In the Laboratory
Teaching the Fundamentals of Pulsed NMR Spectroscopy in an Undergraduate Physical Chemistry Laboratory
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Gary A. Lorigan,* Robert E. Minto, and Wei Zhang Department of Chemistry and Biochemistry, Miami University, Oxford, OH 45056; *
[email protected] Pulsed nuclear magnetic resonance (NMR) spectroscopy has a wide applicability to a diverse array of molecular and biological studies. The wealth of detailed connectivity, spatial, and dynamic information assures the dominance of NMR as an analytical method for the foreseeable future (1–5). Chemists and biochemists routinely use a NMR spectrometer to characterize synthesized and isolated materials (1, 3–6 ). Despite its importance, however, instructors will lightly gloss over the theories of pulsed NMR spectroscopy to avoid confusing students because the physical, quantum mechanical, and instrumental concepts are very difficult to visualize and comprehend (2). Furthermore, most state-of-the-art and many routine NMR experiments require very little understanding of pulsed techniques or sophisticated instrumentation. Although it is important for students to be exposed to state-of the-art instrumentation, this alone does not allow the fundamental concepts or physical parameters associated with NMR spectroscopy to be fully grasped. These include 90° and 180° pulses, time-dependent pulse sequences, free induction decay (FID), spin–lattice relaxation time (T1), and spin–spin relaxation time (T2). Students who utilize a modern pulsed NMR spectrometer often consider it a “black box”. In a typical undergraduate laboratory class, students conducting a pulsed NMR experiment simply click on a mouse button and collect a spectrum, without fully understanding the mechanics of the instrument (7– 10). To resolve all of these issues, we describe in this paper the use of a bench-top pulsed-NMR spectrometer (PS1-B) from Teach Spin, Inc. in an experiment that focuses the students’ attention upon the foundations of this spectroscopic method (11). This instrument is a working modular pulsed NMR spectrometer specifically designed to provide students with an interactive approach to learning the basic principles of pulsed NMR spectroscopy. The theory behind NMR spectroscopy is thoroughly discussed in several textbooks and is beyond the scope of this paper (1, 3). Experimental Procedure
Experimental Apparatus and Material The Teach Spin Inc. PSI-B pulsed NMR spectrometer consists of a pulse programmer, a 15 MHz amplifier/mixer/ receiver, and a permanent magnet interfaced with a Tektronix TDS 210 digital oscilloscope. The relatively low magnetic field strength of the spectrometer is below limits reported to be safe for individuals wearing a pacemaker (14 ). Additional experiments and assembly instructions for the spectrometer are located in the Teach Spin Inc. instrument manual (11). The experimental data were processed on a Power Macintosh G3 computer utilizing the data analysis software programs Igor Pro (Wavemetrics, Inc.) and Microsoft Excel. The NMR samples consisted of mineral oil and glycerin.
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The laboratory experiment has three parts, each utilizing the PS1-B pulsed NMR spectrometer, which can be completed in one laboratory period (less than four hours). This experiment fits into a standard junior/senior-level undergraduate physical chemistry laboratory curriculum. The specific step-by-step experimental procedures for this laboratory are described in detail in the supplemental material.W
Setting Up the Pulsed NMR Spectrometer In the first part of the lab, the students assemble the individual mechanical and electronic components of the pulsed NMR spectrometer and connect the spectrometer to the digital oscilloscope to analyze the pulses and acquire the NMR data. After the students are able to properly generate an rf pulse (as observed on the oscilloscope), a round, flatbottom glass sample tube 4.2 cm long containing 1 mL of mineral oil is placed into the probe of the PS1-B spectrometer (1H Larmor frequency is approximately 15 MHz). Initially, the students utilize a simple π/2 pulse sequence to explore rf pulses as a function of pulse width, power, and recycle delay time. They discover on their own that a shorter pulse width requires more power than a longer one to flip the magnetization 90°. This experiment demonstrates the importance of selecting an appropriate recycle delay time between pulse trains to allow the bulk magnetization to relax back to equilibrium. Finally, students learn how to program more complicated pulse sequences, such as a spin–echo sequence and an inversion–recovery sequence. Overall, the lab provides the students with a “nuts and bolts” approach to learning about the components of a pulsed NMR spectrometer and helps them understand the basics of pulse sequence programming and the mechanics of the spin echo phenomenon. This part of the experiment is also applicable to an instrumental analysis laboratory course because it gives undergraduate students an inside look into the operation and individual components of an NMR spectrometer.
Determination of the Spin–Lattice Relaxation Time via an Inversion–Recovery Pulse Sequence The 1H spin–lattice relaxation time of a glycerin sample is measured utilizing a standard inversion–recovery pulse sequence: π- - -τ- - -π/2–FID (1, 12). The first pulse (π) inverts the z component of the magnetization from Mz to Mz. The π/2 pulse is used to rotate the net z component of the magnetization into the xy plane. The initial π pulse inverts the population of the 1H nuclear spins and a mechanism must exist for the nuclear spins to return to their equilibrium population as dictated by the Boltzmann distribution. This mechanism or process is called spin–lattice relaxation and occurs with a characteristic time constant T1. The return to equilibrium
Journal of Chemical Education • Vol. 78 No. 7 July 2001 • JChemEd.chem.wisc.edu
ln
Meq − M(τ) Meq
ln(Echo Amplitude)
In the Laboratory
0
20
40
60
0
80
10
τ / ms
20
30
40
50
2τ / ms
Figure 1. Determination of the spin–lattice relaxation time for glycerin at room temperature. The experimental data points are shown as circles. The solid line represents a linear least squares fit of the experimental data to eq 2. The slope of the linear fit indicates that T1 is equal to 23 ms.
Figure 2. Estimate of the spin–spin relaxation time for glycerin at room temperature. The experimental data points are shown as triangles. The solid line represents a linear least squares fit of the experimental data to eq 4. The slope of the linear fit indicates that T2 is equal to 19 ms.
(after the population inversion) occurs via an exponential relaxation process as illustrated in the following expression:
echo sequence: π/2- - -τ- - -π- - -τ- - -echo (1, 12). The first π/2 pulse is used to rotate the magnetization at thermal equilibrium (Meq) from the z axis to the y axis.W The delay time τ allows the nuclear spins precessing at slightly different frequencies to dephase in the xy plane. The second pulse (π) flips the magnetization across the xy plane. The second delay time τ allows the spins to refocus together and generate a spin-echo. Students set up this pulse sequence and discover that the spin echo observed on the oscilloscope is actually a back-to-back FID. With this pulse sequence, T2 can be determined by systematically varying the interpulse time τ and measuring the maximum amplitude of the spin echo at each time interval (τ). The exponential decay of the magnetization to zero is represented by
M(τ) = M eq(1 – eτ/T1)
(1)
where M(τ) represents the magnetization (voltage from scope) as a function of the interpulse time τ, M eq is the magnetization at equilibrium, and τ is the variable interpulse delay. Equation 1 can be easily transformed to the form
ln
M eq – M τ M eq
=
τ T1
(2)
where a plot of the ln[(Meq – M(τ))/Meq ] versus τ reveals a linear graph with a slope equal to 1/T1. The students program the inversion–recovery pulse sequence into the spectrometer by manually setting switches to adjust the pulses to the correct widths (µs). After the π/2 pulse, the maximum height of the FID is measured as a function of τ. The interpulse time τ is systematically varied to a maximal value (close to Meq) as determined by the students. Figure 1 shows experimental data gathered from a student’s inversion–recovery experiment on glycerin fit to eq 2. The plot is linear over the entire τ range and reveals an overall 1H T1 value of 23 ms for glycerin, comparable to a theoretically calculated T1 value of 16 ms (13). This segment of the experiment illustrates to students the principles of spin–lattice relaxation and the significance of the time-dependent pulse sequences that are routinely used in multidimensional NMR spectroscopy. Proper measurements of relaxation times are important because they enable data to be collected more efficiently and provide pertinent dynamic information.
Determination of the Spin–Spin Relaxation Time by the Spin-Echo Method The spin–spin relaxation time (T2) describes the decay rate of the magnetization within the xy plane after a π/2 pulse. T2 can be estimated by utilizing a standard two-pulse spin-
M(2τ) = M eqe 2τ/T2
(3)
Equation 3 can be transformed to ln[M(2τ)] = (2τ/T2) + ln(Meq)
(4)
and a plot of the ln[M(2τ)] versus 2τ should reveal a straight line with a slope equal to 1/T2. Thus, by performing a linear least squares fit of the experimental data, T2 can be obtained from the slope. Figure 2 represents this plot for the spin-echo experiment performed on glycerin by a student. The slope of the fitted data indicates that T2 was 19 ms at room temperature. Conclusion The experiment described in this paper gives students an interactive experience on a pulsed NMR spectrometer that enables them to better understand the principles, concepts, and instrumentation associated with NMR spectroscopy. Acknowledgments The pulsed NMR spectrometer was purchased through a Learning Technologies Enrichment Program grant sponsored
JChemEd.chem.wisc.edu • Vol. 78 No. 7 July 2001 • Journal of Chemical Education
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In the Laboratory
by Miami University. We would like to thank Jonathan F. Reichert of Teach Spin Inc. for sharing his expertise with the PS1-B pulsed NMR spectrometer. W
Supplemental Material
The step-by-step experimental procedures for this laboratory are described in detail in this issue of JCE Online. Literature Cited 1. Sanders, J. K. M.; Hunter, B. K. Modern NMR Spectroscopy: A Guide for Chemists, 2nd ed.; Oxford University Press: Oxford, 1993. 2. Slichter, C. P. Principles of Magnetic Resonance, 3rd ed.; Springer: New York, 1992. 3. Ernst, R. R.; Bodenhausen, G.; Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Oxford University Press: Oxford, 1992. 4. Wutrich, K. NMR of Protein and Nucleic Acids; Wiley: New York, 1986.
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5. Evans, J. N. Biomolecular NMR Spectroscopy; Oxford University Press: Oxford, 1995. 6. Cavanagh, J.; Fairbrother, W. J.; Palmer, A. G.; Skelton, N. J. Protein NMR Spectroscopy: Principles and Practice; Academic: San Diego, 1996. 7. McElveen, S. R.; Gavardinas, K.; Stamberger, J. A.; Mohan, R. S. J. Chem. Educ. 1999, 76, 535. 8. Shadwick, S. R.; Mohan, R. S. J. Chem. Educ. 1999, 76, 1121. 9. Sgariglia, E. A.; Schopp, R.; Gavardinas, K.; Mohan, R. S. J. Chem. Educ. 2000, 77, 79. 10. Jameson, D. L.; Anand, R. J. Chem. Educ. 2000, 77, 88. 11. Reichert, J. F. Operation Manual of the PS1-B Pulsed Nuclear Magnetic Resonance Spectrometer; TeachSpin, Inc.: New York, 1998. 12. Braun, S.; Kalinowski, H. O.; Berger, S. 150 and More Basic NMR Experiments—A Practical Course, 2nd ed.; Wiley-VCH: New York, 1998. 13. Koivula, E.; Punkkinen, M.; Tanttila, W. H.; Ylinen, E. E. Phys. Rev. B 1985, 32, 4556. 14. Shellock, F. G.; O’Neil, M.; Ivans, V.; Kelly, D.; O’Connor, M.; Toay, L.; Crues, J. V. Am. J. Roentgenol. 1999, 172, 165.
Journal of Chemical Education • Vol. 78 No. 7 July 2001 • JChemEd.chem.wisc.edu
