1H Detected Relayed Dynamic Nuclear Polarization

Abstract

Recently, it has been shown that methods based on the dynamics of ¹H nuclear hyperpolarization in magic angle spinning (MAS) NMR experiments can be used to determine mesoscale structures in complex materials. However, these methods suffer from low sensitivity, especially since they have so far only been feasible with indirect detection of ¹H polarization through dilute heteronuclei such as ¹³C or ²⁹Si. Here we combine relayed-DNP (R-DNP) with fast MAS using 0.7 mm diameter rotors at 21.2 T. Fast MAS enables direct ¹H detection to follow hyperpolarization dynamics, leading to an acceleration in experiment times by a factor 16. Furthermore, we show that by varying the MAS rate, and consequently modulating the ¹H spin diffusion rate, we can record a series of independent R-DNP curves that can be analyzed jointly to provide an accurate determination of domain sizes. This is confirmed here with measurements on microcrystalline l-histidine·HCl·H₂O at MAS frequencies up to 60 kHz, where we determine a Weibull distribution of particle sizes centered on a radius of 440 ± 20 nm with an order parameter of k = 2.2.

Figure 1

Principle of Relayed DNP. A material is impregnated with a solution of a DNP polarizing agent. Once frozen, upon μwave irradiation, the ¹H spins in the solvent phase are hyperpolarized. The hyperpolarization then spontaneously diffuses into the bulk material.

Figure 2

21.2 T ¹H DNP MAS NMR spectrum of l-histidine·HCl·H₂O impregnated with 32 mM HyTEK-2 in TCE, at an MAS rate of 60 kHz, recorded with (top, blue), or without (bottom, orange) TCE solvent suppression. Solvent suppression here was achieved using a 60 ms ¹H spin-lock followed by a short ¹H spin echo (to prevent baseline distortion).

Figure 3

¹H polarization build-up time of dry l-histidine·HCl·H₂O powder recorded as a function of MAS frequency, at 21.2 T and ∼100 K. No significant variation of T_b,dry was observed between the resolved ¹H signals, thus the full ¹H spectra was integrated to obtain the T_b,dry at each MAS rate.

Figure 4

DT₁/L² as a function of the MAS rate. The dots represent the experimental values calculated from the steady-state DNP enhancement measurements on l-histidine·HCl·H₂O impregnated with a solution of 32 mM HyTEK-2 in TCE. The solid line shows the best fit to the data assuming that D is inversely proportional to the MAS rate, and T₁ and L are independent of MAS rate. Error bars were estimated by adding 5% random noise to (ε_∞, ε₀) and measuring the deviation of the resulting DT₁/L²; this was repeated 1000 times.

Figure 5

¹H DNP enhancement as a function of polarization time recorded for l-histidine·HCl·H₂O impregnated with a solution of 32 mM HyTEK-2 in TCE. The MAS rate is varied from 20 kHz to 60 kHz. The points show the experimental data. (a) Solid lines represent the simultaneous best fit of all the data to an R-DNP model considering spherical particles of a single radius, where we find R = 0.55 μm. (b) Particle sizes are assumed to follow a Weibull distribution. The parameters found to provide the best fit (solid lines) are a scale parameter of μ = 0.44 μm and an order parameter of k = 2.2. The errors on the observed values of the steady-state enhancements are estimated to be ±0.08 at 20 kHz and ±0.01 at 60 kHz. The reported errors correspond to the error of the fit, they were estimated by adding 10% of random noise over the modelized ε(t), measuring the deviation of the resulting fit. The process was repeated 1000 times.

Figure 6

Comparison of the distributions of the particle radii determined experimentally from the R-DNP (blue) and SEM (red) measurements. The dashed orange vertical line indicates the particle radius as measured using R-DNP and if we assume only a single particle radius. Both the distributions are normalized to have an area of 1.0.