Nuclear dipolar relaxation induced by interacting ground state electron spins

Spectral diffusion and dynamic nuclear polarization: Beyond the high temperature approximation

Dynamic nuclear polarization via the cross effect and thermal mixing: A. The role of triple spin flips.

Microwave driven dynamic nuclear polarization (DNP) is a process in which the large polarization present in an electron spin reservoir is transferred to nuclei, thereby enhancing NMR signal intensities. In solid dielectrics there are three mechanisms that mediate this transfer--the solid effect (SE), the cross effect (CE), and thermal mixing (TM). Historically these mechanisms have been discussed theoretically using thermodynamic parameters and average spin interactions. However, the SE and the CE can also be modeled quantum mechanically with a system consisting of a small number of spins and the results provide a foundation for the calculations involving TM. In the case of the SE, a single electron-nuclear spin pair is sufficient to explain the polarization mechanism, while the CE requires participation of two electrons and a nuclear spin, and can be used to understand the improved DNP enhancements observed using biradical polarizing agents. Calculations establish the relations among the electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR) frequencies and the microwave irradiation frequency that must be satisfied for polarization transfer via the SE or the CE. In particular, if δ, Δ < ω(0I), where δ and Δ are the homogeneous linewidth and inhomogeneous breadth of the EPR spectrum, respectively, we verify that the SE occurs when ω(M) = ω(0S) ± ω(0I), where ω(M), ω(0S) and ω(0I) are, respectively, the microwave, and the EPR and NMR frequencies. Alternatively, when Δ > ω(0I) > δ, the CE dominates the polarization transfer. This two-electron process is optimized when ω(0S(1))-ω(0S(2)) = ω(0I) and ω(M)~ω(0S(1)) or ω(0S(2)), where ω(0S(1)) and ω(0S(2)) are the EPR Larmor frequencies of the two electrons. Using these matching conditions, we calculate the evolution of the density operator from electron Zeeman order to nuclear Zeeman order for both the SE and the CE. The results provide insights into the influence of the microwave irradiation field, the external magnetic field, and the electron-electron and electron-nuclear interactions on DNP enhancements.

Proton Dynamic Nuclear Polarization (DNP) experiments were conducted on a 3.4 T homebuilt hybrid pulsed-EPR-NMR spectrometer, on static samples containing 10 mM or 40 mM TEMPOL in frozen glassy solutions of DMSO/water. During DNP experiments proton-NMR signals are enhanced with the help of microwave (MW) irradiation on or close to the Electron Paramagnetic Resonance (EPR) spectrum of the free radicals in the sample, transferring polarization from the free electrons to the nuclei. In the solid state a distinction is made between three DNP enhancement mechanisms: the Solid Effect (SE), the Cross Effect (CE) and Thermal Mixing (TM). In an effort to determine the dominant DNP mechanisms responsible for the enhancement of the nuclear signals, electron and nuclear spin-lattice relaxation rates, enhancement buildup times and microwave (MW) swept DNP spectra were measured as a function of temperature and MW irradiation strength. We observed lineshape variations of the DNP spectra that indicated changes in the relative contributions of SE-DNP and CE-DNP with temperature and MW power. Using a theoretical model describing the SE-DNP and CE-DNP the DNP spectra could be analyzed without involving the TM-DNP mechanism and the relative SE-DNP and CE-DNP contributions to the nuclear enhancement could be determined. From this analysis it follows that lowering the temperature beyond 20 K increases the SE-DNP and decreases the CE-DNP contributions. Possible explanations for this behavior are suggested.

The goal of dynamic nuclear polarization (DNP) is to enhance NMR signals by transferring electron spin polarization to the nuclei. Although mechanisms such as the solid effect and thermal mixing can be used for DNP in the solid state, currently, the only practical mechanism in solutions is the Overhauser effect (OE), which usually arises due to dipolar relaxation between electrons and the nuclei. At magnetic fields greater than approximately 1 T, dipolar relaxation does not result in a useful enhancement and therefore the conventional wisdom is that DNP should not work in solutions at high magnetic fields. However, scalar relaxation due to time-dependent scalar couplings has a different magnetic field dependence and can lead to substantial OE enhancements. At room temperature and at a magnetic field of 5 T (211 MHz for protons, 140 GHz for electrons), we have observed that scalar relaxation between electrons and nuclei results in NMR signal enhancements of 180, 42, -36, and 8, for 31P, 13C, 15N, and 19F, respectively.

The available theoretical approaches aiming at describing Dynamic Nuclear spin Polarization (DNP) in solutions containing molecules of biomedical interest and paramagnetic centers are not able to model the behaviour observed upon varying the concentration of trityl radicals or the polarization enhancement caused by moderate addition of gadolinium complexes. In this manuscript, we first show experimentally that the nuclear steady state polarization reached in solutions of pyruvic acid with 15 mM trityl radicals is substantially independent on the average internuclear distance. This evidences a leading role of electron (over nuclear) spin relaxation processes in determining the ultimate performances of DNP. Accordingly, we have devised a variant of the Thermal Mixing model for inhomogenously broadened electron resonance lines which includes a relaxation term describing the exchange of magnetic anisotropy energy of the electron spin system with the lattice. Thanks to this additional term, the dependence of the nuclear polarization on the electron concentration can be properly accounted for. Moreover, the model predicts a strong increase of the final polarization upon shortening the electron spin-lattice relaxation time, providing a possible explanation for the effect of gadolinium doping.

We present a detailed analytical and numerical analysis of the nuclear spin dynamics in parabolic quantum wells. The shallow potential of parabolic quantum wells permits substantial modification of the electronic wave function in small electric fields. The nuclear spin relaxation via the hyperfine interaction depends on the electronic local density of states, therefore the local nuclear relaxation time depends sensitively on the electric field. For an inhomogeneous nuclear magnetization, such as generated by dynamic nuclear polarization, the total nuclear magnetization dynamics can similarly be altered. We examine this effect quantitatively and the effect of temperature, field, well thickness, and nuclear spin diffusion.

A comparison of the data on nuclear spin relaxation and ultrasonic relaxation is made. It is suggested the correlation time, τc, used in explaining nuclear spin effects is related to the shear and volume relaxational processes occurring in a liquid. The results of comparing the nuclear and ultrasonic processes indicate the following. (1) The average shear relaxation time found for glycerol is close in value to τc (2) The value for τc for water is shown to be very close to the volume relaxation time calculated by Hall. (3) The variation in the nuclear relaxation times in going from water to glycerol are closely related to the variation in the volume relaxation times. (4) Setting τc, proportional to the average shear relaxation time offers an explanation as to why the pressure dependence of the nuclear relaxation time is not a simple function of the viscosity as predicted by present nuclear relaxation theory.

Nuclear spin-lattice relaxation in carbon nanostructures

For symmetric top molecules the role of nuclear spin symmetry is included in the derivation of the nuclear magnetic relaxation rate. It is assumed that this is dominated by a spin-rotation mechanism. Of the three nuclear spin species which exist for ZX3Y' symmetric tops, it is found that the "zero frequency" K = −1 to +1 term results in two of the species relaxing with a different rate from the third. The difference, which allows a direct NMR evaluation of the relative values of [Formula: see text] and [Formula: see text], is enhanced at low temperatures.

Dynamic nuclear polarization (DNP) employs paramagnetic species to increase the NMR signal of nuclear spins. In liquids, the efficiency of the effect depends on the strength of the interaction between the electron and nuclear spins and the time scales on which this interaction is modulated by the physical motion of the spin-bearing molecules. An approach to quantitatively predict the contribution of molecular motions to the DNP enhancement using molecular dynamics (MD) simulations is developed and illustrated for the nitroxide radical TEMPOL in liquid toluene. A multi-resolution strategy that combines explicit treatment of the solvent at short distances from the free radical with implicit description at large intermolecular distances is adopted. Novel analytical expressions are obtained to correct for the finite spatial extent of the MD simulations. The atomistic and analytical descriptions are sewn seamlessly together by ensuring that for molecular trajectories that start in the near (explicit) region and end in the distant (implicit) region the analytical dipolar spectral densities reproduce the MD estimates. The spectral densities obtained from the developed approach are used to calculate DNP coupling factors separately for the ring and methyl protons of toluene. The agreement with previously reported experimental DNP data at a magnetic field of 3.4 T is noteworthy and encouraging. Maximum obtainable DNP enhancements at other magnetic fields are predicted.

The interaction between nuclear and electronic spins is of interest for structural characterization of biomolecules and biomedical imaging based on nuclear magnetic resonance. The polarization of the nuclear spins can be increased significantly if the electron spin polarization is kept out of equilibrium. We employ semiclassical relaxation theory to analyze the electronic polarization of the two-spin system characteristic of nitroxide radicals. Atomistic molecular dynamics simulations of the nitroxide TEMPOL in water are performed to account for the effects of tumbling and spin-rotation coupling on the spin-spin and spin-lattice relaxation times. Concentration effects on the electron saturation are introduced by allowing for Heisenberg spin exchange between two nitroxides. Polarization enhancement profiles, calculated from the computed saturation, are directly compared with liquid-state dynamic nuclear polarization experiments conducted at 260 GHz/400 MHz. The contribution of the separate hyperfine lines to the saturation can be easily disentangled using the developed formalism.

The dynamic nuclear polarization of 13C nuclei in a suite of seven natural type Ia and Ib diamonds, using continuous wave S- and X-band microwave radiation, is described. The 13C signal enhancement and polarization time have been measured for one of the type Ib diamonds as a function of magnetic field in the vicinity of the resonance field. The total paramagnetic impurity concentration (P1 and other centers) in this diamond is 2×1018 cm−3 (23 atomic parts per million), while the concentration of P1 centers is 9.3 ppm. Since the central electron spin resonance (ESR) linewidth HL is comparable with H0γC/γe, flip–flip and flip–flop forbidden transitions take place simultaneously. Consequently thermal mixing plays an important role in the 13C signal enhancement. However, the 13C spin-lattice relaxation rate is determined to a large extent by the solid state effect (forbidden transitions). The 13C polarization rates have been measured for the suite of diamonds by executing dynamic nuclear polarization (DNP) experiments on both hyperfine and central ESR lines. It is shown that the polarization rate is proportional to the paramagnetic impurity concentration of the sample, in agreement with the existing theory. It has been found that in type Ib diamonds with relatively low nitrogen impurity concentrations the dynamic nuclear polarization of a single hyperfine line yields an equilibrium 13C polarization that is one-quarter of that obtained in the case of dynamic nuclear polarization of the central line. In samples containing P1 and P2 centers (type Ia), or in type Ib samples with relatively high concentrations of P1 centers, the same equilibrium 13C polarization is obtained for the DNP of hyperfine and central transitions. This phenomenon is explained in terms of a model in which thermal contact is established between the electron Zeeman reservoir and the nuclear spin reservoirs via the spin–spin interaction reservoir if HL⩾H0γC/γe.

Review: 47 refs.

Experiments of dynamic nuclear polarization by electron spins in the photoexcited triplet state were made using single crystal and polycrystalline samples of 99.21%-deuterated naphthalene doped with 0.015 mol% pentacene. In the single crystal sample, the polarization of the residual protons was built up to 0.7 at 105 K, reaching the ultimate polarization equal to the photo-induced electron spin polarization. A doublet due to the two protons which happen to be adjacent to each other in a deuterated naphthalene molecule was observed in the single crystal under deuteron double-quantum decoupling; it exhibits polarization-induced asymmetry when observed by a small-tip angle pulse. In the polycrystalline sample the resultant 1 H polarization was 0.033. The 1 H NMR lineshape under deuteron decoupling in the single crystal and the inhomogeneous 1 H distribution in a deuterated naphthalene molecule are discussed.