Research ArticleCHEMICAL PHYSICS

Direct observation of hyperpolarization breaking through the spin diffusion barrier

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Science Advances  30 Apr 2021:
Vol. 7, no. 18, eabf5735
DOI: 10.1126/sciadv.abf5735
  • Fig. 1 Hyperpolarization resurgence.

    Saturation recovery recorded with small-angle pulses at 7.05 T and 3.8 K in static mode for sample I, after performing DNP in either positive or negative mode (i.e., yielding positive or negative nuclear polarization). Polarization surges far above and below from thermal equilibrium, respectively, before it finally relaxes toward it. The saturation recovery experiment recorded without prior microwave irradiation is shown for comparison.

  • Fig. 2 Dipolar coupling and spin diffusion barrier.

    (A) Dipolar coupling of a proton and an electron spin taking the angular dependence into account d(r,θ) or as the root mean square dRMS(r), where r and θ are the distance between the electron and the nucleus and the angle between the vector connecting the electron and the nucleus and the main magnetic field, respectively. The black solid line represents the radius of the mean volume per electron in the case of sample I. The blue and red domains correspond to areas where proton spins are expected to contribute to the NMR line or not, respectively. (B) Representation of the spin diffusion barrier rb for the solvent protons of sample I according to Blumberg (17), Khutsishvili (19, 54), and Hovav et al. (32, 33). (red spheres) compared with the mean volume per electron spin rMV(e) (blue sphere). The black sphere represents the electron.

  • Fig. 3 HypRes experiment.

    Schematic representation of the HypRes experiment and its steps. During the preparation phase, polarization is built by microwave irradiation of the electron resonance (represented by the “μw” block). The polarization of the visible spins is then annihilated by a train of hard pulses (represented by the “Sat” block) during the detection phase. The polarization of the visible spins is monitored by small-angle pulses (represented by black rectangles) separated by variable delays (VD). The curves show the evolution of the visible and hidden spins during the course of the experiment. The circles below represent the polarization of the visible and hidden reservoirs (outer and inner circle, respectively), with darker shading indicating higher polarization.

  • Fig. 4 Processing of HypRes results.

    The HypRes experiment is recorded with and without microwave irradiation, resulting in the microwave-on and -off curves, respectively. The microwave-off curve is subtracted to the microwave-on curve to yield a curve of polarization excess with respect to thermal equilibrium. Note that the microwave-off curve corresponds to a conventional saturation recovery experiment.

  • Fig. 5 Two-reservoir model.

    Schematic representation of the model used to analyze HypRes results. The relaxation rate constant of the visible spins R1,v is assumed to be negligible. Polarization flows between the visible and hidden reservoirs at flow rate Rf, while the hidden spins relax to thermal equilibrium at rate R1,h.

  • Fig. 6 Diffusion versus temperature.

    (A) Results of the HypRes experiment at 7.05 T in static mode between 1.2 and 4.2 K for sample I, monitored with small-angle pulses expressed in terms of polarization excess with respect to thermal equilibrium. The gray crosses and the black lines represent the experimental data and the fit of the two-reservoir model, respectively. (B) Fitted parameters of the two-reservoir model plotted against temperature. The size of the hidden reservoir is given according to the two-reservoir model (χh) and according to Eq. 7 (χh). The error bars correspond to the error of the fit with 95% confidence.

  • Fig. 7 Quantification of the hidden spins.

    (A) Relative proton signal as a function of TEMPOL radical concentration in DNP juice recorded at 7.05 T and 3.8 K in static mode (open circles) showing that the presence of the radical quenches ~30% of the NMR signal for sample I. The dashed line represents linear interpolation of the first two points. (B) Simulated fraction of the spins that are hidden because they are unaffected by rf pulses as a function of the pulse bandwidth. Δω and ω1 are the paramagnetic shift and nutation frequency of the pulses, respectively, used to discriminate between visible and hidden spins. (C) Simulated fraction of the spins that are hidden because their transverse relaxation time constant is below the dead time of the spectrometer as a function of the correlation time of the electron spin state. T2,para and τd are the transverse paramagnetic relaxation time constant and the spectrometer dead time, respectively, used to discriminate between visible and hidden spins. The light blue and pink areas represent the visible and hidden fraction of the proton spins, respectively. See the Supplementary Materials for details of the simulations.

  • Fig. 8 HypRes experiment with inversion pulses.

    (A) Pulse sequence of the HypRes experiment including a broadband adiabatic pulse at the end of the preparation step (represented by the shape labeled “Inv”). (B) Results of the HypRes experiment with inversion pulses at 7.05 T and 3.8 K in static mode recorded with small-angle pulses for sample I with inversion widths from 0.5 to 4 MHz, in logarithmic and linear scale. (C) Estimated relative polarization profiles of the proton spins at the end of the preparation as a function of Larmor frequency shift taking into account the imperfection of the pulses (see the Supplementary Materials for more information on the pulse imperfections). The dip near zero is due to the narrow band saturation at the end of the preparation phase. (D) Estimated relative polarization profiles of the proton spins at the end of the preparation as a function of the distance to the electron spin, converted from (C) using Eq. 8. The numbers by the curves in (B) to (D) indicate the theoretical widths of inversion chirp pulses in megahertz.

  • Fig. 9 HypRes under MAS.

    (A) Proton spectrum of sample II at 14.0 T and 100 K under MAS at 8 kHz obtained by DNP. (B) Corresponding HypRes curves. Contrary to experiments in static mode at low temperatures, these measurements were obtained with π/2 pulses, each point being an individual measurement.

  • Fig. 10 DNP performance vs. temperature.

    (A) DNP build-up curves for sample I at 7.05 T in static mode between 1.2 and 4.2 K, monitored with small-angle pulses. The colored circles and the black lines represent the experimental data and the biexponential model, respectively. (B) Fit parameters of the biexponential model (see Eq. 9), DNP build-up rates RDNP,a and RDNP,b, and polarization at the DNP steady state PDNPmax plotted against temperature. The error bars correspond to the error of the fit with 95% confidence.

Supplementary Materials

  • Supplementary Materials

    Direct observation of hyperpolarization breaking through the spin diffusion barrier

    Quentin Stern, Samuel François Cousin, rédéric Mentink-Vigier, Arthur César Pinon, Stuart James Elliott, Olivier Cala, Sami Jannin

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