1H Detected Relayed Dynamic Nuclear Polarization.

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.

Introduction

Modern functional materials such as drug delivery systems,[1,2] formulated pharmaceuticals,[3] energy materials (e.g. organic solar cells, batteries, or hybrid perovskites),[4−6] or porous solids[7] are usually multicomponent materials whose interfaces, structural hierarchies, and domain sizes are complex and play an important role in determining the final functional properties. Although many techniques, such as electron microscopy, can provide important insight, there are still many challenges associated with fully determining such aspects in modern materials.

NMR spectroscopy is today well established as a method of choice to determine atomic-level structure and dynamics in complex materials.[8−20] NMR can also be used to reveal longer range aspects of structure.[8,17] In particular, pioneering work by Schmidt-Rohr, Spiess, and co-workers showed that 1H spin diffusion is a powerful mechanism that allows to explore sample homogeneity and measure polymer domain sizes.[21−23]

Dynamic nuclear polarization (DNP) under magic angle spinning (MAS) is a hyperpolarization method that relies on the transfer of electron spin polarization to nuclear spins upon microwave (μwave) irradiation at or near the EPR frequency of the electron spins.[24,25] To achieve this in materials, as shown in Figure , the material is typically impregnated with a radical containing solution.[26] Once frozen at ∼100 K, μwave irradiation induces transfer of polarization from electrons to nearby 1H, and finally the hyperpolarization is spontaneously propagated throughout the impregnated material via 1H spin diffusion, and then typically transferred to a heteronucleus for observation.[27,28]

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.

Capitalizing on early work by Van Der Wel et al.[28] and Rossini et al.,[27] in 2017 Pinon et al. combined 1H spin diffusion with hyperpolarization from DNP and quantitative numerical models to measure domain sizes in crystalline powders, mesoporous silica materials, and mixed composition cellulose-based films.[29] The method, denoted Relayed DNP (R-DNP), has since been successfully applied to determine the de novo structure of lipid nanoparticles (such as those used to deliver mRNA-based vaccines),[30] changes in the topology of lignins in biomass subjected to extraction,[31] the core–shell structure of organic crystalline drug nanoparticles (CNPs),[32] the presence of an insoluble amorphous form of a drug at the surface of crystalline particles of the salt form,[33] and the spatial distribution of functional groups in cellulose ethers.[34]

Although R-DNP is a powerful method to measure domain sizes, it suffers from low sensitivity. Indeed, while DNP enhanced spectra offer substantial gains in sensitivity, and generally accelerate experiments, the R-DNP approach relies on recording the dynamics of the DNP enhancement as a function of the polarization time, which requires recording signal build-up experiments with and without μwave irradiation. Typical experimental conditions are at a magnetic field of 9.4 T, with a sample spinning at 8–12.5 kHz, at a temperature of ∼100 K, where the 1H polarization must be monitored through a transfer experiment to heteronuclei (typically 13C or 29Si) to afford spectral differentiation of the sample components. Recording signal build-ups without μwaves often requires days of signal averaging!

In 2020, we reported DNP MAS experiments using 0.7 mm diameter rotors.[35] Such rotors enabled DNP experiments with MAS rates up to 65 kHz, at ∼100 K, and under μwave irradiation. At 21.2 T, DNP enhancements as high as 200 were reported at 65 kHz MAS rates using the HyTEK-2 polarizing agent.[35,36] We also obtained the best 1H resolution directly observed in MAS DNP experiments so far. This unprecedented 1H resolution enabled the implementation of 1H detected 1H–13C DNP HETCOR experiments.[35]

Here we combine R-DNP with fast MAS (up to 60 kHz) using 0.7 mm diameter rotors at 21.2 T, to follow the hyperpolarization dynamics in a microcrystalline powder of l-histidine·HCl·H2O impregnated with 32 mM HyTEK-2 in 1,1,2,2-tetrachloroethane (TCE). We find that a very significant reduction in experimental times can be achieved by implementing direct 1H detection, instead of detection through a heteronucleus, specifically here a reduction in time by a factor of ∼16 (by direct comparison of the experimental times reported in ref (29) and here). Furthermore, with this accelerated approach 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 (and spin diffusion coefficients).

Experimental Section

Experiments were carried out on l-histidine·H2O·HCl purchased from Sigma-Aldrich and used without further purification. The as received powder was ground manually with a pestle and mortar for about 15 min to reduce the size of the particles. All samples were prepared using the same batch of ground powder to reduce any potential variability due to impurities or particle size distributions between samples.

For DNP NMR experiments, ∼ 3 mg of the ground l-histidine·HCl·H2O was impregnated with ∼0.5 μL of a 32 mM HyTEK-2 solution in 1,1,2,2-tetrachloroethane (TCE). The powder was then transferred into a 0.7 mm zirconia rotor and closed with vespel drive and bottom caps. A second 0.7 mm rotor was prepared with neat ground l-histidine·H2O·HCl.

DNP NMR experiments were performed on a 21.2 T Bruker wide-bore NMR Avance Neo spectrometer operating at 900.14 MHz for 1H frequency using a 0.7 mm DNP low temperature MAS probe able to spin samples at the magic angle at rates up to 65 kHz at a temperature of about 100 K, in double resonance 1H–13C configuration.[35] The probe operates in connection with to a control system providing bearing, drive, and VT N2(g) flows cooled to about 100 K. The MAS frequency was set to and stabilized at values between 20 kHz to 60 kHz, and spinning is typically stable to within ±9 Hz.[35] Samples were degassed using five freeze–thaw cycles prior to measurement.[37] The spectrometer is equipped with a 593 GHz gyrotron μwave source, fine-tuned to the maximum enhancement of HyTEK-2 by adjusting the cavity temperature, and producing ∼15W continuous μwaves at the probe base.

The 1H polarization build-up times in the dry (unimpregnated) materials Tb,dry were measured using a 1H saturation recovery experiment. A spin echo of a total of eight rotor periods was used to remove the 1H probe background.

The DNP build-up times in the solvent were measured using 1H saturation recovery experiments followed by cross-polarization (CP) to 13C to allow 13C detection of the solvent. MAS rates from 20 to 60 kHz were used, and the experiments were performed under continuous μwave irradiation.

At each MAS rate between 20 to 60 kHz, the solvent DNP enhancements ε0(ω) were measured by recording two direct 1H experiments, one with μwave irradiation and a second without μwave irradiation. A short spin echo (eight rotor periods) was used to remove the 1H probe background. The recycle delay between scans was set to 5 s. The solvent DNP enhancements were calculated by taking the ratio of the integrated 13C TCE signal with and without μwaves.

The DNP enhancements of l-histidine·HCl·H2O as a function of polarizing delays were measured by recording two direct 1H experiments, one with μwave irradiation and a second without μwave irradiation. A 1H spin lock at 100 kHz during 100–60 ms was used to remove the TCE solvent 1H signal, followed by a short spin echo (2–8 rotor periods) to avoid baseline distortions (values vary with MAS rate and more details are provided in Table S1). DNP enhancements were recorded with MAS rates from 20 kHz to 60 kHz and were calculated by taking the ratio of the integrated 1H signal of the secondary amine at 17 ppm with and without μwaves.

Numerical simulations of R-DNP were performed using either the HPC facilities of the Scientific IT and Application Support Center of EPFL running Matlab R2019b (©MathWorks) with 28 cores (Intel Xeon 2.6 GHz) on a single calculation node with 128 GB of RAM, or an Apple Mac Pro (2019) running Matlab R2020b with 28 cores (Intel Xeon 2.5 GHz) and 192 GB RAM.

Scanning electron micrographs were performed on a Zeiss GeminiSEM300 at the EPFL CIME facility. The samples were treated with gold vapor deposition prior to analysis.

Results and Discussion

1H Detected R-DNP at fast MAS

Figure shows the DNP enhanced 1H NMR spectra of l-histidine·HCl·H2O impregnated with 32 mM HyTEK-2 in TCE at a MAS rate of 60 kHz. While the 1H TCE solvent signal dominates the spectrum (orange), the use of a 1H spin lock prior to acquisition following ref (38) was found to efficiently reduce the solvent signal, and it allowed detection of well resolved 1H signals from the l-histidine·HCl·H2O particles (blue). Such resolution, enabled by fast spinning, allowed the implement of 1H detected R-DNP experiments, as the 1H signals of l-histidine·HCl·H2O, such as Ha, Hb or H2,3, can be directly integrated without the need to transfer polarization to a heteronucleus, i.e., here 13C.

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).

MAS Dependence of R-DNP

We note that not only should fast MAS experiments allow access to 1H detected R-DNP curves but also that Prisco et al.[39] have recently highlighted the key role of 1H spin diffusion in MAS DNP experiments in their general approach to determining hyperpolarization transfer rates using the competitive rates of spin polarization generation, propagation, and dissipation that govern hyperpolarization transfer between large coupled spin ensembles. Since changing the MAS rate will modulate the 1H spin diffusion coefficient, it will lead to different relayed-DNP dynamics at different spinning rates. This in turn suggests that measuring R-DNP curves at different spinning rates will provide a set of independent data that should lead to more accurate determination of domain sizes than through the measurement of a curve at a single rate. We outline the details of this approach and provide experimental verification in the following.

Spin–Lattice Relaxation of l-Histidine·HCl·H2O

Figure shows the measured 1H polarization build-up time Tb,dry recorded on a dry powder of l-histidine·HCl·H2O at MAS rates from 20 kHz to 60 kHz at a sample temperature of ∼100 K and at 21,15 T. Tb,dry slowly increases from 740 to 823 s as the MAS rate increases. In the R-DNP context, the 1H spin–lattice relaxation time T1 is defined as the build-up time of the dry spinning powder, sometime referred to as the intrinsicT1 (i.e. free from 1H spin diffusion effects). T1 in rigid organic solids, in the absence of any significant internal motion, is usually induced by random fluctuation of magnetic moments near the Larmor frequency, i.e., here 900 MHz, and are usually due to the presence of paramagnetic impurities or defects in the solid that links the 1H spins to the thermal reservoir.[40] Spinning of the sample around the magic angle up to 60 kHz is far too slow to notably interfere with the T1intrinsic relaxation mechanisms. Nonetheless, as shown by Kessemeier et al.,[41]1H spin diffusion contributes to the apparentT1 in solids as it connects spins to remote impurities, and thus increasing of the MAS rate decreases the 1H spin diffusion rate, and the apparentT1 can increase. The weak MAS rate dependence observed for Tb,dry can be attributed to this contribution. A potential source of impurities is oxygen absorbed into the particles.[42] Fortunately, in our sample, Figure shows that 1H spin diffusion of sink relaxation in l-histidine·HCl·H2O has minimal effect in the 20–60 kHz range. Consequently we make the following assumptions: (i) the effect of 1H spin diffusion on the relaxation in l-histidine·HCl·H2O is negligible (ii) T1 can be approximated by Tb,dry at 60 kHz. We note that (i) is verified here for l-histidine·H2O·HCl, but it might not be valid for other samples, where one might have to explicitly take into account 1H spin diffusion of sink relaxation in addition to the relay of hyperpolarization in the R-DNP model.

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 Tb,dry was observed between the resolved 1H signals, thus the full 1H spectra was integrated to obtain the Tb,dry at each MAS rate.

MAS Dependence of the Diffusion Coefficient

A key parameter for R-DNP simulations is the 1H spin diffusion coefficient D and its dependence on the MAS frequency ωr. The exact MAS dependence of D is a subject of debate. It is expected that increasing ωr reduces 1H spin diffusion rate, as homonuclear dipolar couplings, the cause of spin diffusion, are progressively averaged out. Maricq and Waugh showed that in the limit of a 2-spin system treated with average Hamiltonian theory, the dipolar coupling vanishes with the inverse of ωr.[43] Nonetheless, D is a multispin effect and cannot be fully described with a 2-spin system. For example, the large dipolar couplings present in a static sample could lead to homonuclear analogies of “self-decoupling” effects,[44] which can reduce the effective couplings. Slow magic angle spinning can then actually increase effective couplings, and Roos et al. made the counterintuitive observation that D in polystyrene and polyethylene actually increases at slow ωr, reaches a maximum at about ωr = 2–3 kHz, and then decreases at faster ωr.[45] Similar observations were since made in the context of weakly magnetic nuclei.[46] Halse et al. used first-principles simulations in Liouville space to calculate D for spinning solid samples of ice and l-histidine for ωr = 5–20 kHz, and found a good fit to a 1/ωr dependence.[47] Hansen and co-workers studied D between 2 and 12 kHz MAS in high density polyethylene and used the Bloembergen–Purcell–Pound equation to rationalize the dependence on ωr.[48] Since here we are exploring a much higher spinning rate regime, between 20 to 60 kHz, we propose to extract a phenomenological MAS dependence directly from the R-DNP data.

We previously showed[29] that in the case of a solid impregnated with a polarizing solution, the steady-state DNP enhancement ε∞ is dominated by 1H spin diffusion and 1H spin–lattice relaxation and we derived the following formula for spherical particles:where ε0 is the DNP enhancement in the polarizing solution, T1 is the intrinsic spin–lattice relaxation time of the solid, and L the radius of the (here spherical) solid particle. Knowing the pair (ε∞, ε0) for each MAS frequency, it is possible to calculate the value of DT1L2 as a function of ωr ((ε∞, ε0) are given in Table S2). Figure reports the value obtained for l-histidine·HCl·H2O impregnated with HyTEK-2 in TCE for ωr between 20 and 60 kHz. As neither L nor T1 depend on the MAS rate, the observed dependence is the sole consequence of the MAS dependence of D. We found that our experimental data are in best agreement with D being inversely proportional to the MAS rate over the 20–60 kHz regime. Then, the proportionality coefficient was obtained using the value of D from Halse et al. at 5 kHz of 0.15 nm2.ms–1.[47] This leads to the following empirical dependence of the 1H spin diffusion coefficient D of l-histidine·HCl·H2O as a function of ωr:

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.

MAS Rate Modeling of R-DNP for a Single Particle Size

Figure a shows the experimental DNP enhancement ε(t) (data points) as a function of the polarizing time t for MAS rates ranging from 20 to 60 kHz. As described in ref,[29] the 1H hyperpolarization generated in the presence of μwaves in the HyTEK-2/TCE phase is transported via 1H spin diffusion to the l-histidine·HCl·H2O particles (see Figure ). In absence of μwaves, there is still transport of polarization between the two phases since they do not have the same 1H build-up times and since the DNP polarizing agent induces depolarization in the HyTEK-2/TCE phase. Assuming the l-histidine·HCl·H2O powder is made up of spherical particles of radius R, the transport of polarization can be simulated by numerically solving the 1H spin diffusion equations in presence and absence of μwaves. In a system with a spherical symmetry:where P(r,t) is the polarization at position r and time t; D(ω,r) is the 1H spin diffusion coefficient, which can depend on r (i.e., it can vary from one phase to another) and which depends on ω as described above. P0(r) is the local equilibrium polarization in the absence of 1H spin diffusion given bywhere ε0(ω) is the solvent DNP enhancement measured at MAS rate ω and ε = 0.7 is the contribution factor of HyTEK-2 (which was measured to be independent of ω for HyTEK-2 between 10 to 40 kHz).[36] This definition translates to, in the absence of spin diffusion, spins located in the HyTEK-2/TCE phase hyperpolarized to ε0(ω) in the presence of μwaves and accounts for depolarization ε in presence/absence of μwaves; and that the polarization of the l-histidine·HCl·H2O phase relaxes to 1.[29]p is the slope the tanh function defining the separation between the two phases. T1(r) is defined aswhere T1 is the spin–lattice relaxation time of l-histidine·HCl·H2O (see discussion above); and T(ω) is the DNP build-up time of the solvent; and p is 400 μm–1. The measured values of ε0(ω) and T(ω) are reported in the Supporting Information. The 1H resolution gives the possibility to calculate the l-histidine·HCl·H2O enhancement as a function of time for each MAS rate:Allowing the size of the particle R and the slope p to vary, the full set of experimental data can be simultaneously fit, and we find that the model converges to a radius for the histidine particles of R = 550 ± 30 nm. This is made with the simplified hypothesis that the powder is comprised of spherical particles of the same radius R.

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.

The SEM analysis of the l-histidine·HCl·H2O powder indicates that particle sizes follow a Weibull distribution centered on a radius of 374 nm with an order parameter of k = 2.2 as shown in Figure (see Figure S1 and S2, and eq for the Weibull distribution function).[49] Thus, the particle size obtained with the 1H detected variable MAS rate R-DNP curves up to 60 kHz appears to be in relatively good agreement with the radius obtained with SEM. Moreover, using 1H detection here significantly reduced the experimental time, the measurement of the DNP enhancement ε(t) as a function of the polarizing time required only 4 h of signal averaging for each MAS frequency (experimental times are detailed in the Supporting Information).

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.

MAS Rate Modeling of R-DNP with a Distribution of Particle Sizes

Although the simplifying assumption that the l-histidine·HCl·H2O powder is comprised of spherical particles of the same size yields an R-DNP particle size measurement in fairly good agreement with the SEM measurement, explicitly taking into account a particle size distribution is an obvious correction that should improve the agreement.[27] To do so, for each MAS rate, we calculated the NMR signal of spherical histidine particles with radii ranging from R = 0.05 to 5 μm in increment of 0.01 μm, with and without μwave irradiation of the sample:For a distribution of sizes in the powder, the NMR signals with μwave on/off are then calculated by summing over all the crystallites. The probability of finding a crystallite of radius R is given by the particle size distribution function. Specifically, here we used a Weibull distribution:which is centered on a radius of μ (also referred to as the scale parameter) and with an order parameter k and which is typically the type of distribution expected for powders formed by fragmentation or crushing[49,50] (of course, other distributions could be evaluated). The resulting DNP enhancement as a function of time can be calculated asThis treatment is similar to Rossini et al.,[27] except instead of calculating series of ε(t) for each particle size, we computed a series of signals for all particle size . Figure b shows the results of a fit of the experimental R-DNP data fit to a fixed order parameter k = 2.2 (taken from the SEM) which converges to a Weibull distribution centered at μ = 440 nm and shown in Figure . When comparing to the fit for a single radius in Figure a, we see that the inclusion of the distribution makes a significant difference, and results in a more accurate measurement of the particle size. The distribution centered at μ = 440 nm is very close to the measurement performed with SEM, with the difference within the uncertainty of the SEM method to estimate the particle size distribution. Figure compares the distributions determined by the SEM and R-DNP measurements and illustrates the good agreement between both.

Conclusions

To conclude, we have first demonstrated that fast MAS (here up to 60 kHz) enables rapid acquisition of 1H detected R-DNP curves. With this new development in hand, we have shown how variable MAS rate R-DNP curves have different shapes, due to the modulation of 1H spin diffusion coefficients. We show that, not unexpectedly, D scales as 1/ωr in the fast MAS regime and that a set of variable rate R-DNP curves can be modeled to obtain an accurate determination of the distribution of particle sizes present in a microcrystalline sample of l-histidine·H2O·HCl.