Citation
Fast fourier transformed acoustic resonances with sonic transform

Material Information

Title:
Fast fourier transformed acoustic resonances with sonic transform
Creator:
McGill, Kenneth C., 1957- ( Dissertant )
Colgate, Samuel O. ( Thesis advisor )
Ohrn, N. Yngve ( Thesis advisor )
Bailey, Thomas ( Reviewer )
Eyler, John R. ( Reviewer )
Weltner, William ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
University of Florida
Publication Date:
Copyright Date:
1990
Language:
English

Subjects

Subjects / Keywords:
Acoustic velocity ( jstor )
Argon ( jstor )
Bellows ( jstor )
Calibration ( jstor )
Fast Fourier transformations ( jstor )
High temperature ( jstor )
Low temperature ( jstor )
Signals ( jstor )
Sound ( jstor )
Supersonic transport ( jstor )
Chemistry thesis, Ph.D.
Dissertations, Academic -- Chemistry -- UF
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
In this study, a novel approach for detecting one or more speeds of sound was developed. By employing a Sonic Transform (ST), the data are transformed in real time to a domain that is directly related to the speed of sound within a cavity. The transform is of order < n2 and is equivalent to a Fast Fourier Transform in computation time. The study contains a discussion of the apparatus design as well as interfacing techniques involved in its operation. Source code and algorithms that describe the analysis and data acquisition in detail are also contained within the study.
Thesis:
Thesis (Ph.D.)--University of Florida, 1990.
Bibliography:
Includes bibliographic references (leaves 95-96).
General Note:
Vita.

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FAST FOURIER TRANSFORMED ACOUSTIC RESONANCES
WITH SONIC TRANSFORM
















By

KENNETH C. MCGILL


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSIT~i OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1990


































Copyright 1990

by

'Kenneth Charles McGill















DEDICATION



This work is dedicated to the three people whom I owe so much: To my mother Martha Senogles who gave me life; to my late wife Natalie McGill who gave me her life; and to my wife Susan McGill who is giving me a new life in my first child.















ACKNOWLEDGMENTS


I would like to thank Dr. S.0. Colgate personally for his support and guidance during the development of this technique.

I would also like to thank Chadin Dejsupa and Joe

Shalosky for assisting in the construction of various parts of the apparatus, Casey Rentz for the use of his computer and Evan House for convincing me to join the Colgators.

In addition, I would like to thank Dr. Grant Schrag for the development of the tapered ram seal used for the electrical feed-throughs of the transducers, Dr. Cliff Watson for his assistance in programming the Fast Fourier Transform and Steve Miles for his contribution on the development of the magnetic pump.

Also, I thank my wife, Susan, for instructing me on the use of WordPerfect so that I could perfect the format of this dissertation.

























































FAST FOURIER TRANSFORM SOURCE CODE . SONIC TRANSFORM SOURCE CODE . EQUATION OF STATE FOR ARGON SOURCE CODE . DATA ACQUISITION SOURCE CODE .


APPENDICES

A

B C D


TABLE OF CONTENTS
pA Le
ACKNOWLEDGMENTS . IV LIST OF TABLES . vii LIST OF FIGURES . ix ABSTRACT . xi CHAPTERS


1

8

9
18 29 30
34 34 35 37

42 44 45 46 48 69



76 80

84 87


1 INTRODUCTION .

2 THEORY .

Theory of Design .
Theory of Operation .

3 EXPERIMENTAL .

Interfacing .
Apparatus .
Spherical Cavity .
Pump .
The Bellows .

4 DATA AND RESULTS .

Time Domain Plots .
Frequency Domain Plots .
Sonic Domain Plots .
Volume and Pressure Calibration .

5 CONCLUSION .









E DATA CONVERSION SOURCE CODE . 93 BIBLIOGRAPHY . 95 BIOGRAPHICAL S = CH . 97















LIST OF TABLES
joage
Table 2-1. The values of the roots to the first
derivative of a Bessel function of the first
kind . 12

Table 2-2. Reduced second viral coefficients for
the Lennard-Jones 6-12 potential . 20

Table 2-3. Reduced third viral coefficients and
their derivatives for the Lennard-Jones 6-12
potential . 22

Table 4-1. Low temperature time domain parameters of
argon . 53

Table 4-2. Low temperature frequency domain parameters
of argon . 54

Table 4-3. First sonic domain parameters of argon at
low temperature . 55

Table 4-4. Second sonic domain parameters of argon at
low temperature . 56

Table 4-5. Third sonic domain parameters of argon at
low temperature . 57

Table 4-6. Fourth sonic domain parameters of argon at
low temperature . 58

Table 4-7. High temperature time domain parameters
of argon . 59

Table 4-8. High temperature frequency domain parameters
of argon . 60

Table 4-9. First sonic domain parameters of argon at
high temperature . 61

Table 4-10. Second sonic domain parameters of argon at
high temperature . 62

Table 4-11. Third sonic domain parameters of argon at
high temperature . 63


vii









Table 4-12. Fourth sonic domain parameters of argon at
high temperature . 64 Table 4-13. Outside volume calibration . 65 Table 4-14. Total volume of apparatus . 66 Table 4-15. Bellows volume calibration . 67 Table 4-16. Compiled results of sonic speeds of argon at
low and high temperatures for various roots . 68


viii















LIST OF FIGURES
page
Figure 3-1. Instrument rack . 32 Figure 3-2. Spherical cavity sections and clamping
flanges . 36 Figure 3-3. Pump assembly . 38 Figure 3-4. The bellows and bellows chamber . 39 Figure 3-5. Apparatus assembly . 41 Figure 4-1. Theoretical ADC signal for 350 m/s speed
of sound . 50 Figure 4-2. Theoretical ADC signal for 150 m/s and
350 m/s speeds of sound . 50 Figure 4-3. FFT of theoretical ADC signal for
350 m/s speed of sound . 51 Figure 4-4. FFT of theoretical ADC signal for
150 m/s and 350 m/s speeds of sound . 51 Figure 4-5. ST of FFT of theoretical ADC signal
for 350 m/s . 52 Figure 4-6. ST of FFT of theoretical ADC signal
for 150 m/s and 350 m/s speeds of sound . 52 Figure 4-7. ADC signal of argon at low temperature . 53 Figure 4-8. Expanded section of Figure 4-7 . 53 Figure 4-9. FFT of ADC signal of argon at low
temperature . 54 Figure 4-10. Expanded section of Figure 4-9 . 54 Figure 4-11. First ST of argon at low temperature . 55 Figure 4-12. Expanded section of Figure 4-11 . 55 Figure 4-13. Second ST of argon at low temperature . 56









Figure 4-14. Expanded section of Figure 4-13 . 56 Figure 4-15. Third ST of argon at low temperature . 57 Figure 4-16. Expanded section of Figure 4-15 . 57 Figure 4-17. Fourth ST of argon at low temperature . 58 Figure 4-18. Expanded section of Figure 4-17 . 58 Figure 4-19. ADC signal of argon at high temperature . 59 Figure 4-20. Expanded section of Figure 4-19 . 59 Figure 4-21. FFT of ADC signal of argon at high
temperature . 60 Figure 4-22. Expanded section of Figure 4-21 . 60 Figure 4-23. First ST of argon at high temperature . 61 Figure 4-24. Expanded section of Figure 4-23 . 61 Figure 4-25. Second ST of argon at high temperature . 62 Figure 4-26. Expanded section of Figure 4-25 . 62 Figure 4-27. Third ST of argon at high temperature . 63 Figure 4-28. Expanded section of Figure 4-27 . 63 Figure 4-29. Fourth ST of argon at high temperature. 64 Figure 4-30. Expanded section of Figure 4-29 . 64 Figure 4-31. Outside volume calibration . 65 Figure 4-32. Total volume of apparatus . 66 Figure 4-33. Bellows calibration plot . 67
















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


FAST FOURIER TRANSFORMED ACOUSTIC RESONANCES WITH SONIC TRANSFORM

By

Kenneth C. McGill

December 1990


Chairman: S.O. Colgate
Major Department: Chemistry


In this study, a novel approach for detecting one or more speeds of sound was developed. By employing a Sonic Transform (ST), the data are transformed in real time to a domain that is directly related to the speed of sound within a cavity. The transform is of order < n 2 and is equivalent to a Fast Fourier Transform in computation time. The study contains a discussion of the apparatus design as well as interfacing techniques involved in its operation. source code and algorithms that describe the analysis and data acquisition in detail are also contained within the study.















CHAPTER 1
INTRODUCTION

The measurement of state variables is of interest to researchers in thermodynamics. The two most commonly measured state variables are temperature and pressure. Techniques for their measurement have been developed that have high accuracy and speed of operation and are relatively easy to use. The equation of state for even the simplest system, for example, a single component gas, requires at least another variable. For whatever additional variable is chosen, it is desirable that its measurement be performed as quickly and as easily as those of temperature and pressure.

The most commonly measured third state variable is

volume. The measurement of volume is often done by a batch process where a fluid substance is placed in a vessel of calibrated volume. This process is time-comsuming and is prone to error. Individual error can occur in recording the measurement and it is impossible to do real time processing of the data.

There are other state variables that could be measured, such as entropy, enthalpy, and free energy, but these are even more difficult to measure in a batch process or in real time. If a reliable equation of state relating three state variables is available, then the magnitude of the third

1











variable may be calculated after measuring the other two. This method works well for single component gases, but it is not very accurate for multicomponent mixtures of gases or for any gas near its critical region.

In this work, emphasis is placed on the development of a novel sonic speed 'measurement technique to facilitate the use of this state variable along with temperature, pressure and volume in physical relationships. An effort to make the measurement of the speed of sound as accurate and as easy as temperature and pressure has been made; that is, a process has been developed that can operate in real time with high accuracy and with little interaction from the user. The measurements of volume and speed of sound are similar; one way to measure the volume of a gas involves the geometry of the vessel in which the gas is contained and, similarly, one way to measure the speed of sound in a gas involves the geometry of the vessel in which the gas is contained. 8y knowing the geometry of the vessel, the volume can be calculated by measuring the dimensions of the vessel. The speed of sound can be found by measuring the acoustic resonances within the cavity. The speed of sound is also dependent on the density and-mass of the gas being measured.

An accurate method for measuring the speed of sound involves examination of the resonances that occur in an acoustic cavity. The selection of the geometry of the cavity can make a significant difference in the ease of











interpretation of the resonance frequencies. For example, resonances in a cylindrical cavity are complicated by problems, such as unresolved modes and viscous drag along the longitudinal walls. These problems have been examined in detail elsewhere.1

Another potential problem with any shaped cavity

results from a precondensation effect that occurs on the surface of the cavity.2 This effect appears most strongly at low frequencies in resonators with large surface-tovolume ratios. To avoid these problems, a spherical cavity was chosen since: 1) Viscous drag does not occur for the radial vibrations within a spherical cavity; 2) surface-tovolume ratio is minimized for spherical geometry; and 3) the acoustic energy is highest at the center of the sphere.

In a study that included a treatment of the

precondensation effect in a spherical cavity, the speed of sound of a gas was measured with an accuracy approaching � 0.0005% or 5 ppm.3 Neglecting the precondensation effect,

1 J.B. Mehl and M.R. Moldover, "Precision Acoustic Measurements with a Spherical Resonator: Ar and C2H4, " Journal of Chemical Physics 74 (April 1981): 4062-4077; A.R. Colclough, "Systematic Errors in Primary Acoustic Thermometry in the Range 2-20 K," MetroloQia 9 (1973): 75.

2 J.B. Mehl and M.R. Moldover, "Precondensation Phenomena in Acoustic Measurements," Journal of Chemical Physics 77 (July 1982): 455-465.
3 M.R. Moldover, J.B. Mehl, and M. Greenspan, "GasFilled Spherical Resonators: Theory and Experiment," Journal of the Acoustical Society of America 79 (February 1986): 253-271.











accuracies of 0.01% are readily obtained for physical properties inferred from sonic speed measurements, these include reference state heat capacities,4 thermophysical properties of alkanes,5 and heat capacity ratios.6 In all of these experiments, the first step is to analyze a frequency spectrum and then select only a few of the resonances, at most five or six depending upon the experiment, to measure the speed of sound.7 This interaction from the user requires an intuition as to where the resonances occur, and locating them with confidence is often tedious and can take a considerable amount of experimental time. This places an added burden on the maintenance of the system's state. The measurement of temperature and pressure can be very accurate, but maintaining them for long periods of time is not easy. All



4 S.O. Colgate, C.F. Sona, K.R. Reed, and A.
Sivaraman, "Experimental Ideal Gas Reference State Heat Capacities of Gases and Vapors," Journal of Chemical and EnqineerinQ Data 35 (1990): 1-5.


5 M.B. Ewing, A.R.H. Goodwin, and J.P.M. Trusler, "Thermophysical Properties of Alkanes from Speeds of Sound Determined Using a Spherical Resonator 3. n-Pentane," Journal of Chemical Thermodynamics 21 (1989): 867-877.
6 S.O. Colgate, K.R. Williams, K. Reed, and C. Hart, VIC CV Ratios by the Sound Velocity Method Using a Spherical Resonator," Journal of Chemical Education 64 (June 1987): 553-556.
7 M.B. Ewing, M.L. McGlashan, and J.P.M. Trusler, "The Temperature-Jump Effect and the Theory of the Thermal Boundary Layer for a Spherical Resonator, Speeds of Sound in Argon at 273.16 K," Metrologia 22 (1986): 93-102.










of these methods assume that only one speed of sound is present within the-medium of interest. If multiple speeds of sound are present within a medium, the difficulties of the job of analysis are seriously compounded. Ideally, a method that can identify the resonances as well as calculate a close approximation of the speed of sound very quickly would represent a significant advance in the art of sonic speed measurements.

Since the number of possible resonances is of the order of the number of molecules, it is for all practical purposes infinite. Ideally, a broad band of resonances should be used to determine the speed of sound within the gas. one such attempt at measuring a truncated set of resonances was

made by Tewfik et al.8 This study modeled two dimensional waves such as the waves on the ocean. Their method involved a rather large calculation employing Householder routines to solve an nXn linear matrix problem. A Householder routine 9

is an operation of order n3 for which even a relatively small set of resonances becomes costly in computation time. Hence, although the Householder routine is capable of high accuracy, it can not be considered useful as a real time process.


8 A.H. Tewfik, B.C. Levy, and A.S. Willsky, "An Eigenstructure Approach for the Retrieval of Cylindrical Harmonics," Signal Processing 13 (September 1987): 121-139.

9 G.H. Golub and C.F. Van Loan, Matrix Computations (Baltimore: Johns Hopkins University Press, 1985), 38.











In order to overcome these boundaries, a technique was developed in the present work to transform the Fourier coefficients of a captured time domain signal to the sonic domain. once in this domain, the speed of sound is easily determined. For the development of this technique, a spherical cavity and a truncated set of resonances were used. The truncated set of resonances was transformed from a measured time domain signal to the sonic domain using a

transform operation of order nlog2n + nm, where m is the number of resonances.

To test the method, a theoretical (computer

synthesized) frequency spectrum was created and then the speed (or speeds) of sound were found from the spectrum and compared to the speed (or speeds) of sound used to produce the spectrum. Once satisfied that the method could reproduce the speed of sound from a simulated spectrum, some experimental spectra were analyzed. The transformed speeds of sound obtained from these experimental spectra were then compared to known values, which for the gas in question, argon, have been shown to be in accord with those directly calculated using a truncated viral equation of state. The transformed speeds of sound may be lower than the calculated speeds since the latter are the speeds of sound at zero frequency and the transformed ones are an average speed of sound over all the frequencies within the spectrum.









7

The following chapters describe the theory of design as well as the theory of operation of this transformation technique. The design of the apparatus is similar to other acoustic devices with a few exceptions. The seal technology employed allows operation over wider temperature and pressure ranges. Another unique feature of the apparatus is the ability to vary its volume with a specially designed bellows assembly. This apparatus has the capability to measure four state variables simultaneously. In addition, the source code for all measurement techniques has been included in the appendices to describe the operation of the apparatus in detail.















CHAPTER 2
THEORY


Two basic theoretical constructs central to the present novel sonic speed technique are explained in this chapterthe theory of design and the theory of operation. The theory of design begins with established theories of wave phenomena and applies modern computational methodologies to them. A new algorithm developed here facilitates the computations.

The theory of operation is presented to reveal the

order of events that lead to the measurement of the speed of sound with this technique. The equations and operational bounds may seem trivial to anyone familiar with Fast Fourier Transform (FFT) techniques, but, to the newcomer, these will likely seem arbitrary and unbounded. They are, in factf very closely interrelated. The two parameters that govern the operation of any FFT spectrometer are the buffer size and the sample rate of the ADC; other parameters may be deduced from them. The operation of many of the basic theories described are transparent to the user since they are contained mainly within the source code given in the appendices.










Theory of Design

The dynamics associated with the acoustical field of a nondissipating gas were first examined by Rayleigh in

1872.1 Rayleigh's development revealed a basis set of resonant frequencies of sound for a gas in a cavity. Experimentally these frequencies have heretofore been measured by observing the response of the gas to a slowly varying periodic stimulus. The present work is concerned with obtaining the information implicit in the frequency spectrum very rapidly. Acquisition of the frequency domain may be accomplished by a Fast Fourier Transform (FFT) of a time domain signal from an Analog to Digital Converter (ADC). Through a Sonic Transformation (ST) of the Fourier coefficients, this information can be further transformed into the sonic domain which readily reveals the speed of sound and other features of the acoustic field.

First, assume there exists a velocity potential * such that

V--V* Equation 2-1.


where v is the velocity of the gas. The standing wave produced in the gas with a speed of sound (c) is related to

by the standard wave equation




1 J.W.S. Rayleigh, Theory of Sound (New York: Dover, 1894), reprinted 1945, Section 331.











V2*_ - tffiA
C 29 at2


Equation 2-2.


Assuming a time separable solution to the above equation


Equation 2-3.


where *0 is then the solution to a scaler Helmholtz equation


V o+ (( o) _ 0,


Equation 2-4.


then the analytical expression for *0 2 is


* 0 1 () Pf(cos()) (Asin(mp) + Bcos(my)

Equation 2-5.




The function j, is a Bessel function of the first kind and Pm is an associated Legendre polynomial in cos(O). Since, by definition, a nondissipating gas is contained, the boundary condition of the radial component is that the velocity of the gas is zero at the rigid wall


a V'dd- O. Surf


Equation 2-6.


2 H.G. Ferris, "The Free Vibrations of a Gas Contained within a Spherical Vessel," Journal of the Acoustical Society of America 24 (January 1952): 57.


-$o 0z,, o) ei'











For a spherical cavity, the surface is described by dg-g2sin (6)dOdpf, Equation 2-7.


where g is a geometric factor or the radius of the spherical cavity. Substitution of the gradient of *p in Equation 2-6 yields


f- fb P'r(cos (0) ) (Asin (mg) +Bcos (rp) )g2sin0)dd'

Surf Z
Equation 2-8.





Since this must be zero for all values of a and b, then a.j Wr)Ig 0 Equation 2-9.




For a given value of 1, there are an infinite number of roots for the above relation. The lowest positive root is denoted by n=1, the next root is n=2, the following n=3, and so forth. These integral values represent the modes of vibration for that given 1. The roots of the above relations have been calculated in increasing magnitude as shown in Table 2-1.3


3 Ferris.













Table 2-1. The values of the roots to the first derivative of a Bessel function of the first kind.

i Ri n

1 2.08158 1 1
2 3.34209 2 1
3 4.49341 0 1
4 4.51408 3 1
5 5.64670 4 1
6 5.94036 1 2
7 6.75643 5 1
8 7.28990 2 2
9 7.72523 0 2
10 7.85107 6 1
11 8.58367 3 2
12 8.93489 7 1
13 9.20586 1 3
14 9.84043 4 2
15 10.0102 8 1
16 10.6140 2 3
17 10.9042 0 3
is 11.0703 5 2
19 11.0791 9 1
20 11.9729 3 3
21 12.1428 10 1
22 12.2794 6 2
23 12.4046 1 4
24 13.2024 11 .1
25 13.2956 4 3
26 13.4721 7 2
27 13.8463 2 4
28 14.0663 0 4
29 14.2580 12 1
30 14.5906 5 3
31 14.6513 8 2
32 15.2446 3 4
33 15.3108 13 1
34 15.5793 1 5
35 15.8193 9 2
36 15.8633 6 3
37 16.3604 14 1
38 16.6094 4 4
39 16.9776 10 2
40 17.0431 2 5
41 17.1176 7 3
42 17.2207 0 5









13


Table 2-1 continued.

i Ri 1 n

43 17.4079 15 1
44 17.9473 5 4
45 18.1276 11 2
46 18.3565 8 3
47 18.4527 16 1
48 18.4682 3 5
49 18.7428 1 6
50 19.2628 6 4
51 19.2704 12 2
52 19.4964 17 1
53 19.5819 9 3
54 19.8625 4 5
55 20.2219 2 6
56 20.3714 0 6
57 20.4065 13 2
58 20.5379 18 .1
59 20.5596 7 4
60 20.7960 10 3
61 21.2312 5 5
62 21.5372 14 2
63 21.5779 19 1
64 21.6667 3 6
65 21.8401 8 4
66 21.8997 1 7
67 22.0000 11 3
68 22.5781 6 5
69 22.6165 20 1
70 22.6625 15 2
71 23.0829 4 6
72 23.1067 9 4
73 23.1950 12 3
74 23.3906 2 7
75 23.5194 0 7
76 23.6534 21 1
77 23.7832 16 2
78 23.9069 7 5
79 24.3608 10 4
80 24.3821 13 3
81 24.4749 5 6
82 24.6899 22 1
83 24.8503 3 7
84 24.8995 17 2











A solution to the above equation occurs when


-i g-R1 Equation 2-10.
C



and the frequency of the standing wave within the cavity at speed c is then


G~l- 2-m l -- R cEquation 2-11.
g



where g is a geometric f actor and R, is the ith tabulated root.

The previous equation describes the frequency basis for all standing waves or resonant excitations in the cavity. Experimentally, the resonant frequencies are acquired in the Fourier format (see Appendix A) where


F F( ) COEquation






If multiple speeds of sound occur within the cavity medium, each having an almost infinite number of resonant frequencies, the job of determining the speeds of sound from the corresponding frequencies is tedious. Even with a truncated basis of roots (as in Table 2-1), finding the speed is not easy and requires considerable analysis. The









15
ST developed below facilitates this task. It transforms the coefficients of the FFT directly to the sonic speed domain.

Consider a system through which sound propagates at one or more speeds. Let the associated frequencies be weighted by some values ki, where


00
F s (t) -kif (ci, t)


Equation 2-13.


and


00
f ( ci, t) -Z (aijsin (gciRj t) +bijcos (gciRj t)).


Equation 2-14.







If we assume that all signals detected in the Fourier coefficients are acoustic resonances


Equation 2-15.


then it follows that


00 00
AP-Z 1 kiaij (W P, gciRj)
1 -7


Equation 2-16.


F F(t) -FS(t) ,











where the value of 6 is as follows,


gci). , (a)P-gcjRj" Equation 2-17.
PI gj~j -ijO,C.W*gciR~j



The values of k are of greater interest than the Fourier coefficients. One method to acquire n coefficients for a truncated sum of m roots would be to perform n truncated least square operations of order 2m+1 to obtain n functions f(ci,t) and then perform one more least square operation of order n to obtain the coefficients ki. Each least square operation is approximately an n-cubed operation (FLOPs4 n3). By performing the transformation shown below, weights that are proportional to ki can be obtained with considerably fewer FLOPs.

Let

n o
W, E Apl., Equation 2-18.
m p




then by substituting AP from Equation 2-16 into the above expression,







4 FLOP is a FLoating point OPeration (see Chapter 3, Theory of Operation).











n w1
.kiaij8j j8 p.m" Equation 2-19. m P 1




Since 1 is fixed, then for a given m and p, the only nonzero values occurs when i=l and j=m. This reduces the above expression to

nfo
W-n E kajm8P lm Equation 2-20.
m p




For a given 1 and m, there is only one nonzero value p, hence

n n
W1,ijn k aE -k11 aim-kn, -l Equation 2-22.
m m




where a, is the average amplitude over n roots of the Ith speed. Most importantly, this result shows that this choice of weights is directly proportional to the sonic coefficients k,. The relative values of w, cannot be used for determining relative values of k,. Since there is an overlap of different Ri values, the weights can be used to detect the presence of resonant speed of sound within the cavity.











Theory of Operation

For the purpose of evaluating the sonic transform technique, its use on a gas with known properties is required. Argon was chosen for this purpose because of its relative simplicity and well-documented physical behavior. The speed of sound in argon has been carefully measured and shown to be in agreement with values calculated with the virial equation of state.5

At moderate pressures (< 10 atm) two terms in the virial expansion are sufficient to give sonic speeds within experimental uncertainty. For this work the sonic speed in argon was calculated from the virial equation of state (truncated after the third term) using reduced virial coefficients obtained from a Lennard-Jones 6-12 potential. The speed of sound at zero frequency6 may be related to either the adiabatic or isothermal partial derivative of pressure with respect to molar density. Specifically, the square of the speed of sound is


C 2_1- Equation 2-22.
0M(, ap )S MV2_ ap





5 R. Byron Bird, "Numerical Evaluation of the Second Virial Coefficient," The Virial Equation of State CM-599 (Madison: University of Wisconsin, May 10, 1950), 47-52.
6 J.0. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids (New York: Wiley and Sons, 1954), 369.









19

where P is pressure, M is the molecular weight and p is the molar density. Using the constant temperature form of the above equation, where y is the ratio of heat capacities, the speed of sound can be found by solving for the individual values of CpI Cv and the constant temperature derivative. There is no equation of state that can be expressed in a single analytical expression that has high enough accuracy for this experiment. The best possible solution is a truncated virial equation with numerically calculated coefficients at various temperatures. The values of the second virial coefficients are given in Table 2-2 and the values of the third virial coefficients are given in Table 2-3. The accuracy of this numerical solution has been investigated by Bird.7 Using the truncated virial equation of state in terms of reduced virial coefficients given by:


Key Terms, Symbols and Definitions for Truncated Virial Equation of State

B = Second Virial k = Boltzmann's constant
Coefficient

C = Third Virial R = Gas constant
Coefficient

b0 = Ra3 B* = B/b0

a = Lennard-Jones 6-12 C* = C/b20
collision diameter

e= Lennard-Jones 6-12 T* = kT/E
maximum energy attraction or depth of N = Avogadro's Number
potential well


7 Bird.













Table 2-2. Reduced second viral coefficients for the Lennard-Jones 6-12 potential. T* B* B1* B2 Bi * -B*


0.30 0.35
0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15
1.20 1.25 1.30 1.35
1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95
2.00 2.10 2.20 2.30
2.40 2.50 2.60 2.70 2.80


-27.880581
-18.754895
-13.798835
-10.754975
-8.720205
-7.2740858
-6.1979708
-5.3681918
-4.7100370
-4.1759283
-3.7342254
-3.3631193
-3.0471143
-2.7749102
-2.5380814
-2.3302208
-2.1463742
-1.9826492
-1.8359492
-1.7037784
-1.5841047
-1.4752571
-1.3758479
-1.2847160
-1.2008832
-1.1235183
-1.0519115
-0.98545337
-0.92361639
-0.86594279
-0.81203328
-0.76153734
-0.71414733
-0.66959030
-0.62762535
-0.55063308
-0.48170997
-0.41967761
-0.36357566
-0.31261340
-0.26613345
-0.22358626
-0.18450728


76.607256
45.247713 30.267080 21.989482 16.923690 13.582156
11.248849
9.5455096 8.2571145 7.2540135
6.4541400 5.8034061
5.2649184 4.8127607
4.4282616 4.0976659 3.8106421 3.5592925 3.3374893
3.1404074 2.9642040 2.8057826 2.6626207 2.5326459
2.4141403 2.3056683 2.2060215 2.1141772 2.0292621 1.9505276 1.8773287 1.8091057 1.7453722 1.6857016 1.6297207
1.5275444 1.4366294 1.3552188 1.2819016 1.2155320 1.1551691 1.1000353
1.0494802


-356.87679
-189.46536
-116.36604
-78.87795
-57.33952
-43.88245
-34.91869
-28.64050
-24.06266
-20.61311
-17.94190
-15.82546
-14.11557
-12.71081
-11.53985
-10.55133
-9.70744
-8.97985
-8.34700
-7.79217
-7.30227
-6.86692
-6.47777
-6.12805
-5.81225
-5.52578
-5.26485
-5.02628
-4.80738
-4.60587
-4.41980
-4.24750
-4.08753
-3.93863
-3.79972
-3.54814
-3.32647
-3.12974
-2.95401
-2.79614
-2.65355
-2.52416
-2.40623


104.488 64.003 44.066 32.744 25.644 20.8563
17.4468 14.9137 12.9672
11.4299 10.1884 9.1665 8.3120 7.5877 6.9663 6.4279 5.9570
5.5419 5.1734
4.8442 4.5483 4.2810 4.0385 3.8174 3.6150
3.4292 3.2579 3.0996 2.9529 2.8165 2.6894 2.5706
2.4595 2.3553 2.2573 2.0782 1.9183 1.7749 1.6455 1.5281
1.4213 1.3236
1.2340













Table 2-2 continued. T* B* BI B2* Bl*-B*


2.90 3.00 3.10 3.20 3.30
3.40 3.50 3.60 3.70 3.80 3.90
4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 6.00 7.00 8.00 9.00 10.00
20.00 30.00
40.00 50.00 60.00 70.00 80.00 90.00 100.00
200.00 300.00
400.00


-0.14850215
-0.11523390
-0.08441245
-0.05578696
-0.02913997
-0.00428086 0.01895684
0.04072012 0.06113882 0.08032793 0.09839014
0.11541691 0.13149021 0.14668372 0.16106381 0.17469039 0.18761774 0.19989511 0.21156728 0.22267507 0.23325577
0.24334351 0.32290437 0.37608846
0.41343396 0.44059784 0.46087529 0.52537420 0.52692546 0.51857502 0.50836143 0.49821261 0.48865069 0.47979009
0.47161504 0.46406948 0.41143168 0.38012787 0.35835117


1.0029572 0.9600031 0.9202229 0.8832774 0.8488746 0.8167606 0.7867145 0.7585430 0.7300758 0.7071630 0.6836715 0.6614830
0.6404922 0.6206045 0.6017352 0.5838082 0.5667545 0.5505118 0.5350237 0.5202387 0.5061101 0.4925951 0.3839722 0.3082566
0.2524801 0.2097011 0.1758670 0.0286638
-0.0174929
-0.0393115
-0.0516478
-0.0593621
-0.0645039
-0.0680819
-0.0706470
-0.0725244
-0.0775400
-0.0765245
-0.0747534


-2.29831
-2.19920
-2.10785
-2.02340
-1.94511
-1.87231
-1.80447
-1.74108
-1.68174
-1.62605
-1.57371
-1.52441
-1.47789
-1.43394
-1.39234
-1.35291
-1.31548
-1.27991
-1.24606
-1.21381
-1.18305
-1.15367
-0.919393
-0.757930
-0.639879
-0.549792
-0.478779
-0.170403
-0.072012
-0.024109 0.003927
0.022147 0.034817
0.044056
0.051031
0.056441 0.077296
0.081397 0.082055


1.1515 1.0752
1.0046 0.93906 0.87802
0.82104 0.76776 0.71782 0.67094 0.62684 0.58528 0.54607 0.50900 0.47392
0.44067 0.40912 0.37914 0.35062
0.32346 0.29756 0.27285
0.24925 0.06107
-0.06783
-0.16095
-0.23090
-0.28501
-0.49671
-0.54442
-0.55789
-0.56001
-0.55758
-0.55316
-0.54787
-0.54226
-0.53659
-0.48897
-0.45665
-0.43310


Source: J.0. Hirschfelder, C.F. Bird, Molecular Theory of Gases York: Wiley and Sons, 1954), 11


Curtiss, and R.B. and Liquids (New


14.













Table 2-3. Reduced third viral coefficients and their derivatives for the Lennard-Jones 6-12 potential.

T* C* C 1 C 2


0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15
1.20 1.25 1.30 1.35
1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95
2.00 2.10 2.20 2.30
2.40 2.50 2.60 2.70 2.80 2.90 3.00


-3.37664
-1.79197
-0-84953
-0.27657 0.07650 0.29509
0.42966 0.51080 0.55762 0.58223
0.59240 0.59326 0.58815 0.57933 0.56831 0.55611 0.54339 0.53059 0.51803 0.50587
0.49425 0.48320 0.47277
0.46296 0.45376
0.44515 0.43710 0.42260 0.40999 0.39900 0.38943 0.38108 0.37378 0.36737 0.36173 0.35675
0.35234


28.68 18.05 11.60 7.561
4.953 3.234 2.078 1.292 0.7507 0.3760 0.1159
-0.0646
-0.1889
-0.2731
-0.3288
-0.3641
-0.3845
-0.3943
-0.3963
-0.3929
-0.3858
-0.3759
-0.3643
-0.3516
-0.3382
-0.3245
-0.3109
-0.2840
-0.2588
-0.2355
-0.2142
-0.1950
-0.1777
-0.1621
-0.1482
-0.1358
-0.1247


-220.
-140.
-92.1
-62.1
-42.7
-29.8
-21.0
-14.9
-10.6
-7.52
-5.29
-3.66
-2.46
-1.57
-0.910
-0.420
-0.050
0.224 0.427 0.572 0.680 0.755 0.806 0.837
0.854 0.859 0.856 0.830
0.794 0.749 0.700 0.651 0.602 0.557
0.514 0.473 0.439













Table 2-3 continued. T* C* C1 C2


Source: J.0. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids (New York: Wiley and Sons, 1954), 1116.


3.10 3.20 3.30
3.40 3.50 3.60 3.70 3.80 3.90
4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 6.00 7.00 8.00 9.00 10.00
20.00 30.00
40.00 50.00 60.00 70.00 80.00 90.00 100.00
200.00 300.00
400.00


0.34842 0.34491 0.34177 0.33894 0.33638 0.33407 0.33196 0.33002 0.32825 0.32662 0.32510 0.32369 0.32238 0.32115 0.32000 0.31891 0.31788 0.31690 0.31596 0.31508 0.30771 0.30166 0.29618 0.29103 0.28610
0.24643 0.21954 0.20012 0.18529 0.17347 0.16376 0.15560
0.14860 0.14251 0.10679 0.08943 0.07862


-0.1148
-0.1060
-0.09826
-0.09133
-0.08510
-0.07963
-0.07462
-0.07024
-0.06634
-0.06286
-0.05989
-0.05709
-0.05458
-0.05237
-0.05040
-0.04865
-0.04712
-0.04579
-0.04461
-0.04359
-0.03893
-0.03989
-0.04231
-0.04529
-0.04825
-0.06437
-0.06753
-0.06714
-0.06566
-0.06388
-0.06203
-0.06025
-0.05857
-0.05700
-0.04599
-0.03970
-0.03551


0.400 0.369
0.340 0.313 0.288 0.266
0.246 0.227
0.210 0.194 0.183 0.169 0.156
0.145 0.134 0.125 0.116 0.108 0.100
0.0934 0.0449 0.0258 0.0192 0.0183 0.0199 0.0502
0.0654 0.0717
0.0742 0.0750 0.0748
0.0741 0.0732 0.0722 0.0619
0.0547 0.0496














Equation 2-23.


B~*2( -2(~ d__dT *2 *


The constant pressure and constant volume heat capacities, respectively, are given by


5 B*2 (B--Bl'D2-C+cI- c;f
C;R2 V* (V*) 2










Cv.(3 2B5+B25 2C+C2. Eq
2 V* 2 (V*) 2


Equation
2-24.


nation 2-25.


The constant temperature derivative is given by P RT(v+ B* + (v*)2


Equation 2-26.


-R 1+2B +3 *
1 V" (V*) 2
-V T


and










A copy of the source code for the calculation of the

speed of sound using the truncated virial equation of state for argon is given in Appendix C.

The FFT was performed using the base 2 Cooley Tukey

algorithm.8 The base 2 algorithm was chosen to optimize the round of f error. Although the base 3 algorithm has a more efficient Floating Point Operation (FLOP) count,9 a digital computer, which also operates normally in base 2, preferentially accommodates calculations which use the base 2 number system. This then calls for the number of samples to be some integral power of 2. The operational bounds of the FFT are as follows:

The magnitude of the frequency domain is Equation
n ns S = no. of sames2=27.
f 2 f =no . of samp nl e12- 7





the Nyquist limit of maximum frequency is f sample rate*Euto
mx2 1 qain2-28.





8 J.W. Cooley and J.W. Tukey, "An Algorithm for the Machine Calculation of Complex Fourier Series," Mathematical Computations 19 (April 1965): 297-301.

9 G.D. Bergland, "A Fast Fourier Transform Algorithm for Real-Valued Series," Communications of the ACM 11 (October 1968) : 703-710.











the period for sampling is


ns
(sample ra te)


Equation 2-29.


the frequency resolution is


f ifa fres n
fl


Equation 2-30.


and the FLOP count is


FLOP - n, log2 n,.


Equation 2-31.


The ST was performed using the following algorithm


denom- 2 n gfres For i-,nmax
za tio0 ci
denom
w2-O
For j-l, nr
index - integer (ratio*Rj)
Wi - wi+aindex


Equation
2-32.


The maximum speed is limited by insuring that all ST frequencies of the roots exist within the FFT frequency domain












max fx2 7r g
Rn,


Equation 2-33.


where nr = number of roots in the truncated ST basis set. Since


Acres fres
Cmax fmax


Equation 2-34.


then the resolution of the algorithm and magnitude of the sonic domain are, respectively,


Cmax
Cres


Equation 2-35.


with a FLOP count of


FLOPs - nax2nr.


Equation 2-36.


The theory of design is related to the construction of the apparatus in that building a very precisely known spherical cavity provides a geometry factor (g) that is simply the radius of the sphere. Once the geometry factor is known and an ADC is chosen, the rest of the parameters are fixed. For a given buffer size and sample rate, the frequency range and resolution are set; and for a given set of roots, the sonic range and resolution are set. The


- max
Ces .
nmax









28

selection of an ADC should consider the geometry of the apparatus as well as the sonic range of interest. in the next chapter the interfacing employing an ADC as well as the design of the apparatus are described.














CHAPTER 3
EXPERIMENTAL


The experimental design of this technique must address two principal problems, the computer interfacing of the data acquisition methods and the mechanical design of the apparatus. In a modern laboratory, data acquisition is no longer the tedious matter of turning dials, reading meters and logging data. Even the most impartial researcher tends to be inconsistent when manually measuring large amounts of data over long periods of time. The digital computer has taken over these more tedious tasks with much better speed and consistency. The first part of this chapter describes the interfacing of the computer involving data acquisition.

in addition, as more tasks are controlled by the

computer, more time remains for the scientist to evaluate results and implement design improvements. Specifically during this work, volume control was added for the first time. Knowing the exact volume of the apparatus has always been necessary, but this volume has in the past been fixed. Many experiments, however, would benefit from a direct measurement of the effect of volume change. For example, V 2 (aplaV)T could be substituted into Equation 2-22 along with the speed of sound at zero frequency (co) and the









30
molecular weight (14) for a direct measurement of y. To this end, an extremely accurate variable volume control was designed for this apparatus.



Interfacingr

Data collection utilizes five basic devices and two computers. The physical parameters measured are temperature, equilibrium pressure, amplitude (-c acoustic pressure) and time. The first two of these measurements were made using standard laboratory instruments. Temperature is obtained by measuring the resistance of a platinum Resistance Temperature Device (RTD) using a Keithley 195a Digital Multi-Meter (DM14). The acquired resistance was updated and sent to the 8088 Central Processing Unit (CPU) along the National Instruments General Purpose Interface Bus (GPIB or IEEE) every 0.1 seconds. Resistance was then converted to temperature, in accordance with the RTD manufacturer's specifications, by the 8088 CPU. Pressure was read from a calibrated pressure sensitive Beckman Digital Strain Gauge in units of Pounds per Square Inch Absolute (PSIA). These readings were updated and sent to the CPU along the IEEE bus every 0.5 seconds.

Amplitude and time were measured simultaneously by the WAAG II Analog to Digital Converter (ADC). The WAAG ADC has eight-bit resolution, a 32768 point buffer and multiple sample rates of 40M4Hz, 4MHz, 400kHz, 40kHz and 4kHz. The











measurements are read and stored into the buffer sequentially. As a new measurement is added to the buffer, the oldest value is discarded. Once polled by the computer, the WAAG II dumps its entire buffer to the 8088 Random Access Memory (RAM) and then proceeds to acquire new data. The algorithm for the acquisition (source code provided in Appendix D) is as follows

Fox 1-1,n
r-resi stance rtd
T1-convert(r)
P-reading for strain guage. Equation 3-1. amp- dump ADC buffer
dump amp on hard drive
dump T on hard drive dump P on hard drive











U sing Equation 2-28, a sample rate of 40kHz leads to a

maximum frequency (fX of 20 kHz. With a buffer size of 32768, the period of sampling (T) and frequency magnitude

(nf) were found from Equations 2-29 and 2-27, respectively, to be 0.8192 seconds and 16384. The resulting frequency resolution (f .) from Equation 2-30 was approximately 1.22 Hz.

The excitation frequency is generated by a Hewlett

Packard HP3325b function synthesizer. When the HP3325b is put into discrete sweep mode, it generates a frequency-
































Figure 3-1. Instrument rack.

modulated-phase-consistent sinewave that sweeps from 0 Hz to 20 kHz in 0.8192 seconds, then repeats from 0Hz to 20kHz with a peak-to-peak voltage of 20.0 Volts. A TTL reference wave is sent to a Stanford Research SR510 lock-in amplifier from the HP3325b. The return signal from the resonator is also sent to the SR510, and all frequencies except for the reference frequency are filtered out by the frequency dependent band pass filter in the SR510. The resulting signal is then amplified and sent to the WAAG II ADC. All gain and power settings can be sent to the instruments along the IEEE bus.

The waveform collected by the ADC is dumped to hard drive in binary format while temperature and pressure are stored in an array but are later dumped to hard drive in binary format just before the program terminates. The











binary data are then sent to the DELL system 310 micro computer, the processing computer system. The binary format of the 8088 (8 bit) is different from the binary format of the DELL (32 bit), so the data must be translated to a common format. Since the data ranges in values from 0 to 255, two hexadecimal numbers can contain one datum (for source code, see Appendix E). The binary data are transformed to hexadecimal by the DELL then further transformed into the frequency domain.

Because the resulting large data set was limited to

eight-bit resolution, a time correlation method was used to reduce floating point error. This method simply doubles the data set by adding the waveform to itself. It should be noted that this does not increase resolution by having a double basis set but simply lessens round off error of the computer; the frequency domain data are unaffected. The data are then dumped to the DELL hard drive. Data are then transformed to the sonic domain and dumped to the DELL hard drive in binary format (see Appendix B for source code). Three of the data sets--time domain 8088 binary format, frequency domain DELL binary format, and sonic domain DELL binary format--are then stored, along with all the source code used in the process, on tape. The process was then repeated for different temperatures.











Apparatus

The apparatus consists of four basic parts--the spherical cavity, the volume-controlling bellows, the reciprocating pump and the Delta Design series 9000 environmental chamber.



Spherical cavity

The spherical cavity was constructed from two solid

pieces of 303 stainless steel; a three-inch radius spherical cavity was cut from the center. Excess material was removed from the outer portion to lower the mass of the sphere thereby making it easier to control its temperature. To assure safe operation at the highest intended pressure (4000 PSIA), the minimum wall thickness was set at 6.4 mm (0.25 in). This dimension was based on a calculation of the bursting pressure in a spherical shell obtained by setting the force acting to stretch the walls equal to the tensile strength of the stainless steel. A safety factor of 4 was used.

The top portion of the sphere contains the two

transducer mounts. A Macor insulated electrical feedthrough was mounted by employing a customized tapered ram seal with annealed copper gaskets. The inner threaded portion was used to align the transducer. The transducers were Piezoelectric lead-Zirconate lead-Titanate (PZT) bimorphs which have high motion sensitivity. They were








35

placed as close as possible to the surface of the sphere in order to minimize departure from the sphericity. The two halves of the sphere were sealed together using an annealed copper gasket with a conflat type knife-edge seal and held together with two mild steel clamps as shown in Figure 3-2. Inlet ports for the gas were constructed on the top and bottom of the spherical cavity. The entire assembly was pressure tested to 3500 PSIA at room temperature.



PUMD

The pump chamber (Figure 3-3) was constructed of a 304 stainless steel tube, 13 inches long with 1.250 inch outside diameter and 0.148 inch wall. The top portion was sealed by brazing a 304 stainless seal plug 1/2 inch thick with a 1/16 inch bore. The bottom portion was sealed by a 304 stainless steel plate with an annealed copper gasket on a conflat knife-edge seal. Seven magnetic field coils aligned concentrically on the tube create the pumping action by successively attracting a magnetic piston free to move inside the stainless steel tube. The bottom two coils are switched on remotely; the third coil from the bottom is activated as the bottom coil is turned off. This action is repeated until the magnetic piston reaches the top of the tube. Then a reversed action moves the magnetic piston to the bottom of the tube to complete one pumping cycle. Doubled-pumping action is created by use of four one-way





Figure 3-2. spherical cavity sections and clamping flanges.










valves placed outside the assembly. The strength of the 'magnetic field as well as the frequency of field oscillation are adjusted remotely. At the highest field strength and frequency of oscillation, a pumping speed of 200 mL per second at room temperature and pressure was recorded. An aluminum mount was constructed to hold the pump in an upright position.



The Bellows

The addition of the bellows assembly brings on-line

volume or density control to this technology for the first time. The collapsible bellows, constructed of 0.005 inch thick 304 stainless steel, was welded to a 1 inch thick plate which had a 1/4 inch hole bored horizontally to connect the adjustable volume of the bellows to the spherical cavity.

The outer portion of the bellows is contained in a

chamber that was constructed from a solid piece of stainless steel and sealed to the lower plate with a triangular

annealed copper seall. The volume of the outer chamber was isolated from the spherical cavity and maintained at pressures slightly below (approximately 20 PSI) that of the spherical cavity. This then maintained the bellows in an expanded position. The volume of the bellows was controlled by a threaded ram bolted to the top of the outer chamber.


Technology developed by S.O. Colgate in 1990.






















MAGNETIC- FIELD COILS PIS TON













Figure 3-3. Pump assembly.






co















III I


WAVAW


VW \Mb


z


Figure 3-4. The bellows and bellows chamber.











The position of the ram was externally controlled by a customized micrometer to within 0.001 inch. The pressure was monitored by two Sensotec pressure transducers. The pressure transducers were not able to operate in the harsh conditions of the environmental chamber so they were placed outside the chamber and connected to the apparatus by two stainless steel capillary tubes. These capillary tubes prevented a large volume of the sample from being outside the temperature-controlled volume. The assembled apparatus was connected as shown in Figure 3-5.

The completely assembled apparatus was then placed into the environmental chamber. The environmental chamber operates over the temperature range of 150oC to -170oC and is controlled by the manufacturer's programming language sent along the IEEE bus. The assembled apparatus was pressure tested up to 2800 PSIA.

The calibrated apparatus presently requires that only one parameter, the volume, be monitored and controlled by the user. The other three state variables, temperature, pressure and speed of sound, are acquired automatically by the computer. Typical results are displayed in the next chapter.













TO PRESSURE TRANSDUCERS ,


Signat From Rack


Signor To Rac


Figure 3-5. Apparatus assembly.


PUMP














CHAPTER 4
DATA AND RESULTS

The data and plots resulting from this experiment are discussed in three groups. This includes a theoretical computer synthesized set of data, an experimentally acquired set of data for argon at low temperatures and then a discussion of argon at high temperatures.

Figure 4-1 depicts a theoretical waveform based on

using the first 84 resonances in a spherical cavity (radius of 3 inches) filled vith a fluid medium which propagates sound at 350 m/s. Figure 4-2 depicts a similar theoretical waveform again using the first 84 resonances in the same cavity but now containing a fluid medium which propagates a speed of sound at two speeds, 350 m/s and 150 m/s. These two waveforms simulate those which would be acquired by the ADC under ideal conditions.

Figure 4-3 depicts the FFT of the waveform. shown in

Figure 4-1 while Figure 4-4 depicts the FFT of the waveform shown in Figure 4-2. Figure 4-5 displays the final results of the ST of the FFT described in Figure 4-3 and Figure 4-6 displays the results of the ST of the FFT in Figure 4-4. These six figures portray the chronological order of acquisition and calculation for the simulated set of data.










Note that ST transforms shown in Figures 4-5 and 4-6 correctly recover the input sonic speeds (350 m/s and 150 M/s).

Figure 4-7 is an experimentally acquired waveform of

the resonances of argon at a low temperature (-31.56oC) in a spherical cavity with a 3.000 inch radius. The experimental conditions are given in Table 4-1. An expanded view of a section of Figure 4-7 is given in Figure 4-8 to show the resolution with which the waveform is acquired in other regions. The FFT of the waveform of Figure 4-7 is shown in Figure 4-9 and the relevant physical and computational parameters are given in Table 4-2. As seen in Figure 4-9, the baseline is not very stable in the region of 10,000 Hz. An expanded view of this region is shown in Figure 4-10. Several STs were performed on the data in Figure 4-9 using different numbers of roots. The resulting ST weights employing the first 21 roots are shown in Figure 4-11 with an expanded view of the region that contains the known speed of sound in argon shown in Figure 4-12. The experimental and computational parameters are given in Table 4-3. Four STs were performed on the same FFT data in which only the number of roots used in the ST were changed. The results are shown in Figures 4-11 through 4-18 while parameters are listed in Tables 4-3 through 4-6. These results reveal the important features of the technique; they are described later in this chapter.










The same experiment was performed at a higher

temperature (50.93oC). Figure 4-19 shows the experimentally acquired waveform with the experimental and computational parameters given in Table 4-7. The expanded view shown in Figure 4-20 indicates that more of the resolution of the ADC was utilized. The baseline of the FFT shown in Figure 4-21 is considerably better than that of the low temperature experiment (Figure 4-9). The expanded view shown in Figure 4-22 indicates that the sharp acoustic resonances are larger than the perturbed baseline and are better resolved than those in Figure 4-10. The four STs using the different sets of basis functions at this temperature are shown in Figures 4-23 through 4-30 along with the corresponding parameters in Tables 4-9 through 4-12.

Interpretations of the data and graphs presented above are organized as follows. The first section discusses the characteristics of the time domain signal and how it deviates from ideality. The second discusses the characteristics of the frequency domain while the third section examines the sonic domain and the influence of

varying the number of roots (nd - In addition, the volume calibration data are included at the end of the chapter.



Time Domain Plots

Figures 4-1 and 4-2 show two computer simulated ADC signals. Figure 4-1 was generated from the sum of 84









45

sinewaves with frequencies generated from Equation 2-11 for a sonic speed (c) of 350 m/s, a geometric factor (g) of 3 inches and assuming equal amplitudes of the resonances. Figure 4-2 was generated from two sets of 84 sinewaves--one for c = 150 m/s, the other for c = 350 m/s. Both waveforms are similar in that they show no beat patterns or interference. Figure 4-7 shows a low temperature ADC signal where the resolution is quite low except for when the excitation frequency corresponds closely to a resonance frequency. This is an indication that the resonances are decaying rapidly. Figure 4-19 shows a high temperature ADC signal where the resolution is better since clearly the resonances are not decaying as rapidly as in the low temperature case. In other words, Figure 4-19 is approaching the characteristic of Figures 4-1 and 4-2. Ideally, an evenly distributed waveform uses the entire resolution of the ADC as was seen in the expanded Figures 48 and 4-20; that is not the case here. The resolution acquired is less than half the ADC resolution.



Frequency Domain Plots

The baselines of the frequency domain plots in Figures 4-3 and 4-4 indicate that the amplitudes are perturbed due to floating point calculation error. The low temperature frequency domain plot in Figure 4-9 shows an extremely large broad peak in the center of the frequency spectrum. The









46
expanded view shown in Figure 4-10, however, shows the sharp gas resonances imposed on top of this large peak. As the temperature is increased and the decaying of the resonances decreases, the broad peak decreases in size as well as frequency. All of these characteristics indicate that this portion of the signal is associated with vibrations of a solid, perhaps along the walls of the sphere or in the transducers themselves.



Sonic Domain Plots

The two sonic domain plots in Figures 4-5 and 4-6

indicate that the amplitude perturbations of the frequency domain do not affect the amplitudes in the sonic domain, but that much of the floating point calculation noise is carried through. The plots do show that the ST will resolve multiple speeds of sound if present in the data, although all of the low and high temperature plots shown in the * remaining figures have considerably different baselines. The baselines are attributed to the reproducible apparatus frequencies which are not due to normal mode vibrations of the cavity fluid. These are called nonacoustic frequencies. The reason that they are identifiable as being nonacoustic is that they do not move across the baseline as the basis set of roots is changed. The four low temperature figures (4-11 to 4-18) as well as the four high temperature figures (4-19 to 4-30) show that the baseline maps predominately










with respect to index and not speed. Only resonances that are acoustic will be speed dependent and not index dependent. As the absorption of energy by the gas increases in the high temperature spectra, the amplitude of the speed of sound begins to predominate as would be expected. It should be recalled here that the time domain signal is the same for all sonic domain plots of a given temperature; the only thing that was changed was the number roots used to form the basis. In addition, the size of the basis did not seem to have a large effect on the resolution. It was not

until nr = 63 that the resolution saw any significant increase, but this could be due to where the resonance was with respect to the noise and does not necessarily reflect an increase in gain.

The speeds of sound in argon calculated from the

truncated viral equation (see Appendix C) are 291.644 m/s for the low temperature data (@ -31.56oC and 870.5 PSIA) and 350.245 m/s for the high temperature data (@ 50.93oC and 1285.5 PSIA). The ST speeds of sound are given in Tables 41 through 4-12. The ST basis assumes a perfect sphere with a radius of 3 inches. Even using this simplification, the ST method gives sonic speeds within less than 0.5% deviation from the calculated values. The other three physical measurements (temperature, pressure and volume) employed standard techniques and were calibrated as discussed in the next section.











Volume and Pressure Calibration

The volume and pressure calibration required two

standard devices. For the pressure calibration, a Ruska Model 2465 Dead Weight Pressure Gauge was used. The accuracy of the Ruska gauge was � 0.001 PSIA with a range from 0.000 PSIA to 650.000 PSIA. For the volume calibration, the Ruska gauge as well as a Ruska Model 25652 volumetric pump was used. The accuracy of the Ruska pump was � 0.01 mL. The actual calibration of the Sensotec pressure transducers was the three point calibration described in the Beckman 620 owner's manual. The three pressures chosen were 0.000 PSIA, 320.000 PSIA and 640.000 PSIA. Since the accuracy of the Sensotec pressure transducers was only � 0.5 PSIA, the accuracy of the three calibration pressures was more than necessary.

The volume calibration involved taking several volume and pressure measurements and employing the ideal gas equation to deduce the absolute volume as shown below PO- i(V + A Vi)
PiA Pi Equation 4-1.
VO- P0






where P0 is the initial pressure and V0 is the total volume of the apparatus at that pressure. P and AV, are measured by the Ruska gauge and pump, respectively. The outside









49

volume of the calibration equipment was found from the data in Figure 4-31. The total volume of the apparatus as well as the calibration equipment was then found from the data in Figure 4-32. The volumes were all compared to a common point on the Ruska pump since the pump has its own volume that must be considered. The outside volume of the calibration equipment was then subtracted from the combined total to obtain the true total volume of the apparatus. Once the total volume was found, the change in volume due to the bellows from the same common point was found from the data in Figure 4-33. The change in volume with respect to the change in length of the external adjustment ram was observed to correlate best to a second order polynomial fit. The result (Table 4-15) was an expression for the total volume of the apparatus as a function of the external ram setting. The uncertainty in a total volume for a given ram setting was 0.01%. The range of the total volume of the apparatus was from 2350.00 to 2878.00 mL.


























0


30






10 .


0


-10


-20


-30
0 0. 0. 0.3 0.4 05 0.6 0.7 0. 09

Time s


-- --- a
Figure 4-1. Theoretical ADC signal for 350 m/s of speed of sound.


I r


20






0


-10


-20


-30
0 0.1 02 03 0.4 0. 0.6 0.7 0.8 0.9

Time s


Figure 4-2. Theoretical ADC signal for 150 m/s and 350 m/s speeds of sound.



































Figure 4-3. for 350 m/s


140x104


w8oo


FFT of theoretical ADC signal speed of sound.


Frequency = X/0.8192 Hz


Figure 4-4. FFT of theoretical ADC signal for 150 m/s and 350 m/s speeds of sound.














1.80110'_1.-- - -- - - -- --- - -- - . . . . . . . . . . . . . . . . .
1.60z10 . . . . . . .

1-0 ' .-. , I . T -----.




000


4000 . . . .

2000 . . .
0t . .i . .~ ~ . [. . .
0 50 100 150 200 250 3W0 350 400

Speed of Sound /(m/s)

Figure 4-5. ST of FFT of theoretical ADC signal for 350 m/s.


1.6ft IO' . . : . .:. -- - - - - I.-- . i. . .
1.60z10' ' :' :

. . . . . . . . .
la~,] * . . .: . . . . . . .
1.00 I, - - --- - . i . . . . . . . . . .

6 W . . . . . . . . .! . . . . . . . . . . . . . . .

. . L . . . '. . .
00 -------000

40

0 50 100 150 200 250 300 350 400

Speed of Sound /(m/s)


Figure 4-6. ST of FFT of theoretical ADC signal for 150 m/s and 350 m/s speeds of sound.
















250 - - - - - - - - - - - - -

20 .L . . . . . .





W

U* 10 -------100 . . . . . .




s o - - - -- ---- -. . " -. . .: 0 . . . . . . . . . . . I,. . .




0 i.O0xio 2o 1o4 3.0o0Io4

Time = X/40000 s Figure 4-7. ADC signal of argon at low temperature.


Table 4-1. Low temperature time domain parameters of argon. T = -31.56 � .lOoC P = 870.5 � .5 PSIA ns = 32768

Sample rate = 40 kHz


Figure 4-8. Expanded section of Figure 4-7.









































Figure 4-9. FFT of ADC signal temperature.


of argon at low


07MW M5 MW
Frcqueny -


MW "M M X/U.819 HZ


Table 4-2. Low temperature frequency domain parameters of argon.

T = -31.56 � .10oC P = 870.5 � .5 PSIA nf = 16384 fmx = 20 kHz


5.ooxlo'



4.O0xlO' 3.00xlO' V30X10'


Frequency = X/0.8192 Hz


"W~O, 4.5~kW

"3 cOklOj






0 650


Figure 4-10. Expanded section of Figure 4-9.


7 i i i i l . . . . . . .i i i l . ------ ii iil




. . .- .i


I









55






7.00xklO

6.00x10 . . . . .

S.00X106

4. 06 O ----- -- ----. C . . :.- - il

1.0& 0 . . . . . . .
0 . . .






0 100 200 3M0 400 500 600 700 800

Speed of Sound /(m/s)



Figure 4-11. First ST of argon at low temperature.





Table 4-3. First sonic 3O domain parameters of
. . argon at low
SL --temperature.
T = -31.56 + .10oC P = 870.5� .5 PSIA
---------- c = 290.91 � .05 m/s
ucm = 788.532 m/s . :. . n r = 2 1
2 NY 2 29 2 2 M 2 2 2 Note: See Equations
Sed of Sound (In/s) 2-33, 2-35.


Figure 4-12. Expanded section of Figure 4-11.









































Figure 4-13. Second ST of argon at low temperature.






Table 4-4. Second sonic domain parameters of & . . . arg on at low temperature.

T = -31.56 � .10oC
. . P = 870.5 � .5 PSIA
c = 290.96 � .03 m/s .--- . . . C x = 556 .016 m /s

4O n = 42
M6 MW no M 2H 2% MW
SpeedofSound/(mls) Note: See Equations
Fiaure 4-14. Exnanded section 2-33, 2-35.


of Figure 4-13.


7.OOxlO6 6.00xlO'









�.00110'




0


Speed of Sound /(m/s)


]









































Figure 4-15. Third ST of argon at low temperature.




Table 4-5. Third sonic domain parameters of argon at low temperature.

T = -31.56 �.l0oC P = 870.5 + .5 PSIA c = 290.962 � .027 m/s
Crx= 443.741 m/s

nr = 63
4AvdV Note: See Equations
SpWd Of Sod/(mls) 2-33, 2-35.


7"0'

&OOXlO '.




. . -.*---.
5.00 - . . . . .









0X106 ----0 .'. . . . . L . . . . :. . . . .

0 50 100 150 200 250 300 350 400 450

Speed of Sound /(m/s)


Figure 4-16. Expanded section of Figure 4-15.









































Figure 4-17. Fourth ST of argon at low temperature.



Table 4-6. Fourth sonic domain parameters of
7 lV argon at low
temperature.

. . T = -31.56 � .10oC
P = 870.5 � .5 PSIA . c = 290.962 � .023
m/s
low# C 384.545 m/s
Snr = 84

M 2290 231 292 3 294 2 2" ng Note: See Equations
Spwd of Soud/(m/s) 2-33, 2-35.


. . . - ,-.


-- --- - --- .

S ,.OW P . . . . .-M4Jdk10 -. - -----I - ----------

3.O0 . -- -- . -------- .



L0~I0-------------4----2 0 ( . . . . .:. . . . . .', . .


0 50 100 150 200 250 300 350 400

Speed of Sound /(m/s)


Figure 4-18. Expanded section of Figure 4-17.


I









































Figure 4-19. ADC signal of argon at high temperature.


1 I Tm e = X/40a00
Figure 4-20. Expanded section of Figure 4-19.


Table 4-7. High temperature time domain parameters of argon.

T = 50.93 � .06oC

P = 1285.5 � .8 PSIA

ns = 32768

Sample rate = 40 kHz


250 200 S150



100 $50



0
0


Time = X/40000 s


I
a









































Figure 4-21. temperature.


FFT of ADC signal of argon at high


m d e . . . . . .i . i.
~ ~ ~ ~ ~ ~ ~ ~--- .--. --. .i. -.


L



0 . . . i.i . . . . p. i . .


Frequency - X/0.8192 Hz
Figure 4-22. Expanded section
of Figure 4-21.


Table 4-8. High temperature frequency domain parameters of argon.

T = 50.93 _ .06oC

P = 1285.5 + .8 PSIA

nf = 16384

fmx = 20 kHz


3.00x10



250x1O6 .



~2.00x1OV --- - - - - - - - - -*- -




~1.S 0x1 o - - - - - - - -




S.OXOP - -- -- - -- ---- -- -- --


0 U
0


I Frequency = X/0.8192 Hz









































Figure 4-23. First ST of argon at high temperature.





Table 4-9. First sonic 3J ~ .domain parameters of argon at high temperature.

a5I T = 50.93 + .06oC
P = 1285.5 � .8 PSIA . c = 348.90 � .05 m/s
Cmx = 788.532 m/s M t. .
nr = 21
3 4 343 347 34 3ff 35 351 3M 3M Note: See Equations
Spdeof Sound/(m/s) 2-33, 2-35.


Figure 4-24. Expanded section of Figure 4-23.









62





4.50110'


4.00xl . . . . . . . ------t: .O O6 . . . . . . . . . . . . . . . . . . . .









2.5 0 P . . . . . . . .--
3.Sox~o'






342 34 34 348 350 352 354

Speed of Sound /(m/s) Figure 4-25. Second ST of argon at high temperature.





Table 4-10. Second 43WOV sonic domain parameters
of argon at high temperature.

T = 50.93 + .06oC . .P =1285.5� .8 PSIA c = 348.79 � .03 m/s . . .cx = 556.016 m/s

nr = 42
3a3 3 4 "0 M 3 Note: See Equations
Sped of Sound /(m/s) 2-33, 2-35.


Figure 4-26. Expanded section of Figure 4-25.









63






6.&kIOg



34M




".0046 ---.-.--- .




2.00xl06
1.0I,.

0. 1 . . . . . . -:. . . . . . . . . .




0 50 100 150 200 250 300 350 4W0 450 Speed of Sound /(m/s)



Figure 4-27. Third ST of argon at high temperature.




Table 4-11. Third sonic domain parameters of ss~isargon at high
temperature. 4J't1OS. . . T = 50.93 � .O6oC
P 1285.5 .8 PSIA c - 348.806 � .027
-m/s
cm = 443.741 m/s
- nr = 63

w 3 ]a M 3 Note: See Equations
Speed of Smd /m/s) 2-33, 2-35.


Figure 4-28. Expanded section of Figure 4-27.









64






6.001105
* ~3477ii.5.001106 - - - . . . . . . . .




0 . . ii
4 .0 x O ---------- - -- -- --- -


C4.00- -------------- -- - -~ -


2.004106 --0 . . . . ; . . . . ; . . . . , . . . . , . . . . , . .
0 50 100 150 200 250 300 350 4W0 Speed of Sound /(m/s)



Figure 4-29. Fourth ST of argon at high temperature.




Table 4-12. Fourth sonic domain parameters of argon at high Temperature.
T = 50.93 + .06oC P = 1285.5 + .8 PSIA � " i " 7 7 ".' --'- -------c = 348.797 � .023
0, -m/s
cx 384.545 m/s

230910 nr = 84

M7 W 30 "0 3M M . MS Note: See Equations
Speed of Sound/(mls) 2-33, 2-35.


Figure 4-30. Expanded section of Figure 4-29.









































[1 PRPO

Figure 4-31. Outside volume calibration.








Table 4-13. outside volume calibration.

slope = -235.074 mL

intercept = 235.0671 mL

V = 235.071 � .007 mL

V250 = 100.953 � .007 mL

correlation coefficient = 0.9999945


60 50


~40

0
S 30 > 20


10 0









































I PRPO

Figure 4-32. Total volume of apparatus.







Table 4-14. Total volume of apparatus.

slope =-2498.55 mL

intercept = 2498.517 mL

V = 2498.54 � .03 mL

V250 = 2463.82 �.03 mL

Vt=2362.87 �.03 mL at L = .250 inches

correlation coefficient = .999999


600 500


~40


S300


>200


100


0


0' 0.8 0.85 09 09


0.9 0.95







































Length /in


Figure 4-33. Bellows calibration plot.









Table 4-15. Bellows volume calibration.

First order coefficient =251.60 � 0.25
niL/in

Second order coefficient = -8.25 � 0.10
niL/in 2

Vt = 2300.19 + 251.60 L -8.25L2

Correlation coefficient =.999999













Table 4-16. Compiled results of sonic speeds of argon at low and high temperatures for various roots.


Speed No. of Other
(m/s)1' Roots Parameters


----- - -Low Temperature------ --- - -- -- -- -290.91 � .05 21 T = -31.56 �.1000
290.96 � .03 42 P = 870.5 �.5 PSIA
290.962 � .027 63 UJ 6-12 speed of sound
290.962 � .023 84 c =291.644 rn/s
% difference = 0.2


----- - -High Temperature------ --- - -- -- -- -348.90 �.05 21 T = 50.93 �.0600
348.79 �.03 42 P = 1285.5 �.8 PSIA
348.806 �.027 63 LJ 6-12 speed of sound
348.797 �.023 84 c = 350.245 m/s
%difference = 0.4















CHAPTER 5
CONCLUSION

From the results in Figures 4-5 and 4-6, one sees that the ST can correctly resolve the speed of sound or speeds of sound in an idealized spherical acoustic cavity. The identifiable speed of sound in Figure 4-5 is 350.000 mls which is precisely the speed used to develop the time domain signal. In Figure 4-6, the identifiable speeds of sound were 150.000 m/s and 350.000 m/s which also matched precisely the speeds used to calculate the time domain signal. As discussed previously in the introduction, this transform assumes that there is no frequency dependence on the speed of sound. The speed that has thermodynamic significance as seen in Equation 2-22 is the speed of sound at zero frequency. This speed can be calculated by using the speed from the ST to identify the frequencies. once these are identified and measured precisely, the speed at each frequency can be calculated by rearrangement of Equation 2-10 and a plot of speed vs. frequency can be developed. Extrapolation of this data to zero frequency will reveal the thermodynamically significant speed of sound at zero frequency.











This still does not account f or the precondensation

effects with the walls of the cavity.'1 Precondensation effects will also show up in the frequency domain. The actual magnitude of this effect can be very accurately investigated once the data are acquired. Although, the most accurate method of determining the speed of sound at zero frequency is still not certain, the present method is the first step to complete automation of this measurement. Even with no analysis or calibration (see Table 4-16), the ST speed of sound obtained from measurements on argon is within 0.5% of the calculated thermodynamic speed of sound at zero frequency.

The ST baseline for the experimental data had

considerable noise due to the assumption made in Equation 212 that all frequencies detected by the FFT are acoustic. Clearly the baseline represents nonacoustic resonances of some kind. There are, of course, several ways to reduce this problem by increasing the gain of the acoustic frequencies. One way would involve isolating the transducers from any contact with the cavity and acoustically insulating the outer portion of the sphere. Another method would be to excite the acoustic frequencies selectively; or, in other words, perform an inverse ST to produce an arbitrary waveform that could be sent to the


1 Mehl and Moldover, "Precondensation Phenomena in Acoustic Measurements."










driving transducer by a Digital to Analog Converter (DAC). By coupling the ADC signal to the waveform produced by the DAC, a sonic sweep could be performed where the arbitrary wave is swept over a sonic range and the sonic speed spectrum recorded. This would be analogous to the frequency swept method used in the past.

Even without resorting to the use of methods to enhance the baseline of the sonic spectrum, it is apparent from consideration of Figures 4-23 through 4-30 that the speed of sound can be expeditiously deduced with this technique. The time of acquisition is approximately 10 seconds with the equipment used in this experiment; thus, technically this is not a real time measurement. Bear in mind, however, that the acquisition was performed with an 8088 CPU (8 bit) computer. If a larger and faster computer were used, such as an 80386 (32 bit) computer, the total time of processing would be slightly more than the time of acquisition or approximately 1 second. By decreasing the sonic resolution, even shorter acquisition times could be achieved. These would then be comparable to the acquisition times of temperature and pressure measurement. For the ADC used in this experiment with an 84 root basis, a sonic resolution of 0*.023 m/s or a full scale resolution of 6 ppm was achieved. This far exceeds state-of-the-art pressure resolution and is comparable to the resolution of high quality temperature measurements.











The basic device developed here has many potential

applications. For example, it has recently been discovered that a single fluid can propagate sound at more than one

speed.2 The technique used for detecting this unexpected phenomenon did not involve a resonance behavior, but rather the traverse time of flight of pressure-pulse generated waves. If the phenomenon of multiple speeds of sound in a fluid is well-founded, there must be observable resonance effects corresponding to those speeds. The theoretical results in Figure 4-6 show that the ST method would be well suited for investigating this phenomenon.

Also, with sensitive enough detection such that no

external excitation is needed, a similar device could simply listen to the noise already in a cavity and from that deduce the speed of sound. For a pipeline in which the fluid is energized by the pumping action, one could detect the speed of sound in a passing fluid by simply listening to the fluid. The fluid motion leads to an apparent separation of sonic speed via the Doppler effect and a ST determination of that separation would lead to a direct measurement of the flow velocity. Since fluid density may be related to the sonic speed, the mass flow rate could also be determined. Combining these with pressure and temperature measurements,


2 J. Bosse, G. Jacucci, M. Ronchetti, and W. Schirmacher, "Fast Sound in Two-Component Liquids" Physical Review Letters 57 (December 1986): 3277.








73

valuable information about flowing streams could be obtained by passive noninvasive processes. Representatives of the petroleum and pipeline industries have already shown a strong interest in this new art. Negotiations are presently underway to cooperate with these industries in further development of the technique.

Measuring critical phenomena of fluids with sonic techniques is difficult when using a frequency tracking method. When the fluid is close to the critical temperature and density, the mixture approaches a chaotic state and the speed of sound approaches zero. As this occurs, the spectrum collapses and bunches all the frequencies closer together while the speed of sound and resonance frequency are dropping rapidly. It is easy to lose the frequency being tracked since it is moving very rapidly. With the ST, all frequencies would be measured for a given basis set of roots and then transformed automatically to the sonic domain providing that resonances can be detected.

Another area with good potential for the utilization of a sonic speed meter is that of reaction kinetics. The sonic speed is highly sensitive to all changes in the structure or composition of a material system and thus could be used to monitor the progress of a chemical or physical transformation. The chemical industry has again expressed interest in this newly evolving technology as a possible











means of remotely following the kinetics of a complex polymerization reaction in large batch reactor.

The applications that have been mentioned thus far are only a few of the possibilities for this new technique. To list all potential possibilities would be like listing all of the applications of a thermometer. The most important result of this study is the application of an ideal numerical model of a physical phenomena to a real experiment. The data of many phenomena can be transferred from an arbitrary domain to a domain that communicates more information. For example, these same principles could relate molecular geometries to vibrational spectra or trajectories to ion cyclotron resonance spectra. Any phenomenon that has an ideal or reference state model could be transformed to an ideal domain. The frequency domain spectra are necessary for investigation of fine structure. In fact, the transform to an ideal domain should demonstrate these deviations readily.

The availability of fast computational processes has facilitated this blend of theory and experiment on a numerical level. Since modern modeling techniques generally involved numerical solutions, it is natural that the communication of these theories to experiments should also be numerical. This experiment is representative of the current influence of numerical mathematics on scientific research, which will significantly change the perceptions








75

and interpretations of future physical experiments. In the future, numerical mathematics should not be avoided in applications of experimental science, but rather employed vigorously throughout all of experimental science.
















APPENDIX A
FAST FOURIER TRANSFORM SOURCE CODE


IMPLICIT REAL*8 (A-H,O-Z) IMPLICIT INTEGER*4 (I-N)
INTEGER*2 HEX(256),HIGH,LOW,TAF(16384)
CHARACTER*1 A(64)
CHARACTER*20 FILENAME, FILEOUT DIMENSION XR(65536),XI(65536)
COMMON XMAX, PI, NU,NDP, NDPDIV2 , NDPDIV4,NDPMIN1, IND C USE FFT TRANSFORM WITH REAL DATA IN XR ARRAY
PI=2.0*ACOS(0.0)
NU=16
NDP=2**NU NREAD=1024
NDPDIV2=NDP/2 NDPDIV4=NDP/ 4 NDPMIN1=NDP-1
IND=-I
CALL HEXGET(HEX) C START TIME AVG
DO 20 IF=100,599
WRITE(FILENAME,'(A8,I3,A4)') 'E:\\HEX\\F',IF,'.OUT'
OPEN (10, FILE=FILENAME, STATUS=' OLD')
READ(10,*) T,P
DO 30 I=1,NREAD
READ(10,300) (A(K),K=1,64)
300 FORMAT(64A1)
DO 50 K=2,64,2
HIGH=HEX(ICHAR(A(K-1)) ) *16
LOW=HEX(ICHAR(A(K)))
XR( (I-l) *32+K/2)=FLOAT(HIGH+LOW)
50 CONTINUE
30 CONTINUE
CLOSE (10)
DO 70 I=1,NDPDIV2
XR (NDPDIV2+I) =XR (I) 70 CONTINUE CALL BASELINE (XR, XI)
CALL BLACK(XR) CALL FFT(XR,XI)
XMAX=0.0
DO 41 L=1,400
XR(L) =0
41 CONTINUE












DO 40 L=101,NDPDIV2
XMAX=AMAX1 (XMAX,XR(L))
40 CONTINUE
DO 60 L=2,NDPDIV2,2
TAF(L/2)=INT((XR(L)+XR(L-1))/XMAX*8192)
60 CONTINUE
WRITE(FILEOUT,'(A7,I3,A4)') 'E:\\FD\\F',IF,'.FFT'
WRITE(*,200) FILEOUT
OPEN (10, FILE=FILEOUT, FORM= 'UNFORMATTED')
WRITE(10) T,P WRITE(10) TAF
CLOSE(10)
20 CONTINUE 200 FORMAT(A)
END



C234567
SUBROUTINE BASELINE (XR, XI)
IMPLICIT REAL*8 (A-H,O-Z)
IMPLICIT INTEGER*4 (I-N)
DIMENSION XR(1),XI(1)
COMMON XMAX, PI, NU, NDP, NDPDIV2, NDPDIV4, NDPMIN1, IND
ARX = 0.0
DO 100 I = 1 , NDP
ARX = ARX + XR(I) 100 CONTINUE ARX = ARX / FLOAT(NDP)
DO 200 I = 1,NDP
XR(I) = XR(I) - ARX 200 CONTINUE
DO 300 I=1,NDP
XI(I)=0.0 300 CONTINUE RETURN
END


SUBROUTINE BLACK (XR)
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION XR(i)
COMMON XMAX,PI,NUNDP,NDPDIV2, NDPDIV4, NDPMINI, IND
DO 100 I = 1,NDP
C = 2.0*PI*FLOAT(I)/FLOAT(NDP)
A = 0.49755 * COS(C)
B = 0.07922 * COS(2.0*C)
XR(I) = XR(I) * (0.42423 - A + B) 100 CONTINUE RETURN
END













SUBROUTINE FFT (XR, XI)
IMPLICIT REAL*8 (A-H,O-Z) IMPLICIT INTEGER*4 (I-N)
DIMENSION XR(i) ,XI(i)
COMMON XMAX, PI,NU, NDP, NDPDIV2, NDPDIV4, NDPMINI,IND
DO 100 L = INU
LE = 2**(NU+1-L)
LEI = LE/2
Ul = 1.0 U2 = 0.0
ARG = PI/LEI C = COS (ARG)
S = IND*SIN(ARG) DO 101 J = 1,LE1
DO 102 I = J,NDP,LE
IP = I + LEI
Ti = XR(I) + XR(IP) T2 = XI(I) + XI(IP) T3 = XR(I) - XR(IP) T4 = XI(I) - XI(IP)
XR(IP) = T3*UI-T4*U2 XI(IP) = T4*UI+T3*U2
XR(I) = Ti XI(I) = T2 102 CONTINUE
U3 = U1*C-U2*S U2 = U2*C+Ui*S
U1 = U3
101 CONTINUE
100 CONTINUE
J = 1
DO 104 I = 1,NDPMIN1
IF (I .GE. J) GOTO 25
TEMP = XR(I) XR(I) = XR(J) XR(J) = TEMP TEMP = XI(I) XI(I) = XI(J) XI(J) = TEMP 25 K = NDPDIV2
20 IF (K .GE. J) GOTO 30
J = J-K K = K/2 GOTO 20
30 J = J + K
104 CONTINUE
DO 60 I = 1 , NDPDIV2
XR(I) = SQRT(XR(I)*XR(I)+XI(I)*XI(I)) 60 CONTINUE
RETURN
END













SUBROUTINE HEXGET (HEX) IMPLICIT REAL*8 (A-H,O-Z) IMPLICIT INTEGER*4 (I-N) INTEGER*2 HEX(256) HEX(ICHAR(' '))=O HEX(ICHAR( 0'))=0 HEX(ICHAR( 1'))=i HEX(ICHAR( '2))=2 HEX(ICHAR('3'))=3 HEX(ICHAR( 4'))=4 HEX(ICHAR( 5'))=5 HEX(ICHAR( 6'))=6 HEX(ICHAR( 7'))=7 HEX(ICHAR(84) )=8 HEX(ICHAR( 9'))=9 HEX(ICHAR( 'A') )=10 HEX(ICHAR( 'B') )=ii HEX(ICHAR('C') )=12 HEX(ICHAR( 'D'))=13 HEX (ICHAR( 'E') )=14 HEX(ICHAR( 'F') )=15 RETURN
END















APPENDIX B SONIC TRANSFORM SOURCE CODE


IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION ROOT(84),SMAG(16384),T(500),P(500)
INTEGER*2 CO(16384),C,SPO(16384)
CHARACTER*20 FILEIN,FILEOUT
TWOPI=4.0*ACOS(0.0)
CALL RTGET(ROOT)
TAVG=0.0 PAVG=0.0 NROOT=84
CMAX=200.0*TWOPI*3.0*2.54/ROOT(NROOT)
CRES=CMAX/16384.0
NMAX=16384
FRES=20000.0/16384
DENOM=TWOPI*3.0*2.54/100*FRES
DO 40 I=100,599
INDX=I-99
WRITE(FILEIN,'(A7,13,A4)') 'E\:\\FD\\F',I,'.FFT'
WRITE(*,100) FILEIN 100 FORMAT(A)
OPEN(1,FILE=FILEIN,FORM='UNFORMATTED')
READ(l) T(INDX),P(INDX)
READ(l) CO
CLOSE(i) XMAX=0.0
DO 10 C=1,NMAX
SPEED=FLOAT(C)*CRES
RATIO=SPEED/DENOM
SMAG(C)=0.0
DO 20 J=1,NROOT
INDEX=INT(RATIO*ROOT(J)+0.5)
IF(INDEX.GT.16384) THEN
TEMP=0.0
ELSE
TEMP=DBLE(CO(INDEX))
ENDIF
SMAG (C) =SMAG (C) +TEMP 20 CONTINUE
XMAX=AMAX1 (XMAX, SMAG (C)) 10 CONTINUE
DO 30 C=1,NMAX
SPO(C)=INT(SMAG(C)/XMAX*16384.0) 30 CONTINUE











WRITE(FILEOUT,'(A7,I3,A4)') 'E\:\\SD\\F',I,'.SPD'
OPEN (1 ,FILE=FILEOUT, FORM= 'UNFORMATTED')
WRITE(l) T(INDX),P(INDX)
WRITE(1) SPO
CLOSE (1)
TAVG=TAVG+T (INDX) PAVG=PAVG+P (INDX)
WRITE(*,*) T(INDX),P(INDX)
40 CONTINUE
TAVG=TAVG/500.0 PAVG=PAVG/ 500.0
SDT=0.0 SDP=0.0
DO 50 I=1,500
SDT=SDT+(TAVG-T(I)) **2 SDP=SDP+(PAVG-P(I)) **2
50 CONTINUE
SDT=SDT/499.0/500.0
SDT=1. 96*SQRT (SDT)
SDP=SDP/499.0/500.0
SDP=1. 96*SQRT (SDP)
WRITE(*,200) TAVG,SDT,PAVG,SDP
200 FORMAT(F1O.4,'+/-',F7.4,FIO.4,'+/-',F7.4)
WRITE(*,300) CRES
300 FORMAT(' RESOLUTION OF SONIC DOMAIN=',FIO.5)
END

C
C
C
C
C
C
SUBROUTINE RTGET (ROOT)
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION ROOT(i)
ROOT (1) =2.08158 ROOT(2)=3.34209 ROOT (3)=4.49341 ROOT (4) =4.51408 ROOT (5) =5.64670
ROOT (6) =5. 94036 ROOT (7) =6.75643 ROOT(8) =7. 28990 ROOT (9) =7.72523
ROOT(10)=7.85107 ROOT(11) =8.58367 ROOT(12)=8.93489 ROOT(13)=9.20586 ROOT (14) =9. 84043 ROOT(15) =10. 0102 ROOT(16) =10. 6140










ROOT(17)=10.9042 ROOT (18) =11. 0703 ROOT (19) =11. 0791 ROOT (20)=11. 9729 ROOT(21) =12.1428 ROOT(22)=12.2794 ROOT(23)=12.4046 ROOT(24)=13.2024 ROOT(25) =13.2956 ROOT (26) =13. 4721 ROOT (27) =13.8463 ROOT (28) =14.0663 ROOT (29) =14.2850 ROOT (30) =14. 5906 ROOT ( 3 1) =14. 6513 ROOT (32)=15. 2446 ROOT (33) =15. 3108 ROOT(34)=15. 5793 ROOT (35) =15. 8193 ROOT(36) =15.8633 ROOT(37)=16. 3604 ROOT(38)=16. 6094 ROOT (39) =16. 9776 ROOT (40) =17.0431 ROOT (41) =17. 1176 ROOT(42) =17. 2207 ROOT (43)=17. 4079 ROOT (44) =17. 9473 ROOT (45) =18. 1276 ROOT (46) =18.3565 ROOT (47) =18.4527 ROOT(48) =18. 4682 ROOT(49)=18.7428 ROOT(50)=19.2628
ROOT (51) =19. 2704 ROOT (52) =19. 4964 ROOT (53) =19. 5819 ROOT(54)=19.8625 ROOT (55) =20. 2219 ROOT (56) =20. 3714 ROOT (57) =20. 4065 ROOT(58) =20.5379 ROOT (59) =20. 5596 ROOT (60) =20. 7960 ROOT (61) =21. 2312 ROOT (62) =21. 5372 ROOT (63) =21. 5779 ROOT (64) =21. 6667 ROOT(65) =21. 8401 ROOT (66) =21. 8997 ROOT(67)=22.0000 ROOT (68) =22. 5781











ROOT(69)=22. 6165 ROOT (70) =22.6625 ROOT(71) =23.0829 ROOT (72) =23. 1067 ROOT (73) =23. 1950 ROOT(74)=23. 3906 ROOT (75) =23. 5194 ROOT (76) =23.6534 ROOT (77) =23. 7832 ROOT(78)=23.9069 ROOT(79)=24.3608 ROOT (80) =24.3821 ROOT (81) =24. 4749 ROOT (82) =24. 6899 ROOT (83) =24. 8503 ROOT (84)=24. 8995 RETURN
END
















APPENDIX C EQUATION OF STATE FOR ARGON SOURCE CODE


IMPLICIT REAL*8 (A-H,O-Z)
REAL*8 B(100),BI(100),B2(100),T(100)
REAL*8 C(100),CI(100),C2(100),BD(100),N
EPK=119.8D 00
BO=49.80D-03
PCON=6. 8046D-02
KEL=273.15
OPEN (10,FILE='E\:\\SOURCE\\TVC.CON',STATUS='OLD')
DO 25 I=1,74
READ(10, *)
CT(I) ,B(I),BI(I),B2(I),BD(I),C(I) ,C1(I) ,C2(I) 25 CONTINUE
CLOSE (10)
100 WRITE(*,*) ' INPUT TEMPERATURE (Celcius) AND
CPRESSURE (psia)'
READ(*,*) TEMP,P
P=P*PCON
TEMP=TEMP+KEL
TS=TEMP/EPK
CALL
CQAND(BS,BS1,BS2,BSD,CS,CSI,CS2,TS,T,
CB,B1,B2,BD,C, Cl, C2)
BV=BS*BO
CV=CS*BO*BO
CALL VERVOL(P,V,TEMP,BV,CV)
VS=V/BO
CALL SPEED(CAR,TEMP,BS,BS1,BS2 ,BSD,CS,CS1,CS2,VS)
WRITE(*,*) ' SPEED=',CAR
GOTO 100
END
C
C
C
C
C
C
C
SUBROUTINE
CQAND(BS,BS1,BS2,BSD,CS,CS1,CS2,TS,T,B,B1,B2
C,BD,C,Cl,C2)
IMPLICIT REAL*8 (A-H,O-Z)












REAL*8 B(1),BI(1),B2(1),T(1),C(1),CI(1),C2(1),BD(1)
REAL*8 M
DO 20 I=2,74
IF (TS.GT.T(I-1).AND.TS.LT.T(I)) THEN
M=(TS-T(I-))/(T(I)-T(I-))
BS=B (I-l) +M* (B(I) -B(I-))
BS2=B2 (I-l) +M* (B2 (I) -B2 (I-l)) BS2=B2(I-1)+M*(B2(I)-B2(I-1))
BSD=BD(I-)+M*(BD(I)-BD(I-l))
CS=C(I-)+M*(C(I)-C(I-1))
CSI=CI (I-l) +S*(CI (I)-CI (I-l))
CS2=C2 (I-I)+M* (C2 (I)-C2 (I-l))
RETURN
ENDIF
20 CONTINUE
WRITE(*,*)lTSTAR OUT OF RANGE'
RETURN
END
C
C
C
C
C
C
C
SUBROUTINE VERVOL(P,V,T,B,CV)
IMPLICIT REAL*8 (A-H,O-Z)
R=8. 20575D-02
TOL=1. OD-16 C INPUT P IN ATM C INPUT T IN KELVIN
V=R*T/P
10 VN=R*T/P*(I.OD 00 + B/V + CV/V/V)
TEST=V/VN
IF(TEST.GT.1.0) THEN
TEST=1.OD 00 - 1.OD 00/TEST
ELSE
TEST=1.OD 00 -TEST
ENDIF V=VN
IF(TEST.GT.TOL) GOTO 10
RETURN
END
C
C
C
C
C
C
C
SUBROUTINE SPEED(C,T,BS,BS1,BS2,BSD,CS,CS1,CS2,VS)
IMPLICIT REAL*8 (A-H,O-Z)









86

REAL*8 M,DSQRT
M=39. 948D-03
R=8.31441D 00
GAMA=
C5.ODO/2.0D0-BS2/VS+(BSD*BSD-CS+CS1-0.5D0*CS2)/VS/VS
GAMA=GAMA/(3.ODO/2.ODO-(2.ODO*BSI+BS2)/VS@(2.ODO*CS1+CS2)/2.ODO/VS/VS)
C=GAMA*R*T/M* (1. OD 00+2.0D0*BS/VS+3.ODO*CS/VS/VS)
C=DSQRT (C)
RETURN
END















APPENDIX D
DATA ACQUISITION SOURCE CODE


#include #include #include #include #include "DECL.H" libraries */ #include #include #include #include


#define #define #def ine #define #define #define


PORTO PORT1 PORT2 PORT3 COMMA NOERR


0x178 0x179 Oxl7A Oxl7B Ox2c
0


/* supplied with driver


/* default setting */
/* all switches are off */


/* driver library functions */
I****************************** extern int ibfind(; extern void ibtmoo; extern void ibclr(); extern void ibeoso; extern void ibrd(; extern void ibwrt(); extern void ibcmdo; extern void ibsic(; extern void ibloc(); extern void ibrsp(); extern void ibwait();

FILE *stream; char *dacoutput=(char*)OxDO0OOO; int addr=0x20;

unsigned char io[32768]; long timeout[500]; float pout[500]; double tout[500]; long t,tO,tday;













/* sends temperature in celcius to the oven, */
/********************************************** void wrtoven(float setpoint)
{
int j,ovn; char ostring[14],fp[10];
gcvt(setpoint,5,fp);
strcpy(ostring,"setpoint ");
ostring[9]=fp[O];
ostring[1O]=fp[l]; ostring(11]=fp[2]; ostring[12]=fp[3]; ostring[13]=fp[4];
ostring[14]='\O';
ovn = ibfind ("oven");
ibwrt( ovn, ostring, 15);
printf( " %s\n",ostring);
return;


/********************************************** /* reads temp in celcius form rtd, */
/***********************************************
double rdrtd()
{
int i,rtd; double res,rc,aldel,ptl,pt2,pt3,pt4,t2; double r0=99.98; double alpha=0.0039076; double delta=1.5205; char rstring[16];
rtd = ibfind("k195a");
ibrd( rtd, rstring, 17 );
for(i=O; i<4; i++) rstring[i]=' ';
for(i=15; i<17; i++) rstring[i]=' ';
res=atof(rstring); aldel=alpha*delta;
rc=res/rO; rc=rc-1.0;
ptl=aldel/100.0;
ptl=ptl+alpha;
pt2=ptl*ptl;
pt3=4.0*rc;
pt3=pt3*aldel;
pt3=pt3/10000.0;
pt4=2.0*aldel;
pt4=pt4/10000.0; t2=sqrt(pt2-pt3);
t2=ptl-t2;











return (t2/pt4);



/********************************************** /* reads the pressure transducer, *


float rdpress()
{
int ptrans;
char pstring[9];
ptrans = ibfind("beckman"); ibrd( ptrans, pstring, 10 );
pstring[7]=' '; pstring[8]=' '; pstring[9]=' ';
return (atof(pstring));



/* gets the time in milliseconds */
/***********************************

void getmilli()
{
*char tmp[l]; long h,m,s;

struct timeb timebuffer;
char *timeline;

ftime(&timebuffer);
timeline = ctime(&(timebuffer.time));

tmp[O]=timeline[ll]; tmp[l]=timeline[12];
h=atol(tmp);
h=h*3600;
tmp[O]=timeline[14]; tmp[l]=timeline[15]; m=atol(tmp); m--m*60;
tmp[O]=timeline[17]; tmp[l]=timeline[18]; s=atol(tmp); t=h+m;
t=t+s;
* t=t*l000; t=t+timebuffer.millitm; s=t-tO;
if(s < 0 ) {




Full Text

PAGE 1

GENETIC, DEVELOPMENTAL, AND MOLECULAR CHARACTERIZATION OF A HIGH OLEIC ACID PEANUT (Arachis hypogaea L.) By KIMM. MOORE 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

PAGE 2

ACKNOWLEDGEMENTS The author expresses his most sincere appreciation to his major advisor, Dr. David Knauft, for his advice, encouragement, and expert editorial assistance in completing this manuscript. Appreciation is also extended to Dr. Al Norden for his initial encouragement to pursue this particular research project. A special thanks is extended to Dr. Sherlie West for his support, advice, and understanding that led to the completion of this project. Appreciation is also extended to the other members of his advisory committee, Dr. Ken Buhr, Dr. Paul Lyrene, and Dr. Ken Quesenberry, for their thoughtful suggestions in this dissertation. A very special thanks is extended to Dr. Rex Smith who, although not a member of the advisory committee, provided excellent support and invaluable input. Thanks is also extended to Dr. Kamal Chowdhury for his assistance on the analysis of RFLPs. Thanks is also extended for the technical assistance of Karen Bedigian, Harry Wood, Jeff Seib, and Natalie McGill. The author also wishes to acknowledge both the Florida Foundation Seed Association and Proctor and Gamble, Incorporated, for their funding of portions of this research. ii

PAGE 3

TABLE OF CONTENTS ACKNOWLEDGEMENTS LIST OF TABLES .. LIST OF FIGURES . . ABSTRACT CHAPTERS I II III IV INTRODUCTION .. THE INHERITANCE OF HIGH OLEIC ACID IN PEANUT. . . . . . . . . . . . . . . Introduction ..••...•.•.. Materials and Methods .•.•.. Results and Discussion Saponification Versus Direct Esterification •.. Cross with F78114 .•. Cross with F519-9 ..... . Cross with PI 262090. Summary . . . . . . . . . . . . . . VARIATION IN FATTY ACID COMPOSITION IN DEVELOPING SEED OF Arachis hypogaea L. Introduction •..... Materials and Methods .. Results and Discussion RESTRICTION FRAGMENT LENGTH POLYMORPHISM IN THE GENUS Arachis. . . . . .. Introduction ...•...•.•..•• Materials and Methods. DNA Extraction ..•.. Extraction 1 (CTAB) ..•.•. iii Page ii V . . viii xi 1 17 17 19 24 24 26 34 37 37 41 41 43 46 70 70 72 73 73

PAGE 4

V REFERENCES Extraction 1 (CTAB) ...••.•. 73 Extraction 2 (potassium acetate) 75 Southern Blotting. . . . . . . •. 77 Probe Preparation 78 Radio-labeling Probes 80 Prehybridization and Hybridization of Blots. . . . . 81 Results and Discussion. . 82 SUMMARY. 109 BIOGRAPHICAL SKETCH. 112 120 iv

PAGE 5

LIST OF TABLES Table Page 1-1 Oleic and linoleic acid content of vegetable oils ........ . 9 2-1 Oleic and linoleic acid content of the four peanut breeding lines used in crossing .... 21 2-2 A comparison of two methods of fatty acid analysis, saponified versus nonsaponified. Palmitic, stearic, oleic, linoleic, arachidic, and benhenic acid contents are shown from four different oil sources. Also shown are values of tcalc . . . . . . 25 2-3 A comparison of total areas integrated on chromatographs of saponified oils versus nonsaponified oils. Four different oil sources are included. Also included is the percent of the total fatty acids measured when saponification is performed that are measured when saponification is not performed . . . . . . . . . . . . . . . 2-4 F 1 progeny from the cross between high (F435) and normal (F519-9), (F78114), and (PI 27 262090) oleic acid phenotypes ........ 28 2-5 Segregation data for F 2 progeny from the cross between high (F435) and normal (F78114) oleic acid lines .•.....• 2-6 BC 1 oleic acid phenotypic segregation ratios for two peanut lines (F78114 and F519-9) crossed to a high-oleic-acid peanut line 31 (F435). . . . . . . . . . . . . . . . . . 32 2-7 Phenotypic segregation of F 3 families from crosses between high (F435) and normal (78114 or F519-9) oleic acid peanut lines .. 33 V

PAGE 6

Table 2-8 2-9 3-1 Phenotypic segregation of oleic acid content for F progeny from the cross between high (F435j and normal (F519-9) oleic acid peanut 1 ines . . . . . . . . . . . . . . . . . . Segregation data for F 2 progeny from the cross between high (F435) and normal (PI 262090) oleic acid lines ...•... Oleic and linoleic acid content of three peanut breeding lines .....•..•. 36 38 44 3-2 R 2 values of individual plants and for a composite of all plants for each genotype for maturity versus dry matter . . . 47 3-3 R 2 values for regressions of the percent oleic acid with maturity rating as the independent variable compared with dry matter as the independent variable for three genotypes, F519-9, F435, and F78114 51 3-4 The percent oleic acid and standard errors for high, moderate, and low oleic acid peanut genotypes sampled at various stages of dry matter deposition ..•..•........ 60 3-5 The percent palmitic acid and standard errors for high, moderate, and low oleic acid peanut genotypes sampled at various stages of dry matter deposition ..•..•.•...•.• 63 3-6 The percent linoleic acid and standard errors for high, moderate, and low oleic acid peanut genotypes sampled at various stages of dry matter deposition ......•....... 64 4-1 Absorbances of DNA extracts from four Ahypogaea lines and four perennial Arachis species at two wavelengths. Extraction was method 1 (CTAB) using young mature leaf tissue. . . . . . . . . . . . . . . . . . . . 83 4-2 Absorbances of DNA extracts from four Ahypogaea lines and four perennial Arachis species at two wavelength. Extraction was method 2 (potassium acetate) using young mature leaf tissue .........•.... 84 vi

PAGE 7

Table Page 4-3 Absorbances of DNA extracts from four Ahypogaea lines and four perennial Arachis species at two wavelengths. Extraction was method 1 (CTAB) using immature leaf tissue .. 88 4-4 Genomic DNA clones, library cell locations, and approximate sizes of inserts isolated for production of radio-labeled probes 92 4-5 Gene clones used as radio-labeled probes. 93 4-6 Pair-wise indices of genetic similarity of four Ahypogaea lines and four Arachis species. The similarity index was calculated by dividing the total number of DNA fragments common between two genotypes by the total number of unique fragment sizes represented by the paired genotypes ......•.•.• 107 vii

PAGE 8

Figure 1-1 1-2 LIST OF FIGURES End use of peanuts as percent of the total 1984 u. s. production .•. The fatty acid percentages of the total fatty acid composition of peanut oil .• 1-3 The currently proposed biochemical pathway for desaturation of oleic acid to linoleic Page 4 6 acid in higher plants .........•.. 14 2-1 Frequency distribution of number of F 2 offspring in phenotypic classes based on oleic acid content. Data has been pooled for all families from the cross of F78114 and F435 •. 30 2-2 Frequency distribution of number of F 2 offspring in phenotypic classes based on oleic acid content. Data has been pooled for all families from the cross of F519-9 and F4 3 5. . . . . . . . . . . 3 5 2-3 Frequency distribution of number of F 2 offspring in phenotypic classes based on oleic acid content. Data has been pooled for all families from the cross of PI 262090 and F435. . . . . . . . . . . . . . . . 39 3-1 Regression plot of the percent dry matter versus maturity classification of peanut seed sampled from all four plants of line F519-9 . 48 3-2 Regression plot of the percent dry matter versus maturity classification of peanut seed sampled from all four plants of line F435 .. 52 3-3 Regression plot of the percent dry matter versus maturity classification of peanut seed sampled from all four plants of line F78114 . 53 viii

PAGE 9

Figure 3-4 3-5 3-6 3-7 3-8 3-9 3-10 3-11 3-12 3-13 4-1 4-2 Regression plot of the percent oleic acid versus maturity classification of peanut seed sampled from all four plants of line F519-9 54 Regression plot of the percent oleic acid versus maturity classification of peanut seed sampled from all four plants of line F435 .. 55 Regression plot of the percent oleic acid versus maturity classification of peanut seed sampled from all four plants of line F78114 . 56 Regression plot of the percent oleic acid versus the percent dry matter of peanut seed sampled from all four plants of line F519-9. 57 Regression plot of the percent oleic acid versus the percent dry matter of peanut seed sampled from all four plants of line F435 .. 58 Regression plot of the percent oleic acid versus the percent dry matter of peanut seed sampled from all four plants of line F78114 . 59 Regression plot of the percent palmitic acid versus the percent dry matter of peanut seed sampled from all four plants of line F519-9 . 62 Regression plot of percent linoleic acid versus percent dry matter of peanut seed sampled from all four plants of line F435 65 Regression plot of percent linoleic acid versus percent dry matter of peanut seed sampled from all four plants of line F519-9 . 66 Regression plot of percent linoleic acid versus percent dry matter of peanut seed sampled from all four plants of line F78114 . 67 DNA extracts from eight peanut genotypes using extraction method 1 on mature leaf tissue. . . . . . . . . . . . . . . . . . DNA extracts from eight peanut genotypes using extraction method 2 on mature leaf tissue. . . . . . . . . . . . . . . . . . ix 86 87

PAGE 10

Figure 4-3 4-4 4-5 DNA extracts from eight peanut genotypes using extraction method 1 on immature leaf tissue . ....... . Clones separated from pUC .. Autoradiograph of probe atpa on peanut genotypes illustrating an unacceptable autoradiograph based on poor fragment definition •.•.......••... 89 91 94 4-6 Autoradiograph of probe HPI16 on peanut genotypes with fragment sizes in kilobases. 95 4-7 Autoradiograph of probe HPI6 on peanut genotypes with fragment size in kilobases 96 4-8 Autoradiograph of probe atp6 on peanut genotypes with fragment sizes in kilobases .• 98 4-9 Autoradiograph of probe cox! on peanut 4-10 4-11 4-12 4-13 4-14 4-15 genotypes with fragment sizes in kilobases. 99 Autoradiograph of probe HPI67 on peanut genotypes with fragment sizes in kilobases .. 100 Autoradiograph of probe HPI72 on peanut genotypes with fragment sizes in kilobases .. 101 Autoradiograph of probe HPI58 on peanut genotypes with fragment sizes in kilobases .. 102 Autoradiograph of probe HPI52 on peanut genotypes with fragment sizes in kilobases .. 103 Autoradiograph of probe rrn5-rrn18 on peanut genotypes with fragment sizes in kilobases .• 104 Autoradiograph of probe HPI54 on peanut genotypes with fragment sizes in kilobases .. 105 X

PAGE 11

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 GENETIC, DEVELOPMENTAL, AND MOLECULAR CHARACTERIZATION OF A HIGH OLEIC ACID PEANUT (Arachis hypogaea L.) By Kim M. Moore May 1990 Chairman: David A. Knauft Major Department: Agronomy Shelf life and nutritional value are important factors affecting the quality of peanuts and peanut products. These factors are directly related to the chemical composition of the oil. Peanut oil is composed of 95% triacylglycerides which vary in their composition by the relative proportions of component fatty acids. Typically, 90% of the total fatty acid composition is made up of three fatty acids, palmitic, oleic, and linoleic acids. Oleic acid has been shown to be more desirable for both stability and nutrition than palmitic or linoleic acids. In 1987, a peanut line high in oleic acid was identified. This peanut line was crossed with four other peanut lines and cultivars to determine the mode of inheritance of the oil character. Segregating F 2 populations were analyzed along with F 1 , F 3 , and backcross xi

PAGE 12

generations. Among the four crosses, three F 2 crosses produced segregating ratios of 3 normal to 1 high oleic acid phenotype. One of the crosses produced a segregating ratio of 15 normal to 1 high oleic acid phenotype. Analysis of the F 3 and backcross data further supported a hypothesis of inheritance by two genes, each with a dominant and recessive allele. Further investigations were conducted to determine if variation in gene action occurred during development. Seeds of three peanut genotypes that were low (F78114), moderate (F519-9), and high (F435) in oleic acid were analyzed for fatty acids at different developmental stages. Oleic acid content increased in the early stages of development of all three genotypes. Linoleic acid content was relatively unchanged during development of F519-9 and F78114 but declined during development of the high oleic acid line. Early stages of development may be the best time to isolate mRNA to produce cDNA for screening to characterize the genes. The high oleic acid genotype along with F519-9, F78114, PI 262090, and four species of perennial peanut were compared by variation in DNA fragment length polymorphism. The four Ahypogaea lines were uniform and showed few polymorphic fragments. Polymorphisms were more readily detected among the four perennial peanut species. xii

PAGE 13

CHAPTER I INTRODUCTION The peanut, Arachis hypogaea L., is a native legume of South America. It is a member of the family Leguminosae, tribe Aeschynomeneae, subtribe Stylosanthyenae. The genus, Arachis, is divided into seven sections based on morphology and cross-compatibility. The sectional arrangement of the genus follows the ecological and geographic features of its continent of origin, South America. The currently accepted center of origin for the genus is the Mato Grosso area of Brazil, located just north and east of Paraguay (Wynne and Halward, 1989). The cultivated peanut, A hypogaea, is a member of the section Arachis. This section shows considerable diversity in the area west of the Paraguay River through northern Bolivia to the Andes mountains. Arachis hypogaea can be divided into two subspecies, based on morphological differences. These subspecies are hypogaea and fastigiata. The subspecies hypogaea is subdivided into variety hypogaea, also known as the Virginia type, and variety hirsuta, also known as the Peruvian runner type. The subspecies fastigiata is subdivided into variety fastigiata, commonly 1

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2 known as Valencia type, and variety vulgaris, also known as Spanish type (Stalker and Moss, 1987). Peanut was cultivated before the European exploration of the Americas but has been limited in range to warmer regions of the western hemisphere (Hammons, 1982). The earliest dated peanuts found in association with human activities were estimated at 3800 years old by radiocarbon dating (Hammons, 1982). These samples originated from an archeological site near Las Haldas, Peru. By the time of the European exploration and colonization of the Americas, peanut was grown throughout the warmer regions of the western hemisphere, including the islands of the Caribbean. It was probably on the island of Hispaniola where Europeans first encountered peanut culture. Peanut was then spread by European explorers and travelers to Asia, the Pacific Islands, Europe, southeastern U.S., and both coasts of Africa (Hammons, 1982). Currently, there are twenty-four countries that each produce more than three million kg of peanuts annually. China leads the world in total production with 6,400,000 metric tons produced in 1987. India is second with 4,350,000 metric tons and the United States third with 1,620,000 metric tons. World production in 1987 was over nineteen million metric tons (Commodity Research Bureau, 1988). These production numbers are elevated considerably, relative to twenty years ago, due to the increasing value of

PAGE 15

3 peanut as a source of high-quality edible oil (McGill, 1973). Unlike most countries, where peanut is grown for oil, only 24% of the 1984 U. s. production of shelled peanuts were crushed for oil, as shown in Figure 1-1 (Commodity Research Bureau, 1984). The typical oil content of peanut is approximately 52% (Cobb and Johnson, 1973). With this high level of oil, any factors affecting the quality of the oil will in turn affect the total product quality. The quality of the oil is of particular interest not only to the oil producer, but also to the processors and roasters of peanuts. A number of methods have been developed to measure oil quality quantitatively. Peroxide value, iodine number, and fatty acid content have all been used to quantify oil quality, and all are directly related to the chemical composition of the oil (Cobb and Johnson, 1973). The two principal quality characteristics most affected by the chemical composition are the storage stability of the oil and the nutritional value or liability. Both of these factors are directly related to the degree of unsaturation of the oil and more specifically related to the fatty acid composition. Peanut oil, like other vegetable oils, is composed of monoacylglycerides, diacylglycerides, triacylglycerides, and free fatty acids. An acylglyceride is a glycerol molecule, C 3 H 5 (0H) 3 , to which organic acids (fatty acids) are bound, substituting for one, two, or all three of the hydroxyl

PAGE 16

15.9 " 37.0 " 0.97 " 24.0 " 7.0 " Candy Salted Butter 0 Roasted Iii Crushed for OIi Other Figure 1-1. End use of peanuts as percent of the total 1984 U.S. production.

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5 groups, e.g., mono-, di-, and triacylglycerides. In peanut oil, triaclyglcerides account for more than 95% of the total lipids (Sanders, 1980a). The remainder is made up of approximately 1.7% diacylglycerides, 0.3% monoacylglycerides, 0.7% free fatty acids, and the remaining 2.3% is made up of polar lipids, sterols, and hydrocarbon sterol esters. The fatty acid composition of the triacylglycerides is variable. Typically, however, 90% of the fatty acid composition of peanut oil is made up of three fatty acids: palmitic, oleic, and linoleic (Cobb and Johnson, 1973). Palmitic acid is a 16-carbon, completely saturated, fatty acid. Oleic acid and linoleic are both 18carbon chains with one and two double bonds, respectively. A generalized breakdown of peanut oil fatty acid composition is given in Figure 1-2. Of the oil quality factors dependent on fatty acid composition, storage-stability is most directly related to the degree of fatty acid saturation. The most common cause of oil degradation in storage is oxidation, and the result is termed oxidative rancidity. Although some fatty acids are more prone to degradation than others, regardless of the degree of saturation, the loss of wholesomeness is most commonly caused by oxidative rancidity. This type of rancidity is directly related to the degree of unsaturation of an oil. Oxidation of the double bond in the triacylglycerides and free fatty acids results in the

PAGE 18

11.0 " 1. 1 " 2.5 " 1.4 " Palmitic Stearic ~Oleic fL:J Linoleic D Arachidic fil Behenic Lignoc•ic Figure 1-2. The fatty acid percentages of the total fatty acid composition of peanut oil.

PAGE 19

formation of peroxide groups at or near the double bond. 7 The peroxides then decompose to form acids, alcohols, aldehydes, ketones, and other hydrocarbons that result in the odors commonly associated with rancidity (St. Angelo and Ory, 1973). Therefore, the advantage of more saturation is more stability. The second quality factor, nutritional composition, is also important in the establishment of edible oil quality. Fat chemical composition and level of dietary fat intake have been found to affect level and composition of serum cholesterol (Gustafsson et al., 1985; Bronsgeest-Schoute et al., 1979; Kuusi et al., 1985; Schonfeld et al., 1982). Cholesterol and cholesterol fatty esters are components of the atherosclerotic plaques that restrict arterial blood flow and contribute to heart disease. By altering dietary fat intake both in level and/or composition, serum cholesterol levels can be reduced. A compositional change in dietary fat that has recently been shown to reduce serum cholesterol is a high monounsaturated diet. In a study conducted in 1986, it was concluded that diets high in monounsaturates, i.e., oleic acid, were as effective in reducing serum cholesterol levels as low-fat diets (Grundy, 1986). Since the degree of unsaturation is critical to both nutritional quality and storage-stability, relative proportions of fatty acids in an oil are important in determining total oil quality. Oils higher in

PAGE 20

8 monounsaturated fatty acids would be desirable for both nutrition quality and storage stability. In Table 1-1, a comparison of seven different vegetable oils is shown with their respective oleic acid (monounsaturate) and linoleic acid (polyunsaturate) content (USDA, 1975). As shown in the table, peanut is second only to olive oil in oleic acid content. Variation of fatty acid composition in peanut oil has been shown to be influenced by several factors. It may vary according to variety, location, year-to-year variation, environmental variation, and physiological maturity (Bovi, 1982; Jamieson et al., 1921; Knauft et al., 1986; Worthington et al., 1972; Hartzook, 1969; Norden et al., 1987; Rachmeler, 1988; Worthington and Hammons, 1971; Worthington, 1969; Young et al., 1974). In a comparison of peanut genotypes grouped as Virginia Runner, Virginia Bunch, and Spanish Bunch with respect to growth habit, it was found that oleic and linoleic acid contents varied significantly among groups (Raheja et al., 1987). Total oil content of the three genotypes was very uniform, ranging only from 48.9% to 49.8%. Oleic acid content was much more varied, ranging from 37.6% as a low in the Virginia Bunch to 54.7% as a high in the Virginia Runner type. Linoleic acid was also varied both within and among

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Table 1-1. Oleic and linoleic acid content of vegetable oils. Oil Source % Oleic Acid % Linoleic Corn 28 53 Cottonseed 21 50 Olive 76 7 Peanut 47 29 Safflower 15 72 Sesame 38 42 Soybean 20 52 (USDA, 1975) 9 Acid

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10 peanut types, ranging as low as 29.7 in the Virginia Runner to 46.7% in the Virginia Bunch. In a survey of 110 genotypes, some assayed over more than one growing season, wide variation in fatty acid composition was observed (Worthington and Hammons, 1971). The genotypes consisted of Virginia, Spanish, and runner market types and plant introductions. Palmitic, oleic, and linoleic were the fatty acids with the most variability. Palmitic acid ranged from 6.7% to 13.7%, and the average of all 110 genotypes was 10%. Oleic acid ranged from 35.8% to 71.4%, and with an average of 45.0%. Linoleic acid ranged from 11.1% to 40.1% with an average of 29.9%. The oleic and linoleic acid contents had a strong negative correlation and the genotype with the highest oleic acid level also had the lowest linoleic content. In the Worthington and Hammons study and the Raheja et al. study, the Spanish varieties consistently showed lower oleic acid and higher linoleic content than the Virginia and runner varieties. Higher peroxide values, indicating less stability, have been previously reported for Spanish varieties compared with runner and Virginia varieties (Picket and Holley, 1951) (Fore et al., 1953). In another study, 82 peanut genotypes were tested for their fatty acid composition (Worthington et al., 1972). The genotypes represented a wide variation in genetic background. The three major fatty acids varied as follows:

PAGE 23

11 palmitic 7.4-12.9; oleic 35.7-68.5; and linoleic 14.1-40.3. Another study of 40 peanut cultivars also included 12 plant introductions representing all four A. hypogaea botanical types and two other Arachis species, Amonticola and nambyguarae (Treadwell et al., 1983). Palmitic acid ranged from 7.5-11.8%; oleic acid ranged from 39.3-56.6%; and linoleic acid ranged from 26.0-38.9%. These values are well within the range recorded throughout the literature. The highest oleic and lowest linoleic values recorded for peanut are 80% oleic and 2% linoleic (Norden et al., 1987). The variant fatty acid levels were found in an experimental breeding line, F435, of Spanish botanical type. The highest oleic acid level previously published was 71.4% and the lowest linoleic acid level was 11.1%. Earlier evaluations of F435 were found to have typical Spanish botanical type values for oleic and linoleic, 50% oleic and 26% linoleic. The oleic and linoleic acid contents of F435 deviated sufficiently from previously established ranges within Arachis to justify a genetic study of the character. Variant fatty acid phenotypes have been identified in other oil seed crops and some have been found to be controlled by major genes. In a mutant soybean [Glycine max (L.) Merr.J line, high linoleic acid was found to be controlled by two alleles at one locus (Wilcox and Cavins, 1985). In flax (Linum usitatissimum L.) two mutant lines were found to have increased linoleic and reduced linolenic

PAGE 24

12 acid in the seed oil. Analysis of progeny from crosses between the mutants and normal parental lines showed that the variation in linoleic and linolenic was controlled by two unlinked genes with additive gene action (Green, 1986). In a high oleic acid sunflower (Helianthus annuus L.) line the phenotype was found to be controlled by two genes, one with partial dominance (Miller et al., 1987). For the high oleic acid character to be expressed one gene must have at least one dominant allele present. When inheritance is simple it is sometimes possible to trace the character to a single protein or enzyme in a biochemical pathway. In the production of plant storage fats and oils, many enzymes are involved. Fat synthesis begins in the plastids, using translocated sugars as the carbon source. The synthesis of fats from carbohydrates proceeds by the esterification of fatty acids onto a glycerol backbone. The glycerol is derived from glycolysis and is formed by the reduction of dihydroxyacetone phosphate (Salisbury and Ross, 1985). The fatty acids are synthesized from molecules of acetyl CoA adding two carbons at a time to the chain. More than 99% of the fatty acids in peanut oil are made of even-numbered carbon chains. These even numbered fatty acid chains are formed through the fatty acid synthase system. Fatty acid synthase catalyzes a series of reactions where one molecule of acetyl-CoA and seven molecules of a three-carbon compound, malonic acid in the

PAGE 25

13 form of its CoA thioester malonyl-CoA, are linked to form palmitic acid (16:0). The reaction evolves seven molecules of carbon dioxide and requires the reducing power of 14 NADPH (nicotinamide adenine dinucleotide phosphate) (Lehninger, 1982). Palmitic acid is formed in plastids, where it is also lengthened by two carbons forming stearic acid (18:0). Stearic acid, still in the plastid, is then desaturated to oleic acid (18:1) with the enzyme stearoyl ACP desaturase. This system is well understood and established up to the formation of oleic acid. The mode of introduction of the second and third double bonds are not so clearly defined. The substrates are not firmly established and the enzyme system appears to be membrane bound (Stumpf, 1989). The most probable mechanism is outlined in Figure 13. One carrier protein and at least three important enzymes that have not been characterized may affect the protein structure of the enzymes or carrier protein, which will also affect the activity of these species. Changes in the activities of the enzymes will affect the formation of the fatty acids and ultimately alter the final ratios of the various fatty acids. Experimental data have shown that the system is also affected by the type of tissue examined, the temperature at which the tissue is grown, the light regime to which the tissue was exposed, and the age of the tissue (Stumpf, 1989).

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NADH Carrier ( oxid) 2-Linoleoyl PC/PE t Carrier (red) + 2-0leoyl PC/PE NADH:Carrier {oxid) Reductase a12 Desaturase 2-Lyso PC/PE + NAO = reduced nicotinamide adenine dinucleotide NADH = oxidized nicotinamide adenine dinucleotide CoA = coenzyme A red = reduced oxid = oxidized CoA Oleoyl transferase Oleoyl CoA PC/PE = phosphotidylcholine/phosphotidylethanolamine Figure 1-3. The currently proposed biochemical pathway for desaturation of oleic acid to linoleic acid in higher plants.

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15 Variation in fatty acid composition has been shown to be related to the maturity of the peanut seeds tested, which corroborates in vitro experimental data. In 1969, Worthington reported varying fatty acid contents of peanuts of four different maturity classes. The maturity classes were measured in weeks from gynophore penetration of the soil. Oleic acid content ranged from 41.2% in the earliest maturity class to 52.1% in the most mature class. A reduction in linoleic acid content also occurred over maturity, ranging from 32.3% in the most immature to 28.9% in the most mature. In another study, a comparison was made between the fatty acid composition of the triacylglycerides versus the free fatty acids over varying maturity classes of 'Florunner' peanut oil (Sanders, 1980b). Some fatty acids, palmitic and oleic, varied over maturity in both triacylglyceride and free fatty acid forms. Linoleic acid was relatively stable over maturity in both triacylglyceride and free fatty acid forms. If the high oleic acid character in peanut is controlled by major genes, the mutant line may be helpful in determining the pathways of fatty acid synthesis. Since it is known that the rate of synthesis of both oleic and linoleic acid varies during seed maturation in peanut, a comparison of rates between a normal peanut line and the mutant (F435 line) may be valuable in determining the

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16 biochemical pathway of oleic acid desaturation to linoleic acid. To date, simply inherited characters of economic value have not been identified in peanut. If the high oleic acid character is controlled by only a few major genes, it could be an important subject for gene isolation and transformation into other peanut cultivars and possibly other oil seed species as well. Preliminary work necessary for molecular transformation would require the development or adaptation of protocol compatible with genus Arachis and ultimately A hypogaea. The objectives of this dissertation research were threefold. The initial objective was to determine the mode of inheritance of the high oleic acid character. The second objective was to determine if the rate of formation of oleic acid or linoleic acid varied in the high oleic acid line in relation to a particular stage of seed development. The third objective was to develop or adapt molecular genetic protocol that could lay the ground work for the gene isolation and molecular transformation of the high oleic acid character.

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CHAPTER II THE INHERITANCE OF HIGH OLEIC ACID IN PEANUT Introduction Fatty acid composition is an important determinant of quality in edible oils. Oil stability and nutritional quality are both dependent on the relative proportions of the saturated and unsaturated fatty acids that constitute the oil. Oxidative rancidity increases with increased levels of polyunsaturated fatty acids. Oxidation of the carbon double bonds of fatty acids produces acids, aldehydes, ketones, and other hydrocarbons that cause odors and flavors commonly associated with rancidity (St. Angelo and Ory, 1973). Therefore, the total amount of unsaturation is inversely proportional to the keeping quality of the oil. Fats with more saturation are less prone to oxidation during storage and processing than polyunsaturates. From a nutritional standpoint, polyunsaturates have been desirable for their role in lowering plasma cholesterol levels. However, a recent study showed that human diets containing oils high in monounsaturates were as effective in lowering serum cholesterol levels as were low-fat diets (Grundy, 1986). It was also demonstrated that beef cattle and swine fed diets high in monounsaturates produced meats with 17

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18 significantly higher levels of unsaturation (St. John et al., 1987). Peanut oil varies in both quantity and relative proportion of fatty acids. Although there are eight fatty acids in peanut found in quantities greater than 1.0%, palmitic (16:0), oleic (18:1), and linoleic (18:2) constitute approximately 90% of the total fatty acid composition (Cobb and Johnson, 1973). Generally, palmitic acid constitutes nearly 10%, and the oleic and linoleic acid proportions together make up 80% of the fatty acid composition in peanut oil (Ahmed and Young, 1982). The variation in composition has been related to maturity, temperature, planting date, location, market grade, and peanut genotype (Bovi, 1982; Harris and James, 1969; Holaday and Pearson, 1974; Knauft et al., 1986; Mozingo et al., 1988; Norden et al., 1987; Young et al., 1972; Young et al., 1974). In 1987, Norden et al. reported a peanut line, F435, with 80% oleic acid and 2% linoleic acid. This line extended the known variability of these two fatty acids, which had been reported to range from 36% to 71% for oleic acid and from 11% to 43% for linoleic acid (Bovi, 1982; Norden et al., 1987; Treadwell et al., 1983). The F435 line is a Spanish botanical type (Ahypogaea ssp. fastigiata var. vulgaris). This botanical type accounts for only 10.8% of the total U.S. peanut acreage. The Virginia botanical type (A. hypogaea ssp. hypogaea var.

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19 hypogaea) is the predominant botanical type grown in the U.S., with over 80% of the total U.S. acreage (Holbrook and Kvien, 1989). Spanish lines are generally lower yielding than Virginia types and are not as well adapted to the principal peanut production regions of the U.S., i.e., the warm, humid Southeast. Besides being a Spanish botanical type, F435 is a breeding line with a pod-splitting characteristic that has made it unsuitable for release as a cultivar. To improve the oil quality of the more widely cultivated botanical types, it would be necessary to transfer this high oleic acid characteristic from the Spanish F435 breeding line to Virginia and runner peanut cultivars and adapted lines. An understanding of the mode of inheritance will allow most efficient transfer of this trait to adapted breeding lines and runner and Virginia market type cultivars. The following study was conducted to elucidate the genetic basis of the high oleic/low linoleic acid character. Materials and Methods In the spring of 1986, seed from the high oleic acid line, F435, were planted in a greenhouse along with seed from F78114, a Virginia market type, and F519-9, a component line of the runner market type cultivar, •sunrunner' (Norden et al., 1985). The F78114 had an oleic acid content of 45.4%, which is lower than the midpoint of the range of peanut (Table 2-1). F519-9 had an oleic acid content of

PAGE 32

20 53.6%, which is near the midpoint of the range of oleic in peanut (Table 2-1). Crosses were made between F435 and F78114 and between F435 and F519-9. In both cases reciprocal crosses were made. Seed from the F 1 generation were planted in the field at the University of Florida Agronomy Farm, near Gainesville, in July 1986. These F 1 plants produced F 2 seed that were harvested in December of the same year. These F 2 seed were analyzed for fatty acid composition. Fatty acid analysis was also performed on all parents used in crossing. Fatty acid determinations were made by first extracting oil from the seeds, esterifying the oil, and using gas chromatography to determine the relative proportions of the various fatty acids. Saponification prior to esterification was omitted since the relative proportions of free fatty acids were found to be the same as relative proportions of total fatty acids. This was determined by comparing fatty acid analysis with and without saponification on four different peanut oil sources, F435, F519-9, F78114, and commercial cold press peanut oil. Saponification was performed for comparison by adding 2 ml of 10% KOH in methanol/water (4:1 v/v) to the reaction vials containing the oil extracts and heating the vials to 80C for 90 minutes. The vials were then cooled and 1 ml of 1.8 M H 2 so 4 added to each. One ml of petroleum ether was added to each vial and vigorously shaken. The vials were allowed to stand

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Table 2-1. Oleic and linoleic acid content of the four peanut breeding lines used in crossing. Fatty Acid % Oleic % Linoleic Genotype Mean Range Std. Err. Mean Range Std. Err. F78114 45.4 43.3-46.4 0.42 34.3 32.6-36.8 0.55 F519-9 55.6 50.9-61.5 1.08 25.9 21.1-30.4 0.99 PI 262090 59.8 52.8-63.9 1.56 22.5 19.3-28.3 0.93 F435 80.1 72.6-82.3 1.01 2.2 1. 2-3. 6 0.22 Based on a 10-seed sample from each line.

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22 for a phase separation, but in some cases centrifugation was necessary. The upper petroleum ether phase was pipetted off, and this procedure was repeated. Prior to saponification and/or esterification, the oil was extracted by cutting approximately 0.1 g slices from the end of the cotyledons of an individual seed and soaking these slices in 2 ml of petroleum ether in a 13Xl00 mm culture tube overnight. Embryo ends of the seeds were saved for later planting to produce the subsequent generations. The petroleum ether was then pipetted into a 5 ml reaction vial. For saponification, the petroleum ether was removed by evaporation, leaving the oil extracted from the seed sample. The oil samples in the reaction vials were then ready for saponification. When saponification was not performed, oil was esterified immediately following extraction. Boron-trifluoride in methanol (BF 3 ) was added directly to the vials containing the extracted oil in petroleum ether (Metcalfe and Schmitz, 1961). This mixture was shaken briefly and then heated to 100c for 3 minutes. After heating, the reaction vials were cooled and 1 ml of deionized H 2 0 added to each of the vials. The vials were shaken vigorously and then allowed to stand for clearing and a phase separation. The upper petroleum ether phase containing the fatty acid methylesters was sampled and a 1 l aliquot injected into a gas chromatograph (GC). The first 1000 samples were run on a Varian 3700 with manual

PAGE 35

23 injection and strip chart recorder. All subsequent determinations were performed on a Hewlett-Packard 3690a with automatic sampler, integrator, and flame ionization detector. Both the injector and detector temperatures were 250C. The oven temperature was programed for an initial temperature setting of 190C for 3 minutes, then increasing at the rate of 3C per minute until reaching a final temperature of 220c. The column was a 2 m glass column packed with 10% cyanosilicone (Supelco SP2330) on 100/120 Chromosorb WAW. The detector, column, and settings were the same for both instruments. The relative proportions of the fatty acids were calculated as the percent of the total area under the recorded peaks. Frequency distributions of the fatty acid phenotypes were recorded. Individuals were arranged by percent oleic acid, in classes of 4% increments. Segregating ratios were tested to determine the goodness-of-fit to proposed genetic ratios using the chi-square test. The crosses F435 X F78114 and F435 X F519-9 were repeated in the summer of 1987 and an additional cross of F435 X PI 262090 was also included. The F 1 seed produced from these crosses were analyzed using the same aforementioned procedure. The embryo ends of these seeds were saved and planted to produce subsequent generations. The F 1 , F 2 , F 3 , and backcross generations were produced in a greenhouse at the University of Florida Agronomy Farm near

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24 Gainesville. Seed of the F 2 generation were analyzed for fatty acid composition with same technique, and the embryo ends were planted in the same greenhouse. The F 3 seed produced were also analyzed for fatty acid composition. Backcrosses were also made between F 1 progeny from the F435 X F78114 cross and each parent, and backcrosses between F 1 progeny of the F435 X F519-9 cross and each of those parents. All seed were analyzed for fatty acid composition using the method previously described. Results and Discussion Saponification Versus Direct Esterification Saponification of oil breaks the ester linkages that bind fatty acids to glycerol. Therefore, GC analysis of methyl ester preparations from saponified oil would represent total fatty acid content. However, if the relative proportions of free fatty acids and fatty acids released by the esterification reagent (BF 3 ) were found to be in the same proportions as total fatty acids, saponification would not be necessary. When fatty acid profiles of four different peanut oil sources saponified versus nonsaponified were compared using at-test, there were no differences in palmitic, stearic, oleic, linoleic, arachidic, nor behenic acid contents between the two procedures (Table 2-2). During esterification with BF 3 , some fatty acids may be dissociated from glycerol. Total

PAGE 37

Table 2-2. A comparison of two methods of fatty acid analysis, saponified versus nonsaponified. Palmitic, stearic, oleic, linoleic, arachidic, and benhenic acid contents are shown from four different oil sources. Also shown are values of tea Le. F435 F519-9 F78114 Commercial oil non non non non Fatty Acid sapon sapon sapon sapon sapon sapon sapon sapon *tcalc Palmitic 6.7% 9.2% 9.3% 10.6% 8.2% 10.1% 10.6% 11. 5% 1.70 Stearic 2.0% 3.2% 2.0% 1.8% 3.7% 2.6% 1.9% 1. 7% 0.30 Oleic 80.8% 79.% 54.2% 53.9% 48.2% 47.6% 47.3% 47.4% 0.04 Linoleic 2.5% 2.9% 26.5% 26.7% 35.8% 35.2% 32.1% 33.4% 0.03 Arachidic 1.1% 2.5% 1.2% 1.0% 0.4% 0.5% 1.0% 0.9% 0.80 Behenic 1.4% 2.5% 1.4% 0.9% 0.3% 0.4% 1.5% 1.0% 0.04 * tcalc compares the means of each fatty acid saponified versus nonsaponified. N Ul

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26 area integrated on the chromatograph is an indicator of sample concentration. If samples were measured approximately equal prior to saponification and/or esterification, then the difference in area integrated between the saponified and nonsaponified samples should be equal to the difference between the total fatty acid content and the free fatty acid content of peanut oil. It has been reported that more than 95.0% of peanut oil is made up of triacylglycerides and less than 0.05% free fatty acid (Sanders, 1980a). The difference in integrated areas on the chromatograph between saponified and nonsaponified is not as great as the difference between percent triacylglycerides and percent free fatty acids (Table 2-3). This difference indicates that some saponification is occurring but that the BF 3 is not strong enough for complete saponification. However, the degree of saponification by BF 3 is apparently sufficient to produce a representative sample of the total fatty acid content in peanut oil. Since saponification was found to be unnecessary to determine the content of the fatty acids of interest in this study, the saponification step was omitted. Crosses with F78114 When the high oleic acid line, F435, was crossed with F78114, all F 1 seed had oleic acid levels similar to the F78114 parent (Table 2-4), regardless of the genotype on which the seed were borne. F 2 seed from this family

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27 Table 2-3. A comparison of total areas integrated on chromatographs of saponified oils versus nonsaponified oils. Four different oil sources are included. Also included is the percent of the total fatty acids measured when saponification is performed that are measured when saponification is not performed. Area Integrated Source Saponified Nonsaponified % Nonsaponified* F435 3,048,100 374,215 12.3% 519-9 3,999,500 374,530 7.3% F78114 3,567,899 289,789 8.1% Commercial oil 4,699,600 604,060 12.9% * calculated by area nonsaponified divided by area saponified, times 100.

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Table 2-4. F 1 progeny from the cross between high (F435) and normal (F519-9), (F78114), and (PI 262090) oleic acid phenotypes. Oleic Acid Classification Phenoty12ic Range Cross Normal High % Oleic % Linoleic F78114 X F435 37 0 38.0-65.1 17.2-40.3 F435 X F78114 30 0 36.7-60.4 25.8-36.7 F519-9 X F435 9 0 44.3-70.5 11.4-36. 7 F435 X F519-9 20 0 42.0-71.4 11. 3-39. 3 PI 262090 X F435 13 0 61. 4-67. 9 14.9-20.7 F435 X PI 262090 31 0 61.2-69.8 11.4-19.2 f\J 00

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29 displayed bimodal distributions (Figure 2-1), and were classified as either normal oleic acid (less than 70%) or high oleic acid (70% or greater). This division between high and normal oleic acid content was established from parental phenotypes (Table 2-1) used in the crosses. There was a well defined break in the phenotypic distributions of the F 2 populations which allowed for definitive grouping of individuals into either high oleic acid or normal oleic acid classes. A test of homogeneity was conducted on all F 2 families and there were no differences among families (Table 2-5). In the F 2 segregating population the proportion of seed in the two categories (Table 2-5) was consistent with a 15:1 ratio, indicating that two recessive genes were responsible for the high oleic acid characteristic. F 1 plants used as both male and female parents in crosses with F78114 produced all normal oleic acid seed in the BC 1 generation (Table 2-6), and the backcross to F435 produced a phenotypic distribution consistent with the expected ratio of 3:1 (normal to high oleic acid seed). F 2 embryo ends of sampled seed were used to generate F 3 families. Three F 3 families (Table 2-7), derived from high oleic acid seed, consisted entirely of the high oleic acid phenotype. F 3 families, derived from normal oleic acid seed, consisted of either all normal oleic acid seed or normal to high oleic acid phenotypes in 15:1 or 3:1 ratios.

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30 Cl) 25 0 :l "'C > 20 "'C C \to15 0 'Cl) .!l 10 E :l z 5 5 0 ~u:JiC~..ca..llQI..Da..llOILDCl..110d.J~~~04.1~~61.J&!sa.AZl..21ill_. __ _.fSi~~!RSa..t21J ,,F.... 'l-1!0 .... ~~Ar .... ~'='-;,. .... .... Ar~-,. Ar 1-J. ':J ,-,. ':J'='-,. ':J~-,. E>~-,. o1-,. 1 '-,. 1'='-,. 1q-J. ,,_g .., J .Jg "',,. 1rE>.... c-:,0.... c-:,Ar.... ':J'6.... 0 '}..... 0 E>.... 10.... 1 Ar.... 1'6 .... Percent Oleic Acid Figure 2-1. Frequency distribution of number of F 2 offspring in phenotypic classes based on oleic acid content. Data has been pooled for all families from the cross of F78114 and F435. w 0

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31 Table 2-5. Segregation data for F 2 progeny from the cross between high (F435) and normal (F78114) oleic acid lines. Oleic Acid Classification Family Cross Normal High xz 15:1 1 F78114 X F435 49 3 0.02 .90-.75 2 F78114 X F435 32 2 0.13 .75-.50 3 F435 X F78114 56 5 0.77 .50-.25 4 F435 X F78114 40 0 2.67 .25-.10 5 F435 X F78114 28 3 0.62 .50-.25 6 F435 X F78114 26 3 0.77 .50-.25 7 F435 X F78114 18 1 0.03 .90-.75 Pooled 249 17 0.01 .95-.90 Homogeneity 5.00 .75-.50

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32 Table 2-6. BC 1 oleic acid phenotypic segregation ratios for two peanut lines (F78114 and F519-9) crossed to a high oleic acid peanut line (F435). Observed Ex:gected Low High ratio Cross Oleic Oleic Low:High p F435 X F78114 BC (F 1 X F78114) 17 0 1:0 BC (F 1 X F78114) 37 0 1:0 BC (F 1 X F435) 11 1 3:1 .2-.s F435 X F519-9 BC (F 1 X F435) 7 4 1:1 .2-.s BC (F 1 X F435) 6 5 1:1 .5-.9

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Table 2-7. Phenotypic segregation of F 3 families from crosses between high and normal (F78114 or F519-9) oleic acid peanut lines. Oleic Acid Com2osition F3 Observed F 3 Expected Cross F2 Normal High Ratio F78114 X F435 High 0 54 all high F78114 X F435 High 0 42 all high F78114 X F435 High 0 40 all high F78114 X F435 Normal 47 3 15:1 F519-9 X F435 High 0 45 all high F519-9 X F435 Normal 20 0 all normal F519-9 X F435 Normal 20 0 all normal F519-9 X F435 Normal 16 0 all normal F519-9 X F435 Normal 20 5 3:1 F519-9 X F435 Normal 20 5 3:1 F519-9 X F435 Normal 35 15 3:1 F519-9 X F435 Normal 39 11 3:1 F519-9 X F435 Normal 36 14 3:1 (F435) w w

PAGE 46

34 Cross with F519-9 F 1 seed from the cross of the 'Sunrunner' component line F519-9 with F435 also showed no high oleic acid types, nor were there any reciprocal-cross differences. F 2 seed from this cross also showed a bimodal distribution (Figure 2-2), with seed containing between 45% and 70% oleic acid classified as normal and those containing between 70% and 85% oleic acid classified as high. Classification ambiguities were resolved by considering the proportion of linoleic acid in the seed. All seed classified as high oleic acid had less than 5% linoleic acid, whereas all seed classified as normal oleic acid had more than 10% linoleic acid. F 2 seed from this cross segregated in a 3:1 ratio (Table 2-8) of normal to high oleic acid level, indicating that a single-recessive-gene difference between F435 and F519-9 was responsible for the high oleic acid, with the homozygous recessive condition required for expression of the high oleic acid character. The embryo-ends of the sampled F 2 generation seed were planted to produce F 3 families. In the families analyzed, the F 3 data were consistent with the single-recessive-gene hypothesis (Table 2-7). High oleic acid seed were expected to be homozygous recessive and would breed true in the subsequent generation. The normal oleic acid seed were expected to be either homozygous dominant or heterozygous and either breed true for normal oleic acid or segregated in

PAGE 47

en C "'O > "'O C '+0 L. Cl> ..c E z 35 30 29 25 20 15 10 5 1 0 0 0 1..1&,;1--.........&,;L&.1~.IIUllll~l..&.lu.,a~&.L,1~~~1,.&;lL,l.ll~;,m.J~ca,..aci:L.,CC:LJCa.Jll~:lCI..ICQ.mJILCIC:1J ':,-,. ~~-,_ 6r "!,-,. 6r 1-t':, ,-,. ':,':,-,. ':,~-,. & "!,-,. &1-,. 1 \-,_ 1 ':,-,. 1 ~-,_ tt,"!J-,. "!JAr,... "!J't>,... t, 'i,... t,&,... ':,0,... ':,Ar,... ':,f>,... 0 'i,... 0 &,... 10,... 1 Ar,... 1'6,... tt,'i,... Percent Oleic Acid Figure 2-2. Frequency distribution of number of F 2 offspring in phenotypic classes based on oleic acid content. Data has been pooled for all families from the cross of F519-9 and F435. w U1

PAGE 48

Table 2-8. Phenotypic segregation of oleic acid content for F 2 progeny from the cross between high (F435) and normal (F519-9) oleic acid peanut lines. Oleic Acid Corngosition Family Cross Normal High xz .E (3:1) 1 F519-9 X F435 65 19 0.25 .75-.50 2 F519-9 X F435 32 8 0.53 .50-.25 3 F519-9 X F435 34 13 0.18 .25-.10 4 F519-9 X F435 28 12 0.48 .50-.25 5 F519-9 X F435 9 4 0.23 .75-.50 6 F435 X F519-9 9 5 0.86 .50-.25 7 F435 X F519-9 30 6 1.33 .25-.10 8 F435 X F519-9 25 5 1.11 .50-.25 Pooled 232 72 4.07 .90-.75 Homogeneity 0.90 .99 36

PAGE 49

a ratio of 3:1, normal oleic acid to high oleic acid content. 37 When F 1 plants from the F519-9 X F435 cross were backcrossed to the F435 parent, offspring fit a 1:1 ratio of high to normal oleic acid (Table 2-6). This is again consistent with a single-gene hypothesis, where a homozygous recessive (F435) is crossed to a heterozygote (F519-9) and result in a phenotypic ratio of 1:1. Cross with PI 262090 F 1 seed from the cross of F435 with the PI 262090 were found to have oleic and linoleic acid contents similar to the normal oleic acid parent (PI 262090) (Table 2-4). All F 2 families from this cross segregated in a 3:1 ratio of normal to high oleic acid phenotypes (Table 2-9) (Figures 23) Summary Simple inheritance of fatty acid variants have been reported in other oilseed crop species. In sunflower, (Helianthus annuus L.) it has been reported that a single partially dominant gene is responsible for a high oleic acid phenotype (Urie, 1985). In soybean [Glycine max (L.) Merr.J, two additive alleles at a single locus were found to control linoleic acid content (Wilcox and Cavins, 1985). Induced mutants in rapeseed (Brassica napus L.) produced high linoleic acid and low linolenic acid oil by the effects of two additive alleles at each of two independent loci

PAGE 50

38 Table 2-9. Segregation data for F 2 progeny from the cross between high (F435) and normal (PI 262090) oleic acid lines. Oleic Acid Com12osition Family Cross Normal High xz ( 3: 1) 1 PI 262090 X F435 19 7 0.05 .90-.75 2 PI 262090 X F435 18 6 0.0 1.00 3 F435 X PI 262090 18 6 o.o 1.00 4 F435 X PI 262090 27 6 0.82 .50-.25 5 F435 X PI 262090 23 7 0.04 .90-.75 Pooled 105 32 0.20 .75-.50 Homogeneity 0.71 .50-.25

PAGE 51

Cl) 0 :::, -0 > -0 C 0 L. Q) ..0 E :::, z 20 19 15 10 5 01,.Jg~-ex~..DC101-~~IQQa...1~:lll....ll1001L..M~1..1i0.oa....Dir:~...D0.o...~::.a....ooa..J~~~._.~u ,-,. ~~-,. ~':J-,. ~1-I~~-,. o ,-,. o~-,. o':J-,. 01-Io~-,. 1 '-,. 1~-,. 1':J-,. 11-I1~-,. ,-,. ':Jo" ':J'J:' ':J,_,, ':J 0 " ':Jto" oo" o'l:' 01c" o 0 " o"" 10" 1'J:' 11c" 1" 1to" too" Percent Oleic Acid Figure 2-3. Frequency distribution of number of F 2 offspring in phenotypic classes based on oleic acid content. Data has been pooled for all families from the cross of PI 262090 and F435. l,J \D

PAGE 52

40 (Brunklaus-Jung and Robbelen, 1987). Results presented here indicated major genes control the oleic and linoleic acid content in peanut. Together, the F 1 , F 2 , F 3 , and BC 1 generation data from all three peanut crosses reported, support the hypothesis that the high oleic acid character is controlled by two recessive genes. While the combination of the two genes has not been reported previously, the current study showed one recessive gene to be present in two separate lines (F519-9 and PI 262090). This information about the simple inheritance of high oleic acid in peanut will facilitate genetic improvement of the nutritional quality and storage stability of peanut oil. Transfer of this high oleic acid characteristic to desirable lines and cultivars may be accomplished by traditional backcross breeding. Also, with the development of protocol appropriate to peanut, it may be possible to move this character within Arachis and to other species through molecular genetic methods.

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CHAPTER III VARIATION IN FATTY ACID COMPOSITION IN DEVELOPING SEED OF Arachis hypogaea L. Introduction A number of studies have been conducted to assess changes in fatty acid composition of developing peanut seed (Holaday and Pearson, 1974; Sanders, 1980a; Sanders, 1980b; Sanders et al., 1982; Worthington, 1969; Young et al., 1968). In these studies, seed from several peanut cultivars commonly cultivated in the southeastern U. s. were assayed for fatty acid and lipid class composition over the course of seed development. The general conclusion of past studies and of principal interest in this study is that the oleic acid content of the oil increased during seed development. It was also noted that palmitic acid decreases as seed matures, and that the linoleic acid composition was relatively stable, though some researchers report a slight decline (Sanders et al., 1982; Young et al., 1968). The high level of oleic acid in peanut line F435 was established in Chapter II to be controlled by two recessive genes. Those two genes are assumed to produce a pronounced alteration of one or more enzymes involved in fatty acid synthesis. Since previous work has shown that oleic acid varies over the course of development in common cultivars, 41

PAGE 54

42 it was thought that there may be additional variation in oleic acid production or rate of production in the developing seeds of line F435. If a unique pattern of oleic and/or linoleic acid production was observed in the F435 line as compared to normal lines, this information could be of considerable value in understanding the biochemical control of linoleic acid synthesis. This information could also be important in the molecular isolation of the gene through further understanding of the fatty acid synthase system. An impediment to developmental studies in peanut has been the lack of a uniform method to determine physiological maturity. Days from pegging is unreliable since the rate of maturation is affected by the location of the peg on the plant. Proposed methods for determination of maturity have included visual examination of the color and structural characteristics of the pod mesocarp (Williams and Drexler, 1981), visual classification of reproductive growth stages (Boote, 1982), dry matter deposition, and level of free arginine in the seed (Tai and Young, 1977). Two of these methods were employed in the current study, the non destructive method by Williams and Drexler and dry matter deposition.

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43 Materials and Methods On February 3, 1989, seeds of three peanut lines were planted in pots in a greenhouse. The lines planted were F78114, F519-9, and F435. F78114 is low in oleic acid; F519-9 is moderate in oleic acid; and F435 is high is oleic acid (Table 3-1). Five seed of each line were planted in each of four pots. One week after emergence, plants were thinned to one plant per pot. After 122 days, plants were removed from the pots and ten pods from each plant were sampled. Due to the indeterminate nature of peanut, a sample of ten pods was considered adequate to represent the greatest variation in maturity possible for each individual plant. Maturity was evaluated using the non-destructive method by Williams and Drexler (1981). This rating system consists of seven developmental stages. Within each stage, there are four distinct subclasses. For the purposes of this study the developmental stages and subclasses were numbered consecutively from 1 to 28 with 1 corresponding to stage 1 subclass g and 28 corresponding to stage 7 subclass g. A total of forty seed per genotype, ten seed per plant, was sampled for analysis. The maturity rating was recorded and the seed immediately sampled for dry matter. In each pod, the seed proximal to the peg was used as the sample

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Table 3-1. Oleic and linoleic acid content of three peanut breeding lines. Fatty Acid % Oleic % Linoleic Genotype Mean Range Std. Err. Mean Range Std. Err. F78114 45.4 43.3-46.4 0.42 34.3 32.6-36.8 0.55 F519-9 55.6 50. 9-61. 5 1.08 25.9 21.1-30.4 0.99 F435 80.l 72.6-82.3 1.01 2.2 3. 6-1. 2 0.22 Based on a 10-seed sample from each line.

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45 seed. These seed were weighed and placed in a temperature controlled oven at 110c. After at least 17 hours the seeds were removed and allowed to cool in a desiccator, then weighed again. The percent dry matter was calculated from these weights. After dry matter was determined, the dried whole seeds were chopped and soaked overnight in approximately 2 ml of petroleum ether. The petroleum ether was then pipetted into a 5 ml reaction vial. The petroleum ether was removed by evaporation, leaving the oil extracted from the seed sample. The oil samples in the reaction vials were then ready for saponification. To the reaction vials containing the oil extracts, 2 ml of 10% KOH in methanol/water (4:1 v/v) was added and the vials heated in a water bath to ao•c for 90 minutes. The vials were then cooled and 1 ml of 1.8 H H 2 So 4 added to each. One ml of petroleum ether was added to each vial and vigorously shaken. The vials were allowed to stand for a phase separation but in some cases centrifugation was necessary. The upper petroleum ether phase was pipetted off and this extraction procedure repeated. The free fatty acids in the 2 ml sample of petroleum ether from each sample were then esterified as previously described (Chapter II) using boron trifluoride in methanol as the esterification reagent. Samples of the fatty acid methyl esters in petroleum ether were then injected into a Hewlett-Packard model 5890a gas chromatograph, also as

PAGE 58

46 previously described (Chapter II). Fatty acid percentages were calculated based on percent area by a Hewlett-Packard 3392 integrator. Dry matter, palmitic acid, oleic acid, and linoleic acid percentages were collected and recorded along with maturity ratings. Linear and non-linear regression analyses were performed on the data and the corresponding correlation coefficients were calculated. Correlation comparisons were made between maturity rating and dry matter accumulation for each genotype. Correlation comparisons for each genotype were also made between dry matter and percent oleic acid, dry matter and percent palmitic acid, and dry matter and percent linoleic acid. Results and Discussion The method of maturity rating by visual examination of pod mesocarp was initially performed to get a quick estimate of maturity prior to chemical analysis. Dry matter deposition was expected to be the preferred method of measuring maturity because of its objectivity over the more subjective visual rating. The two methods had not been previously compared. Non-linear regression analysis showed that a logarithmic function most accurately described the correlation between dry matter and maturity rating for all genotypes. The highest R 2 values for dry matter versus maturity rating were found in the analysis of the F519-9 seeds (Table 3-2) (Figure 3-1). The highest R 2 value for the

PAGE 59

Table 3-2. R 2 values of individual plants and for a composite of all plants for each genotype for maturity versus percent dry matter. Genotype Plant Rz F519-9 1 0.87 2 0.84 3 0.46 4 0.92 1-4 0.64 F435 1 0.47 2 0.47 3 0.69 4 0.37 1-4 0.43 F78114 1 0.59 2 0.54 3 0.59 4 0.55 1-4 0.49 47

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% Dry Matter :: L ... .. ........................... l 60 ........ . D .... .. ~ i:t .... . .. . . . .............. !?. .. ................ . ................. . ............ l 50 .. ..... ............................ .......................................... ] 40 ~.... . ...................................................................... ........................................ JO r .................................................................................. :: ............ : .................... .................... ; ................... ................... .................. 0 5 10 15 20 25 30 Maturity Rating X Dry Matter a . R2 0.64 Y 34.1 + 10.5InX Figure 3-1. Regression plot of the percent dry matter versus maturity classification of peanut seed sampled from all four plants of line F519-9.

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49 F519-9 was 0.92 for plant 4. The overall R 2 for F519-9 was 0.64. This value was the highest of the three genotypes. The original work on the maturity rating system used in this study was performed on 'Florunner'. Since F519-9 is closely related to 'Florunner', a different botanical type from F435, and a different market type from F78114, it may be more likely to conform to the 'Florunner' maturity classification. Therefore, the highest R 2 values might be expected for F519-9. The value of R 2 for dry matter versus maturity rating on the F78114 Virginia market type was lower than for the F519-9 runner line (Table 3-3, Figure 3-2). The F435 R 2 value was slightly lower than the F78114 R 2 values (Figure 3-3). Dry matter has been concluded to indicate level of maturity in peanut (Tai and Young, 1977). However, in the same study, it was also shown that the rate of accumulation and total dry matter at maturity may vary among genotypes. Nevertheless, dry matter appears to be a more definitive measure of maturity than the color and morphology of the mesocarp. Maturity based on color and morphological characteristics can be subjective, besides being genotype dependent. Although there was a correlation between percentage dry matter and maturity rating, dry matter was used as the independent variable in the regression analysis of the fatty acids, palmitic, oleic, and linoleic acids. The maturity rating was used only as the independent

PAGE 62

50 variable in regressions on percentage of oleic acid for the three genotypes. By comparison, the R 2 values associated with maturity rating were found to be lower than the R 2 values of regressions where dry matter was the independent variable (Table 3-3, Figures 3-4 through 3-9). The relative oleic acid percentage increased in all genotypes as dry matter increased from 10% to 50% (Table 34). In line F78114, the oleic acid content increased from 36.2% to 44.1%; in line F519-9, the oleic acid content increased from 25.6% to 53.3%; and in line F435, the oleic acid content increased from 73.7% to 76.7%. The R 2 value for F519-9 was the highest of the three genotypes at 0.62. The R 2 for F78114 was 0.24 and for F435 was only 0.13. Though the R 2 values are low, examination of the figures reveals that there was only one sample of F435 that had less than 40% dry matter and even that sample was well within the range of the oleic acid distribution for that genotype. In all genotypes, however, the samples under 40% dry matter had the lowest oleic acid contents. Previous studies have shown that oleic acid increases with maturity (Sanders, 1980b). If more immature seeds had been sampled, under 40% dry matter, with correspondingly lower oleic acid contents, more of a trend may have been established and R 2 values may have been higher. It may be necessary to sample more seeds to show this in all genotypes.

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51 Table 3-3. R 2 values for regressions of the percent oleic acid with maturity rating as the independent variable compared with percent dry matter as the independent variable for three genotypes, F519-9, F435, and F78114. Genotype F519-9 F435 F78114 Maturity 0.30 0.12 0.21 Dry Matter 0.62 0.13 0.24

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% Dry Matter 80 r _ 70 L ................................... .. .. g-.... ht ............................... .. l I 8 so 0 -~ ... ... -... 0 so .. .. .o .. a ............................................................... ................... . 40 ......... ..... ............................................................................. . Jo 20 r _______ 1 ________________________ _, 0 5 R 2 0.-43 Y 39.74 + 9.71nX 10 15 Maturity Rating X Ory Matter B 20 25 Figure 3-2. Regression plot of the percent dry matter versus maturity classification of peanut seed sampled from all four plants of line F435 U1 IV

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% Dry Matter 70 ,------------------------------60 50 8 .. _, •:.:.:• •;;••~~~••~•...,.._..!ff':': -:':' ':': ':: ::-. B a c c c -~ c a ........... g . . . . . ......... C C C C 40 C 30 ......•. .... Q .. ............. .. .................... .. ...................... ............... .... 20 ............ ...................................................................... ........................................... . 10 ______________________ ......_ _____________ __, 0 5 10 15 20 25 Maturity Rating R 20.41 X Ory Matter a V 21.74 + 12.4.X Figure 3-3. Regression plot of the percent dry matter versus maturity classification of peanut seed sampled from all four plants of line F78114. U1 w

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% Oleic Acid 70 60 .. ...................... . CCC C C 8 C C 50 CB C c 0 .................. l;l ............................................................................................................................................ . C 40 ........................................................................................................................................................................................................................ C 30 .................................... .................................... . C 20 0 5 10 15 20 25 30 Maturity Rating " Olelc Acld a R 1 0.30 Y '42.0 + 0.11lnX Figure 3-4. Regression plot of the percent oleic acid versus maturity classification of peanut seed sampled from all four plants of line F519-9.

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% Oleic Acid 82 80 ........................................................................................... 1:J .............................................................................................................................. . C C C C C a 78 ............ _g .. .. .o .... ........ . C a 76 Cl C ......... .. . ........•.•.. ... . c ................... 5 ....... a ................................................... . C 74 C C 72 ~----+-----.J.-----...J-----....L.----....l 0 5 10 15 20 25 Maturity Rating X Oleic Acid a R 1 0.12 Y 74.95 + 1.0llnX Figure 3-5. Regression plot of the percent oleic acid versus maturity classification of peanut seed sampled from all four plants of line F435. Ul Ul

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% Oleic Acid 50 ,------------------------------C C C C C 45 ...a . . 40 35 C C C C CC C D ....... .. ............................. . Cl C CC C .............................................................................................................................. ,_ ................ . C 30 a......-----'------...J------.L--------1------l 0 5 10 15 20 25 Maturity Rating X Olelc Acid B Figure 3-6. Regression plot of the percent oleic acid versus maturity classification of peanut seed sampled from all four plants of line F78114. 01 CTI

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% Oleic Acid :: ~----------------------------------oo-C C C C C C _____ .. ~r,-C so .. ...................... 0 ...... ....... . ............... . .................... . C 40 ..................................... ' .............................................................. . C 30 ......................................................................................... , ................................... . C 20 .._ ___ .._ ___ ........ ___ _._ ___ --1. ___ -J'--,---J.-----l 10 20 30 40 50 60 70 80 % Dry Matter X Oleic Acid R 1 0.12 B Y 8.32 + 0.411nX Figure 3-7. Regression plot of the percent oleic acid versus the percent dry matter of peanut seed sampled from all four plants of line F519-9. U1 ...J

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% Oleic Acid 82 ------------80 ................................................................................................................................................... ,. ........................ .. a a a 'il 78 a 76 a a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . ... . . .... . ................... a ... '=t:i ........... c .... -EJ a 74 .................................................................................................................................................. a a a a 72 -------------------------------20 30 40 50 60 70 80 % Dry Matter " Olelc Acid B R 2 0.13 Y 61.l + J.9lnX Figure 3-8. Regression plot of the percent oleic acid versus the percent dry matter of peanut seed sampled from all four plants of line F435. Ul (X)

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% Oleic Acid 50 .----------------------------a C a 45 a a ........................ '05 ... Q .. 40 a C C C cC ..................................... :a~ ....................................... . C a C 35 .................................................................................................................................... a 30 '---------'------.L.-------L-----.L-----_J 20 30 R 1 0.24 Y 11.3 + 0.22X 1.11 40 50 % Dry Matter X Olelc Acid B 60 70 Figure 3-9. Regression plot of the percent oleic acid versus the percent dry matter of peanut seed sampled from all four plants of line F78114. lJ1 1..0

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60 Table 3-4. The percent oleic acid and standard errors for high, moderate, and low oleic acid peanut genotypes sampled at various stages of dry matter deposition. Percent Oleic Percent F78114 Dry Matter Mean *SE 10-29 36.2 30-39 36.8 1.50 40-49 44.1 1.04 50-59 42.7 0.49 60-69 70-79 * standard error of the mean. 1 Insufficient data. Acid and Standard Error GenotyQes F519-9 F435 Mean SE Mean SE 25.6 45.9 9.64 73.3 53.3 1.49 76.7 0.90 56.5 2.70 77.5 0.51 55.3 0.37 77.5 0.40 77.0 0.96

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61 The proportion of palmitic acid was found to be unchanged over seed development in the F519-9 line {Figure 3-10). However, there were only three seeds sampled that had less than 40% dry matter. Both the F435 and F78114 showed a decline in percent palmitic acid as dry matter increased (Table 3-5). The greatest change in palmitic acid content occurred before dry matter deposition had reached 50%. In line F435, 50% dry matter corresponded to a maturity rating of less than 5 and in the F78114 line less than 10. These maturity ratings correspond to very immature stages of development. The seeds sampled were not only high in moisture but small in size. The oil sample extracted was estimated to be near the minimum limit of the analytical methodology. However, the greatest changes in oil composition appear to be in these earliest developmental stages. A more accurate description of the rate of specific fatty acid deposition may be obtained from sampling seed only in maturity classes under rating ten. Linoleic acid percentages declined slightly from 5.9% to 3.8% during the accumulation of dry matter in the F435 line {Table 3-6 and Figure 3-11). In the F519-9, there may have been a slight increase in linoleic acid content, but no change was indicated in the F78114 line {Figures 3-12 and 3-13). A previous study using 'Florunner' indicated no change in linoleic acid percentage during development {Sanders, 1980b).

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% Palmitic Acid 12 11 ........................................................................................................................................ ........... Cl .................................................................. . C 10 ....................................................................... .. .. C C 9 C C ........... ...................................................... H ... a C C 8 ............................ c ..................... . 7 10 R 1 0.01 20 Y 1.71 0.00IX 30 C 40 50 60 70 80 % Dry Matter X Palmltlc Acid a Figure 3-10. Regression plot of the percent palmitic acid versus the percent dry matter of peanut seed sampled from all four plants of line F519-9.

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63 Table 3-5. The percent palmitic acid and standard errors for high, moderate, and low oleic acid peanut genotypes sampled at various stages of dry matter deposition. Percent Palmitic Acid and Standard Er;ror Genoty:ges Percent F78114 F519-9 F435 Dry Matter Mean *SE Mean SE Mean SE 10-29 15.7 _, 8.9 30-39 14.2 0.56 10.8 1.59 9.0 40-49 11.7 0.35 9.8 0.18 7.8 0.22 50-59 12.2 0.13 9.3 0.21 7.9 0.17 60-69 9.2 0.13 7.6 0.16 70-79 7.7 0.19 * Standard error of the mean. , Insufficient data.

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64 Table 3-6. The percent linoleic acid and standard errors for high, moderate, and low oleic acid peanut genotypes sampled at various stages of dry matter deposition. Percent Linoleic Acid and Standard Error Genoty12es Percent F78114 F519-9 F435 Dry Matter Mean *SE Mean SE Mean SE 10-29 37.8 _, 10.7 30-39 37.1 2.07 30.3 5.65 5.9 40-49 34.2 0.94 26.7 1.39 4.5 0.80 50-59 36.2 0.40 25.5 0.55 4.4 0.31 60-69 25.1 0.46 3.3 0.21 70-79 3.8 0.42 * Standard error of the mean. 1 Insufficient data.

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% Linoleic Acid 8 C 7 ...................................... ..................... C C 6 .. ...................................................................................................... . a a a 5 a a 4 ................................ .................... a a 3 a O a a ...... .. .. ...... .. .. .... ... .. .... .... .. .... .. .. ...... .... u 9 .. .. 0 C rfl lg 2 20 R 2 0.23 Y 7.1 0.07)( 30 40 50 60 % Dry Matter X Linolelc Acid a Figure 3-11. Regression plot of percent linoleic acid versus of line F435. of peanut seed sampled from all four plants 70 percent 80 dry matter O'I Ul

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% Linoleic Acid 40 35 ...................................... Q ............................................................................................... . 30 .................................................... .. e....... c ............................................................ . C ts C 25 C .................................................................. ...... . C C CD 20 15 ........................... .................................................. . 10 .................. c ................................................................................................................................................................................ , ............... . 5 10 R 2 0.11. Y 7.IX 20 30 40 50 60 % Dry Matter X Llnolelc Acid B Figure 3-12. Regression plot of percent linoleic acid versus of peanut seed sampled from all four plants of line F519-9. 70 80 percent dry matter

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% Linoleic Acid 42 .------------------------------a 40 ....................................................................... Cl .............................................................................................. . 38 ............. c ........................................................ a .......... .. ................................. . a a a a 36 _ ............................................................................................................................................................... -............ .. ,A ,_ a u o .. a c 34 .......................... c ......................... ;; .... : ........... 1:1 ... --i .. ;;i .. a---............................ .. 32 ...... .............. ........... ................ ..... ......... ...... .. ......... .. .. .... .. ......... ..... ........ ..... .. a 30 ...... .. .. .. ......... ..... ......... .. .......... .............. .. .... .............. .............................. . !" a 28 I I I I 20 30 40 50 60 70 % Dry Matter " Lfnoleic Acid a R 2 0.0008 Y 35.32 + 0.009X Figure 3-13. Regression plot of percent linoleic acid versus percent dry matter of peanut seed sampled from all four plants of line F78114. ' -..J

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68 One objective of this study was to identify a stage of development where a proportionate increase in the percentage of oleic acid, relative to other fatty acids, may indicate variation in enzyme activity. A change in the relative percentage of fatty acids during seed development may also indicate separate systems operating at different times. Based on dry matter, the difference in oleic acid content from the most immature to most mature was from 73.3% to 77.9%. This amount of variation is minimal and is within the range of normal variation for the line (Table 3-1). The amount of variation in linoleic acid due to maturity was also found to be minimal over the stages of development sampled. These results indicate that there is limited, if any, differential enzyme activity during the development period after 30% dry matter deposition. Since the greatest variation in the fatty acid composition occurs in the earliest stages of development, less than 30% dry matter deposition, it may be valuable to sample more of these immature seeds and more closely examine these developmental stages. If, however, the high oleic acid character is a result of reduced activity of the enzymes in the oleic acid desaturase system, and the fatty acid composition of the oil is relatively stable over development, then the stage of development that would yield the most active transcription of the desaturase enzymes would simply be the stage at which the total oil content is most rapidly increasing. In

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69 'Florunner', total lipid content has been shown to increase most rapidly in the earliest stages of development, stages 1-5 (Sanders, 1980a). However, since rate of dry matter deposition has also been shown to be genotype specific, further investigation would be appropriate to examine the rate of oil deposition in F435 to find the developmental stage where genes for fat synthesis are most active.

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CHAPTER IV RESTRICTION FRAGMENT LENGTH POLYMORPHISM IN THE GENUS ARACHIS Introduction In the development of improved cultivars, genetic markers can be valuable tools for the plant breeder (Helentjaris, 1989). Markers can be used for determining incidence of natural outcrossing, identifying genetic linkages, construction of genome maps, determining degree of relatedness, and differentiating selfs and crosses. In recent years, a new class of genetic markers has been revealed with the use of restriction endonucleases. These markers are referred to as restriction fragment length polymorphisms (RFLP). RFLPs have several advantages over morphological markers. In many crops they are more numerous than morphological markers (Beckmann, 1983). There is also a lack of dominance in RFLP markers. There are no multiallelic forms in RFLP markers nor pleiotropic affects on economically important traits. RFLP markers also have potential in mapping quantitative traits, screening genetic resources for important quantitative traits, determining the relationship between quantitative trait loci and "Mendelian" 70

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genetic loci, isolation of causative genes, varietal identification, and determining ancestry and taxonomic relationships (Helentjaris, 1989). 71 RFLP clone sets and linkage maps are currently available in maize (Zea mays L.), tomatoes (Lycopersicon esculentum Mill.), Brassica spp., wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), lettuce (Lactuca sativa L.), soybeans [Glycine max (L.) Merr.J, and rice (Oryza sativa L.). The establishment of protocol specific to peanut is necessary to begin the development of the RFLP clone sets and linkage maps. It has been noted that there are substantial RFLP marker differences between species and genera. Considerable information has been obtained on maize and Brassica. However, self-pollinated species, such as tomato, wheat, and soybean, have not yielded much polymorphism among cultivars and mapping has been difficult (Apuya et al., 1988; Keim et al., 1989; Helentjaris et al., 1986). Peanut is also self-pollinated, and like soybean, it is very uniform with few morphological markers. There are also few isozyme markers in peanut (Cherry and Ory, 1972; Thomas and Neucere, 1974). To date, no work has been published on RFLPs in peanut, (Arachis spp.). With an economically important trait, such as the high oleic acid character in peanut, there can be significant advantages to the development of RFLP markers. Varietal identification can be important, especially since a U. s.

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72 patent application has been filed for the the high oleic acid trait. The isolation of DNA fragments unique to the high oleic acid line may lead to the molecular characterization of the gene. The identification of linkage between the simply inherited high oleic acid character and quantitatively inherited characters could also benefit breeders in the development of improved cultivars. Initial steps in development of RFLP in peanut include: the isolation of purified nuclear DNA; the construction of a genomic DNA library; the isolation of suitable random genomic DNA clones for use as labeled probes; and the hybridization of labeled probes to Southern blots to identify polymorphism. These initial steps were the objectives of this study. All of these steps are described herein, with the exception of the genomic DNA library which was constructed by Dr. M. K. U. Chowdhury. This DNA library was constructed from genomic DNA extracted from the high oleic acid peanut line, F435. The F435 DNA was restriction digested with PstI and cloned with vector pUC19. Clones derived from this library were used as probes in screening for RFLP among the Arachis species and genotypes. Materials and Methods DNA was isolated from four lines of Ahypogaea: line F435, the high oleic acid line; line F519-9, a 'Sunrunner' component line; line F78114, a high yielding Virginia botanical type; and PI 262090, a Virginia botanical type

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73 plant introduction. In addition, DNA was isolated from four species of perennial peanut: Arachis (not speciated); Aglabrata; Apintoi; and Arepens. Two methods of DNA isolation were employed and compared. One was a modification of the method used by Saghai-Mahoof et al. (1984) using a buffer of alkyltrimethyl-ammonium bromide (CTAB extraction). The other was a modification of the potassium acetate precipitation method of Dellaporta et al. (1983). DNA Extraction Extraction 1 (CTAB) Young mature leaf tissue was collected from the selected peanut lines and species. After collection it was immediately frozen in liquid nitrogen and stored at -1o•c. The tissue was removed from the -70C storage as needed. Prior to extraction the tissue was ground under liquid nitrogen to a fine powder and again stored at -70C until needed. Total cellular DNA was isolated from the powdered leaf tissue by a modified version of Saghai-Maroof et al. (1984). To approximately 500 mg of each ground tissue was added seven ml of CTAB extraction buffer [50 mM Tris (pH 8.0), 0.7 M NaCl, 10 mM EDTA, 1% hexadecyltrimethylammonium bromide (CTAB), 0.1% 2-mercaptoethanol (BME)] . The tissue and buffer was mixed vigorously to a homogenous suspension, then incubated at 65C for 90 minutes. During incubation, tubes

PAGE 86

74 were mixed by inversion every fifteen minutes. After incubation, tubes were air cooled for five minutes. Then 4.5 ml of chloroform/isoamyl alcohol (24:1) was added and the tubes mixed by inversion for five minutes. Tubes were then centrifuged at room temperature for 10 minutes at 2500 rpm. After spinning, the upper aqueous layer was pipetted off into new tubes, and extracted with equal volume of the chloroform/isoamyl alcohol (24:1). Again, tubes were mixed by inversion for five minutes then centrifuged for 10 minutes, and the supernatant pipetted off into new tubes. To these tubes were added 50 l of 10 mg/ml RNase A (Promega Inc.) in 10 mM Tris-HCl (pH 7.5) and 15 mM NaCl. The tubes were then mixed by inversion for five minutes and incubated at room temperature for 30 minutes. After incubation, DNA was precipitated by adding equal volume of isopropanol to the tube and mixing gently by inversion. Precipitated DNA was removed with a wire hook and rinsed first with 3-4 ml of 0.2 M NaOAc in 76% ethanol. The precipitate remained suspended in the ethanol for 20 minutes. The precipitate was then rinsed with 10 mM NH 4 0Ac in 76% ethanol and transferred to a 5 ml Eppendorf tube containing 1.0 ml TE [10 mM Tris and 1 mM ethylenediaminetetraacetic acid (EDTA), pH 8.0]. Quantity and quality was determined by measuring absorbance at 260 nm and 280 nm. DNA quality was further confirmed by agarose gel electrophoresis. DNA samples from each of the lines and species were diluted to uniform

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75 concentrations. Restriction endonuclease digestions were made using DNA and 30 units of EcoRI restriction enzyme according to the manufacturer's recommendations. Three l of RNase mix were also added and the tubes incubated at 37C for five hours. Two l of loading buffer were added and each digestion loaded onto an agarose gel. A lambda HindIII-digested marker was also included in each gel as a reference for measuring fragment sizes. The gel was run for fifteen hours at 22 volts and 65 milliamps. It was then rinsed with distilled water, stained with 500 l of ethidium bromide, and photographed under 300 nm wavelength ultraviolet light. The photographs were then examined to evaluate the quality and the concentration of the DNA extracts. Extraction 2 (potassium acetate) The eight ground frozen tissue samples used in the extraction 1 method were weighed to the same approximate quantities (500 mg) and placed into eight separate 30 ml Oak Ridge tubes. To each tube was added 15 ml of extraction buffer [50 mM EDTA (pH 8.0), 100 mM Tris (pH 8.0), 500 mM NaCl, 10 mM BME] and 1.0 ml of 20% sodium dodecyl sulfate (SOS). The contents of the tubes were then mixed thoroughly and incubated in water bath at 65C for ten min. The tubes were then cooled and 5.0 ml of 5 M potassium acetate were added to each. The contents of the tubes were then mixed vigorously followed by incubation at oc for 20 minutes.

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76 After incubation, the tubes were centrifuged in a refrigerated centrifuge at 25,000 X g for 20 min. The supernatant from each tube was poured through Miracloth filter (Calbiochem) into clean 30 ml tubes, and the DNA precipitated by adding equal volume of isopropanol. The contents of the tubes were mixed gently, incubating at -20c for 30 min. The precipitated DNA was pelleted by centrifugation at 20,000 X g for 15 minutes. The supernatant was gently poured off and the pellet dried by inverting the tube over a paper towel for 30 min. The DNA pellets were then removed from the Oak Ridge tubes and placed into Eppendorf tubes with 700 l of DNA buffer, TE. After the pellets were dissolved, the tubes were spun in a microfuge for 10 minutes to remove insoluble debris. The supernatants were then transferred to new Eppendorf tubes and purified with a phenol/chloroform extraction. An equal volume of phenol was added to each tube and mixed gently by inversion. The upper buffer phase was pipetted off into clean Eppendorf tubes and equal volumes of phenol/chloroform (1:1) added and gently mixed. The upper buffer phase was pipetted off and mixed with an equal volume of chloroform. These upper buffer phases were then pipetted off into clean Eppendorf tubes to each of which was also added 75 l of 3M sodium acetate and 500 l of isopropanol. After mixing, the DNA was pelleted by microfuge spinning for 10 seconds. The supernatant was discarded and the pellets washed with 80%

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77 ethanol. The pellets were redissolved in 400 l of DNA buffer TE. Quality and quantities of the DNA extracts were determined as in the extraction 1 procedure. The extraction method 1 was repeated using tissue samples collected from the same species and genotypes. For this extraction, the samples collected were immature not fully expanded leaf tissue plucked from stem apices. For the first extraction, leaves were young but fully mature. Southern Blotting Samples of DNA extracted from the four genotypes of~ hypogaea and the four Arachis species that had been determined to be of acceptable quality were digested with EcoRl and run out on a gel as previously described. A lambda marker was also included on the gel. Gels were stained and photographed, also as previously described. The blotting procedure used was adapted from E. M. Southern (1975). After staining and photographing, gels were treated for 10 min. with a 0.25 M solution of HCl. The gels were then rinsed twice and soaked with constant stirring for 45 minutes in a denaturing solution of 1.5 M NaCl and 0.5 M NaOH. The gels were then neutralized by soaking 45 minutes in 1 M Tris with 1.5 M NaCl (pH 8.0), also with constant stirring. DNA was transferred from the gel to Hybond N blotting membrane (Amersham Corp.) using the capillary method described by Maniatis et al. (1982) with 3X SSC (lX SSC= 0.15 M NaCl and 0.015 M sodium citrate). This

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blotting structure was then allowed to stand for 12-24 hours. The filter was then removed from the stack and soaked in 3X SSC for 5 minutes at room temperature. Next, the filter was wrapped in a clear plastic wrap and the DNA side of the filter exposed to ultraviolet light for 6 minutes. The blot was then air dried and stored in a plastic bag at 4C until needed. Probe Preparation 78 Plasmid DNA was isolated by a method adapted from Birnboim and Doly (1979). Inocula from individual library colonies were placed into tubes containing 5 mls of LB broth (10 g Bacto-typtone (Difeo), 5 g yeast extract (Difeo), and 5 g NaCl in 1 liter of water with pH adjusted to 7.2]. The LB broth also contained 0.2% maltose and 0.1 g ampicillin. The genomic DNA used to construct the peanut library was isolated from the high oleic acid peanut line F435. It was digested and cloned into the PstI site of pUC19. The cultures in broth were then transferred to 10 ml centrifuge tubes and centrifuged in a table-top centrifuge for seven minutes. The supernatants were discarded and the pellets resuspended in 800 l of cold STET buffer (80 g sucrose, Triton x-100, 200 ml of 0.25 M EDTA, 50 ml of 1 M Tris-HCl, and deionized H 2 O to a total of 1 L with pH adjusted to 8.0) in 1.5 ml Eppendorf tubes. Each tube then received 60 l of 10 mg/ml lysozyme and was placed in boiling water for two minutes. The tubes were then spun in

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79 a microfuge for 20 minutes. The gelatinous pellets were removed with toothpicks and discarded. Supernatants were purified with phenol/chloroform extraction and digested with RNase A. The plasmid DNA was then precipitated, dissolved in 100 l TE, and stored at -20c as described in the plant DNA isolation above. Clones were evaluated for insert size by digesting 2 g plasmid DNA with 8 units PstI, then electrophoresing and staining as described above. Clones that could be isolated from the vector were selected to be used as probes. Isolation of inserts was done by PstI-digesting 40 l of plasmid DNA as previously described. The separation was by electrophoresis and gels were stained and examined under ultraviolet light to determine the location of the inserts on the gel. Incisions were made in the gel 1-2 mm to the advance of the insert. Pieces of NA45 membrane (Schleicher and Schuell, Inc., Keene, NH), approximately 5 X 25 mm in size, were soaked in gel buffer. One piece of membrane was inserted into each incision. The gel was then returned to the electrophoresis apparatus and run for an additional 30 minutes at the same voltage. The membranes containing bound DNA inserts were rinsed with 400 l of low salt buffer, then eluted with high salt buffer (lM NaCl, 0.1 mM EDTA, 20mM Tris, and 0.5 M Arginine). To elute the DNA, tubes were heated to 10c and after 20 minutes the membranes were turned in the tubes.

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80 After another 25 minutes at 70"C, the membranes were removed from the tubes and the eluate extracted with 400 l of phenol/chloroform (1:1) and again with chloroform. The aqueous phase was then pipetted into another clean Eppendorf tube to which was added 100 l of 7.5 M ammonium acetate and 800 l of absolute alcohol. The tubes were incubated overnight at -2oc. DNA pellets were recovered by microfuging for 15 minutes then washing with 500 l of 70% ethanol. The DNA was air dried and redissolved in 20 l of TE buffer. Two l of each isolated DNA was mixed with 18 l of H 2 0 and run on an agarose gel. The lambda marker was also included on the gel. The relative concentrations and fragment sizes were estimated from this gel. The tubes with the remaining inserts in DNA buffer were stored at -2o•c until needed for oligolabeling. Radio-labeling Probes Probes were labeled with 32 P by the primer extension method of Feinberg and Vogelstein (1983). The method consisted of denaturing the DNA by heating to 95"C for 10 min. then rapid cooling on ice to prevent renaturing. The appearance of the gel from the insert isolation procedure was used to estimate the amount of insert DNA used. Two to four microliters of the insert DNA were placed in a 500 l Eppendorf tube. Also into the tube were placed 10 l of OLB (Finberg and Vogelstein, 1983), 6 l of bovine serum albumen 3mg/ml (BSA), 2 l of Klenow enzyme (lU/l), 4 l of 32 P

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81 labeled deoxycytidine 5 1 -triphosphate (dCT 32 P) (3000ci/mM), and enough double-distilled H 2 0 to bring the total volume to 50 l. The tubes were then incubated at 37C for 30 minutes. Then to each tube 50 l of OLB stop mix [2.0 ml of 1 M Tris HCl (pH 7.0), 400 ml 5 M NaCl, 0.5 M EDTA (pH 8.0), and 12.5 l 20% SDS] were added. Unincorporated nucleotides were removed by liquid chromatography with G50 Sephadex in lX NTE buffer (100 mM NaCl, 10 mM Tris-HCl, and 1 mM EDTA). Probes were then denatured by boiling for 5 minutes and immediately placed in ice for 5 min. The probes were then ready for immediate use. Prehybridization and Hybridization of Blots Southern blots were pre-hybridized to prepare for probe hybridization. Blots were first soaked for a few seconds in deionized water, then in 3X SSC. Next blots were placed into a heat sealed plastic bag along with 30 mls of prehybridization solution (7% SDS in 3X SSC with 30 l of denatured salmon sperm DNA). Prehybridization was conducted for 3-4 hours at 65C. Denatured probes were then injected into the sealed bag containing the blot and the pre-hybridization solution. Hybridization was conducted for 16 hrs. at 65C. Blots were washed for two times for 15 min. each in 3.5 liters of 3X SSC at 65C. A third rinsing was done at the same temperature and for the same time but in 0.3X SSC. Blots were then removed and allowed to air dry on paper towels.

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82 Using a Geiger counter, the radioactivity was checked to estimate the exposure time necessary for autoradiography. Blots were then place into a film case with a piece of Kodak XAR-5 x-ray film and Cronex Hi-Plus intensifying screens (E. I. Dupont de Nemours and Co.). The film was exposed at -1oc for 3 days to 2 weeks depending on the radioactivity of the blot. After appropriate exposure, the film was developed and the hybridization patterns examined. Results and Discussion The quality and quantity of DNA can be estimated from calculations using the absorbance measured at 260 nanometers (nm) and 280 nm. The absorbance at 260 nm divided by the absorbance at 280 nm indicates the purity of DNA with respect to protein contamination (Berger, 1987). The closer the ratio is to 1.8 the more pure the DNA. Concentrations can be estimated by multiplying the absorbance measured at 260 nm by a factor of 50 and then times the dilution rate of the sample analyzed. Absorbances measured on the DNA extracted using extraction method 1 with young but mature leaf tissue is shown in Table 4-1. Two genotypes, F435 and ~repens, showed ratios close to 1.8 indicating good quality DNA. The absorbance ratios of the other genotypes were less than the 1.8 optimum. None of the genotypes extracted using extraction method 2 were of optimum quality (Table 4-2). Photographs of stained gels and hybridization patterns of mature leaf DNA extracted by both methods were

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83 Table 4-1. Absorbances of DNA extracts from four ft. hypogaea lines and four perennial Arachis species at two wavelengths. Extraction was method 1 (CTAB) using young mature leaf tissue. Absorbances Genotype Wave length Concentration 260nm 280nm 260/280 q/l* F435 0.202 0.114 1.77 1.01 F519-9 0.085 0.052 1.63 0.43 F78114 0.052 0.037 1.41 0.26 PI 262090 0.197 0.137 1.43 0.99 ft. 0.101 0.066 1.53 0.51 ft. glabrata 0.033 0.027 1.22 0.17 ft. pintoi 0.092 0.024 1.56 0.46 ft. repens 0.044 0.024 1.83 0.22 * Calculated by A 2 ~ X 50 X dilution rate of 100.

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84 Table 4-2. Absorbances of DNA extracts from four Ahypogaea lines and four perennial Arachis species at two wavelength. Extraction was method 2 (potassium acetate) using young mature leaf tissue. Absorbances Genotype Wave Length Concentration 260nm 280nm 260/280 uglul* F435 0.053 0.039 1.36 0.27 F519-9 0.037 0.027 1.37 0.19 F78114 0.066 0.047 1.40 0.33 PI 262090 0.037 0.033 1.23 0.19 A.film• 0.058 0.043 1.35 0.29 Aglabrata 0.052 0.040 1.30 0.26 Apintoi 0.045 0.032 1.41 0.23 Arepens 0.072 0.051 1.41 0.38 * Calculated by A 260 X 50 X dilution rate of 100.

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85 compared to determine DNA quality (Figure 4-1). The overall quality of the DNA, as indicated by the gel, was not acceptable because of lane to lane variation in DNA concentration and fragment distribution. There was also narrowing of the lanes which appeared to affect the running rates of the fragments. Narrow lanes ran slower, probably due to compounds binding to the DNA and restricting its migration through the gel. Because extraction method 1 was slightly faster, less complex, and at least equal to or better than, in the quality of DNA extracted by method 2 (Figure 4-2), all subsequent DNA extractions were performed using extraction method 1. To further improve the quality of DNA extracted, another tissue source was examined using extraction method 1. Immature leaves that were not fully unfolded and had not entirely emerged from the apical bud were used as the tissue source. Absorbances were measured and are shown in Table 43. There was improvement of extracted DNA quality from every genotype, as seen by the 260/280 absorbance ratios (Table 4-3). Gels of the endonuclease digested DNA showed a good quality by the even, non-narrowed band width along the length of the lanes (Figure 4-3). Because of the improvement in DNA quality associated with the immature leaf tissue, all subsequent isolations were made from that tissue source.

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86 2 3 4 5 6 7 8 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm• 6 A. glabrata 7 A12intoi 8 Are12ens Figure 4-1. DNA extracts from eight peanut genotypes using extraction method 1 on mature leaf tissue.

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87 2 3 4 5 6 7 8 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afil2l2. 6 Aglabrata 7 A 12intoi 8 Are12ens Figure 4-2. DNA extracts from eight peanut genotypes using extraction method 2 on mature leaf tissue.

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88 Table 4-3. Absorbances of DNA extracts from four Ahypogaea lines and four perennial Arachis species at two wavelengths. Extraction was method 1 (CTAB) using immature leaf tissue. Absorbances Genotype Wave Length Concentration 260nm 280nm 260/280 g/l* F435 0.179 0.099 1.81 0.90 F519-9 0.148 0.079 1.87 0.74 F78114 0.086 0.047 1.83 0.43 PI 262090 0.093 0.053 1.75 0.46 Afil2R 0.180 0.098 1.84 0.90 Aglabrata 0.088 0.053 1.66 0.44 Apintoi 0.053 0.029 1.82 0.27 Arepens 0.022 0.012 1.83 0.11 * Calculated by A 260 X 50 X dilution rate of 100.

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89 2 3 4 5 6 7 8 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm 6 Aglabrata 7 AQintoi 8 Are12ens Figure 4-3. DNA extracts from eight peanut genotypes using extraction method 1 on immature leaf tissue.

PAGE 102

90 After DNA was isolated, blots were made and probes were isolated from the peanut genomic DNA library (Figure 4-4). Seventy-six library clones were amplified and plasmids were isolated from them. Eighteen of the 76 plasmid inserts were radiolabeled for use as probes (Table 4-4.). In addition to the probes from the genomic peanut DNA library, clones of six maize mitochondrial genes and a rat liver desaturase clone were used as probes (Table 4-5). Five peanut DNA probes and three mitochondrial gene probes produced readable autoradiographs of single or low copy number fragments that could be used in evaluating polymorphism between the genotypes. Unacceptable autoradiographs had poor definition of fragments and in some cases apparent variation in DNA running rates on the original gels that were blotted. Poor definition of fragments is illustrated in Figure 4-5. This type of radiograph can result from a poor quality DNA isolate or from a probe with a complimentary nucleotide sequence occurring at a high copy rate in the DNA on the blot. Variation in DNA running rates on a gel cannot be probe related but only associated with variation in DNA quality. Figures 4-6 and 4-7 illustrate the variation in DNA running rates. DNA from F519-9 (lane 2) on both of the autoradiographs (Figure 4-6 and 4-7) appears to have fragments slightly smaller than DNA from F435 (lane 1) and F78114 (lane 3) on either side. The original gel photograph shows the F519-9 lane wider and with greater accumulation of

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Figure 4-4 Clones separated from pUC. Marker J. 91

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92 Table 4-4. Genomic DNA clones, library cell locations, and approximate sizes of inserts isolated for production of radio-labeled probes. Clones Cell No. Size (basepairs) HPI2 AS 2200 HPI6 All 1000 HPI16 B9 1000 HPI24 D1 5200 HPI33 El 4400 HPI40 Fl 1275 HPI41 F2 600 HPI45 F6 1275 HPI48 F9 850 HPI49 Fll 250 HPI52 G2 1050 HPI54 G4 1050 HPI58 G8 850 HPI60 Gl0 2300 HPI61 Gll 1300 HPI66 HS 600 HPI67 H6 2000 HPI72 Hll 2100

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93 Table 4-5. Gene clones used as radio-labeled probes. Gene Gene Product Source pDs3 Stearyl-CoA desaturase Thiede et al., 1986 atpa ATPase subunit alpha Braun and Levings, 1985 atp6 ATPase subunit 6 Dewey et al., 1985a atp9 ATPase subunit 9 Dewey et al., 1985b coxI Cytochrome c oxidase Isaac et al., 1985 rrn26 26S rRNA Dale et al., 1984 rrn5-rrn18 18S-5S rRNA Chao et al., 1984

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94 3 4 5 6 7 8 --1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm• 6 A glabrata 7 A12intoi 8 Are12ens Figure 4-5. Autoradiograph of probe at12a on peanut genotypes illustrating an unacceptable autoradiograph based on poor fragment definition.

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2 3 4 5 lil.Lf. f. '1 1 u~ I I I 1 F435 2 F519-9 3 F78114 4 PI 262090 5 A.film. 6 Aglabrata 7 A. Qintoi 8 Are12ens 6 7 8 .. 4.5 .. 3.0 .. 2.0 Figure 4-6. Autoradiograph of probe HPI16 on peanut genotypes with fragment sizes in kilobases. 95

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2 3 4 5 6 7 8 .. 4.5 1 F435 2 F519-9 3 F78114 4 PI 262090 5 A,. .film• 6 A. glabrata 7 A. :gintoi 8 A. re:gens Figure 4-7. Autoradiograph of probe HPI6 on peanut genotypes with fragment size in kilobases. 96

PAGE 109

97 DNA at the end of the lane than the lanes on either side. This amount of variation visible on the original gel along with the repeating pattern of lane 2 appearing to have slightly smaller fragments, stimulated doubt in the reliability of four autoradiographs of four separate probes. The DNA quality is suspect and the probes should be tested again on blots with better DNA. Acceptable quality radiographs showed that there is DNA fragment length polymorphism within the Arachis genus. Variation in fragments between the species were demonstrated by probes atp6, coxI, HPI72, HPI67, HPI2, HPI58, HPI52, and rrn5-rrnl8 (Figures 4-8 through 4-15). Limited polymorphism was found among the Ahypogaea lines. The most prominent difference found among the four Ahypogaea lines was seen with the hybridization of the coxI probe (Figure 4-9). This autoradiograph showed a fragment absent in F435 that was found in all other lines. Other fragment variations among Ahypogaea lines were produced by probes HPI58, HPI52, and possibly by HPI16 though the quality of the autoradiograph of HPI16 makes it unreliable and the hybridization should be repeated. The relationships between the eight peanut genotypes were analyzed by comparing the number of common fragments between each possible paired combination. Only the best eight autoradiographs were used in this comparison (Figures 4-8 through 4-15). Pair-wise indices of genetic similarity

PAGE 110

2 3 4 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm• 6 Aglabrata 7 A Qintoi 8 AreQens 5 6 7 8 .. 8.0 .. 6.1 .. 4.3 .. 2.0 .. 1.0 Figure 4-8. Autoradiograph of probe atQ6 on peanut genotypes with fragment sizes in kilobases. 98

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2 3 4 5 6 7 8 .. 8.0 +4.3 .. 1.8 .. 1.0 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm• 6 A glabrata 7 A2intoi 8 Are2ens Figure 4-9. Autoradiograph of probe coxI on peanut genotypes with fragment sizes in kilobases. 99

PAGE 112

.23.0 .8.0 .4 . 2 .. 1.1 .0.2 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm 6 Aglabrata 7 A12intoi 8 Are12ens Figure 4-10. Autoradiograph of probe HPI67 on peanut genotypes with fragment sizes in kilobases. 100

PAGE 113

2 3 4 1 F435 2 F519-9 3 F78114 4 PI 262090 5 A gm. 6 Aglabrata 7 A 12intoi 8 Are12ens 5 6 7 8 .. 23.0 .. 9.4 ._ 5.4 .. 4.3 Figure 4-11. Autoradiograph of probe HPI72 on peanut genotypes with fragment sizes in kilobases. 101

PAGE 114

2 3 4 1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm• 6 Aglabrata 7 Agintoi 8 Aregens 5 6 7 8 .. 16.0 .. 8.0 .. 3.5 .. 2.2 .. 1.5 Figure 4-12. Autoradiograph of probe HPI58 on peanut genotypes with fragment sizes in kilobases. 102

PAGE 115

2 3 4 1 F435 2 F519-9 3 F78114 4 PI 262090 5 A.film• 6 Aglabrata 7 A. Qintoi 8 AreQens 5 6 7 8 .. 8.0 +3.1 .. 1.9 .. 1.5 Figure 4-13. Autoradiograph of probe HPI52 on peanut genotypes with fragment sizes in kilobases. 103

PAGE 116

1 F435 2 F519-9 3 F78114 4 PI 262090 5 Afilm• 6 Aglabrata 7 A12intoi 8 Are12ens 20.0 6.2 .. 1.9 .. 1.0 104 Figure 4-14. Autoradiograph of probe rrn5-rrn18 on peanut genotypes with fragment sizes in kilobases.

PAGE 117

2 3 4 5 6 7 8 .. 9.8 .. 6.0 .. 1.7 1 F435 2 F519-9 3 F78114 4 PI 262090 5 A. gm. 6 A. glabrata 7 A. 12intoi 8 A,. re12ens Figure 4-15. Autoradiograph of probe HPI54 on peanut genotypes with fragment sizes in kilobases. 105

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106 {Table 4-6) were calculated by dividing the total number of DNA fragments common between two genotypes by the total number of unique fragment size found in the pair of genotypes {Smith et al., 1988). As expected, the highest similarity indices were found between the four Ahypogaea lines. In comparing these four lines the greatest index value was 0.96 found between F78114 and PI 262090. These two lines are both Virginia market-types and are very similar in vegetative growth habit. The other two hypogaea lines {F435 and F519-9) represent two completely different market types. F435 is a Spanish market type, subspecies fastigiata variety vulgaris and the F519-9 line is a runner market type, subspecies hypogaea variety hypogaea. similarity index values calculated between these four lines were as expected based on growth habit and market types. Indices calculated between species showed similar levels of common fragments, whether between one of the Ahypogaea lines and another Arachis species or between two perennial Arachis species. Of the four perennial species, Arepens and Apintoi were most closely related taxonomically. Both have been classified in the same section, Caulorhizae, while Aglabrata and the Afil2P• are in section Rhizomatosae. repens and Apintoi had a similarity index of 0.23, which was not the highest of the species comparisons. The range the indices when two different Arachis species were compared

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Table 4-6. Pair-wise indices of genetic similarity of four Ahypogaea lines and four Arachis species. The similarity index was calculated by dividing the total number of DNA fragments common between two genotypes by the total number of unique fragment sizes represented by the paired genotypes. Genotypes F435 F519-9 F78114 PI 262090 Aglabrata Apintoi 2 0.70 Genotypes* 3 4 5 6 7 8 Similarity Index 0.57 0.58 0.38 0.24 0.24 0.23 0.59 0.61 0.33 0.23 0.27 0.17 0.96 0.24 0.26 0.24 0.26 0.35 0.35 0.28 0.23 0.33 0.38 0.24 0.28 0.32 0.23 *Genotypes: 1-4 Ahypogaea lines l-F435; 2-F519-9; 3-F78114; 4-PI 262090; 5-A . ..PR. line 30b; 6-Aglabrata line 44; 7-Apintoi line 8710; 8-Arepens line 75. I-' 0 -.J

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108 was from 0.17 to 0.38. In comparing two different species, low similarity indices, even between species within the same section of the genus, indicate there are more unique fragments than common fragments between species. These similarity indices then indicate that DNA fragment length polymorphisms are numerous enough to be useful in separating these Arachis species. Further development of RFLPs in peanut may be beneficial as a taxonomic tool where relationships and species demarcations are not clearly defined. The relative lack of polymorphism among hypogaea lines has been observed in other self-pollinated species such as tomato and soybean. Therefore, it would appear that unique DNA fragments are more rare in these genomes. Since only eight probes produced autoradiographs of a quality suitable for evaluation, this is not enough data to suggest fragment length polymorphism cannot be identified in Ahypogaea. Further evaluation using additional unique probes may yield more polymorphic fragments. Other polymorphic fragments may be revealed by different restriction enzymes. By developing more fragment polymorphisms, lines and cultivars of Ahypogaea could be more definitively distinguished. Probes produced from low copy DNA such as mitochondrial genes or probes already known to reveal polymorphism in other self-pollinated species may also be good sources for peanut genome probes.

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CHAPTER V SUMMARY The oil content of peanut is approximately 50%. Since the proportion of oil is so great, the quality of the oil is one of the most important factors in determining the quality of peanut products. Fatty acid composition is an important determinant of oil quality. Therefore, the ability to alter or control fatty acid composition can be a valuable tool to peanut researchers. A number of factors have been shown to affect the fatty acid composition of peanut oil. However, striking differences in fatty acid composition can be achieved by genetic manipulation. With the identification of the high oleic acid peanut line, the known variation of oleic and linoleic acids was sharply increased. Since these two fatty acids are important determinants of peanut oil quality, the increase in phenotypic variation allowed for greater potential of improved oil quality in new peanut cultivars. To use the high oleic acid character in the development of new cultivars it was necessary to determine the mode of inheritance of the character. Crosses were made between the high oleic acid line and three other peanut lines. F 1 , F 2 , F 3 , and backcross generation data showed the character to be 109

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110 controlled by two genes, each with two alleles. The homozygous recessive condition was found to be necessary for the expression of the high oleic acid character. Since the character was found to be simply inherited, further studies were conducted to obtain basic information required in the molecular isolation of the genes. This information included improved understanding of the biochemical synthesis of oleic and linoleic acid and the development of molecular techniques required for molecular genetic manipulations. A study was conducted to determine the developmental changes in the relative proportions of the major fatty acid components of peanut oil. Results corroborate previous research in common peanut cultivars that showed oleic acid increases relative to other fatty acids during development and that linoleic acid remains relatively stable. However, in the high-oleic-acid line it was found that the variation in oleic acid content over development was minimal. Results also indicate that further investigation in changes in fatty acid proportions at more immature stages of development could reveal greater variation in relative proportions of fatty acids. A third investigation was conducted to develop techniques for molecular studies of the Arachis genus. DNA was successfully isolated from five Arachis species and restriction fragment length polymorphisms compared. Molecular variation was found to be limited among the four

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111 A. hypogaea genotypes examined. There was, however, much more variation among the different species examined. It was concluded that for RFLP to be useful in molecular characterization of cultivated peanut additional probes must be tested and DNA from more genotypes evaluated. One fragment difference was found in the high oleic acid line that made it unique from the other Ahypogaea genotypes evaluated. However, further investigation would be necessary to determine if this fragment was a portion of the gene responsible for the high oleic acid character.

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REFERENCES Ahmed, E. M. and c. T. Young. 1982. Composition, quality, and flavor of peanuts. Chap. 17, 655-688. In: Peanut Science and Technology, Editors: H. E. Pattee and c. T. Young. American Peanut Research Education Society, Yoakum, TX. Apuya, N. A., B. Frazier, P. Keim, J.E. Roth, and K. G. Lark. 1988. Restriction fragment length polymorphisms as genetic markers in soybean, Glycine max (L.) merrill. Theoretical and Applied Genetics, 75:889-892. Beckmann, J. S. and M. Soller. 1983. Restriction fragment length polymorphisms in genetic improvement: Methodologies, mapping and costs. Theoretical and Applied Genetics, 67:35-43. Berger, s. L. 1987. Quantifying 32 P-labeled and unlabeled nucleic acids. Chap. 6, 49-54. In: Methods in Enzymology, Volume 152, Guide to Molecular Cloning Techniques. Editors: S. L. Berger and A. R. Kimmel. Academic Press, Orlando, FL. Birnboim, H. C. and J. Doly. 1979. A rapid alkaline extraction procedure for screening recombinant plasmid DNA. Nucleic Acids Research, 7(6):1513-1523. Boote, K. J. 1982. hypogaea L.). Growth stages of peanut (Arachis Peanut Science, 9:35-40. Bovi, M. L.A. 1982. Genotypic and environmental effects on fatty acid composition, iodine value, and oil content of peanut (Arachis hypogaea L.). Ph.D. dissertation, University of Florida, Gainesville. Braun, c. J. and c. s. Levings, III. 1985. Nucleotide sequence of the F 1 ATPase alpha subunit gene from maize mitochondria. Plant Physiology, 79:571-577. Bronsgeest-Schoute, D. c., R. J. J. Hermus, G. M. Dallinga Thie, and J. G. A. J. Hautvast. 1979. Dependence of the effects of dietary cholesterol and experimental conditions on serum lipids in man. The American Journal of Clinical Nutrition, 32:2188-2192. 112

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113 Browse, J., P. J. Mccourt, and c. R. Somerville. 1986. Fatty acid composition of leaf lipids determined after combined digestion and fatty acid methyl ester formation from fresh tissue. Analytical Biochemistry, 152:141-145. Brunklaus-Jung, E. and G. Robbelen. 1987. Genetical and physiological investigations on mutants for polyenoic fatty acids in rapeseed (Brassica napus L.). Plant Breeding, 98:9-16. Buchanan, s. ands. Gaylinn (Editors). 1988. 1988 CRB Commodity Year Book. Commodity Research Bureau, New York. Chao, S., R.R. Sederoff, and c. s. Levings, III. 1984. Nucleotide sequence and evolution of the 18S ribosomal RNA gene in maize mitochondria. Nucleic Acids Research, 12:6629-6644. Cherry, J. P. and R. L. Ory. 1973. Electrophoretic characterization of six selected enzymes of peanut cultivars. Phytochemistry, 12:283-289. Cobb, W. Y. and B. R. Johnson. 1973. Physiochemical properties of peanuts. Chap. 6, 209-257. In: Peanuts--Culture and Uses. Editor: c. T. Wilson. American Peanut Research and Education Association Inc., Stillwater, OK. Conn, E. E., P. K. Stumpf, G. Bruening, R.H. Doi. 1987. Outlines of Biochemistry. 5th ed. John Wiley & Sons New York. Crawford, R. V. and T. P. Hilditch. 1950. The component fatty acid and glycerides of groundnut oils. Journal of the Science of Food and Agriculture, 1:372-379. Dale, R. M. K., N. Mendu, and H. Ginsburg. 1984. Sequence analysis of the maize mitochondrial 26S rRNA gene and flanking regions. Plasmid 11:141-150. Dellaporta, S. L., J. Wood, and J. B. Hicks. 1983. A plant miniprepration: Version II. Plant Molecular Biology Reporter, 4:19-21. Dewey, R. E., C. s. Levings, III, and D. H. Timothy. 1985a. Nucleotide sequence of ATPase subunit 6 gene of maize mitochondria. Plant Physiology, 79:914-919.

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114 Dewey, R. E., A. M. Schuster, c. S. Levings, III, and D. H. Timothy. 1985b. Nucleotide sequence of F 0 -ATPase proteolipid (subunit 9) gene of maize mitochondria. Proceedings of the National Academy of Science, 82:1015-1019. Erickson, E. A., J. R. Wilcox, and J. F. Cavins. 1988. Fatty acid composition of the oil in reciprocal crosses among soybean mutants. Crop Science, 28:644-646. Feinberg, A. P. and B. Vogelstein. 1983. A technique for radiolabeling DNA restriction endonuclease fragments to high specific activity. Analytical Biochemistry, 132:6-13. Fore, s. P., N. J. Morris, c. H. Mack, A. F. Freeman, and W. G. Bickford. 1953. Factors affecting the stability of crude oils of 16 varieties of peanuts. Journal of the American Oil Chemists Society, 30:298-301. Grande, F., J. T. Anderson, and A. Keys. 1970. Comparison of effect of palmitic and stearic acids in the diet on serum cholesterol in man. American Journal of Clinical Nutrition, 23:1184-1193. Green, A.G. 1986. Genetic control of polyunsaturated fatty acid biosynthesis in flax (Linum usitatissimum) seed oil. Theoretical and Applied Genetics, 72:654661. Gregory, w. c., A. Krapovickas, and M. P. Gregory. 1978. Structure, variation, evolution, and classification in Arachis. Pages 469-481. In: Advances in Legume Science, Editors: R. J. Summerfield and A.H. Bunting, Royal Botanic Garden Surrey, England. Grundy, S. M. 1986. Comparison of monounsaturated fatty acids and carbohydrates for lowering plasma cholesterol. New England Journal of Medicine, 314:745-748. Gustafsson, I., B. Vessby, B. Karlstrom, J. Boberg, M. Boberg, and H. Lithell. 1985. Effects on the serum lipoprotein concentrations by lipid-lowering diets with different fatty acid compositions. Journal of the American College on Nutrition, 4:241-248. Hammons, R. o. 1982. Origin and peanut. Chap 1, 1-20. In: Technology. Editors: H. E. American Peanut Research and Yoakum, TX. early history of the Peanut Science and Pattee and E.T. Young. Education Society,

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Harris, P. and A. T. James. 1969. The effect of low temperature on fatty acid biosynthesis in plants. Biochemistry Journal, 112:325-330. 115 Hartzook, A. 1969. The effect of maturity upon fatty acid composition in the oil groundnut (Arachis hypogaea L.) seeds. Current Science, 38:176. Helentjaris, T. 1989. Future directions for plant RFLP technology and its applications. Pages 268-289. In: Current Communications in Molecular Biology. Editors: T. Helentjaris and B. Burr. Cold Spring Harbor Laboratory, Cold Spring Harbor, New York. Helentjaris, T., M. Slocum, s. Wright, A. Schaefer, and J. Nienhuis. 1986. Construction of genetic linkage maps in maize and tomato using restriction fragment length polymorphisms. Theoretical and Applied Genetics, 72:761-769. Holaday, c. E. and J. L. Pearson. 1974. Effects of genotype and production area on the fatty acid composition, total oil, and total protein in peanuts. Journal of Food Science, 39:1206-1209. Holbrook, C. c. and c. s. Kvien. 1989. 1988 cultivar census. Peanut Research, 27(1):4. Isaac, P. G., V. P. Jones, and c. J . Leaver. 1985. The maize cytochrome c oxidase subunit I gene: Sequence expression and rearrangement in cytoplasmic male sterile plants. European Molecular Biology Organization Journal, 4:1617-1623. Jamieson, G. S., w. s. Baughman, and D. H. Brauns. 1921. The chemical composition of peanut oil. Journal of the American Oil Chemists Society, 43:1272-1381. Keim, P., B. W. Diers, R. G. Palmer, and R. c. Shoemaker. 1989. Qualitative and quantitative studies of soybean with RFLP markers. Pages 123-141 In: Current Communications in Molecular Biology. Editors: T. Helentjaris and B. Burr. Cold Spring Harbor Laboratory, Cold Spring Harbor, New York. Knauft, D. A., A. J. Norden, and D. W. Gorbet. 1986. The effect of three digging dates on oil quality, yield, and grade of five peanut genotypes grown without leafspot control. Peanut Science, 13(2):82-85.

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116 Kuusi, T., c. Ehnholm, J. Huttunen, E. Kostiainen, P. Pietinen, u. Leino, U. Uusitalo, T. Nikkari, J.M. Iacono, and P. Puska. 1985. Concentration and composition of serum lipoproteins during a low-fat diet at two levels of polyunsaturated fat. Journal of Lipid Research, 26:360-367. Lehninger, A. L. 1982. Principles of Biochemistry. Worth Publishing, New York. Maniatis, T., E. F. Fritsch, and J. Sambrook. 1982. Molecular cloning: A laboratory manual. Cold Spring Harbor Laboratory, Cold Spring Harbor, New York. Metcalfe, L. D. and A. A. Schmitz. 1961. The rapid preparation of fatty acid esters for gas chromatographic analysis. Analytical Chemistry, 33(3) :363-364. McGill, J. F. 1973. Economic importance of peanuts. Chap. 1, pp. 1-15 In: Peanuts-Culture and Uses. Editor: c. T. Wilson. American Peanut Research and Education Society, Stillwater, OK. Miller, J. F., D. C. Zimmerman, and B. A. Vick. 1987. Genetic control of high oleic acid content in sunflower oil. Crop Science, 27:923-926. Mozingo, R. w., T. A. Coffelt, and J. c. Wynne. 1988. Market grade effects on fatty acid composition of five peanut cultivars. Agronomy Journal, 80:73-75. National Peanut Council of America. 1986. USA Peanuts. J. Grimsley. Alexandria, VA. Norden, A. J., o. W. Gorbet, and D. A. Knauft. 1985. Registration of 'Sunrunner' peanut. Crop Science, 25:1126. Norden, A. J., D. W. Gorbet, D. A. Knauft, and C. T. Young. 1987. Variability in oil quality among peanut genotypes in the Florida breeding program. Peanut Science, 14:7-11. Pickett, T. A. and L. T. Holley. 1951. Susceptibility of types of peanuts to rancidity development. Journal of American Oil Chemists Society, 28:478-479. Rachmeler, D. N. 1988. Inheritance of early maturity and fatty acid composition in peanut (Arachis hypogaea L. ) Ph.D. dissertation. North Carolina State University, Raleigh, NC.

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117 Raheja, R. K., s. K. Batta, K. L. Ahuja, K. s. Labana, and M. Singh. 1987. Comparison of oil content and fatty acid composition of peanut genotypes differing in growth habit. Plant Foods for Human Nutrition, 37:103108. Rennie, B. D., J. Zilka, M. M. Cramer, and w. D. Beversdorf. 1988. Genetic analysis of low linoleic acid levels in the soybean line PI 361088B. Crop Science, 28:655-657. Saghai-Maroof, M.A., K. M. Soliman, R. A. Jorgensen, and R. W. Allard. 1984. Ribosomal DNA spacer-length polymorphisms in barley: Mendelian inheritance, chromosomal location, and population dynamics. Proceedings of the National Academy of Sciences, 81:8014-8018. Salisbury, F. B. and c. W. Ross. 1985. Plant Physiology. 3rd. ed. Wadsworth Publishing, Belmont, CA. Sanders, T. H. 1980a. Effects of variety and maturity on lipid class composition of peanut oil. Journal of the America Oil Chemists Society, 57(1):8-11. Sanders, T. H. 1980b. Fatty acid composition of lipid classes in oils from peanuts differing in variety and maturity. Journal of the American Oil Chemists Society, 57(1) :12-15. Sanders, T. H., J. A. Lansden, R. L. Greene, J. s. Drexler, and E. J. Williams. 1982. Oil Characteristics of peanut fruit separated by a nondestructive maturity classification method. Peanut Science, 9:20-23. Schonfeld, G., W. Patsch, L. L. Rudel, C. Nelson, M. Epstein, and R. E. Olson. 1982. Journal of Clinical Investigation, 69:1072-1080. Smith, R. L., M. K. U. Chowdhury, and S. C. Schank. 1988. Use of restriction fragment-length polymorphism (RFLP) markers in genetics and breeding of napiergrass. Soil and Crop Science Society of Florida, Proceedings, 48:13-19. Southern, E. M. 1975. Detection of specific sequences among DNA fragments separated by gel electrophoresis. Journal of Molecular Biology, 98:503-517. st. Angelo, A. J. and R. L. Ory. 1973. Investigations of causes and prevention of fatty acid peroxidation in peanut butter. Journal of the American Peanut Research and Education Association, 5:128-133.

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118 St. John, L. c., c. R. Young, D. A. Knabe, L. D. Thompson, S.T. Schelling, S. M. Grundy, and S. B. Smith. 1987. Fatty acid profiles and sensory and carcass traits of tissues from steers and swine fed an elevated monounsaturated fat diet. Journal of Animal Science, 64:1441-1447. Stalker, H. T. and J. P. Moss. 1987. Speciation, cytogenetics, and utilization of Arachis species. Advances in Agronomy, 41:1-40. Stumpf, P. K. 1989. Biosynthesis of fatty acids in higher plants. Chap. 3, 38-67. In: Oil Crops of the World. Editors: G. Robbelen, R. K. Downey, and A. Ashri. McGraw-Hill, New York. Stumpf, P. K., J. B. Ohlrogge, K. C. Oo, and M. R. Pollard, 1977. Biosynthesis of fatty acids and possible chain termination mechanisms in plant tissues. Pages 234-258 In: Regulation of fatty acid and glycerolipid metabolism. Editors: P. K. Stumpf and M. R. Pollard. Pergamon Press, Oxford. Tai, P. Y. P. and c. T. Young. 1977. Inheritance of dry matter deposition and free arginine level in maturing peanuts, Arachis hypogaea L. Peanut Science, 4(1):1-6. Thiede, M.A., J. Ozois, and P. Strittmatter. 1986. Construction and sequence of cDNA for rat liver stearyl coenzyme A desaturase. The Journal of Biological Chemistry, 261(28):13230-13235. Thomas, D. L. and N. J. Neucere. 1974. A comparative investigation of peroxidases from germinating peanuts (Arachis hypogaea): Electrophoresis. American Journal of Botany, 61:457-463 Treadwell, K., c. T. Young, and J. c. Wynne. 1983. Evaluation of fatty acid content of forty peanut cultivars. Oleagineux, 38(6):381-385. Urie, A. L. 1985. Inheritance of high oleic acid in Sunflower. Crop Science, 25:986-989. United States Department of Agriculture, (USDA). 1975. Composition of foods. Agricultural Handbook No. 8 Washington, D. c. United States Department of Agriculture, (USDA). 1979. Agricultural Statistics. Washington, D. c.

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119 Wilcox, J. R. and J. F. Cavins. 1985. Inheritance of low linolenic acid content of the seed oil of a mutant in Glycine max. Theoretical and Applied Genetics, 71:7478. Williams, E. J. and J. s. Drexler. 1981. A non-destructive method for determining peanut pod maturity. Peanut Science, 8:134-141. Worthington, R. E. 1969. Developmental changes in peanut lipid Fatty acids. Pages 87-98 In: The Proceedings of the Fifth National Peanut Research Conference. Worthington R. E. and R. o. Hammons. 1971. Genotypic variation in fatty acid composition and stability of Arachis hypogaea L. oil. Oleagineux, 26(11):695-700. Worthington, R. E., R. o. Hammons, and J. R. Allison. 1972. Varietal differences and seasonal effects on fatty acid composition and stability of oil from 82 peanut genotypes. Journal of Agricultural Food Chemistry, 20:727-730. Wynne, J. c. and T. M. Halward. 1989. Cytogenetics and genetics of Arachis. Critical Reviews in Plant Sciences, 8(3):189-220. Young, c. T., M. E. Mason, R. s. Matlock, and G. R. Waller. 1972. Effect of maturity on the fatty acid composition and stability of eight varieties of peanut grown and Perkins, Oklahoma in 1968. Journal of the American Oil Chemists Society, 49:314-317. Young, C. T., R. E. Worthington, R. o. Hammons, R. s. Matlock, G. R. Waller, and R. D. Morrison. 1974. Fatty acid composition of Spanish peanut oils as influenced by planting location, soil moisture conditions, variety, and season. Journal of American Oil Chemists Society, 51:312-315.

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BIOGRAPHICAL SKETCH Kim M. Moore was born on May 23, 1951, in Boulder, Colorado. He lived in Colorado for his primary education but completed his secondary education in Sepulveda, California, where he graduated from James Monroe High School in 1969. He began his higher education at the University of California at Santa Barbara and later transferred to Colorado State University, where he received a B. s. degree in animal science in 1976. After completion of his B. s., he accepted a position as a food technologist for star-Kist Foods, Inc., in their product development division. In 1979, he was promoted to quality control manager of the El Paso, Texas, production facility. In 1984, he enrolled at the University of Florida, Gainesville, Florida, as a graduate student in the Department of Agronomy and received a Master of Science degree in May of 1987 and a Doctor of Philosophy degree in May of 1990. 120

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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. David A. Knauft, Ch rman Associate Professor of Agronomy 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. Kenneth L. Buhr Assistant Professor of Agronomy 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. Kenneth H. Quesenberry Professor of Agronomy 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 / el l~~ l(uJ~ Sherlie H. West Professor of Agronomy

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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. Professor of Horticultural Science This dissertation was submitted to the Graduate Faculty of the College of Agriculture and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. May 1990 Dean, of Ag culture Dean, Graduate School

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UNIVERSITY OF FLORIDA II I II IIIIII Ill Ill lllll lllll II IIIIII IIII II llllll 11111111111111111 3 1262 08553 4500



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FAST FOURIER TRANSFORMED ACOUSTIC RESONANCES WITH SONIC TRANSFORM By KENNETH C. MCGILL A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSIT~ OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1990

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Copyright 1990 by Kenneth Charles McGill

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DEDICATION This work is dedicated to the three people whom I owe so much: To my mother Martha Senogles who gave me life; to my late wife Natalie McGill who gave me her life; and to my wife Susan McGill who is giving me a new life in my first child.

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ACKNOWLEDGMENTS I would like to thank Dr. s.o. Colgate personally for his support and guidance during the development of this technique. I would also like to thank Chadin Dejsupa and Joe Shalosky for assisting in the construction of various parts of the apparatus, Casey Rentz for the use of his computer and Evan House for convincing me to join the Colgators. In addition, I would like to thank Dr. Grant Schrag for the development of the tapered ram seal used for the electrical feed-throughs of the transducers, Dr. Cliff Watson for his assistance in programming the Fast Fourier Transform and Steve Miles for his contribution on the development of the magnetic pump. Also, I thank my wife, Susan, for instructing me on the use of WordPerfect so that I could perfect the format of this dissertation. iv

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TABLE OF CONTENTS ACKNOWLEDGMENTS . . . iv LIST OF TABLES . •...•..........•.......•..........•....... vii LIST OF FIGURES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi CHAPTERS 1 2 3 INTRODUCTION . THEORY ....... . Theory Theory of of Design .... . Operation .. . EXPERIMENTAL . ...........••••..•..•......•..•••. Interfacing ........... . Apparatus ............. . Spherical Cavity .. . Pump The Bellows. 4 DATA AND RESULTS . Time Domain Plots ..... . Plots .. Frequency Domain Sonic Domain Volume and Pressure Plots ..... Calibration .. 5 CONCLUSION . ..........•.............••.........• APPENDICES 1 8 9 18 29 30 34 34 35 37 42 44 45 46 48 69 A FAST FOURIER TRANSFORM SOURCE CODE 76 B SONIC TRANSFORM SOURCE CODE ...........••..•.... 80 C EQUATION OF STATE FOR ARGON SOURCE CODE ........ 84 D DATA ACQUISITION SOURCE CODE ................... 87 V

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E DATA CONVERSION SOURCE CODE .................... 93 BIBLIOGRA.PHY. . . . . . . . . . . .. 95 BIOGRA.PHICAL SKETCH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 vi

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LIST OF TABLES Table 2-1. The values of the roots to the first derivative of a Bessel function of the first kind................................................ 12 Table 2-2. Reduced second virial coefficients for the Lennard-Jones 6-12 potential .•........•....••... 20 Table 2-3. Reduced third virial coefficients and their derivatives for the Lennard-Jones 6-12 potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Table 4-1. Low temperature time domain parameters of argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Table 4-2. Low temperature frequency domain parameters of argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Table 4-3. First sonic domain parameters of argon at low temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Table 4-4. Second sonic domain parameters of argon at low temperature.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Table 4-5. Third sonic domain parameters of argon at low temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 7 Table 4-6. Fourth sonic domain parameters of argon at low temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Table 4-7. High temperature time domain parameters of argon ............................................ 59 Table 4-8. High temperature frequency domain parameters of argon ............................................ 60 Table 4-9. First sonic domain parameters of argon at high temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Table 4-10. Second sonic domain parameters of argon at high temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Table 4-11. Third sonic domain parameters of argon at high temperature.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 vii

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Table 4-12. Fourth sonic domain parameters of argon at high temperature........................ . . . . . . . . . . . . 64 Table 4-13. Outside volume calibration 65 Table 4-14. Total volume of apparatus ................... 66 Table 4-15. Bellows volume calibration .................. 67 Table 4-16. Compiled results of sonic speeds of argon at low and high temperatures for various roots ......... 68 viii

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LIST OF FIGURES Figure 3-1. Instrument rack ....................•........ 32 Figure 3-2. Spherical cavity sections and clamping flanges ............................................. 36 Figure 3-3. Pump assembly ...............•.............•. 38 Figure 3-4. The bellows and bellows chamber 39 Figure 3-5. Apparatus assembly. . . . . . . . . . . . . . . . . . . . . . . . . . 41 Figure 4-1. Theoretical ADC signal for 350 m/s speed of sound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Figure 4-2. Theoretical ADC signal for 150 m/s and 350 m/s speeds of sound ...•..............•........•• 50 Figure 4-3. FFT of theoretical ADC signal for 350 m/s speed of sound .............................. 51 Figure 4-4. FFT of theoretical ADC signal for 150 m/s and 350 m/s speeds of sound ................. 51 Figure 4-5. ST of FFT of theoretical ADC signal for 350 m/s ......................................... 52 Figure 4-6. ST of FFT of theoretical ADC signal for 150 m/s and 350 m/s speeds of sound ............. 52 Figure 4-7. ADC signal of argon at low temperature 53 Figure 4-8. Expanded section of Figure 4-7 .......•..•.•• 53 Figure 4-9. FFT of ADC signal of argon at low temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Figure 4-10. Expanded section of Figure 4-9 . ............ 54 Figure 4-11. First ST of argon at low temperature ....... 55 Figure 4-12. Expanded section of Figure 4-11 . ........... 55 Figure 4-13. Second ST of argon at low temperature ...... 56 ix

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Figure 4-14. Expanded section of Figure 4-13 . ........... 56 Figure 4-15. Third ST of argon at low temperature 57 Figure 4-16. Expanded section of Figure 4-15 . ........... 57 Figure 4-17. Fourth ST of argon at low temperature ....•• 58 Figure 4-18. Expanded section of Figure 4-1 7 . ........... 58 Figure 4-19. ADC signal of argon at high temperature ..•. 59 Figure 4-20. Expanded section of Figure 4-19 . ........... 59 Figure 4-21. FFT of ADC signal of argon at high temperature. .....•.......................•......•..• 60 Figure 4-22. Expanded section of Figure 4-21 . ........... 60 Figure 4-23. First ST of argon at high temperature 61 Figure 4-24. Expanded section of Figure 4-2 3 61 Figure 4-25. Second ST of argon at high temperature ...•. 62 Figure 4-26. Expanded section of Figure 4-2 5 . ........... 62 Figure 4-27. Third ST of argon at high temperature .....• 63 Figure 4-28. Expanded section of Figure 4-2 7 . ........... 63 Figure 4-29. Fourth ST of argon at high temperature 64 Figure 4-30. Expanded section of Figure 4-2 9 . ........... 64 Figure 4-31. Outside volume calibration ................. 65 Figure 4-32. Total volume of apparatus .....•..•.•.•..•.. 66 Figure 4-33. Bellows calibration plot . .................. 67 X

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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 FAST FOURIER TRANSFORMED ACOUSTIC RESONANCES WITH SONIC TRANSFORM By Kenneth C. McGill December 1990 Chairman: s.o. Colgate Major Department: Chemistry In this study, a novel approach for detecting one or more speeds of sound was developed. By employing a Sonic Transform {ST), the data are transformed in real time to a domain that is directly related to the speed of sound within a cavity. The transform is of order< n 2 and is equivalent to a Fast Fourier Transform in computation time. The study contains a discussion of the apparatus design as well as interfacing techniques involved in its operation. Source code and algorithms that describe the analysis and data acquisition in detail are also contained within the study. xi

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CHAPTER 1 INTRODUCTION The measurement of state variables is of interest to researchers in thermodynamics. The two most commonly measured state variables are temperature and pressure. Techniques for their measurement have been developed that have high accuracy and speed of operation and are relatively easy to use. The equation of state for even the simplest system, for example, a single component gas, requires at least another variable. For whatever additional variable is chosen, it is desirable that its measurement be performed as quickly and as easily as those of temperature and pressure. The most commonly measured third state variable is volume. The measurement of volume is often done by a batch process where a fluid substance is placed in a vessel of calibrated volume. This process is time-comsuming and is prone to error. Individual error can occur in recording the measurement and it is impossible to do real time processing of the data. There are other state variables that could be measured, such as entropy, enthalpy, and free energy, but these are even more difficult to measure in a batch process or in real time. If a reliable equation of state relating three state variables is available, then the magnitude of the third 1 . ,

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2 variable may be calculated after measuring the other two. This method works well for single component gases, but it is not very accurate for multicomponent mixtures of gases or for any gas near its critical region. In this work, emphasis is placed on the development of a novel sonic speed measurement technique to facilitate the use of this state variable along with temperature, pressure and volume in physical relationships. An effort to make the measurement of the speed of sound as accurate and as easy as temperature and pressure has been made; that is, a process has been developed that can operate in real time with high accuracy and with little interaction from the user. The measurements of volume and speed of sound are similar; one way to measure the volume of a gas involves the geometry of the vessel in which the gas is contained and, similarly, one way to measure the speed of sound in a gas involves the geometry of the vessel in which the gas is contained. By knowing the geometry of the vessel, the volume can be calculated by measuring the dimensions of the vessel. The speed of sound can be found by measuring the acoustic resonances within the cavity. The speed of sound is also dependent on the density and mass of the gas being measured. An accurate method for measuring the speed of sound involves examination of the resonances that occur in an acoustic cavity. The selection of the geometry of the cavity can make a significant difference in the ease of

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interpretation of the resonance frequencies. For example, resonances in a cylindrical cavity are complicated by problems, such as unresolved modes and viscous drag along the longitudinal walls. These problems have been examined in detail elsewhere. 1 3 Another potential problem with any shaped cavity results from a precondensation effect that occurs on the surface of the cavity. 2 This effect appears most strongly at low frequencies in resonators with large surface-to volume ratios. To avoid these problems, a spherical cavity was chosen since: 1) Viscous drag does not occur for the radial vibrations within a spherical cavity; 2) surface-to volume ratio is minimized for spherical geometry; and 3) the acoustic energy is highest at the center of the sphere. In a study that included a treatment of the precondensation effect in a spherical cavity, the speed of sound of a gas was measured with an accuracy approaching 0.0005% or 5 ppm. 3 Neglecting the precondensation effect, 1 J.B. Mehl and M.R. Moldover, "Precision Acoustic Measurements with a Spherical Resonator: Ar and C 2 H 4 ," Journal of Chemical Phvsics 74 (April 1981): 4062-4077; A.R. Colclough, "Systematic Errors in Primary Acoustic Thermometry in the Range 2-20 K," Metrologia 9 (1973)! 75. 2 J.B. Mehl and M.R. Moldover, "Precondensation Phenomena in Acoustic Measurements," Journal of Chemical Physics 77 (July 1982): 455-465. 3 M.R. Moldover, J.B. Mehl, and M. Greenspan, "GasFilled Spherical Resonators: Theory and Experiment," Journal of the Acoustical Society of America 79 (February 1986): 253-271. . ,

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accuracies of 0.01% are readily obtained for physical properties inferred from sonic speed measurements, these include reference state heat capacities, 4 thermophysical properties of alkanes, 5 and heat capacity ratios. 6 In all of these experiments, the first step is to analyze a frequency spectrum and then select only a few of the resonances, at most five or six depending upon the experiment, to measure the speed of sound. 7 This interaction from the user requires an intuition as to where the resonances occur, and locating them with confidence is often tedious and can take a considerable amount of experimental time. This places an added burden on the maintenance of the system's state. The measurement of temperature and pressure can be very accurate, but maintaining them for long periods of time is not easy. All 4 S.O. Colgate, C.F. Sona, K.R. Reed, and A. Sivaraman, "Experimental Ideal Gas Reference State Heat Capacities of Gases and Vapors," Journal of Chemical and Engineering Data 35 (1990): 1-5. 5 M.B. Ewing, A.R.H. Goodwin, and J.P.M. Trusler, "Thermophysical Properties of Alkanes from Speeds of Sound Determined Using a Spherical Resonator 3. n-Pentane," Journal of Chemical Thermodynamics 21 (1989): 867-877. 4 6 s.o. Colgate, K.R. Williams, K. Reed, and c. Hart, "Cp/Cv Ratios by the Sound Velocity Method Using a Spherical Resonator," Journal of Chemical Education 64 (June 1987): 553-556. 7 M.B. Ewing, M.L. McGlashan, and J.P.M. Trusler, "The Temperature-Jump Effect and the Theory of the Thermal Boundary Layer for a Spherical Resonator, Speeds of sound in Argon at 273.16 K," Metrologia 22 (1986): 93-102.

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5 of these methods assume that only one speed of sound is present within the medium of interest. If multiple speeds of sound are present within a medium, the difficulties of the job of analysis are seriously compounded. Ideally, a method that can identify the resonances as well as calculate a close approximation of the speed of sound very quickly would represent a significant advance in the art of sonic speed measurements. Since the number of possible resonances is of the order of the number of molecules, it is for all practical purposes infinite. Ideally, a broad band of resonances should be used to determine the speed of sound within the gas. One such attempt at measuring a truncated set of resonances was made by Tewfik et al. 8 This study modeled two dimensional waves such as the waves on the ocean. Their method involved a rather large calculation employing Householder routines to solve an nXn linear matrix problem. A Householder routine 9 is an operation of order n 3 for which even a relatively small set of resonances becomes costly in computation time. Hence, although the Householder routine is capable of high accuracy, it can not be considered useful as a real time process. 8 A.H. Tewfik, B.C. Levy, and A.S. Willsky, "An Eigenstructure Approach for the Retrieval of Cylindrical Harmonics," Signal Processing 13 (September 1987): 121-139. 9 G.H. Golub and C.F. Van Loan, Matrix Computations (Baltimore: Johns Hopkins University Press, 1985), 38.

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In order to overcome these boundaries, a technique was developed in the present work to transform the Fourier coefficients of a captured time domain signal to the sonic domain. Once in this domain, the speed of sound is easily determined. For the development of this technique, a spherical cavity and a truncated set of resonances were used. The truncated set of resonances was transformed from a measured time domain signal to the sonic domain using a transform operation of order nlog 2 n + nm, where mis the number of resonances. 6 To test the method, a theoretical (computer synthesized) frequency spectrum was created and then the speed (or speeds) of sound were found from the spectrum and compared to the speed (or speeds) of sound used to produce the spectrum. Once satisfied that the method could reproduce the speed of sound from a simulated spectrum, some experimental spectra were analyzed. The transformed speeds of sound obtained from these experimental spectra were then compared to known values, which for the gas in question, argon, have been shown to be in accord with those directly calculated using a truncated virial equation of state. The transformed speeds of sound may be lower than the calculated speeds since the latter are the speeds of sound at zero frequency and the transformed ones are an average speed of sound over all the frequencies within the spectrum.

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7 The following chapters describe the theory of design as well as the theory of operation of this transformation technique. The design of the apparatus is similar to other acoustic devices with a few exceptions. The seal technology employed allows operation over wider temperature and pressure ranges. Another unique feature of the apparatus is the ability to vary its volume with a specially designed bellows assembly. This apparatus has the capability to measure four state variables simultaneously. In addition, the source code for all measurement techniques has been included in the appendices to describe the operation of the apparatus in detail.

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CHAPTER 2 THEORY Two basic theoretical constructs central to the present novel sonic speed technique are explained in this chapterthe theqry of design and the theory of operation. The theory of design begins with established theories of wave phenomena and applies modern computational methodologies to them. A new algorithm developed here facilitates the computations. The theory of operation is presented to reveal the order of events that lead to the measurement of the speed of sound with this technique. The equations and operational bounds may seem trivial to anyone familiar with Fast Fourier Transform (FFT) techniques, but, to the newcomer, these will likely seem arbitrary and unbounded. They are, in fact; very closely interrelated. The two parameters that govern the operation of any FFT spectrometer are the buffer size and the sample rate of the ADC; other parameters may be deduced from them. The operation of many of the basic theories described are transparent to the user since they are contained mainly within the source code given in the appendices. 8

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Theory of Design The dynamics associated with the acoustical field of a nondissipating gas were first examined by Rayleigh in 1872. 1 Rayleigh's development revealed a basis set of resonant frequencies of sound for a gas in a cavity. Experimentally these frequencies have heretofore been measured by observing the response of the gas to a slowly varying periodic stimulus. The present work is concerned with obtaining the information implicit in the frequency spectrum very rapidly. Acquisition of the frequency domain may be accomplished by a Fast Fourier Transform (FFT) of a time domain signal from an Analog to Digital Converter (ADC). Through a Sonic Transformation (ST) of the Fourier coefficients, this information can be further transformed into the sonic domain which readily reveals the speed of sound and other features of the acoustic field. First, assume there exists a velocity potential v such that v--Vv Equation 2-1. where vis the velocity of the gas. The standing wave produced in the gas with a speed of sound (c) is related to v by the standard wave equation J.W.S. Rayleigh, Theory of Sound (New York: Dover, 1894), reprinted 1945, Section 331. 9

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10 Equation 2-2. Assuming a time separable solution to the above equation Equation 2-3. where Vo is then the solution to a scaler Helmholtz equation Equation 2-4. then the analytical expression for Vo 2 is 111 0 j 1 ( ~r) Pt(cos(8)) (Asin(mcp) + Bcos(mcp)). Equation 2-5. The function jl is a Bessel function of the first kind and Pr is an associated Legendre polynomial in cos(8). Since, by definition, a nondissipating gas is contained, the boundary condition of the radial component is that the velocity of the gas is zero at the rigid wall Equation 2-6. 2 H.G. Ferris, "The Free Vibrations of a Gas Contained within a Spherical Vessel," Journal of the Acoustical Society of America 24 (January 1952): 57. l

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11 For a spherical cavity, the surface is described by da-g 2 sin (0) d0dcpf, Equation 2-7. where g is a geometric factor or the radius of the spherical cavity. Substitution of the gradient of• in Equation 2-6 yields lab Pf'(cos(8)) (Asin(mcp)+Bcos(mcp))g 2 sin(8)d0dcp oajl lr_g _ 0. Surf I Equation 2-8. Since this must be zero for all values of a and b, then Equation 2-9. For a given value of 1, there are an infinite number of roots for the above relation. The lowest positive root is denoted by n=l, the next root is n=2, the following n=3, and so forth. These integral values represent the modes of vibration for that given 1. The roots of the above relations have been calculated in increasing magnitude as shown in Table 2-1. 3 3 Ferris.

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12 Table 2-1. The values of the roots to the first derivative of a Bessel function of the first kind. i Ri 1 n 1 2.08158 1 1 2 3.34209 2 1 3 4.49341 0 1 4 4.51408 3 1 5 5.64670 4 1 6 5.94036 1 2 7 6.75643 5 1 8 7.28990 2 2 9 7.72523 0 2 10 7.85107 6 1 11 8.58367 3 2 12 8.93489 7 1 13 9.20586 1 3 14 9.84043 4 2 15 10.0102 8 1 16 10.6140 2 3 17 10.9042 0 3 18 11.0703 5 2 19 11.0791 9 1 20 11.9729 3 3 21 12.1428 10 1 22 12.2794 6 2 23 12.4046 1 4 24 13.2024 11 1 25 13.2956 4 3 26 13.4721 7 2 27 13.8463 2 4 28 14.0663 0 4 29 14.2580 12 1 30 14.5906 5 3 31 14.6513 8 2 32 15.2446 3 4 33 15.3108 13 1 34 15.5793 1 5 35 15.8193 9 2 36 15.8633 6 3 37 16.3604 14 1 38 16.6094 4 4 39 16.9776 10 2 40 17.0431 2 5 41 17.1176 7 3 42 17.2207 0 5

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13 Table 2-1 continued. i Ri 1 n 43 17.4079 15 1 44 17.9473 5 4 45 18.1276 11 2 46 18.3565 8 3 47 18.4527 16 1 48 18.4682 3 5 49 18.7428 1 6 50 19.2628 6 4 51 19.2704 12 2 52 19.4964 17 1 53 19.5819 9 3 54 19.8625 4 5 55 20.2219 2 6 56 20.3714 0 6 57 20.4065 13 2 58 20.5379 18 1 59 20.5596 7 4 60 20.7960 10 3 61 21.2312 5 5 62 21.5372 14 2 63 21.5779 19 1 64 21.6667 3 6 65 21.8401 8 4 66 21.8997 1 7 67 22.0000 11 3 68 22.5781 6 5 69 22.6165 20 1 70 22.6625 15 2 71 23.0829 4 6 72 23.1067 9 4 73 23.1950 12 3 74 23.3906 2 7 75 23.5194 0 7 76 23.6534 21 1 77 23.7832 16 2 78 23.9069 7 5 79 24.3608 10 4 80 24.3821 13 3 81 24.4749 5 6 82 24.6899 22 1 83 24.8503 3 7 84 24.8995 17 2

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14 A solution to the above equation occurs when <,J . __ i g-Rc l. Equation 2-10. and the frequency of the standing wave within the cavity at speed c is then Rc (,J .-21tf .--l.I l. l. g Equation 2-11. where g is a geometric factor and Riis the ith tabulated root. The previous equation describes the frequency basis for all standing waves or resonant excitations in the cavity. Experimentally, the resonant frequencies are acquired in the Fourier format (see Appendix A) where 00 FF(t)-E (APsin(<,.>Pt)+BPcos(<,.>Pt)). p Equation 2-12. If multiple speeds of sound occur within the cavity medium, each having an almost infinite number of resonant frequencies, the job of determining the speeds of sound from the corresponding frequencies is tedious. Even with a truncated basis of roots (as in Table 2-1), finding the speed is not easy and requires considerable analysis. The

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15 ST developed below facilitates this task. It transforms the coefficients of the FFT directly to the sonic speed domain. Consider a system through which sound propagates at one or more speeds. Let the associated frequencies be weighted by some values k;, where and 00 00 F 5 (t)-I;kif(ci, t) 1. Equation 2-13. f(ci, t) -I; (aiJsin(gciRJt) +biJcos (gciRJt)). J Equation 2-14. If we assume that all signals detected in the Fourier coefficients are acoustic resonances Equation 2-15. then it follows that 00 00 Equation 2-16. . I

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16 where the value of o is as follows, 11 {1, c.>P-gciRJ} Equat1 on 2 17 u ( Ca) P' gciR) -u pij0 Ca) ~gc ,R . . I p 1 J The values of ki are of greater interest than the Fourier coefficients. One method to acquire n coefficients for a truncated sum of m roots would be to perform n truncated least square operations of order 2m+l to obtain n functions f(c;,t) and then perform one more least square operation of order n to obtain the coefficients k;• Each least square operation is approximately an n-cubed operation (FLOPs 4 n 3 ). By performing the transformation shown below, weights that are proportional to ki can be obtained with considerably fewer FLOPs. Let Equation 2-18. then by substituting AP from Equation 2-16 into the above expression, 4 FLOP is a FLoating point OPeration (see Chapter 3, Theory of Operation).

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noooooo W1-_!_ LL LI; kiaijt, pijt, plm• nm p i J 17 Equation 2-19. Since 1 is fixed, then for a given m and p, the only nonzero values occurs when i=l and j=m. This reduces the above expression to Equation 2-20. For a given 1 and m, there is only one nonzero value p, hence Equation 2-22. where al is the average amplitude over n roots of the 1th speed. Most importantly, this result shows that this choice of weights is directly proportional to the sonic coefficients k 1 The relative values of wl cannot be used for determining relative values of kl. Since there is an overlap of different Ri values, the weights can be used to detect the presence of resonant speed of sound within the cavity.

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18 Theory of Operation For the purpose of evaluating the sonic transform technique, its use on a gas with known properties is required. Argon was chosen for this purpose because of its relative simplicity and well-documented physical behavior. The speed of sound in argon has been carefully measured and shown to be in agreement with values calculated with the virial equation of state. 5 At moderate pressures (< 10 atm) two terms in the virial expansion are sufficient to give sonic speeds within experimental uncertainty. For this work the sonic speed in argon was calculated from the virial equation of state (truncated after the third term) using reduced virial coefficients obtained from a Lennard-Jones 6-12 potential. The speed of sound at zero frequency 6 may be related to either the adiabatic or isothermal partial derivative of pressure with respect to molar density. Specifically, the square of the speed of sound is cJ-l:.(aP) _ 1 (aP), M ap s M ap T Equation 2-22. 5 R. Byron Bird, "Numerical Evaluation of the Second Virial Coefficient," The Virial Equation of State CM-599 (Madison: University of Wisconsin, May 10, 1950), 47-52. 6 J.O. Hirschfelder, c.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids (New York: Wiley and Sons, 1954), 369.

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19 where Pis pressure, Mis the molecular weight and pis the molar density. Using the constant temperature form of the above equation, where y is the ratio of heat capacities, the speed of sound can be found by solving for the individual values of CP, cv and the constant temperature derivative. There is no equation of state that can be expressed in a single analytical expression that has high enough accuracy for this experiment. The best possible solution is a truncated virial equation with numerically calculated coefficients at various temperatures. The values of the second virial coefficients are given in Table 2-2 and the values of the third virial coefficients are given in Table 2-3. The accuracy of this numerical solution has been investigated by Bird. 7 Using the truncated virial equation of state in terms of reduced virial coefficients given by: Key Terms, Symbols and Definitions for Truncated Virial Equation of state B = Second Virial k = Boltzmann's constant Coefficient C = Third Virial R = Gas constant Coefficient ho = rrNa 3 B* = B/b 0 (1 = Lennard-Jones 6-12 c* = C/b20 collision diameter = Lennard-Jones 6-12 T* = kT/ maximum energy attraction or depth of N = Avogadro's Number potential well 7 Bird.

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20 Table 2-2. Reduced second virial coefficients for the Lennard-Jones 6-12 potential. T* B* B,* B2* B 1 *-B* 0.30 -27.880581 76.607256 -356.87679 104.488 0.35 -18.754895 45.247713 -189.46536 64.003 0.40 -13.798835 30.267080 -116.36604 44.066 0.45 -10.754975 21.989482 -78.87795 32.744 0.50 -8.720205 16.923690 -57.33952 25.644 0.55 -7.2740858 13.582156 -43.88245 20.8563 0.60 -6.1979708 11. 248849 -34.91869 17.4468 0.65 -5.3681918 9.5455096 -28.64050 14.9137 0.70 -4.7100370 8.2571145 -24.06266 12.9672 0.75 -4.1759283 7.2540135 -20.61311 11.4299 0.80 -3.7342254 6.4541400 -17.94190 10.1884 0.85 -3.3631193 5.8034061 -15.82546 9.1665 0.90 -3.0471143 5.2649184 -14.11557 8.3120 0.95 -2.7749102 4.8127607 -12.71081 7.5877 1.00 -2.5380814 4.4282616 -11.53985 6.9663 1.05 -2.3302208 4.0976659 -10.55133 6.4279 1.10 -2.1463742 3.8106421 -9.70744 5.9570 1.15 -1.9826492 3.5592925 -8.97985 5.5419 1.20 -1.8359492 3.3374893 -8.34700 5.1734 1.25 -1.7037784 3.1404074 -7.79217 4.8442 1.30 -1.5841047 2.9642040 -7.30227 4.5483 1.35 -1.4752571 2.8057826 -6.86692 4.2810 1.40 -1.3758479 2.6626207 -6.47777 4.0385 1.45 -1.2847160 2.5326459 -6.12805 3.8174 1.50 -1.2008832 2.4141403 -5.81225 3.6150 1.55 -1. 1235183 2.3056683 -5.52578 3.4292 1.60 -1.0519115 2.2060215 -5.26485 3.2579 1.65 -0.98545337 2.1141772 -5.02628 3.0996 1.70 -0.92361639 2.0292621 -4.80738 2.9529 1.75 -0.86594279 1.9505276 -4.60587 2.8165 1.80 -0.81203328 1. 8773287 -4.41980 2.6894 1.85 -0.76153734 1. 8091057 -4.24750 2.5706 1.90 -0.71414733 1. 7453722 -4.08753 2.4595 1.95 -0.66959030 1.6857016 -3.93863 2.3553 2.00 -0.62762535 1. 6297207 -3.79972 2.2573 2.10 -0.55063308 1.5275444 -3.54814 2.0782 2.20 -0.48170997 1.4366294 -3.32647 1.9183 2.30 -0.41967761 1.3552188 -3.12974 1.7749 2.40 -0.36357566 1.2819016 -2.95401 1.6455 2.50 -0.31261340 1. 2155320 -2.79614 1.5281 2.60 -0.26613345 1.1551691 -2.65355 1.4213 2.70 -0.22358626 1. 1000353 -2.52416 1.3236 2.80 -0.18450728 1. 0494802 -2.40623 1.2340

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Table 2-2 continued. T* 2.90 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 6.00 7.00 8.00 9.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 200.00 300.00 400.00 B* -0.14850215 -0.11523390 -0.08441245 -0.05578696 -0.02913997 -0.00428086 0.01895684 0.04072012 0.06113882 0.08032793 0.09839014 0.11541691 0.13149021 0.14668372 0.16106381 0.17469039 0.18761774 0.19989511 0.21156728 0.22267507 0.23325577 0.24334351 0.32290437 0.37608846 0.41343396 0.44059784 0.46087529 0.52537420 0.52692546 0.51857502 0.50836143 0.49821261 0.48865069 0.47979009 0.47161504 0.46406948 0.41143168 0.38012787 0.35835117 1.0029572 0.9600031 0.9202229 0.8832774 0.8488746 0.8167606 0.7867145 0.7585430 0.7300758 0.7071630 0.6836715 0.6614830 0.6404922 0.6206045 0.6017352 0.5838082 0.5667545 0.5505118 0.5350237 0.5202387 0.5061101 0.4925951 0.3839722 0.3082566 0.2524801 0.2097011 0.1758670 0.0286638 -0.0174929 -0.0393115 -0.0516478 -0.0593621 -0.0645039 -0.0680819 -0.0706470 -0.0725244 -0.0775400 -0.0765245 -0.0747534 -2.29831 -2.19920 -2.10785 -2.02340 -1.94511 -1.87231 -1.80447 -1. 74108 -1.68174 -1.62605 -1.57371 -1.52441 -1.47789 -1.43394 -1. 39234 -1. 35291 -1. 31548 -1.27991 -1.24606 -1. 21381 -1.18305 -1.15367 -0.919393 -0.757930 -0.639879 -0.549792 -0.478779 -0.170403 -0.072012 -0.024109 0.003927 0.022147 0.034817 0.044056 0.051031 0.056441 0.077296 0.081397 0.082055 1.1515 1.0752 1.0046 0.93906 0.87802 0.82104 0.76776 0.71782 0.67094 0.62684 0.58528 0.54607 0.50900 0.47392 0.44067 0.40912 0.37914 0.35062 0.32346 0.29756 0.27285 0.24925 0.06107 -0.06783 -0.16095 -0.23090 -0.28501 -0.49671 -0.54442 -0.55789 -0.56001 -0.55758 -0.55316 -0.54787 -0.54226 -0.53659 -0.48897 -0.45665 -0.43310 Source: J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liquids (New York: Wiley and Sons, 1954), 1114. 21

PAGE 33

22 Table 2-3. Reduced third virial coefficients and their derivatives for the Lennard-Jones 6-12 potential. T* C* c,• Cz* 0.70 -3.37664 28.68 -220. 0.75 -1. 79197 18.05 -140. 0.80 -0.84953 11.60 -92.1 0.85 -0.27657 7.561 -62.1 0.90 0.07650 4.953 -42.7 0.95 0.29509 3.234 -29.8 1.00 0.42966 2.078 -21.0 1.05 0.51080 1.292 -14.9 1.10 0.55762 0.7507 -10.6 1.15 0.58223 0.3760 -7.52 1.20 0.59240 0.1159 -5.29 1.25 0.59326 -0.0646 -3.66 1.30 0.58815 -0.1889 -2.46 1.35 0.57933 -0.2731 -1.57 1.40 0.56831 -0.3288 -0.910 1.45 0.55611 -0.3641 -0.420 1.50 0.54339 -0.3845 -0.050 1.55 0.53059 -0.3943 0.224 1.60 0.51803 -0.3963 0.427 1.65 0.50587 -0.3929 0.572 1.70 0.49425 -0.3858 0.680 1.75 0.48320 -0.3759 0.755 1.80 0.47277 -0.3643 0.806 1.85 0.46296 -0.3516 0.837 1.90 0.45376 -0.3382 0.854 1.95 0.44515 -0.3245 0.859 2.00 0.43710 -0.3109 0.856 2.10 0.42260 -0.2840 0.830 2.20 0.40999 -0.2588 0.794 . , 2.30 0.39900 -0.2355 0.749 2.40 0.38943 -0.2142 0.700 2.50 0.38108 -0.1950 0.651 2.60 0.37378 -0.1777 0.602 2.70 0.36737 -0.1621 0.557 2.80 0.36173 -0.1482 0.514 2.90 o. 35675 -0.1358 0.473 3.00 0.35234 -0.1247 0.439

PAGE 34

23 Table 2-3 continued. T* C* c,* C2* 3.10 0.34842 -0.1148 0.400 3.20 0.34491 -0.1060 0.369 3.30 0.34177 -0.09826 0.340 3.40 0.33894 -0.09133 0.313 3.50 0.33638 -0.08510 0.288 3.60 0.33407 -0.07963 0.266 3.70 0.33196 -0.07462 0.246 3.80 0.33002 -0.07024 0.227 3.90 0.32825 -0.06634 0.210 4.00 0.32662 -0.06286 0.194 4.10 0.32510 -0.05989 0.183 4.20 0.32369 -0.05709 0.169 4.30 0.32238 -0.05458 0.156 4.40 0.32115 -0.05237 0.145 4.50 0.32000 -0.05040 0.134 4.60 0.31891 -0.04865 0.125 4.70 0.31788 -0.04712 0.116 4.80 0.31690 -0.04579 0.108 4.90 0.31596 -0.04461 0.100 5.00 0.31508 -0.04359 0.0934 6.00 0.30771 -0.03893 0.0449 7.00 0.30166 -0.03989 0.0258 8.00 0.29618 -0.04231 0.0192 9.00 0.29103 -0.04529 0.0183 10.00 0.28610 -0.04825 0.0199 20.00 0.24643 -0.06437 0.0502 30.00 0.21954 -0.06753 0.0654 40.00 0.20012 -0.06714 0.0717 50.00 0.18529 -0.06566 0.0742 60.00 0.17347 -0.06388 0.0750 70.00 0.16376 -0.06203 0.0748 80.00 0.15560 -0.06025 0.0741 90.00 0.14860 -0.05857 0.0732 100.00 0.14251 -0.05700 0.0722 200.00 0.10679 -0.04599 0.0619 300.00 0.08943 -0.03970 0.0547 400.00 0.07862 -0.03551 0.0496 Source: J.O. Hirschfelder, C.F. Curtiss, and R.B. Bird, Molecular Theory of Gases and Liguids (New York: Wiley and Sons, 1954), 1116.

PAGE 35

24 Equation 2-23. The constant pressure and constant volume heat capacities, respectively, are given by and Equation 2-24. Equation 2-25. The constant temperature derivative is given by ( aP) i B --R 1+2-+3 a_! v V T Equation 2-26.

PAGE 36

25 A copy of the source code for the calculation of the speed of sound using the truncated virial equation of state for argon is given in Appendix c. The FFT was performed using the base 2 Cooley Tukey algorithm. 8 The base 2 algorithm was chosen to optimize the round off error. Although the base 3 algorithm has a more efficient Floating Point Operation (FLOP) count, 9 a digital computer, which also operates normally in base 2, preferentially accommodates calculations which use the base 2 number system. This then calls for the number of samples to be some integral power of 2. The operational bounds of the FFT are as follows: The magnitude of the frequency domain is fns no. of samples } lnE no. of frequencies i the Nyquist limit of maximum frequency is Equation 2-27. f _ sample rate. max 2 , Equation 2-28. 8 J.W. Cooley and J.W. Tukey, "An Algorithm for the Machine Calculation of Complex Fourier Series," Mathematical Computations 19 (April 1965): 297-301. 9 G.D. Bergland, "A Fast Fourier Transform Algorithm for Real-Valued Series," Communications of the ACM 11 (October 1968): 703-710.

PAGE 37

26 the period for sampling is (sample rate) Equation 2-29. the frequency resolution is Equation 2-30. and the FLOP count is Equation 2-31. The ST was performed using the following algorithm denom-21tgfres For i-1,~ C ratiod 1 enom wi-o For j-1,nr index integer (ratio*RJ) Wi Wi+aindex Equation 2-32. The maximum speed is limited by insuring that all ST frequencies of the roots exist within the FFT frequency domain

PAGE 38

C max 27 Equation 2-33. where nr = number of roots in the truncated ST basis set. Since Equation 2-34. then the resolution of the algorithm and magnitude of the sonic domain are, respectively, cmax cres---, I2max with a FLOP count of Equation 2-35. Equation 2-36. The theory of design is related to the construction of the apparatus in that building a very precisely known spherical cavity provides a geometry factor (g) that is siEply the radius of the sphere. Once the geometry factor is known and an ADC is chosen, the rest of the parameters are fixed. For a given buffer size and sample rate, the frequency range and resolution are set; and for a given set of roots, the sonic range and resolution are set. The

PAGE 39

28 selection of an ADC should consider the geometry of the apparatus as well as the sonic range of interest. In the next chapter the interfacing employing an ADC as well as the design of the apparatus are described.

PAGE 40

CHAPTER 3 EXPERIMENTAL The experimental design of this technique must address two principal problems, the computer interfacing of the data acquisition methods and the mechanical design of the apparatus. In a modern laboratory, data acquisition is no longer the tedious matter of turning dials, reading meters and logging data. Even the most impartial researcher tends to be inconsistent when manually measuring large amounts of data over long periods of time. The digital computer has taken over these more tedious tasks with much better speed and consistency. The first part of this chapter describes the interfacing of the computer involving data acquisition. In addition, as more tasks are controlled by the computer, more time remains for the scientist to evaluate results and implement design improvements. Specifically during this work, volume control was added for the first time. Knowing the exact volume of the apparatus has always been necessary, but this volume has in the past been fixed. Many experiments, however, would benefit from a direct measurement of the effect of volume change. For example, V 2 (aP;av)r could be substituted into Equation 2-22 along with the speed of sound at zero frequency (c 0 ) and the 29

PAGE 41

30 molecular weight (M) for a direct measurement of y. To this end, an extremely accurate variable volume control was designed for this apparatus. Interfacing Data collection utilizes five basic devices and two computers. The physical parameters measured are temperature, equilibrium pressure, amplitude acoustic pressure) and time. The first two of these measurements were made using standard laboratory instruments. Temperature is obtained by measuring the resistance of a platinum Resistance Temperature Device (RTD) using a Keithley 195a Digital Multi-Meter (DMM). The acquired resistance was updated and sent to the 8088 Central Processing Unit (CPU) along the National Instruments General Purpose Interface Bus (GPIB or IEEE) every 0.1 seconds. Resistance was then converted to temperature, in accordance with the RTD manufacturer's specifications, by the 8088 CPU. Pressure was read from a calibrated pressure sensitive Beckman Digital Strain Gauge in units of Pounds per Square Inch Absolute (PSIA). These readings were updated and sent to the CPU along the IEEE bus every 0.5 seconds. Amplitude and time were measured simultaneously by the WAAG II Analog to Digital Converter (ADC). The WAAG ADC has eight-bit resolution, a 32768 point buffer and multiple sample rates of 40MHz, 4MHz, 400kHz, 40kHz and 4kHz. The

PAGE 42

31 measurements are read and stored into the buffer sequentially. As a new measurement is added to the buffer, the oldest value is discarded. Once polled by the computer, the WAAG II dumps its entire buffer to the 8088 Random Access Memory (RAM) and then proceeds to acquire new data. The algorithm for the acquisition (source code provided in Appendix D) is as follows For i-1,n r-resistance rtd Ti-convert (r) P-zeadingfor strain guage_ Equation 3-1. amp-dump ADC buff er dump amp on hard drive dump T on hard drive dump Pon hard drive Using Equation 2-28, a sample rate of 40kHz leads to a maximum frequency (f~x> of 20 kHz. With a buffer size of 32768, the period of sampling (r) and frequency magnitude (nf) were found from Equations 2-29 and 2-27, respectively, to be 0.8192 seconds and 16384. The resulting frequency resolution (fres> from Equation 2-30 was approximately 1. 22 Hz. The excitation frequency is generated by a Hewlett Packard HP3325b function synthesizer. When the HP3325b is put into discrete sweep mode, it generates a frequency

PAGE 43

32 I \JAAG II Anolog to Digitol I 8088 Converter 1 Bus \ I Intel 8088 CPU Signal Frori Sphere I z ;u IEEE p (/) I .+ I I SRSlO Ar-,pli.Pier I 0 ::, f\J Locl-
PAGE 44

33 binary data are then sent to the DELL system 310 micro computer, the processing computer system. The binary format of the 8088 (8 bit) is different from the binary format of the DELL (32 bit), so the data must be translated to a common format. Since the data ranges in values from Oto 255, two hexadecimal numbers can contain one datum (for source code, see Appendix E). The binary data are transformed to hexadecimal by the DELL then further transformed into the frequency domain. Because the resulting large data set was limited to eight-bit resolution, a time correlation method was used to reduce floating point error. This method simply doubles the data set by adding the waveform to itself. It should be noted that this does not increase resolution by having a double basis set but simply lessens round off error of the computer; the frequency domain data are unaffected. The data are then dumped to the DELL hard drive. Data are then transformed to the sonic domain and dumped to the DELL hard drive in binary format (see Appendix B for source code). Three of the data sets--time domain 8088 binary format, frequency domain DELL binary format, and sonic domain DELL binary format--ar then stored, along with all the source code used in the process, on tape. The process was then repeated for different temperatures.

PAGE 45

Apparatus The apparatus consists of four basic parts--the spherical cavity, the volume-controlling bellows, the reciprocating pump and the Delta Design series 9000 environmental chamber. Spherical Cavity 34 The spherical cavity was constructed from two solid pieces of 303 stainless steel; a three-inch radius spherical cavity was cut from the center. Excess material was removed from the outer portion to lower the mass of the sphere thereby making it easier to control its temperature. To assure safe operation at the highest intended pressure (4000 PSIA), the minimum wall thickness was set at 6.4 mm (0.25 in). This dimension was based on a calculation of the bursting pressure in a spherical shell obtained by setting the force acting to stretch the walls equal to the tensile strength of the stainless steel. A safety factor of 4 was used. , The top portion of the sphere contains the two transducer mounts. A Macor insulated electrical feed through was mounted by employing a customized tapered ram seal with annealed copper gaskets. The inner threaded portion was used to align the transducer. The transducers were Piezoelectric lead-Zirconate lead-Titanate (PZT) bimorphs which have high motion sensitivity. They were

PAGE 46

35 placed as close as possible to the surface of the sphere in order to minimize departure from the sphericity. The two halves of the sphere were sealed together using an annealed copper gasket with a conflat type knife-edge seal and held together with two mild steel clamps as shown in Figure 3-2. Inlet ports for the gas were constructed on the top and bottom of the spherical cavity. The entire assembly was pressure tested to 3500 PSIA at room temperature. Pump The pump chamber (Figure 3-3) was constructed of a 304 stainless steel tube, 13 inches long with 1.250 inch outside diameter and 0.148 inch wall. The top portion was sealed by brazing a 304 stainless seal plug 1/2 inch thick with a 1/16 inch bore. The bottom portion was sealed by a 304 stainless steel plate with an annealed copper gasket on a conflat knife-edge seal. Seven magnetic field coils aligned concentrically on the tube create the pumping action by successively attracting a magnetic piston free to move inside the stainless steel tube. The bottom two coils are switched on remotely; the third coil from the bottom is activated as the bottom coil is turned off. This action is repeated until the magnetic piston reaches the top of the tube. Then a reversed action moves the magnetic piston to the bottom of the tube to complete one pumping cycle. Doubled-pumping action is created by use of four one-way

PAGE 47

Figure 3-2. Spherical cavity sections and clamping flanges.

PAGE 48

37 valves placed outside the assembly. The strength of the magnetic field as well as the frequency of field oscillation are adjusted remotely. At the highest field strength and frequency of oscillation, a pumping speed of 200 mL per second at room temperature and pressure was recorded. An aluminum mount was constructed to hold the pump in an upright position. The Bellows The addition of the bellows assembly brings on-line volume or density control to this technology for the first time. The collapsible bellows, constructed of 0.005 inch thick 304 stainless steel, was welded to a 1 inch thick plate which had a 1/4 inch hole bored horizontally to connect the adjustable volume of the bellows to the spherical cavity. The outer portion of the bellows is contained in a chamber that was constructed from a solid piece of stainless steel and sealed to the lower plate with a triangular annealed copper seal 1 The volume of the outer chamber was isolated from the spherical cavity and maintained at pressures slightly below (approximately 20 PSI) that of the spherical cavity. This then maintained the bellows in an expanded position. The volume of the bellows was controlled by a threaded ram bolted to the top of the outer chamber. Technology developed by S.O. Colgate in 1990.

PAGE 49

MAGNETIC Figure 3-3. Pump assembly. w 00

PAGE 50

Figure 3-4. The bellows and bellows chamber. w \0

PAGE 51

40 The position of the ram was externally controlled by a customized micrometer to within 0.001 inch. The pressure was monitored by two Sensotec pressure transducers. The pressure transducers were not able to operate in the harsh conditions of the environmental chamber so they were placed outside the chamber and connected to the apparatus by two stainless steel capillary tubes. These capillary tubes prevented a large volume of the sample from being outside the temperature-controlled volume. The assembled apparatus was connected as shown in Figure 3-5. The completely assembled apparatus was then placed into the environmental chamber. The environmental chamber operates over the temperature range of 150C to -170C and is controlled by the manufacturer's programming language sent along the IEEE bus. The assembled apparatus was pressure tested up to 2800 PSIA. The calibrated apparatus presently requires that only one parameter, the volume, be monitored and controlled by the user. The other three state variables, temperature, pressure and speed of sound, are acquired automatically by the computer. Typical results are displayed in the next chapter.

PAGE 52

Signo.l Frol"'I Ro.ck Signal To Rock PUMP BELLO\./S Figure 3-5. Apparatus assembly.

PAGE 53

CHAPTER 4 DATA AND RESULTS The data and plots resulting from this experiment are discussed in three groups. This includes a theoretical computer synthesized set of data, an experimentally acquired set of data for argon at low temperatures and then a discussion of argon at high temperatures. Figure 4-1 depicts a theoretical waveform based on using the first 84 resonances in a spherical cavity (radius of 3 inches) filled with a fluid medium which propagates sound at 350 m/s. Figure 4-2 depicts a similar theoretical waveform again using the first 84 resonances in the same cavity but now containing a fluid medium which propagates a speed of sound at two speeds, 350 m/s and 150 m/s. These two waveforms simulate those which would be acquired by the ADC under ideal conditions. Figure 4-3 depicts the FFT of the waveform shown in Figure 4-1 while Figure 4-4 depicts the FFT of the waveform shown in Figure 4-2. Figure 4-5 displays the final results of the ST of the FFT described in Figure 4-3 and Figure 4-6 displays the results of the ST of the FFT in Figure 4-4. These six figures portray the chronological order of acquisition and calculation for the simulated set of data. 42

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43 Note that ST transforms shown in Figures 4-5 and 4-6 correctly recover the input sonic speeds (350 m/s and 150 m/s). Figure 4-7 is an experimentally acquired waveform of the resonances of argon at a low temperature (-31.56C) in a spherical cavity with a 3.000 inch radius. The experimental conditions are given in Table 4-1. An expanded view of a section of Figure 4-7 is given in Figure 4-8 to show the resolution with which the waveform is acquired in other regions. The FFT of the waveform of Figure 4-7 is shown in Figure 4-9 and the relevant physical and computational parameters are given in Table 4-2. As seen in Figure 4-9, the baseline is not very stable in the region of 10,000 Hz. An expanded view of this region is shown in Figure 4-10. Several STs were performed on the data in Figure 4-9 using different numbers of roots. The resulting ST weights employing the first 21 roots are shown in Figure 4-11 with an expanded view of the region that contains the known speed of sound in argon shown in Figure 4-12. The experimental and computational parameters are given in Table 4-3. Four STs were performed on the same FFT data in which only the number of roots used in the ST were changed. The results are shown in Figures 4-11 through 4-18 while parameters are listed in Tables 4-3 through 4-6. These results reveal the important features of the technique; they are described later in this chapter.

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44 The same experiment was performed at a higher temperature (50.93C). Figure 4-19 shows the experimentally acquired waveform with the experimental and computational parameters given in Table 4-7. The expanded view shown in Figure 4-20 indicates that more of the resolution of the ADC was utilized. The baseline of the FFT shown in Figure 4-21 is considerably better than that of the low temperature experiment (Figure 4-9). The expanded view shown in Figure 4-22 indicates that the sharp acoustic resonances are larger than the perturbed baseline and are better resolved than those in Figure 4-10. The four STs using the different sets of basis functions at this temperature are shown in Figures 4-23 through 4-30 along with the corresponding parameters in Tables 4-9 through 4-12. Interpretations of the data and graphs presented above are organized as follows. The first section discusses the characteristics of the time domain signal and how it deviates from ideality. The second discusses the characteristics of the frequency domain while the third section examines the sonic domain and the influence of varying the number of roots (nr) In addition, the volume calibration data are included at the end of the chapter. Time Domain Plots Figures 4-1 and 4-2 show two computer simulated ADC signals. Figure 4-1 was generated from the sum of 84

PAGE 56

45 sinewaves with frequencies generated from Equation 2-11 for a sonic speed (c) of 350 m/s, a geometric factor (g) of 3 inches and assuming equal amplitudes of the resonances. Figure 4-2 was generated from two sets of 84 sinewaves--one for c = 150 m/s, the other for c = 350 m/s. Both waveforms are similar in that they show no beat patterns or interference. Figure 4-7 shows a low temperature ADC signal where the resolution is quite low except for when the excitation frequency corresponds closely to a resonance frequency. This is an indication that the resonances are decaying rapidly. Figure 4-19 shows a high temperature ADC signal where the resolution is better since clearly the resonances are not decaying as rapidly as in the low temperature case. In other words, Figure 4-19 is approaching the characteristic of Figures 4-1 and 4-2. Ideally, an evenly distributed waveform uses the entire resolution of the ADC as was seen in the expanded Figures 48 and 4-20; that is not the case here. The resolution acquired is less than half the ADC resolution. Frequency Domain Plots The baselines of the frequency domain plots in Figures 4-3 and 4-4 indicate that the amplitudes are perturbed due to floating point calculation error. The low temperature frequency domain plot in Figure 4-9 shows an extremely large broad peak in the center of the frequency spectrum. The

PAGE 57

46 expanded view shown in Figure 4-10, however, shows the sharp gas resonances imposed on top of this large peak. As the temperature is increased and the decaying of the resonances decreases, the broad peak decreases in size as well as frequency. All of these characteristics indicate that this portion of the signal is associated with vibrations of a solid, perhaps along the walls of the sphere or in the transducers themselves. Sonic Domain Plots The two sonic domain plots in Figures 4-5 and 4-6 indicate that the amplitude perturbations of the frequency domain do not affect the amplitudes in the sonic domain, but that much of the floating point calculation noise is carried through. The plots do show that the ST will resolve multiple speeds of sound if present in the data, although all of the low and high temperature plots shown in the remaining figures have considerably different baselines. The baselines are attributed to the reproducible apparatus frequencies which are not due to normal mode vibrations of the cavity fluid. These are called nonacoustic frequencies. The reason that they are identifiable as being nonacoustic is that they do not move across the baseline as the basis set of roots is changed. The four low temperature figures (4-11 to 4-18) as well as the four high temperature figures (4-19 to 4-30) show that the baseline maps predominately

PAGE 58

47 with respect to index and not speed. Only resonances that are acoustic will be speed dependent and not index dependent. As the absorption of energy by the gas increases in the high temperature spectra, the amplitude of the speed of sound begins to predominate as would be expected. It should be recalled here that the time domain signal is the same for all sonic domain plots of a given temperature; the only thing that was changed was the number roots used to form the basis. In addition, the size of the basis did not seem to have a large effect on the resolution. It was not until nr = 63 that the resolution saw any significant increase, but this could be due to where the resonance was with respect to the noise and does not necessarily reflect an increase in gain. The speeds of sound in argon calculated from the truncated virial equation (see Appendix C) are 291.644 m/s for the low temperature data(@ -31.56C and 870.5 PSIA) and 350.245 m/s for the high temperature data(@ 50.93C and 1285.5 PSIA). The ST speeds of sound are given in Tables 41 through 4-12. The ST basis assumes a perfect sphere with a radius of 3 inches. Even using this simplification, the ST method gives sonic speeds within less than 0.5% deviation from the calculated values. The other three physical measurements (temperature, pressure and volume) employed standard techniques and were calibrated as discussed in the next section.

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48 Volume and Pressure Calibration The volume and pressure calibration required two standard devices. For the pressure calibration, a Ruska Model 2465 Dead Weight Pressure Gauge was used. The accuracy of the Ruska gauge was 0.001 PSIA with a range from 0.000 PSIA to 650.000 PSIA. For the volume calibration, the Ruska gauge as well as a Ruska Model 25652 volumetric pump was used. The accuracy of the Ruska pump was 0.01 mL. The actual calibration of the Sensotec pressure transducers was the three point calibration described in the Beckman 620 owner's manual. The three pressures chosen were 0.000 PSIA, 320.000 PSIA and 640.000 PSIA. Since the accuracy of the Sensotec pressure transducers was only 0.5 PSIA, the accuracy of the three calibration pressures was more than necessary. The volume calibration involved taking several volume ahd pressure measurements and employing the ideal gas equation to deduce the absolute volume as shown below PoVo Pi(Vo + ..1Vi) Pi..1 Vi p . --Vo V:-.1 Po o Po Equation 4-1. where P 0 is the initial pressure and V 0 is the total volume of the apparatus at that pressure. Pi and AVi are measured by the Ruska gauge and pump, respectively. The outside

PAGE 60

49 volume of the calibration equipment was found from the data in Figure 4-31. The total volume of the apparatus as well as the calibration equipment was then found from the data in Figure 4-32. The volumes were all compared to a common point on the Ruska pump since the pump has its own volume that must be considered. The outside volume of the calibration equipment was then subtracted from the combined total to obtain the true total volume of the apparatus. Once the total volume was found, the change in volume due to the bellows from the same common point was found from the data in Figure 4-33. The change in volume with respect to the change in length of the external adjustment ram was observed to correlate best to a second order polynomial fit. The result {Table 4-15) was an expression for the total volume of the apparatus as a function of the external ram setting. The uncertainty in a total volume for a given ram setting was 0.01%. The range of the total volume of the apparatus was from 2350.00 to 2878.00 mL.

PAGE 61

0 "O a :.= t 30 20 10 0 -10 -20 0 0.1 0.2 0.3 O.S 0.6 0. 7 o.B 0.9 Time s Figure 4-1. Theoretical ADC signal for 350 m/s of speed of sound. 0 "O a :.= t 30 20 10 0 -10 -20 30 0 0.1 0.2 0.3 0.4 o.s 0.6 0.7 0.8 0.9 Time s Figure 4-2. Theoretical ADC signal for 150 m/s and 350 m/s speeds of sound. 50

PAGE 62

1.40do' 1.20xlo' ---.. 1.
PAGE 63

1.80ua4 1 . 60:da4 1 . 40:tla4 C) 1.20:da4 't:I L OO:do' t 8000 6000 4000 2000 0 0 ... -. -. .. . . . . . ' . . . . . . . . '---' . . . ' . . ' . ' ' . ----------' ' . ' ' . . . . ' ' . . ' ' --,--,---,--.. . ... . .... , .......... . . ' ' ' ' . ' ' . ' . ' ' . ... . ' . ' . . . ' ' ' . ' ' ' ' . ' ' ' ' ' ' ' ' ' ---. ---, -----. --' ' ' ---------, ,----SO 100 150 200 250 300 350 400 S eed of Sound Figure 4-5. ST of FFT of theoretical ADC si nal for 350 ms. 1.80ua4 1 .60xlo' . ' . . .. .. ...... . .. . ... . . .. .. .. . .... ,,, _____ , _ __ _ _ . . . . . . ' ' ' ' t o I O I L40:tla4 . ' . . --------------J ..... , . . . .. 0 t I o I . . . . . . . . . . . . . . C) 1 .20:da4 't:I . . . . . . . ' ' . . ' ' ' ' ' . ' ' ' ::s :E 1. 00:do' t 8000 ' . . . . ' . . ' . --.---. ----.--,----, --' . . . . -.. . .. . . . .. . . ' . .. . . . ' ' . . . I O O O 0 6000 I O O O 0 I O O I 0 .. ..... . . J . . . ... ' ' . . . ' . . ' . . . . . . ' . . . . ,4()()() . : : . . : :: . ' . . . 0 I t t . . ' . 2000 ' ' 0 0 50 100 150 200 250 300 350 400 S eed o f Sound Figure 4-6. ST of FFT of theo r etical ADC signal for 150 m/s and 350 m/s speeds of sound . 52

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250 . ... .. ,. .. . .. ' 200 . . . . . .. .. . . . . . .. . r;I.I ..... a ::> u 150 0 100 .. . .. ... ! . . . . .a J: so . . .. .. .. ... .... .. .... .. . ' 0 0 1.00x1<>4 2.00x1 <>4 3.00xl<>4 Time = X 40000 s Figure 4-7. ADC signal of argon at low temperature. 160 ~-----~ i,o 1 IJD l lY 100 ...... . . . . ...... . . . . 90 UOalO' I.JOalO' L411110' 1-'0IIO' UQi.10' Time X 40000 s Figure 4-8. Expanded section of Figure 4-7. Table 4-1. Low temperature time domain parameters of argon. T = -31.56 .10C P = 870.5 .5 PSIA ns = 32768 Sample rate= 40 kHz 53

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5.00x1o' 4.00xlo' .................. r .......... ... . . . .. .. .. .... . .. 1 .. . .. , ... u ] 3.00xlo' . . ........... ...... ........ .. .. .. . . •"'"4 l 2.00do' . . --------------. . 1.00xlo' 0 0 4000 8000 1.60xllr Frequency = X/0.8192 Hz Figure 4-9. FFT of ADC signal of argon at low temperature. 5.lllud ~-------------, 4Jl0rld UJCaJd 5.lllud •:-: ---. . . .. . . , . . ........... . ...... . . . . . . . . . .. . .. . . ... . ' . . --. . . . o 6500 1IDl 7500 llllO 1:5(1) ,cm 9500 UJCaJd Frequency X/0.8192 Hz. Figure 4-10. Expanded section of Figure 4-9. Table 4-2. Low temperature frequency domain parameters of argon. T = -31.56 .10C P = 870.5 .5 PSIA nf = 16384 fmax = 20 kHz 54

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7.0Cbtlo' 6.0Cbtlo' 5,0Cbtlo' .g ,a :-= A. 3.00zlo' t; 2.0Cbtlo' 1.0Cbtlo' 0 ' ' ' . . . -. . .. .. .... ' . ' . . .. . . .... ' ' ' ... ..... .. .. ...... ... ...... ' . ' ... ... J ' ' ' ' l . ... . ; I I I I .. ............ .. .... , ....... , .. . I O I I I O I -----------. -----1 I I I I I I Speed of Sound /(m/s) Figure 4-11. First ST of argon at low temperature. JJJQ,Jlf ~--------~ 2.80ull' liOLIII' -8 2.,1(1,Jlf ;;220dl' f lJXaj .. !;; UOollf UOull' UOull' Figure 4-12. Expanded section of Figure 4-11. Table 4-3. First sonic domain parameters of argon at low temperature. T = -31.56 .lQoC P = 870.5 .5 PSIA c = 290.91 .05 m/s cmax = 788.532 m/s Note: See Equations 2-33, 2-35. 55

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7.00ll106 15.00x106 5.00x106 u '0 .a 4 . 00x106 ;:::2 Q, 3.00x106 t; 2.00x106 1..00x106 0 0 . . . . .. ... .. -. .... .. . i ... .. . i .... .. .. ' ' ..... . .. .. ...... . . . .. ... ... ..... .. .. . . . . . . . ... . . .. , ...... ' .... f I O I I .. .. ......... .. .. ...... ... ... .. .. .. .. .. .. .... .. I I I I I 100 200 300 400 500 600 Speed of Sound /(m/s) Figure 4-13. Second ST of argon at low temperature. 7.lXl,J~ ~----~ .!.OlloJ~ Figure 4-14. Expanded section of Figure 4-13. Table 4-4. Second sonic domain parameters of argon at low temperature. T = -31.56 .10C P = 870.5 .5 PSIA c = 290.96 .03 m/s c~x = 556.016 m/s Note: See Equations 2-33, 2-35. 56

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7.00Xld' 6.00xld' 5.00xld' u 't, .a 4'.DOxld' ;.::l Q. 3.00xld' 2.00x1d' 1.00xld' 0 I I I I ..... , .. . -,. .. I I I I ..... . . . . .... I I I I .. ....... .I ... .. I O I I I I I ... r ' ....... -.. ...... ..... I I I O t I I I .................................. _ ............................... .. I I t I I t I I Speed of Sound /(m/s) Figure 4-15. Third ST of argon at low temperature. Figure 4-16. Expanded section of Figure 4-15. Table 4-5. Third sonic domain parameters of argon at low temperature. T = -31.56 .lOoC P = 870.5 .5 PSIA C = 290.962 .027 m/s c~x = 443.741 m/s Note: See Equations 2-33, 2-35. 57

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8.00J(lo' 7.00Xto' 6.00xl.O" .g 5.00xtO" t 4.00xlO" f-1 3.00xtO" tll 2.00xlO" l.OOllO" 0 0 ... ' ... _, ,I " . . . J,. J L I t I I ~. --... _._ J ... ..... &. I I I I I I I 50 100 150 200 250 300 350 400 Speed of Sound / (m/s) Figure 4-17. Fourth ST of argon at low temperature. 7.AJIIIJII' ~----------, -86.00olll' r-t;'-Ollu .. :•: i .. 4.IIOdll' .........,~=.......,..........._ .....,_~~=..,.,. :ml :119 Z90 2'1 2':I 293 2M ffl 2'6 '1!TI M Figure 4-18. Expanded section of Figure 4-17. Table 4-6. Fourth sonic domain parameters of argon at low temperature. T = -31.56 .lOoC P = 870.5 .5 PSIA C = 290.962 .023 m/s c~x = 384.545 m/s Note: See Equations 2-33, 2-35. 58

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250 ... .... .. .. .. ... -,i .. .. 200 0 0 1.00xlD4 200xla4 3.00xlc4 Time = X/40000 s Figure 4-19. ADC signal of argon at high temperature. 160 r---------~ 150 140 IO ~ 10' ,............~ UOll ~ O' ~IACkl ............. rf ,..........._ ~l-'Clll ~ O' ..,._._._~ UOl ............,_ 10' ~ Tune X/~ s Figure 4-20. Expanded section of Figure 4-19. Table 4-7. High temperature time domain parameters of argon. T = 50.93 .06oC P = 1285.5 .8 PSIA n 5 = 32768 Sample rate= 40 kHz 59

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3.00xln8 2.50xle>6 C) 2.00x1e>6 "C a t 1.50xle>6 1.00xle>6 5.00xlo' 0 0 I I t I -------.. .. ......... . o I O I .. r r "' ....... .. .. ... 1. .... ... 1. .. 4000 8000 1.20x104 Frequency = X/0.8192 Hz Figure 4-21. FFT of ADC signal of argon at high temperature. tAOa . UI' ---:--:-. .... .. . . . 1. , . . ' ' ' ' ' ' Frequency X/0 . 8192 1h Figure 4-22. Expanded section of Figure 4-21. Table 4-8. High temperature frequency domain parameters of argon. T = 50.93 .06oC P = 1285.5 .8 PSIA nf = 16384 fmax = 20 kHz 60

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5.00x106 4.50xl06 4.00xlo' 3.50xl06 u ] 3.00xlo' = t2.50xl06 200x1ot 1.50x106 LOOxlo' 5.00xlo' 0 0 . . ' . .. . ., . .. .. , . . ............. .. . . .. .. .. ... ....... .. ... -.. ... ' ' ' .. . .. ..... ... -....... .. ... ,J ....... .. \. ... I I I I I I I 100 200 300 400 500 600 700 800 Speed of Sound / (m/s) Figure 4-23. First ST of argon at high temperature. l-Olldll' Figure 4-24. Expanded section of Figure 4-23. Table 4-9. First sonic domain parameters of argon at high temperature. T = 50.93 .06oC P = 1285.5 .8 PSIA c = 348.90 .05 m/s cmax = 788.532 m/s Note: See Equations 2-33, 2-35. 61

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4.50x1D6 4.00xlo' 0 3.SOxlo' "t:, .a r-OOdO' t; 2.SOxlo' 2.00x1D6 1.50xlD6 342 I I I O I ..... ,.. ...... , .. .. -. . . .. . ; .. .. .... . ' . . . . . . ................... . . . . .......... .. .. . . . ' ' . . .. .. .. -... .. .. J .. ... . . . . . . . .... ........... _,_ .. 4 . . . 344 346 348 350 352 354 S eed of Sound m s Figure 4-25. Second ST of argon at high temperature. UOllo' ,---------~ 2.00alo' Figure 4-26. Expanded section of Figure 4-25. Table 4-10. Second sonic domain parameters of argon at high temperature. T = 50.93 .06oC P = 1285.5 .8 PSIA c = 348.79 .03 m/s c~x = 556.016 m/s Note: See Equations 2-33, 2-35. 62

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15.00l:106 5.00l:106 I I I I I I -, -,,r i 0 4.00l:106 0 0 I t I I ---------.. .. ----1 I I I I I l ,3.00t106 ., ... ...... .. , .. ... .... &. .. .. ., .... I I I t ti; 2.00l:106 I O I I t 0 .. , .. .. ... ... . .. .. , . . ...... .. " .. ... , 1.00t106 0 0 Speed of Sound / (m/s) Figure 4-27. Third ST of argon at high temperature. lllllr ..------------, !.CIQ,I .. <.!!Odo' -8 S4JIOLlr JllkJ .. . . . ; .. . .. . t; l.llOLlo' Figure 4-28. Expanded section of Figure 4-27. Table 4-11. Third sonic domain parameters of argon at high temperature. T = 50.93 .06C P = 1285.5 .8 PSIA C = 348.806 .027 m/s cmax = 443.741 m/s Note: See Equations 2-33, 2-35. 63

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6.00x106 .s.00x106 u 4.00x106 ] ;::t ,3.00xla6 t; 200x106 1.00x106 0 0 I I I I I .. ... ... , -. ... ..... i . .. .. .. ' .. .. ' ...... .... .. .. ! .... .. .. I I I I I I so 100 150 200 250 300 3SO 400 Speed of Sound / (m/s) Figure 4-29. Fourth ST of argon at high temperature. 2Jl0tlei' . . . . . . . . ,., * 347 ,.. ,., 15 1 m l5J 154 m Figure 4-30. Expanded section of Figure 4-29. Table 4-12. Fourth sonic domain parameters of argon at high temperature. T = 50.93 .06oC P = 1285.5 .8 PSIA C = 348.797 .023 m/s c~x = 384.545 m/s Note: See Equations 2-33, 2-35. 64

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60 so 40 .......... 0 .......... 30 > 20 Q 10 0 0.7 0.75 0.8 0.85 P Po 0.9 0.95 Figure 4-31. Outside volume calibration. Table 4-13. Outside volume calibration. slope= -235.074 mL intercept= 235.0671 mL V = 235.071 .007 mL V 250 = 100. 953 007 mL correlation coefficient= 0.9999945 65

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600 500 400 ........ 0 ........ 300 -P-4 > 200 Cl 100 0 0.75 0.8 0.85 0.9 0.95 P Po Figure 4-32. Total volume of apparatus. Table 4-14. Total volume of apparatus. slope= -2498.55 mL intercept= 2498.517 mL V = 2498.54 .03 mL V 250 = 2 4 6 3 8 2 0 3 mL Vt= 2362.87 .03 mL at L = .250 inches correlation coefficient= .999999 66

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600 500 400 -... 300 > Q 200 100 0 Len in Figure 4-33. Bellows calibration plot. Table 4-15. Bellows volume calibration. First order coefficient= 251.60 0.25 mL/in Second order coefficient= -8.25 0.10 mL/in 2 Vt= 2300.19 + 251.60 L 8.25 L 2 Correlation coefficient= .999999 67

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Table 4-16. Compiled results of sonic speeds of argon at low and high temperatures for various roots. Speed (m/s) 1 Low 290.91 .05 290.96 .03 290.962 .027 290.962 .023 No. of Roots Other Parameters Temperature21 T = -31.56 .10C 42 P = 870.5 .5 PSIA 63 LJ 6-12 speed of sound 84 c = 291.644 m/s % difference= 0.2 68 High 348.90 .05 Temperature348.79 .03 348.806 .027 348.797 .023 21 T = 50.93 .06C 42 P = 1285.5 .8 PSIA 63 LJ 6-12 speed of sound 84 c = 350.245 m/s % difference= 0.4

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CHAPTER 5 CONCLUSION From the results in Figures 4-5 and 4-6, one sees that the ST can correctly resolve the speed of sound or speeds of sound in an idealized spherical acoustic cavity. The identiiable speed of sound in Figure 4-5 is 350.000 m/s which is precisely the speed used to develop the time domain signal. In Figure 4-6, the identifiable speeds of sound were 150.000 m/s and 350.000 m/s which also matched precisely the speeds used to calculate the time domain signal. As discussed previously in the introduction, this transform assumes that there is no frequency dependence on the speed of sound. The speed that has thermodynamic significance as seen in Equation 2-22 is the speed of sound at zero frequency. This speed can be calculated by using the speed from the ST to identify the frequencies. Once these are identified and measured precisely, the speed at each frequency can be calculated by rearrangement of Equation 2-10 and a plot of speed vs. frequency can be developed. Extrapolation of this data to zero frequency will reveal the thermodynamically significant speed of sound at zero frequency. 69

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70 This still does not account for the precondensation effects with the walls of the cavity. 1 Precondensation effects will also show up in the frequency domain. The actual magnitude of this effect can be very accurately investigated once the data are acquired. Although, the most accurate method of determining the speed of sound at zero frequency is still not certain, the present method is the first step to complete automation of this measurement. Even with no analysis or calibration (see Table 4-16), the ST speed of sound obtained from measurements on argon is within 0.5% of the calculated thermodynamic speed of sound at zero frequency. The ST baseline for the experimental data had considerable noise due to the assumption made in Equation 212 that all frequencies detected by the FFT are acoustic. Clearly the baseline represents nonacoustic resonances of some kind. There are, of course, several ways to reduce this problem by increasing the gain of the acoustic frequencies. One way would involve isolating the transducers from any contact with the cavity and acoustically insulating the outer portion of the sphere. Another method would be to excite the acoustic frequencies selectively; or, in other words, perform an inverse ST to produce an arbitrary waveform that could be sent to the 1 Mehl and Holdover, "Precondensation Phenomena in Acoustic Measurements."

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71 driving transducer by a Digital to Analog Converter (DAC). By coupling the ADC signal to the waveform produced by the DAC, a sonic sweep could be performed where the arbitrary wave is swept over a sonic range and the sonic speed spectrum recorded. This would be analogous to the frequency swept method used in the past. Even without resorting to the use of methods to enhance the baseline of the sonic spectrum, it is apparent from consideration of Figures 4-23 through 4-30 that the speed of sound can be expeditiously deduced with this technique. The time of acquisition is approximately 10 seconds with the equipment used in this experiment; thus, technically this is not a real time measurement. Bear in mind, however, that the acquisition was performed with an 8088 CPU (8 bit) computer. If a larger and faster computer were used, such as an 80386 (32 bit) computer, the total time of processing would be slightly more than the time of acquisition or approximately 1 second. By decreasing the sonic resolution, even shorter acquisition times could be achieved. These would then be comparable to the acquisition times of temperature and pressure measurement. For the ADC used in this experiment with an 84 root basis, a sonic resolution of 0~023 m/s or a full scale resolution of 6 ppm was achieved. This far exceeds state-of-the-art pressure resolution and is comparable to the resolution of high quality temperature measurements.

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72 The basic device developed here has many potential applications. For example, it has recently been discovered that a single fluid can propagate sound at more than one speed. 2 The technique used for detecting this unexpected phenomenon did not involve a resonance behavior, but rather the traverse time of flight of pressure-pulse generated waves. If the phenomenon of multiple speeds of sound in a fluid is well-founded, there must be observable resonance effects corresponding to those speeds. The theoretical results in Figure 4-6 show that the ST method would be well suited for investigating this phenomenon. Also, with sensitive enough detection such that no external excitation is needed, a similar device could simply listen to the noise already in a cavity and from that deduce the speed of sound. For a pipeline in which the fluid is energized by the pumping action, one could detect the speed of sound in a passing fluid by simply listening to the fluid. The fluid motion leads to an apparent separation of sonic speed via the Doppler effect and a ST determination of that separation would lead to a direct measurement of the flow velocity. Since fluid density may be related to the sonic speed, the mass flow rate could also be determined. Combining these with pressure and temperature measurements, 2 J. Bosse, G. Jacucci, M. Ronchetti, and W. Schirmacher, "Fast sound in Two-Component Liquids" Physical Review Letters 57 (December 1986): 3277.

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73 valuable information about flowing streams could be obtained by passive noninvasive processes. Representatives of the petroleum and pipeline industries have already shown a strong interest in this new art. Negotiations are presently underway to cooperate with these industries in further development of the technique. Measuring critical phenomena of fluids with sonic techniques is difficult when using a frequency tracking method. When the fluid is close to the critical temperature and density, the mixture approaches a chaotic state and the speed of sound approaches zero. As this occurs, the spectrum collapses and bunches all the frequencies closer together while the speed of sound and resonance frequency are dropping rapidly. It is easy to lose the frequency being tracked since it is moving very rapidly. With the ST, all frequencies would be measured for a given basis set of roots and then transformed automatically to the sonic domain providing that resonances can be detected. Another area with good potential for the utilization of a sonic speed meter is that of reaction kinetics. The sonic speed is highly sensitive to all changes in the structure or composition of a material system and thus could be used to monitor the progress of a chemical or physical transformation. The chemical industry has again expressed interest in this newly evolving technology as a possible

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means of remotely following the kinetics of a complex polymerization reaction in large batch reactor. 74 The applications that have been mentioned thus far are only a few of the possibilities for this new technique. To list all potential possibilities would be like listing all of the applications of a thermometer. The most important result of this study is the application of an ideal numerical model of a physical phenomena to a real experiment. The data of many phenomena can be transferred from an arbitrary domain to a domain that communicates more information. For example, these same principles could relate molecular geometries to vibrational spectra or trajectories to ion cyclotron resonance spectra. Any phenomenon that has an ideal or reference state model could be transformed to an ideal domain. The frequency domain spectra are necessary for investigation of fine structure. In fact, the transform to an ideal domain should demonstrate these deviations readily. The availability of fast computational processes has facilitated this blend of theory and experiment on a numerical level. since modern modeling techniques generally involved numerical solutions, it is natural that the communication of these theories to experiments should also be numerical. This experiment is representative of the current influence of numerical mathematics on scientific research, which will significantly change the perceptions

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75 and interpretations of future physical experiments. In the future, numerical mathematics should not be avoided in applications of experimental science, but rather employed vigorously throughout all of experimental science.

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APPENDIX A FAST FOURIER TRANSFORM SOURCE CODE IMPLICIT REAL*8(A-H,O-Z) IMPLICIT INTEGER*4 (I-N) INTEGER*2 HEX(256),HIGH,LOW,TAF(16384) CHARACTER*l A(64) CHARACTER*20 FILENAME,FILEOUT DIMENSION XR(65536),XI(65536) COMMON XMAX,PI,NU,NDP,NDPDIV2,NDPDIV4,NDPMIN1,IND C USE FFT TRANSFORM WITH REAL DATA IN XR ARRAY PI=2.0*ACOS(0.0) NU=16 NDP=2**NU NREAD=1024 NDPDIV2=NDP/2 NDPDIV4=NDP/4 NDPMINl=NDP-1 IND=-1 CALL HEXGET(HEX) C START TIME AVG DO 20 IF=l00,599 WRITE(FILENAME,'(A8,I3,A4) ') 'E:\\HEX\\F',IF,'.OUT' OPEN(l0,FILE=FILENAME,STATUS='OLD') READ(l0,*) T,P DO 3 0 I=l, NREAD READ ( 10 , 3 0 0 ) ( A ( K) , K = 1 , 6 4 ) 300 FORMAT(64Al) DO 50 K=2,64,2 HIGH=HEX(ICHAR(A(K-1)))*16 LOW=HEX(ICHAR(A(K))) XR((I-1)*32+K/2)=FLOAT(HIGH+LOW) 50 CONTINUE 30 CONTINUE CLOSE(l0) DO 70 I=l,NDPDIV2 XR(NDPDIV2+I)=XR(I) 70 CONTINUE CALL BASELINE(XR,XI) CALL BLACK(XR) CALL FFT(XR,XI) XMAX=0.0 DO 41 L=l,400 XR(L)=0 41 CONTINUE 76

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DO 40 L=101,NDPDIV2 XMAX=AMAXl (XMAX,XR(L)) 40 CONTINUE DO 60 L=2,NDPDIV2,2 TAF(L/2)=INT((XR(L)+XR(L-1))/XMAX*8192) 60 CONTINUE WRITE(FILEOUT, 1 (A7,I3,A4) ') 'E:\\FD\\F' ,IF, 1 .FFT' WRITE(*,200) FILEOUT OPEN(l0,FILE=FILEOUT,FORM='UNFORMATTED') WRITE(l0) T,P WRITE(l0) TAF CLOSE(l0) 20 CONTINUE 200 FORMAT(A) END 77 C*********************************************************** C234567 SUBROUTINE BASELINE(XR,XI) IMPLICIT REAL*8(A-H,O-Z) IMPLICIT INTEGER*4 (I-N) DIMENSION XR(l),XI(l) COMMON XMAX,PI,NU,NDP,NDPDIV2,NDPDIV4,NDPMIN1,IND ARX = 0.0 DO 100 I= 1, NOP ARX = ARX + XR(I) 100 CONTINUE ARX = ARX / FLOAT(NDP) DO 200 I= 1,NDP XR(I) = XR(I) ARX 200 CONTINUE DO 300 I=l,NDP XI(I)=0.0 300 CONTINUE RETURN END C********************************************************* SUBROUTINE BLACK(XR) IMPLICIT REAL*8(A-H,O-Z) DIMENSION XR(l) COMMON XMAX,PI,NU,NDP,NDPDIV2,NDPDIV4,NDPMIN1,IND DO 100 I= 1,NDP C = 2.0*PI*FLOAT(I)/FLOAT(NDP) A= 0.49755 * COS(C) B = 0.07922 * COS(2.0*C) XR(I) = XR(I) * (0.42423 A+ B) 100 CONTINUE RETURN END

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C************************************************ SUBROUTINE FFT(XR,XI) IMPLICIT REAL*8(A-H,O-Z) IMPLICIT INTEGER*4 (I-N) DIMENSION XR(l),XI(l) COMMON XMAX,PI,NU,NDP,NDPDIV2,NDPDIV4,NDPMIN1,IND DO 100 L = 1,NU LE= 2**(NU+l-L) LEl = LE/2 Ul = 1.0 U2 = 0.0 ARG = PI/LEl C = COS (ARG) S = IND*SIN(ARG) DO 101 J = 1,LEl DO 102 I= J,NDP,LE IP= I+ LEl Tl= XR(I) + XR(IP) T2 = XI(I) + XI(IP) T3 = XR(I) XR(IP) T4 = XI(I) XI(IP) XR(IP) = T3*Ul-T4*U2 XI(IP) = T4*Ul+T3*U2 XR(I) = Tl XI(I) = T2 102 CONTINUE U3 = Ul*C-U2*S U2 = U2*C+Ul*S Ul = U3 101 CONTINUE 100 CONTINUE J = 1 DO 104 I= 1,NDPMINl IF (I .GE. J) GOTO 25 TEMP= XR(I) XR(I) = XR(J) XR(J) = TEMP TEMP= XI(I) XI(I) = XI(J) XI(J) = TEMP 25 K = NDPDIV2 20 IF (K .GE. J) GOTO 30 J = J-K K = K/2 GOTO 20 30 J = J + K 104 CONTINUE DO 60 I= 1 , NDPDIV2 XR(I) = SQRT(XR(I)*XR(I)+XI(I)*XI(I)) 60 CONTINUE RETURN END 78

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79 C*********************************************************** *** SUBROUTINE HEXGET(HEX) IMPLICIT REAL*B(A-H,O-Z) IMPLICIT INTEGER*4 (I-N) INTEGER*2 HEX(256) HEX (ICHAR( I I)) =0 HEX(ICHAR('0'))=0 HEX(ICHAR('l'))=l HEX(ICHAR('2'))=2 HEX(ICHAR( 1 3 1 ))=3 HEX(ICHAR('4'))=4 HEX(ICHAR{'5'))=5 HEX(ICHAR('6'))=6 HEX(ICHAR('7'))=7 HEX(ICHAR('8'))=8 HEX(ICHAR('9'))=9 HEX ( I CHAR ( 'A 1 ) ) = 10 HEX(ICHAR('B'))=ll HEX(ICHAR('C'))=12 HEX(ICHAR('D 1 ))=13 HEX(ICHAR('E'))=14 HEX(ICHAR('F'))=15 RETURN END

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APPENDIX B SONIC TRANSFORM SOURCE CODE IMPLICIT REAL*8 (A-H,O-Z) DIMENSION ROOT(84),SMAG(16384),T(500) ,P(500) INTEGER*2 C0(16384),C,SP0(16384) CHARACTER*20 FILEIN,FILEOUT TWOPI=4.0*ACOS(O.O) CALL RTGET(ROOT) TAVG=O.O PAVG=0.0 NROOT=84 CMAX=200.0*TWOPI*3.0*2.54/ROOT(NROOT) CRES=CMAX/16384.0 NMAX=16384 FRES=20000.0/16384 DENOM=TWOPI*3.0*2.54/100*FRES DO 40 I=l00,599 INDX=I-99 WRITE(FILEIN, 1 (A7,I3,A4) ') 'E\:\\FD\\F' ,I,' .FFT' WRITE(*,100) FILEIN 100 FORMAT(A) OPEN(l,FILE=FILEIN,FORM='UNFORMATTED') READ(l) T(INDX),P(INDX) READ(1) CO CLOSE(l) XMAX=O.O DO 10 C=l,NMAX SPEED=FLOAT(C)*CRES RATIO=SPEED/DENOM SMAG(C)=O.O DO 20 J=l,NROOT INDEX=INT(RATIO*ROOT(J)+0.5) IF(INDEX.GT.16384) THEN TEMP=O.O ELSE TEMP=DBLE(CO(INDEX)) ENDIF SMAG(C)=SMAG(C)+TEMP 20 CONTINUE XMAX=AMAXl(XMAX,SMAG(C)) 10 CONTINUE DO 30 C=l,NMAX SPO(C)=INT(SMAG(C)/XMAX*16384.0) 30 CONTINUE 80

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C C C C C C WRITE(FILEOUT, 1 (A7,I3,A4) ') 'E\: \ \SD\ \F' ,I,' .SPD' OPEN(l,FILE=FILEOUT,FORM='UNFORMATTED') WRITE(l) T(INDX),P(INDX) WRITE(l) SPO CLOSE(l) TAVG=TAVG+T(INDX) PAVG=PAVG+P(INDX) WRITE(*,*) T(INDX),P(INDX) 40 CONTINUE TAVG=TAVG/500.0 PAVG=PAVG/500.0 SDT=O.O SDP=O.O DO 50 I=l,500 SDT=SDT+(TAVG-T(I))**2 SDP=SDP+(PAVG-P{I))**2 50 CONTINUE SDT=SDT/499.0/500.0 SDT=l.96*SQRT(SDT) SDP=SDP/499.0/500.0 SDP=l.96*SQRT(SDP) WRITE(*,200) TAVG,SDT,PAVG,SDP 200 FORMAT(Fl0.4, '+/-',F7.4,Fl0.4,'+/-',F7.4) WRITE(*,300) CRES 300 FORMAT(' RESOLUTION OF SONIC DOMAIN=',Fl0.5) END SUBROUTINE RTGET(ROOT) IMPLICIT REAL*8 (A-H,O-Z) DIMENSION ROOT(l) ROOT(1)=2.08158 ROOT(2)=3.34209 ROOT(3)=4.49341 ROOT(4)=4.51408 ROOT(5)=5.64670 ROOT(6)=5.94036 ROOT(7)=6.75643 ROOT(8)=7.28990 ROOT(9)=7.72523 ROOT(l0)=7.85107 ROOT(ll)=S.58367 ROOT(l2)=8.93489 ROOT(13)=9.20586 ROOT(14)=9.84043 ROOT(15)=10.0102 ROOT(16)=10.6140 81

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ROOT(17)=10.9042 ROOT(lS)=ll.0703 ROOT(19)=11.0791 ROOT(20)=11.9729 ROOT(21)=12.1428 ROOT(22)=12.2794 ROOT(23)=12.4046 ROOT(24)=13.2024 ROOT(25)=13.2956 ROOT(26)=13.4721 ROOT(27)=13.8463 ROOT(28)=14.0663 ROOT(29)=14.2850 ROOT(30)=14.5906 ROOT(31)=14.6513 ROOT(32)=15.2446 ROOT(33)=15.3108 ROOT(34)=15.5793 ROOT(35)=15.8193 ROOT(36)=15.8633 ROOT{37)=16.3604 ROOT(38)=16.6094 ROOT(39)=16.9776 ROOT(40)=17.0431 ROOT(41)=17.1176 ROOT(42)=17.2207 ROOT(43)=17.4079 ROOT(44)=17.9473 ROOT(45)=18.1276 ROOT(46)=18.3565 ROOT(47)=18.4527 ROOT(48)=18.4682 ROOT(49)=18.7428 ROOT(50)=19.2628 ROOT(51)=19.2704 ROOT(52)=19.4964 ROOT(53)=19.5819 ROOT(54)=19.8625 ROOT(55)=20.2219 ROOT(56)=20.3714 ROOT(57)=20.4065 ROOT(58)=20.5379 ROOT(59)=20.5596 ROOT(60)=20.7960 ROOT(61)=21.2312 ROOT(62)=21.5372 ROOT(63)=21.5779 ROOT(64)=21.6667 ROOT(65)=21.8401 ROOT(66)=21.8997 ROOT(67)=22.0000 ROOT(68)=22.5781 82

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ROOT(69)=22.6165 ROOT(70)=22.6625 ROOT(71)=23.0829 ROOT(72)=23.1067 ROOT (73) =23 .1950 ROOT(74)=23.3906 ROOT(75)=23.5194 ROOT(76)=23.6534 ROOT(77)=23.7832 ROOT (78) =23. 9069 ROOT(79)=24.3608 ROOT(80)=24.3821 ROOT(81)=24.4749 ROOT(82)=24.6899 ROOT(83)=24.8503 ROOT(84)=24.8995 RETURN END 83

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C C C C C C C APPENDIX C EQUATION OF STATE FOR ARGON SOURCE CODE IMPLICIT REAL*8 (A-H,O-Z) REAL*8 B(l00) ,B1(100),B2(100),T(100) REAL*8 C(l00),Cl(l00),C2(100),BD(l00),N EPK=l19.8D 00 B0=49.80D-03 PCON=6.8-046D-02 KEL=273.15 OPEN (10,FILE='E\:\\SOURCE\\TVC.CON',STATUS='OLD') DO 25 I=l,74 READ(l0,*) CT(I) ,B(I) ,Bl(I) ,B2(I) ,BD(I) ,C(I) ,Cl(I) ,C2(I) 25 CONTINUE CLOSE (10) 100 WRITE{*,*) 1 INPUT TEMPERATURE (Celcius) AND CPRESSURE {psia) I READ(*,*) TEMP,P P=P*PCON TEMP=TEMP+KEL TS=TEMP/EPK CALL CQAND(BS,BS1,BS2,BSD,CS,CS1,CS2,TS,T, CB,Bl,B2,BD,C,Cl,C2) BV=BS*B0 CV=CS*B0*B0 CALL VERVOL(P,V,TEMP,BV,CV) VS=V/B0 CALL SPEED(CAR,TEMP,BS,BS1,BS2,BSD,CS,CS1,CS2,VS) WRITE(*,*) 1 SPEED=',CAR GOTO 100 END SUBROUTINE CQAND(BS,BS1,BS2,BSD,CS,CS1,CS2,TS,T,B,Bl,B2 C,BD,C,Cl,C2) IMPLICIT REAL*8 {A-H,O-Z) 84

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C C C C C C C 85 REAL*8 B(l) ,Bl(l) ,B2(1) ,T(l) ,C(l) ,Cl(l) ,C2(1) ,BD(l.) REAL*8 M DO 20 I=2,74 IF (TS.GT.T(I-1) .AND.TS.LT.T(I)) THEN M=(TS-T(I-1))/(T(I)-T(I-1)) BS=B(I-l)+M*(B(I)-B(I-1)) BSl=Bl(I-l)+M*(Bl(I)-Bl(I-1)) BS2=B2(I-l)+M*(B2(I)-B2(I-1)) BSD=BD(I-l)+M*(BD(I)-BD(I-1)) CS=C(I-l)+M*(C(I)-C(I-1)) CSl=Cl(I-l)+M*(Cl(I)-Cl(I-1)) CS2=C2(I-l)+M*(C2(I)-C2(I-1)) RETURN ENDIF 20 CONTINUE WRITE(*,*) 1 TSTAR OUT OF RANGE' RETURN END SUBROUTINE VERVOL(P,V,T,B,CV) IMPLICIT REAL*8 (A-H,O-Z) R=S.20575D-02 TOL=l. 0D-16 C INPUT PIN ATM C INPUT TIN KELVIN V=R*T/P C C C C C C C 10 VN=R*T/P*(l.0D 00 + B/V + CV/V/V) TEST=V/VN IF(TEST.GT.1.0) THEN TEST=l.0D 00 1.0D 00/TEST ELSE TEST=l.0D 00 -TEST ENDIF V=VN IF(TEST.GT.TOL) GOTO 10 RETURN END SUBROUTINE SPEED(C,T,BS,BS1,BS2,BSD,CS,CS1,CS2,VS) IMPLICIT REAL*8 (A-H,O-Z)

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REAL*8 M,DSQRT M=39.948D-03 R=S.31441D 00 GAMA= CS.0D0/2.0D0-BS2/VS+(BSD*BSD-CS+CS1-0.5D0*CS2)/VS/VS GAMA=GAMA/(3.0D0/2.0D0-(2.0D0*BSl+BS2)/VS@(2.0D0*CSl+CS2)/2.0D0/VS/VS) C=GAMA*R*T/M*(l.0D 00+2.0D0*BS/VS+3.0D0*CS/VS/VS) C=DSQRT(C) RETURN END 86

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APPENDIX D DATA ACQUISITION SOURCE CODE #include #include #include #include #include "DECL.H" libraries*/ #include #include #include #include #define PORTO 0x178 #define PORTl 0x179 #define PORT2 Ox17A #define PORT3 0x17B #define COMMA 0x2c #define NOERR 0 /****************************/ /* driver library functions*/ /****************************/ extern int ibfind(); extern void ibtmo(); extern void ibclr(); extern void ibeos(); extern void ibrd(); extern void ibwrt(); extern void ibcmd(); extern void ibsic(); extern void ibloc(); extern void ibrsp(); extern void ibwait(); FILE *stream; /* supplied with driver /* default setting */ /* all switches are off*/ char *dacoutput=(char*)0xoooooooo; int addr=0x20; unsigned char io[32768]; long timeout[500]; float pout[S00]; double tout[500]; long t,t0,tday; 87

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/*********************************************/ /* sends temperature in celcius to the oven, */ /*********************************************/ void wrtoven(float setpoint) { int j,ovn; char ostring[14],fp(l0]; gcvt(setpoint,5,fp); strcpy(ostring,"setpoint "); ostring(9]=fp[O]; ostring(lO]=fp[l]; ostring[ll]=fp[2]; ostring(12]=fp[3]; ostring(13]=fp[4]; ostring(l4]='\0'; } ovn = ibfind("oven"); ibwrt( ovn, ostring, 15); printf(" %s\n",ostring); return; /*********************************************/ /* reads temp in celcius form rtd, */ /*********************************************/ double rdrtd () { int i,rtd; double res,rc,aldel,ptl,pt2,pt3,pt4,t2; double r0=99.98; double alpha=0.0039076; double delta=l.5205; char rstring(16]; rtd = ibfind("k195a"); ibrd( rtd, rstring, 17 ); for(i=O; i<4; i++) rstring[i]=' '; for(i=15; i<17; i++) rstring(i]=' '; res=atof(rstring); aldel=alpha*delta; rc=res/ro; rc=rc-1.0; pt1=aldel/100.0; ptl=ptl+alpha; pt2=ptl*ptl; pt3=4.0*rc; pt3=pt3*aldel; pt3=pt3/10000.0; pt4=2.0*aldel; pt4=pt4/10000.0; t2=sqrt(pt2-pt3); t2=ptl-t2; 88

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return (t2/pt4); } /*********************************************/ /* reads the pressure transducer, */ /*********************************************/ float rdpress() { int ptrans; char pstring[9]; ptrans = ibfind("beckman"); ibrd( ptrans, pstring, 10 ); pstring[7]=' '; pstr ing [ 8 J = ' ' ; pstr ing [ 9] =' ' ; return (atof(pstring)); } /**********************************/ /* gets the time in milliseconds */ /**********************************/ void get_milli() { char tmp [ 1 J ; long h,m,s; struct timeb timebuffer; char *timeline; ftime(&timebuffer); timeline = ctime(&(timebuffer.time)); tmp[O]=timeline[ll]; tmp[l]=timeline[12]; h=atol(tmp); h=h*3600; tmp[OJ=timeline[14]; tmp[l]=timeline[15]; m=atol(tmp); lll.=m*60; tmp[O]=timeline[17]; tmp[l]=timeline[18]; s=atol(tmp); t=h+m; t=t+s; . t=t*lOOO; t=t+timebuffer.millitm; s=t-to; if (s < o ) { 89

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} t0=t0-tday; t=t-t0;} else t=s; return; /**************************************/ /* collects data from dac */ I* *I /**************************************/ unsigned int sample(size) unsigned int size; { int busy; int count; 90 outpw(PORT2,0xa03f); outpw(PORT0,0xffff); outpw(PORT0,0xffff); count= -(size+ 0xff); outpw(PORT0,count); outpw(PORT0,count); outp(PORT2, 0x3c); /* initialize single input*/ /* clear counter*/ 20kHz,40kHz*/ /* correct count*/ /* load count*/ /* start the counter busy= inp(PORT2); /* wait for sampling to be completed*/ while (busy= inp(PORT2));/* sampling is done*/ } outp(PORT2,0x3f); return(inpw(PORT0)); /* enabled WAAGII ram*/ /* read trigger address*/ /************************************************/ /* clears HP-IB, initializes instrument timeout*/ /* initializes varibles */ /************************************************/ void init () { } tday=0; t0=0; get milli(); tday=24*3600; tday=tday*l000; t0=t; return; main{)

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{ char filename(BJ,num[2]; unsigned int size=16384; /* number of sample points*/ unsigned int trigger,i,j; unsigned short ih,il,ihigh,index,iloop,nloop; float setpoint,step; unsigned int sample(unsigned int); void wrtoven(float); double rdrtd(void); float rdpress(void); void get milli(void); void init(void); init(); /* step=0.01;*/ step=0.0; printf(" input setpoint -0.09 > # > 0.09\n"); scanf("%f",&setpoint); nloop=600; for(iloop=l00; iloop
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} } stream= fopen("temp.out", "wb"); fwrite((char *)tout,sizeof(double),500,stream); fclose(stream); stream= fopen("press.out", "wb"); twrite((char *)pout,sizeof(float),500,stream); fclose(stream); stream= fopen("time.out", "wb"); fwrite{(char *)timeout,sizeof(long),500,stream); fclose(stream); 92

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APPENDIX E DATA CONVERSION SOURCE CODE #include #include #include FILE *stream; unsigned char io[32768]; double tout[500]; float pout(500]; char filein[15],fileout[15]; main() { unsigned int index,i,j,k; char num(2]; stream= fopen("e:\\raw\\temp.out", "rb"); fread((char *)tout,sizeof(double),500,stream); fclose(stream); stream= fopen("e:\\raw\\press.out", "rb"); fread((char *)pout,sizeof(float),500,stream); fclose(stream); for(i=lOO; i<600; i++) { index=i-100; gcvt(i,3,num); filein[O]='e'; filein[l]='\: '; filein[2]='\\'; filein[3]='r'; filein[4]='a'; filein[5]='w'; filein[6]='\\'; filein(7]='f'; filein[S]=num(O]; filein[9J=num(l]; 93

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} } filein[lO]=num[2]; filein[ll]='. '; filein[12J='d'; filein[13]='a'; filein(14]='t'; filein[15]='\0'; stream=fopen(filein,"rb"); fread((char *)io,sizeof(unsigned char) ,32768,stream); fclose(stream); fileout(O]='e'; fileout(l]='\:'; fileout[2)='\\'; fileout(3]='h'; fileout[4J='e'; fileout[5]='x'; fileout(6]='\\'; fileout(7]='f'; fileout(8]=num(OJ; fileout[9J=num(l]; fileout(lO]=num[2]; fileout[ll)='.'; fileout[12]='o'; fileout[13]='u'; fileout[14)='t'; fileout[15)='\0'; stream=fopen(fileout,"w"); 94 fprintf(stream,"%.3f %.lf'',tout[indexJ,pout[indexJ); printf("%u %.3f %.lf\n",index,tout[index],pout[index)); for(j=O; j<1024; j++){ fprintf(stream,"\n"); for(k=O; k<32; k++) fprintf(stream,"%2X",io[j*32+k]); } fclose(stream);

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Bergland, G.D. Real-Valued Series." 1968): 703-710. BIBLIOGRAPHY "A Fast Fourier Transform Algorithm for Communications of the ACM 11 (October Bird, R. Byron. "Numerical Evaluation of the Second Virial Coefficient." The Virial Equation of State CM-599. Madison: University of Wisconsin, May 10, 1950. Bosse, J., Jacucci, G., Ronchetti, M., and W. Schirmacher. "Fast Sound in Two-Component Liquids." Physical Review Letters 57 (December 1986): 3277-3279. Colclough, A.R. "Systematic Errors in Primary Acoustic Thermometry in the Range 2-20 K." Metrologia 9 (1973): 7598. Colgate, S.O., Sona, C.F., Reed, K.R., and A. sivaraman. "Experimental Ideal Gas Reference State Heat Capacities of Gases and Vapors." Journal of Chemical and Engineering Data 35 (1990): 1-5. Colgate, s.o., Williams, K.R., Reed, K., and c. Hart. "C/Cv Ratios by the Sound Ve~ocity Meth?d Using a Spherical Resonator." Journal of Chemical Education 64 (June 1987): 553-556. Cooley, J.W., and J.W. Tukey. "An Algorithm for the Machine Calculation of Complex Fourier Series." Mathematical Computations 19 (April 1965): 297-301. Ewing, M.B., Goodwin, A.R.H., and J.P.M. Trusler. "Thermophysical Properties of Alkanes from Speeds of Sound Determined Using a Spherical Resonator 3. n-pentane." Journal of Chemical Thermodynamics 21 (1989): 867-877. Ewing, M.B., McGlashan, M.L., and J.P.M. Trusler. "The Temperature-Jump Effect and the Theory of the Thermal Boundary Layer for a Spherical Resonator, Speeds of Sound in Argon at 273.16 K." Metrologia 22 (1986): 93-102. Ferris, H.G. "The Free Vibrations of a Gas Contained within a Spherical Vessel." Journal of the Acoustical Society of America 24 (January 1952): 57-65. 95

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96 Golub, G.H., and C.F. Van Loan. Matrix Computations. Baltimore: Johns Hopkins University Press, 1985. Hirschfelder, J.O., Curtiss, C.F., and R.B. Bird. Molecular Theory of Gases and Liquids. New York: Wiley and Sons, 1954. Mehl, J.B., and M.R. Moldover. "Precision Acoustic Measurements with a Spherical Resonator: Ar and C 2 H 4 ." Journal of Chemical Physics 74 (April 1981): 4062-4077. Mehl, J.B., and M.R. Moldover. Phenomena in Acoustic Measurements." Physics 77 (July 1982): 455-465. "Precondensation Journal of Chemical Moldover, M.R., Mehl, J.B., and M. Greenspan. "Gas Filled Spherical Resonators: Theory and Experiment." =J-o-u=r~n=a=l~=o=f~t=h=e'--'A=c==o=u=s~t~i~c~a=l~~S=o~c~i~e~t-y.__o~f~=Am=--e=r-i_c_a= 79 (February 1986): 253-271. Rayleigh, J.W.S. Theory of Sound. New York: Dover, 1894, reprinted 1945. Tewfik, A.H., Levy, B.C., and A.S. Willsky. "An Eigenstructure Approach for the Retrieval of Cylindrical Harmonics." Signal Processing 13 (September 1987): 121139.

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BIOGRAPHICAL SKETCH Kenneth c. McGill was born June 6, 1957, in Port Arthur, Texas, the youngest child and second son of Martha and Edward McGill. Ken moved to Topeka, Kansas, at the age of three where he attended grade school, junior and senior high. Upon graduation from Topeka West High and Kaw Valley Area VoTech in 1975, Ken worked as a welder for several factories in the Topeka area. In 1979, Ken returned to school, attending Washburn University in Topeka while also serving as a reservist in the Air National Guard. He graduated magna cum laude (G.P.A. of 3.67 of 4.00) in 1985 with dual B.S. degrees in physics and chemistry. In 1985, Ken entered the University of Florida as a doctoral student in physical chemistry. He studied quantum theory for about two years under Yngve Ohrn before joining Dr. s.o. Colgate's experimentalist group. Principal areas of research interest are currently data acquisition techniques in acoustic measurements, thermodynamics of acoustics and fluid mixtures. Upon graduation, Ken has earned a one-year post-doctoral position with Dr. Colgate to further investigate Sonic Transformation techniques. Ken, a widower, has recently remarried and he and his wife are expecting their first child in March 1991. 97

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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 .. ;.: / I / / ..._ ,f...1_ C. , "'ll/Zf (_/ r ~ ''. // ~ ;< ;.;( Samuel o. Colgate, Chairman Associate Professor of 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 i _ ) J / \; \ '\JV ,.,. ,::ft#:{,,'-N. Yngv~ / Ohr~, Cochairman Professor in }Chemistry and Physics 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 Doc or Philosophy. Thomas Bailey Professor of Phys 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. John R. Eyler 1 / Prdfessor of Chemistry

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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 1 .. ~. William Weltner, Jr. Professor of Chemistry 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

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