- Email: [email protected]
Solid-state NMR as an analytical tool: Quantitative aspects
ARTICLE IN PRESS
Solid State Nuclear Magnetic Resonance 29 (2006) 214–218 www.elsevier.com/locate/ssnmr
Solid-state NMR as an analytical tool: Quantitative aspects Fabio Ziarellia, Stefano Caldarellib, a
Spectropole, Fe´de´ration des Sciences Chimiques de Marseille, Campus de Saint Je´roˆme, 13013 Marseille, France b JE 2421 TRACES, Universite´ d’Aix Marseille I et III, Campus de Saint Je´roˆme, 13013 Marseille, France Received 1 July 2005; received in revised form 22 August 2005 Available online 17 October 2005 Dedicated to Alexander Pines on occasion of his 60th birthday
Abstract Analytical methods based on solid-state NMR are becoming increasingly popular. However, these flourishing activities bring up the issue of how accurately NMR can assess an analyte proportion in a solid sample. The use of a chemical intensity reference for this purpose is a natural but often unsuitable choice, due to sample stability or preciousness. We propose here a protocol to perform quantitative measurements in solid-state NMR, by calibration of the circuit response through a low-power pulse injected during the acquisition (the so-called ERETIC method). Although this method has been in use for some time in liquid-phase and in vivo NMR, we point out here some peculiarities and useful applications typical of solids. Namely, the temperature dependence of the signal intensity imposes care in the application to MAS experiments. r 2005 Elsevier Inc. All rights reserved. Keywords: ERETIC; MAS; CPMAS
1. Introduction One of the points that made the success of NMR is its quantitative response, a rather unique feature among fellow spectroscopic methods. This property is easily used for measuring relative concentrations, for example in the case of mixtures or for assessing the population of distinguishable sites in a given material. Although in principle straightforward, the full onset of procedures to estimate absolute quantities has been more elusive, essentially because of the difficulty of choosing a proper intensity reference. In fact, while using an internal reference is the ideal analytical choice, this may turn out to be impractical due to chemical interferences, spectral overlap or preciousness of the sample. Conversely, the use of an external reference has all the drawbacks of not performing the intensities comparison in the same electronic conditions. Corresponding author. Fax: +33 491282897.
E-mail address: [email protected] (S. Caldarelli). 0926-2040/$ - see front matter r 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ssnmr.2005.08.013
In recent times the use of a synthetic signal as an intensity reference has been proposed [1–3]. A low-power RF pulse modulated at the observation frequency is applied during the acquisition time. After Fourier transform, the corresponding signal can be calibrated against mass or concentration values. The interest of this approach is that it could be considered in a sense both an internal (with respect to the circuit) and external (with respect to the sample) referencing. This so-called ERETIC method has been finding increasing applications in liquid-phase [3–9], in vivo [10] and diffusion measurements [11], especially for demanding analytical applications, such as the popular isotopic distribution analysis [8]. In this work we introduce the ERETIC method to solidstate NMR. We demonstrate its usefulness in MAS experiments, while pointing out some peculiarities linked to the Curie’s law dependence of the NMR signal. In perspective, external shift scaling has been recently proposed as a general tool for solid-state NMR [12]. In conjunction with the ERETIC calibration pulse, the entire referencing process could be relocated outside the analyte
ARTICLE IN PRESS
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F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
2. Materials and methods All spectra were recorded on a Bruker DSX 400, equipped with commercial probeheads (Bruker 400WB 4 mm H/BB CP VTN and 2.5 mm H-F/BB CP VTN) operating at a 13C and 207Pb resonances frequencies of 100.7 and 83.7 MHz respectively. For the pulse-acquire experiments, the 13C adamantane repetition time was of 15 s and the excitation pulse of 5.5 ms, corresponding to a 901 rotation. In the case of 207Pb in Pb(NO3)2, the repetition time and pulse length were 40 s and 3.5 ms, respectively. In both cases the acquisition time was 100 ms, the spectral width of 14000 Hz and 128 scans were summed up. The 1H–13C CPMAS experiment on tyrosine chlorohydrate was performed recording 512 scans with a contact time of 2 ms and a repetition time of 3 s, with an acquisition time of 40 ms and a spectral width of 90000 Hz. The circuit was realized according to the scheme in Fig. 1 (the directional coupler was EME HF-Technik Mod. 7020/30). The chemical shifts were referenced to solid glycine (carbonyl resonance at 176.5 ppm) and to a 1.1 molal aqueous solution of Pb(NO3)2 at 295 K (2965.7 ppm), for carbon-13 and lead-207, respectively. 2.1. The ERETIC setup The Eretic pulse was set to the length of the acquisition time, with an intensity of 8.6 102 mVpp. The intensity of the ERETIC magnetic field can be quickly adapted to produce intensities of the same order of the observed sample by varying this intensity. An exponentially decaying shaped pulse was used to perfectly mimic a NMR signal. The decay time constant was chosen as a fifth of the overall duration. The ERETIC pulse was taken directly from the synthesizer, prior to amplification. This arrangement has the advantage of not introducing any noise from the broadband amplifier. In common MAS probeheads, the ERETIC pulse can be safely injected using a channel not
13
C
1000W
F2
1
H
1000W
F3
13
F1
C
Probe
Receiver
Synthesizer
Duplexer
Directional Coupler
X
1
H
Fig. 1. Relevant elements of the circuit setup for inserting the ERETIC pulse into a double resonance experiment.
200
180
160
140
120
100
80
*** **
*
*
( *) SSB
60
40
20
0
ppm
Fig. 2. CPMAS experiment on L-tyrosine chlorohydrate. The ERETIC signal is shown at 0 ppm. Spinning sidebands are labeled by asterisks.
used for the observation. In the case of double-resonance experiments in a two-channel probehead, a directional coupler allows the simultaneous introduction of the ERETIC and of the second-frequency pulse, without any significant impedance break. Fig. 2 demostrates a CPMAS spectrum (on tyrosine), using the setup illustrated above. Since the ERETIC pulse is generated externally, it has to be phase-synchronized with the receiver. A pulse program for this purpose can be obtained from the authors. 3. Results and discussion The magnetic field associated to the macroscopic magnetization of a sample originates from the analyte concentration, C, as well as from Curie’s law for the single spin magnetization, M0: Bsignal ¼ CM 0 ¼ N g2 ðh=ð2pÞÞ2 B0 IðI þ 1Þ=ð3kTÞ. The concentration C is the product of the number of nuclei of interest in the coil times the natural abundance of the observed isotopes, that is the number of active spins detected by the coil. The principle of the ERETIC method is to inject in the receiving line a synthetic signal of known amplitude, Ber. The field associated with the macroscopic magnetization of the sample is thus measured relative to this reference. The current arising from an oscillating magnetic field in a tuned circuit is directly proportional to its quality factor, Q, a degradation of which results in a loss of the signal amplitude. The same law determines the efficiency of the RF entering the circuit; therefore, a reciprocity principle has been defined in the literature [13] that allows normalization of the signal measured at a certain Q level to any other one through the measure of the corresponding 901 pulse length, the product of these two quantities being a constant. In the case of ERETIC, both
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the reference and the signal fields are submitted to the same observation path and suffer equal circuit-related attenuation factors. The ERETIC referencing would be thus Qindependent, if the associated magnetic field in the circuit also remains constant. Since the reference pulse is introduced in the probe through a channel completely detuned with respect to the observation frequency (i.e. tuned to another frequency), the derivative of the Q around the observation (i.e. ERETIC) frequency is very small, guaranteeing the required reproducibility of the calibration pulse intensity. As shown in the Methods session, this setup is easily realized in a common double-resonance probehead, by exploiting the channel not used for observation for the ERETIC pulse. Provided this latter channel is tuned to the same frequency (typically the proton one), the RF leakage originating the ERETIC signal does not appear to be sensitive to even large changes in the Q of this side of the circuit. However, it should be kept in mind that in the case of large variations of the Q of the observe channel, due for example to different dielectric properties among samples, the associated changes of the reading pulse flip-angle should be still assessed for an accurate comparison of the relative intensities. In the case of double resonance experiments, such as the cross-polarization spectrum shown in Fig. 2, we observed no interference between the ERETIC pulse and the presence of a decoupling sequence. A quantitative response can be obtained from ss-NMR only if all the sample introduced in the coil contributes homogeneously to the signal. For instance, MAS rotors come in various internal and external sizes, and probeheads have specific coil geometries. On the overall, in common analysis a part of the sample may lay on the edges or even outside the coil, thus experiencing peculiar RF excitation and detection conditions. A similar problem is encountered in experiments requiring highly homogeneous RF pulses, as in the case of homonuclear decoupling. A qualitative solution to this nuisance is the limitation of the analyzed volume, either physically or by frequency-labeling the rotor sections with magnetic field gradients [15,16] This situation is fundamentally different from lp-NMR, where a concentration measurement is sought, so that the solution fraction outside the coil does not hamper the measurement, as in the case of the spin counting approach of solids. As a first step in any ss-NMR quantitative approach and to demonstrate the ss-ERETIC idea, we scrutinized the contribution to the signal from different sections of a 4 mm external diameter rotor. This was achieved by observing the increase of the signal spectra as a function of the addition of more amount of material (Fig. 3). At the same time, we measured the depth of the rotor occupied by the sample. Although MAS centrifugal forces commonly induce a conical rearrangement of the powder in the rotor, the deviation from a cylindrical arrangement of the sample in the rotor is relevant only for very limited loadings. Fig. 3 and 4 show that the first (as well as the last)
eretic
F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
75
80
mg
Fig. 3. Growth of the 13C NMR signal in a MAS rotor upon successive additions of adamantane. The spectra were recorded in the presence of an ERETIC reference.
mg 0
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Fig. 4. Normalized contribution to the NMR signal from different sections of a 4 mm rotor, as obtained from an adamantane sample with a pulse-acquire experiment. The dots were obtained from the intensity values of Fig. 3, by subtracting two successive spectra, using the ERETIC signal as reference. The light- and dark-gray areas correspond to the available volume for a 50 and 12 ml rotor, respectively.
milligrams of compound in a full rotor essentially do not contribute much to the signal, supporting our approximation of a cylindrical arrangement of the analyzed powder. Fig. 4 represents the same results in the form of the activity of the rotor portions with respect to the NMR signal. About 20 mg of the adamantane sample, at a depth level between 6.5 and 10.5 mm, respond homogeneously to the NMR excitation. For this setup, this volume can be thus safely used for quantitative analysis. Again, it should be kept in mind that for accurate measurements, such a calibration should be repeated for each probehead/coil setup. 3.1. Temperature effects As an implication of Curie’s law, the accuracy of the measurement is directly linked to the exact knowledge of the working temperature. For ss-NMR, this is a sensitive issue since increasing MAS rates produce a warming of the sample. The effect of the temperature on the ERETIC calibration is demonstrated in Fig. 5, on lead nitrate, which conveniently acts as an internal thermometer [14].
ARTICLE IN PRESS F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
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Fig. 5. Evolution as a function of the temperature of the MAS-NMR signal of a lead nitrate sample in the presence of the ERETIC reference. All spectra were recorded on a 2.5 mm probehead, spinning at 5 kHz MAS rate.
Comparison of Fig. 5a–c shows the variation in relative intensity of the ERETIC and signal peaks, due to the temperature. The reference intensity has a drop of about 2% over 571, which derives from an increase of the thermal noise. The lead-207 signal integral is reduced according to its inverse dependence on the temperature. If a mild error of a few percent can be tolerated, the ERETIC reference can be used directly with the values calibrated at one temperature. For more precise measurements, it would be necessary to calibrate the effects of the circuit response on the ERETIC integral over the temperature range of interest. 3.2. Spinning rate effects
(a)
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Fig. 6. Effect of varying the 207Pb-MAS frequency on a lead nitrate sample in the presence of the ERETIC signal. (a) 5 kHz, (b) 10 kHz, (c) 20 kHz, (d) 30 kHz. The spectra were recorded on a 2.5 mm probehead.
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Fig. 6 shows the well-known variations of the lead nitrate average position and line shape due to temperature variations and gradients induced by friction forces, as the MAS rate the spinning rate increases from 5 to 30 kHz. Faster spinning rates correspond to higher temperatures, and a consistent behavior is followed by the signal integral (as demonstrated in Fig. 7). A broadened and increasingly distorted line shape is the signature of the temperature gradients [17]. On the other hand, the ERETIC signal remains constant, as the temperature variation affects mainly the rotor area rather than the whole circuit. Incidentally, Fig. 6 also demonstrates that the precision of this method is about 1%. The 207Pb signal intensity also decays, with an essentially perfect correlation with the temperature indicated by the lead chemical shift (Fig. 7). The small deviation from the correlation can be ascribed to the presence of a temperature distribution across the sample in the case of MAS induced heating.
Fig. 7. Evolution of the lead nitrate integral in the experiment in Figs. 5 and 6, referenced to ERETIC at 297 K. The effective experimental temperature was calibrated from the lead chemical shift of the maximum of the 207Pb lineshape.
4. Conclusions We introduced to solid-state NMR the ERETIC calibration method for quantitative analysis using NMR spectra. We demonstrated its feasibility in both single and double resonance experiments, namely CPMAS. Provided that some caution is taken, especially considering the temperature variations induced by MAS, this technique can be used promptly to precisions estimated at about 1%. We are currently demonstrating the interest of the ERETIC calibration on mixtures and paramagnetic compounds.
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References [1] L. Barantin, A. LePape, S. Akoka, Magn. Reson. Med. 38 (1997) 179. [2] S. Akoka, M. Trierweiler, Instrum. Sci. Technol. 30 (2002) 21. [3] N. Michel, S. Akoka, J. Magn. Reson. 168 (2004) 118. [4] I. Billault, S. Akoka, Instrum. Sci. Technol. 28 (2000) 233. [5] V. Silvestre, S. Goupry, M. Trierweiler, R. Robins, S. Akoka, Anal. Chem. 73 (2001) 1862. [6] I. Billault, R. Robins, S. Akoka, Anal. Chem. 74 (2002) 5902. [7] C. Dalvit, M. Flocco, M. Veronesi, B.J. Stockman, Comb. Chem. High Throughput Screen. 5 (2002) 605. [8] F. Le Grand, S. Akoka, C. R. Chim. 7 (2004) 233.
[9] I.W. Burton, M.A. Quilliam, J.A. Walter, Anal. Chem. 77 (2005) 3123. [10] F. Franconi, C. Chapon, L. Lemaire, V. Lehmann, L. Barantin, S. Akoka, Magn. Reson. Imag. 20 (2002) 587. [11] V. Molinier, B. Fenet, J. Fitremann, A. Bouchu, Y. Queneau, J.Colloid Interface Sci. 286 (2005) 360. [12] C.R. Morcombe, K.W. Zilm, J. Magn. Reson. 162 (2003) 479. [13] D.I. Hoult, R.E. Richards, J. Magn. Reson. 24 (1976) 71. [14] C. Dybowski, G. Neue, Prog. NMR. Spectr. 41 (2002) 153. [15] P. Charmont, A. Lesage, S. Steuernagel, F. Engelke, L. Emsley, J. Magn. Reson. 145 (2000) 334. [16] P. Charmont, D. Sakellariou, L. Emsley, J. Magn. Reson. 154 (2002) 136. [17] T. Mildner, H. Ernst, D. Freude, Solid State NMR 5 (1995) 269.
Solid State Nuclear Magnetic Resonance 29 (2006) 214–218 www.elsevier.com/locate/ssnmr
Solid-state NMR as an analytical tool: Quantitative aspects Fabio Ziarellia, Stefano Caldarellib, a
Spectropole, Fe´de´ration des Sciences Chimiques de Marseille, Campus de Saint Je´roˆme, 13013 Marseille, France b JE 2421 TRACES, Universite´ d’Aix Marseille I et III, Campus de Saint Je´roˆme, 13013 Marseille, France Received 1 July 2005; received in revised form 22 August 2005 Available online 17 October 2005 Dedicated to Alexander Pines on occasion of his 60th birthday
Abstract Analytical methods based on solid-state NMR are becoming increasingly popular. However, these flourishing activities bring up the issue of how accurately NMR can assess an analyte proportion in a solid sample. The use of a chemical intensity reference for this purpose is a natural but often unsuitable choice, due to sample stability or preciousness. We propose here a protocol to perform quantitative measurements in solid-state NMR, by calibration of the circuit response through a low-power pulse injected during the acquisition (the so-called ERETIC method). Although this method has been in use for some time in liquid-phase and in vivo NMR, we point out here some peculiarities and useful applications typical of solids. Namely, the temperature dependence of the signal intensity imposes care in the application to MAS experiments. r 2005 Elsevier Inc. All rights reserved. Keywords: ERETIC; MAS; CPMAS
1. Introduction One of the points that made the success of NMR is its quantitative response, a rather unique feature among fellow spectroscopic methods. This property is easily used for measuring relative concentrations, for example in the case of mixtures or for assessing the population of distinguishable sites in a given material. Although in principle straightforward, the full onset of procedures to estimate absolute quantities has been more elusive, essentially because of the difficulty of choosing a proper intensity reference. In fact, while using an internal reference is the ideal analytical choice, this may turn out to be impractical due to chemical interferences, spectral overlap or preciousness of the sample. Conversely, the use of an external reference has all the drawbacks of not performing the intensities comparison in the same electronic conditions. Corresponding author. Fax: +33 491282897.
E-mail address: [email protected] (S. Caldarelli). 0926-2040/$ - see front matter r 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ssnmr.2005.08.013
In recent times the use of a synthetic signal as an intensity reference has been proposed [1–3]. A low-power RF pulse modulated at the observation frequency is applied during the acquisition time. After Fourier transform, the corresponding signal can be calibrated against mass or concentration values. The interest of this approach is that it could be considered in a sense both an internal (with respect to the circuit) and external (with respect to the sample) referencing. This so-called ERETIC method has been finding increasing applications in liquid-phase [3–9], in vivo [10] and diffusion measurements [11], especially for demanding analytical applications, such as the popular isotopic distribution analysis [8]. In this work we introduce the ERETIC method to solidstate NMR. We demonstrate its usefulness in MAS experiments, while pointing out some peculiarities linked to the Curie’s law dependence of the NMR signal. In perspective, external shift scaling has been recently proposed as a general tool for solid-state NMR [12]. In conjunction with the ERETIC calibration pulse, the entire referencing process could be relocated outside the analyte
ARTICLE IN PRESS
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F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
2. Materials and methods All spectra were recorded on a Bruker DSX 400, equipped with commercial probeheads (Bruker 400WB 4 mm H/BB CP VTN and 2.5 mm H-F/BB CP VTN) operating at a 13C and 207Pb resonances frequencies of 100.7 and 83.7 MHz respectively. For the pulse-acquire experiments, the 13C adamantane repetition time was of 15 s and the excitation pulse of 5.5 ms, corresponding to a 901 rotation. In the case of 207Pb in Pb(NO3)2, the repetition time and pulse length were 40 s and 3.5 ms, respectively. In both cases the acquisition time was 100 ms, the spectral width of 14000 Hz and 128 scans were summed up. The 1H–13C CPMAS experiment on tyrosine chlorohydrate was performed recording 512 scans with a contact time of 2 ms and a repetition time of 3 s, with an acquisition time of 40 ms and a spectral width of 90000 Hz. The circuit was realized according to the scheme in Fig. 1 (the directional coupler was EME HF-Technik Mod. 7020/30). The chemical shifts were referenced to solid glycine (carbonyl resonance at 176.5 ppm) and to a 1.1 molal aqueous solution of Pb(NO3)2 at 295 K (2965.7 ppm), for carbon-13 and lead-207, respectively. 2.1. The ERETIC setup The Eretic pulse was set to the length of the acquisition time, with an intensity of 8.6 102 mVpp. The intensity of the ERETIC magnetic field can be quickly adapted to produce intensities of the same order of the observed sample by varying this intensity. An exponentially decaying shaped pulse was used to perfectly mimic a NMR signal. The decay time constant was chosen as a fifth of the overall duration. The ERETIC pulse was taken directly from the synthesizer, prior to amplification. This arrangement has the advantage of not introducing any noise from the broadband amplifier. In common MAS probeheads, the ERETIC pulse can be safely injected using a channel not
13
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H
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F3
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Receiver
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X
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H
Fig. 1. Relevant elements of the circuit setup for inserting the ERETIC pulse into a double resonance experiment.
200
180
160
140
120
100
80
*** **
*
*
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Fig. 2. CPMAS experiment on L-tyrosine chlorohydrate. The ERETIC signal is shown at 0 ppm. Spinning sidebands are labeled by asterisks.
used for the observation. In the case of double-resonance experiments in a two-channel probehead, a directional coupler allows the simultaneous introduction of the ERETIC and of the second-frequency pulse, without any significant impedance break. Fig. 2 demostrates a CPMAS spectrum (on tyrosine), using the setup illustrated above. Since the ERETIC pulse is generated externally, it has to be phase-synchronized with the receiver. A pulse program for this purpose can be obtained from the authors. 3. Results and discussion The magnetic field associated to the macroscopic magnetization of a sample originates from the analyte concentration, C, as well as from Curie’s law for the single spin magnetization, M0: Bsignal ¼ CM 0 ¼ N g2 ðh=ð2pÞÞ2 B0 IðI þ 1Þ=ð3kTÞ. The concentration C is the product of the number of nuclei of interest in the coil times the natural abundance of the observed isotopes, that is the number of active spins detected by the coil. The principle of the ERETIC method is to inject in the receiving line a synthetic signal of known amplitude, Ber. The field associated with the macroscopic magnetization of the sample is thus measured relative to this reference. The current arising from an oscillating magnetic field in a tuned circuit is directly proportional to its quality factor, Q, a degradation of which results in a loss of the signal amplitude. The same law determines the efficiency of the RF entering the circuit; therefore, a reciprocity principle has been defined in the literature [13] that allows normalization of the signal measured at a certain Q level to any other one through the measure of the corresponding 901 pulse length, the product of these two quantities being a constant. In the case of ERETIC, both
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the reference and the signal fields are submitted to the same observation path and suffer equal circuit-related attenuation factors. The ERETIC referencing would be thus Qindependent, if the associated magnetic field in the circuit also remains constant. Since the reference pulse is introduced in the probe through a channel completely detuned with respect to the observation frequency (i.e. tuned to another frequency), the derivative of the Q around the observation (i.e. ERETIC) frequency is very small, guaranteeing the required reproducibility of the calibration pulse intensity. As shown in the Methods session, this setup is easily realized in a common double-resonance probehead, by exploiting the channel not used for observation for the ERETIC pulse. Provided this latter channel is tuned to the same frequency (typically the proton one), the RF leakage originating the ERETIC signal does not appear to be sensitive to even large changes in the Q of this side of the circuit. However, it should be kept in mind that in the case of large variations of the Q of the observe channel, due for example to different dielectric properties among samples, the associated changes of the reading pulse flip-angle should be still assessed for an accurate comparison of the relative intensities. In the case of double resonance experiments, such as the cross-polarization spectrum shown in Fig. 2, we observed no interference between the ERETIC pulse and the presence of a decoupling sequence. A quantitative response can be obtained from ss-NMR only if all the sample introduced in the coil contributes homogeneously to the signal. For instance, MAS rotors come in various internal and external sizes, and probeheads have specific coil geometries. On the overall, in common analysis a part of the sample may lay on the edges or even outside the coil, thus experiencing peculiar RF excitation and detection conditions. A similar problem is encountered in experiments requiring highly homogeneous RF pulses, as in the case of homonuclear decoupling. A qualitative solution to this nuisance is the limitation of the analyzed volume, either physically or by frequency-labeling the rotor sections with magnetic field gradients [15,16] This situation is fundamentally different from lp-NMR, where a concentration measurement is sought, so that the solution fraction outside the coil does not hamper the measurement, as in the case of the spin counting approach of solids. As a first step in any ss-NMR quantitative approach and to demonstrate the ss-ERETIC idea, we scrutinized the contribution to the signal from different sections of a 4 mm external diameter rotor. This was achieved by observing the increase of the signal spectra as a function of the addition of more amount of material (Fig. 3). At the same time, we measured the depth of the rotor occupied by the sample. Although MAS centrifugal forces commonly induce a conical rearrangement of the powder in the rotor, the deviation from a cylindrical arrangement of the sample in the rotor is relevant only for very limited loadings. Fig. 3 and 4 show that the first (as well as the last)
eretic
F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
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80
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Fig. 3. Growth of the 13C NMR signal in a MAS rotor upon successive additions of adamantane. The spectra were recorded in the presence of an ERETIC reference.
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Fig. 4. Normalized contribution to the NMR signal from different sections of a 4 mm rotor, as obtained from an adamantane sample with a pulse-acquire experiment. The dots were obtained from the intensity values of Fig. 3, by subtracting two successive spectra, using the ERETIC signal as reference. The light- and dark-gray areas correspond to the available volume for a 50 and 12 ml rotor, respectively.
milligrams of compound in a full rotor essentially do not contribute much to the signal, supporting our approximation of a cylindrical arrangement of the analyzed powder. Fig. 4 represents the same results in the form of the activity of the rotor portions with respect to the NMR signal. About 20 mg of the adamantane sample, at a depth level between 6.5 and 10.5 mm, respond homogeneously to the NMR excitation. For this setup, this volume can be thus safely used for quantitative analysis. Again, it should be kept in mind that for accurate measurements, such a calibration should be repeated for each probehead/coil setup. 3.1. Temperature effects As an implication of Curie’s law, the accuracy of the measurement is directly linked to the exact knowledge of the working temperature. For ss-NMR, this is a sensitive issue since increasing MAS rates produce a warming of the sample. The effect of the temperature on the ERETIC calibration is demonstrated in Fig. 5, on lead nitrate, which conveniently acts as an internal thermometer [14].
ARTICLE IN PRESS F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
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(c)
-3500 ppm
Fig. 5. Evolution as a function of the temperature of the MAS-NMR signal of a lead nitrate sample in the presence of the ERETIC reference. All spectra were recorded on a 2.5 mm probehead, spinning at 5 kHz MAS rate.
Comparison of Fig. 5a–c shows the variation in relative intensity of the ERETIC and signal peaks, due to the temperature. The reference intensity has a drop of about 2% over 571, which derives from an increase of the thermal noise. The lead-207 signal integral is reduced according to its inverse dependence on the temperature. If a mild error of a few percent can be tolerated, the ERETIC reference can be used directly with the values calibrated at one temperature. For more precise measurements, it would be necessary to calibrate the effects of the circuit response on the ERETIC integral over the temperature range of interest. 3.2. Spinning rate effects
(a)
-3500 ppm
(b)
-3500 ppm
(c)
-3500 ppm
(d)
-3500 ppm
Fig. 6. Effect of varying the 207Pb-MAS frequency on a lead nitrate sample in the presence of the ERETIC signal. (a) 5 kHz, (b) 10 kHz, (c) 20 kHz, (d) 30 kHz. The spectra were recorded on a 2.5 mm probehead.
5 kHz 10 kHz
25 24
20 kHz
23 30 kHz
22 %
-3450
(a)
21 20
MAS exp.
19
VT exp.
18 2.6
2.8
3.0
3.2
3.4
1000/T (K-1)
Fig. 6 shows the well-known variations of the lead nitrate average position and line shape due to temperature variations and gradients induced by friction forces, as the MAS rate the spinning rate increases from 5 to 30 kHz. Faster spinning rates correspond to higher temperatures, and a consistent behavior is followed by the signal integral (as demonstrated in Fig. 7). A broadened and increasingly distorted line shape is the signature of the temperature gradients [17]. On the other hand, the ERETIC signal remains constant, as the temperature variation affects mainly the rotor area rather than the whole circuit. Incidentally, Fig. 6 also demonstrates that the precision of this method is about 1%. The 207Pb signal intensity also decays, with an essentially perfect correlation with the temperature indicated by the lead chemical shift (Fig. 7). The small deviation from the correlation can be ascribed to the presence of a temperature distribution across the sample in the case of MAS induced heating.
Fig. 7. Evolution of the lead nitrate integral in the experiment in Figs. 5 and 6, referenced to ERETIC at 297 K. The effective experimental temperature was calibrated from the lead chemical shift of the maximum of the 207Pb lineshape.
4. Conclusions We introduced to solid-state NMR the ERETIC calibration method for quantitative analysis using NMR spectra. We demonstrated its feasibility in both single and double resonance experiments, namely CPMAS. Provided that some caution is taken, especially considering the temperature variations induced by MAS, this technique can be used promptly to precisions estimated at about 1%. We are currently demonstrating the interest of the ERETIC calibration on mixtures and paramagnetic compounds.
ARTICLE IN PRESS 218
F. Ziarelli, S. Caldarelli / Solid State Nuclear Magnetic Resonance 29 (2006) 214–218
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