In the Laboratory
An NMR Experiment Based on Off-the-Shelf Digital Data-Acquisition Equipment Christian Hilty* and Sean Bowen Center for Biological NMR, Department of Chemistry, Texas A&M University, College Station, Texas 77843 *
[email protected] Nuclear magnetic resonance (NMR) is an analytical tool that most chemists will use at some point in their career. However, teaching an NMR laboratory experiment can be challenging owing to the nontrivial underlying physics, as well as to the expense involved in the purchase and operation of highfield NMR magnets. Several NMR apparatuses for teaching purposes are commercially available (1, 2); see the laboratory experiment by Lorigan and co-workers (3) using an earth's field NMR (1). In recent years, the performance of low-cost digitalto-analog and analog-to-digital converters has improved considerably. As an alternative to commercially available instruments, a low-field NMR spectrometer with direct digital-pulse generation and signal acquisition can at present be realized using off-the-shelf data-acquisition hardware. This implementation offers increased transparency in hardware and software, and provides the basis for a laboratory experiment that teaches the foundations of NMR while providing an introduction to modern scientific data-acquisition and processing techniques to students. Instrumentation For the purpose of teaching the principles of NMR, the chemical shift resolution provided by spectrometers using superconducting magnets is not required. The NMR spectrometer that we have constructed for our laboratory experiment operates on the basic principle of first prepolarizing nuclear spins in the relatively weak field of an electromagnet, then shutting off the electromagnet and conducting an NMR experiment in the magnetic field of the earth. This approach to low-field NMR has been shown to offer superior magnetic-field homogeneity without the need for complicated hardware (4). The core of our low-field NMR instrument is a standard data-acquisition (DAQ) board (National Instruments PCIe6259) that provides analog and digital inputs and outputs (Figure 1). This hardware allows direct programmatic control to synthesize output waveforms that form NMR pulse sequences and to acquire data, while preserving phase coherence. Its functions are controlled using the LabView software package, which allows students to interact with it via a convenient graphical programming interface. Also using LabView, we have created a tool to view and to export the acquired data into formats suitable for further processing, for example, in a spreadsheet application. In addition to signal generation and data acquisition, the NMR instrument needs a magnet and radio frequency (RF) coil, the design of which we have loosely based upon the description of Callaghan and co-workers (4). A pulsed field gradient unit is also controlled by a digital-to-analog converter of the data-acquisition
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board and realized similar to the setup described by Halse and co-workers (5). The spectrometer allows for a sample volume of ca. 400 mL. Additionally, amplifiers are required for delivering pulses and for driving the prepolarization coil, as well as a signal preamplifier. We have opted to use commercially available components for this purpose (see the supporting information); alternatively, it would be possible to realize substantial savings by assembling some electronics in-house. Pedagogical Format The low-field NMR spectrometer allows for considerable flexibility in the design of a laboratory experiment. In our redesigned physical chemistry laboratory course (6), groups of 2-4 students work with the spectrometer for three periods of 3 h each. The experiment is balanced between conveying the theory of magnetic resonance through an inquiry-based process, and demonstrating the concepts of modern, digital instrument control and data acquisition. The first laboratory period is dedicated to instrumentation. Students assemble the signal path of the spectrometer according to a diagram that is provided (see the supporting information). The placement of the magnet perpendicular to the ambient magnetic field is performed with the aid of a Gauss meter. From the measured field, the precession frequency of proton spins is calculated (approximately 3 kHz). Students tune the RF coil, which they have previously assembled as part of an LC circuit, to this frequency. Subsequently, an NMR signal of, for example, a bottle of water can be measured. At this point, students are introduced to the software that is controlling the instrument. The “code” created in LabView is based on a diagram of functional blocks that can be rearranged to generate the desired NMR experiment, largely without prior knowledge of computer programming. This ease of use was the primary determinant in our choice of the LabView software package. An experiment is set up for determining the length of a 90 RF pulse. This pulse length is crucial as it will be required in all subsequent experiments to convert the longitudinal magnetization into an observable coherence. Parameters pertaining to data acquisition, such as analog filter and sampling interval, need to be set, providing an introduction to the Nyquist theorem and oversampling. The experiment provides opportunities to expand on its scope by an inquiry-driven process. For example, from the impulse response, it is possible to calculate the Q-factor of the resonant circuit (7). Further, data-processing techniques, including Fourier transformations, may be explored using external programs such as Matlab or Octave.
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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 7 July 2010 10.1021/ed1002724 Published on Web 05/19/2010
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In the Laboratory
signal intensity, I, that is exponentially decaying from an initial value I0, due to T2 relaxation (Figure 2), I ¼ I0 e - t=T2
Figure 1. Principal hardware components. Arrows indicate the paths of the generated and acquired signals.
Students consult external references to explain variations in T1 and T2 relaxation times for different substances. Both of these relaxation times are affected by the spectral density of stochastic molecular motions at frequencies related to the NMR frequency. Local magnetic field fluctuations induced by these motions through a variety of mechanisms, such as the coupling of nuclear spins based on their dipolar magnetic interaction, cause spin relaxation. For example, the spin-lattice relaxation time of water drops from between 2 and 3 to 1.5 s if 20% glycerol is added. This change can be explained by the increased viscosity of the sample, which increases the correlation time for molecular tumbling (8). Paramagnetic relaxation, which is due to interaction with an unpaired electron spin, forms the basis for contrast agents in magnetic resonance imaging in the human body. To illustrate this concept, relaxation rates R1 = 1/T1 and R2 = 1/T2 of solutions containing the free radical 4-hydroxy-2,2,6,6-tetramethylpiperidinyloxy (TEMPOL) are measured and found to increase linearly with increasing radical concentration (9). Finally, the pulsed field gradient makes the precession frequency dependent on position and provides the capability of spatial resolution. In the third laboratory period, we use pulsed field gradients for the measurement of self-diffusion. The obtained diffusion parameters represent a direct physical characteristic of the substance. As such, it should be possible to use a simple model for understanding trends. Indeed, based on the measured diffusion constant, D, and estimated radius r of a solvent molecule, the Stokes-Einstein relation (10) D ¼
Figure 2. (A) Train of spin-echoes acquired for determining the T2 relaxation time using a CPMG pulse sequence (RF pulses are removed). (B) Expanded view of the first echo.
Easily accessible yet meaningful NMR parameters are the spin-lattice and spin-spin relaxation times. These parameters form the basis for the second 3-h laboratory period. The spin-lattice relaxation time T1 is measured by reprogramming the software to carry out a series of experiments with increasing prepolarization time t, where the signal intensity, I, builds up asymptotically to the equilibrium value, I¥, I ¼ I¥ ð1 - e - t=T1 Þ
ð1Þ
The spin-spin relaxation time T2 can be determined by a Carr-Purcell-Meiboom-Gill (CPMG) sequence, which consists of a train of spin-echoes that refocus the loss of coherence owing to macroscopic magnetic field inhomogeneities, yielding a 748
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ð2Þ
kT 6τηr
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can be used for a crude estimate of the viscosity of the solvent, η. The calculation based on data measured for water (see the supporting information), for example, yields a viscosity η = 8.7 10-4 m-1 kg s-1 for T = 293 K. A literature value is η = 10.0 10-4 m-1 kg s-1 (11), and students are asked to determine both conceptual and experimental sources of errors. In three semesters of implementation, the experiment has proven a robust addition to our physical chemistry curriculum. The low-field experiment is different from a typical high-field experiment because chemical shifts are collapsed and typical NMR spectra cannot be obtained. However, the experiment provides a concise introduction to magnetic resonance and the principles of digital data acquisition. We assess our experiment with end-of-semester questionnaires. Not surprisingly, some students note that this experiment is more challenging than the typical single-period laboratory, but many have expressed that they feel they have learned more. While the described experiments conclude the formal part of the NMR module in our physical chemistry laboratory, other possible uses of the spectrometer include the measurement of relaxation and diffusion parameters in various foods, which exhibit different NMR properties primarily owing to their differing viscosity. Also noteworthy is the ability to distinguish soft drinks of both regular and diet varieties
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based on their T2 relaxation times. While high-field NMR is incompatible with metal objects, this measurement can be carried out at earth field even without opening the aluminum can. The reason is that the skin depth of the induced alternating current at the frequency of 3 kHz in the aluminum wall of the can is larger than the wall thickness, allowing RF waves to penetrate (12). NMR measurements on foods are also related to commercial applications of low-field NMR in industrial quality control (13). Hazards Electrical currents up to 20 A and voltages up to 120 V may be present in the system. This presents a burn and electric shock hazard. Exposed leads must not be touched while the system is operating, and metal enclosures must be properly grounded. Toluene is flammable and toxic. Isopropanol is flammable and harmful. Glycerol and 4-hydroxy-2,2,6,6-tetramethylpiperidine 1-oxyl (TEMPOL) are harmful. Acknowledgment We thank Simon North for leading the redesign effort of the physical chemistry laboratory, Holly Gaede for useful suggestions, Amanda Schuckman for assistance with the construction of the instrument, and Texas A&M University for financial support. C.H. acknowledges the Camille and Henry Dreyfus Foundation for a New Faculty Award, and S.B. was supported by the Texas A&M University Chemistry-Biology Interface program, as well as by a Texas A&M University diversity fellowship.
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Literature Cited 1. TeachSpin Home Page. http://www.teachspin.com/ (accessed Apr 2010). 2. Earth's Field NMR Science Home Page. http://www.magritek. com/earthsfieldscience.html (accessed Apr 2010). 3. Lorigan, G.; Minto, R.; Zhang, W. J. Chem. Educ. 2001, 78, 956–958. 4. Callaghan, P. T.; Eccles, C. D.; Seymour, J. D. J. Rev. Sci. Instrum. 1997, 68, 4263–4270. 5. Halse, M. E.; Coy, A.; Dykstra, R.; Eccles, C.; Hunter, M.; Ward, R.; Callaghan, P. T. J. Magn. Reson. 2006, 182, 75–83. 6. Batteas, J.; Brown, L.; Cremer, P.; Hilty, C.; Gao, Y.; Gaede, H.; North, S.; Son, D.; Soriaga, E. manuscript in preparation. 7. Hoult, D. I. Prog. Nucl. Magn. Reson. Spectrosc. 1978, 12, 41–77. 8. Cavanagh, J. Protein NMR Spectroscopy: Principles and Practice; Academic Press: San Diego, CA, 1996. 9. Wood, M. L.; Hardy, P. A. J. Magn. Reson. Imaging 1993, 3, 149–156. 10. Atkins, P.; de Paula, J. Physical Chemistry, 7th ed.; Oxford University Press: Oxford, 2002. 11. CRC Handbook of Chemistry and Physics; Lide, D. R., Ed.; Taylor and Francis: Boca Raton, FL, 2007. 12. Mo.ssle, M.; Han, S.; Myers, W. R.; Lee, S.; Kelso, N.; Hatridge, M.; Pines, A.; Clarke, J. J. Magn. Reson. 2006, 179, 146–151. 13. Todt, H.; Guthausen, G.; Burk, W.; Schmalbein, D.; Kamlowski, A. Food Chem. 2006, 96, 436–440.
Supporting Information Available Student manual; construction plans; materials for the instructor; LabView program files and example data sets are available via the Internet at http://pubs.acs.org or from the authors.
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