Effects of radial radio-frequency field inhomogeneity on MAS solid-state NMR experiments

Abstract

Abstract. Radio-frequency field inhomogeneity is one of the most common imperfections in NMR experiments. They can lead to imperfect flip angles of applied radio-frequency (rf) pulses or to a mismatch of resonance conditions, resulting in artefacts or degraded performance of experiments. In solid-state NMR under magic angle spinning (MAS), the radial component becomes time-dependent because the rf irradiation amplitude and phase is modulated with integer multiples of the spinning frequency. We analyse the influence of such time-dependent MAS-modulated rf fields on the performance of some commonly used building blocks of solid-state NMR experiments. This analysis is based on analytical Floquet calculations and numerical simulations, taking into account the time dependence of the rf field. We find that, compared to the static part of the rf field inhomogeneity, such time-dependent modulations play a very minor role in the performance degradation of the investigated typical solid-state NMR experiments.

Residual proton line width under refocused frequency-switched Lee-Goldburg decoupling in MAS NMR

“… 9 An additional broadening is observed when the MAS-modulated rf-field inhomogeneity is taken into account (solid lines). 22 Under a spin-echo sequence (middle and right column of Fig. 4 ), the distribution of chemical shifts due to the static rf inhomogeneity is refocused and similar line widths result for a perfectly homogeneous rf field and simulations including the static rf inhomogeneity in the central third or the complete 1.9 mm rotor (dotted lines).…”

“…Moreover, it can be seen that the rf inhomogeneity leads to a strong broadening in the first-order term. This has been shown to originate from the re-introduction of dipolar coupling terms in the first-order effective Hamiltonian due to periodic rf-field amplitude and phase modulations that arise from the radial contribution to the rf-field inhomogeneity 22 and interfere with the first-order MAS averaging. This additional broadening is also present in Hahn echo simulations as the dipolar coupling cannot be refocused by a π pulse.…”

“…A more detailed description of the treatment of the rf-field inhomogeneity including the time-dependent modulations of the relative rf-field amplitude and phase can be found in ref. 22 .…”

“…S1 in the ESI†) was computed based on physical models of the solenoid coil 31,32 and used as input for numerical simulations. In order to separate the effects of the rf-field modulations due to the radial rf-field inhomogeneity from the static contribution, two distinct cases were studied 22…”

“…They can originate from the MAS modulation of the phase and amplitude due to the radial contribution to the rf inhomogeneity. 22 In this case, ω 1,rel ( t ) and ϕ 1,rel ( t ) will be periodic with the rotor frequency ω r and the rf Hamiltonian will only have a period of finite length if the modulation frequency of the pulse sequence and the MAS frequency are commensurate. Including the radial rf inhomogeneity in a theoretical treatment therefore requires cω m = ω r , where c is an integer that should be greater than four in order to avoid resonance conditions up to and including second order.…”