In the Laboratory
Determination of Spin–Lattice Relaxation Time Using
13C
NMR
W
An Undergraduate Physical Chemistry Laboratory Experiment Zbigniew L. Gasyna* and Antoni Jurkiewicz Department of Chemistry, The University of Chicago, Chicago, IL 60637; *
[email protected] Nuclear magnetic resonance (NMR) spectroscopy has become an indispensable technique for chemists and biochemists in the analysis of conformational, structural, and dynamic properties of molecular and biological systems. Therefore, there is considerable interest in the incorporation of NMR spectroscopy in the undergraduate chemistry curriculum. The principles of NMR are well described in the literature (1). A series of articles by King and Williams published in this Journal (2–6) can serve as an excellent source of information on the Fourier transform NMR as well as multiple-pulse NMR techniques. The subject is also covered in physical chemistry textbooks (7, 8). The majority of NMR experiments published in this Journal are relevant for the organic chemistry laboratory where the analysis of chemical structure plays an important role. A number of NMR-based dynamic experiments have also been described (9–11), including a recent article that deals with 1 H spin–lattice and spin–spin relaxation processes (12). We propose an experiment designed for the physical chemistry laboratory where 13C NMR is applied to determine the spinlattice relaxation time for carbon atoms in n-hexanol. Our experiment takes advantage of the spectral simplicity of 13C NMR in studies of dynamic aspects of the chemical system. The method provides information about the rate of the internal motion of functional groups in a molecule. Determination of T1 by the Inversion-Recovery Method When a sample containing 13C is placed in a static magnetic field, the nuclear spins of 13C will split into two energetically different populations, one up and the other down. The energy difference between these two states depends upon the strength of the magnetic field. When electromagnetic radiation is applied to the nuclear spin system at a resonant frequency, nuclear spin flip transitions are induced between the two energy levels. After the pulse has been applied, a radiationless mechanism called spin–lattice relaxation causes the nuclear spins to return to their equilibrium population as dictated by the Boltzmann distribution. This spin–lattice relaxation occurs with a characteristic time, T1, that depends on the nature and physical state of the sample. A standard inversion-recovery technique is used to determine T1 (13). In this method, the pulse sequence is: delay, 180⬚ pulse, delay τ, 90⬚ pulse, acquisition (FID). For a description of the spin–lattice relaxation, the Bloch equation (14) can be used, M − M0 dM z = − z T1 dτ
(1)
where T1 is the spin–lattice relaxation time, Mz is the Z component of magnetization at the time τ, and M0 is the Z com1038
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ponent of the magnetization when the process reaches thermal equilibrium. Mz is equal to ᎑M0 at the delay time τ = 0. The direct integration of eq 1 gives:
(
Mz = M0 1 − 2 e − τ /T1
)
(2)
A series of Mz values is obtained by varying the delay time, τ, between the 180⬚ and 90⬚ pulses. The recovery is observed as an exponential decay when Mz is plotted versus τ. From the curve, T1 can be determined by using a nonlinear fitting procedure. A plot of ln{[M0 − Mz(t)]兾2M0} versus τ should yield a straight line with slope equal to ᎑1兾T1. Experimental Procedure The spin–lattice relaxation times of carbon atoms in nhexanol are determined using the following procedure.
The Sample The sample for the NMR analysis contains about 70% (v兾v) n-hexanol and 30% (v兾v) CDCl3 sealed in a standard 5-mm o.d. NMR tube. NMR Spectrometer The spectrometer used is a Bruker Model DRX 400 MHz NMR instrument designed to run multinuclear experiments. The spectrometer was tuned to the frequency for 13C. XWINNMR software was used to run the spectrometer and to collect and analyze the raw data. Hazards Strong magnetic fields are present in the NMR laboratory. Standard precautions should be used when handling the sample. CDCl3 is a highly toxic compound and is suspected to cause cancer. 1-Hexanol is a stong irritant. Determination of T1 for 13C in n-Hexanol A spin-decoupling technique is applied to decouple the spin–spin interaction of 1H with 13C, which greatly simplifies the NMR spectra. CDCl3 is used as the lock solvent. The parameters for the acquisition of NMR spectra are set to default values. The students vary the delay time, τ, and can change the number of acquisition scans. For multiple acquisition scans the delay time between each acquisition should be set to a value greater than 5T1 for the relaxation process to be complete. Results and Discussion Although the natural abundance of the 13C isotope is low (1.1%), there is a great advantage in using 13C in NMR spectroscopy: spectral simplicity, especially when proton spin
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In the Laboratory
decoupling is applied. A set of partially relaxed 13C NMR spectra following 180-τ-90 pulse sequences for a sample of n-hexanol is shown in Figure 1. The assignment of the spectrum is indicated. The characteristic upfield shift of the resonance for 13C that is located at a γ position from the oxygen atom is the result of a hyperconjugation effect (15). Individual T1 values for 13C in n-hexanol can be determined from the absolute or integrated peak intensities based on eq 2. Spin–lattice relaxation times are shown in Figure 1. The spin–lattice relaxation of carbon atoms in alkyl chains is overwhelmingly dominated by dipole–dipole interactions with the attached hydrogen atoms. The dipole–dipole interaction depends on the strength of dipolar coupling which in turn depends on the orientation and distance between the interacting nuclei and on the molecular motion. The relaxation time for a carbon atom is related to the effective correlation time for rotational reorientation τc by the following
equation (1, 16), 1 µ0 = N 4π T1
2 2
h γC2 γ H2 τc rCH6
(3)
where µ0 is the permeability of vacuum, γC and γH are gyromagnetic ratios of 13C and 1H, N is the number of directly bonded hydrogen atoms, and rCH is the C–H distance. Equation 3 applies in the “extreme narrowing” limit when 1兾τc is much greater than the resonance frequencies of 13 C and 1H nuclei. The effective correlation times computed from eq 3 are shown in Figure 1. There is a factor of four decrease in correlation time when going from the ⫺CH2OH carbon to the methyl carbon in n-hexanol. This indicates a large degree of internal motion of the methyl group. Internal motion has a large effect on the τc values for alkyl chains only when the overall reorientation of the molecule is restricted. In the case of n-hexanol this restriction is caused by intermolecular hydrogen bonding. Conclusion The experiment described in this article gives students a valuable experience on pulsed NMR methods and instrumentation. Students learn the principles and concepts of NMR spectroscopy as well as dynamics NMR experiments. They find the experiment attractive but challenging with regard to data analysis. W
Supplemental Material
Instructions for the students and notes for the instructor are available in this issue of JCE Online. Literature Cited
Figure 1. Partially relaxed, proton-decoupled 13C NMR spectra of n-hexanol sample containing 30% (v/v) CDCl3 at 100 MHz and 298 K. The interval τ between the 180⬚ pulse and the subsequent 90⬚ pulse is indicated next to each spectrum. The horizontal scale is in ppm from TMS. Spin–lattice relaxation times and effective rotational correlation times are indicated above each carbon. Data are taken from a student’s experiment.
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1. Abragam, A. The Principles of Nuclear Magnetism; Claredon Press: Oxford, U.K., 1961. 2. King, R. W.; Williams, K. R. J. Chem. Educ. 1989, 66, A213. 3. King, R. W.; Williams, K. R. J. Chem. Educ. 1989, 66, A243. 4. Williams, K. R.; King, R. W. J. Chem. Educ. 1990, 67, A93. 5. King, R. W.; Williams, K. R. J. Chem. Educ. 1990, 67, A100. 6. Williams, K. R.; King, R. W. J. Chem. Educ. 1989, 67, A125. 7. Skoog, D. A.; Holler, F. J.; Nieman, T. A. Principles of Instrumental Analysis, 5th ed.; Brooks/Cole: Monterey, CA, 1998; Chapter 19, p 445. 8. Atkins, P.; de Paula, J. Physical Chemistry, 7th ed.; W. H. Freeman and Company: New York, 2002; Chapter 18, p 579. 9. Gasparro, F. P.; Kolodny, N. H. J. Chem. Educ. 1977, 54, 258. 10. Brown, K. C.; Tyson, R. L.; Weil, J. A. J. Chem. Educ. 1998, 75, 1632. 11. Davis, D. S.; Moore, D. E. J. Chem. Educ. 1999, 76, 1617. 12. Lorigan, G. A.; Minto, R. E.; Zhang, W. J. Chem. Educ. 2001, 78, 956. 13. Jackman, L. M.; Cotton, F. A. Dynamic Nuclear Magnetic Resonance Spectroscopy; Academic Press: New York, 1975. 14. Bloch, F. Phys. Rev. 1946, 70, 460. 15. Eliel, E. L.; Bailey, W. F.; Kopp, L. D.; Willer, R. L.; Grant, D. M.; Bertrand, R.; Christensen, K. A.; Dalling, D. K.; Duch, M. W.; Wenkert, E.; Schell, F. M.; Cochran, D. W. J. Am. Chem. Soc. 1975, 97, 322. 16. Hertz, H. G. Prog. Nucl. Magn. Reson. Spectrosc. 1967, 3, 159.
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