Category Archives: Theory

Factors Affecting DNP NMR in Polycrystalline Diamond Samples

Casabianca, L. B.; Shames, A. I.; Panich, A. M.; Shenderova, O.; Frydman, L. The Journal of Physical Chemistry C 2011, 115, 19041.

http://dx.doi.org/10.1021/jp206167j

This work examines several polycrystalline diamond samples for their potential as polarizing agents for dynamic nuclear polarization (DNP) in NMR. Diamond samples of various origin and particle sizes ranging from a few nanometers to micrometers were examined by EPR, solid-state NMR and DNP techniques. A correlation was found between the size of the diamond particles and the electron spin-lattice relaxation time, the 13C nuclear spin-lattice relaxation times in room temperature magic-angle-spinning experiments, and the ability of the diamond carbons to be hyperpolarized by irradiating unpaired electrons of inherent defects by microwaves at cryogenic temperatures. As the size of the diamond particles approaches that of bulk diamond, both electron and nuclear relaxation times become longer. NMR signal enhancement through DNP was found to be very efficient only for these larger size diamond samples. The reasons and implications of these results are briefly discussed, in the light of these EPR, DNP, and NMR observations.

Tensors and rotations in NMR

This article does not cover DNP. However, for those of us who still like to write their own simulation programs it is a very helpful article.

Mueller, L. J. Concepts in Magnetic Resonance Part A 2011, 38A, 221.

http://dx.doi.org/10.1002/cmr.a.20224

The transformation of second-rank Cartesian tensors under rotation plays a fundamental role in the theoretical description of nuclear magnetic resonance experiments, providing the framework for describing anisotropic phenomena such as single crystal rotation patterns, tensor powder patterns, sideband intensities under magic-angle sample spinning, and as input for relaxation theory. Here, two equivalent procedures for effecting this transformation—direct rotation in Cartesian space and the decomposition of the Cartesian tensor into irreducible spherical tensors that rotate in subgroups of rank 0, 1, and 2—are reviewed. In a departure from the standard formulation, the explicit use of the spherical tensor basis for the decomposition of a spatial Cartesian tensor is introduced, helping to delineate the rotational properties of the basis states from those of the matrix elements. The result is a uniform approach to the rotation of a physical system and the corresponding transformation of the spatial components of the NMR Hamiltonian, expressed as either Cartesian or spherical tensors. This clears up an apparent inconsistency in the NMR literature, where the rotation of a spatial tensor in spherical tensor form has typically been partnered with the inverse rotation in Cartesian form to produce equivalent transformations. © 2011 Wiley Periodicals, Inc. Concepts Magn Reson Part A 38: 221–235, 2011.

Tensors and rotations in NMR

This article does not cover DNP. However, for those of us who still like to write their own simulation programs it is a very helpful article.

Mueller, L. J. Concepts in Magnetic Resonance Part A 2011, 38A, 221.

http://dx.doi.org/10.1002/cmr.a.20224

The transformation of second-rank Cartesian tensors under rotation plays a fundamental role in the theoretical description of nuclear magnetic resonance experiments, providing the framework for describing anisotropic phenomena such as single crystal rotation patterns, tensor powder patterns, sideband intensities under magic-angle sample spinning, and as input for relaxation theory. Here, two equivalent procedures for effecting this transformation—direct rotation in Cartesian space and the decomposition of the Cartesian tensor into irreducible spherical tensors that rotate in subgroups of rank 0, 1, and 2—are reviewed. In a departure from the standard formulation, the explicit use of the spherical tensor basis for the decomposition of a spatial Cartesian tensor is introduced, helping to delineate the rotational properties of the basis states from those of the matrix elements. The result is a uniform approach to the rotation of a physical system and the corresponding transformation of the spatial components of the NMR Hamiltonian, expressed as either Cartesian or spherical tensors. This clears up an apparent inconsistency in the NMR literature, where the rotation of a spatial tensor in spherical tensor form has typically been partnered with the inverse rotation in Cartesian form to produce equivalent transformations. © 2011 Wiley Periodicals, Inc. Concepts Magn Reson Part A 38: 221–235, 2011.

Dynamic Nuclear Polarization in NMR

Chandrakumar, N. Journal of the Indian Institure of Science 2010, 90, 133.

http://journal.library.iisc.ernet.in/vol201001/Chandrakumar.pdf

Dynamic nuclear polarization was first predicted — and, shortly thereafter, established experimentally — in 1953, the first demonstration being on Lithium metal. The basic approach involves the saturation of the ESR of a paramagnetic species in the system, while the NMR is observed. Initial applications of DNP involved low and moderate field studies that focused especially on investigations of molecular hydrodynamics. Applications to MRI provided a subsequent fillip to the technique. In the meanwhile, the closely related nuclear Overhauser effect (NOE) — which involves saturation, as well as observation of different NMR signals — had become an essential technique for the structure elucidation of both small molecules, as well as biomolecules. Most recently, DNP is witnessing rejuvenation, with high field applications to sensitivity enhancement in NMR. We present in the following an overview of Dynamic nuclear polarization (DNP). The elementary general theory of the phenomenon is discussed. Four different DNP mechanisms that are currently recognized are briefly introduced and different modes of the experiment — involving either cw ESR irradiation, or pulsed ESR excitation — are pointed out. A brief run down of various possible implementations is presented, including our own early work at moderate fields in cw mode, as well as hardware configurations and requirements for high field DNP. Different current implementations of DNP experiments are summarized, including solid state, as well as in situ and ex situ dissolution DNP variants. Typical results of DNP enhanced high resolution NMR are then briefly discussed, including the results of our own early work on differential 19F enhancements at moderate fields. Design of free radicals that satisfy the requirements to establish an efficient cross effect DNP is discussed. Recent experiments that have succeeded in detecting an intermediate in the photocycle of bacteriorhodopsin are alluded to. Finally, the implementation of ultrafast multi-dimensional NMR techniques under DNP conditions is briefly discussed, as an approach to further exploitation of the prospects that are on offer.

Dynamic Nuclear Polarization in NMR

Chandrakumar, N. Journal of the Indian Institure of Science 2010, 90, 133.

http://journal.library.iisc.ernet.in/vol201001/Chandrakumar.pdf

Dynamic nuclear polarization was first predicted — and, shortly thereafter, established experimentally — in 1953, the first demonstration being on Lithium metal. The basic approach involves the saturation of the ESR of a paramagnetic species in the system, while the NMR is observed. Initial applications of DNP involved low and moderate field studies that focused especially on investigations of molecular hydrodynamics. Applications to MRI provided a subsequent fillip to the technique. In the meanwhile, the closely related nuclear Overhauser effect (NOE) — which involves saturation, as well as observation of different NMR signals — had become an essential technique for the structure elucidation of both small molecules, as well as biomolecules. Most recently, DNP is witnessing rejuvenation, with high field applications to sensitivity enhancement in NMR. We present in the following an overview of Dynamic nuclear polarization (DNP). The elementary general theory of the phenomenon is discussed. Four different DNP mechanisms that are currently recognized are briefly introduced and different modes of the experiment — involving either cw ESR irradiation, or pulsed ESR excitation — are pointed out. A brief run down of various possible implementations is presented, including our own early work at moderate fields in cw mode, as well as hardware configurations and requirements for high field DNP. Different current implementations of DNP experiments are summarized, including solid state, as well as in situ and ex situ dissolution DNP variants. Typical results of DNP enhanced high resolution NMR are then briefly discussed, including the results of our own early work on differential 19F enhancements at moderate fields. Design of free radicals that satisfy the requirements to establish an efficient cross effect DNP is discussed. Recent experiments that have succeeded in detecting an intermediate in the photocycle of bacteriorhodopsin are alluded to. Finally, the implementation of ultrafast multi-dimensional NMR techniques under DNP conditions is briefly discussed, as an approach to further exploitation of the prospects that are on offer.

Dynamic Nuclear Polarization Assited Spin Diffusion for the Solid Effect Case

Hovav et al., Dynamic Nuclear Polarization Assited Spin Diffusion for the Solid Effect Case, J. Chem. Phys, 2011, 134, 074509

http://dx.doi.org/10.1063/1.3526486

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole–dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core–bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and crossrelaxation rates. 

The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of 13C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.

Dynamic Nuclear Polarization Assited Spin Diffusion for the Solid Effect Case

Hovav et al., Dynamic Nuclear Polarization Assited Spin Diffusion for the Solid Effect Case, J. Chem. Phys, 2011, 134, 074509

http://dx.doi.org/10.1063/1.3526486

The dynamic nuclear polarization (DNP) process in solids depends on the magnitudes of hyperfine interactions between unpaired electrons and their neighboring (core) nuclei, and on the dipole–dipole interactions between all nuclei in the sample. The polarization enhancement of the bulk nuclei has been typically described in terms of a hyperfine-assisted polarization of a core nucleus by microwave irradiation followed by a dipolar-assisted spin diffusion process in the core–bulk nuclear system. This work presents a theoretical approach for the study of this combined process using a density matrix formalism. In particular, solid effect DNP on a single electron coupled to a nuclear spin system is considered, taking into account the interactions between the spins as well as the main relaxation mechanisms introduced via the electron, nuclear, and crossrelaxation rates. 

The basic principles of the DNP-assisted spin diffusion mechanism, polarizing the bulk nuclei, are presented, and it is shown that the polarization of the core nuclei and the spin diffusion process should not be treated separately. To emphasize this observation the coherent mechanism driving the pure spin diffusion process is also discussed. In order to demonstrate the effects of the interactions and relaxation mechanisms on the enhancement of the nuclear polarization, model systems of up to ten spins are considered and polarization buildup curves are simulated. A linear chain of spins consisting of a single electron coupled to a core nucleus, which in turn is dipolar coupled to a chain of bulk nuclei, is considered. The interaction and relaxation parameters of this model system were chosen in a way to enable a critical analysis of the polarization enhancement of all nuclei, and are not far from the values of 13C nuclei in frozen (glassy) organic solutions containing radicals, typically used in DNP at high fields. Results from the simulations are shown, demonstrating the complex dependences of the DNP-assisted spin diffusion process on variations of the relevant parameters. In particular, the effect of the spin lattice relaxation times on the polarization buildup times and the resulting end polarization are discussed, and the quenching of the polarizations by the hyperfine interaction is demonstrated.

Theoretical Aspects of Dynamic Nuclear Polarization in the Solid State – The Solid Effect

Y. Hovav et al., Theoretical Aspects of Dynamic Nuclear Polarization in the Solid State – The Soild Effect, J. Magn. Reson., 2010, 207(2), 176-189

http://dx.doi.org/10.1016/j.jmr.2010.10.016

Dynamic nuclear polarization has gained high popularity in recent years, due to advances in the experimental aspects of this methodology for increasing the NMR and MRI signals of relevant chemical and biological compounds. The DNP mechanism relies on the microwave (MW) irradiation induced polarization transfer from unpaired electrons to the nuclei in a sample. In this publication we present nuclear polarization enhancements of model systems in the solid state at high magnetic fields.

These results were obtained by numerical calculations based on the spin density operator formalism. Here we restrict ourselves to samples with low electron concentrations, where the dipolar electron–electron interactions can be ignored. Thus the DNP enhancement of the polarizations of the nuclei close to the electrons is described by the Solid Effect mechanism. Our numerical results demonstrate the dependence of the polarization enhancement on the MW irradiation power and frequency, the hyperfine and nuclear dipole–dipole spin interactions, and the relaxation parameters of the system. The largest spin system considered in this study contains one electron and eight nuclei. In particular, we discuss the influence of the nuclear concentration and relaxation on the polarization of the core nuclei, which are coupled to an electron, and are responsible for the transfer of polarization to the bulk nuclei in the sample via spin diffusion.

Theoretical Aspects of Dynamic Nuclear Polarization in the Solid State – The Solid Effect

Y. Hovav et al., Theoretical Aspects of Dynamic Nuclear Polarization in the Solid State – The Soild Effect, J. Magn. Reson., 2010, 207(2), 176-189

http://dx.doi.org/10.1016/j.jmr.2010.10.016

Dynamic nuclear polarization has gained high popularity in recent years, due to advances in the experimental aspects of this methodology for increasing the NMR and MRI signals of relevant chemical and biological compounds. The DNP mechanism relies on the microwave (MW) irradiation induced polarization transfer from unpaired electrons to the nuclei in a sample. In this publication we present nuclear polarization enhancements of model systems in the solid state at high magnetic fields.

These results were obtained by numerical calculations based on the spin density operator formalism. Here we restrict ourselves to samples with low electron concentrations, where the dipolar electron–electron interactions can be ignored. Thus the DNP enhancement of the polarizations of the nuclei close to the electrons is described by the Solid Effect mechanism. Our numerical results demonstrate the dependence of the polarization enhancement on the MW irradiation power and frequency, the hyperfine and nuclear dipole–dipole spin interactions, and the relaxation parameters of the system. The largest spin system considered in this study contains one electron and eight nuclei. In particular, we discuss the influence of the nuclear concentration and relaxation on the polarization of the core nuclei, which are coupled to an electron, and are responsible for the transfer of polarization to the bulk nuclei in the sample via spin diffusion.

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