Time domain DNP at 1.2 T

Abstract

We present the results of an experimental pulsed DNP study at 1.2 T (33.5 GHz/51 MHz electron and ¹H Larmor frequencies, respectively). The results include a comparison of constant-amplitude NOVEL (CA-NOVEL), ramped-amplitude NOVEL (RA-NOVEL) and the frequency-swept integrated solid effect (FS-ISE) experiments all of which were performed at the NOVEL matching condition, ω_1S = ω_0I, where ω_1S is the electron Rabi frequency andω_0I the proton Larmor frequency. To the best of our knowledge, this is the first pulsed DNP study carried out at field higher than X-band (0.35 T) using the NOVEL condition. A combination of high microwave power (~150 W) and a microwave cavity with a high Q (~500) allowed us to satisfy the NOVEL matching condition. We also observed stretched solid effect (S²E) contributions in the Zeeman field profiles when chirped pulses are applied. Furthermore, the high quality factor of the cavity limits the concentration of the radical to ~5 mM and generates a hysteresis in the FS-ISE experiments. Nevertheless, we observe very high DNP enhancements that are comparable to the results at X-band. These promising outcomes suggest the importance of further studies at even higher fields that delineate the instrumentation and methods required for time domain DNP.

1. Introduction

The last two decades witnessed the rapid development of methods to perform dynamic nuclear polarization (DNP) experiments aimed at enhancing the sensitivity of structural NMR experiments at low temperatures and high magnetic fields [1–4]. The essential instrumentation required for these experiments is a continuous wave (CW) microwave oscillator operating in the sub-THz frequency regime, either a gyrotron [5–7] or klystron [8–10], a low temperature magic angle spinning (MAS) probe [10–12] and suitable polarizing agents [13–21]. The first successful demonstrations of DNP using a klystron [8] and gyrotron were performed at 5 T (140 GHz/211 MHz) in 1992/93 [6,7,22]. Subsequently, in 2010 the first commercial DNP/NMR spectrometer operating at 9.4 T (263 GHz/400 MHz) [23] appeared and the field has since rapidly expanded. At present there are ~50 commercial CW DNP/NMR spectrometers operating at magnetic fields up to 21.1 T [23,24].

To date, the DNP enhancements obtained at high field, although very enabling, still amount to only a small fraction of the theoretical limit. This situation is at least partially due to the fact that current CW DNP mechanisms, including the solid effect (SE) and cross effect (CE), scale as ω_0I⁻ⁿ where n ~ 2 [25,26], and has provided the impetus to develop new DNP methods that do not suffer from this issue. Recently, we demonstrated the performance of time domain DNP using the NOVEL [27–29], the integrated solid effect [30–32], and the TOP-DNP [33] pulse sequences at 0.35 T [34–36]. Although our data showed very high efficiency, it is important to extend this ensemble of approaches to higher fields to determine the manner in which the experiments scale with B₀ and to optimize the methodology for high field DNP.

In this report we present a detailed study of pulsed DNP at 1.2 T that explores the NOVEL experiment at a field higher than X-band. We obtained DNP enhancements of ~100–300 with various sequences including constant amplitude NOVEL (CA-NOVEL), ramped amplitude NOVEL (RA-NOVEL) and the frequency swept integrated solid effect (FS-ISE) and a newly observed mechanism, the stretched solid effect (S²E). We use a combination of high microwave power, a high Q microwave cavity, and an arbitrary waveform generator (AWG) to generate high-power, arbitrarily shaped microwave pulses for the aforementioned experiments. Our study suggests that it is entirely possible to perform these experiments at higher fields (9.0 T, ~250 GHz for electrons) where commercial microwave drivers and gyroamplifers are currently available [37].

2. Experimental and simulations

EPR/NMR/DNP experiments were performed on a Bruker BioSpin E580 (Billerica, Massachusetts, USA) Q-band EPR spectrometer equipped with a pulse ENDOR resonator (EN 5107D2). In this system, the pulses are first formed and modulated by an arbitrary waveform generator (AWG) at X-band and then up-converted to the Q-band frequency (33.5 GHz) by mixing with a 24 GHz local oscillator. The resulting pulses are amplified by a TWT microwave amplifier with a gain of ~51 dB, ~150 W maximum output, duty cycle of 10% and maximum pulse length of 100 μs. For EPR detection, the Q-band signal is down-converted to an X-band frequency. For NMR/DNP experiments, the RF coil of the ENDOR resonator is connected to an external tuning/matching circuit (courtesy of Thorsten Marquardsen) that provides an excellent tuning range (40–60 MHz) with a Q ~ 40 across that band. Typically, the coil was tuned to ~51 MHz in our experiments. All experiments were performed at 80 K on a sample of glycerol-d₈/D₂O/H₂O (60/30/10 vol ratio) doped with 5 mM trityl-OX063. The radical concentration was chosen because higher radical concentrations yielded severely distorted EPR lineshapes on this instrument.

Simulations of the NOVEL microwave field profiles and of the Zeeman field profiles were performed with a program DNPSOUP (DNP Simulations Optimized with a Unified Propagator). The FS-ISE DNP field profile was simulated with a separate MATLAB script. The DNPSOUP program employs a novel analytical theory to treat the time evolution of the density operator under the effects of both coherent Hamiltonians and stochastic relaxation and is described in a separate publication [38]. For the simulations described below we used a 4-spin model system comprised of an electron and three protons. Two of the protons were directly hyperfine coupled to the electron, while the third proton—whose polarization is monitored—is dipolar coupled to the other two protons to mimic spin diffusion. The coordinates of the electron and the three protons are (0, 0, 0), (−2, 2, 0), (4.5, 0, 0), and (5.5, 0, 1), respectively (in Å). 55 crystalline orientations were averaged using the 2-angles ZCW powder scheme [39–42]. The g-tensor for the electron was (2.00315, 2.00315, 2.00258). T_1n and T_2n of the two hyperfine-coupled protons were set to 1 s and 1 ms. For simulations at 1.2 T, T_1e and T_2e were set as 2 ms and 20 ms, respectively. T_1n and T_2n of the detected proton are 20 s and 10 ms. We use a microwave center frequency of 33.52 GHz and 51 MHz electron Rabi field for the Zeeman field profile. To resemble experimental observations, a shorter 1 ns flip pulse was used for partial flipping, followed by 20 μs mixing, and then 200 μs recycle delay. For simulations at 0.35 T, T_1e of 1 ms and T_2e of 0.2 μs were used. The detected proton has a T₁ of 5 s and T₂ of 10 ms. A microwave field strength of 15 MHz was used for the Zeeman field profile, centered at 9.8 GHz. A 16 ns flip pulse was used, along with 500 ns mixing time and 100 μs recycle delay. The microwave sequence was repeated 200 times before acquisition for experiments at both fields. As will be seen below, these parameters while approximate do produce field profiles in reasonable agreement with the experimentally observed results.

3. Results

The timing diagrams for the pulse sequences used in our study are summarized in Fig. 1 and include CA-NOVEL [34,35], RA-NOVEL [43] and the FS-ISE [44]. In all cases, the electron Rabi frequency was set at or near the NOVEL condition ω_1S/2π = ω_0I/2π = 51 MHz The combination of a high-Q microwave cavity and ~150 W of microwave power was employed to achieve these Rabi fields. Fig. 2a shows a plot of the microwave field strength that was measured as a function of the frequency and yields Q ~ 1,500, and Fig. 2b illustrates the Rabi field strengths as a function of the amplitude of the input to the TWT. It is evident that the amplifier has a non-linear performance, especially near the saturation (~80 MHz Rabi field). At the 150 W maximum power level, a Rabi frequency as high as ~80 MHz was achieved with a modest inhomogeneity of the microwave field, ~10%. For experiments that require modulation of the microwave pulses such as RA-NOVEL and FS-ISE, we employed an arbitrary waveform generator (AWG). Fig. 2c demonstrates one of the benefits of the AWG, in the case of CA-NOVEL, in which the phase of the locking pulse was incremented, and the optimum performance of this sequence was obtained at 90° phase shift as expected.

Fig. 1.

Sequences for pulsed DNP including constant amplitude NOVEL (a), ramped-amplitude NOVEL (b), and frequency-swept integrated solid effect (c). All sequences were performed at the NOVEL matching condition, which matches the Rabi frequency of electron with the Larmor frequency of proton. The ¹H NMR signal was recorded using a solid echo sequence, which refocuses the homonuclear dipolar coupling in static samples.

Fig. 2.

Instrumentation required to satisfy the NOVEL conditions involved a combination of (a) a high-Q microwave cavity with Q = 1,500, and (b) a high power TWT amplifier resulting in a Rabi frequency up to ~80 MHz. The maximum output power from the microwave amplifier is 150 W corresponding to 100% input amplitude. In (c) the phase of the spin-locking pulse in CA-NOVEL was varied using the AWG function. As expected, the efficiency is maximum with a 90° phase shift relative to the first 90° pulse.

Fig. 3a compares the microwave field profile of the CA-NOVEL sequence at X- and Q-band. The normalized enhancements were measured at varying microwave field strength ω_1S/2π and plotted as functions of the ratio between the electron Rabi and the proton Larmor frequencies ω_1S/ω_0I. The data at both fields clearly show the NOVEL matching condition at ω_1S/ω_0I = 1, and the matching condition is narrower at the higher field. Such features were reproduced using numerical simulations as shown in Fig. 3b. Fig. 3c shows the Zeeman field profiles obtained at the NOVEL condition at Q-band. The magnetic field was incremented while the microwave frequency and the μw field strength were held constant. The field profile was obtained with and without the initial 90° pulse in the spin lock sequence. In the absence of the π/2 pulse, the field profile resembles that of the unresolved solid effect as opposed to the resolved solid effect in a low-power CW experiment. In the presence of the π/2 pulse, the field profile obtained with CA-NOVEL shows a maximum at a frequency slightly off resonance. Subtracting the field profile obtained without the π/2 pulse from that obtained with the pulse yields a Gaussian-like curve resembling the EPR lineshape (Fig. 3c and d). Besides, we also note the presence of three-spin solid effect DNP at ±2ω_0I, driven by efficient saturation of the forbidden transitions using high microwave power [45].

Fig. 3.

(a) Microwave field profile in CA-NOVEL experiment at 0.35 T (blue, open square) and 1.2 T (red, solid circle). The Larmor frequencies for ¹H were ~14.7 MHz and ~51 MHz, respectively. (b) Simulated microwave field profile at 0.35 T (blue square) and 1.2 T (red triangle) on a static sample (c) The Zeeman DNP field profiles at 1.2 T using CA-NOVEL sequence (red circle), without the 90° pulse (black square), and their difference (blue triangle) yields an EPR-like lineshape. (d) Simulated Zeeman DNP field profile. Data were acquired on a sample containing 5 mM trityl-OX063 in glycerol-d₈/D₂O/H₂O (60/30/10 vol ratio). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

In addition, we investigated the performance of RA-NOVEL sequence. The microwave center frequency was applied on-resonance with the trityl’s EPR signal. The length of the locking pulse was varied up to 80 μs (Fig. 4a), which is an order of magnitude longer than can be achieved at X-band due to the high duty cycle of the Q-band TWT amplifier. This permitted us not only to confirm the improvement of RA-NOVEL over CA-NOVEL, but also observe the decay of the enhancement at longer locking pulses—a known effect which is indicative of the electron’s rotating frame relaxation time,T_1ρ;e. Ramping the microwave field strength from 36 to 66 MHz (Δv = 30 MHz) improved the enhancement by a factor of 1.6 (Fig. 4b) compared to CA-NOVEL at 51 MHz, and it continues to grow to ~2.1 with at Δω_1S/2π = 50 MHz (ramp 26 to 76 MHz). Note that we cannot use a larger Δv value because the maximum microwave field strength is limited to ~80 MHz/150 W. We believe the large ramp size is necessary because (1) the trityl radical has a comparable linewidth (~1 mT) and (2) the first 90° excitation pulse does not uniformly excite all the EPR spin packets to the transverse plane.

Fig. 4.

(a) Buildup of the DNP enhancement with respect to the contact time in CA-NOVEL (blue, open circle) and in RA-NOVEL with a 30 MHz ramp (red, solid circle). In both cases, the optimum enhancements were found at a contact time of 30 μs. The efficiency decreases at longer contact times due to the electron T_1ρ. (b) The improved enhancement factor as a function of the ramp size at 30 μs contact time. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

We then studied the FS-ISE sequence at the NOVEL condition at 1.2 T. We note that a very high Q will lead to a non-uniform Rabi field across the frequency range of the sweep. Thus, for this experiment we overcoupled the microwave cavity to lower the Q factor so that the maximum field strength was slightly higher than the ¹H Larmor frequency. In particular, we used a Q ~ 465 and the corresponding maximum field strength was ω_1S/2π = 55 MHz at 150 W microwave power (Fig. 5a). Note the optimal contact time of 2 μs (corresponding to a sweep rate of 45 MHz/μs) shown in Fig. 5b confirms the adiabatic nature of the FS-ISE sequence at the NOVEL condition. The Zeeman field profiles were measured at three different sweep widths, Δ = 0 and Δ = ±90 MHz (Fig. 5c). With a constant microwave frequency (Δ = 0), the field profile is identical to the solid effect data in Fig. 3c. However, with Δ = ±90 MHz, we observe three interesting features in the field profiles. First, we observed the characteristic profiles of the FS-ISE consisting of the ISE contribution in the middle sandwiched by the negative and positive stretched solid effect (S²E) field profile. Second, we found that the sign of the S²E did not change with respect to the direction of the sweep, whereas the sign of the ISE enhancements inverts as we changed the direction of the sweep. These observations are consistent with our previous observations at 95 GHz using a low-Q bucket resonator [46]. Fig. 5d shows that both features were successfully reproduced in numerical simulation. Third, the Δ = +90 MHz sweep in Fig. 5c shows a sinusoidal shape between 1.196 T and 1.198 T suggesting a coupling between the time dependent microwave field and the cavity. Interestingly this behavior is not present when the direction of the field sweep is reversed to Δ = −90 MHz. As illustrated in Fig. S1 in the supporting information we have seen this phenomena in other experiments associated with the adiabatic solid effect [47]. Also illustrated in Fig. S1 is the fact that the experimental features are very reproducible. In particular, we can reverse the vertical and horizontal axis of the Δ = −90 MHz data and superimpose it on the Δ = +90 MHz sweep (Fig. S1b). Note in the figure that the superposition is quantitative except in the interval 1.196 T → 1.198 T. Similarly, the Δ = −90 MHz data from a lower-power but longer-duration experiments (Fig. S1c and S1d) experiments can be treated similarly and quantitively fits the Δ = +90 MHz sweep except for the interval 1.205 T → 1.207 T. Finally, we note that these features were not observed in the 95 GHz experiments, where a low-Q resonator was used. We are currently performing additional nutation experiments to characterize the response of the DNP probe circuit to a time dependent microwave field.

Fig. 5.

(a) In order to perform the FS-ISE sequence, the bandwidth of the cavity was increased by lowering the Q factor (465 vs. 1,500 in Fig. 2a). Nevertheless, the maximum field strength was ~55 MHz which still slightly above the NOVEL condition (~51 MHz). (b) The buildup curve shows maximum efficiency at 2 μs corresponding to sweep rate of 45 MHz/μs, indicative of the adiabatic nature of the FS-ISE sequence when operating at the NOVEL condition. (c) FS-ISE Zeeman DNP field profiles obtained without frequency sweeping (0 MHz, black) and with frequency sweeping up (+90 MHz, red) or down (−90 MHz, blue). (d) Simulations of the FS-ISE Zeeman DNP field profiles. Note the departure from the simulated behavior. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

4. Discussion

Fig. 3a shows that the NOVEL microwave field profile is sharper at higher Zeeman fields. Taken alone the X-band data suggest that NOVEL can be performed at a modest power level and still achieve significant enhancement, but at higher field it appears that this approach will be more challenging. In particular, at Q-band we did not see any enhancement when ω_1S/ω_0I < 0.75, whereas at X-band the enhancement reached 50% of that obtained at optimum condition with the same ω_1S/ω_0I ratio [35,36]. As indicated in the simulation of Fig. 3b this is because the mismatch tolerance is primarily determined by the size of the hyperfine coupling (~1 MHz). Note that 1 MHz bandwidth represent ~7% of the NOVEL matching condition at 0.35 T (15 MHz), but this becomes ~2% at 1.2 T (51 MHz). Hence, this yields an apparent sharpening of the NOVEL matching condition as the magnetic field increases. This could impose a stringent microwave field inhomogeneity requirement for high-field NOVEL experiments that we plan to perform in the future. For instance, the Rabi field in a NOVEL experiment should have <0.3% inhomogeneity across the sample at 9 T/250 GHz for efficient polarization transfer.

Furthermore, the profile is also sharper on the high field side of the NOVEL condition. In the case of diphenyl-nitroxide at 0.35 T/9.7 GHz, the broadening of this tail is very dramatic and is due to the hyperfine coupling to 10 ¹H’s and higher order processes involving one electron and multiple protons [34]. Both perturbation effects are truncated by decreasing the number of ¹H couplings and increasing ω₀, leading to NOVEL field profiles as shown in Fig. 3. We anticipate that at higher field (>9 T), the microwave field profile will become more symmetric with smaller broadening effects from the hyperfine coupling and the proton-proton coupling will be attenuated further.

The Zeeman field profiles in Fig. 3c and d suggest that the NOVEL field profile can be decomposed into the field profile arising from the pulsed SE (only locking pulse) and that from an intrinsic NOVEL profile, which resembles the EPR lineshape. As a result, the observed maximum enhancement is shifted slightly off resonant. In this case, the off resonance is ~4 G and yields ~50% larger enhancement compared to on-resonance irradiation. We note that the pulsed SE field profile does not change with respect to the phase of the locking pulse, whereas when the phase of the locking pulsed is inverted, the phase the intrinsic NOVEL enhancement changes sign and the maximum enhancement is negative and appears at negative off set. Roughly speaking, the field profiles obtained with opposite phases of the locking pulse are point symmetry images of one another.

The enhancement curves in Fig. 4 clearly indicate that RA-NOVEL experiments offer improved enhancements over CA-NOVEL, and when it is possible to ramp the microwave field then RA-NOVEL is the preferred approach. The ramps used here are simple linear shapes and AWG technology will permit exploration of more sophisticated shapes involving phase, amplitude and frequency as variables.

Our initial motivation for performing the FS-ISE sequence was to obtain an enhancement when the microwave irradiation is on resonant with the EPR line. However, the Zeeman field profile also reveals the “stretched SE” (S²E) which is more efficient than the intrinsic ISE reaching a value of ε = 330 at Q-band. Although the effects of frequency modulated CW DNP and the possibility of the S²E were discussed theoretically, most experiments were performed on nitroxide polarizing agents which are much broader than the trityl’s. Therefore, the S²E was severely convoluted with the normal SE and ISE effects—It was not easy to identify S²E. In addition, the S²E was not observed in previous pulsed DNP experiments using photo-excited triplet states [31,32]. The reason for that was probably due to the pressing requirement for very fast transfer in the experimental protocol in those field-sweep. For a photo-excited triplet state, the lifetime of the excited state is short, but we found that polarization can be transferred in the ISE in ~20 μs. Thus, it is possibly short enough for many photo-excited triplet states in high field ISE experiments.

Finally, in Fig. 5 we also documented for the second time the interaction of the time-dependent microwave field with a high-Q ENDOR cavity. This is a topic that deserves further attention since we anticipate that a high-Q system will be required to approach the NOVEL condition in pulsed DNP experiments at high field (>9 T).

5. Conclusions

In summary, we have demonstrated the performance of three different pulsed DNP experiments operating at or near the NOVEL condition at the highest possible magnetic field (1.2 T/33.5 GHz/51 MHz) using a high Q (up to ~1,500) ENDOR resonator. Such a high Q cavity, in addition to a TWT amplifier, enables the NOVEL matching condition to be satisfied at this field. Our result shows that NOVEL condition narrows when compared to X-band. In addition, RA-NOVEL shows a significant improvement over NOVEL if sufficiently high-power microwave sources are available. Otherwise, the stretched solid effect may well offer the optimal enhancements.