Journal of Magnetic Resonance 225 (2012) 14–16

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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 Department of Chemistry, Kent State University, Kent, OH 44240, USAb 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 2012Revised 18 September 2012Available online 8 October 2012

Keywords:Radiation dampingPulse sequenceSuppressionConcentrated sample

1090-7807/$ - see front matter � 2012 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.jmr.2012.09.010

⇑ Corresponding author.E-mail address: akhitrin@kent.edu (A.K. Khitrin).

a b s t r a c t

Radiation damping is known to cause line-broadening and frequency shifts of strong resonances in NMRspectra. While several techniques exist for the suppression of these effects, many require specializedhardware, or are only compatible with the presence of few strong resonances. We describe a simple pulsesequence for radiation damping suppression in spectra with many strong resonances. The sequence canbe used as-is to generate simple spectra or as a signal excitation part in more advanced experiments.

� 2012 Elsevier Inc. All rights reserved.

NMR signal detection relies on an efficient coupling of the mag-netization to the radio-frequency coil. When this coupling is verystrong, it leads to a distortion of the spectrum due to radiationdamping (RD) [1–4]. Phenomenologically, RD can be described bya self-induced back-action field. The precessing magnetizationcreates a current in the coil, and the current, in turn, creates amagnetic field that acts back on the sample. This transverseradio-frequency field is 90� phase-shifted (under perfect matchingconditions) with respect to the transverse magnetization andcauses a rotation of the total magnetization vector. For high-fieldNMR spectrometers, and standard probes, this field for protons ina water sample can reach 100 Hz and beyond. The result of thisprocess is a significant line broadening on the order of the RD fieldstrength. In addition, the lineshape is distorted, and the intensitiesno longer reflect the numbers of spins (although the integrals typ-ically do). For example, a nutation experiment (or pulse-calibrationcurve) would show a sawtooth-like intensity profile instead of asine curve. A further undesirable effect is that large frequencyshifts may arise (�±20 Hz), which depend on tuning conditionsand on the amount of z-magnetization [5,6].

Several methods for reducing RD effects have been described inthe past. A common procedure is sample dilution. When dilution isinconvenient or undesirable, one can also use very small fillingfactors to the same effect. Detuning the probe can improve thespectrum to a certain degree, but at the same time a large portionof the transmitted pulse power is reflected, and pulse durationsbecome very long. Modifications of electronic circuits including

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overcoupling or Q-switching [7–9] and active electronic feedback[10–12] have been developed. Further methods used multi-pulseDANTE sequence during signal acquisition [13], or gradients andcomplicated pulse shapes for spatially encoding/decoding noise[14]. Methods of compensating RD during the action of longselective pulses have been proposed as well [15,16]. Solventsuppression can provide excellent RD suppression, but it alsodestroys the signals, and does not work in a broad-band fashion.It would further not allow one to measure signals in closeproximity to or underneath the larger signals. It can be notedthat, when the spectrum is not distorted, large signals from thesolvent can be eliminated by algorithmic subtraction [17]. Despiteconsiderable efforts vested in the RD suppression schemes andnumerous interesting proposals, the existing techniques requirehardware modifications, or complicated pulse and processingmethods.

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 thetransverse magnetization, using a small flip angle of the excitationpulse does not eliminate the line distortion. This can be illustratedfor a single spectral line by a simple scheme in Fig. 1. After a small-angle y-pulse, the transverse component of magnetization isoriented along x. Subsequently, a RD field is induced along the neg-ative y-axis. The residual z-component of the magnetization isrotated by the induced RD field and creates a magnetizationcomponent along the negative x-axis, thus reducing the originalx-magnetization. At smaller flip angles, the RD field decreases inproportion to a decreased x-magnetization, so that the rate ofcreating negative x-magnetization is also decreased. However,the relative contribution remains the same, resulting in the same

Fig. 1. Rotation of magnetization components by the radiation damping field.

Communication / Journal of Magnetic Resonance 225 (2012) 14–16 15

rate of exponential decay of x-magnetization. For the same reasonsas outlined above, the selective excitation of a small active volumewithin a sample using gradients and selective pulses (voxel selec-tion) also fails in reducing RD.

To reduce RD one therefore needs to create a small transversemagnetization and simultaneously eliminate z-magnetization. Thisstrategy can be accomplished in many different ways; however,although one would think this task should be easy, many ap-proaches fail in achieving it. The main difficulties are RF field inho-mogeneity and the appearance of signals from peripheral part ofthe sample. Although the phases of the RF pulses can be controlledmore accurately than the flip angles over the sample volume, it isdesirable 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 weabbreviated NORD (NO Radiation Damping) can generate high-quality quantitative proton spectra for concentrated samples. Inthis sequence, we use a 90� pulse excitation, followed by an echosequence, including two slightly different gradients. The secondgradient eliminates any residual signal created by the 180�-pulse,but refocuses a fraction of the signal that was dephased by the firstgradient. As a result, the z-magnetization is largely eliminated, andthe transverse magnetization is reduced as well. Therefore,RD-induced broadening is significantly decreased and RD-inducedfrequency 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 and2 ms gradient-recovery delays. These parameters are not criticaland can be changed over a wide range without affecting the qualityof the spectra. The only parameter which needs to be adjusted is thedifference in amplitude between the first and the second gradient.For 1 ms z-gradients, we used the first gradient, which was only0.05 G/cm weaker than the second gradient. For longer/shortergradients this difference should be decreased/increased

900Y 1800

X

τ τ

G1 G2

Acq.

Fig. 2. NORD pulse sequence.

accordingly. Alternatively, one can use gradients of the samestrength, but of slightly different duration. In the echo experimentwe describe, the difference between the two gradients acts topartially dephase and reduce the transverse component of magne-tization. The optimization of the difference between the gradientstrengths was performed by gradually increasing it until the lineshapes remained free of distortions. The distortion appeared inthe form of small negative side lobes of the spectral peaks. Thisdistortion comes from the non-uniform z-field in peripheral partsof the sample (for ideally uniform field such distortions would beabsent). Therefore, the optimized value of the difference betweenthe two gradients depends on the geometry of the RF and gradientcoils and on the shim quality.

If desired, one can also create artificial line narrowing by usingthe 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 (masereffect, imagine that the z-magnetization in Fig. 1 is negative).Such artificial narrowing was not used for the spectra presentedbelow.

Fig. 3 shows single-transient proton NMR spectra of a sampleof Smirnoff vodka recorded after a single pulse with a 10� flipangle (Fig. 3a) and by using the NORD pulse sequence (Fig. 3b).A further decrease of the flip angle in a single-pulse experimentonly decreases the intensity without changing the shape of thespectrum. A common water/ethanol OH peak at 5 ppm is natu-rally broadened by exchange. Fig. 4 shows the aliphatic regionof the spectrum for a sample of unspecified regular gasoline froma pump. The spectra are recorded by using exactly the sameparameters as in the experiments in Fig. 3. The triplet at1.2 ppm (Fig. 4b) is the CH3 peak of ethanol. There are corre-sponding CH2 and OH resonances of hydrated ethanol at 3.7and 4.9 ppm (not shown). We also present for comparison a con-ventional spectrum of the same sample of gasoline diluted to 5%in CDCl3. One can see a similar quality of the spectra in Fig. 4band c. One can also notice that the dilution produces non-uniformshifts of spectral peaks due to solvent effects. All the spectra arepresented after Fourier transformation and phasing without anyadditional post-processing.

Even though the signal is partially dephased and, therefore,reduced, our pulse sequence does not compromise sensitivity. Infact, the intensities of the spectral peaks in Figs. 3b and 4b,recorded with the NORD sequence, are about eight times greaterthan for corresponding peaks in Figs. 3a and 4a obtained by usinga single 10� pulse. This effect provides probably the best illustra-tion of the efficiency of RD suppression. As a result, much larger

Fig. 3. 1H NMR spectrum of Smirnoff vodka sample recorded with (a) singleexcitation pulse with 10� flip angle and (b) NORD pulse sequence.

Fig. 4. 1H NMR spectrum of a regular gasoline sample recorded with (a) singleexcitation pulse with 10� flip angle, (b) NORD pulse sequence, and (c) conventionalspectrum of 5% gasoline, diluted in d-chloroform.

16 Communication / Journal of Magnetic Resonance 225 (2012) 14–16

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 pro-duce high-resolution quantitative proton NMR spectra of concen-trated samples. This sequence is very simple, its optimizationdoes not require any changes in standard settings for liquid-stateNMR, and it can make sample dilution unnecessary. The sequencecan be used as-is for generating simple spectra or as a signalexcitation part in some more advanced NMR experiments.

Acknowledgments

A.K. acknowledges NSF support (CHE-1048645) for purchasingAgilent 500 MHz NMR spectrometer used in this work. A.J.acknowledges NSF support under Grant CHE-0957586.

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