Solid-State NMR 13C sensitivity at high magnetic field

Abstract

Sensitivity is the foundation of every NMR experiment, and the signal-to-noise ratio (SNR) should increase with static (B₀) magnetic field, by a proportionality that primarily depends on the design of the NMR probe and receiver. In the low B₀ field limit, where the coil geometry is much smaller than the wavelength of the NMR frequency, SNR can increase in proportion to B₀ to the power 7/4. For modern magic-angle spinning (MAS) probes, this approximation holds for rotor sizes up to 3.2 mm at 14.1 Tesla (T), corresponding to 600 MHz ¹H and 151 MHz ¹³C Larmor frequencies. To obtain the anticipated benefit of larger coils and/or higher B₀ fields requires a quantitative understanding of the contributions to SNR, utilizing standard samples and protocols that reproduce SNR measurements with high accuracy and precision. Here, we present such a systematic and comprehensive study of ¹³C SNR under MAS over the range of 14.1 to 21.1 T. We evaluate a range of probe designs utilizing 1.6, 2.5 and 3.2 mm rotors, including 24 different sets of measurements on 17 probe configurations using five spectrometers. We utilize N-acetyl valine as the primary standard and compare and contrast with other commonly used standard samples (adamantane, glycine, hexamethylbenzene, and 3-methylglutaric acid). These robust approaches and standard operating procedures provide an improved understanding of the contributions from probe efficiency, receiver noise figure, and B₀ dependence in a range of custom-designed and commercially available probes. We find that the optimal raw SNR is obtained with balanced 3.2 mm design at 17.6 T, that the best mass-limited SNR is achieved with a balanced 1.6 mm design at 21.1 T, and that the raw SNR at 21.1 T reaches diminishing returns with rotors larger than 2.5 mm.

Keywords: (13)C detection; High magnetic field; MAS SSNMR; Probe design; Sensitivity.

Figure 1.

¹³C CPMAS spectra of NAV, the vertical expansion of the baseline and the pure noise spectrum. (a) ¹³C CP spectrum of 20% uniformly ¹³C, ¹⁵N labeled NAV with peak assignments acquired using 750 MHz spectrometer with 3.2 mm Balun probe in double resonance ¹H-¹³C mode. (b) Full bandwidth presentation of the same spectrum as (a). (c) Noise floor of (a), vertically expanded by a factor of 20. First-order spinning sidebands of the carbonyl peak are indicated with asterisks. (d) Pure noise spectrum, vertically expanded by a factor of 20, acquired under the same conditions as the spectrum in (a).

Figure 2.

Dependence of $\text{SNR}$ on probe efficiencies in triple and double resonance modes. (a, b) Methyl region of na NAV spectra acquired with 600 MHz Varian T3 1.6 mm probe in triple resonance mode (a) and double resonance mode (b) along with the corresponding full-width noise spectra vertically expanded by a factor of 10. The two signal spectra are scaled to the same noise levels. (c, d) Methyl region of na NAV spectra acquired with 600 MHz Phoenix T3 3.2 mm probe in triple resonance mode (c) and double resonance mode (d) along with the corresponding full-width noise spectra vertically expanded by a factor of 10. The two signal spectra are scaled to the same noise levels.

Figure 3.

Dependence of $\text{SNR}$ on spectrometer noise figures. (a, b) Noise spectra without external noise source input (a), or the “cool state”, and with 5.2 dB external noise source input (b), or the “hot state”, in a configuration where the spectrometer $\text{NF}$ is 1.5 dB. (c, d) Noise spectra without external noise source input (c), or the “cool state”, and with 5.2 dB external noise source input (d), or the “hot state”, in a configuration where the spectrometer $\text{NF}$ is 11.5 dB. The noise spectra in (b) and (d) are scaled to the same level. (e, f) Methyl region of na NAV spectrum acquired with 900 MHz 1.6 mm Black Fox probe in double resonance mode in a configuration where the spectrometer $\text{NF}$ is 3.9 dB (e) and 2.3 dB (f) along with the corresponding full-width noise spectra vertically expanded by a factor of 10. The two spectra are scaled to the same average peak heights.

Figure 4.

$\text{SNR}$ of all configurations investigated in this study categorized by rotor sizes and field strengths and labeled by manufacture and probe configurations. The best $\text{SNR}$ is plotted in case where a configuration was measured multiple times for easier visualization of trends. In the labels, VRN stands for Varian, PHX stands for Phoenix, BF stands for Black Fox, BRK stands for Bruker and TW stands for thin-wall.

Figure 5.

$\text{SNR}$ of all configurations (a) normalized by the amount of sample, and (b) normalized by the amount of sample and corrected by spectrometer $\text{NF}$. The best $\text{SNR}$ is plotted in case where a configuration was measured multiple times for easier visualization of trends. In the labels, VRN stands for Varian, PHX stands for Phoenix, BF stands for Black Fox, BRK stands for Bruker and TW stands for thin-wall.

Figure 6.

The dependency on B₀ field of sensitivity of (a) all data and (b) all 1.6 mm and 3.2 mm standard-wall pencil-style rotors normalized by the amount of sample and number of scans and corrected by RF efficiency and spectrometer $\text{NF}$.

Figure 7.

Spectra of conventional ¹³C $\text{SNR}$ standard compounds acquired using Varian 750 MHz 3.2 mm Balun probe and standard wall rotors, and the corresponding molecular structures. (a) CP spectrum of MGA with 16.667 kHz MAS. (b) CP spectrum of α-glycine with 16.667 kHz MAS. (c) CP spectrum of HMB with 16.667 kHz MAS. (d) DP spectrum of adamantane with 18 kHz MAS and low power ¹H decoupling.

Figure 8.

The aliphatic region of I88 Cδ1 strip in ¹³C-¹³C 2D correlation spectrum of α-synuclein fibril formed in Tris-HCl buffer with (a) 50 ms DARR mixing and (b) 500 ms DARR mixing with unambiguous assignments and $\text{SNR}$ corresponding to distances. All $\text{SNR}$ values in the figure were calculated for spectra processed with exponential line broadening matched to the linewidth of I88 Cδ1 peaks (50 Hz in direct dimension, 60 Hz in indirect dimension). The 2D spectra and 1D slices shown in the figure were processed with sine bell apodization with a 60° offset to achieve optimal resolution. The first contour in the 2D strip in (a) is drawn at 16 σ, and the first contour in the 2D strip in (b) is drawn at 5 σ. The distances according to α-synuclein fibril formed in phosphate buffer structure (PDB: 2N0A) and $\text{SNR}$ of all 16 unambiguously assigned cross peaks in (b) are plotted in (c). The primary vertical axis on the left of (c) follows the convention for reporting $\text{SNR}$ of 1D spectra, where $\text{SNR=S/2N}$. The secondary vertical axis on the right of (c) follows the common practice for reporting $\text{SNR}$ of multi-dimensional spectra, where $\text{SNR=S/N}$.