Amplification of Dynamic Nuclear Polarization at 200 GHz by Arbitrary

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Spectroscopy and Photochemistry; General Theory

Amplification of Dynamic Nuclear Polarization at 200 GHz by Arbitrary Pulse Shaping of the Electron Spin Saturation Profile. Ilia Kaminker, and Songi Han J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01413 • Publication Date (Web): 18 May 2018 Downloaded from http://pubs.acs.org on May 18, 2018

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The Journal of Physical Chemistry Letters

Amplification of Dynamic Nuclear Polarization at 200 GHz by Arbitrary Pulse Shaping of the Electron Spin Saturation Profile. Ilia Kaminker1 and Songi Han*,1,2 Department of Chemistry and Biochemistry, University of California Santa Barbara, CA 93106 USA Department of Chemical Engineering, University of California Santa Barbara, CA 93106 USA *

Corresponding Author

ABSTRACT. Dynamic nuclear polarization (DNP) takes center stage in nuclear magnetic resonance (NMR) as a tool to amplify its signal by orders of magnitude through the transfer of polarization from electron to nuclear spins. In contrast to modern NMR and electron paramagnetic resonance (EPR) that extensively rely on pulses for spin manipulation in the time domain, the current mainstream DNP technology exclusively relies on monochromatic continuous wave (CW) irradiation. This study introduces arbitrary phase shaped pulses that constitute a train of coherent chirp pulses in the time domain at 200 GHz (7 Tesla) to dramatically enhance the saturation bandwidth and DNP performance compared to CW DNP, yielding up to 500-fold in NMR signal enhancements. The observed improvement is attributed to

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the recruitment of additional electron spins contributing to DNP via the cross-effect mechanism, as experimentally confirmed by two-frequency pump-probe Electron-Electron Double Resonance (ELDOR).

Recent developments in Dynamic nuclear polarization (DNP) transformed nuclear magnetic resonance (NMR) spectroscopy by inducing signal enhancement by orders of magnitudes, and so enabled chemical, biological and material studies previously deemed impossible.

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In DNP,

NMR signal amplification is achieved by transferring part of the larger polarization of the electron spins to nuclear spins. With the notable exception of a recently introduced frequencyagile gyrotron by the Barnes group12, and several reports that utilized frequency modulation (FM)

13,14

the current state of the art in DNP at NMR-relevant fields for electron spin

manipulation virtually exclusively relies on monochromatic continuous wave (CW) irradiation. This applies to microwave sources used for high-field DNP at or above 7 Tesla today, whether under Magic Angle Spinning (MAS), dissolution or static DNP conditions. This is in contrast to contemporary NMR and Electron Paramagnetic Resonance (EPR) that rely on pulsed irradiation to achieve the desired spin manipulations that permit multi-dimensional correlation experiments – the hallmark of modern magnetic resonance.15 To date, pulsed DNP experiments were only demonstrated on static (non-spinning) samples and at low (by NMR standards) magnetic fields,


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where high power > 1 kWatt amplifiers and suitable hardware are available through existing high power, pulsed, EPR instruments.15–21 At higher magnetic fields and when using nitroxide radicals as the DNP-polarizing agent, improvements over monochromatic CW DNP was reported with a frequency-modulated DNP (FM-DNP) at magnetic fields of 3.3 T

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and 6.7 T

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on static

samples. The hardware capabilities introduced in this work, however, significantly enhance the current state of the art in DNP, and extends sinusoidal frequency modulation (FM)13,14 to arbitrary waveform generated (AWG) shaped pulses at 200 GHz. AWG allows for pulse bandwidth exceeding 2 GHz and overcomes other limitations associated with the FM hardware, such as the limited rate of frequency modulation. Combined with the wide tunability (195 ± 5 GHz) of a solid-state source, AWG will enable DNP experiments with transition metals (V(iv), Fe(III)) whose g-anisotropy spans several GHz at high magnetic fields and facilitate time-domain DNP experiments. This study debuts AWG-enhanced DNP with the example of chirp-DNP, where a coherent chirp pulse train achieved manipulation of spins over bandwidths exceeding 0.5 GHz that resulted in a 4-fold improvement in DNP enhancements compared to CW irradiation at 200 GHz in a static sample. More sophisticated pulse shaping can be implemented in the future, depending on the application that may rely on static DNP NMR of transition metal and/or quadrupolar nuclei containing samples or rotor synchronized pulsed MAS DNP. While CW-DNP under static conditions can proceeds via distinct DNP mechanisms of solid effect (SE), cross effect (CE)2,22 and thermal mixing (TM),23,24 chirp-DNP mainly proceeds via the CE DNP mechanism, as we will demonstrate. The CE requires two dipolar-coupled electron spins with difference in their resonance frequencies equaling the Larmor frequency of the coupled nucleus, i.e. − = known as the CE condition. The extent of the so


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transferred nuclear polarization per e1; e2 electron pair fulfilling the cross-effect conditions scales with: 25,26

∝

− 1 − ∙

(1)

Here, is the electron polarization at frequency . This implies that the nuclear polarization per e1;e2 is maximal when the difference in electron spin polarization between e1;e2 is maximal, such as when one of the electrons is fully saturated, or better inverted, and the other fully polarized. At 200 GHz and 4 K the electron spin polarization at thermal equilibrium is = 0.85, and as such the denominator of Eq. (1) cannot be disregarded. For inhomogeneously broadened EPR spectra the integral nuclear polarization, , scales proportionally to the integral over the entire electron polarization across the EPR spectrum, weighted by the simultaneous probability to find one electron at resonance frequency and another one at which,

for the two electron spins fulfilling the cross-effect condition becomes ± .25 For clarity, we term these integral contribution of the electrons to the nuclear polarization an electron

polarization potential under CE, , yielding Eq. (2), similar to what has been derived in the

literature25,27 :

= −

+ +

− − 1 − −

− + 1 − +

(2)

Here, is the EPR spectral intensity and the steady state electron polarization at

frequency , the Larmour frequency of the nucleus participating in the CE, and the integral is

taken over the entire EPR spectrum. Typical absorption EPR spectrum of a nitroxide radical is shown in Figure 1a. The schematic electron polarization profile achieved under CW irradiation is


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illustrated in Figure 1b. When electron spins are at equilibrium ≡ , and if the electron

spins are completely saturated = 0. When e1 electrons are fully saturated on-resonance,

the e1;e2 CE pair maximally contributes to DNP via the CE mechanism, and approaches . In an ideal case, the electron spin polarization potential, , is maximized by adjusting the

saturation of the EPR spectrum, such that the saturation profile width equals with sharp edges, as schematically illustrated in Figure 1c. In this case, the polarization differential is maximized for all CE-fulfilling electron pairs over the whole bandwidth (note in this case the polarization differential is maximized for both e1;e2 and e’1;e’2 electron pairs). In real experiments, the EPR lineshape has to be taken into account, and the idealized profile illustrated in Figure 1c replaced with a “cut out” from the EPR spectrum, such that the number of electron spins constructively contributing to DNP is maximal, as expressed in Eq. (2).


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Figure 1. Simulated frequency-swept EPR spectrum of a nitroxide radical at 6.9 T (a); schematic representation of a normalized electron polarization profile under CW monochromatic irradiation (b); idealized electron polarization profile that maximizes CE DNP (c); pulse sequences for CWDNP (d) and chirp-DNP (e) experiments; comparison of experimentally observed NMR signal enhancements for CW DNP and chirp-DNP experiments (f). Insert in (a) shows the structures of the nitroxide radicals used in this study.

We set out to demonstrate that (i) the electron polarization potential can be deliberately

and experimentally maximized using a chirp-pulse train with a well-defined pulse bandwidth (chirp-DNP) and (ii) that this results in enhanced DNP performance compared to CW irradiation.


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All experiments were performed with a homebuilt 7 T DNP / EPR spectrometer28 equipped with AWG capabilities,29 with the details of the upgraded hardware setup required to perform chirpDNP and chirp ELDOR experiments presented in the SI. Each DNP experiment is preceded by a saturation train at the 1H Larmor frequency to ensure zero residual 1H magnetization at the beginning of the pulse sequence. The (DNP enhanced) 1H NMR signal is detected using a solid echo pulse sequence. In chirp-DNP, monochromatic CW irradiation at ~200 GHz (Figure 1d) is substituted with a train of chirp pulses centered around the "# carrier frequency (Figure 1e). The chirp pulses are repeated continuously for the total duration required to build up the nuclear polarization (tbuildup) via the CE DNP process, typically over the course of tens of seconds to minutes. Comparison of the NMR enhancements for tbuildup = 60 s between CW DNP and chirp-DNP, using microwave power up to Pmw~0.15 Watt at the source output, and under a range of experimental conditions, is presented on Figure 1f. Notably, under all experimental conditions and samples tested, chirp-DNP clearly outperforms CW DNP. Differences in the CW DNP performance across different samples are consistent with the previously published trends: for a given radical, the DNP efficiency increases with increasing radical concentration (up to a threshold), and with decreasing temperature. For a given spin concentration, the biradical (TOTAPOL / AMUPOL) outperforms the monoradical (4AT), presumably given the increased CE probability. With the exception of 10mM AMUPoL at 4K, the improvement factor of chirpDNP over CW-DNP lied between 4 < εchirp-DNP / εCW DNP < 5, while the improvement in NMR enhancement with chirp-DNP did not require longer buildup times, tbuildup, compared to CW DNP (Figure S1).


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Figure 2. Pulse sequences for pulsed ELDOR (a) and chirp-ELDOR (b) experiments. Time dependence of ωmw during the pump pulse / chirp pulse-train is depicted with a dashed line in (a) and (b). Experimental ELDOR and chirp ELDOR spectra measured on 2.5 mM 4AT (c) and 10mM AMUPOL (d) at 4 K. Experimental parameters (c): tpump =100 ms; tchirp = 100 µs and Δ%&'() = 300 MHz; echo detection with tp-τ-tp- τ-echo pulse sequence; tp = 850 ms; τ = 600 ns; repetition time 500 ms; 2-shots per point / 2 step phase cycle; ω1 was ~0.5 MHz; T = 4 K. Experimental parameters (d): tpump =100ms; tchirp = 300 µs and Δ%&'() = 300 MHz; echo detection with tp-τ-tp- τ-echo pulse sequence; tp = 750ms; τ = 600ns; repetition time 500 ms; 2shots per point / 2 step phase cycle; ω1 was ~0.5 MHz; T = 4 K. Assignment of the resolved peaks in ELDOR spectra is available in the SI.

Next, we investigated whether the improved performance of chirp-DNP is due to broader saturation of the EPR line that maximizes . To address this question, we probed the EPR


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saturation profile by pulsed ELDOR—a two frequency pump-probe EPR experiment where changes in the EPR echo intensity at a probe frequency, *+ , is monitored as function of the

pump pulse at frequency ),") of duration tpump (Figure 2a).26,30 To probe conditions during chirp-DNP, a train of chirp pulses is used for the pump pulse (Figure2b) in an experiment we refer to as chirp ELDOR. A comparison of the chirp ELDOR spectrum (with = 300 MHz; k = 1 MHz / µs) and a regular ELDOR spectrum relying on a monochromatic pump pulse is presented on Figure 2c for the monoradical 4AT at dilute 2.5 mM concentration, and on Figure 2d for the biradical AMUPoL at 10 mM (20 mM electron) spin concentration, both prepared in “DNP juice” solvent (60% d8-glycerol; 30% D2O; 10% H2O) and at 4K. Additional pulsed ELDOR (Figure S3) and chirp ELDOR (Figure S4) spectra for these two samples with other *+ values can be found in the SI . For the spectra on Figure 2c, chirp ELDOR (red and neon green traces) confirms that a complete saturation of the EPR spectrum over the full Δ%&'() = 300 MHz bandwidth (indicated by black double-sided arrows) is achieved. This exceeds the electron spin ω1 of 0.4 – 0.5 MHz

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by a factor > 600, and is in stark contrast to the narrow ω1H that diminishes .

Remarkably, this precisely corresponds to the experimental observation, where maximum DNP enhancement was observed at Δ%&'() ≈ . ≈300 MHz (in this study . = 294.026 MHz) for all samples and experimental conditions other than 10 mM AMUPOL at 4 K (Figure 3b). The 10mM AMUPOL sample at 4K is an outlier to the presented trend but is of particular interest as its condition is considered “close to optimal” for achieving high CW DNP performance. Thus, a factor of ~2 in additional improvements gained with chirp- over CW DNP for this sample and experimental condition is of high significance. A signature characteristic of this sample is a dominant eSD effect (Figure 2d). In CW DNP, efficient eSD effects increase by recruiting off-resonance electron spins, and thus achieving high DNP performance even

with monochromatic irradiation. In contrast, under chirp-DNP eSD broadens the electron spin polarization profile beyond the desired bandwidth (effect known as “oversaturation”34), leading


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to reduced and consequently suboptimal DNP performance. Experimentally, the extent of

electron spin depolarization can be controlled by lowering the microwave power (see for example SI of reference 35) or by adjusting ∆ωchirp that tunes . It follows that there must be

different combinations for ∆ωchirp and Pmw that lead to maximal DNP performance. Indeed, we confirm that a maximum DNP enhancement of ε ≈ 500 could be observed either by setting ∆ωchirp = 100 MHz (< ∆ωn) and Pmw = 45 milliWatt, or by setting ∆ωchirp = 200 MHz (< ∆ωn) and Pmw = 62 (Figure S7), with ε diminishing with either increasing ∆ωchirp or Pmw, unless both values are adjusted together. Importantly chirp-DNP dramatically lowers the requirement for high microwave power, where maximum DNP enhancement could be achieved with Pmw = 45 milliWatt compared to Pmw = 90 milliWatt for CW DNP. The dependence of the DNP enhancement on either ∆ωchirp or Pmw is rationalized by the modulation in from a combined

effect of chirp-pulse train excitation and eSD. We demonstrated in this study that substitution of monochromatic CW irradiation with a train of coherent, broad-band, chirp pulses results in consistently enhanced DNP performance at 7 Tesla (300 MHZ 1H). AWG DNP represent a leap forward from CW or FM-driven DNP, given the control, flexibility and performance (e.g. bandwidth, speed) granted with shaped microwave pulses. Even with the simplest chirp pulse train DNP, there are significant advantages over FMDNP, from the increased flexibility in the control over the experimental parameters ∆ωchirp and k granted by the AWG hardware. Essentially, we designed chirp-DNP experiments that proceeds via a directly microwave-driven CE mechanism, where electron spins with multiple resonances spanning the ∆ωchirp bandwidth constructively contribute to DNP. This shifts the burden of improving the DNP from designing DNP radicals and optimizing sample conditions towards microwave pulse sequence design, potentially broadening the range of samples and experimental


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conditions amenable for DNP. Importantly, the scope of AWG DNP goes well beyond the use of chirp pulses. In the future, more advanced shaped microwave pulses can be implemented to tailor to the DNP application of interest, from DNP relying on transition metals with several GHz broad EPR lines to new, mixed, radical/metal and/or multi-radical probes that display multiple EPR frequencies.

ASSOCIATED CONTENT Supporting Information. Sample preparation details, EPR and DNP experimental procedures, description of the AWG hardware, additional ELDOR spectra and DNP profiles. AUTHOR INFORMATION The authors declare no competing financial interests.

ACKNOWLEDGMENT We thank Blake Wilson and Alisa Leavesley for acquiring the 240GHz EPR spectra in the laboratory of Prof. Mark Sherwin. Ryan Barnes is acknowledged for his help with the AWG implementation at 200 GHz. Boris Epel is acknowledged for implementation of the upgraded AWG user interface and constant support of the SpecMan4EPR software. This work is supported by the Binational Science Foundation (Grant #2014149), National Institute of Health (R21EB022731) and the National Science Foundation (CHE-1505038). IK acknowledges support of the long-term postdoctoral fellowship by the Human Frontier Science Foundation. REFERENCES


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Amplification of Dynamic Nuclear Polarization at 200 GHz by Arbitrary

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