The elucidation of the rotational diffusion tensor of a spin probe using NMR and ESR

A combination of ESR lineshape studies and NMR relaxation time measurements permits the complete elucidation of the rotational diffusion tensor of a spin probe. The technique employs both paramagnetic (Cu(II)) and deuterated diamagnetic (Ni(II)) homologs of bis[pyrollidine-N-carbodithioato]metal(II) complexes. The lineshape and relaxation time measurements were analyzed in terms of spectral densities which in turn were inverted to give the principal elements of the diffusion tensor. The results obtained insights into the pitfalls of the commonly made assumption of isotropic rotational diffusion.     

Evaluation of Conformational dynamics properties of spin-labelled proteins at different degrees of nitroxide radicals immobilization

Spin-labelling has found wide applications in elucidation of the dynamic behaviour of biological macromolecules in aqueous media and biomembranes. Most of the proposed methods aimed at estimation of macromolecular correlation times (τ_c) assume, however, spin label molecules rigidly bound within the protein matrix. To avoid this limitation theoretical models which involve additional dynamic parameters to characterize the spin label motion should be considered. We have used ESR spectra analysis technique which permits quantitative separation of slow macromolecular rotation (described by the rotational correlation time, τ_c) and fast anisotropic relative to protein nitroxyl radical motion (described by the “order parameter”,S). This method was applied to study: i) conformational dynamics of covalently and non-covalently spin-labelled human serum albumin (HSA) in solution; ii) protein-protein (antigen-antibody) interactions in a model system containing spin-labelled bovine serum albumin (BSA) and anti-BSA immunoglobulin (IgG) in solution; and iii) dynamic properties of membrane-bound proteins: H⁺-ATPase (CF₁-CF₀ coupling factor of photophosphorylation) and Photosystem I pigment-protein reaction centre complex (PSI RC) isolated from spinach chloroplasts and reconstituted in proteoliposomes.     

Electron spin-lattice relaxation in noncommon metals YBa2Cu3Ox and Rb1C60

Using an original modulation technique, the electron spin-lattice relaxation have been investigated in two noncommon metals: YBa₂Cu₃O_x, high-T_c material doped with 1% Gd, and Rb₁C₆₀, linear polymer phase fulleride. In the first case, the Korringa-like temperature dependence of the Gd³⁺ longitudinal relaxation time T₁, is found forx = 6.59 in a wide temperature range 4.2 <T < 200 K, both above and below T_c = 56 K. Atx = 6.95 (T_c = 90 K), the T₁ behavior within 50 <T < 200 K is evidently affected by spin gap opening with the gap value of about 240 K. At 200 K, an unexpected acceleration of the relaxation rate takes place, suggesting some change in the relaxation mechanism. The data are discussed in terms of the Barnes-Plefke theory with allowance made for microscopic separation of the normal and superconducting phases. In Rb₁C₆₀, the evolution of the ESR line and relaxation rates have been studied accurately in the range of the metal-insulator transition (below 50 K). Interpretation is suggested which takes into account breaking down the relaxation bottleneck due to opening of the energy gap near the Fermi surface. The gap value of about 100 cm^?1 is estimated from the analysis of relaxation rates, lineshape and spin susceptibilities.     

Mössbauer spectroscopic studies of spin crossover in tris(N, N′-dialkyldithiocarbamato) iron (III) complexes: effect of alkyl substituents

Spin crossover behavior in tris(N,N′-dialkyldithiocarbamato) iron(III) complexes with varying alkyl groups has been studied by variable temperature magnetic moment and Mössbauer spectral studies. All the complexes may be divided into three broad groups; high spin (μ _eff > 4.8 BM), intermediate spin (μ _eff?=?3.5???4.6 BM) and low spin (μ _eff?< 3.2 B.M). Room temperature (RT) Mössbauer spectra exhibit an asymmetric doublet resolved into two doublets corresponding to high and low spin states. Estimated % contributions of HS and LS states and calculated μ _eff were comparable with the experimentally determined values. It has been shown that some complexes undergo spin crossover, ⁶A₁g→²T₂g whereas others exhibit spin transitions ⁶A₁g →⁴T₁g or ⁴T₁g → ²T₂g. IR spectra show characteristic ν _(Fe???S) bands in the region 208–285 (HS) and 311–380 cm^???1 (LS). Nature of alkyl groups affects the spin state.     

Spin gap, phase separation and d-wave pairing as revealed by electron spin-lattice relaxation in 123 and 124 YBaCuO systems doped with Gd3+

With an original modulation technique, the Gd³⁺ electron spin-lattice relaxation has been investigated in normal and superconducting states of YBa₂Cu₃O_6+x (123) and YBa₂Cu₄O₈ (124) compounds doped with 1% Gd. In the 123 sample withx = 0.9T _c = 90 K), theT ₁ behavior within 50 <T< 200 K reveals the [1 ? tanh²(Δ/2kT)]/T dependence typical of a spin gap opening with Δ ≈ 240 K. Below 50 K, the exponential slowing down ofT ₁ is limited by the Korringa-like behaviorT ₁ T = const); the same Korringa-like law is found in the 123 sample withx = 0.59 (T _c = 56 K) within the total 4.2–200 K temperature range. This is interpreted in terms of microscopic separation of the normal and superconducting phases allowing for the electron spin cross-relaxation between them. In the 124 sample (T _c = 82 K), the Gd³⁺ relaxation rate below 60 K is found to obey a power lawT _n with an exponentn ≈ 3. Such a behavior (previously reported for nuclear spin relaxation) is indicative of the d-wave superconducting pairing. Additional paramagnetic centers characterized by relatively slow spin-lattice relaxation are found in both 123 and 124 systems. A well-pronounced change in theT ₁ temperature dependence atTT* ≈ 180–200 K is observed for these slowly relaxing centers as well as for the conventional, fast-relaxing Gd³⁺ ions, suggesting microscopic phase separation and a change in the relaxation mechanism due to electronic crossover related with the opening of the spin gap. This hypothesis is supported by some “180 K anomalies” previously reported by other authors.     

Temperature dependence of the electronic spin relaxation of DCNQI salts

For the elucidation of the charge and spin dynamics of the radical anion salts of DCNQI with metallic counterions we have performed cw- and pulsed ESR experiments (βB _pp,T _1e ^?1 andT _2e ^?1 ) between 300 and 4 K at nine salts differing in counterions and sidegroups, respectively. We can explain the relaxation rates by dipolar electron-electron interaction and spin-orbit contribution. In the high temperature range we have a gradual decrease in the number of charge carriers by interband transitions without a slowing down of the mobility. With complete localization of the electron spins (no mobile electrons anymore) exchange interaction governs the spectral density, becoming strongly temperature dependent due to effective spin exchangeJ _eff(T), explained by an extended REHAC-model. This effective spin exchangeJ _eff(T) includes for the first time a contribution by the metallic counterions. For spin-orbit interaction we developed a model based on F. Adrian [1] not depending on the mixture of Bloch and spin states as given by Elliott [2]. This is achieved by the inclusion of the electronic probability on atoms with higher atomic numbers, modulated by phonons. This model explains the drastic changes in the ESR linewidth of different radical ion salts of DCNQI and allows inductively the prediction of the electronic properties of new radical ion systems of which just the molecular and crystal structure is known.     

Experiment and dynamic simulations of radiation damping of laser-polarized liquid<Superscript>129</Superscript>Xe at low magnetic field in a flow system

Radiation damping is generally observed when a sample with high spin concentration and high gyromagnetic ratio is placed in a high magnetic field. However, we firstly observed liquid-state¹²⁹Xe radiation damping with laser-enhanced nuclear polarization at low magnetic field in a flow system in which the polarization enhancement factor for the liquid-state¹²⁹Xe was estimated to be 5000, and, furthermore, theoretically simulated the envelopes of the¹²⁹Xe free induction decay and spectral lineshape in the presence of both relaxation and radiation damping with different pulse flip angles and ratios ofT ₂ ^* /T _rd. The radiation damping time constantT _rd of 5 ms was derived on the basis of the simulations. The reasons of depolarization and the further possible improvements were also discussed.     

Effects of off-resonance irradiation, cross-relaxation, and chemical exchange on steady-state magnetization and effective spin-lattice relaxation times

In the presence of an off-resonance radiofrequency field, recovery of longitudinal magnetization to a steady state is not purely monoexponential. Under reasonable conditions with zero initial magnetization, recovery is nearly exponential and an effective relaxation rate constant R_1eff = 1/T_1eff can be obtained. Exact and approximate formulas for R_1eff and steady-state magnetization are derived from the Bloch equations for spins undergoing cross-relaxation and chemical exchange between two sites in the presence of an off-resonance radiofrequency field. The relaxation formulas require that the magnetization of one spin is constant, but not necessarily zero, while the other spin relaxes. Extension to three sites with one radiofrequency field is explained. The special cases of off-resonance effects alone and with cross-relaxation or chemical exchange, cross-relaxation alone, and chemical exchange alone are compared. The inaccuracy in saturation transfer measurements of exchange rate constants by published formulas is discussed for the creatine kinase reaction.     

〈S0〉Cs and 〈S0〉Rb relaxation in the presence of buffer gas and the spin exchange between Cs and Rb

〈S⁰〉_Rb and 〈S⁰〉_Cs relaxation is studied in the presence of buffer gas and spin exchange between Cs and Rb. Spin exchange collisions are found to equalize the relaxation rates of Rb and Cs polarization. This result is completely confirmed experimentally for the relaxation of the first diffusion mode.     

NMR spectral densities and two dimensional diffusion in TiS2(NH3)1.0 and TaS2(NH3)x

NMR measurements of proton spin-lattice relaxation times T₁ and T_1? in the layered intercalation compounds TiS₂(NH₃)_1.0 and TaS₂(NH₃)_x (x = 0.8, 0.9, 1.0) are reported as functions of frequency and temperature (100 K – 300 K). These observations probe the spectral density of magnetic fluctuations due to motions of the intercalated molecules at frequencies accessible to the T₁ (4–90 MHz) and T_1? (1–100 kHz) measurements. Since the average molecular hopping time (τ) can be changed by varying temperature, different regions of the spectral density can be examined. For T > 200 K, both T^?1₁ and T^?1_1? vary logarithmically with frequency, reflecting the two dimensional character of the molecular diffusion. The temperature dependence of T₁ suggests that a more accurate picture of the short time dynamics is required. No dependence of relaxation rate on vacancy concentration is found.     

Diffusion and NMR spin lattice relaxation of 1H in α′ TaHx and NbHx

The concentration and temperature dependence of the self diffusion coefficient, D, of H in Group V transition metals Nb and Ta has been measured for the α^' phase. The nuclear magnetic resonance spin lattice relaxation time, T₁, was measured in Ta only. A pulsed field gradient, NMR spin echo technique was utilized to measure D. In both systems, the activation energy increases with hydrogen concentration while the pre-exponential factor is not strongly concentration dependent. The diffusion results are compared with published values of the macroscopic diffusion coefficient, $\text{D}{}^1$, obtained from Gorsky effect measurements. Values of the thermodynamic factor [$\text{(}\text{ρ}\text{kT}\text{)(}\text{?μ}\text{(?ρ)}$] are found for selected ρ and T, where μ is the chemical potential and ρ is the density of hydrogen atoms. These values agree with known determinations of the same factor obtained from the Gorsky effect relaxation strengths, but the agreement with results from solubility measurements is less satisfactory. NMR relaxation is partitioned into conduction electron (T^?1_1e) and dipolar (T^?1_1d) relaxation rates. The observed x dependence of ($\text{D}\text{T}{}_{\mathrm{1d}}$) is inconsistent with random occupancy of tetrahedral sites, and it is suggested that a repulsive interaction exists between H atoms on nearest neighbor sites.     

Temperature dependence of the rotational life times in solid H2

We have studied the temperature dependence of the nuclear transverse and longitudinal relaxation times in solid H₂ for ortho concentrations 10^-3 < X < 10^-2 between 0.4 K and the triple point, 13.9 K. We find a striking temperature dependence in T₂ over the whole temperature range. This new effect is ascribed to a coupling between molecular rotation and lattice vibrations, which is brought into evidence by the narrow width of the spectral density of the rotational fluctuations at low X.     

Spin diffusion in the nuclear magnetic relaxation of isotopically labelled (CH)x

Isotopically labelled (CH)_x samples have been studied to probe the influence of nuclear spin diffusion on the relaxation mechanisms of polyacetylene. The results are discussed in terms of two spin species: those relaxing by direct interaction with solitons and those diffusing by mutual flip-flop towards this well relaxed core. Predictions are made for the time dependence of magnetization recovery and for the frequency dependence of long T₁.     

NMR investigations of dynamical processes in orientationally ordered and disordered NaCN,RbCN and CsCN

The nuclear spin lattice relaxation timeT ₁ of the²³Na,⁸⁵Rb,⁸⁷Rb,¹³³Cs,¹⁴N nuclei is measured in NaCN, RbCN and CsCN as a function of temperature below and above the ferroelastic phase transition temperatureT _c. BelowT _c the behaviour ofT ₁ of the alkali nuclei renders possible to determine the flip frequency of the CN molecules and its temperature dependence. AboveT _c from the¹⁴NT ₁ the correlation time τ_c of the rotational motions of the CN molecules and its temperature dependence is determined. An empirical rule is verified demonstrating that atT _c the correlation times take nearly the same values for all cyanides. For the high and low temperature phases one obtains atT _c about τ_c=5·10^?13s and τ_c=5·10^?11s, respectively. The results are discussed with respect to the mechanism of the phase transition.     

Pulsed EPR hole-burning experiment on dangling bond centers in a-Si:H aerosol particles formed by thermal decomposition of silane

Si dangling bond centers in aerosol particles of amorphous hydrogenated silicon formed by thermal decomposition of SiH₄ in Ar were studied by pulsed electron paramagnetic resonance. The hole-burning and inversion-recovery experiments demonstrate that large-scale rapid spectral diffusion takes place in the samples with high spin concentration. Correlation times τ_c of the spectral diffusion and spin-lattice relaxation timesT ₁ were obtained in the temperature range between 77 and 290 K. Above 130 K, τ_c andT ₁ are proportional one to the other. The unusual feature of this spectral diffusion is that the shape of the central part of the spectral hole does not change when the delay time increases. The other paramagnetic centers previously investigated showed a remarkable change of the hole shape which was induced by modulation of dipolar interaction due to spin flips. It is suggested that the observed anomaly in the Si dangling bond centers arises due to cooperative spin flips.     

Separation of Anisotropy and Exchange Broadening Using N CSA–N–H Dipole–Dipole Relaxation Cross-Correlation Experiments

Based on the measurement of cross-correlation rates between ¹⁵N CSA and ¹⁵N–¹H dipole–dipole relaxation we propose a procedure for separating exchange contributions to transverse relaxation rates (R₂ = 1/T₂) from effects caused by anisotropic rotational diffusion of the protein molecule. This approach determines the influence of anisotropy and chemical exchange processes independently and therefore circumvents difficulties associated with the currently standard use of T₁/T₂ ratios to determine the rotational diffusion tensor. We find from computer simulations that, in the presence of even small amounts of internal flexibility, fitting T₁/T₂ ratios tends to underestimate the anisotropy of overall tumbling. An additional problem exists when the N–H bond vector directions are not distributed homogeneously over the surface of a unit sphere, such as in helix bundles or β-sheets. Such a case was found in segment 4 of the gelation factor (ABP 120), an F-actin cross-linking protein, in which the diffusion tensor cannot be calculated from T₁/T₂ ratios. The ¹⁵N CSA tensor of the residues for this β-sheet protein was found to vary even within secondary structure elements. The use of a common value for the whole protein molecule therefore might be an oversimplification. Using our approach it is immediately apparent that no exchange broadening exists for segment 4 although strongly reduced T₂ relaxation times for several residues could be mistaken as indications for exchange processes.     

Proton spin relaxation of butenes and butane in CaNaA zeolites

Using nmr pulse techniques the temperature dependence of proton spin relaxation times T₁ and T₂ of n-butene and butane molecules adsorbed on CaNaA zeolites with different content of Ca⁺⁺ ions has been investigated. The observed diminution of correlation times with rising degree of Ca⁺⁺ exchange can only be explained if translational motions, i.e. jumps between the supercages, dominate the proton spin relaxation of the adsorbates. Peculiarities in the microdynamical behaviour of the various n-butenes are in accordance with the model of electrostatic interactions between molecular dipole moments and electric fields in A zeolites as proposed by Tempère and Imelik in order to explain the stereoselectivity of the isomerization of n-butenes in A zeolites. Applying Torrey's well-known theory of nmr relaxation as dominated by translational jumps with arbitrary lengths, the mean time between two subsequent jumps has been estimated. In combination with measurements of self-diffusion coefficients by Kärger and Renner, these values lead to mean jump lengths which are reasonable compared with the distance of two neighbouring large zeolitic cavities. In order to interpret the methyl reorientation which dominates the longitudinal proton spin relaxation of the adsorbed hydrocarbons at lower temperatures, a model for calculating the intermolecular contribution to the relaxation rate has been discussed.     

Pulsed ESR on the organic ion radical salt: 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-[TCNQ]2

We present firstT _1e ^?1 andT _2e ^?1 measurements on the organic ion radical salt 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-(TCNQ)₂ as function of temperature and of orientation. The electronic spin diffusion constant could be determined directly by the electron spin echo field gradient technique:D (300 K)=0.03±0.02 cm²/sec. Pulsed ESR experiments have — in comparison to conventional cw-ESR — the advantage to monitor viaT _1e ^?1 andT _2e ^?1 the spectral density of dynamical processes at different frequencies. This is shown in a general manner on 3,3′-diethyl-4,4′-dimethyl-2,2′-thiazolocyanine-(TCNQ)₂. Between 300 and 60 K,T _1e ^?1 andT _2e ^?1 are close in amplitude and have a similar temperature dependence. At 60 K their degeneracy is lifted, yielding a quantitative value for the effective spin exchange between localized spinsτ _ex ^?1 sec^?1 and via the absolute value of the relaxation an average distance of the localized centers of about 12 Å. The dynamical data as evaluated above cannot be correlated with the conductivity, clearly indicating that the conduction electrons are a minority, not being monitored by the ESR-experiments.     

H and K spin-lattice relaxation, ionic motion and Raman processes in the proton conducting KHSeO4 single crystal

The spin-lattice relaxation rates of ¹H and ³⁹K nuclei in KHSeO₄ crystals were studied in the temperature range 160-400 K. The spin-lattice relaxation recovery of ¹H nucleus in this crystal can be represented with a single exponential function, and the relaxation T₁⁻¹ curve of ¹H can be represented with the Bloembergen-Purcell-Pound (BPP) function. The relaxation process of ³⁹K with dominant quadrupole relaxation can be described by a linear combination of two exponential functions. T₁⁻¹ for the ³⁹K nucleus was found to have a very strong temperature dependence, T₁⁻¹=βT⁷. Rapid variations in relaxation rates are associated with critical fluctuations in the electronic spin system. The T⁷ temperature dependence of the Raman relaxation rate is shown here to be due to phonon-magnon coupling.     

Critical behaviour of the ising model in a transverse field

A theory for the critical behaviour of the Ising model in a transverse field is presented. The existence of a central component in the spectral density of the longitudinal spin relaxation function is shown to result self-consistently from decay into itself and energy-fluctuation diffusion mode. Estimates of the various quantities are made forT nearT _c , the damping is seen to be temperature dependent. Our theory is appropriate for the caseΓ ～J whereΓ andJ are the magnitudes of the transverse field and the exchange interaction between the spins respectively. Its relevance to neutron scattering data on Van Vleck paramagnets is discussed.