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Development and Applications of a

Low-Field Portable NMR System

A thesis presented in partial fulfillment of the

requirements for the degree of Doctor of Philosophy

in Physics at Massey University, Manawatu, New Zealand.

Robert L. Ward

October 2011

Abstract

Nuclear magnetic resonance (NMR) is a phenomenon similar to MRIin which radio frequency signals are used to excite and manipulate atomicnuclei within a static magnetic field. Following excitation, the nuclei returnto equilibrium, all the while offering valuable molecular level informationpertaining to the sample.

Within the last decade, the development of small and inexpensive NMRspectrometers and permanent magnet NMR sensors has been a significantfocus within the NMR community. More recently, application scientists havesought practical applications for the new technologies.

In this thesis, a prototype NMR apparatus consisting of a spectrometerand 3.2MHz permanent magnet sensor was extended to enable scientificmeasurements. This involved developing radio frequency electronic circuitryfor the spectrometer front-end, and electromagnetic noise shielding and tem-perature regulation for the magnetic sensor. Experimental results confirmedthat repeatable measurements using the modified apparatus were indeedpossible.

The NMR apparatus was thereafter successfully used to study flow,diffusion and kiwifruit using several different experimental techniques. Asignificantly larger effort was then expended upon the study of T2 relaxation inpectin model systems using pH as the adjustable parameter. The fascinatingexperimental results were successfully interpreted and modeled across threepH zones in terms of a proton chemical exchange model and molecularconformational changes. In addition, it was found that pectin carboxylde-protonation was significantly less than expected. Further experimentsperformed upon galacturonic acid monomers, dimers and trimers appearedto further illuminate the pectin results. Future experiments are planned.

Also while studying pectin solutions, an unexpected pH-dependent watertransverse relaxation behavior was observed at both 3.2MHz and 400MHz.The only references found in the literature were from a small publicationalmost 50 years ago, and a 2011 publication.

Altogether, this thesis contributed to original knowledge in several ways:it showed how a low-field apparatus and single-sided sensor could be im-proved and utilized for a variety of scientific measurements; it showed bothexperimentally and theoretically how T2 for pectin solutions change withpH; it revealed an unexpected de-protonation limit for pectin molecules; itrevealed a T2 pH dependence for water.

To my wife Lizwho has endured

much over the years.

Acknowledgements

Many people have contributed to this thesis in many different ways. First andforemost I would like to thank my wife who has stood beside me in relative povertyfor too many years. It’s almost over... and it’s time we took a holiday together.

Second, I would like to thank my two daughters, Rebekah and Hannah, forputting up with my absence. Rebekah was born two months before we started myuniversity adventure, and Hannah was born two years later. Again, it’s almostover... and it’s time we went on some adventures together.

Third, I would like to thank my supervisors, Dr. Bill Williams and Dr. RobinDykstra. I have thoroughly enjoyed working with you guys. You have not onlybeen supervisors during this project, but also friends. Bill – dude – your love ofscience is contagious and has inspired me greatly. Perhaps it is time for us to drinksome beers, play some guitar, and talk some philosophy :-)

Many other people need to be thanked and acknowledged for their assistanceduring this project.

In no particular order, my thanks go to: Dr. Jason Hindmarsh for many chatsabout interesting things like kiwifruit, and occasional help on the “real” NMRsystems. Dr. Pat Edwards for teaching me how to use the other “real” NMR systems,and for allowing me to pull apart expensive probe-heads. Dr. Aurelie Cucheval,whose French I could sometimes understand, for being a charming assistant duringmy pectin-making exploits. Mary-Helen Ward for being the only non-scientistwith the skills and perseverance to suffer reading my thesis, and for pointing outa few typos that I’d missed. Michael Adams for encouraging me in black-magic,otherwise known as RF electronics. It was great, and I wish you could have stayeda lot longer. Keith Whitehead for arguing with me, and finally converting me tothe Cult of MacHeads. Terry Southern for many interesting conversations about allsorts of things. Rinni Williamson (nee Singh) for arguing, laughing, crying, beingfun, and for one joke I will never forget. Dr. Bob O’Driscoll for the interestingconversations that oscillated between Macs and electronics. Dr. Craig Eccles for hisassistance with Prospa and the Mole. Steve Denby and Noel Foot in the mechanicalworkshop who usually said no, then did it. Dr. Mark Hunter and Ben Parkinson

vii

for Mole assistance. Erich Schuster for the pectin images. Dr. Gavin Hedwig forthe offer of a water bath. Dr. Lara Matia-Merino for the emulsions.

Table of contents

Acknowledgements vii

Table of contents ix

List of abbreviations xv

List of tables xix

List of figures xxi

Introduction 1

1 NMR theory 31.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Nuclear properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Nuclear spin angular momentum . . . . . . . . . . . . . . . 41.2.2 Nuclear magnetism . . . . . . . . . . . . . . . . . . . . . . . 51.2.3 Space quantization . . . . . . . . . . . . . . . . . . . . . . . 61.2.4 Magnetic moment precession . . . . . . . . . . . . . . . . . . 71.2.5 Energy quantization . . . . . . . . . . . . . . . . . . . . . . 8

1.3 Ensemble properties . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3.1 Boltzmann distribution . . . . . . . . . . . . . . . . . . . . . 101.3.2 Curie’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Spin manipulation and signal detection . . . . . . . . . . . . . . . . 121.4.1 The B1 field . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4.2 The rotating frame . . . . . . . . . . . . . . . . . . . . . . . 141.4.3 Detecting the nuclear magnetization . . . . . . . . . . . . . 17

1.5 Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.5.1 Dipole-dipole coupling . . . . . . . . . . . . . . . . . . . . . 191.5.2 T1 relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 201.5.3 T2 relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 201.5.4 T2

* relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 21

ix

x Table of contents

1.6 Spin-echoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211.6.1 Ring-down and recovery time . . . . . . . . . . . . . . . . . 231.6.2 T2 CPMG macro . . . . . . . . . . . . . . . . . . . . . . . . 24

2 Experimental apparatus 272.1 The basic apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.1.1 Kea spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 272.1.2 The Mole probe . . . . . . . . . . . . . . . . . . . . . . . . . 292.1.3 Prospa software . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 Preliminary use of the apparatus . . . . . . . . . . . . . . . . . . . 332.2.1 Improving the signal-to-noise . . . . . . . . . . . . . . . . . 332.2.2 The defective Mole probe . . . . . . . . . . . . . . . . . . . 342.2.3 Switching regulator problems . . . . . . . . . . . . . . . . . 342.2.4 Temperature instability . . . . . . . . . . . . . . . . . . . . . 35

2.3 Solving the EMI and temperature drift problems . . . . . . . . . . . 362.3.1 Investigating Mole EMI shielding . . . . . . . . . . . . . . . 362.3.2 Investigating temperature control options . . . . . . . . . . . 372.3.3 Designing and building the environmental chamber . . . . . 39

2.4 Testing the apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . 442.4.1 Environmental chamber EMI shielding . . . . . . . . . . . . 442.4.2 Switching power supplies and other noise sources . . . . . . 442.4.3 Intermittent noise . . . . . . . . . . . . . . . . . . . . . . . . 452.4.4 T 2 bi-exponential stability . . . . . . . . . . . . . . . . . . . 452.4.5 T 2 mono-exponential stability . . . . . . . . . . . . . . . . . 462.4.6 Mole proton frequency versus temperature . . . . . . . . . . 492.4.7 Effects of frequency mismatch . . . . . . . . . . . . . . . . . 492.4.8 Water T2 versus temperature . . . . . . . . . . . . . . . . . 522.4.9 Optimal sample location and volume . . . . . . . . . . . . . 522.4.10 Sample heating . . . . . . . . . . . . . . . . . . . . . . . . . 56

2.5 Problems encountered . . . . . . . . . . . . . . . . . . . . . . . . . 592.5.1 Electrical noise sources . . . . . . . . . . . . . . . . . . . . . 592.5.2 Damaged tuning capacitor . . . . . . . . . . . . . . . . . . . 592.5.3 Prospa and DSP problems . . . . . . . . . . . . . . . . . . . 602.5.4 Damaged Central Magnet . . . . . . . . . . . . . . . . . . . 602.5.5 Acoustic ringing . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.6 Summary and future improvements . . . . . . . . . . . . . . . . . . 65

3 Pre-amplifier duplexer 673.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.2 Design requirements and functionality . . . . . . . . . . . . . . . . . 68

3.2.1 Signal routing . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Table of contents xi

3.2.2 Signal amplification . . . . . . . . . . . . . . . . . . . . . . . 693.2.3 Wobble functionality . . . . . . . . . . . . . . . . . . . . . . 69

3.3 PAD relay version design implementation . . . . . . . . . . . . . . . 693.3.1 Relay considerations . . . . . . . . . . . . . . . . . . . . . . 71

3.4 PAD standard version design implementation . . . . . . . . . . . . 733.5 The duplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.5.1 Diode switches . . . . . . . . . . . . . . . . . . . . . . . . . 753.5.2 Quarter-wave line . . . . . . . . . . . . . . . . . . . . . . . . 77

3.6 Directional couplers . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.6.1 PAD relay version directional coupler . . . . . . . . . . . . . 783.6.2 PAD standard version directional coupler . . . . . . . . . . . 78

3.7 Pre-amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.8 Pi attenuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823.9 Power supplies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.10 Relay and RF switch control . . . . . . . . . . . . . . . . . . . . . . 843.11 RF switch biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863.12 Printed circuit board design . . . . . . . . . . . . . . . . . . . . . . 903.13 EMI shielding and the milled box . . . . . . . . . . . . . . . . . . . 913.14 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

3.14.1 Signal routing . . . . . . . . . . . . . . . . . . . . . . . . . . 933.14.2 Signal amplification and noise measurements . . . . . . . . . 933.14.3 Wobble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.15 Future improvements . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4 Studying pectin solutions 994.1 Pectins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.2 Preparing galacturonic acid and pectin solutions . . . . . . . . . . . 1004.3 Performing experiments on the solutions . . . . . . . . . . . . . . . 1034.4 Titration and relaxation results . . . . . . . . . . . . . . . . . . . . 104

4.4.1 Galacturonic acid . . . . . . . . . . . . . . . . . . . . . . . . 1044.4.2 Apple (HM) pectin . . . . . . . . . . . . . . . . . . . . . . . 1064.4.3 LM12 pectin . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.4.4 Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.5 Pectin stability and reversibility . . . . . . . . . . . . . . . . . . . . 1124.5.1 Apple pectin reversibility . . . . . . . . . . . . . . . . . . . . 1164.5.2 LM12 pectin reversibility . . . . . . . . . . . . . . . . . . . . 118

4.6 Interpreting the relaxation data . . . . . . . . . . . . . . . . . . . . 1214.6.1 Correlation times or proton exchange? . . . . . . . . . . . . 1234.6.2 Dobies et al’s. interpretation . . . . . . . . . . . . . . . . . . 124

4.7 Interpretation using the proton exchange model . . . . . . . . . . . 1274.7.1 Defining the Carver-Richards model . . . . . . . . . . . . . . 127

xii Table of contents

4.7.2 Determining Pb experimentally . . . . . . . . . . . . . . . . 1294.7.3 Determining Pb theoretically . . . . . . . . . . . . . . . . . . 1314.7.4 Comparing experimental and theoretical Pb . . . . . . . . . 1324.7.5 Reconciling experimental and theoretical Pb . . . . . . . . . 1354.7.6 Understanding experimental Pb . . . . . . . . . . . . . . . . 1404.7.7 Extracting T2b + k -1 for galacturonic acid and pectins . . . 1424.7.8 Interpreting T2–versus–pH for GalA solutions . . . . . . . . 1434.7.9 Interpreting T2–versus–pH for the pectins . . . . . . . . . . 147

4.8 Modeling the pectin solutions . . . . . . . . . . . . . . . . . . . . . 1564.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1674.10 Postscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

5 Water 1735.1 Studying water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

5.1.1 Water T2-vs-pH using the Mole probe . . . . . . . . . . . . . 1745.1.2 Water T2-vs-NaOH using the Mole probe . . . . . . . . . . . 1745.1.3 Water T2-vs-pH using the Bruker 400MHz . . . . . . . . . . 1775.1.4 Changing the pulse spacing on the 400MHz . . . . . . . . . 1795.1.5 Summary so far . . . . . . . . . . . . . . . . . . . . . . . . . 1805.1.6 Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . 1805.1.7 Measuring T1, diffusion, and convection . . . . . . . . . . . . 1815.1.8 Older water measurements . . . . . . . . . . . . . . . . . . . 1825.1.9 Recent water measurements . . . . . . . . . . . . . . . . . . 1835.1.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

6 Other experiments 1876.1 Flow experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1876.2 Diffusion experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 1926.3 Kiwifruit experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 197

6.3.1 Katikati experiments . . . . . . . . . . . . . . . . . . . . . . 200

7 Conclusion 205

8 Future work 2098.1 Future apparatus development work . . . . . . . . . . . . . . . . . . 2098.2 Future experimental work . . . . . . . . . . . . . . . . . . . . . . . 210

A Circuit diagrams 213

B Making pectin solutions 219

C Software 221

Table of contents xiii

C.1 T2 drift test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

D Recommended reading 223

E Equipment list 225

Bibliography 227

List of abbreviations

γ The magnetogyric (or gyromagnetic) ratioω Frequency in radians per secondωeff Effective frequency in the rotating frame in radians per secondA AmpsAFM Atomic force microscopyAC Alternating currentARRL American Radio Relay LeagueB0 Static magnetic field oriented along the z-axisB1 Oscillating magnetic field oriented along the x-axisCE capillary electrophoresisCC Counterion condensationCLI Command line interfaceCOOH CarboxylCPL CoupledCP Carr PurcellCPMG Carr Purcell Meiboom GillCSV Comma separated valuesCTR Current transfer ratioD-D Dipole-dipole couplingDa Dalton: 1/12th of the mass of a carbon atom at rest in its ground stateDC Direct currentDE Direct echoDM Degree of methyl-esterificationDP Degree of polymerizationDSP Digital signal processorEMF Electro motive force, or voltageEMI Electromagnetic interferenceFID Free induction decayGalA Galacturonic acidGDL Glucono delta-lactoneGUI Graphical user interface

xv

xvi List of abbreviations

HCl Hydrochloric acidHDD Hard disk driveHM High methoxylHPA High-power amplifierHz Frequency in HertzIC Integrated circuitJ(ω) Spectral density as a function of frequencykDa KilodaltonKea NMR spectrometerkHz KilohertzLED Light emitting diodeLM Low methoxylM Molarity, measured in mol·L−1

Mr Molecular weightµA Micro ampsµF Micro FaradsµH Micro HenriesmA Milli ampsMole MObile Lateral Explorer or MObile Liquid Explorermole ∼ 6.022× 1023 atoms of moleculesMRI Magnetic resonance imagingnF Nano FaradsNaOH Sodium hydroxideNdFeB Neodymium iron boronNIB Neodymium iron boronNMR Nuclear magnetic resonanceOH HydroxylpKa Acid dissociation constantPAD Pre-amplifier duplexerPCB Printed circuit board(π) 180 RF pulse(π/2) 90 RF pulsepF Pico FaradsPID Proportional-integral-derivativeProspa NMR softwarePSU Power supply unitPt100 Platinum resistance thermometer (100Ω resistance at 0C)QST Amateur radio enthusiasts magazine published by the ARRLQ Quality factor of a inductor, capacitor, or tuned circuitR1 Longitudinal (or spin-lattice) relaxation rate

List of abbreviations xvii

R2 Transverse (or spin-spin) relaxation rateRX Receive or receiverRF Radio frequencyRMS Root mean squareReff Concentration ratio of calcium ions to de-protonated carboxylsRS Radio Spares ComponentsRS-485 Serial differential hardware communications protocolSAR Specific absorption rateSAXS Small-angle X-ray scatteringSmCo Samarium CobaltSMPSU Switched mode power supply unitSNR Signal to noise ratioSE Stimulated echoSMA SubMiniature version ASMB SubMiniature version BT Magnetic flux density (Tesla)T1 Longitudinal (or spin-lattice) relaxation timeT1ρ Longitudinal (or spin-lattice) relaxation time in the rotating frameT2 Transverse (or spin-spin) relaxation timetE Echo timeTX Transmit or transmitterUSB Universal serial busV Voltswt% Weight percent

List of tables

1.1 Properties of nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.1 Pectin sources and their weight fractions . . . . . . . . . . . . . . . . . 1014.2 Pectin molecular behavior at different pH values . . . . . . . . . . . . . 1164.3 Modeled GalA and pectin COOH and OH coefficients and pKa values . 139

E.1 Chemicals used for this thesis . . . . . . . . . . . . . . . . . . . . . . . 225E.2 Software and hardware used for this thesis . . . . . . . . . . . . . . . . 226

xix

List of figures

1.1 Angular momentum space quantization . . . . . . . . . . . . . . . . . . 61.2 Precessing magnetic moment . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Zeeman splitting due to B0 field . . . . . . . . . . . . . . . . . . . . . . 91.4 Ensemble of nuclear spins with and without B0 field . . . . . . . . . . . 101.5 Mole probe B1 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.6 Precessing bulk magnetization vector ~M0 . . . . . . . . . . . . . . . . . 131.7 The effective field ~Beff in the rotating frame . . . . . . . . . . . . . . . 161.8 Free induction decay and its Fourier transformation . . . . . . . . . . . 181.9 Spin echo pulse sequence . . . . . . . . . . . . . . . . . . . . . . . . . . 221.10 CPMG pulse sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.1 The NMR apparatus, modules, and interconnections . . . . . . . . . . 282.2 The Mole probe and tune/match circuitry . . . . . . . . . . . . . . . . 302.3 Mole probe B1 circuit, original and modified . . . . . . . . . . . . . . . 312.4 CPMG macro GUI showing typical settings . . . . . . . . . . . . . . . 322.5 Environmental chamber temperature control circuitry . . . . . . . . . . 412.6 Completed temperature controller unit . . . . . . . . . . . . . . . . . . 422.7 Environmental chamber and Mole temperature probe connections . . . 432.8 Bi-exponential T2 relaxation data over 22 day period . . . . . . . . . . 472.9 Mono-exponential T2 relaxation data over 62 hour period . . . . . . . . 482.10 Mole proton Larmor frequency versus temperature . . . . . . . . . . . 502.11 T2 amplitude variations due to frequency variations . . . . . . . . . . . 512.12 Milli-Q water T2 relaxation time versus temperature . . . . . . . . . . . 532.13 Signal amplitudes from two different sized vials . . . . . . . . . . . . . 552.14 Perspex vial holder and glass vial . . . . . . . . . . . . . . . . . . . . . 562.15 B1 sample heating of 10mL water sample . . . . . . . . . . . . . . . . . 582.16 Measuring the Mole B0 field profile along the z-axis . . . . . . . . . . . 612.17 Damaged Mole B0 profile measured along the z-axis . . . . . . . . . . . 622.18 Mole B0 profile along z-axis for differing central magnet heights . . . . 632.19 Central magnet, holder, cap, and copper shields . . . . . . . . . . . . . 65

xxi

xxii List of figures

3.1 Pre-amp duplexer relay version . . . . . . . . . . . . . . . . . . . . . . 703.2 Pre-amp duplexer relay version block diagram . . . . . . . . . . . . . . 713.3 Pre-amp duplexer standard version . . . . . . . . . . . . . . . . . . . . 743.4 Pre-amp duplexer standard version block diagram . . . . . . . . . . . . 753.5 Pre-amp duplexer crossed diodes and λ/4 line . . . . . . . . . . . . . . 763.6 Mini-Circuits SYDC-20-61HP+ bi-directional coupler . . . . . . . . . . 783.7 Directional coupler circuitry built from discrete parts . . . . . . . . . . 793.8 50Ω 4dB π attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . 833.9 24V/15V/2.5V linear voltage regulation circuitry . . . . . . . . . . . . 833.10 Optical isolation circuitry . . . . . . . . . . . . . . . . . . . . . . . . . 853.11 RF switch circuitry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873.12 Modified RF switch circuitry . . . . . . . . . . . . . . . . . . . . . . . . 893.13 Milled box housing for PAD standard version . . . . . . . . . . . . . . 923.14 Comparing time-domain noise between the two PAD modules . . . . . 953.15 Comparing frequency-domain noise between the two PAD modules . . 963.16 Wobble signals from two PAD designs . . . . . . . . . . . . . . . . . . 98

4.1 Hydrated galacturonic acid monomer . . . . . . . . . . . . . . . . . . . 1024.2 Section of a pectin molecule . . . . . . . . . . . . . . . . . . . . . . . . 1024.3 Apple pectin CPMG echo sum and fitted T2 relaxation data . . . . . . 1054.4 pH titration data for three GalA solutions . . . . . . . . . . . . . . . . 1064.5 T2-versus-pH for three GalA solutions . . . . . . . . . . . . . . . . . . . 1074.6 pH titration data for apple pectin solution . . . . . . . . . . . . . . . . 1084.7 T2-versus-pH for apple pectin solution . . . . . . . . . . . . . . . . . . 1094.8 pH titration data for five LM12 pectin solutions . . . . . . . . . . . . . 1104.9 T2-versus-pH for five LM12 pectin solutions . . . . . . . . . . . . . . . 1114.10 Apple and LM12 pectin solutions in Schott bottles post titration . . . . 1134.11 GalA, apple and LM12 pectin solutions in glass vials post titration . . 1144.12 Beta-elimination reaction in pectin molecules . . . . . . . . . . . . . . 1164.13 Apple pectin T2-vs-pH range traversal . . . . . . . . . . . . . . . . . . 1174.14 GalA and apple pectin pre/post T2 measurements . . . . . . . . . . . . 1194.15 LM12 pectin T2-vs-pH range traversal . . . . . . . . . . . . . . . . . . . 1204.16 T2-versus-pH composite graph for GalA, apple and LM12 pectin . . . . 1224.17 Experimentally measured Pb-versus-pH for GalA solutions . . . . . . . 1334.18 Experimentally measured Pb-versus-pH for apple and LM12 solutions . 1344.19 Percentage of protonated COOH groups versus pH . . . . . . . . . . . 1364.20 Percentage of protonated COOH + OH groups versus pH . . . . . . . . 1374.21 Experimental and modeled Pb with coefficient adjustments . . . . . . . 1384.22 (T2b + k−1)-versus-pH for GalA solutions . . . . . . . . . . . . . . . . . 1444.23 (T2b + k−1)-versus-pH for apple and LM12 solutions . . . . . . . . . . . 1454.24 Two-fold and three-fold helical pectin conformations . . . . . . . . . . 149

List of figures xxiii

4.25 Apple and LM12 pectin behaviors versus pH . . . . . . . . . . . . . . . 1574.26 Comparing experimental and modeled 1.5 wt% apple pectin data . . . 1594.27 Comparing experimental and modeled 0.5 wt% LM12 pectin data . . . 1604.28 Comparing experimental and modeled 1.0 wt% LM12 pectin data . . . 1614.29 Comparing experimental and modeled 1.5 wt% LM12 pectin data . . . 1624.30 Comparing experimental and modeled 2.0 wt% LM12 pectin data . . . 1634.31 Comparing experimental and modeled 2.5 wt% LM12 pectin data . . . 1644.32 Tri-galacturonic acid solution and magnetic stirrer, post titration . . . 170

5.1 Water T2-vs-pH on Mole . . . . . . . . . . . . . . . . . . . . . . . . . . 1755.2 Water T2 on Mole versus increasing Na+ concentration . . . . . . . . . 1765.3 Water T2-vs-pH on 400MHz magnet . . . . . . . . . . . . . . . . . . . . 178

6.1 Glass flow tube and attached piping . . . . . . . . . . . . . . . . . . . . 1896.2 Direct echo and stimulated echo peak amplitudes at various flow rates . 1906.3 Direct and stimulated echo amplitude ratios versus flow rate . . . . . . 1916.4 Diffusion measurements for various substances . . . . . . . . . . . . . . 1956.5 Diffusion coefficients versus diffusion slope . . . . . . . . . . . . . . . . 1966.6 Firm versus soft kiwifruit tri-exponential T2 relaxation times . . . . . . 1986.7 Firm versus soft kiwifruit tri-exponential T2 relaxation amplitudes . . . 1996.8 T2 relaxation data from five regions within Haywards kiwifruit . . . . . 202

A.1 PAD standard version duplexer/directional coupler schematic . . . . . 213A.2 PAD standard version duplexer/directional coupler PCB . . . . . . . . 214A.3 PAD standard version schematic . . . . . . . . . . . . . . . . . . . . . 215A.4 PAD standard version PCB . . . . . . . . . . . . . . . . . . . . . . . . 216A.5 PAD relay version schematic . . . . . . . . . . . . . . . . . . . . . . . . 217A.6 PAD relay version PCB . . . . . . . . . . . . . . . . . . . . . . . . . . 218