Category Archives: Solid-Effect

Theoretical Aspects of Magic Angle Spinning – Dynamic Nuclear Polarization

Mentink-Vigier, F., et al., Theoretical Aspects of Magic Angle Spinning – Dynamic Nuclear Polarization. J. Magn. Reson., 2015.

Magic Angle Spinning combined with Dynamic Nuclear Polarization has been proven in recent years to be a very powerful method for increasing solid state NMR signals. Since the advent of biradicals such as TOTAPOL to increase the nuclear polarization new classes of radicals, with larger molecular weight and/or different spin properties have been developed. These have led to unprecedented signal gain, with varying results for different experimental parameters, in particular the microwave irradiation strength, the static field, and the spinning frequency. Recently it has been shown that spinning of the sample imposes DNP enhancement processes that differ from the DNP processes enhancing the nuclear polarizations in static samples. During the sample spinning the DNP enhancements are the results of energy level anticrossings occurring periodically during each rotor cycle. In this work we present experimental results of the MAS spinning frequency DNP enhancement profiles of four nitroxide based radicals at two different sets of temperature 110 and 160 K. These results emphasize the reduction of these enhancements for increasing spinning frequencies. The simulation code calculating MAS-DNP powder enhancements of small model spin systems has been improved to extend our studies of the influence of variations in the interaction and relaxation parameters on powder enhancements. These studies provide a better understanding of the impact of changes in these parameters on the MAS-DNP mechanism. To accomplish this we simulated the spin dynamics of a single three-spin system { e a – e b – n } during its steady state rotor periods and used the Landau-Zener formula to characterize the influence of the different anti-crossings on the polarizations of the system and their necessary action for reaching steady state conditions together with spin relaxation processes. Based on these model calculations we demonstrate that the maximal steady state nuclear polarization cannot become larger than the maximal polarization difference between the two electrons during the steady state rotor cycle. This study also shows the complexity of the MAS-DNP process and therefore the necessity to rely on numerical simulations for understanding parametric dependences of the enhancements. Finally an extension of the three-spin system allowed us to probe the first steps of the transfer of polarization from the nuclei coupled to the electrons to further away nuclei, demonstrating a decrease in the spin-diffusion barrier under MAS conditions.

Simultaneous DNP enhancements of (1)H and (13)C nuclei: theory and experiments

Shimon D, Hovav Y, Kaminker I, Feintuch A, Goldfarb D, Vega S. Simultaneous DNP enhancements of (1)H and (13)C nuclei: theory and experiments. Phys Chem Chem Phys. 2015;17(17):11868-83.

DNP on heteronuclear spin systems often results in interesting phenomena such as the polarization enhancement of one nucleus during MW irradiation at the \”forbidden\” transition frequencies of another nucleus or the polarization transfer between the nuclei without MW irradiation. In this work we discuss the spin dynamics in a four-spin model system of the form {ea-eb-((1)H,(13)C)}, with the Larmor frequencies omegaa, omegab, omegaH and omegaC, by performing Liouville space simulations. This spin system exhibits the common (1)H solid effect (SE), (13)C cross effect (CE) and in addition high order CE-DNP enhancements. Here we show, in particular, the \”proton shifted (13)C-CE\” mechanism that results in (13)C polarization when the model system, at one of its (13)C-CE conditions, is excited by a MW field at the zero quantum or double quantum electron-proton transitions omegaMW = omegaa +/- omegaH and omegaMW = omegab +/- omegaH. Furthermore, we introduce the \”heteronuclear\” CE mechanism that becomes efficient when the system is at one of its combined CE conditions |omegaa – omegab| = |omegaH +/- omegaC|. At these conditions, simulations of the four-spin system show polarization transfer processes between the nuclei, during and without MW irradiation, resembling the polarization exchange effects often discussed in the literature. To link the \”microscopic\” four-spin simulations to the experimental results we use DNP lineshape simulations based on \”macroscopic\” rate equations describing the electron and nuclear polarization dynamics in large spin systems. This approach is applied based on electron-electron double resonance (ELDOR) measurements that show strong (1)H-SE features outside the EPR frequency range. Simulated ELDOR spectra combined with the indirect (13)C-CE (iCE) mechanism, result in additional \”proton shifted (13)C-CE\” features that are similar to the experimental ones. These features are also observed experimentally in (13)C-DNP spectra of a sample containing 15 mM of trityl in a glass forming solution of (13)C-glycerol/H2O and are analyzed by calculating the basic (13)C-SE and (13)C-iCE shapes using simulated ELDOR spectra that were fitted to the experimental ones.

Mechanisms of dynamic nuclear polarization in insulating solids

Can, T.V., Q.Z. Ni, and R.G. Griffin, Mechanisms of dynamic nuclear polarization in insulating solids. J Magn Reson, 2015. 253(0): p. 23-35.

Dynamic nuclear polarization (DNP) is a technique used to enhance signal intensities in NMR experiments by transferring the high polarization of electrons to their surrounding nuclei. The past decade has witnessed a renaissance in the development of DNP, especially at high magnetic fields, and its application in several areas including biophysics, chemistry, structural biology and materials science. Recent technical and theoretical advances have expanded our understanding of established experiments: for example, the cross effect DNP in samples spinning at the magic angle. Furthermore, new experiments suggest that our understanding of the Overhauser effect and its applicability to insulating solids needs to be re-examined. In this article, we summarize important results of the past few years and provide quantum mechanical explanations underlying these results. We also discuss future directions of DNP and current limitations, including the problem of resolution in protein spectra recorded at 80-100K.

Effects of the electron polarization on dynamic nuclear polarization in solids

Hovav, Y., et al., Effects of the electron polarization on dynamic nuclear polarization in solids. Phys Chem Chem Phys, 2015. 17(8): p. 6053-65.

Dynamic Nuclear Polarization (DNP) experiments on solid dielectrics can be described in terms of the Solid Effect (SE) and Cross Effect (CE) mechanisms. These mechanisms are best understood by following the spin dynamics in electron-nuclear and electron-electron-nuclear model systems, respectively. Recently it was shown that the frequency swept DNP enhancement profiles can be reconstructed by combining basic SE and CE DNP spectra. However, this analysis did not take into account the role of the electron spectral diffusion (eSD), which can result in a dramatic loss of electron polarization along the EPR line. In this paper we extend the analysis of DNP spectra by including the influence of the eSD process on the enhancement profiles. We show for an electron-electron-nuclear model system that the change in nuclear polarization can be caused by direct MW irradiation on the CE electron transitions, resulting in a direct CE (dCE) enhancement, or by the influence of the eSD process on the spin system, resulting in nuclear enhancements via a process we term the indirect CE (iCE). We next derive the dependence of the basic SE, dCE, and iCE DNP spectra on the electron polarization distribution along the EPR line and on the MW irradiation frequency. The electron polarization can be obtained from ELDOR experiments, using a recent model which describes its temporal evolution in real samples. Finally, DNP and ELDOR spectra, recorded for a 40 mM TEMPOL sample at 10-40 K, are analyzed. It is shown that the iCE is the major mechanism responsible for the bulk nuclear enhancement at all temperatures.

Dynamic nuclear polarization of high-density atomic hydrogen in solid mixtures of molecular hydrogen isotopes

If you are interested in this article, you should also have a look at this article by Can et al., describing the Overhauser Effect in insulating solids:

Sheludiakov, S., et al., Dynamic nuclear polarization of high-density atomic hydrogen in solid mixtures of molecular hydrogen isotopes. Phys Rev Lett, 2014. 113(26): p. 265303.

We report on magnetic resonance studies of high-density atomic hydrogen and deuterium in solid hydrogen matrices at temperatures below 1 K. Average concentrations of H atoms approximately 3×10^{19} cm^{-3} are obtained in chemical tunneling reactions of isotope exchange with D atoms. The products of these reactions are closely located pairs of H atoms near D_{2} molecules with strong exchange interactions. We discovered a dynamic nuclear polarization effect on H atoms created by pumping the center of the H electron spin resonance spectrum, similar to the Overhauser effect in metals. Our results indicate that H atoms may be arranged inside molecular matrices at separations equivalent to local concentrations of 2.6×10^{21} cm^{-3}. This opens up a way to build a metallic state of atomic hydrogen at zero pressure.

Overhauser effects in insulating solids

Can, T.V., et al., Overhauser effects in insulating solids. J Chem Phys, 2014. 141(6): p. 064202.

We report magic angle spinning, dynamic nuclear polarization (DNP) experiments at magnetic fields of 9.4 T, 14.1 T, and 18.8 T using the narrow line polarizing agents 1,3-bisdiphenylene-2-phenylallyl (BDPA) dispersed in polystyrene, and sulfonated-BDPA (SA-BDPA) and trityl OX063 in glassy glycerol/water matrices. The (1)H DNP enhancement field profiles of the BDPA radicals exhibit a significant DNP Overhauser effect (OE) as well as a solid effect (SE) despite the fact that these samples are insulating solids. In contrast, trityl exhibits only a SE enhancement. Data suggest that the appearance of the OE is due to rather strong electron-nuclear hyperfine couplings present in BDPA and SA-BDPA, which are absent in trityl and perdeuterated BDPA (d21-BDPA). In addition, and in contrast to other DNP mechanisms such as the solid effect or cross effect, the experimental data suggest that the OE in non-conducting solids scales favorably with magnetic field, increasing in magnitude in going from 5 T, to 9.4 T, to 14.1 T, and to 18.8 T. Simulations using a model two spin system consisting of an electron hyperfine coupled to a (1)H reproduce the essential features of the field profiles and indicate that the OE in these samples originates from the zero and double quantum cross relaxation induced by fluctuating hyperfine interactions between the intramolecular delocalized unpaired electrons and their neighboring nuclei, and that the size of these hyperfine couplings is crucial to the magnitude of the enhancements. Microwave power dependent studies show that the OE saturates at considerably lower power levels than the solid effect in the same samples. Our results provide new insights into the mechanism of the Overhauser effect, and also provide a new approach to perform DNP experiments in chemical, biophysical, and physical systems at high magnetic fields.

Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator

Karabanov, A., G. Kwiatkowski, and W. Köckenberger, Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator. Mol. Phys., 2014: p. 1-17.

Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad?Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad?Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation.

Role of Electron Spin Dynamics on Solid-State Dynamic Nuclear Polarization Performance

Siaw, T.A., et al., Role of Electron Spin Dynamics on Solid-State Dynamic Nuclear Polarization Performance. Phys. Chem. Chem. Phys., 2014.

For the broadest dissemination of solid-state dynamic nuclear polarization (ssDNP) enhanced NMR as a materials characterization tool, the ability to employ generic mono-nitroxide radicals as spin probes is critical. A better understanding of the factors contributing to ssDNP efficiency is needed to rationally optimize the experimental condition for the practically accessible spin probes at hand. This study seeks to advance the mechanistic understanding of ssDNP by examining the effect of electron spin dynamics on the ssDNP performance at liquid helium temperatures (4-40 K). The key observation is that bi-radicals and mono-radicals can generate comparable nuclear spin polarization at 4 K and 7 T, which is in contrast to ssDNP at liquid nitrogen temperatures (80-150 K) that find bi-radicals to clearly outperform mono-radicals. To rationalize this observation, we analyze the change in the DNP-induced nuclear spin polarization (Pn) and the characteristic ssDNP signal buildup time as a function of electron spin relaxation rates that are modulated by the mono- and bi-radical spin concentration. Changes in Pn are consistent with a systematic variation in the product of the electron spin-lattice relaxation time and the electron spin flip-flop rate that constitutes an integral saturation factor of an inhomogeneously broadened EPR spectrum. We show that the comparable Pn achieved with both radical species can be reconciled with a comparable integral EPR saturation factor. Surprisingly, the largest Pn is observed at an intermediate spin concentration for both the mono- and bi-radicals. At the highest radical concentration, the stronger inter-electron spin dipolar coupling favors ssDNP, while oversaturation diminishes Pn, as experimentally verified with the observation of a maximum Pn at an intermediate, not the maximum, microwave ([small mu ]w) power. At the maximum [small mu ]w power, oversaturation reduces the electron spin population differential that must be upheld between electron spins that span a frequency difference matching the 1H NMR frequency-characteristic of the cross effect DNP. This new mechanistic insight allows us to rationalize experimental conditions where generic mono-nitroxide probes can offer competitive ssDNP performance to that of custom designer bi-radicals, and thus helps vastly expand the application scope of ssDNP for the study of functional materials and solids.

Static (1)H dynamic nuclear polarization with the biradical TOTAPOL: a transition between the solid effect and the cross effect

Shimon, D., et al., Static (1)H dynamic nuclear polarization with the biradical TOTAPOL: a transition between the solid effect and the cross effect. Phys Chem Chem Phys, 2014. 16(14): p. 6687-99.

To study the solid state (1)H-DNP mechanism of the biradical TOTAPOL under static conditions the frequency swept DNP enhancement spectra of samples containing 20 mM and 5 mM TOTAPOL were measured as a function of MW irradiation time and temperature. We observed that under static DNP conditions the biradical TOTAPOL behaves similar to the monoradical TEMPOL, in contrast to MAS DNP where TOTAPOL is considerably more effective. As previously done for TEMPOL, the TOTAPOL DNP spectra were analyzed taking a superposition of a basic SE-DNP lineshape and a basic CE-DNP lineshape with different amplitudes. The analysis of the steady state DNP spectra showed that the SE was dominant in the 6-10 K range and the CE was dominant above 10 K. DNP spectra obtained as a function of MW irradiation time allowed resolving the individual SE and CE buildup times. At low temperatures the SE buildup time was faster than the CE buildup time and at all temperatures the CE buildup time was close to the nuclear spin-lattice relaxation time, T1n. Polarization calculations involving nuclear spin-diffusion for a model system of one electron and many nuclei suggested that the shortening of the T1n for increasing temperatures is the reason why the SE contribution to the overall enhancement was reduced.

Observation of strongly forbidden solid effect dynamic nuclear polarization transitions via electron-electron double resonance detected NMR

Smith, A.A., et al., Observation of strongly forbidden solid effect dynamic nuclear polarization transitions via electron-electron double resonance detected NMR. J Chem Phys, 2013. 139(21): p. 214201.

We present electron paramagnetic resonance experiments for which solid effect dynamic nuclear polarization transitions were observed indirectly via polarization loss on the electron. This use of indirect observation allows characterization of the dynamic nuclear polarization (DNP) process close to the electron. Frequency profiles of the electron-detected solid effect obtained using trityl radical showed intense saturation of the electron at the usual solid effect condition, which involves a single electron and nucleus. However, higher order solid effect transitions involving two, three, or four nuclei were also observed with surprising intensity, although these transitions did not lead to bulk nuclear polarization–suggesting that higher order transitions are important primarily in the transfer of polarization to nuclei nearby the electron. Similar results were obtained for the SA-BDPA radical where strong electron-nuclear couplings produced splittings in the spectrum of the indirectly observed solid effect conditions. Observation of high order solid effect transitions supports recent studies of the solid effect, and suggests that a multi-spin solid effect mechanism may play a major role in polarization transfer via DNP.

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