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2 - Theory of NMR diffusion and flow measurements

Published online by Cambridge University Press:  06 August 2010

William S. Price
William S. Price
Affiliation:
University of Western Sydney
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Summary

Introduction

As soon as the spin-echo was discovered by Hahn in 1950 it was realised that it could form the basis of self-diffusion measurements. Indeed, certainly within the next decade the concept of spin-echo-based diffusion measurements using static magnetic gradients (i.e., Steady Gradient Spin-Echo or SGSE NMR) had become widespread and used in quite sophisticated measurements such as on water and 3He. Many of the experimental limitations of static gradient measurements were removed with the suggestion in 1963 by McCall, Douglass and Anderson and experimental introduction in 1965 by Stejskal and Tanner of applying the magnetic gradients as pulses in the spin-echo sequence (i.e., Pulsed Gradient Spin-Echo NMR or PGSE NMR). Carr and Purcell were the first to discuss NMR flow measurements and in 1960 NMR flow measurements were considered for the purpose of measuring sea-water motion.

Virtually all contemporary NMR diffusion (and flow experiments) are based on some form of spin-echo. Indeed, for all but the simplest cases the dependence of the observed echo amplitudes on diffusion rapidly becomes very complicated and this can be exacerbated in pulse sequences where the magnetisation is kept in a steady state. However, in the following discussions we will assume, unless otherwise noted, that all pulse sequences start with the spin system being in thermal equilibrium (i.e., M0). As the diffusing species necessarily contains a nuclear spin, the terms spin and particle will henceforth become synonymous.

Type
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NMR Studies of Translational Motion
Principles and Applications
 , pp. 69 - 119
Publisher: Cambridge University Press
Print publication year: 2009

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References

Hahn, E. L., Spin Echoes. Phys. Rev. 80 (1950), 580–94.CrossRefGoogle Scholar
Simpson, J. H. and Carr, H. Y., Diffusion and Nuclear Spin Relaxation in Water. Phys. Rev. 111 (1958), 1201–2.CrossRefGoogle Scholar
Garwin, R. L. and Reich, H. A., Self-Diffusion and Nuclear Relaxation in He3. Phys. Rev. 115 (1959), 1478–92.CrossRefGoogle Scholar
McCall, D. W., Douglass, D. C., and Anderson, E. W., Self-Diffusion Studies by Means of Nuclear Magnetic Resonance Spin-Echo Techniques. Ber. Bunsenges. Phys. Chem. 67 (1963), 336–40.CrossRefGoogle Scholar
Stejskal, E. O. and Tanner, J. E., Spin Diffusion Measurements: Spin Echoes in the Presence of a Time-Dependent Field Gradient. J. Chem. Phys. 42 (1965), 288–92.CrossRefGoogle Scholar
Carr, H. Y. and Purcell, E. M., Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments. Phys. Rev. 94 (1954), 630–8.CrossRefGoogle Scholar
Hahn, E. L., Detection of Sea-Water Motion by Nuclear Precession. J. Geophys. Res. 65 (1960), 776–7.CrossRefGoogle Scholar
Das, T. P. and Saha, A. K., Mathematical Analysis of the Hahn Spin-Echo Experiment. Phys. Rev. 93 (1954), 749–56.CrossRefGoogle Scholar
Woessner, D. E., Effects of Diffusion in Nuclear Magnetic Resonance Experiments. J. Chem. Phys. 34 (1961), 2057–61.CrossRefGoogle Scholar
Nelson, R. J., Maguire, Y., Caputo, D. F., Leu, G., Kang, Y., Pravia, M., Tuch, D., Weinstein, Y. S., and Cory, D. G., Counting Echoes: Application of a Complete Reciprocal-Space Description of Spin Dynamics. Concepts Magn. Reson. 10 (1998), 331–41.3.0.CO;2-Y>CrossRefGoogle Scholar
Kaiser, R., Bartholdi, E., and Ernst, R. R., Diffusion and Field-Gradient Effects in NMR Fourier Spectroscopy. J. Chem. Phys. 60 (1974), 2966–79.CrossRefGoogle Scholar
Wu, E. X. and Buxton, R. B., Effect of Diffusion on the Steady-State Magnetization with Pulsed Field Gradients. J. Magn. Reson. 90 (1990), 243–53.Google Scholar
Callaghan, P. T., Principles of Nuclear Magnetic Resonance Microscopy. (Oxford: Clarendon Press, 1991).Google Scholar
Sørenson, O. W., Eich, G. W., Levitt, M. H., Bodenhausen, G., and Ernst, R. R., Product Operator Formalism for the Description of NMR Pulse Experiments. Prog. NMR Spectrosc. 16 (1983), 163–92.CrossRefGoogle Scholar
Kessler, H., Gehrke, M., and Griesinger, C., Two-Dimensional NMR Spectroscopy: Background and Overview of the Experiments. Angew. Chem. (Int. Ed. Engl) 27 (1988), 490–536.CrossRefGoogle Scholar
Kingsley, P. B., Product Operators, Coherence Pathways, and Phase Cycling. Part I: Product Operators, Spin-Spin Coupling, and Coherence Pathways. Concepts Magn. Reson. 7 (1995), 29–47.CrossRefGoogle Scholar
Kingsley, P. B., Product Operators, Coherence Pathways, and Phase Cycling. Part II: Coherence Pathways in Multipulse Sequences: Spin Echoes, Simulated Echoes, and Multiple-Quantum Coherences. Concepts Magn. Reson. 7 (1995), 115–36.CrossRefGoogle Scholar
Kingsley, P. B., Product Operators, Coherence Pathways, and Phase Cycling. Part III: Phase Cycling. Concepts Magn. Reson. 7 (1995), 167–92.CrossRefGoogle Scholar
Blum, K., Density Matrix Theory and Applications, 2nd edn. (New York: Plenum Press, 1996).CrossRefGoogle Scholar
Callaghan, P. T. and Stepišnik, J., Generalized Analysis of Motion Using Magnetic Field Gradients. Adv. Magn. Opt. Reson. 19 (1996), 325–88.CrossRefGoogle Scholar
Allard, P., Helgstrand, M., and Härd, T., The Complete Homogeneous Master Equation for a Heteronuclear Two-Spin System in the Basis of Cartesian Product Operators. J. Magn. Reson. 134 (1998), 7–16.CrossRefGoogle ScholarPubMed
Levitt, M., Spin Dynamics – Basic Principles of NMR Spectroscopy, 2nd edn. (New York: Wiley, 2008).Google Scholar
Bain, A. D., Operator Formalisms: An Overview. Concepts Magn. Reson. 28A (2006), 369–83.CrossRefGoogle Scholar
Traficante, D. D., Phase-Sensitive Detection. Part II: Quadrature Phase Detection. Concepts Magn. Reson. 2 (1990), 181–95.CrossRefGoogle Scholar
Bain, A. D. and Burton, I. W., Quadrature Detection in One or More Dimensions. Concepts Magn. Reson. 8 (1996), 191–204.3.0.CO;2-U>CrossRefGoogle Scholar
Fukushima, E., Nuclear Magnetic Resonance as a Tool to Study Flow. Annu. Rev. Fluid Mech. 31 (1999), 95–123.CrossRefGoogle Scholar
Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series, and Products, 7th edn. (New York: Academic Press, 2007).Google Scholar
Callaghan, P. T., MacGowan, D., Packer, K. J., and Zelaya, F. O., High-Resolution q-Space Imaging in Porous Structures. J. Magn. Reson. 90 (1990), 177–82.Google Scholar
Deville, G., Bernier, M., and Delrieux, J. M., NMR Multiple Echoes Observed in Solid 3He. Phys. Rev. B 19 (1979), 5666–88.CrossRefGoogle Scholar
Saarinen, T. R. and Johnson, C. S., Jr., Imaging of Transient Magnetization Gratings in NMR. Analogies with Laser-Induced Gratings and Applications to Diffusion and Flow. J. Magn. Reson. 78 (1988), 257–70.Google Scholar
Maas, W. E. and Cory, D. G., Discrete Magnetization Gratings in NMR Spectroscopy. Chem. Phys. Lett. 254 (1995), 165–9.CrossRefGoogle Scholar
Kimmich, R. and Fischer, E., One- and Two-Dimensional Pulse Sequences for Diffusion Experiments in the Fringe Field of Superconducting Magnets. J. Magn. Reson. A 106 (1994), 229–35.CrossRefGoogle Scholar
Sodickson, A. and Cory, D. G., A Generalized gradient or diffusion weighting factor, more commonly written as b-Space Formalism for Treating the Spatial Aspects of a Variety of NMR Experiments. Prog. NMR Spectrosc. 33 (1998), 77–108.CrossRefGoogle Scholar
Song, Y.-Q. and Tang, X., A One-Shot Method for Measurement of Diffusion. J. Magn. Reson. 170 (2004), 136–48.CrossRefGoogle ScholarPubMed
Mansfield, P. and Grannell, P. K., ‘Diffraction’ and Microscopy in Solids and Liquids by NMR. Phys. Rev. B 12 (1975), 3618–34.CrossRefGoogle Scholar
Lever, L. S., Bradley, M. S., and Johnson, C. S., Jr., Comparison of Pulsed Field Gradient NMR and Holographic Relaxation Spectroscopy in the Study of Diffusion of Photochromic Molecules. J. Magn. Reson. 68 (1986), 335–44.Google Scholar
Keeler, J., Clowes, R. T., Davis, A. L., and Laue, E. D., Pulsed-Field Gradients: Theory and Practice. Methods Enzymol. 239 (1994), 145–207.CrossRefGoogle ScholarPubMed
Price, W. S., Gradient NMR. In Annual Reports on NMR Spectroscopy, ed. Webb, G. A.. vol. 32. (London: Academic Press, 1996), pp. 51–142.Google Scholar
Price, W. S., Water Signal Suppression in NMR Spectroscopy. In Annual Reports on NMR Spectroscopy, ed. Webb, G. A.. vol. 38 (London: Academic Press, 1999), pp. 289–354.Google Scholar
Singer, J. R., NMR Diffusion and Flow Measurements and Introduction to Spin Phase Graphing. J. Phys. E: Sci. Instrum. 11 (1978), 281–91.CrossRefGoogle Scholar
Arfken, G. and Weber, H. J., Mathematical Methods for Physicists, 4th edn. (New York: Academic Press, 1995).Google Scholar
Hong, X. and Dixon, W. T., Measuring Diffusion in Inhomogeneous Systems in Imaging Mode Using Antisymmetric Sensitizing Gradients. J. Magn. Reson. 99 (1992), 561–70.Google Scholar
Callaghan, P. T., Pulsed Gradient Spin Echo NMR for Planar, Cylindrical and Spherical Pores under Conditions of Wall Relaxation. J. Magn. Reson. A 113 (1995), 53–9.CrossRefGoogle Scholar
Hürlimann, M. D., Schwartz, L. M., and Sen, P. N., Probability of Return to the Origin at Short Times: A Probe of Microstructure in Porous Media. Phys. Rev. B 51 (1995), 14936–40.CrossRefGoogle ScholarPubMed
Stejskal, E. O., Use of Spin Echoes in a Pulsed Magnetic-Field Gradient to Study Anisotropic Restricted Diffusion and Flow. J. Chem. Phys. 43 (1965), 3597–603.CrossRefGoogle Scholar
Tanner, J. E. and Stejskal, E. O., Restricted Self-Diffusion of Protons in Colloidal Systems by the Pulsed-Gradient, Spin-Echo Method. J. Chem. Phys. 49 (1968), 1768–77.CrossRefGoogle Scholar
Callaghan, P. T., Pulsed Field Gradient Nuclear Magnetic Resonance as Probe of Liquid State Molecular Organization. Aust. J. Phys. 37 (1984), 359–87.CrossRefGoogle Scholar
Kärger, J. and Heink, W., The Propagator Representation of Molecular Transport in Microporous Crystallites. J. Magn. Reson. 51 (1983), 1–7.Google Scholar
Kärger, J. and Stallmach, F., PFG NMR Studies of Anomalous Diffusion. In Diffusion in Condensed Matter, ed. Heitjans, P. and Kärger, J.. (Berlin: Springer, 2006), pp. 417–59.Google Scholar
Callaghan, P. T., How Two Pairs of Gradient Pulses Give Access to New Information about Molecular Dynamics. In Diffusion Fundamentals, ed. Kärger, J., Grinberg, F., and Heitjans, P.. (Leipzig: University of Leipzig, 2005), pp. 321–38.Google Scholar
Hahn, E. L., Echo Phenomena and Non-Linearity. Concepts Magn. Reson. 6 (1994), 193–9.CrossRefGoogle Scholar
Shkarin, P. and Spencer, R. G. S., Direct Simulation of Spin Echoes by Summation of Isochromats. Concepts Magn. Reson. 8 (1996), 253–68.3.0.CO;2-Y>CrossRefGoogle Scholar
Brewer, R. G. and Hahn, E. L., Atomic Memory. Sci. Am. 251 (1984), 42–9.CrossRefGoogle Scholar
Burstein, D., Stimulated Echoes: Description, Applications, Practical Hints. Concepts Magn. Reson. 8 (1996), 269–78.3.0.CO;2-X>CrossRefGoogle Scholar
Tanner, J. E., Use of the Stimulated Echo in NMR Diffusion Studies. J. Chem. Phys. 52 (1970), 2523–6.CrossRefGoogle Scholar
Wu, D., Chen, A., and Johnson, C. S., Jr., An Improved Diffusion-Ordered Spectroscopy Experiment Incorporating Bipolar-Gradient Pulses. J. Magn. Reson. A 115 (1995), 260–4.CrossRefGoogle Scholar
Kimmich, R., NMR: Tomography, Diffusometry, Relaxometry. (Berlin: Springer Verlag, 1997).CrossRefGoogle Scholar
Tanner, J. E., Erratum: Use of the Stimulated Echo in NMR Diffusion Studies. J. Chem. Phys. 57 (1972), 3586.CrossRefGoogle Scholar
Callaghan, P. T., Komlosh, M. E., and Nydén, M., High Magnetic Field Gradient PGSE NMR in the Presence of a Large Polarizing Field. J. Magn. Reson. 133 (1998), 177–82.CrossRefGoogle ScholarPubMed
Price, W. S., Pulsed Field Gradient NMR as a Tool for Studying Translational Diffusion, Part I. Basic Theory. Concepts Magn. Reson. 9 (1997), 299–336.3.0.CO;2-U>CrossRefGoogle Scholar
Avent, A. G., Spin Echo Spectroscopy of Liquid Samples. In Encyclopedia of Nuclear Magnetic Resonance, ed. Grant, D. M. and Harris, R. K.. vol. 7. (New York: Wiley, 1996), pp. 4524–30.Google Scholar
Packer, K. J., The Study of Slow Coherent Molecular Motion by Pulsed Nuclear Magnetic Resonance. Mol. Phys. 17 (1969), 355–68.CrossRefGoogle Scholar
Meiboom, S. and Gill, D., Modified Spin-Echo Method for Measuring Nuclear Relaxation Times. Rev. Sci. Instrum. 29 (1958), 688–91.CrossRefGoogle Scholar
Packer, K. J., Rees, C., and Tomlinson, D. J., A Modification of the Pulsed Magnetic Field-Gradient Spin Echo Method of Studying Diffusion. Mol. Phys. 18 (1970), 421–3.CrossRefGoogle Scholar
Kärger, J., Pfeifer, H., and Heink, W., Principles and Applications of Self-Diffusion Measurements by Nuclear Magnetic Resonance. Adv. Magn. Reson. 12 (1988), 1–89.CrossRefGoogle Scholar
Stepišnik, J., Analysis of NMR Self-Diffusion Measurements by a Density Matrix-Calculation. Physica B & C 104 (1981), 350–64.CrossRefGoogle Scholar
Torrey, H. C., Bloch Equations with Diffusion Terms. Phys. Rev. 104 (1956), 563–5.CrossRefGoogle Scholar
Abragam, A., The Principles of Nuclear Magnetism. (Oxford: Clarendon Press, 1961).Google Scholar
Jeener, J., Macroscopic Molecular Diffusion in Liquid NMR, Revisited. Concepts Magn. Reson. 14 (2002), 79–88.CrossRefGoogle Scholar
Lowe, I. J., The Measurement of Diffusion Using Pulsed NMR. Bull. Magn. Reson. 3 (1981), 163–71.Google Scholar
Grebenkov, D. S., NMR Survey of the Reflected Brownian Motion. Rev. Mod. Phys. 79 (2007), 1077–136.CrossRefGoogle Scholar
Maple 12, Waterloo Maple Inc., Waterloo, ON, Canada (2008).
Karlicek, R. F., Jr. and Lowe, I. J., A Modified Pulsed Gradient Technique for Measuring Diffusion in the Presence of Large Background Gradients. J. Magn. Reson. 37 (1980), 75–91.Google Scholar
Price, W. S. and Kuchel, P. W., Effect of Nonrectangular Field Gradient Pulses in the Stejskal and Tanner (Diffusion) Pulse Sequence. J. Magn. Reson. 94 (1991), 133–9.Google Scholar
Douglass, D. C. and McCall, D. W., Diffusion in Paraffin Hydrocarbons. J. Phys. Chem. 62 (1958), 1102–7.CrossRefGoogle Scholar
Murday, J. S. and Cotts, R. M., Self-Diffusion Coefficient of Liquid Lithium. J. Chem. Phys. 48 (1968), 4938–45.CrossRefGoogle Scholar
Neuman, C. H., Spin Echo of Spins Diffusing in a Bounded Medium. J. Chem. Phys. 60 (1974), 4508–11.CrossRefGoogle Scholar
Kuchel, P. W., Lennon, A. J., and Durrant, C. J., Analytical Solutions and Simulations for Spin-Echo Measurements of Diffusion of Spins in a Sphere with Surface and Bulk Relaxation. J. Magn. Reson. B 112 (1996), 1–17.CrossRefGoogle Scholar
Feller, W., An Introduction to Probability Theory and Its Applications, vol. 1, 3rd edn. (New York: Wiley, 1968).Google Scholar
Gardiner, C. W., Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, 2nd edn. (Berlin: Springer-Verlag, 1996).Google Scholar
Kampen, N. G., Stochastic Processes in Physics and Chemistry, 3rd edn. (Amsterdam: North Holland, 2001).Google Scholar
Barzykin, A. V., Theory of Spin Echo in Restricted Geometries Under a Step-Wise Gradient Pulse Sequence. J. Magn. Reson. 139 (1999), 342–53.CrossRefGoogle Scholar
Gross, B. and Kosfeld, R., Anwendung der Spin-Echo-Methode bei der Messung der Selbstdiffusion. Messtechnik 7 (1969), 171–7.Google Scholar
Callaghan, P. T. and Stepišnik, J., Frequency-Domain Analysis of Spin Motion Using Modulated-Gradient NMR. J. Magn. Reson. A 117 (1995), 118–22.CrossRefGoogle Scholar
Stepišnik, J., Measuring and Imaging Flow. Prog. NMR Spectrosc. 17 (1985), 187–209.CrossRefGoogle Scholar
Johnson, C. S., Jr., Diffusion Measurements by Magnetic Field Gradient Methods. In Encyclopedia of Nuclear Magnetic Resonance, ed. Grant, D. M. and Harris, R. K.. vol. 3. (New York: Wiley, 1996), pp. 1626–44.Google Scholar
Schachter, M., Does, M. D., Anderson, A. W., and Gore, J. C., Measurements of Restricted Diffusion Using an Oscillating Gradient Spin-Echo Sequence. J. Magn. Reson. 147 (2000), 232–7.CrossRefGoogle ScholarPubMed
Parsons, E. C., Does, M. D., and Gore, J. C., Modified Oscillating Gradient Pulses for Direct Sampling of the Diffusion Spectrum Suitable for Imaging Sequences. Magn. Reson. Imaging 21 (2003), 279–85.CrossRefGoogle ScholarPubMed
Momot, K. I., Kuchel, P. W., and Chapman, B. E., Acquisition of Pure-Phase Diffusion Spectra Using Oscillating-Gradient Spin Echo. J. Magn. Reson. 176 (2005), 151–59.CrossRefGoogle ScholarPubMed
Bodenhausen, G., Freeman, R., and Turner, D. L., Suppression of Artifacts in Two-Dimensional J Spectroscopy. J. Magn. Reson. 27 (1977), 511–14.Google Scholar
Stepišnik, J. and Callaghan, P. T., The Long Time Tail of Molecular Velocity Correlation in a Confined Fluid: Observation by Modulated Gradient Spin-Echo NMR. Physica B 292 (2000), 296–301.CrossRefGoogle Scholar
Oppenheim, I. and Mazur, P., Brownian Motion in Systems of Finite Size. Physica 30 (1964), 1833–45.CrossRefGoogle Scholar
Kennan, R. P., Gao, J.-H., Zhong, J., and Gore, J. C., A General Model of Microcirculatory Blood Flow Effects in Gradient Sensitized MRI. Med. Phys. 21 (1994), 539–45.CrossRefGoogle ScholarPubMed
Callaghan, P. T. and Codd, S. L., Flow Coherence in a Bead Pack Observed Using Frequency Domain Modulated Gradient Nuclear Magnetic Resonance. Phys. Fluids 13 (2001), 421–7.CrossRefGoogle Scholar
Meerwall, E. D., Interpreting Pulsed-Gradient Spin-Echo Diffusion Experiments in Polydisperse Specimens. J. Magn. Reson. 50 (1982), 409–16.Google Scholar
Meerwall, E. and Bruno, K. R., Pulsed-Gradient Spin-Echo Diffusion Study of Polydisperse Paraffin Mixtures. J. Magn. Reson. 62 (1985), 417–27.Google Scholar
Meerwall, E. and Palunas, P., The Effects of Polydispersity on Pulsed-Gradient NMR Diffusion Experiments in Polymer Melts. J. Polym. Sci. 25 (1987), 1439–57.CrossRefGoogle Scholar
Callaghan, P. T. and Pinder, D. N., A Pulsed Field Gradient NMR Study of Self-Diffusion in a Polydisperse Polymer System: Dextran in Water. Macromolecules 16 (1983), 968–73.CrossRefGoogle Scholar
Fleischer, G., Geschke, D., Kärger, J., and Heink, W., Peculiarities of Self-Diffusion Studies on Polymer Systems by the Pulsed Field Gradient Technique. J. Magn. Reson. 65 (1985), 429–43.Google Scholar
Stilbs, P., Molecular Self-Diffusion Coefficients in Fourier Transform Nuclear Magnetic Resonance Spectrometric Analysis of Complex Mixtures. Anal. Chem. 53 (1981), 2135–7.CrossRefGoogle Scholar
Stilbs, P., Fourier Transform Pulsed-Gradient Spin-Echo Studies of Molecular Diffusion. Prog. NMR Spectrosc. 19 (1987), 1–45.CrossRefGoogle Scholar
Morris, G. A., Diffusion-Ordered Spectroscopy (DOSY). In Encyclopedia of Nuclear Magnetic Resonance, ed. Grant, D. M. and Harris, R. K.. vol. 9. (New York: Wiley, 2002), pp. 35–44.Google Scholar
Callaghan, P. T. and Pinder, D. N., Influence of Polydispersity on Polymer Self-Diffusion Measurements by Pulsed Field Gradient Nuclear Magnetic Resonance. Macromolecules 18 (1985), 373–9.CrossRefGoogle Scholar
Callaghan, P. T. and Lelievre, J., The Size and Shape of Amylopectin: A Study Using Pulsed Field Gradient Nuclear Magnetic Resonance. Biopolymers 24 (1985), 441–60.CrossRefGoogle Scholar
Fleischer, G., The Effect of Polydispersity on Measuring Polymer Self-Diffusion with the N.M.R. Pulsed Field Gradient Technique. Polymer 26 (1985), 1677–82.CrossRefGoogle Scholar
Price, W. S., NMR Gradient Methods in the Study of Proteins. In Annual Reports on the Progress in Chemistry Section C, ed. Webb, G. A.. vol. 96. (Cambridge: Royal Society of Chemistry, 2000), pp. 3–53.Google Scholar
Vergara, A., Paduano, L., D'Errico, G., and Sartorio, R., Network Formation in Polyethyleneglycol Solutions. An Intradiffusion Study. Phys. Chem. Chem. Phys. 1 (1999), 4875–9.CrossRefGoogle Scholar
Price, W. S., Tsuchiya, F., and Arata, Y., Lysozyme Aggregation and Solution Properties Studied Using PGSE NMR Diffusion Measurements. J. Am. Chem. Soc. 121 (1999), 11503–12.CrossRefGoogle Scholar
Martin, R. B., Comparisons of Indefinite Self-Association Models. Chem. Rev. 96 (1996), 3043–64.CrossRefGoogle ScholarPubMed
Price, W. S., Tsuchiya, F., and Arata, Y., Time-Dependence of Aggregation in Crystallizing Lysozyme Solutions Probed Using NMR Self-Diffusion Measurements. Biophys. J. 80 (2001), 1585–90.CrossRefGoogle ScholarPubMed
Nydén, M. and Söderman, O., An NMR Self-Diffusion Investigation of Aggregation Phenomena in Solutions of Ethyl(hydroxyethyl)cellulose. Macromolecules 31 (1998), 4990–5002.CrossRefGoogle ScholarPubMed
Williams, G. and Watts, D. C., Non-Symmetrical Dielectric Relaxation Behaviour Arising from a Simple Empirical Decay Function. J. Chem. Soc., Faraday Trans. 66 (1970), 80–5.CrossRefGoogle Scholar
Nyström, Bo., Walderhaug, H., and Hansen, F. K., Dynamic Crossover Effects Observed in Solutions of a Hydrophobically Associating Water-Soluble Polymer. J. Phys. Chem. 97 (1993), 7743–52.CrossRefGoogle Scholar
Walderhaug, H., Hansen, F. K., Abrahmsén, S., Persson, K., and Stilbs, P., Associative Thickeners: NMR Self-Diffusion and Rheology Studies of Aqueous Solutions of Hydrophobically Modified Poly(oxyethylene) Polymers. J. Phys. Chem. 97 (1993), 8336–42.CrossRefGoogle Scholar
Liu, M., Mao, X.-A., Ye, C., Huang, He., Nicholson, J. K., and Lindon, J. C., Improved WATERGATE Pulse Sequences for Solvent Suppression in NMR Spectroscopy. J. Magn. Reson. 132 (1998), 125–9.CrossRefGoogle Scholar
Zheng, G., Stait-Gardner, T., Kumar, P. G. Anil, Torres, A. M., and Price, W. S., PGSTE-WATERGATE: A Stimulated-Echo-Based PGSE NMR Sequence with Excellent Solvent Suppression. J. Magn. Reson. 191 (2008), 159–63.CrossRefGoogle Scholar
Morris, K. F. and Johnson, C. S., Jr., Diffusion-Ordered Two-Dimensional Nuclear Magnetic Resonance Spectroscopy. J. Am. Chem. Soc. 114 (1992), 3139–41.CrossRefGoogle Scholar
Morris, K. F. and Johnson, C. S., Jr., Resolution of Discrete and Continuous Molecular Size Distributions by Means of Diffusion-Ordered 2D NMR Spectroscopy. J. Am. Chem. Soc. 115 (1993), 4291–99.CrossRefGoogle Scholar
Hinton, D. P. and Johnson, C. S., Jr., Diffusion Ordered 2D NMR Spectroscopy of Phospholipid Vesicles: Determination of Vesicle Size Distributions. J. Phys. Chem. 97 (1993), 9064–72.CrossRefGoogle Scholar
Johnson, C. S., Jr., Diffusion Ordered Nuclear Magnetic Resonance Spectroscopy: Principles and Applications. Prog. NMR Spectrosc. 34 (1999), 203–56.CrossRefGoogle Scholar
Davies, B., Integral Transforms and Their Applications, 3rd edn. (Berlin: Springer-Verlag, 2002).CrossRefGoogle Scholar
Morris, G. A. and Barjat, H., High Resolution Diffusion Ordered Spectroscopy. In Methods for Structure Elucidation by High-Resolution NMR, ed. Batta, G., Köver, K. E., and Szántay, C., Jr. (Amsterdam: Elsevier, 1997), pp. 209–26.Google Scholar
Pelta, M. D., Barjat, H., Morris, G. A., Davis, A. L., and Hammond, S. J., Pulse Sequences for High-Resolution Diffusion-Ordered Spectroscopy (HR-DOSY). Magn. Reson. Chem. 36 (1998), 706–14.3.0.CO;2-W>CrossRefGoogle Scholar
Gounarides, J. S., Chen, A., and Shapiro, M. J., Nuclear Magnetic Resonance Chromatography: Applications of Pulse Field Gradient Diffusion NMR to Mixture Analysis and Ligand – Receptor Interactions. J. Chromatogr. B 725 (1999), 79–90.CrossRefGoogle ScholarPubMed
Antalek, B., Using Pulsed Gradient Spin Echo NMR for Chemical Mixture Analysis: How to Obtain Optimum Results. Concepts Magn. Reson. 14 (2002), 225–58.CrossRefGoogle Scholar
Antalek, B., Hewitt, J. M., Windig, W., Yacobucci, P. D., Mourey, T., and Le, K., The Use of PGSE NMR and DECRA for Determining Polymer Composition. Magn. Reson. Chem. 40 (2002), S60–71.CrossRefGoogle Scholar
Huo, R., Wehrens, R., Duynhoven, J., and Buydens, L. M. C., Assessment of Techniques for DOSY NMR Data Processing. Anal. Chim. Acta 490 (2003), 231–51.CrossRefGoogle Scholar
Cobas, J. C., Groves, P., Martin-Pastor, M., and Capua, A., New Applications, Processing Methods and Pulse Sequences Using Diffusion NMR. Current Analytical Chemistry 2 (2005), 289–306.CrossRefGoogle Scholar
Chen, A., Wu, D.-H., and Johnson, C. S., Jr., Determination of the Binding Isotherm and Size of the Bovine Serum Albumin–Sodium Dodecyl Sulfate Complex by Diffusion-Ordered 2D NMR. J. Phys. Chem. 99 (1995), 828–34.CrossRefGoogle Scholar
Apanasovich, V. V. and Novikov, E. G., The Method of Fluoresence Decays Simultaneous Analysis. Rev. Sci. Instrum. 67 (1996), 48–54.CrossRefGoogle Scholar
Provencher, S. W., An Eigenfunction Expansion Method for the Analysis of Exponential Recovery Decay Curves. J. Chem. Phys. 64 (1976), 2772–7.CrossRefGoogle Scholar
Borgia, G. C., Brown, R. J. S., and Fantazzini, P., Uniform-Penalty Inversion of Multiexponential Decay Data. J. Magn. Reson. 132 (1998), 65–77.CrossRefGoogle ScholarPubMed
Istratov, A. I. and Vyvenko, O. F., Exponential Analysis in Physical Phenomena. Rev. Sci. Instrum. 70 (1999), 1233–57.CrossRefGoogle Scholar
Song, Y.-Q., Venkataramanan, L., and Burcaw, L., Determining the Resolution of Laplace Inversion Spectrum. J. Chem. Phys. 122 (2005), 104104-1–104104-10.CrossRefGoogle ScholarPubMed
Stilbs, P., Component Separation in NMR Imaging and Multidimensional Spectroscopy Through Global Least-Squares Analysis, Based on Prior Knowledge. J. Magn. Reson. 135 (1998), 236–41.CrossRefGoogle ScholarPubMed
Edzes, H. T., The Nuclear Magnetization as the Origin of Transient Changes in the Magnetic Field in Pulse NMR Experiments. J. Magn. Reson. 86 (1990), 293–303.Google Scholar
Augustine, M. P. and Zilm, K. W., Observation of Bulk Susceptibility Effects in High-Resolution Nuclear Magnetic Resonance. J. Magn. Reson. A 123 (1996), 145–56.CrossRefGoogle Scholar
Levitt, M. H., Demagnetization Field Effects in Two-Dimensional Solution NMR. Concepts Magn. Reson. 8 (1996), 77–103.3.0.CO;2-L>CrossRefGoogle Scholar
Warren, W. S., Huang, S. Y., Ahn, S., and Lin, Y.-Y., Understanding Third-Order Dipolar Effects in Solution Nuclear Magnetic Resonance: Hahn Echo Decays and Intermolecular Triple-Quantum Coherences. J. Chem. Phys. 116 (2002), 2075–84.CrossRefGoogle Scholar
Sousa, P. Loureiro de, Gounot, D., and Grucker, D., Flow Effects in Long-Range Dipolar Field MRI. J. Magn. Reson. 162 (2003), 356–63.CrossRefGoogle Scholar
Bowtell, R., Bowley, R. M., and Glover, P., Multiple Spin Echoes in Liquids in a High Magnetic Field. J. Magn. Reson. 88 (1990), 643–51.Google Scholar
Bedford, A. S., Bowtell, R., and Bowley, R. M., Multiple Spin Echoes in Multicomponent Liquids. J. Magn. Reson. 93 (1991), 516–32.Google Scholar
Einzel, D., Eska, G., Hirayoshi, Y., Kopp, T., and Wölfle, P., Multiple Spin Echoes in a Normal Fermi Liquid. Phys. Rev. Lett. 53 (1984), 2312–15.CrossRefGoogle Scholar
Ardelean, I., Kimmich, R., Stapf, S., and Demco, D. E., Multiple Nonlinear Stimulated Echoes. J. Magn. Reson. 127 (1997), 217–24.CrossRefGoogle ScholarPubMed
Ardelean, I. and Kimmich, R., Principles and Unconventional Aspects of NMR Diffusometry. In Annual Reports on NMR spectroscopy, ed. Webb, G. A.. vol. 49. (London: Elsevier, 2003), pp. 43–115.Google Scholar

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