Adiabatic Solid Effect

Abstract

The solid effect (SE) is a two spin dynamic nuclear polarization (DNP) mechanism that enhances the sensitivity in NMR experiments by irradiation of the electron-nuclear spin transitions with continuous wave (CW) microwaves at ω_0S ± ω_0I, where ω_0S and ω_0I are electron and nuclear Larmor frequencies, respectively. Using trityl (OX063), dispersed in a 60/40 glycerol/water mixture at 80 K, as a polarizing agent, we show here that application of a chirped microwave pulse, with a bandwidth comparable to the EPR line width applied at the SE matching condition, improves the enhancement by a factor of 2.4 over the CW method. Furthermore, the chirped pulse yields an enhancement that is ∼20% larger than obtained with the ramped-amplitude NOVEL (RA-NOVEL), which to date has achieved the largest enhancements in time domain DNP experiments. Numerical simulations suggest that the spins follow an adiabatic trajectory during the polarization transfer; hence, we denote this sequence as an adiabatic solid effect (ASE). We foresee that ASE will be a practical pulsed DNP experiment to be implemented at higher static magnetic fields due to the moderate power requirement. In particular, the ASE uses only 13% of the maximum microwave power required for RA-NOVEL.

Figure 1.

(a) Experimental and (b) simulated DNP field profile using either a constant-frequency pulse (black) or a chirped pulse (red) on SABDPA in DNP juice at X-band (0.35 T). Reprinted with permission from Can et al. and Tan et al.

Figure 2.

(a) Amplitudes of the chirp pulses are frequency-dependent (the colors denote the frequency) due to a finite-Q value in a resonator. The measured data (blue) was interpolated with a cubic function (red) and fitted with a Lorentzian function (black), which yields Q ~ 1650 ± 100 (see Supporting Information for details of the fit and calculation). Experimental and simulated DNP field profiles for the (b) SSE and (c) ASE sequence. In (b), we show the EPR spectrum (magenta) of trityl OX063.

Figure 3.

(a) Calculated effective fields ${\omega }_{\text{eff}}=\sqrt{{\omega }_{1\text{S}}^2+{\Omega }^2}$ (eq 1) during the Δ = 16 MHz, τ_p= 15 μs chirped pulse. The vertical dotted line indicates the time at which the SE matching conditions are satisfied (ω_0I = ω_eff) for three different crystallites, whose β Euler angles with respect to the magnetic fields are 68°, 71°, and 75°, respectively. The α and γ angles are set to 0 for all crystallites. The offset frequency Ω(α,β,γ,t) = ω_e(α,β,γ) − ω_μw(t) depends on the electron Larmor frequency ω_e(α,β,γ) and the instantaneous microwave frequency of the chirped pulse ω_μw(t). Simulated (b) build-up curve of the nuclear I_z spin and the (c) electron S_z spin at trajectory at the ZQ-SE condition. Note that only the first 5 μs of the chirped pulsed is shown here.

Figure 4.

Optimization of the (a) Rabi frequency ω_1S to verify the NOVEL matching condition at ~53 MHz (b) and sweep width Δ of the Rabi frequencies (for RA-NOVEL) and the offset frequency Ω (for ASE) at τ ~ 8 s. (c) Measured build-up curves of ASE, SSE, and RA-NOVEL using the optimized Δ and a repetition time τ_rep ~ 1 ms for the three sequences. Figure S1 illustrates a timing diagram for the pulse sequence, and Table S1 contains addition experimental parameters used in the experiments.