Dynamic nuclear polarisation

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Dynamic nuclear polarization (DNP) results from transferring spin polarization from electrons to nuclei, thereby aligning the nuclear spins to the extent that electron spins are aligned. Note that the alignment of electron spins at a given magnetic field and temperature is described by the Boltzmann distribution under the thermal equilibrium. It is also possible that those electrons are aligned to a higher degree of order by other preparations of electron spin order such as chemical reactions (leading to Chemical-Induced DNP, CIDNP), optical pumping and spin injection.

When electron spin polarization deviates from its thermal equilibrium value, polarization transfers between electrons and nuclei can occur spontaneously through electron-nuclear cross relaxation and/or spin-state mixing among electrons and nuclei. For example, the polarization transfer is spontaneous after a 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. In particular, mechanisms for the microwave-driven polarizing processes are categorized into the Overhauser effect, the solid effect, the cross effect and thermal mixing.

Contents 1 The Overhauser Effect 2 The solid effect 3 The cross effect 4 Thermal mixing

[edit] The Overhauser Effect

DNP was first realized using the concept of the Overhauser effect, which is the perturbation of nuclear spin level populations observed in metals and free radicals when electron spin transitions are saturated by the microwave irradiation. This effect relies on stochastic interactions between an electron and a nucleus. 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 and initially drew some criticism from Normann Ramsey, Felix Bloch and other renowned physicists of the time on the grounds of being "thermodynamically improbable". The experimental confirmation by Carver and Slichter as well as an apologetic letter from Ramsey both reached Overhauser in the same year.

The so-called electron-nucleus cross-relaxation, which is responsible for the DNP phenomenon is caused by rotational and translational modulation of the electron-nucleus hyperfine coupling. The theory of this process is based essentially on the second-order time-dependent perturbation theory solution of the von Neumann equation for the spin density matrix.

While the Overhauser effect relies on time-dependent electron-nuclear interactions, the remaining polarizing mechanisms rely on time-independent electron-nuclear and electron-electron interactions.

[edit] The solid effect

The solid effect occurs when the electron-nucleus mutual flip transition in an electron-nucleus two-spin system is excited by microwave irradiation. This polarizing mechanism is optimal when the exciting microwave frequency shifts up or down by the nuclear Larmor frequency from the electron Larmor frequency in the discussed two-spin system. The direction of frequency shifts corresponds to the sign of DNP enhancements. Therefore, to prevent the canceling between positive and negative DNP enhancements, it requires that the linewidth of the EPR spectrum of involved unpaired electrons is smaller than the nuclear Larmor frequency. Note 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. As a result, the DNP enhancement from the solid effect scales as B₀^-2.

[edit] The cross effect

The cross effect requires two unpaired electrons as the source of high polarization. While the underlying physics is still of second order nature with respect to the electron-electron and electron-nuclear interactions, the polarizing efficiency can be improved with the optimized EPR frequency separation of the two electrons (close to the nuclear Larmor frequency). As a result, the strength of microwave irradiation is less demanded than that in the solid effect. In practice, the correct EPR frequency separation is accomplished through random orientation of paramagnetic species with g-anisotropy, depending on the probability of desired frequency separation from an inhomogeneously broadened EPR lineshape whose linewidth is broader than the nuclear Larmor frequency. Therefore, as this linewidth is proportional to external magnetic field B₀, the overall DNP efficiency (or the enhancement of nuclear polarization) scales as B₀^-2.

[edit] Thermal mixing

Thermal mixing is an energy exchange phenomena between the electron spin ensemble and the nuclear spin, which can be thought of as using multiple electron spins to provide hyper nuclear polarization. Note that the electron spin ensemble acts as a whole because of stronger inter-electron interactions. 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. Due to the inhomogeneous component of the associated EPR lineshape, the DNP enhancement by this mechanism also scales as B₀^-2.