Electron Spin-lattice Relaxation Rate Research Articles

Rate constants for saturation-recovery EPR and ELDOR of 14N-Spin labels

Saturation-recovery (SR)-EPR can determine electron spin–lattice relaxation rates in liquids over a wide range of effective viscosity, making it especially useful for biophysical and biomedical applications. Here, I develop exact solutions for the SR-EPR and SR-ELDOR rate constants of 14N-nitroxyl spin labels as a function of rotational correlation time and spectrometer operating frequency. Explicit mechanisms for electron spin–lattice relaxation are: rotational modulation of the N-hyperfine and electron-Zeeman anisotropies (specifically including cross terms), spin-rotation interaction, and residual frequency-independent vibrational contributions from Raman processes and local modes. Cross relaxation from mutual electron and nuclear spin flips, and direct nitrogen nuclear spin–lattice relaxation, also must be included. Both the latter are further contributions from rotational modulation of the electron-nuclear dipolar interaction (END). All the conventional liquid-state mechanisms are defined fully by the spin-Hamiltonian parameters; only the vibrational contributions contain fitting parameters. This analysis gives a firm basis for interpreting SR (and inversion recovery) results in terms of additional, less standard mechanisms.

Direct measurement of the triple spin flip rate in dynamic nuclear polarization

A previous study of the effect of Gadolinium doping on the dynamic polarization (DNP) of 13C using trityls showed that the rate at which the polarization builds up is almost independent of the Gadolinium concentration, while the electron spin–lattice relaxation rate varies over an order of magnitude. In this paper we analyze the polarization build-up in detail and show that in this case DNP is due to the cross-effect (CE) and that the build-up rate can be quantitatively interpreted as the rate of the triple spin flips responsible for the CE. Thus this build-up rate presents a direct measurement of this triple spin flip rate.

Spin-lattice relaxation processes of transition metal ions in a heavily cobalt doped ZnO: Phonon heating effect

Inversion recovery with electron spin-echo detection has been used to study the electron spin-lattice relaxation rates 1/T1 for transition metal impurities in heavily cobalt-doped hydrothermally grown ZnO single crystals. The relaxation dynamics of Co2+ ions dominates the phonon bottleneck effect in the Orbach-Aminov process, which involves the modulation of the zero-field-splitting tensor. The relaxation mechanism may be treated in terms of phonon heating with fast rate of energy pump from Co2+ spins into the lattice phonon modes. The measurements reveal the cross-relaxation process in which the single Co2+ ions cross-relax to exchange-coupled clusters of cobalt ions. The higher temperature relaxation of Co2+ indicates an additional Orbach-Aminov process via a state of ∼226 cm−1 above the ground state Kramers doublet. It is shown that in this system Co2+ ions play a role of the rapidly relaxing centers, strongly mediating the spin-lattice relaxation of the other transition metal impurities, such as Mn2+ and Fe3+.

Cross relaxation in nitroxide spin labels

Cross relaxation, and mI-dependence of the intrinsic electron spin-lattice relaxation rate We, are incorporated explicitly into the rate equations for the electron-spin population differences that govern the saturation behaviour of 14N- and 15N-nitroxide spin labels. Both prove important in spin-label EPR and ELDOR, particularly for saturation recovery studies. Neither for saturation recovery, nor for CW-saturation EPR and CW-ELDOR, can cross relaxation be described simply by increasing the value of We, the intrinsic spin-lattice relaxation rate. Independence of the saturation recovery rates from the hyperfine line pumped or observed follows directly from solution of the rate equations including cross relaxation, even when the intrinsic spin-lattice relaxation rate We is mI-dependent.

Quantum critical scaling and superconductivity in heavy electron materials

We use the two fluid model to determine the conditions under which the nuclear spin-lattice lattice relaxation rate, $T_1$, of candidate heavy quantum critical superconductors can exhibit scaling behavior and find that it can occur if and only if their "hidden" quantum critical spin fluctuations give rise to a temperature-independent intrinsic heavy electron spin-lattice relaxation rate. The resulting scaling of $T_1$ with the strength of the heavy electron component and the coherence temperature, $T^*$, provides a simple test for their presence at pressures at which the superconducting transition temperature, $T_c$, is maximum and is proportional to $T^*$. These findings support the previously noted partial scaling of the spin-lattice relaxation rate with $T_c$ in a number of important heavy electron materials and provide additional evidence that in these materials their optimal superconductivity originates in the quantum critical spin fluctuations associated with a nearby phase transition from partially localized to fully itinerant quasiparticles.

Electron spin-lattice relaxation mechanisms of nitroxyl radicals in ionic liquids and conventional organic liquids: temperature dependence of a thermally activated process.

During the past two decades, several studies have established a significant role played by a thermally activated process in the electron spin relaxation of nitroxyl free radicals in liquid solutions. Its role has been used to explain the spin relaxation behavior of these radicals in a wide range of viscosities and microwave frequencies. However, no temperature dependence of this process has been reported. In this work, our main aim was to investigate the temperature dependence of this process in neat solvents. Electron spin-lattice relaxation times of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and 4-hydroxy-TEMPO (TEMPOL), in X-band microwave frequency, were measured by the pulse saturation recovery technique in three room-temperature ionic liquids ([bmim][BF4], [emim][BF4], and [bmim][PF6]), di-isononyl phthalate, and sec-butyl benzene. The ionic liquids provided a wide range of viscosity in a modest range of temperature. An auxiliary aim was to examine whether the dynamics of a probe molecule dissolved in ionic liquids was different from that in conventional molecular liquids, as claimed in several reports on fluorescence dynamics in ionic liquids. This was the reason for the inclusion of di-isononyl phthalate, whose viscosities are similar to that of the ionic liquids in similar temperatures, and sec-butyl benzene. Rotational correlation times of the nitroxyl radicals were determined from the hyperfine dependence of the electron paramagnetic resonance (EPR) line widths. Observation of highly well-resolved proton hyperfine lines, riding over the nitrogen hyperfine lines, in the low viscosity regime in all the solvents, gave more accurate values of the rotational correlation times than the values generally measured in the absence of these hyperfine lines and reported in the literature. The measured rotational correlation times obeyed a modified Stokes-Einstein-Debye relation of temperature dependence in all solvents. By separating the contributions of g-anisotropy, A-anisotropy and spin-rotation interactions from the observed electron spin-lattice relaxation rates, the contribution of the thermally activated process was obtained and compared with its expression for the temperature dependence. Consistent values of various fitted parameters, used in the expression of the thermal process, have been found, and the applicability of the expression of the thermally activated process to describe the temperature dependence in liquid solutions has been vindicated. Moderate solvent dependence of the thermally activated process has also been observed. The rotational correlation times and the spin-lattice relaxation processes of nitroxyls in ionic liquids and in conventional organic liquids are shown to be explicable on a similar footing, requiring no special treatment for ionic liquids.

Phonon spectrum, electron spin–lattice relaxation and spin–phonon coupling of Cu2+ ions in BaF2 crystal

Electron spin–lattice relaxation rate is determined by electron spin echo method in temperature range 4–60K. The Raman relaxation processes dominate and its theory is outlined in a form suitable for calculations of relaxation rate using real phonon spectrum. A few approximations have been considered: when phonon spectrum and Debye temperature are not available; when Debye temperature is available but phonon spectrum is not; and when spin–phonon coupling is known. All these approximations use the Debye model of phonons and give a non-satisfactory description the temperature dependence of the relaxation rate. A perfect description of experimental results is obtained when real phonon spectrum is considered. The value of the spin–phonon coupling parameter was determined as G=〈a|V|b〉=1362cm-1. This value is discussed by a comparison with G-values published for various ions and crystals.

Dynamic nuclear polarization using frequency modulation at 3.34 T

During dynamic nuclear polarization (DNP) experiments polarization is transferred from unpaired electrons to their neighboring nuclear spins, resulting in dramatic enhancement of the NMR signals. While in most cases this is achieved by continuous wave (cw) irradiation applied to samples in fixed external magnetic fields, here we show that DNP enhancement of static samples can improve by modulating the microwave (MW) frequency at a constant field of 3.34T. The efficiency of triangular shaped modulation is explored by monitoring the 1H signal enhancement in frozen solutions containing different TEMPOL radical concentrations at different temperatures. The optimal modulation parameters are examined experimentally and under the most favorable conditions a threefold enhancement is obtained with respect to constant frequency DNP in samples with low radical concentrations. The results are interpreted using numerical simulations on small spin systems. In particular, it is shown experimentally and explained theoretically that: (i) The optimal modulation frequency is higher than the electron spin–lattice relaxation rate. (ii) The optimal modulation amplitude must be smaller than the nuclear Larmor frequency and the EPR line-width, as expected. (iii) The MW frequencies corresponding to the enhancement maxima and minima are shifted away from one another when using frequency modulation, relative to the constant frequency experiments.

Electron spin resonance studies of trityl OX063 at a concentration optimal for DNP.

We have performed temperature-dependent electron spin resonance (ESR) measurements of the stable free radical trityl OX063, an efficient polarizing agent for dissolution dynamic nuclear polarization (DNP), at the optimum DNP concentration (15 mM). We have found that (i) when compared to the W-band electron spin-lattice relaxation rate T1e(-1) of other free radicals used in DNP at the same concentration, trityl OX063 has slower T1e(-1) than BDPA and 4-oxo-TEMPO. At T > 20 K, the T1e(-1)vs. T data of trityl OX063 appears to follow a power law dependence close to the Raman process prediction whereas at T < 10 K, electronic relaxation slows and approaches the direct process behaviour. (ii) Gd(3+) doping, a factor known to enhance DNP, of trityl OX063 samples measured at W-band resulted in monotonic increases of T1e(-1) especially at temperatures below 20-40 K while the ESR lineshapes remained essentially unchanged. (iii) The high frequency ESR spectrum can be fitted with an axial g-tensor with a slight g-anisotropy: g(x) = g(y) = 2.00319(3) and g(z) = 2.00258(3). Although the ESR linewidth D monotonically increases with field, the temperature-dependent T1e(-1) is almost unchanged as the ESR frequency is increased from 9.5 GHz to 95 GHz, but becomes faster at 240 GHz and 336 GHz. The ESR properties of trityl OX063 reported here may provide insights into the efficiency of DNP of low-γ nuclei performed at various magnetic fields, from 0.35 T to 12 T.

Dynamic nuclear polarization in the solid state: a transition between the cross effect and the solid effect

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.

Use of Additional Fast-Relaxing Paramagnetic Species for Improvement of RIDME Performance

A method of improving relaxation-induced dipolar modulation enhancement (RIDME) performance by an artificial increase of electron spin–lattice relaxation rate is introduced and tested on a model nitroxide biradical. A substantial increase of its electron spin–lattice relaxation rate is achieved by the addition of a fast-relaxing paramagnetic holmium complex to the sample solution. The electron spin–spin relaxation rate of the nitroxide does not change dramatically upon this addition. The suggested method allows obtaining a deep dipolar modulation in the RIDME experiment, which is free from distortions caused by spectral diffusion processes.

Electron spin relaxation rates for semiquinones between 25 and 295 K in glass-forming solvents

Electron spin lattice relaxation rates for five semiquinones (2,5-di-t-butyl-1,4-benzosemiquinone, 2,5-di-t-amyl-1,4-benzosemiquinone, 2,5-di-phenyl-1,4-benzosemiquinone, 2,6-di-t-butyl-1,4-benzosemiquinone, tetrahydroxy-1,4-benzosemiquione) were studied by long-pulse saturation recovery EPR in 1:4 glycerol:ethanol, 1:1 glycerol:ethanol, and triethanolamine between 25 and 295 K. Although the dominant process changes with temperature, relaxation rates vary smoothly with temperature, even near the glass transition temperatures, and could be modeled as the sum of contributions that have the temperature dependence that is predicted for the direct, Raman, local mode and tumbling-dependent processes. At 85 K, which is in a temperature range where the Raman process dominates, relaxation rates along the g xx ( g ∼ 2.006) and g yy ( g ∼ 2.005) axes are about 2.7–1.5 times faster than along the g zz axis ( g = 2.0023). In highly viscous triethanolamine, contributions from tumbling-dependent processes are negligible. At temperatures above 100 K relaxation rates in triethanolamine are unchanged between X-band (9.5 GHz) and Q-band (34 GHz), so the process that dominates in this temperature interval was assigned as a local mode rather than a thermally activated process. Because the largest proton hyperfine couplings are only 2.2 G, spin rotation makes a larger contribution than tumbling-dependent modulation of hyperfine anisotropy. Since g anisotropy is small, tumbling-dependent modulation of g anisotropy makes a smaller contribution than spin rotation at X-band. Although there was negligible impact of methyl rotation on T 1, rotation of t-butyl or t-amyl methyl groups enhances spin echo dephasing between 85 and 150 K.

Electron spin–lattice relaxation of nitroxyl radicals in temperature ranges that span glassy solutions to low-viscosity liquids

Electron spin–lattice relaxation rates, 1/ T 1, at X-band of nitroxyl radicals (4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl, 4-oxo-2,2,6,6-tetramethylpiperidin-1-oxyl, 3-carbamoyl-2,2,5,5-tetramethylpyrrolidin-1-oxyl and 3-carbamoyl-2,2,5,5-tetramethylpyrrolin-1-oxyl) in glass-forming solvents (decalin, glycerol, 3-methylpentane, o-terphenyl, 1-propanol, sorbitol, sucrose octaacetate, and 1:1 water:glycerol) at temperatures between 100 and 300 K were measured by long-pulse saturation recovery to investigate the relaxation processes in slow-to-fast tumbling regimes. A subset of samples was also studied at lower temperatures or at Q-band. Tumbling correlation times were calculated from continuous wave lineshapes. Temperature dependence and isotope substitution ( 2H and 15N) were used to distinguish the contributions of various processes. Below about 100 K relaxation is dominated by the Raman process. At higher temperatures, but below the glass transition temperature, a local mode process makes significant contributions. Above the glass transition temperature, increased rates of molecular tumbling modulate nuclear hyperfine and g anisotropy. The contribution from spin rotation is very small. Relaxation rates at X-band and Q-band are similar. The dependence of 1/ T 1 on tumbling correlation times fits better with the Cole–Davidson spectral density function than with the Bloembergen–Purcell–Pound model.

Electron spin relaxation enhancement measurements of interspin distances in human, porcine, and Rhodobacter electron transfer flavoprotein–ubiquinone oxidoreductase (ETF–QO)

Electron transfer flavoprotein–ubiquinone oxidoreductase (ETF–QO) is a membrane-bound electron transfer protein that links primary flavoprotein dehydrogenases with the main respiratory chain. Human, porcine, and Rhodobacter sphaeroides ETF–QO each contain a single [4Fe–4S] 2+,1+ cluster and one equivalent of FAD, which are diamagnetic in the isolated enzyme and become paramagnetic on reduction with the enzymatic electron donor or with dithionite. The anionic flavin semiquinone can be reduced further to diamagnetic hydroquinone. The redox potentials for the three redox couples are so similar that it is not possible to poise the proteins in a state where both the [4Fe–4S] + cluster and the flavoquinone are fully in the paramagnetic form. Inversion recovery was used to measure the electron spin-lattice relaxation rates for the [4Fe–4S] + between 8 and 18 K and for semiquinone between 25 and 65 K. At higher temperatures the spin-lattice relaxation rates for the [4Fe–4S] + were calculated from the temperature-dependent contributions to the continuous wave linewidths. Although mixtures of the redox states are present, it was possible to analyze the enhancement of the electron spin relaxation of the FAD semiquinone signal due to dipolar interaction with the more rapidly relaxing [4Fe–4S] + and obtain point-dipole interspin distances of 18.6 ± 1 Å for the three proteins. The point-dipole distances are within experimental uncertainty of the value calculated based on the crystal structure of porcine ETF–QO when spin delocalization is taken into account. The results demonstrate that electron spin relaxation enhancement can be used to measure distances in redox poised proteins even when several redox states are present.

Impact of molecular size on electron spin relaxation rates of nitroxyl radicals in glassy solvents between 100 and 300 K

Electron spin lattice relaxation rates were measured for 12 nitroxyls with molecular weights between 144 and 438, and for galvinoxyl, 1,3-bisdiphenylene-2-phenylallyl (BDPA), and 2,2-diphenyl-1-picrylhydrazyl (DPPH) in glassy sucrose octaacetate. Relaxation rates for polar nitroxyls also were measured in glassy sorbitol. Dependence on T where V eff is effective molecular volume and γ is a material-specific parameter, was used to compare processes. Values of V eff were determined based on molecular libration in glassy sucrose octaacetate (γ = 3.5), tumbling in viscous decalin at 233 K (γ = 4.7), or tumbling in heavy mineral oil (γ = 6.0). For nitroxyl relaxation there is a master curve: log(1/T 1) vs log( T) (γ = 0.89). The similarity of the values of γ for the Raman process and for the additional process that contributes at higher temperatures, and the absence of frequency dependence between X- and Q-band, support assignment of this additional process as a local mode. For these radicals the contributions from the local mode and the Raman process are correlated and follow trends in spin–orbit coupling. The temperature dependence of spin echo dephasing in sucrose octaacetate is dominated by rotation of methyl groups and by a motional process analogous to the Raman process.

Frequency Dependence of Electron Spin Relaxation of Nitroxyl Radicals in Fluid Solution

Electron spin lattice relaxation rates (1/T1e) of nitroxyl radicals for tumbling correlation times between about 0.1 and 10 ns in water:glycerol or water:sorbitol mixtures at room temperature were measured by saturation recovery at X-band (9.2 GHz), S-band (3.1 GHz), and L-band (1.9 GHz) for natural abundance 2,2,6,6-tetramethylpiperidinyl-1-oxy (tempol), tempol-d17, and 15N-tempol-d17 and for a spin-labeled derivative of ethylenediaminetetraacetic acid. Tumbling correlation times were calculated from the continuous wave EPR line shapes at X-band. The dependence of T1e on tumbling correlation time was modeled with contributions from modulation of nitrogen nuclear hyperfine and g anisotropy, from spin rotation and from one or more thermally activated processes. At these microwave frequencies, modulation of nitrogen hyperfine anisotropy makes a substantially larger contribution than modulation of g anisotropy. Spin rotation makes a very small contribution to T1e at the tumbling correlation times examined in these studies. Replacement of 14N by 15N decreases the relaxation rates as predicted for samples in which modulation of nuclear hyperfine anisotropy contributes to relaxation. Deuteration of the solvent does not affect T1e, which indicates that the electron−nuclear dipolar interaction with solvent nuclei does not make a significant contribution to T1e of nitroxyl radicals in this motional regime. The contributions to relaxation from one or more thermally activated processes that occur at rates comparable to the microwave frequency dominate the relaxation at tumbling correlation times longer than about 2 ns at X-band and S-band. The contributions from the thermally activated process(es) and from modulation of nitrogen nuclear hyperfine anisotropy increase as the microwave frequency is decreased, and the contribution from hyperfine anisotropy dominates at L-band.

Electron spin-relaxation via vibronic level of nickel (I) and nickel (III) cyanide complexes in NaCl single crystals

Electron spin–lattice relaxation rates for the low spin [Ni(CN) 4] 1− and [Ni(CN) 4] 3− complexes in NaCl host lattice were measured by the inversion recovery technique in the temperature range 7–50 K. The data for both paramagnetic species fit very well to a relaxation process involving localized anharmonic vibration modes, also responsible for the g-tensor temperature dependence.

Electron spin relaxation in solids-an application to spontaneously occurring radical centre in phenol-formaldehyde resins

An outline of electron spin-relaxation is briefly presented with mechanisms and processes of spin-lattice relaxation in ionic and amorphous solids. Electron spin resonance (EPR) and pulsed EPR measurements were performed in the temperature range 4-300 K on a radical occurring in a dried resol phenol-formaldehyde resin. The radical appears in a small concentration of about 1/spl times/10/sup 16/ radicals/g in 30/spl deg/C dried samples and the number of the radicals increases continuously with time up to 2/spl times/10/sup 17/ radicals/g after 100 days. Computer simulations of the EPR spectrum show that breaking of the dimethylene ether linkage probably forms the radical during synthesis reactions. Electron spin-lattice relaxation rate increases relatively slowly on heating and at <80 K is determined by interactions with two-level tunnelling systems in the polymer structure. For higher temperatures the relaxation is governed by interactions with centres having energy levels split by 298 cm/sup -1/. Phase relaxation is described by the phase memory time with rigid lattice limit T/sub M//sup 0/=2 /spl mu/s. This time is shortened above 100 K by thermally activated radical molecule motions with activation energy 85 cm/sup -1/. The electron spin echo envelope modulation (ESEEM) spectrum shows unresolved peaks at /sup 1/H indicating strong molecular dynamics and delocalisation of the unpaired electron.

Electron spin relaxation via vibronic level of rhodium(II) hexacyanide complex in KCl crystal.

Electron spin-lattice relaxation rates for the low-spin [Rh(CN)(6)](4-) complex in KCl were measured by the inversion recovery and saturation recovery techniques, in the range of 5 to 30 K. Angular variation experiments indicate that electron spin-lattice relaxation times present axial symmetry. The data fit very well to a relaxation process involving localized anharmonic vibration modes, also responsible for the g tensor temperature dependence.

Frequency dependence of electron spin relaxation for threeS = 1/2 species doped into diamagnetic solid hosts

Electron spin lattice relaxation rates (1/T1) were measured as a function of temperature at two or three microwave frequencies for threeS = 1/2 species in temperature ranges with different dominant relaxation processes. Between 10 and 50 K the contribution from the direct process to the relaxation rate was substantially greater at 94 than at 9.5 GHz for a vanadyl porphyrin doped into zinc tetratolylporphyrin. For bis(diethyldithiocarbamato)copper(II) doped into the diamagnetic Ni(II) analog the relaxation rate between 25 and 100 K is dominated by the Raman process and exhibits little frequency dependence between 9.2 and 94 GHz. For 4-hydroxy-2,2,6,6-tetramethylpiperidinoloxy (tempol) doped into a diamagnetic host the relaxation rate between about 40 and 100 K is dominated by the Raman process. In this temperature range, relaxation rates at 3.2, 9.2, and 94 GHz exhibit little frequency dependence. Above about 130 K, the relaxation rate for tempol decreases in the order S-band s> X-band > W-band. The relaxation rates in this temperature range fit a model in which 1/T1 is dominated by a thermally activated process that is assigned as rotation of the methyl groups on the nitroxyl ring.