- Email: [email protected]
Simple suppression of radiation damping
Journal of Magnetic Resonance 225 (2012) 14–16
Contents lists available at SciVerse ScienceDirect
Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Communication
Simple suppression of radiation damping A.K. Khitrin a,⇑, Alexej Jerschow b a b
Department of Chemistry, Kent State University, Kent, OH 44240, USA Chemistry Department, New York University, New York, NY 10003, USA
a r t i c l e
i n f o
Article history: Received 17 May 2012 Revised 18 September 2012 Available online 8 October 2012 Keywords: Radiation damping Pulse sequence Suppression Concentrated sample
a b s t r a c t Radiation damping is known to cause line-broadening and frequency shifts of strong resonances in NMR spectra. While several techniques exist for the suppression of these effects, many require specialized hardware, or are only compatible with the presence of few strong resonances. We describe a simple pulse sequence for radiation damping suppression in spectra with many strong resonances. The sequence can be used as-is to generate simple spectra or as a signal excitation part in more advanced experiments. Ó 2012 Elsevier Inc. All rights reserved.
NMR signal detection relies on an efficient coupling of the magnetization to the radio-frequency coil. When this coupling is very strong, it leads to a distortion of the spectrum due to radiation damping (RD) [1–4]. Phenomenologically, RD can be described by a self-induced back-action field. The precessing magnetization creates a current in the coil, and the current, in turn, creates a magnetic field that acts back on the sample. This transverse radio-frequency field is 90° phase-shifted (under perfect matching conditions) with respect to the transverse magnetization and causes a rotation of the total magnetization vector. For high-field NMR spectrometers, and standard probes, this field for protons in a water sample can reach 100 Hz and beyond. The result of this process is a significant line broadening on the order of the RD field strength. In addition, the lineshape is distorted, and the intensities no longer reflect the numbers of spins (although the integrals typically do). For example, a nutation experiment (or pulse-calibration curve) would show a sawtooth-like intensity profile instead of a sine curve. A further undesirable effect is that large frequency shifts may arise (±20 Hz), which depend on tuning conditions and on the amount of z-magnetization [5,6]. Several methods for reducing RD effects have been described in the past. A common procedure is sample dilution. When dilution is inconvenient or undesirable, one can also use very small filling factors to the same effect. Detuning the probe can improve the spectrum to a certain degree, but at the same time a large portion of the transmitted pulse power is reflected, and pulse durations become very long. Modifications of electronic circuits including ⇑ Corresponding author. E-mail address: [email protected] (A.K. Khitrin). 1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2012.09.010
overcoupling or Q-switching [7–9] and active electronic feedback [10–12] have been developed. Further methods used multi-pulse DANTE sequence during signal acquisition [13], or gradients and complicated pulse shapes for spatially encoding/decoding noise [14]. Methods of compensating RD during the action of long selective pulses have been proposed as well [15,16]. Solvent suppression can provide excellent RD suppression, but it also destroys the signals, and does not work in a broad-band fashion. It would further not allow one to measure signals in close proximity to or underneath the larger signals. It can be noted that, when the spectrum is not distorted, large signals from the solvent can be eliminated by algorithmic subtraction [17]. Despite considerable efforts vested in the RD suppression schemes and numerous interesting proposals, the existing techniques require hardware modifications, or complicated pulse and processing methods. The theory of RD is well known and can be found in Refs. [1–4]. It is interesting that, even though the RD field is proportional to the transverse magnetization, using a small flip angle of the excitation pulse does not eliminate the line distortion. This can be illustrated for a single spectral line by a simple scheme in Fig. 1. After a smallangle y-pulse, the transverse component of magnetization is oriented along x. Subsequently, a RD field is induced along the negative y-axis. The residual z-component of the magnetization is rotated by the induced RD field and creates a magnetization component along the negative x-axis, thus reducing the original x-magnetization. At smaller flip angles, the RD field decreases in proportion to a decreased x-magnetization, so that the rate of creating negative x-magnetization is also decreased. However, the relative contribution remains the same, resulting in the same
Communication / Journal of Magnetic Resonance 225 (2012) 14–16
Fig. 1. Rotation of magnetization components by the radiation damping field.
rate of exponential decay of x-magnetization. For the same reasons as outlined above, the selective excitation of a small active volume within a sample using gradients and selective pulses (voxel selection) also fails in reducing RD. To reduce RD one therefore needs to create a small transverse magnetization and simultaneously eliminate z-magnetization. This strategy can be accomplished in many different ways; however, although one would think this task should be easy, many approaches fail in achieving it. The main difficulties are RF field inhomogeneity and the appearance of signals from peripheral part of the sample. Although the phases of the RF pulses can be controlled more accurately than the flip angles over the sample volume, it is desirable to use a sequence which can work without phase cycling. For concentrated samples, the internal lock is not always available, therefore a single-transient spectrum is preferred. We have found that the pulse sequence in Fig. 2, which we abbreviated NORD (NO Radiation Damping) can generate highquality quantitative proton spectra for concentrated samples. In this sequence, we use a 90° pulse excitation, followed by an echo sequence, including two slightly different gradients. The second gradient eliminates any residual signal created by the 180°-pulse, but refocuses a fraction of the signal that was dephased by the first gradient. As a result, the z-magnetization is largely eliminated, and the transverse magnetization is reduced as well. Therefore, RD-induced broadening is significantly decreased and RD-induced frequency shifts are eliminated in a broad-band fashion. In the experiments below, with samples in standard 5 mm tubes, filled to 6 cm, we used 20 G/cm z-gradients of 1 ms duration and 2 ms gradient-recovery delays. These parameters are not critical and can be changed over a wide range without affecting the quality of the spectra. The only parameter which needs to be adjusted is the difference in amplitude between the first and the second gradient. For 1 ms z-gradients, we used the first gradient, which was only 0.05 G/cm weaker than the second gradient. For longer/shorter gradients this difference should be decreased/increased
90 0Y
15
accordingly. Alternatively, one can use gradients of the same strength, but of slightly different duration. In the echo experiment we describe, the difference between the two gradients acts to partially dephase and reduce the transverse component of magnetization. The optimization of the difference between the gradient strengths was performed by gradually increasing it until the line shapes remained free of distortions. The distortion appeared in the form of small negative side lobes of the spectral peaks. This distortion comes from the non-uniform z-field in peripheral parts of the sample (for ideally uniform field such distortions would be absent). Therefore, the optimized value of the difference between the two gradients depends on the geometry of the RF and gradient coils and on the shim quality. If desired, one can also create artificial line narrowing by using the first excitation pulse with a flip angle less than 90°. In this case, there is some negative z-magnetization during signal acquisition, which creates a positive feedback for the x-magnetization (maser effect, imagine that the z-magnetization in Fig. 1 is negative). Such artificial narrowing was not used for the spectra presented below. Fig. 3 shows single-transient proton NMR spectra of a sample of Smirnoff vodka recorded after a single pulse with a 10° flip angle (Fig. 3a) and by using the NORD pulse sequence (Fig. 3b). A further decrease of the flip angle in a single-pulse experiment only decreases the intensity without changing the shape of the spectrum. A common water/ethanol OH peak at 5 ppm is naturally broadened by exchange. Fig. 4 shows the aliphatic region of the spectrum for a sample of unspecified regular gasoline from a pump. The spectra are recorded by using exactly the same parameters as in the experiments in Fig. 3. The triplet at 1.2 ppm (Fig. 4b) is the CH3 peak of ethanol. There are corresponding CH2 and OH resonances of hydrated ethanol at 3.7 and 4.9 ppm (not shown). We also present for comparison a conventional spectrum of the same sample of gasoline diluted to 5% in CDCl3. One can see a similar quality of the spectra in Fig. 4b and c. One can also notice that the dilution produces non-uniform shifts of spectral peaks due to solvent effects. All the spectra are presented after Fourier transformation and phasing without any additional post-processing. Even though the signal is partially dephased and, therefore, reduced, our pulse sequence does not compromise sensitivity. In fact, the intensities of the spectral peaks in Figs. 3b and 4b, recorded with the NORD sequence, are about eight times greater than for corresponding peaks in Figs. 3a and 4a obtained by using a single 10° pulse. This effect provides probably the best illustration of the efficiency of RD suppression. As a result, much larger
180 0X
Acq. G2
G1 τ
τ Fig. 2. NORD pulse sequence.
Fig. 3. 1H NMR spectrum of Smirnoff vodka sample recorded with (a) single excitation pulse with 10° flip angle and (b) NORD pulse sequence.
16
Communication / Journal of Magnetic Resonance 225 (2012) 14–16
Acknowledgments A.K. acknowledges NSF support (CHE-1048645) for purchasing Agilent 500 MHz NMR spectrometer used in this work. A.J. acknowledges NSF support under Grant CHE-0957586. References
Fig. 4. 1H NMR spectrum of a regular gasoline sample recorded with (a) single excitation pulse with 10° flip angle, (b) NORD pulse sequence, and (c) conventional spectrum of 5% gasoline, diluted in d-chloroform.
sensitivity can be achieved in many cases with this sequence, which could be useful for fingerprinting complex mixtures. In conclusion, we described a pulse sequence which can produce high-resolution quantitative proton NMR spectra of concentrated samples. This sequence is very simple, its optimization does not require any changes in standard settings for liquid-state NMR, and it can make sample dilution unnecessary. The sequence can be used as-is for generating simple spectra or as a signal excitation part in some more advanced NMR experiments.
[1] G. Suryan, Nuclear magnetic resonance and the effect of the methods of observation, Curr. Sci. 18 (1949) 203. [2] N. Bloembergen, R.V. Pound, Radiation damping in magnetic resonance experiments, Phys. Rev. 95 (1954) 8–12. [3] S. Bloom, Effects of radiation damping on spin dynamics, J. Appl. Phys. 28 (1957) 800. [4] M.P. Augustine, Transient properties of radiation damping, Prog. Nucl. Magn. Reson. Spectrosc. 40 (2002) 111–150. [5] A. Vlassenbroek, J. Jeener, P. Broekaert, Radiation damping in high-resolution liquid NMR – a simulation study, J. Chem. Phys. 103 (1995) 5886–5897. [6] S.Y. Huang, C. Anklin, J.D. Walls, Y.Y. Lin, Sizable concentration-dependent frequency shifts in solution NMR using sensitive probes, J. Am. Chem. Soc. 126 (2004) 15936–15937. [7] L. Picard, M. Vokienlin, M. Decorps, An overcoupled NMR probe for the reduction of radiation damping, J. Magn. Reson. A 117 (1995) 262. [8] W.E. Maas, F.H. Laukien, D.G. Cory, Suppression of radiation damping by Q switching during acquisition, J. Magn. Reson. A 113 (1995) 274. [9] C. Anklin, M. Rindlisbacher, G. Otting, F.H. Laukien, A probehead with switchable quality factor – suppression of radiation damping, J. Magn. Reson. B 106 (1995) 199. [10] A. Szoke, S. Meiboom, Radiation damping in nuclear magnetic resonance, Phys. Rev. 113 (1959) 585. [11] P. Broekaert, J. Jeener, Suppression of radiation damping in NMR in liquids by active electronic feedback, J. Magn. Reson. A 113 (1995) 60. [12] A. Louis-Joseph, D. Abergel, J.Y. Lallemand, Neutralization of radiation damping by selective feedback on a 400 MHz NMR spectrometer, J. Biomol. NMR 5 (1995) 212. [13] H. Barjat, D.L. Mattiello, R. Freeman, Suppression of radiation damping in high resolution NMR, J. Magn. Reson. 136 (1999) 114. [14] C.A. Michal, Defeating radiation damping and magnetic field inhomogeneity with spatially encoded noise, ChemPhysChem 11 (2010) 3445–3447. [15] J.H. Chen, A. Jerschow, G. Bodenhausen, Compensation of radiation damping during selective pulses in NMR spectroscopy, Chem. Phys. Lett. 308 (1999) 397. [16] D.E. Rourke, M.P. Augustine, Exact linearization of the radiation damped spin system, Phys. Rev. Lett. 84 (2000) 1685. [17] J.-S. Lee, A.K. Khitrin, Algorithmic subtraction of high peaks in NMR spectra, Chem. Phys. Lett. 433 (2006) 244–247.
Contents lists available at SciVerse ScienceDirect
Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Communication
Simple suppression of radiation damping A.K. Khitrin a,⇑, Alexej Jerschow b a b
Department of Chemistry, Kent State University, Kent, OH 44240, USA Chemistry Department, New York University, New York, NY 10003, USA
a r t i c l e
i n f o
Article history: Received 17 May 2012 Revised 18 September 2012 Available online 8 October 2012 Keywords: Radiation damping Pulse sequence Suppression Concentrated sample
a b s t r a c t Radiation damping is known to cause line-broadening and frequency shifts of strong resonances in NMR spectra. While several techniques exist for the suppression of these effects, many require specialized hardware, or are only compatible with the presence of few strong resonances. We describe a simple pulse sequence for radiation damping suppression in spectra with many strong resonances. The sequence can be used as-is to generate simple spectra or as a signal excitation part in more advanced experiments. Ó 2012 Elsevier Inc. All rights reserved.
NMR signal detection relies on an efficient coupling of the magnetization to the radio-frequency coil. When this coupling is very strong, it leads to a distortion of the spectrum due to radiation damping (RD) [1–4]. Phenomenologically, RD can be described by a self-induced back-action field. The precessing magnetization creates a current in the coil, and the current, in turn, creates a magnetic field that acts back on the sample. This transverse radio-frequency field is 90° phase-shifted (under perfect matching conditions) with respect to the transverse magnetization and causes a rotation of the total magnetization vector. For high-field NMR spectrometers, and standard probes, this field for protons in a water sample can reach 100 Hz and beyond. The result of this process is a significant line broadening on the order of the RD field strength. In addition, the lineshape is distorted, and the intensities no longer reflect the numbers of spins (although the integrals typically do). For example, a nutation experiment (or pulse-calibration curve) would show a sawtooth-like intensity profile instead of a sine curve. A further undesirable effect is that large frequency shifts may arise (±20 Hz), which depend on tuning conditions and on the amount of z-magnetization [5,6]. Several methods for reducing RD effects have been described in the past. A common procedure is sample dilution. When dilution is inconvenient or undesirable, one can also use very small filling factors to the same effect. Detuning the probe can improve the spectrum to a certain degree, but at the same time a large portion of the transmitted pulse power is reflected, and pulse durations become very long. Modifications of electronic circuits including ⇑ Corresponding author. E-mail address: [email protected] (A.K. Khitrin). 1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2012.09.010
overcoupling or Q-switching [7–9] and active electronic feedback [10–12] have been developed. Further methods used multi-pulse DANTE sequence during signal acquisition [13], or gradients and complicated pulse shapes for spatially encoding/decoding noise [14]. Methods of compensating RD during the action of long selective pulses have been proposed as well [15,16]. Solvent suppression can provide excellent RD suppression, but it also destroys the signals, and does not work in a broad-band fashion. It would further not allow one to measure signals in close proximity to or underneath the larger signals. It can be noted that, when the spectrum is not distorted, large signals from the solvent can be eliminated by algorithmic subtraction [17]. Despite considerable efforts vested in the RD suppression schemes and numerous interesting proposals, the existing techniques require hardware modifications, or complicated pulse and processing methods. The theory of RD is well known and can be found in Refs. [1–4]. It is interesting that, even though the RD field is proportional to the transverse magnetization, using a small flip angle of the excitation pulse does not eliminate the line distortion. This can be illustrated for a single spectral line by a simple scheme in Fig. 1. After a smallangle y-pulse, the transverse component of magnetization is oriented along x. Subsequently, a RD field is induced along the negative y-axis. The residual z-component of the magnetization is rotated by the induced RD field and creates a magnetization component along the negative x-axis, thus reducing the original x-magnetization. At smaller flip angles, the RD field decreases in proportion to a decreased x-magnetization, so that the rate of creating negative x-magnetization is also decreased. However, the relative contribution remains the same, resulting in the same
Communication / Journal of Magnetic Resonance 225 (2012) 14–16
Fig. 1. Rotation of magnetization components by the radiation damping field.
rate of exponential decay of x-magnetization. For the same reasons as outlined above, the selective excitation of a small active volume within a sample using gradients and selective pulses (voxel selection) also fails in reducing RD. To reduce RD one therefore needs to create a small transverse magnetization and simultaneously eliminate z-magnetization. This strategy can be accomplished in many different ways; however, although one would think this task should be easy, many approaches fail in achieving it. The main difficulties are RF field inhomogeneity and the appearance of signals from peripheral part of the sample. Although the phases of the RF pulses can be controlled more accurately than the flip angles over the sample volume, it is desirable to use a sequence which can work without phase cycling. For concentrated samples, the internal lock is not always available, therefore a single-transient spectrum is preferred. We have found that the pulse sequence in Fig. 2, which we abbreviated NORD (NO Radiation Damping) can generate highquality quantitative proton spectra for concentrated samples. In this sequence, we use a 90° pulse excitation, followed by an echo sequence, including two slightly different gradients. The second gradient eliminates any residual signal created by the 180°-pulse, but refocuses a fraction of the signal that was dephased by the first gradient. As a result, the z-magnetization is largely eliminated, and the transverse magnetization is reduced as well. Therefore, RD-induced broadening is significantly decreased and RD-induced frequency shifts are eliminated in a broad-band fashion. In the experiments below, with samples in standard 5 mm tubes, filled to 6 cm, we used 20 G/cm z-gradients of 1 ms duration and 2 ms gradient-recovery delays. These parameters are not critical and can be changed over a wide range without affecting the quality of the spectra. The only parameter which needs to be adjusted is the difference in amplitude between the first and the second gradient. For 1 ms z-gradients, we used the first gradient, which was only 0.05 G/cm weaker than the second gradient. For longer/shorter gradients this difference should be decreased/increased
90 0Y
15
accordingly. Alternatively, one can use gradients of the same strength, but of slightly different duration. In the echo experiment we describe, the difference between the two gradients acts to partially dephase and reduce the transverse component of magnetization. The optimization of the difference between the gradient strengths was performed by gradually increasing it until the line shapes remained free of distortions. The distortion appeared in the form of small negative side lobes of the spectral peaks. This distortion comes from the non-uniform z-field in peripheral parts of the sample (for ideally uniform field such distortions would be absent). Therefore, the optimized value of the difference between the two gradients depends on the geometry of the RF and gradient coils and on the shim quality. If desired, one can also create artificial line narrowing by using the first excitation pulse with a flip angle less than 90°. In this case, there is some negative z-magnetization during signal acquisition, which creates a positive feedback for the x-magnetization (maser effect, imagine that the z-magnetization in Fig. 1 is negative). Such artificial narrowing was not used for the spectra presented below. Fig. 3 shows single-transient proton NMR spectra of a sample of Smirnoff vodka recorded after a single pulse with a 10° flip angle (Fig. 3a) and by using the NORD pulse sequence (Fig. 3b). A further decrease of the flip angle in a single-pulse experiment only decreases the intensity without changing the shape of the spectrum. A common water/ethanol OH peak at 5 ppm is naturally broadened by exchange. Fig. 4 shows the aliphatic region of the spectrum for a sample of unspecified regular gasoline from a pump. The spectra are recorded by using exactly the same parameters as in the experiments in Fig. 3. The triplet at 1.2 ppm (Fig. 4b) is the CH3 peak of ethanol. There are corresponding CH2 and OH resonances of hydrated ethanol at 3.7 and 4.9 ppm (not shown). We also present for comparison a conventional spectrum of the same sample of gasoline diluted to 5% in CDCl3. One can see a similar quality of the spectra in Fig. 4b and c. One can also notice that the dilution produces non-uniform shifts of spectral peaks due to solvent effects. All the spectra are presented after Fourier transformation and phasing without any additional post-processing. Even though the signal is partially dephased and, therefore, reduced, our pulse sequence does not compromise sensitivity. In fact, the intensities of the spectral peaks in Figs. 3b and 4b, recorded with the NORD sequence, are about eight times greater than for corresponding peaks in Figs. 3a and 4a obtained by using a single 10° pulse. This effect provides probably the best illustration of the efficiency of RD suppression. As a result, much larger
180 0X
Acq. G2
G1 τ
τ Fig. 2. NORD pulse sequence.
Fig. 3. 1H NMR spectrum of Smirnoff vodka sample recorded with (a) single excitation pulse with 10° flip angle and (b) NORD pulse sequence.
16
Communication / Journal of Magnetic Resonance 225 (2012) 14–16
Acknowledgments A.K. acknowledges NSF support (CHE-1048645) for purchasing Agilent 500 MHz NMR spectrometer used in this work. A.J. acknowledges NSF support under Grant CHE-0957586. References
Fig. 4. 1H NMR spectrum of a regular gasoline sample recorded with (a) single excitation pulse with 10° flip angle, (b) NORD pulse sequence, and (c) conventional spectrum of 5% gasoline, diluted in d-chloroform.
sensitivity can be achieved in many cases with this sequence, which could be useful for fingerprinting complex mixtures. In conclusion, we described a pulse sequence which can produce high-resolution quantitative proton NMR spectra of concentrated samples. This sequence is very simple, its optimization does not require any changes in standard settings for liquid-state NMR, and it can make sample dilution unnecessary. The sequence can be used as-is for generating simple spectra or as a signal excitation part in some more advanced NMR experiments.
[1] G. Suryan, Nuclear magnetic resonance and the effect of the methods of observation, Curr. Sci. 18 (1949) 203. [2] N. Bloembergen, R.V. Pound, Radiation damping in magnetic resonance experiments, Phys. Rev. 95 (1954) 8–12. [3] S. Bloom, Effects of radiation damping on spin dynamics, J. Appl. Phys. 28 (1957) 800. [4] M.P. Augustine, Transient properties of radiation damping, Prog. Nucl. Magn. Reson. Spectrosc. 40 (2002) 111–150. [5] A. Vlassenbroek, J. Jeener, P. Broekaert, Radiation damping in high-resolution liquid NMR – a simulation study, J. Chem. Phys. 103 (1995) 5886–5897. [6] S.Y. Huang, C. Anklin, J.D. Walls, Y.Y. Lin, Sizable concentration-dependent frequency shifts in solution NMR using sensitive probes, J. Am. Chem. Soc. 126 (2004) 15936–15937. [7] L. Picard, M. Vokienlin, M. Decorps, An overcoupled NMR probe for the reduction of radiation damping, J. Magn. Reson. A 117 (1995) 262. [8] W.E. Maas, F.H. Laukien, D.G. Cory, Suppression of radiation damping by Q switching during acquisition, J. Magn. Reson. A 113 (1995) 274. [9] C. Anklin, M. Rindlisbacher, G. Otting, F.H. Laukien, A probehead with switchable quality factor – suppression of radiation damping, J. Magn. Reson. B 106 (1995) 199. [10] A. Szoke, S. Meiboom, Radiation damping in nuclear magnetic resonance, Phys. Rev. 113 (1959) 585. [11] P. Broekaert, J. Jeener, Suppression of radiation damping in NMR in liquids by active electronic feedback, J. Magn. Reson. A 113 (1995) 60. [12] A. Louis-Joseph, D. Abergel, J.Y. Lallemand, Neutralization of radiation damping by selective feedback on a 400 MHz NMR spectrometer, J. Biomol. NMR 5 (1995) 212. [13] H. Barjat, D.L. Mattiello, R. Freeman, Suppression of radiation damping in high resolution NMR, J. Magn. Reson. 136 (1999) 114. [14] C.A. Michal, Defeating radiation damping and magnetic field inhomogeneity with spatially encoded noise, ChemPhysChem 11 (2010) 3445–3447. [15] J.H. Chen, A. Jerschow, G. Bodenhausen, Compensation of radiation damping during selective pulses in NMR spectroscopy, Chem. Phys. Lett. 308 (1999) 397. [16] D.E. Rourke, M.P. Augustine, Exact linearization of the radiation damped spin system, Phys. Rev. Lett. 84 (2000) 1685. [17] J.-S. Lee, A.K. Khitrin, Algorithmic subtraction of high peaks in NMR spectra, Chem. Phys. Lett. 433 (2006) 244–247.