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. Author manuscript; available in PMC: 2010 Jan 1.
Published in final edited form as: J Magn Reson. 2008 Sep 25;196(1):84–87. doi: 10.1016/j.jmr.2008.09.019

Measurement of sample temperatures under magic-angle spinning from the chemical shift and spin-lattice relaxation rate of 79Br in KBr powder

Kent R Thurber 1, Robert Tycko 1,*
PMCID: PMC2632797  NIHMSID: NIHMS89403  PMID: 18930418

Abstract

Accurate determination of sample temperatures in solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) can be problematic, particularly because frictional heating and heating by radio-frequency irradiation can make the internal sample temperature significantly different from the temperature outside the MAS rotor. This paper demonstrates the use of 79Br chemical shifts and spin-lattice relaxation rates in KBr powder as temperature-dependent parameters for the determination of internal sample temperatures. Advantages of this method include high signal-to-noise, proximity of the 79Br NMR frequency to that of 13C, applicability from 20 K to 320 K or higher, and simultaneity with adjustment of the MAS axis direction. We show that spin-lattice relaxation in KBr is driven by a quadrupolar mechanism. We demonstrate a simple approach to including KBr powder in hydrated samples, such as biological membrane samples, hydrated amyloid fibrils, and hydrated microcrystalline proteins, that allows direct assessment of the effects of frictional and radio-frequency heating under experimentally relevant conditions.

Keywords: solid state NMR, magnetic resonance, magic-angle spinning, temperature calibration

1. Introduction

In nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) NMR, the sample is generally at the center of a rapidly spinning rotor, preventing placement of a conventional temperature sensor at the sample position. The sample temperature can be strongly affected by frictional heating of the rotor (particularly at high MAS frequencies) or absorption of energy from radio-frequency (rf) electric fields (particularly in hydrated samples or other lossy samples). Additionally, when separate gas sources are used for MAS drive and bearings and for temperature control, the temperature of the gas that surrounds the MAS rotor may be uncertain. Temperature gradients across the MAS rotor and in the surrounding gas create further complications.

Several techniques for determination of internal sample temperatures have been proposed, including calibrations by known phase transition temperatures [1–5] and measurements of temperature-dependent chemical shifts for 13C in samarium acetate [6], 15N in TTAA [7], 1H in bulk water [8], 1H in methanol soaked into TTMSS [9], 207Pb in lead nitrate [10–13], 119Sn in Sm2Sn2O7 and other compounds [14,15], 31P in (VO)2P2O7 [16], and 1H and 31P in aqueous solutions of TmDOTP [17]. Alternatively, the temperature dependence of a spin-lattice relaxation rate (1/T1) can be used, e.g., that of 7Li [18]. The shift of quartz crystal resonances [19] and the 35Cl NQR frequency of NaClO3 [20,21] have also been proposed as useful temperature-dependent parameters.

In this Communication, we describe temperature measurements based on the chemical shift and T1 of 79Br in KBr powder. This method has a number of advantages, especially for 13C MAS NMR: (i) The 79Br NMR frequency differs from the 13C NMR frequency by only 0.4%, allowing the 13C channel of the NMR probe to be used with only minor retuning; (ii) The temperature range from 20 K to 320 K or higher can be covered; (iii) The 79Br signal can be used for both temperature and magic-angle monitoring [22]; (iv) The 79Br signal is strong and T1 is short at temperatures above 40 K. Small quantities of KBr are therefore sufficient, which can be included in the sample without sacrificing much sample volume as described below. Additionally, KBr is not highly toxic.

2. Temperature-dependent spin-lattice relaxation

Figure 1a shows the temperature dependence of T1 for 79Br in KBr. T1 changes by almost three orders of magnitude from 100 K to 15 K, providing very good temperature sensitivity. Although the temperature dependence is weaker at higher temperatures, the fast spin-lattice relaxation (T1 = 75 ± 3 ms at 296 K) allows rapid measurement with high signal-to-noise, so that T1 measurements can be used to determine sample temperatures up to at least 320 K.

Figure 1.

Figure 1

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(a) 79Br spin-lattice relaxation time T1 in KBr powder (static sample) as a function of temperature. The solid line is a theoretical expression for quadrupolar relaxation due to phonons [26,27], with the overall normalization fit to the experimental result at 70 K. The dashed line is the empirical expression given in the text. (b) Ratio of T1 values for 79Br and 81Br in KBr as a function of temperature. Solid and dashed lines show the expected ratios for quadrupolar and magnetic relaxation, respectively. T1 values were measured at 9.4 T.

Figure 1b compares T1 values for 79Br and 81Br. Both are spin-3/2 isotopes with high abundance and similar gyromagnetic ratios, allowing comparative measurements without modification of the NMR probe. For quadrupolar relaxation, 1/T1 is proportional to the quadrupole interaction squared, i.e., 1/T1 ∞ νQ2; for magnetic relaxation, 1/T1 is proportional to the magnetic interaction squared, i.e., 1/T1 ∞ γ2 [23]. Thus, the ratio of the 81Br relaxation rate to the 79Br relaxation rate is predicted to be 0.701 for quadrupolar relaxation and 1.16 for magnetic relaxation [24]. Data in Figure 1b demonstrate that spin-lattice relaxation in KBr is dominated by quadrupolar interactions down to at least 20 K. This result suggests that paramagnetic impurities, which might vary between samples, do not play a significant role. In fact, our T1 measurements on KBr powder ground with a mortar and pestle are consistent with previous measurements on an optically pure single crystal [25].

The experimental T1 data for 79Br fit the following empirical expression (dashed line in Figure 1a) to within 5% between 20 K and 296 K: T1 = 0.0145+5330T−2 + (1.42×107)T−4 + (2.48×109)T−6 (seconds). This empirical 1 expression is similar to the theoretical temperature dependence for quadrupolar relaxation using a Debye distribution for lattice phonons. The solid line in Figure 1a shows the theoretical expression with only one adjustable parameter, the overall normalization of the relaxation rate [26,27]. Well above the Debye temperature of ΘD = 177 K [25,28], T1 is proportional to T−2 in theory, consistent with the experimental results. Below the Debye temperature, phonons are frozen out, and the temperature dependence is stronger. In the low temperature limit, T1 is proportional to T−7 in theory [27]. However, this limit is only a good approximation at temperatures below our measurement range (T < 0.02ΘD = 3.5 K) [27].

T1 data in Figure 1 were measured at 9.4 T in a non-spinning helium-cooled probe, based on a customized Janis SuperTran continuous flow cryostat, that provides accurate sample temperatures [29–31] using both Cernox and platinum resistor temperature sensors (Lake Shore Cryotronics). The T1 values were measured by saturation-recovery of the central NMR line (saturation with 5 to 80 π/2 pulses with 0.3 to 10 ms gaps), using a single-exponential fit. In general, spin-lattice relaxation of a nucleus with spin > 1/2 is not single-exponential, and the relaxation of the central and satellite transitions will be different [32]. However, for KBr under MAS, we have found the T1 values of the central NMR line and the MAS sidebands to be equal, both at room temperature and 25 K. We attribute this observation to fast spin exchange among the different transitions across the fairly narrow width (~25 kHz) of the quadrupolar-broadened lineshape. The spin-spin relaxation time of 81Br is 400 μs at room temperature [33], and we have measured ~200 μs for 79Br at 30 K (non-spinning). Also, T1 for 79Br at different MAS frequencies νMAS does not show any change other than that expected from frictional heating up to at least νMAS = 16 kHz (see Figure 2).

Figure 2.

Figure 2

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(a) Correlation of the 79Br chemical shift of KBr powder under MAS with that of 207Pb in lead nitrate, using identical conditions for the two measurements. The temperature scale is determined from the reported temperature dependence of the 207Pb chemical shift [10]. (b) Temperature dependence of the 79Br chemical shift of KBr powder under MAS, with the temperature scale determined by 79Br T1 measurements. Inset shows the 79Br chemical shift in a static sample at lower temperatures. Solid circles in (a) and (b) are data in which heated or cooled nitrogen gas was used to vary the sample temperature. Open circles are data in which the sample temperature was raised above room temperature by MAS at various spinning frequencies. Solid lines are linear fits. Chemical shifts are normalized to 0.0 ppm at 296 K (100.025761 MHz for 79Br, 83.227189 MHz for 207Pb).

3. Temperature-dependent chemical shifts

Sample temperatures can also be determined from the temperature dependence of the 79Br chemical shift. This can be a more rapid and convenient approach than T1 measurements. Figure 2a compares the 79Br chemical shift in KBr powder to the 207Pb chemical shift in lead nitrate at various temperatures, measured with a Varian 3.2 mm MAS probe at 9.4 T. As previously shown by Bielecki and Burum [10], the 207Pb shift has a 0.753 ppm/K temperature dependence, which is used to calibrate the temperature axis in Figure 2a. Both chemical shifts are set to 0.0 ppm at 296 K. Sample temperatures in Figure 2a were varied from 260 K to 324 K by supplying heated or cooled nitrogen gas to the probe’s variable-temperature (VT) input (filled circles) or by varying νMAS (open circles). Corresponding KBr and lead nitrate measurements were made under identical conditions of νMAS, VT gas flow, and VT gas temperature. A linear fit of the 79Br data yields a −0.0249 ± 0.0015 ppm/K slope.

Figure 2b shows temperature-dependent 79Br chemical shift measurements in which sample temperatures were determined from the 79Br T1 measurements described above. A linear fit of these data yields a −0.0250 ± 0.0004 ppm/K slope, in excellent agreement with the slope determined from Figure 2a.. The linear dependence on temperature breaks down below 100 K, as shown by data in the inset to Figure 2b, which were obtained in the non-spinning cryostat.

To use KBr as a temperature sensor within another sample of interest (especially a hydrated sample where dissolution of KBr powder would occur), we use the simple MAS rotor configuration depicted in Figure 3. A plug of KBr powder (2.0 mg) is loaded into a hole in the end of a modified nylon screw (2–56 gauge), which is then threaded into one of the rotor end caps. Epoxy or cyanoacrylate glue is used to seal the KBr powder in place. Equivalent configurations are readily devised, depending on the rotor diameter or other factors. Figure 3 shows examples of 79Br spectra recorded at 14.1 T with a Varian 5 mm MAS probe when the rotor is filled with a hydrated multilamellar 1,2,-dioleoyl-sn-glycero-3-phosphocholine(DOPC) lipid bilayer sample. In Figure 3a, the spectra were recorded at various νMAS values and with various VT nitrogen gas temperatures (100 scfh flow rate), using single-pulse excitation of 79Br and no irradiation on the proton channel of the probe. Each spectrum was acquired in about two seconds (16 scans, 0.1 s recycle delay). Central-transition 79Br NMR frequencies were determined to ±2 Hz by fitting the NMR lines to Gaussian/Lorentzian functions, corresponding to ±0.5° C uncertainties in actual sample temperatures. Dependences of the sample temperature on νMAS and VT gas temperature are easily measured.

Figure 3.

Figure 3

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(a) 79Br NMR spectra of KBr powder within a hydrated DOPC sample, obtained without proton decoupling at MAS frequencies and nominal temperatures indicated in parentheses. Actual sample temperatures reported above the parentheses were determined from the 79Br NMR frequencies. Spectra were obtained at 14.1 T with 16 scans, and show only the central transition. Nominal temperatures are the temperature of nitrogen gas used for temperature control. The NMR frequency corresponding to room temperature (22.0° C) was determined at 2.00 kHz MAS, where frictional heating is negligible. (b) Effect of proton decoupling (71 kHz rf field strength, 30.72 ms free induction decay length) on sample temperature. Spectra were acquired in 32 scans with the indicated recycle delays after equilibration by repeated pulsing for at least one minute.

In Figure 3b, the spectra were recorded at νMAS = 7.00 kHz with various recycle delays and with a 71 kHz proton decoupling field during the 30.72 ms 79Br free induction decay. Dependences on the duty factor (i.e., average decoupling power) are easily measured and are quite large for recycle delays in the 1–2 s range, as commonly used in solid state 13C and 15N NMR experiments. Results in Figure 3 demonstrate the simplicity of internal sample temperature measurements based on 79Br NMR, as well as the importance of doing such measurements prior to MAS NMR experiments on temperature-sensitive samples. To mimic experiments that involve multiple time periods with different decoupling levels, appropriate blocks of rf irradiation can be applied to the proton channel before excitation of the 79Br free induction decay.

4. Conclusion

We expect 79Br chemical shift and T1 measurements to be useful for sample temperature determinations in a variety of settings, including MAS NMR studies of the structural properties of biomolecular systems and studies of molecular dynamics, thermodynamics, or chemical kinetics based on temperature-dependent spin relaxation rates, lineshapes, or NMR signal amplitudes. In addition, progress on the development of technology for low-temperature MAS NMR [21,34] and dynamic nuclear polarization [35] requires measurements of internal sample temperatures and will be facilitated by the methods described above.

Acknowledgments

This work was supported by the Intramural Research Program of the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK), a component of the National Institutes of Health (NIH), and by a grant from the NIH Intramural AIDS Targeted Antiviral Program. We thank Dr. Junxia Lu for assistance with the measurements in Figure 3.

Footnotes

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References

  • 1.Limbach HH, Hennig J, Kendrick R, Yannoni CS. Proton-transfer kinetics in solids: tautomerism in free base porphines by 15N CPMAS NMR. J Am Chem Soc. 1984;106:4059–4060. [Google Scholar]
  • 2.Haw JF, Crook RA, Crosby RC. Solid-solid phase transitions for temperature calibration in magic-angle spinning. J Magn Reson. 1986;66:551–554. [Google Scholar]
  • 3.Bjorholm T, Jakobsen HJ. 31p mas nmr of p4s3. Crystalline-to-plastic phase transition induced by MAS in a double air-bearing stator. J Magn Reson. 1989;84:204–211. [Google Scholar]
  • 4.Anderson-Altmann KL, Grant DM. A solid-state 15N NMR study of the phase transitions in ammonium nitrate. J Phys Chem. 1993;97:11096–11102. [Google Scholar]
  • 5.Klymachyov AN, Dalal NS. Squaric acid as an internal standard for temperature measurements in 13C MAS NMR. Solid State Nucl Magn Reson. 1996;7:127–134. doi: 10.1016/s0926-2040(96)01245-3. [DOI] [PubMed] [Google Scholar]
  • 6.Campbell GC, Crosby RC, Haw JF. 13C chemical shifts which obey the Curie law in CP/MAS NMR spectra. The first CP/MAS chemical-shift thermometer. J Magn Reson. 1986;69:191–195. [Google Scholar]
  • 7.Wehrle B, Aguilar-Parrilla F, Limbach HH. A novel 15N chemical shift NMR thermometer for magic-angle spinning experiments. J Magn Reson. 1990;87:584–591. [Google Scholar]
  • 8.Dvinskikh SV, Castro V, Sandstrom D. Heating caused by radio-frequency irradiation and sample rotation in 13C magic-angle spinning NMR studies of lipid membranes. Magn Reson Chem. 2004;42:875–881. doi: 10.1002/mrc.1477. [DOI] [PubMed] [Google Scholar]
  • 9.Aliev AE, Harris KDM. Simple technique for temperature calibration of a MAS probe for solid state NMR spectroscopy. Magn Reson Chem. 1994;32:366–369. [Google Scholar]
  • 10.Bielecki A, Burum DP. Temperature dependence of 207Pb MAS spectra of solid lead nitrate. An accurate, sensitive thermometer for variable temperature MAS. J Magn Reson A. 1995;116:215–220. [Google Scholar]
  • 11.Gorkom LCMv, Hook JM, Logan MB, Hanna JV, Wasylishen RE. Solid state lead-207 NMR of lead(II) nitrate: localized heating effects at high magic-angle spinning speeds. Magn Reson Chem. 1995;33:791–795. [Google Scholar]
  • 12.Isbester PK, Zalusky A, Lewis DH, Douskey MC, Pomije MJ, Mann KR, Munson EJ. NMR probe for heterogeneous catalysis with isolated reagent flow and magic-angle spinning. Catalysis Today. 1999;49:363–375. [Google Scholar]
  • 13.Takahashi T, Kawashima H, Sugisawa H, Baba T. 207Pb chemical shift thermometer at high temperature for magic-angle spinning experiments. Solid State Nucl Magn Reson. 1999;15:119–123. doi: 10.1016/s0926-2040(99)00039-9. [DOI] [PubMed] [Google Scholar]
  • 14.Grey CP, Cheetham AK, Dobson CM. Temperature-dependent solid-state 119Sn MAS NMR of Nd2Sn2O7, Sm2Sn2O7, and Y1.8Sm0.2Sn2O7. Three sensitive chemical shift thermometers. J Magn Reson A. 1993;101:299–306. [Google Scholar]
  • 15.Langer B, Schnell I, Spiess HW, Grimmer AR. Temperature calibration under ultrafast MAS conditions. J Magn Reson. 1999;138:182–186. doi: 10.1006/jmre.1999.1717. [DOI] [PubMed] [Google Scholar]
  • 16.Pan H, Gerstein BC. NMR of 31P in (Vo)2P2O7 as an internal temperature standard in high-temperature NMR. J Magn Reson. 1991;92:618–619. [Google Scholar]
  • 17.Zuo CS, Metz KR, Sun Y, Sherry AD. NMR temperature measurements using a paramagnetic lanthanide complex. J Magn Reson. 1998;133:53–60. doi: 10.1006/jmre.1998.1429. [DOI] [PubMed] [Google Scholar]
  • 18.Wullen Lv, Schwering G, Naumann E, Jansen M. MAS NMR at very high temperatures. Solid State Nucl Magn Reson. 2004;26:84–86. doi: 10.1016/j.ssnmr.2004.03.001. [DOI] [PubMed] [Google Scholar]
  • 19.Simon G. Quartz crystal temperature sensor for MAS NMR. J Magn Reson. 1997;128:194–198. [Google Scholar]
  • 20.Tycko R. Adiabatic rotational splittings and Berry’s phase in nuclear quadrupole resonance. Phys Rev Lett. 1987;58:2281–2284. doi: 10.1103/PhysRevLett.58.2281. [DOI] [PubMed] [Google Scholar]
  • 21.Thurber KR, Tycko R. Biomolecular solid state NMR with magic-angle spinning at 25 K. J Magn Reson. doi: 10.1016/j.jmr.2008.09.015. under review. [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 22.Frye JS, Maciel GE. Setting the magic angle using a quadrupolar nuclide. J Magn Reson. 1982;48:125–131. [Google Scholar]
  • 23.Abragam A. Principles of nuclear magnetism. New York: Oxford University Press; 2002. [Google Scholar]
  • 24.Lide DR, editor. CRC handbook of chemistry and physics. 86. Boca Raton, FL: CRC Press; 2005. Nuclear spins, moments, and other data related to NMR spectroscopy. [Google Scholar]
  • 25.Wikner EG, Blumberg WE, Hahn EL. Nuclear quadrupole spin-lattice relaxation in alkali halides. Phys Rev. 1960;118:631–639. [Google Scholar]
  • 26.Kranendonk Jv, Walker M. Theory of quadrupolar nuclear spin-lattice relaxation due to anharmonic Raman phonon processes. Phys Rev Lett. 1967;18:701–703. [Google Scholar]
  • 27.Kranendonk Jv. Theory of quadrupolar nuclear spin-lattice relaxation. Physica. 1954;20:781–800. [Google Scholar]
  • 28.Berg WT, Morrison JA. The thermal properties of alkali halide crystals. I. The heat capacity of potassium chloride, potassium bromide, potassium iodide and sodium iodide between 2.8 and 270 degrees K. Proc Royal Soc London Ser A. 1957;242:467–477. [Google Scholar]
  • 29.Michal CA, Tycko R. Stray-field NMR imaging and wavelength dependence of optically pumped nuclear spin polarization in InP. Physical Review B. 1999;60:8672–8679. [Google Scholar]
  • 30.Tycko R, Dabbagh G, Fleming RM, Haddon RC, Makhija AV, Zahurak SM. Molecular dynamics and the phase transition in solid C60. Phys Rev Lett. 1991;67:1886–1889. doi: 10.1103/PhysRevLett.67.1886. [DOI] [PubMed] [Google Scholar]
  • 31.Tycko R, Dabbagh G, Rosseinsky MJ, Murphy DW, Ramirez AP, Fleming RM. Electronic properties of normal and superconducting alkali fullerides probed by 13C nuclear magnetic resonance. Phys Rev Lett. 1992;68:1912–1915. doi: 10.1103/PhysRevLett.68.1912. [DOI] [PubMed] [Google Scholar]
  • 32.Andrew ER, Tunstall DP. Spin-lattice relaxation in imperfect cubic crystals and in non-cubic crystals. Proc Phys Soc. 1961;78:1–11. [Google Scholar]
  • 33.Halstead TK, Osment PA, Sanctuary BC, Tegenfeldt J, Lowe IJ. Multipole NMR. VII. Bromine NMR quadrupolar echoes in crystalline KBr. J Magn Reson. 1986;67:267–306. [Google Scholar]
  • 34.Carravetta M, Danquigny A, Mamone S, Cuda F, Johannessen OG, Heinmaa I, Panesar K, Stern R, Grossel MC, Horsewill AJ, Samoson A, Murata M, Murata Y, Komatsu K, Levitt MH. Solid state NMR of endohedral hydrogen-fullerene complexes. Phys Chem Chem Phys. 2007;9:4879–4894. doi: 10.1039/b707075f. [DOI] [PubMed] [Google Scholar]
  • 35.Maly T, Debelouchina GT, Bajaj VS, Hu KN, Joo CG, Mak-Jurkauskas ML, Sirigiri JR, van der Wel PCA, Herzfeld J, Temkin RJ, Griffin RG. Dynamic nuclear polarization at high magnetic fields. J Chem Phys. 2008;128:052211. doi: 10.1063/1.2833582. [DOI] [PMC free article] [PubMed] [Google Scholar]

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