Editing Dynamic nuclear polarization (section)

{{short description|Spin polarization of atomic nuclei in response to electron spin realignment in a magnetic field}}
{{Anchor|unpaired2016-01-27}}

'''Dynamic nuclear polarization (DNP)''' is one of several [[Hyperpolarization (physics)|hyperpolarization]] methods developed to enhance the sensitivity of [[nuclear magnetic resonance (NMR) spectroscopy]]. While an essential analytical tool with applications in several fields, NMR’s low sensitivity poses major limitations to analyzing samples with low concentrations and limited masses and volumes.<ref name=":0">Abhyankar, N., & Szalai, V. (2021). Challenges and advances in the application of dynamic nuclear polarization to liquid-state NMR spectroscopy. ''The Journal of Physical Chemistry B'', ''125''(20), 5171–5190. <nowiki>https://doi.org/10.1021/acs.jpcb.0c10937</nowiki> </ref> This low sensitivity is due to the relatively low nuclear [[gyromagnetic ratio]]s (''γ<sub>n</sub>'') of NMR active nuclei (<sup>1</sup>H, <sup>13</sup>C, <sup>15</sup>N, etc.) as well as the low [[natural abundance]] of certain nuclei.<ref name=":1">Plainchont, B., Berruyer, P., Dumez, J.-N., Jannin, S., & Giraudeau, P. (2018). Dynamic nuclear polarization opens new perspectives for NMR spectroscopy in Analytical Chemistry. ''Analytical Chemistry'', ''90''(6), 3639–3650. <nowiki>https://doi.org/10.1021/acs.analchem.7b05236</nowiki>  </ref><ref name=":2">ur-Rahman, A., Choudhary, M. I., & tul-Wahab, A. (2016). Chapter 3 - Sensitivity Enhancement. In ''Solving Problems with NMR Spectroscopy'' (2nd ed., pp. 99–132). Academic Press. Retrieved from <nowiki>https://doi.org/10.1016/B978-0-12-411589-7.00003-6</nowiki></ref><ref name=":3">Tanaka, S., & Webb, G. A. (2022). Chapter One - Recent advances in dynamic nuclear polarization-enhanced NMR spectroscopy for organic polymers. In ''Annual Reports on NMR Spectroscopy'' (Vol. 105, pp. 1–46). Academic Press. Retrieved from <nowiki>https://doi.org/10.1016/bs.arnmr.2021.06.002</nowiki>.  </ref> Several techniques have been developed to address this limitation, including hardware adjustments to NMR instruments and equipment (e.g., NMR tubes), improvements to data processing methods, and polarization transfer methods to NMR active nuclei in a sample—under which DNP falls.<ref name=":2" />

Overhauser et al.<ref name="Overhauser" /> were the first to hypothesize and describe the DNP effect in 1953; later that year, Carver and Slichter <ref name=":4" /> observed the effect in experiments using metallic lithium.<ref name=":1" /><ref name=":3" /> DNP involves transferring the polarization of [[Spin (physics)|electron spins]] to neighboring nuclear spins using microwave irradiation at or near [[Electron paramagnetic resonance|electron paramagnetic resonance (EPR)]] transitions. It is based on two fundamental concepts: first, that the electronic gyromagnetic moment (''γ<sub>e</sub>'') is several orders of magnitude larger than ''γ<sub>n</sub>'' (about 658 times more; see below), and second, that the relaxation of electron spins is much faster than nuclear spins.<ref name=":5">Engel, T., & Angerhofer, A. (2019). Chapter 17 - Nuclear Magnetic Resonance Spectroscopy In ''Physical Chemistry: Quantum Chemistry and Spectroscopy'' (4th ed., pp. 467–509). Pearson Education, Inc.</ref>

<math>{P_e \over P_n} \approx {\gamma_e \over \gamma_n} \approx {{1.760859644 \times 10^{11} s^{-1}} \over {2.675221900 \times 10^8 s^{-1}}} \approx 658 </math>,

where

<math>P = \tanh({{\gamma \hbar B_0} \over {2k_BT}}) \approx {{\gamma \hbar B_0} \over {2k_BT}}</math>

is the [[Boltzmann distribution|Boltzmann]] equilibrium spin polarization.<ref name=":5" /> Note that the alignment of electron spins at a given [[magnetic field]] and temperature is described by the [[Boltzmann distribution]] under [[thermal equilibrium]].<ref>{{cite book | last=Goldman | first=Maurice | title=Spin Temperature and Nuclear Magnetic Resonance in Solids | publisher=Oxford University Press | year=1970 | isbn=978-0-19-851251-6}}</ref><ref>
{{cite journal
|author = A. Abragam
|author2 = M. Goldman
|title = Principles of Dynamic Nuclear Polarization
|journal = [[Reports on Progress in Physics]]
|volume = 41 |pages = 395–467
|year = 1976
|doi = 10.1088/0034-4885/41/3/002
|bibcode = 1978RPPh...41..395A
|issue = 3 |s2cid = 250855406
}}</ref><ref>
{{cite journal
|author1=J. Puebla |author2=E.A. Chekhovich |author3=M. Hopkinson |author4=P. Senellart |author5=A. Lemaitre |author6=M.S. Skolnick |author7=A.I. Tartakovskii |title = Dynamic nuclear polarization in InGaAs/GaAs and GaAs/AlGaAs quantum dots under non-resonant ultra-low power optical excitation
|journal = [[Phys. Rev. B]]
|volume = 88 |pages = 9
|year = 2013
|doi = 10.1103/PhysRevB.88.045306
|bibcode =  2013PhRvB..88d5306P|issue = 4 |arxiv = 1306.0469 |s2cid=76658845 }}</ref> A larger gyromagnetic moment corresponds to a larger Boltzmann distribution of populations in spin states; through DNP, the larger population distribution in the electronic spin reservoir is transferred to the neighboring nuclear spin reservoir, leading to stronger NMR signal intensities. The larger γ and faster relaxation of electron spins also help shorten T<sub>1</sub> relaxation times of nearby nuclei, corresponding to stronger signal intensities.<ref name=":2" />

Under ideal conditions (full saturation of electron spins and dipolar coupling without leakage to nuclear spins), the NMR signal enhancement for protons can at most be 659. This corresponds to a time-saving factor of 434,000 for a solution-phase NMR experiment.<ref name=":5" /> In general, the DNP enhancement parameter η is defined as:

<math>\eta = {{I - I_0} \over I_0}</math>

where I is the signal intensity of the nuclear spins when the electron spins are saturated and I<sub>0</sub> is the signal intensity of the nuclear spins when the electron spins are in equilibrium.<ref name=":5" />
[[File:DNP Polarizing Agents.png|thumb|500x500px|Common polarizing agents (PAs) used in DNP experiments.<ref name=":2" /><ref name=":3" />]]
DNP methods typically fall under one of two categories: continuous wave DNP (CW-DNP) and pulsed DNP. As their names suggest, these methods differ in whether the sample is continuously irradiated or pulsed with microwaves.<ref name=":2" /> When electron spin polarization deviates from its thermal equilibrium value, polarization transfers between electrons and nuclei can occur spontaneously through electron-nuclear cross relaxation or spin-state mixing among electrons and nuclei. For example, polarization transfer is spontaneous after a [[homolysis (chemistry)|homolysis]] [[chemical reaction]]. On the other hand, when the electron spin system is in a thermal equilibrium, the polarization transfer requires continuous [[microwave]] irradiation at a frequency close to the corresponding EPR frequency. It is also possible that electrons are aligned to a higher degree of order by other preparations of electron spin order such as chemical reactions (known as chemical-induced DNP or [[CIDNP]]), [[optical pumping]], and spin injection. A polarizing agent (PA)—either an endogenous or exogenous [[Paramagnetism|paramagnetic]] system to the sample—is required as part of the DNP experimental setup. Typically, PAs are stable free [[Radical (chemistry)|radicals]] that are dissolved in solution or doped in solids; they provide a source of [[unpaired electron]]s that can be polarized by microwave radiation near the EPR transitions.<ref name=":1" /> DNP can also be induced using unpaired electrons produced by [[radiation damage]] in solids.<ref>{{cite journal|last1=Solem|first1=J. C.|last2=Rebka Jr.|first2=G. A.|year=1968|title=EPR of atoms and radicals in radiation-damaged H<sub>2</sub> and HD|journal=Physical Review Letters|volume=21|issue=1|pages=19|bibcode = 1968PhRvL..21...19S |doi = 10.1103/PhysRevLett.21.19 }}</ref><ref>{{cite journal|last=Solem|first=J. C.|year=1974|title=Dynamic polarization of protons and deuterons in solid deuterium hydride|journal=Nuclear Instruments and Methods|volume=117|issue=2|pages=477–485|bibcode = 1974NucIM.117..477S |doi = 10.1016/0029-554X(74)90294-8 }}</ref> Some common PAs are shown.

Described below are the four different mechanisms by which the DNP effect operates: the [[Nuclear Overhauser effect|Overhauser effect (OE)]], the solid effect (SE), the cross effect (CE), and thermal mixing (TM). The DNP effect is present in solids and liquids and has been utilized successfully in solid-state and solution-phase NMR experiments.<ref name=":0" /><ref name=":1" /><ref name=":2" /> For solution-phase NMR experiments, only the OE mechanism is relevant, whereas for solid-state NMR any of the four mechanisms can be employed depending on the specific experimental conditions utilized.<ref name=":2" />

The first DNP experiments were performed in the early 1950s at low magnetic fields <ref name=":4">
{{cite journal
|author = T.R. Carver
|author2 = C.P. Slichter
|title = Experimental Verification of the Overhauser Nuclear Polarization Effect
|journal = [[Physical Review]]
|volume = 102 |pages = 975–980
|year = 1956
|doi = 10.1103/PhysRev.102.975
|bibcode = 1956PhRv..102..975C
|issue = 4
}}</ref><ref name=":6" /> but until recently the technique was of limited applicability for high-frequency, high-field NMR spectroscopy because of the lack of microwave (or terahertz) sources operating at the appropriate frequency. Today, such sources are available as turn-key instruments, making DNP a valuable and indispensable method especially in the field of structure determination by high-resolution solid-state NMR spectroscopy.<ref name=":6">
{{cite journal
|author = T. Maly
|author2 = G.T. Debelouchina
|author3 = V.S. Bajaj
|author4 = K.-N. Hu
|author5 = C.G. Joo
|author6 = M.L. Mak-Jurkauskas
|author7 = J.R. Sirigiri
|author8 = P.C.A. van der Wel
|author9 = J. Herzfeld
|author10 = R.J. Temkin
|author11 = R.G. Griffin
|title = Dynamic Nuclear Polarization at High Magnetic Fields
|journal = [[The Journal of Chemical Physics]]
|volume = 128 |pages = 052211–19
|year = 2008
|doi = 10.1063/1.2833582
|bibcode = 2008JChPh.128e2211M
|issue = 5
 |pmid=18266416
 |pmc=2770872}}</ref><ref>
{{cite journal
|author1=A.B. Barnes |author2=G. De Paëpe |author3=P.C.A. van der Wel |author4=K.-N. Hu |author5=C.G. Joo |author6=V.S. Bajaj |author7=M.L. Mak-Jurkauskas |author8=J.R. Sirigiri |author9=J. Herzfeld |author10=R.J. Temkin |author11=R.G. Griffin |title = High-Field Dynamic Nuclear Polarization for Solid and Solution Biological NMR
|journal = Applied Magnetic Resonance
|volume = 34
|issue = 3–4 |pages = 237–263
|year = 2008
|pmid = 19194532
|pmc = 2634864
|doi = 10.1007/s00723-008-0129-1
}}</ref><ref>
{{cite journal
|author = Akbey, U.
|author2 = Linden, A. H.
|author3 = Oschkinat, H.
|name-list-style = amp
|issn = 0937-9347
|journal = Appl. Magn. Reson.
|date=May 2012
|title = High-Temperature Dynamic Nuclear Polarization Enhanced Magic-Angle-Spinning NMR
|volume = 43
|issue = 1–2
|pages = 81–90|doi = 10.1007/s00723-012-0357-2
|s2cid = 254087348
|url = https://zenodo.org/record/3412094
}}
</ref>