Solid-State NMR 13C sensitivity at high magnetic field

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.