in the 35C1 NMR line width is the critical
micelle concentration, cmc,87 where a transition in
structure is made from simple monomeric and dimeric ion-
pairs to higher order aggregates. The cmc for Aliquat in


Absorption Mode of Dielectric Constant
88
35
30
25
20
1 5
10
0
7.5 7.7 7.9 8.1
8.3 8.5 8.7
Log Frequency (Hz)
8.9 9.1 9.3 9.5
Figure 32: Theoretical fit of the observed real component
spectra for solutions of n-butanol and water.


30
separation, with the cmc as the saturation concentration.
This two site model works well for a number of systems:86-88
CgH17NH3Cl, C8H17N(CH3)3C1, C16H33N(CH3) 3C1, CgH-^Nf^Br,
C10H21NH3Br' C9H19N(CH3)3Br, C10H21N(CH3)3Br,
C14H29N(CH3)3Br' C16H33N(CH3)3Br/ and decylpyridinium
bromide. Plots of the relaxation data versus the inverse of
the concentration give two straight lines like that shown in
Figure 8 with the intersection at the cmc for the system.
This value has been found to compare well with other methods
of determining the cmc.87 The model breaks down at high
concentrations of the surfactant. This deviation is
attributed to the transition of the micelle shape from
spherical to the rod shaped88 which leads to a much larger
surface area and alteration in the interactions that affect
the quadrupolar relaxation.
Reversed micelle studies show similar results to those
observed in the micelle studies as seen in the
cetyltrimethyl ammonium bromide, hexanol, and water
system.86,88'91'92 The halide relaxation rate is observed
to be independent of the hexanol concentration below a
critical value. As the concentration exceeds this value,
the relaxation rate increases at a greatly enhanced rate as
seen in Figure 9. It is believed that the halide ions
resides at the core of the micelle where they are highly
hydrated. The environment around the halide remains fairly
constant while the hexanol concentration is below this


100
the spectral data. These artifacts arise from the power
splitter that is used to send the voltage pulse to two
separate cells (one reference, one sample). The splitter
has a tendency to set up a resonance feedback from the
repetitive excitation of the voltage pulse. This feedback
creates artifacts in the high frequency end of the TDR and
distorts the remaining portions of the spectra. The
required specifications for this power splitter limits the
availability of this device from alternative sources.
Several difference units have been tried with similar
results.
The best solution for handling this noise problem is in
the software manipulation of the data. The smoothing and
baseline correction routines used in the Fourier analysis
play an important role in this sensitivity problem. These
routines are used to distinguish between the noise in the
baseline and the observed processes. Systems with small
static dielectric constants are significantly affect by
these smoothing and baseline correction routines. The
spikes and discontinuities in the baseline can be mistaken
for processes, resulting in greatly distorted frequency
domain spectral data. The spikes can be handled by most
smoothing routine with a minimal amount of problems. The
discontinuities in the baseline are more difficult to
handle. The current routines used for the data smoothing
and baseline correction do not contain algorithms to handle


107
DEF FNAN$
1 AZ$ = UCASE$(INKEY$)
IF AZ$ = "" GOTO 1
FNAN$ = AZ$
END DEF
DEF FNINP$
LINE INPUT L$
FNINP$ = UCASE$(L$)
END DEF
DEF FNWAIT (SEC)
STARTING! = TIMER
FINISH! = STARTING! + SEC
IF FINISH! > 86400 THEN
DO UNTIL TIMER = .1
LOOP
FINISH! = STARTING! + SEC 86400
END IF
DO UNTIL TIMER > FINISH!
LOOP
FNWAIT = 1
END DEF
DIM FILENAME$(10), SAMP(10), HEAD$(25)
BLK$ = SPACE$(35)
COM$ = ""
LCOM$ = ""
GOSUB MAINSCREEN
10 LOCATE 5, 3
COM$ = FNINP$
LOCATE 5, 3
PRINT BLK$
LINLEN = LEN(COM$)
IF LINLEN < 2 GOTO 10
IF LINLEN >35 THEN
LOCATE 5, 3
PRINT BLK$
LOCATE 5, 3
PRINT "TOO MANY COMMANDS"
LOCATE 23, 35
PRINT "Any key to continue"
ANY$ = FNAN$
GOSUB MAINSCREEN
GOTO 10
END IF
LCOM$ = COM$
IF COM$ = "DIR" THEN
GOSUB DIR
GOSUB MAINSCREEN
GOTO 10
END IF
IF COM$ = "EXIT" OR COM$ = "QUIT" GOTO 9999
IF COM$ = "HELP" THEN
GOSUB HELP


82
the intensity of the butanol/butanol interactions enabling
us to detect other processes. Furthermore, one can compare
the competition between CC14 and butanol for the hydrophobic
region of Aliguat. The dielectric spectra for various
solutions of approximately 40% butanol in CC14 are shown in
Figures 30 and 31. The spectral data can be fit to a single
process for mole ratio greater than 100/1 butanol to
Aliguat. This single process is that normally observed for
a binary system of butanol and CC14, summarized in Table 7.
The aggregate size of the diluted butanol is smaller than
that normally found in neat butanol; correspondingly, a
larger value is observed for the critical freguency. Two
processes are required to fit the observed spectra for mole
ratios ranging from 13/1 to 100/1 (Table 7) with the fast
process7 critical frequency remaining fairly constant. The
intensity of the slower process increases with increasing
Aliquat with the critical frequency remaining constant. The
spectral data shows that the tail end of the slower process
is just appearing inside the lower frequency range of our
time window, the values obtained for this process are the
upper limit for the critical frequency and the lower limit
for the static dielectric constant. We can only estimate
this slower process from the perturbation made on the
butanol spectrum. When the butanol relaxation disappears,
we lose our probe for estimating the slower process's
critical frequency and static dielectric constant. At high


8
of 180 per second will move only 0.2 in a field that is
alternating at a rate of 1000 cycles per second. In essence
the molecule appears to be frozen in place.
The time scale for the electronic and atomic
polarization is so fast that they appear to be instantaneous
on current instrumentation that is used to measure
dielectric relaxation processes. Consequently, the only
processes that can be studied occur through the dipole
reorientation mechanism. The "high frequency" dielectric
constant, e^, is used to describe the contribution from the
electronic and atomic polarizations.
The first theoretical model for describing the dipole
reorientation in molecular systems was given by Debye.10 It
is assumed that the dipole moment of a molecule moves under
the influence of a torque with full orientational freedom.
The dipolar motion is hindered by internal friction that is
related to the viscosity of the medium. Brownian motion
acts as the randomizing factor which causes the breakdown of
the dipole realignment. The resulting steady-state equation
for a single process in terms of a complex dielectric
function, e*(iw), is given by
e*U) = i. + (2)
1 + WT
where w is the angular frequency with w = 2?rf, f is the
frequency in Hz, t is the process time constant for the


23
important in helping to understand these processes, but are
of limited utility since the body of experimental data is
small, limiting the application of these models. Comparison
of the experimental results with different theories has led
to the preferred use of the extended J-diffusion classical
model over others.49-51 A number of people have studied
alkali halides in aqueous solution: Itoh and Yamagata,44
Hertz,36'37'52-56 Richards and co-workers,57-62 Arnold and
Packer,63 and Bryant.64 The concentration dependence
studies of alkali halides in aqueous solution can be
summarized with the following observations. The relaxation
rate increases with an increase in concentration. The
relative magnitude of the change depends on the size of the
halide ion. The mechanism for the relaxation rate depends
upon a complex interaction involving the alkali halide
concentration as well as the size of the alkali metal ion.
The order of increasing effect on the Cl- and Br relaxation
is K+ < Na+ < Rb+ < Li+ < Cs+ with I-, the position of Na+
and Rb+ are reversed.
Studies involving other inorganic halides like hydrogen
halides,48'57'65'66 ammonium halides,36'55 and alkaline
earth halides36'57'58'67'68 have yielded little additional
information. The observed effects were similar to those
seen for the alkali halides. In the case of hydrogen and
ammonium, similar results to those from the smaller sized
alkali ions were obtained. The alkaline earth ions proved


61
Table 2
Butanol in Carbon Tetrachloride
Butanol
£<=
r x 10"6
100.0
s
18.6
2.2
340
95.4
17.6
2.4
344
89.7
16.8
2.7
335
84.9
15.8
2.7
335
70.1
12.6
2.8
340
49.9
7.2
2.5
414
39.4
4.8
2.1
504
28.9
3.6
2.5
698


43
half the window. It is best to start with 50 nsec/division
(500 nsec window) and work towards 1 nsec/division (10 nsec
window) for new systems.
The use of time windows less than 5 nsec tends to have
problems in the Fourier transform routine. Temperature
instability of the various components causes timing and
electronic drift problems which leads to large errors in the
Fourier transform routines, imposing a practical upper limit
of 3 X 109 Hz on the system. A practical lower limit of
1.5 X 107 Hz is dictated by the manner in which the scope
collects data. This system is capable of collecting a
maximum of 1024 points with its largest window being
500 nsec. This gives spectral data in the range of
15 to 400 X 106 Hz for the 500 nsec window. This limited
range is determined by the width of the time window and the
resolution of data used in the Fourier transform. Several
windows are needed to cover the entire spectral range with
each overlapping window spanning a frequency range of
approximately 1.5 order of magnitude. A single time window
covering the frequency range of 1.5 X 107 to 3 X 109 Hz can
be obtained if the resolution of the collected data in this
500 nsec window is increased by at least one order of
magnitude (a minimum of 10,000 data points).
The voltage/division control setting is determined by
the size of the voltage pulse used. A setting of
50 mV/division is required for the 250 mV pulse outputted by


Critical Frequency X 1 0-6 Hz
70
Mole 7. Solute in n-Butanol
Figure 24: Comparison of the critical frequencies obtained
for the pyridine and carbon tetrachloride
systems.


27
Figure 6: Phase diagram of a ternary system composing of
hexadecyltrimethylammonium bromide (CTAB),
hexanol, and water, reference 84. L1 denotes a
region with water rich solutions; L2 a region
with hexanol rich solutions; D and E are lamellar
and hexagonal liguid crystalline phases,
respectively. In the figure are also
schematically indicated the structures of normal
(region) and reversed (L2) micelles as well as
liquid crystalline phases.


TDR SYSTEM ENHANCEMENTS AND MODIFICATIONS
Studies of various systems have indicated two
limitations of the current TDR setup. The frequency range
and the detection limit need to be addressed to enhance the
usefulness of TDR. The frequency range limits the TDR to
studying systems which have processes with rates similar to
those found in polar liquids. The detection limit of the
TDR require that the system's static dielectric constant be
greater than 3. There are many other interesting systems
like polymers and micelles that do not fit these
requirements.
The detection limit arises from the size of the voltage
pulse, the noise level of the signal, and the manner in
which the data is handled in the Fourier analysis. The
sensitivity can be increased by increasing the size of the
voltage pulse to obtain larger responses through a larger
excitation source. The present size of the voltage pulse is
0.25 V and can be increased to 0.5 V without any
difficulties. Large voltage pulses can cause the sample to
experience a phenomena called dielectric breakdown. This is
the decomposition of the sample through oxidation/reduction
type pathways. The commercial availability of pulse
98


62
Table 3
Primary Alcohols
Static Dielectric Constant
Alcohol
TDR
Lit.
fc x 10
Methanol*
33.2
32.7
Ethanol*
25.5
24.3
980
1-Propanol
21.8
20.1
490
1-Butanol
18.6
17.6
340
1-Hexanol
11.3
13.3
260
1-Octanol*
9.5
9.6
130
1-Decanol*
7.6
7.7
66
1-Dodecanol*
5.7
5.4
56
*Reference 103.


#include
#include
#include
120
void baseline();
void trans_to_diel();
void smooth();
float *zero_fill();
void ratio();
void slow_ft();
float *gen_freq();
void renorm();
main(argc,argv)
int argc;
char *argv[];
{
int i,j,k, npd,nps,nskip, nf, DER_DIF, RAW_OUT;
float *dif_spec,*sum_spec, dtd, dts, *dhold, *shold;
float *frequency, depth, fmax, x;
struct complex *fr_dif, *fr_sum, *diel_spec, rrr,qqq,sss;
FILE *dif, *sum, *outfile, *config;
void output();
void disk_out();
/* the configuration file is a flat ASCII file with the */
/* following format the (A,B) notation refers to a choice */
/* of A or B *is default */
/*
Explanations:
NF No zero Fill
*ZF Zero Fill to 2t
SR Sample and Reference spectra
*SD sum and difference spectra
*DR Transform as derivatives both sum and dif
ND Transform dif as natural function
*NC No Conductivity
CO Conductivity correction if warrented
filenamel Difference spectrum (SD) or
Sample spectrum (SR)
filename2 Sum spectrum (SD) or
Reference spectrum (SR)
filename3 name for output of raw transform data
CARD 1 (NF,ZF) (SR,DS) (DR,ND) (NC,CO)
CARD 2 sample depth (in cm)
CARD 3 NSMOOTH NSKIP
CARD 3 filenamel filename2 filename3
CARD 4..EOF comments on the experiment
*/


108
GOSUB MAINSCREEN
GOTO 10
END IF
IF COM$ = "SERIES" THEN
GOSUB SERIES
LCOM$ = "SERIES completed"
GOSUB MAINSCREEN
GOTO 10
END IF
IF COM$ = "TIMED" THEN
GOSUB TIMED
LCOM$ = "TIMED SERIES completed"
GOSUB MAINSCREEN
IF ENDD$ = "Y" THEN GOTO 9999 ELSE GOTO 10
END IF
FOR I = 1 TO LINLEN 4
IF INSTR(COM$, "SENDX") > 0 THEN
CLS
LOCATE 10, 2
PRINT "Filename to save data in?"
LOCATE 10, 30
NAME$ = FNINP$
NLEN = LEN(NAME$)
IF NLEN = 0 OR SPACE$(NLEN) = NAME$ THEN
LOCATE 10, 30
PRINT BLK$
GOTO 90
END IF
GOSUB MAINSCREEN
GOSUB SENDTDR
LOCATE 9, 3
PRINT BLK$
LOCATE 9, 3
PRINT LCOM$ + completed"
GOTO 10
END IF
NEXT I
GOSUB COMTDR
LOCATE 9, 3
PRINT BLK$
LOCATE 9, 3
PRINT COM$ + was sent"
GOTO 10
9999 END
COMTDR:
OPEN "COMI:9600,N,8,1,RB10000" FOR RANDOM AS 1
PRINT #1, "RQSON"
XYZ = FNWAIT(l)
PRINT #1, COM$


BACKGROUND
Dielectric Theory
A perfect dielectric material is an insulator. The
internal charges are so closely bound that no electric
current may be conducted through it. The atoms are fixed in
its lattice and are not free to move through the material.
In reality, there are no perfect dielectric materials
because atoms are free to shift around their fixed positions
when an external field, EQ, is applied to the material. A
parallel plate capacitor can be used to generate this
external field.7 The dielectric material is placed between
the plates as shown in Figure la. The capacitor is charged
so that one plate is positively charged and the other is
negatively charged. The dielectric material's response to
this external field is to set up its own electric field
(induced field, E-^) to counter the field from the capacitor.
The induced field is produced by the realignment of the
dipoles in the dielectric material. This sets up a surface
charge that is opposite of that for each of the plates in
the capacitor as shown in Figure lb. Typically, the induced
field from dielectric material is less than the external
field. The observed or resultant field, E2, for dielectric
3


86
concentrations of Aliquat, mole ratios less than 10/1, we
can only observe the tail end of this slow process in our
time window. The spectra show only a sloping baseline with
no discernible features.
The intensity and critical frequency of the fast process
are constant over the butanol/Aliquat mole ratio range of
13/1 to no Aliquat. In neat butanol, Aliquat can extract
butanol molecules out of the bulk phase without influencing
the properties of the bulk phase. A constant critical
frequency and decreasing intensity of the butanol relaxation
occur with increasing Aliquat concentration. The observed
trends of this ternary system suggest that the concentration
and aggregate size of the butanol species in CC14 are not
influenced by the addition of Aliquat. The constant
intensity of the butanol relaxation results from the CC14
interfering with the extraction of butanol by Aliquat. This
implies that the butanol is extracted into the hydrophobic
region of Aliquat in neat butanol solutions. Since CC14 is
normally preferred over butanol in hydrophobic interactions,
the butanol in this ternary system is left in the bulk and
is unaffected by the addition of Aliquat. The presence of
the slow process suggests that butanol is coordinating to
the hydrophilic region of Aliquat at mole ratios of butanol
to Aliquat less than 100/1. The intensity of the slow
process increases with increasing Aliquat concentration
indicating a large change in the dipole moment. The simple


125
Program TDRUTIL.C
This is the second module required for the Fourier
routines, please refer to TDRDRIVE.C for description of
these routines.


136
* NPROC + 1
1050
* NPROC
+ 1
GOSUB VERTIX
IF R > BR GOTO 1030
RT = R
FOR I = 1 TO 2
TT(I) = E(I)
NEXT I
F = 2
GOSUB VERTIX
IF R > RT GOTO
1080 FOR I = 1 TO 2
S(I, JW) = E(I)
NEXT I
RI(JW) = R
GOTO 1020
1050 R = RT
FOR I = 1 TO 2
E(I) = TT(I)
NEXT I
GOTO 1080
1030 IF R <= WR GOTO 1080
F = -.5
GOSUB VERTIX
IF R <= WR GOTO 1080
FOR I = 1 TO 2 NPROC + 1
FOR J = 1 TO 2 NPROC + 2
IF J <> JB THEN S(I, J) = (S(I,
NEXT J
NEXT I
GOTO 1020
RETURN
* NPROC + 1
JB) + S(I, J)) / 2
End subroutine Simplex
1100
REM
REM
REM
REM* ****************************************************
REM Set up of parameter matrix
REM*****************************************************
PARMAT:
FOR I = 1 TO 2 NPROC + 1
FOR J = 1 TO 2 NPROC + 2
AI = 0
IF I >= J THEN AI = -1!
S(I, J) = E( I) D( I) AI D( I) / 2
NEXT J
NEXT I
FOR I = 1 TO 2 NPROC + 2
FOR J = 1 TO 2 NPROC + 1
E(J) = S(J, I)
NEXT J
R = FNFUNK
RI(I) = R
NEXT I
RETURN


102
widths. The delay lines used in the current setup will be
inadequate for wider time windows. The delay line is used
to offset the incident and reflected steps observed for the
voltage pulse. Assuming that the speed of light in a
coaxial cable is 3 X 108 m/sec and a time window wide enough
to see a process with a fc of 1 X 104 Hz will require a
cable of 1,640 feet in length to offset the incident and
reflected pulse by 5% of the time window. This offset is
important, it is used as the baseline for the observed
waveform.


133
40 CLS
FOR I = 2 TO NPROC
E(NPROC+I) = E(NPROC+I-1)-(E(NPROC+1)-E(2*NPROC+l))/NPROC
D(NPROC + I) = 1
NEXT I
FOR I = 1 TO 2 NPROC + 1
IF D(I) <> 0 THEN D(I) = E(I) .1
NEXT I
GOSUB SIMPLEX
CLS
AFIX$ = "Rate ## has a fixed freq. of #####.# MHz"
AFLT$ = "Rate ## has a freq. of #####.# MHz"
FOR I = 1 TO 2 NPROC + 1
IF I <= NPROC THEN
IF D(I) = 0 THEN
PRINT USING AFIX$; I; E(I) / 1000000!
ELSE
PRINT USING AFLT$; I; E(I) / 1000000!
END IF
END IF
DCFIX$ = "Dielectric Constant ## is fixed at ###.###"
DCFLT$ = "Dielectric Constant ## is ###.###"
IF I = NPROC THEN PRINT
IF I > NPROC THEN
IF D(I) = 0 THEN
PRINT USING DCFIX$; I NPROC; E(I)
ELSE
PRINT USING DCFLT$; I NPROC; E(I)
END IF
END IF
NEXT I
PRINT
PRINT USING "Reduced CHI squared is ###.#####; BR
PRINT : PRINT
FOR I = 1 TO NH
FOR J = 1 TO NPROC
WT = (10 A (FREQ(I))) / E(J)
DCAMP = E(NPROC + J) E(NPROC + J + 1)
AR(J, I) = DCAMP / (1 + WT A 2)
AI(J, I) = DCAMP WT / (1 + WT A 2)
NEXT J
NEXT I
PRINT "Do you wish to see graphics? Y/N"
11 AN$ = FNAN$
IF AN$ = "N" THEN GOTO 10
IF AN$ <> "Y" THEN GOTO 11
SCREEN 12
VIEW (20, 15)(619, 464), 7
WINDOW (FREQ(1), -.5)-(FREQ(NH), E(NPROC + 1) + 1)
FOR I = 1 TO NH
X = FREQ(I)
Y = DCR(I)


21
direction of the angular momentum and leaves the magnitude
unaffected.
The jump reorientation model looks at the liquid with
activation barriers to rotation or the migration of lattice
defects or holes. Application of this model to the
experimental data presents some difficulties due to the lack
of information about several of the parameters needed in the
analysis. These parameters include the geometry of the
lattice, the energy barriers, the number of vacancies or
defects, etc. A quasilattice random flight model was
proposed by O'Reilly.34'35 The model assumes that the first
solvation shell can be approximated by a lattice and
describes large changes in angular rotation by small-steps
of angular rotation. O'Reilly's model addressed some of the
problems like vacancies and translational diffusion by
vacancy migration, but still require several other
parameters that are lacking for a complete analysis.
The quadrupolar relaxation of halide ions is
intermolecular in nature and result from the interaction
with other ions or dipoles in solution. Two models have
been proposed for the origin of the change in the magnitude
of the field gradient at the nuclei; electrostatic and
electron distortion models. Experimental discrimination
between these two models is difficult due to limited
literature comparison on the merits of each model. The
electrostatic model36-43 looks at the distribution of


92
water increases, the composition of the aggregate changes
from pure butanol to a 1:1 butanol/water aggregate. This
1:1 aggregate is manifested in a constant dielectric spectra
observed for the butanol phase for solutions with water
greater than 50%. The addition of water beyond the 50%
water region forces the formation of water aggregates,
leading to the formation of the second phase.
Ternary System of Water, n-Butanol. and Aliquat 336
Many practical applications of Aliguat 336 have involved
the use of agueous media. In general, little is known about
the interactions that occur with phase transfer agents like
Aliguat 336. Many of the applications are optimized through
trial and error type technigues. A fundamental
understanding of the competition and interactions of water
and butanol for the various sites on Aliguat can enhance and
widen the applicability of this class of compounds. The
relaxation processes of a 10% Aliguat in n-butanol solution
with varying amounts of water added are investigated. The
solutions are homogeneous up to 50% water. The 50% water
solution shows two phases with a third observed for
solutions of higher water concentration. The two phase
system is the separation of the water and butanol phases.
The third phase (a precipitate) shows up in solution with
water greater than 50% is Aliquat. The dielectric spectra
for these solutions are shown in Figures 34 and 35. The


17
aggregation of the alcohol is absent. Often it is assumed
that monomeric species are involved. Similar assumptions
are made in studies of the change in 0-H stretching
freguencies for alcohol-base adducts in dilute CC14
solution.18 In a recent analysis of the "anomalous basicity
of amines,"19 it was shown that the acidity of hydrated
proton species as well as the relative importance of
covalent and electrostatic bonding contributions changed
appreciably with the extent of hydration, i.e. the n value
of H(H20)n+. Similar changes in the acidity or basicity of
(ROH)n molecules may be anticipated as n varies. As a
result, gas phase studies of monomers and solution studies
in inert solvents may determine properties of species that
do not exist in pure solvents. Such information is relevant
to understanding the chemistry in pure protic solvents and
in mixed solvent systems.
Frequency dependent studies of the dielectric constant
show dielectric relaxation corresponding to the making and
breaking of hydrogen bonds in alcohol clusters.20 Three
different relaxation times have been found for each of the
10 primary alcohols from propyl to dodecyl. Sixteen
wavelengths of measurement were used spanning 30,000 to
0.22 cm. The long relaxation occurs over ranges of 1 to
22 X 10-10 sec and corresponds to breaking hydrogen bonds of
terminal OH groups in a cluster concurrent with rotation of
the alcohol as it forms a new hydrogen bond in the same


22
charges from other ions and solvent molecules around the
relaxing ion. The change in the field gradient is caused by
the molecular motion of the surrounding species. Hertz36-38
and Valiev39-43 have both studied this problem using the
electrostatic model with different approaches and varying
degrees of completeness. The most recent work by Hertz,38
being the most elaborate for halides at infinite dilution in
water, calculated 1/T1 using the electrostatic model for
35C1, 81Br, and 127I to be 40, 1350, and 5650 sec-1 compared
to the observed values of 42, 1050, and 5270 sec-1,
respectively.
The electronic distortion model was first proposed by
Itoh and Yamagata.44 The model suggests that the relaxation
is produced by the deformation of the ion's electron cloud
caused by the collision of the relaxing nuclei with other
species in solution. Comparison of the experimental results
with electronic distortion theory is difficult since some of
the important quantities (correlation time, excitation
energy, field gradient, and nuclear magnetic shielding) are
very difficult to estimate.
Covalently bonded halides have been used to study
molecular motion through the correlation time of the
molecule.45-48 Estimates of the correlation time have been
obtained mainly from NMR line widths for various molecules.
The theoretical models that describe the changes in the
field gradient that affect quadrupolar relaxation are


115
IF LEN(LL$) > 2 THEN
LOCATE 3, 42
PRINT SPACE$(LEN(LL$))
GOTO 120
END IF
IF LL$ = "E" GOTO 199
NSAMP = VAL(LL$)
IF NSAMP < 1 OR NSAMP > 999 THEN
LOCATE 3, 42
PRINT "
GOTO 120
END IF
LOCATE 5, 4
PRINT "Reference Waveform Number "
130 LOCATE 5, 32
LL$ = FNINP$
IF LEN(LL$) > 1 THEN
LOCATE 5, 32
PRINT SPACE$(LEN(LL$))
GOTO 130
END IF
REFF = VAL(LL$)
IF REFF < 1 OR REFF > 9 THEN
LOCATE 5, 32
PRINT BLK$
GOTO 130
END IF
LOCATE 7, 4
PRINT "Sample Waveform Number "
140 LOCATE 7, 29
LL$ = FNINP$
IF LEN(LL$) > 1 THEN
LOCATE 7, 29
PRINT SPACE$(LEN(LL$))
GOTO 140
END IF
SSAMP = VAL(LL$)
IF SSAMP < 1 OR SSAMP > 9 OR SSAMP = REFF THEN
LOCATE 7, 29
PRINT "
GOTO 140
END IF
C0M1$ = WFM WFM "
MID$(C0M1$, 1,1)= CHR$(48 + REFF)
MID$(C0M1$, 7, 1) = CHR$(48 + SSAMP)
LOCATE 9, 4
PRINT "Path to send files to "
LOCATE 9, 26
PATHH$ = FNINP$
PLEN = LEN(PATHH$)
IF PLEN = 0 OR SPACE$(PLEN) = PATHH$ THEN
PATHH$ = ""


56
The static dielectric constant of a mixture of non
interacting systems is given by:102
es = NAesA + NBesB
(ID
Over the concentration range 0 to 100 mole percent butanol
in CC14, our results show that the intensity of the static
dielectric is not obeying this relationship (Figure 18).
The observed behavior suggests that the average molecular
weight of the aggregates is staying about the same over the
concentration range 70 to 100% butanol. At lower
concentrations of butanol, the deviation is that expected
for an increase in the concentration of the smaller
aggregates.
The frequency dependence of the real and imaginary
components of the dielectric constant is plotted versus the
log frequency in Figures 19 and 20. The data can be fit to
within experimental error with one average process to
equations (6) and (7) using a Simplex routine program listed
in the Appendix. The critical frequency is constant for the
range of 70 to 100% butanol. At higher dilutions, the
process becomes faster.
Neat butanol has a critical frequency of 3.4 X 108 Hz
with the peak spanning the range of 6 X 107 to 2 X 109 Hz.
This frequency range represents an overlap of the dynamic
process on a large number of aggregates in a three-


Absorption Mode of Dielectric Constant
58
20
18
1 6
1 4
12
10
8
6
4
2
0
i 1
7.5 7.7 7.9
8.1 8.3 8.5 8.7 8.9
Log Frequency (Hz)
9.1 9.3 9.5

Butanol

95.4 mole 7.

89.7 mole 7.

84.9 mole 7.
o
70.1 mole 7.

49.9 mole 7.
O
39.4 mole 7.
A
28.9 mole 7.
Theoretical
Butanol in CCU
Figure 19: Theoretical fit of the observed real component
spectra for solutions of n-butanol and carbon
tetrachloride.


26
hydrophobic cation. The observations tend to exclude direct
ion-ion interactions on the grounds that the change in the
relaxation rate is related to the change in the number and
length of the substituted alkyl groups, the lack of a
competition effect between differing halide ions, and the
presence of relaxation enhancement in uncharged solutes. In
addition, modelling studies of tetraalkylammonium systems
using an ion-ion interaction model failed to produce
reasonable results.69-71'76 With these considerations, it
is proposed that the mechanism for quadrupolar relaxation in
tetraalkylammonium halide systems is indirectly influenced
by the hydrophobic cation.
A natural extension of the substituted alkyl ammonium
halides studies is to look at micelle type systems, since
many of the substituted alkyl ammonium salts can form
micelles. Some of the major problems associated with
studying micelle systems are the drastic changes in phase
equilibria and the different micellar shapes that may
accompany the various composition of the micelle system as
shown in Figure 6. These problems result from the nature of
these amphiphilic substances (surfactants) which consists of
a hydrophilic part that is either charged or highly polar
and a hydrophobic part that is neutral, nonpolar, and
typically a long alkyl chains.82-84
The surfactants behaves as ordinary electrolytes at low
concentrations, but as the concentration increases they


11
(dispersion mode) is called the dielectric loss function
which refers to the power lost through the dielectric
material. The energy absorbed from the applied electric
field (the real component) is dissipated by the "friction"
(the imaginary component) created by the dipole attempting
to align itself to the field. The maximum loss value occurs
at the critical frequency, fc, which is the same point as
the inflection point seen in the real component where ut = 1
and describes the frequency of the observed process. The
imaginary component is symmetric in the log of frequency
around the maximum loss value covering a broad range of
frequencies. A plot of e" versus e', Cole-Cole plot,9 for a
Debye dielectric yields a semicircle as shown in Figure 4.
The maximum loss value is equal to (es e^/2. Materials
that obey the complex dielectric function, equation (2), are
termed Debye dielectrics. The Debye model can be extended
to describe multiple processes10 where equations (3) and (4)
become
n
i
(6)
i=l
n
i=l
(7)


134
CIRCLE (X, Y), .015, 1
PAINT (X, Y), 1
Y = DCI(I)
CIRCLE (X, Y), .015, 4
PAINT (X, Y), 4
IF I < NH THEN
YRT1 = E(2
*
NPROC
+
1)
YRT2 = E(2
*
NPROC
+
1)
YIT1 = 0
YIT2 = 0
FOR J = 1 '
ro
NPROC
Y1 = E(2
*
NPROC
+
1)
+ AR(J,
I)
Y2 = E(2
*
NPROC
+
1)
+ AR(J,
I +
LINE (FREQ(I), Y1)-(FREQ(I + 1), Y2), 8 + J
LINE (FREQ(I), AI(J, I))-(FREQ(1+1), AI(J, 1+1)), 8+J
YRT1 = YRT1 + AR(J, I)
YRT2 = YRT2 + AR(J, I + 1)
YIT1 = YIT1 + AI(J, I)
YIT2 = YIT2 + AI(J, I + 1)
NEXT J
LINE (FREQ(I), YRT1)-(FREQ(I +1), YRT2), 15
LINE (FREQ(I), YIT1)-(FREQ(I +1), YIT2), 15
END IF
NEXT I
AN$ = FNAN$
SCREEN 0
10 PRINT "Do you wish to save this data? Y/N"
21 AN$ = FNAN$
IF AN$ = "N" THEN GOTO 20
IF AN$ <> "Y" THEN GOTO 21
INPUT "Name of OUTPUT DATA FILE"; OUTPT$
OPEN OUTPT$ FOR OUTPUT AS #2
AA$ = "#.##### ###.### ###.### ###.### ###.###"
FOR I = 1 TO NH
CALR = E(2 NPROC + 1)
CALI = 0
FOR J = 1 TO NPROC
CALR = CALR + AR(J, I)
CALI = CALI + AI(J, I)
NEXT J
PRINT #2, USING AA$; FREQ(I); DCR(I); CALR; DCI(I); CALI
NEXT I
CLOSE #2
20 PRINT "Do you wish to run again? Y/N"
25 AN$ = FNAN$
IF AN$ = "N" THEN END
IF AN$ <> "Y" THEN GOTO 25
PRINT "Wish to use the OUTPUT as the NEW ESTIMATES? Y/N"
31 AN$ = FNAN$
IF AN$ = "Y" THEN GOTO 40
IF AN$ <> "N" THEN GOTO 31
GOTO 30


19
range of our current TDR system. Accordingly, no further
discussion of these processes will be presented.
Metals like gold, iridium, manganese, mercury,
molybdenum, nickel, niobium, palladium, platinum, tungsten,
and zirconium have been extracted or separated using
Aliquat 336 (trioctylmethylammonium chloride).21-28 This
quaternary ammonium salt is widely used as a phase transfer
catalyst and as a mobile phase catalyst. The better known
systems involve quaternary ammonium salts with large alkyl
groups. In general, little is known about the dynamics of
this class of compounds in solution or in moving substances
in and out of the different phases. The majority of the
physical characterization studies have been done using
nuclear magnetic resonance to study the quadrupolar
relaxation of chlorine, bromine, and iodine.
Nuclear magnetic quadrupole relaxation29 arises from the
interaction of a quadrupolar nucleus with a time-dependent
electric field gradient. This field gradient depends on two
properties: the molecular motion of the quadrupolar nuclei
and the surrounding species' dielectric properties. The
magnitude of the field gradient, influenced by the
surrounding species, is the major contribution in the
relaxation of halide ions in solution. The molecular motion
of the quadrupolar nuclei alters the direction of the field
gradient, providing the major contribution to the relaxation
mechanism of covalently bonded halides.


101
this type of noise. The addition of a manual baseline
correction routine would be the easiest and most versatile
in correcting this discontinuity problem. The manual
correction routine should allow the study of systems with
static dielectric constant as low as 1.5 with the current
TDR setup.
The maximum frequency range of the TDR is determined by
the pulse generator in the system. Two pulse generator
characteristics govern the frequency range of the system,
the risetime and the pulse width. The risetime determines
the upper limit, while the pulse width determines the lower
limit. Current commercial technology can produce a pulse
generator with a risetime of about 1 psec, which gives a
realistic upper limit of 8 X 1010 Hz. The pulse width can
be set to virtually any value, thus removing the lower
limit. In generally, the lower limit of the pulse generator
is matched to the ability of the sampling device.
Commercially available pulse generators are broken down into
two categories: 1 to 100 psec and 1 to 5 nsec risetime pulse
generators. The fast risetime generators typically have
fixed pulse widths of a microsecond or shorter. The slow
pulse generators have variable pulse widths that can be set
from microseconds to seconds.
The Tektronix TDR setup is designed to use the fast
risetime pulse generators. The acquisition of real time
modules is required to use pulse generators with wider pulse


113
PATHH$ = FNINP$
PLEN = LEN(PATHH$)
IF PLEN = 0 OR SPACE$(PLEN) = PATHH$ THEN
PATHH$ = ""
ELSE
IF 2 <> INSTR(PATHH$, AND 1 <> INSTR(PATHH$, "\") THEN
PATHH$ = "\" + PATHH$
END IF
IF "\" = MID$(PATHH$, PLEN, 1) THEN
PATHH$ = MID$(PATHH$, 1, PLEN 1)
END IF
END IF
LOCATE 7, 26
PRINT BLK$
LOCATE 7, 26
PRINT PATHH$
LOCATE 9, 20
PRINT "Waveform"
LOCATE 9, 30
PRINT "Filename"
FOR ISS = 1 TO NSAMP
LOCATE 9 + ISS, 4
PRINT USING "Sample # is in"; ISS
60 LOCATE 9 + ISS, 24
PRINT
LOCATE 9 + ISS, 24
LL$ = FNINP$
IF LEN(LL$) O 1 OR VAL(LL$) < 1 OR VAL(LL$) > 9 THEN
LOCATE 9 + ISS, 18
PRINT BLK$
GOTO 60
END IF
SAMP(ISS) = VAL(LL$)
IF SAMP(ISS) = REFF THEN
LOCATE 9 + ISS, 24
PRINT BLK$
GOTO 60
END IF
IF ISS <> 1 THEN
FOR ISI = 1 TO ISS 1
IF SAMP(ISS) = SAMP(ISI) THEN
LOCATE 9 + ISS, 24
PRINT BLK$
GOTO 60
END IF
NEXT ISI
END IF
70 LOCATE 9 + ISS, 30
PRINT "
LOCATE 9 + ISS, 30
FILENAME$(ISS) = FNINP$
LLEN = LEN(FILENAME$(ISS))


CONCLUSIONS
Time domain reflectometry is a useful technique in
understanding the fundamental interactions found in
solvation processes. Molecular size and adduct bond
strength have been seen to play important roles in solvation
processes. The mixed alcohol studies help to define the
dependence of the relaxation processes to the size of the
molecules. The statistically weighed averaging of the pure
alcohol critical frequencies and peak intensities allows the
prediction of these characteristics for any binary and
ternary alcohol systems using any primary alcohol from
ethanol to octanol. The pyridine, water, and carbon
tetrachloride in n-butanol studies have shown how the adduct
formation can affect the solvation process. In the case of
pyridine, the butanol aggregates are broken apart by the
coordination of the pyridine. The water which has a similar
dynamic structure to that observed for butanol does not
significantly affect the behavior of butanol at low
concentrations. Higher concentrations of water produce
behavior that is vastly different to that observed for
pyridine. In addition, the behavior does not resemble that
of neat butanol or water suggesting that both the butanol
103


66
and that of hexanol on the mixed and pure clusters is the
same. This is consistent with the hydrogen bond strengths
being similar and the dynamic process being dominated by the
molecular size of the moving group with the average size of
the aggregates being comparable to the average size in the
neat liquids.
Binary System of n-Butanol and Pyridine
This system provides the opportunity to examine the
perturbation made on butanol aggregation by the addition of
strong donor molecules. Pyridine has a relaxation frequency
that is faster than can be observed in our apparatus. Thus,
the main interactions that will influence the spectrum are
butanol/pyridine and butanol/butanol.
The dielectric spectra of various solutions of butanol
and pyridine are shown in Figures 22 and 23. The critical
frequency of these solutions shifts to higher frequencies as
the mole fraction of the pyridine is increased. The data
are fitted to Equations (6) and (7) with a single r value
that increases with pyridine concentration, summarized in
Table 5. The greater influence of pyridine compared to CC14
is shown in Figure 24. The single peak indicates that the
distribution of processes occurring is shifted toward faster
rates of relaxation with a decrease in the intensity of the
response. The direction and non-linear behavior of the
static dielectric constant and the critical frequency


97
structural transition from micelles to some other aggregate
form that is insoluble in this system. The Aliquat is
stripped from solution, converting this ternary system into
a binary butanol/water system. This transformation changes
the concentration of Aliquat found in the butanol phase as
indicated in the increase of the critical frequencies of the
two observed processes.


Voltage
41
Figure 12: Complete waveform obtained from the TDR. Step 1
is the incident pulse. Step 2 is the reflected
pulse. Step 3 is the incident pulse returning to
ground. Step 4 is the reflected pulse returning
to ground.


114
IF LLEN = 0 GOTO 70
IF LLEN > 8 OR SPACE$(LLEN) = FILENAME$(ISS) THEN
LOCATE 9 + ISS, 30
PRINT BLK$
GOTO 70
END IF
IF ISS O 1 THEN
FOR ISI = 1 TO ISS 1
IF FILENAMES(ISS) = FILENAMES(ISI) THEN
LOCATE 9 + ISS, 30
PRINT BLK$
GOTO 70
END IF
NEXT ISI
END IF
NEXT ISS
LOCATE 23, 20
PRINT "Is this correct? Y/N"
LOCATE 23, 41
ANS$ = FNAN$
IF ANS$ <> "Y" GOTO 90
COM1S = WFM WFM "
MID$(C0M1$, 1, 1) = CHR$(48 + REFF)
GOSUB MAINSCREEN
FOR III = 1 TO NSAMP
MID$(C0M1$, 7, 1) = CHR$(48 + SAMP(III))
MID$(C0M1$, 13, 1) =
COM$ = C0M1$
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NAMES = PATHH$ + "\" + FILENAMES(III) + ".DIF"
XYZ = FNWAIT(5)
GOSUB SENDTDR
MID$(C0M1$, 13, 1) = "+"
COM$ = COM1S
GOSUB COMTDR
COM$ = "0 WFM SENDX"
NAMES = PATHHS + "\" + FILENAMES(III) + ".SUM"
XYZ = FNWAIT(5)
GOSUB SENDTDR
NEXT III
99 RETURN
TIMED:
110 CLS
III = 1
LOCATE 3, 4
PRINT "How many samples do you wish to take? (999 max.)"
120 LOCATE 3, 42
LL$ = FNINPS


BIOGRAPHICAL SKETCH
Ngai M. Wong was born on May 8, 1961, in Hong Kong. He
immigrated to the United States in September of 1966.
Upon graduation from Brooklyn Technical High School in
New York, he entered a 3:2 program in chemistry and chemical
engineering at Ithaca College and Cornell University,
respectively. He received a dual degree in chemistry (B.A.)
and chemical engineering (B.S.) in May of 1984.
In August of 1984, he entered the graduate program at
the University of Florida and began working with Dr. Russell
S. Drago. He received a Master of Science degree in August
of 1986 from the University of Florida with a thesis
entitled Extension and Application of the E and C Equation.
144


5
material filled capacitor which is the summation of the
external and induced fields. Since the induced field is
opposite in direction of the external field, the resultant
field is always less than the external field. The ratio of
the external field to the resultant field is the dielectric
constant of the material. The official definition of the
dielectric constant,8 e, is
Q Q'
e = 5 (1)
F r
where F is the force of attraction between the two charges Q
and Q' separated by the distance r in a uniform medium. A
more convenient definition is the relative permittivity
which is the ratio of the electric fields in the gap between
the plates of a capacitor when the plates are separated by
vacuum and by a dielectric material. A more intuitive feel
for the dielectric constant is the material's ability to
store electrical energy (i.e. the greater the charges ([Q
and Q']) the larger the dielectric constant as expressed in
the official definition).
The induced field from the dielectric material occurs
through processes best described as "dielectric
relaxations." Consider a system containing a dipole moment
which responds to the application of an external field. The
nature of the dipole moment may be permanent or induced by


EXPERIMENTAL
Time Domain Reflectometrv
A block diagram of the TDR setup is shown in Figure 11.
The TDR setup is composed of a Tektronix 7854 mainframe
oscilloscope with a waveform calculator, a 7S12 time domain
module, a S-52 pulse generator, and a S6 sampling head. The
sample cell is made from a 7 mm SMA male rebuild kit model
2542 from Midwest Microwave with the center post 1.5 mm in
length. The TDR is connected to the sample cell through
matched low loss 50 ohm impedance coaxial cables from W. L.
Gore models G3S0101078.0 and G3S0101072.0 which are 78.0 and
72.0 inches long, respectively. Communication with the TDR
is done through an IEEE-488 interface on the scope to a
RS232 interface on an IBM PC/AT using a Black Box model
232-488 interface converter.
The power-up sequence of the equipment is very
important. The Black Box converter unit must be turned on
last to eliminate communication handshake problems. Once
this protocol problem occurs, the Black Box converter and
the Tektronix scope must be shut down and powered up again.
The Black Box converter unit is the key to this problem, the
converter on power-up sends a request for service signal to
37


36
Figure 10: 79Br transverse relaxation rates (from line
widths) in non-aqueous and mixed solvent systems
as a function of electrolyte concentration
(reference 100).


78
10
9
c
o
o
c
D
en
en
o
8
7
6
5
o
*i_
A->
<_>
_CL>
QJ
h
4
3
2
1
0 -
7.5

1.0 mole 7.

5.0 mole 7.

7.5 mole 7.

1 0.0 mole %
o
1 5.0 mole %

30.0 mole %
A
50.0 mole 7.
o
Aliquat 336
Theoretical
Aliquat in n Butanol
7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1 9.3 9.5
Log Frequency (Hz)
Figure 28: Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336
and n-butanol.


99
generators that have larger than 0.25 V potential is limited
to generators that have risetimes in the nanosecond range,
reducing the upper frequency limit to about 108 Hz. The
fast risetime pulse generators (faster than 25 psec) are
typically custom designed components and must be
specifically designed for a system (commercial availability
is questionable).
The minimal noise level for the current TDR setup is
2 mV with a typical noise level of 5 to 10 mV. A pulse size
of 0.25 V gives a signal to noise ratio (S/N) of about
100/1. The noise comes from several sources: a glitch in
the power supply, electronic drift, reflections from
impedance mismatches in the connectors, loose connections,
temperature variations, etc. Samples with a large static
dielectric constant show little effect from these noise
sources due to the large response of the sample to the
voltage pulse. The problem arises in samples with a
dielectric constant below 3, where the response is about
30 mV in size with noise in the 10 mV range. The obvious
solution is to eliminate as many of the noise sources as
possible, but one can only go so far in this regard. There
is not much that can be done about the electronic drift, the
temperature variations inside the oscilloscope, the
impedance mismatches in the internal circuits, etc.
Attempts at using a two channel system to help offset some
of these problems has lead to the appearance of artifacts in


91
show the same trends as that observed in the pyridine-
butanol system. The aggregates of butanol are broken apart
by the coordination to pyridine. As the concentration of
pyridine is increased, the system's behavior moves from the
characteristics of neat butanol to neat pyridine indicated
by the changes in the intensity of the static dielectric
constant and the critical freguency. At high water
concentrations, the system deviates in behavior to that
observed for the pyridine system. The change in the static
dielectric constant is similar to that found for pyridine,
but the change in the critical freguency is much less than
expected. An obvious difference between pyridine and water
is that a two phase system is observed for water, but not
for pyridine. The structure for neat pyridine is different
to that observed for neat butanol or water. Pyridine forms
a stacked structure through the interaction of the rings.
Both butanol and water form three-dimensional dynamic
network structures through H-bonding of the hydrogen on the
OH group to the lone pairs on the oxygen. Water is more
efficient at forming this dynamic structure because of the
tetrahedral geometry that the water molecule can assume in
this network structure compared to butanol which is short
one hydrogen (as a conseguence of the R group) to form the
tetrahedral geometry. At low concentrations of water, the
overall dynamic structure of the butanol is maintained and
results in a homogeneous system. As the concentration of


53
observation parameters, acquisition time 0.15 sec, pulse
width 36 nsec, and transients 5000. The viscosity and
linewidth of the samples required the majority of spectra to
be manually phased.
Chemicals
Aliquat 336 (trioctylmethylammonium chloride) was
purchased from Aldrich and used without further
purification. Water with a resistivity of 15 megaohm/cm was
obtained from a Barnstead NANOpure filtration setup. All
other chemicals are of reagent grade and used without
further treatment. All solution concentrations are given in
mole fraction units.


Static Dielectric Constant
80
Mole 7. Aliquot 336 in n-Butanol
Figure 29: Concentration dependence of the observed static
dielectric constant for solutions of Aliquat 336
and n-butanol.


40
the rated value), a pulse size of 250 mV, a pulse width of
700 nsec, and a repetition frequency of 50 kHz. This gives
our TDR setup a theoretical upper and lower limit of
5 X 1010 Hz and 1 X 106 Hz from the risetime and pulse
width, respectively.
The actual use of the TDR starts with the adjustments of
the time-distance control. This control allows the
positioning of the window to be shifted to any portion of
the waveform (from the beginning just prior to the voltage
pulse being emitted to the end where the pulse potential
returns to ground). As one moves through the entire
waveform, four transitions are seen (Figure 12). The first
and second transitions are the incident and reflected steps
of the voltage pulse, respectively. The third and fourth
transitions are due to the voltage pulse returning to
ground. The part of the waveform (reflected step) that
contains the second transition through just before the third
transition contains all the information about the properties
of the sample. The time-distance control is set to observe
only the second transition with a small amount of the
baseline before the transition (typically 10% of the time
window).
The time window of choice is one where the second
transition takes up approximately half of the time window as
shown in Figure 13. This is easily accomplished by
adjusting the time/division control until the process fills


139
16. Stephensen, W. K.; Fuchs, R. Canadian J. Chem.. 1985,
61, 342.
17. Keesee, R. G.; Castleman, A. W. Jr. J. Phys. Chem. Ref.
Data, 1986, 15, 1011.
18. Drago, R. S.; Wong, N. M.; Bilgrien, C.; Vogel, G. C.;
Inoro. Chem.. 1987, 6, 9.
19. Drago, R. S.; Cundari, T. C.; Ferris, D. C. J. Ora.
Chem.. 1989, 54, 1042.
20. Garg, S. K.; Smyth, C. P. J. Phys. Chem.. 1965, 69,
1294.
21. Riveras, P. A. Hydrometalluray. 1989, 24., 135.
22. Sano, M.; Ujito, E.; Shibata, J.; Nishumura, S.; Takao,
H.; Ichushi, S. Proc. Symp. Solvent Extra., 1989, 165.
23. Meno, S. K.; Agrawal, Y. K.; Desai, M. N. Talanto.
1989, 39, 675.
24. Bandypoadhyay, S.; Das, A. K. J. Indian Chem. Soc..
1989, 66, 427.
25. Shah, N.; Menon, S. K.; Desai, M. N.; Agrawal, Y. K.
Anal. Lett.. 1989, 22, 1807.
26. Flieger, A. Chem. Anal. (Warsaw). 1988, 32, 411.
27. Mishra, P. K.; Chakravortty, V.; Dash, K. C.; Das, N.
R.; Bhattacharyya, S. N. J. Radioanal. Nucl. Chem..
1989, 131, 281.
28. Das, N. R.; Chattopadhyay, P. Bull. Chem. Soc. Jpn..
1989, 62, 3278.
29. Lindman, B.; Forsen, S. "Chlorine, Bromine, and Iodine
NMR," Springer-Verlag, Berlin, 1976.
30. Bloembergen, N. "Nuclear Magnetic Relaxation,"
Benjamin, New York, 1961.
31. O'Reilly, D. E. Ber. Bunsenges. Phys. Chem.. 1971, 72,
208.
32. Gierer, A.; Wirtz, K. Z. Naturforsch.. 1953, fia, 532.
33. Gordon, R. G. J. Chem. Phys.. 1966, 44, 1830.


112
XYZ =
PRINT
CLOSE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
LOCATE
RETURN
FNWAIT(l)
#1, "RQSOFF"
5, 3: PRINT BLK$
9, 3: PRINT BLK$
9, 3: PRINT COM$
17, 42: PRINT BLK$
18, 2: PRINT BLK$
19, 42: PRINT BLK$
20, 42: PRINT BLK$
21, 2: PRINT BLK$
21, 42: PRINT BLK$
SERIES:
90 CLS
LOCATE 3, 4
PRINT "How many samples do you need to retrieve?"
40 LOCATE 3, 46
LL$ = FNINP$
IF LEN(LL$) > 1 THEN
LOCATE 3, 46
PRINT SPACE$(LEN(LL$))
GOTO 40
END IF
IF LL$ = "E" GOTO 99
NSAMP = VAL(LL$)
IF NSAMP < 1 OR NSAMP > 8 THEN
LOCATE 3, 46
PRINT "
GOTO 40
END IF
LOCATE 5, 4
PRINT "Reference Waveform Number "
50 LOCATE 5, 32
LINE INPUT LL$
IF LEN(LL$) > 1 THEN
LOCATE 5, 32
PRINT SPACE$(LEN(LL$))
GOTO 50
END IF
REFF = VAL(LL$)
IF REFF < 1 OR REFF > 9 THEN
LOCATE 5, 32
PRINT BLK$
GOTO 50
END IF
LOCATE 7, 4
PRINT "Path to send files to "
LOCATE 7, 26


34
Table 1
Energy of Activation for Bromide
Ion Quadrupole Relaxation in Surfactant Systems
Sample composition
percent by weight
Act. Energy
C16H33N(CH3)3Br H2 C6H13OH Phase kcal/mol
6.0
94.0
micellar
solution
6.5
24.0
76.0

micellar
solution
6.5
62.3
20.0
17.7
lamellar
mesophase
6.5
24.4
45.0
30.6
reversed
micellar
solution
7.5
40.0
10.0
50.0
reversed
micellar
solution
6.8
10.2
9.8
80.0
reversed
micellar
solution
6.5


NMR Line Width (Hz)
75
Figure 26: 35C1 NMR line widths obtained for solutions of
Aliquat 336 in n-Butanol.


i/t2,
29
Figure 7: 79Br relaxation rates (from line widths) at 30C
for aqueous solutions of monoalkylammonium
bromide; o, 0.100M solutions; X, 0.500M
solutions. The upper two curves are an expanded
view of the lower two curves. The left vertical
axis belongs to the upper two curves. The scale
on the right vertical axis belongs to the lower
two curves (reference 71).


142
75. Maijgren, B. "Studies of Internal and External Phase
Boundaries in Aqueous Systems," Thesis, Univ. of
Stockholm, 1974.
76. Wen, W. Y. "Water and Aqueous Solutions," Horne, R. A.,
ed., Wiley-Interscience, New York, 1972, 613.
77. Davidson, D. W. "Water, A Comprehensive Treatise,"
Franks, F., ed., Vol. 2, Plenum Press, New York, 1973,
115.
78. Feil, D.; Jeffrey, G. A. J. Chem. Phys.. 1961, 35.
1863.
79. Hertz, H. G.; Zeidler, M. D. Ber. Bunsenaes. Phys.
Chem. 1964, 68./ 821.
80. Hertz, H. G.; Lindman, B.; Siepe, V. Ber. Bunsenaes.
Phys. Chem.. 1969, 73, 542.
81. Lindman, B.; Forsen, S. "Chlorine, Bromine, and Iodine
NMR," Springer-Verlag, Berlin, 1976, 143.
82. Shinoda, K.; Nakagawa, T.; Tamamushi, B. I.; Isemura,
T. "Colloidal Surfactants," Academic Press, New York,
1963.
83. Tanford, C. "The Hydrophobic Effect: Formation of
Micelles and Biological Membranes," Wiley-Interscience,
New York, 1973.
84. Ekwall, P. Adv. Liquid Cryst.. 1975, 1, 1.
85. Eriksson, J. C.; Johansson, A.; Andersson, L. 0. Acta
Chem. Scand.. 1966, 20, 2301.
86. Lindblom. G.; Lindman, B. "Chemie, physikalische Chemie
und Anwendungstechnik der grenzflachenaktiven Stoff,"
Vol. II, Carl Hanser, Mnchen, 1972, 925.
87. Lindblom, G.; Lindman, B. J. Phys. Chem.. 1973, 77,
2531.
88. Lindblom, G.; Lindman, B.; Mandell, L. J. Colloid
Interface Sci,. 1973, 4£, 400.
89. Lindman, B.; Danielsson, I. J. Colloid Interface Sci..
1972, 39, 349.
90. Lindman, B.; Ekwall, P. Mol. Crvst.. 1968, £, 79.


95
spectra data can be fitted to two processes, summarized in
Table 9. The observed critical frequency for the two
processes are fairly constant for solution less than 40%
water. The faster process's dielectric intensity (e-j^ ew)
increases with increasing water concentration. The slow
process has a lower critical frequency than that found for
Aliquat in neat butanol with a constant dielectric intensity
(eg e-j^). As water concentrations increase, above 40%, the
critical frequency for both processes increase with the slow
process increasing at a slower rate. The butanol phase of
solutions that is in excess of 80% water gives dielectric
spectra similar to those observed in the greater than 50%
water in neat butanol. This behavior suggests two possible
sites: a hydrophobic site for the butanol and a hydrophilic
site for the water. The slow process describing the butanol
aggregate suggests that the concentration and aggregate size
of the butanol is remaining constant in the hydrophobic
region of Aliquat and does not compete with water for the
hydrophilic region. The fast process's critical frequency
is similar to that observed for a solution of 40% water in
neat butanol suggesting that the water aggregate size is
approximately that observed in the butanol/water system.
The change in the fast process's intensity indicates that
the change in dipole moment in this ternary system is much
smaller than that of the butanol/water system. High
concentrations of water causes Aliquat to undergo a


LISTS OF FIGURES
page
1. Dielectric material filled parallel plate
capacitor experiment 4
2. Three mechanisms for describing dielectric
relaxation 7
3. Plot of the frequency dependent complex
dielectric function; real and imaginary
components 10
4. Plot of the imaginary versus the real component
of the complex dielectric constant, Cole-Cole
plot 12
5. 79Br relaxation rates (from line widths) at 30C
for 0.500M aqueous solutions of alkylammonium
bromides 25
6. Phase diagram of a ternary system composing of
hexadecyltrimethylammonium bromide (CTAB),
hexanol, and water 27
7. 79Br relaxation rates (from line widths) at 30"C
for aqueous solutions of monoalkylammonium
bromide solutions 29
8. 35C1 relaxation rates (from line widths) as a
function of the inverse concentration of
octyltrimethylammonium chloride and octylammonium
chloride at 28C 31
9. Observed 81Br relaxation rates (from line widths)
divided by that at infinite dilution in water for
solutions of hexadecyltrimethylammonium bromide
(CTAB) and water in hexanol 32
10. ^Br transverse relaxation rates (from line
widths) in non-aqueous and mixed solvent systems
as a function of electrolyte concentration ... 36
11. Block diagram of TDR setup 38
vi


27. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336 and
n-butanol 77
28. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336
and n-butanol 78
29. Concentration dependence of the observed static
dielectric constant for solutions of Aliquat 336
and n-butanol 80
30. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and carbon tetrachloride 83
31. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and carbon tetrachloride 84
32. Theoretical fit of the observed real component
spectra for solutions of n-butanol and water 88
33. Theoretical fit of the observed imaginary
component spectra for solutions of n-butanol
and water 89
34. Theoretical fit of the observed real component
spectra for solutions of Aliquat 336, n-butanol,
and water 93
35. Theoretical fit of the observed imaginary
component spectra for solutions of Aliquat 336,
n-butanol, and water 94
viii


72
consideration, the static dielectric constant gives a
comparable value for the adduct in CC14 and that made in
neat butanol. No new relaxation processes are observed in
CC14 and the behavior is similar to that for neat butanol.
The variation in cluster size when butanol is diluted in
CC14 is small compared to pyridine addition as seen in
Figure 24.
Surfactant Systems
Binary. System of n-Butanol apd Aliguat 336
The conductivity of the Aliquat solutions (Figure 25)
increase as the concentration of the Aliquat is increased.
The maximum conductivity of this system is found at 10.0%
Aliquat followed by a steady decrease at the higher
concentrations of Aliquat. The conductivity levels off at
about 50.0% Aliquat to the value observed for neat Aliquat.
The increase in the conductivity at low Aliquat
concentrations is that expected for a simple salt being
dissolved. The conductivity of dissolved salts increase
with concentration and then level off as the solubility
limit is reached. The deviation from this behavior suggest
that the Aliquat is ion-paired with aggregation taking place
at the higher concentrations. This effect is even more
dramatic in solvents like methanol and water, where the
conductivity of the dilute Aliquat solution is 25 times


65
Table 4
n-Hexanol and n-Propanol
Hexanol
CM
CM
r x 10
0
s
21.8
493
31
18.5
2.2
431
55
15.8
2.2
345
80
13.8
2.2
315
100
11.3
1.8
263


The formation of micelles can be observed in dielectric
spectra. The critical micelle concentration can be
determined from solution DC conductivity and the static
dielectric constant obtained from TDR dielectric spectra.
The study of Aliquat 336 has shown that solvents like
n-butanol prefer the hydrophobic region of the quaternary
ammonium salt in neat solvent. The addition of a nonpolar
solvent like CC14 to a solution of Aliquat in n-butanol
causes the butanol to leave the hydrophobic sites and
interact with the hydrophilic sites of Aliquat. In
contrast, the addition of water does not influence the
observed interactions of butanol. These effects are
manifested in the intensity of the dielectric constant and
in the critical frequency of the dielectric spectra.
x


31
35C1 relaxation rates (from line widths) as a
function of the inverse concentrations of
octyltrimethylammonium chloride (o) and
octylammonium chloride () at 28C, reference 87.
Figure 8: