Dynamic nuclear polarization

[7] Note that the alignment of electron spins at a given magnetic field and temperature is described by the Boltzmann distribution under thermal equilibrium.

A polarizing agent (PA)—either an endogenous or exogenous paramagnetic system to the sample—is required as part of the DNP experimental setup.

Typically, PAs are stable free radicals that are dissolved in solution or doped in solids; they provide a source of unpaired electrons that can be polarized by microwave radiation near the EPR transitions.

The DNP effect is present in solids and liquids and has been utilized successfully in solid-state and solution-phase NMR experiments.

[3] The first DNP experiments were performed in the early 1950s at low magnetic fields [6][13] 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.

The "dynamic" initially meant to highlight the time-dependent and random interactions in this polarization transfer process.

The DNP phenomenon was theoretically predicted by Albert Overhauser in 1953 [5] and initially drew some criticism from Norman Ramsey, Felix Bloch, and other renowned physicists of the time on the grounds of being "thermodynamically improbable".

The experimental confirmation by Carver and Slichter[16] as well as an apologetic letter from Ramsey both reached Overhauser in the same year.

During DNP a MW irradiation is applied at a frequency ωMW and intensity ω1, resulting in a rotating frame Hamiltonian given by The MW irradiation can excite the electron single quantum transitions ("allowed transitions") when ωMW is close to ωe, resulting in a loss of the electron polarization.

In addition, due to the small state mixing caused by the B term of the hyperfine interaction, it is possible to irradiate on the electron-nucleus zero quantum or double quantum ("forbidden") transitions around ωMW = ωe ± ωn, resulting in polarization transfer between the electrons and the nuclei.

This kind of transition is in general weakly allowed, meaning that the transition moment for the above microwave excitation results from a second-order effect of the electron-nuclear interactions and thus requires stronger microwave power to be significant, and its intensity is decreased by an increase of the external magnetic field B0.

Solid effect exist in most cases but is more easily observed if the linewidth of the EPR spectrum of involved unpaired electrons is smaller than the nuclear Larmor frequency of the corresponding nuclei.

In practice, the correct EPR frequency separation is accomplished through random orientation of paramagnetic species with g-anisotropy.

Therefore, as this linewidth is proportional to external magnetic field B0, the overall DNP efficiency (or the enhancement of nuclear polarization) scales as B0−1.

Usually going to higher field leads to longer nuclear relaxation times and this may partially compensate for the line broadening reduction.

In practice, in a glassy sample, the probability of having two dipolarly coupled electrons separated by the Larmor frequency is very scarce.

[1][19] As in the static case, the MAS-DNP mechanism of cross effect is deeply modified due to the time dependent energy level.

By taking a simple three spin system, it has been demonstrated that the cross-effect mechanism is different in the Static and MAS case.

[18][20] This in turn change dramatically the CE dependence over the static magnetic field which does not scale like B0−1 and makes it much more efficient than the solid effect.

The strong interactions lead to a homogeneously broadened EPR lineshape of the involved paramagnetic species.

The linewidth is optimized for polarization transfer from electrons to nuclei, when it is close to the nuclear Larmor frequency.

The optimization is related to an embedded three-spin (electron-electron-nucleus) process that mutually flips the coupled three spins under the energy conservation (mainly) of the Zeeman interactions.

Some examples are carbonaceous materials such bituminous coal and charcoal (wood or cellulose heated at high temperatures above their decomposition point which leaves a residual solid char).

For small isolated clusters, the free electrons are fixed and give rise to solid-state enhancements (SS).

These electrons give rise to an Overhauser enhancement centered at a microwave offset of ωe – ωH = 0.

Spatial selectivity can finally be obtained using magnetic resonance imaging (MRI) techniques, so that signals from similar parts can be separated based on their location in the sample.

It is important to note that DNP was only performed ex situ as it usually requires low temperature to lower electronic relaxation.