Spin-lattice Relaxation Curves Research Articles

Bayesian Approach to T1 Analysis in NMR Spectroscopy with Applications to Solid State Physics

We applied the Bayesian framework to the analysis of nuclear spin–lattice relaxation curves. In the simplest case, nuclear spin–lattice relaxation is described by a single exponential function. However, relaxations to which the exponential function does not fit well are often observed in real NMR experiments. One of the reasons for those relaxations is the sample inhomogeneity. For such cases, it is common practice to analyze the curve by fitting a stretched exponential function exp(−(t/T1)β) to the data, where T1 is the nuclear spin–lattice relaxation time. Another possibility is the coexistence of different relaxation mechanisms. In this situation, the relaxation curves should be fitted by the summation of several relaxation functions. For scientists to interpret relaxation curves, a data-driven method is required to determine which of the two possibilities is more plausible. In this paper, we propose a Bayesian method to select the appropriate relaxation function and even the number of relaxation components. We demonstrate that our method effectively determines the relaxation model on the basis of numerical experiments and the experimental data of nuclear spin–lattice relaxation of the nonmagnetic semiconductor SmS.

Pseudo-gap in RuGa3: A microscopic point of view

We report a detailed study of the nature of the RuGa3in-gap states by means of precision microscopic methods: nuclear quadrupole resonance (NQR), nuclear magnetic resonance (NMR), and pump-probe spectroscopy. We observe a pronounced splitting of 69Ga nuclear spin-lattice relaxation curves below ∼40 K and between 70 and 145 K, although the corresponding NQR lines remain narrow over the entire temperature range under study. The slow relaxing component behaves like a typical phonon-induced relaxation way, while the fast relaxing one demonstrates signatures of paramagnetic (below ∼40 K) and activation (between 70 and 145 K) mechanisms. Moreover, additional Ga’ and Ga’’ positions with anomalously low electric field gradient were revealed for the first time for IrIn3-type structure gallides, which stay almost unchanged, at least up to 77 K. The observed microscopic features are accompanied with in-gap states saturation or depleting, which is seen as the resistivity mechanism crossover at ∼180 K and electron localization below 145 K evidenced by pump-probe spectroscopy. Based on our experimental results, we associate this pseudo-gap like behavior with inhomogeneously distributed electronic density defects, which manifest at both micro- (nuclear spin and phonon dynamics) and macroscale (bulk transport properties such as resistivity).

Crystallinity and Miscibility of Poly(vinyl isobutyl ether)/Poly(ε-L-lysine) Blends by Solid State 13C NMR Study

The relation between crystallinity and miscibility of semicrystalline polymer blends of poly(vinyl isobutyl ether) (PVIBE) and poly(e-L-lysine) (e-PL) is investigated by 13C cross-polarization with magic-angle-spinning (CPMAS) NMR (nuclear magnetic resonance) and DSC measurements. Analysis of the 1H spin-lattice relaxation curves observed from both PVIBE and e-PL signals, which are indirectly obtained from well-resolved 13C CPMAS NMR spectra, suggested that the domains of e-PL in the blends are in the range of 50–100 nm scale. Two-spin or three-spin models were used to simulate the 1H relaxation curves taking into account the contribution of a 1H spin-diffusion rate between PVIBE and e-PL. Furthermore, it was found that blending e-PL largely influences the crystallinity of PVIBE but that of e-PL is little affected by blending PVIBE except for 10/1 composition. The observed melting point of e-PL shifted towards lower temperature accompanied by PVIBE content. This shift was explained by the Gibbs-Thomson effect that the decrease of thickness of crystalline phase causes the depression of the melting point.

205Tl NMR study of vortex state of Tl 2Ba 2CuO 6+δ

We report a 205Tl NMR study of vortex state for an oriented polycrystalline sample of an overdoped high- T c superconductor Tl 2Ba 2CuO 6+δ ( T c∼85 K) with magnetic field 2 T along the c-axis. An obvious Redfield pattern of the 205Tl NMR spectrum for our sample at T=5 K indicates the vortex lattice state without local antiferromagnetic order at vortex cores. We emphasize that nonexponential nuclear spin-lattice relaxation curves indicate an imperfect vortex lattice or Bragg glass phase.

Pseudo-spin-gap and slow spin fluctuation inLa2−xSrxCuO4(x=0.13and 0.18) via63Cuand139Lanuclear quadrupole resonance

We analyzed nonexponential ${}^{63}\mathrm{Cu}$ nuclear spin-lattice relaxation curves for ${}^{63}\mathrm{Cu}$-enriched high-${T}_{c}$ superconductors: ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ with $x=0.13$ (slightly underdoped) and 0.18 (slightly overdoped), and studied the applicability of an impurity-induced nuclear spin-lattice relaxation theory. We found a remnant of pseudo-spin-gap effect on the host ${}^{63}\mathrm{Cu}$ nuclear spin-lattice relaxation time and slow inhomogeneous spin fluctuation via the impurity-induced relaxation time. The effect of slow spin dynamics was also observed in ${}^{139}\mathrm{La}$ nuclear spin-lattice relaxation. The inhomogeneous electron-spin fluctuation, which is associated with randomly distributed staggered moments on the ${\mathrm{CuO}}_{2}$ plane, smears the pseudo-spin-gap. The fact that the optimal ${T}_{c}\ensuremath{\sim}38\mathrm{K}$ is smaller than ${T}_{c}\ensuremath{\sim}96\mathrm{K}$ of ${\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ can be attributed to the depairing effect due to the slow spin fluctuation.

Formation of magnetic moments in the cuprate superconductor Hg 0.8Cu 0.2Ba 2Ca 2Cu 3O 8+ δ below Tc seen by NQR

We report pure zero field nuclear magnetic resonance (NQR) measurements on the optimally doped three layer high- T c-compounds HgBaCaCuO and HgBaCaCuO(F) with T c=134 K. Above T c two Cu NQR line pairs are observed in the spectra corresponding to the two inequivalent Cu lattice sites. Below T c the Cu NQR spectra show additional lines leading to the extreme broadened Cu NQR spectra at 4.2 K well known for the HgBaCaCuO compounds. The spin–lattice relaxation curves follow a triple exponential function with coefficients depend onto the saturation time (number of saturation pulses), whereas the spin–spin relaxation curve is described by a single exponential function. From the spin–lattice relaxation we deduced a complete removal of the Kramers degeneracy of the Cu quadrupole levels indicating that the additional lines are due to a Zeemann splitting of the 63/65Cu lines due to the spontaneous formation of magnetic moments within the CuO layers. Below 140 K, the spectra are well fitted by a number of 6 63/65Cu line pairs. From the number of the Cu lines, the position of the lines relative to each other and the complete removal of the Kramers degeneracy we deduced an orientation of the magnetic moments parallel to the c-axis with magnitudes of the order of 1000 G. We also discuss the possible microscopic origin of the observed internal magnetic fields.

Proton dynamics in phase II of CsHSO 4 studied by 1H NMR

Proton dynamics in phase II of CsHSO 4 have been studied by 1H NMR. 1H spectral line shapes were traced between 210 and 470 K, and 1H spin-lattice relaxation curves were measured between 310 and 470 K, taking into account the thermal history of the sample. The NMR results demonstrate that proton transfer between two neighboring SO 4 tetrahedra takes place much more easily than the reorientation of the SO 4 tetrahedra in phase II. Thus, the SO 4 reorientation limits the rate of the proton transport. Correlation times of the SO 4 reorientation are estimated from the second moments of 1H NMR spectra. The obtained parameters are τ 0=1.5×10 −9 s and E a=29 kJ/mol. The 1H spin-lattice relaxation in phase II is caused by motions much faster than the SO 4 reorientation.

Zn-doping dependence of the wipeout region around Zn in YBa 2(Cu 1− xZn x) 4O 8

We estimated the spread of the magnetically enhanced regions (wipeout regions) around Zn ions in high- T c superconductors YBa 2(Cu 1− x Zn x ) 4O 8 ( x=0, 0.005, 0.01, and 0.022) at T=4.2 K, via the planar 63Cu nuclear spin–lattice relaxation study with Cu nuclear quadrupole resonance spin-echo technique. From the analysis of nonexponential planar Cu nuclear spin–lattice relaxation curves, we found that the wipeout region per a Zn ion shrinks with Zn doping in the superconducting state. The shrinkage is associated with suppression of the host antiferromagnetic spin correlation, as a result from a dilution effect on the magnetic CuO 2 network.

The state of water in thermoresponsive poly(acryloyl-l-proline methyl ester) hydrogels observed by DSC and 1H-NMR relaxometry

Hydrogels that reversibly swell or shrink in water with decreasing or increasing temperature, respectively, were obtained by γ ray-induced polymerization of acryloyl-l-proline methyl ester in the presence of different amounts of a crosslinking agent. The role of water in the hydrated polymers was investigated by DSC and 1H-NMR relaxometry. From the curves of fusion of water determined by the former it was possible to ascertain that the amount of both freezing and non freezing water decreased with increasing the crosslinker percentage and/or swelling temperature. Moreover, at the temperatures higher than 37°C, the water absorbed by the different hydrogels is mostly present as non freezing water. The 1H-NMR relaxometry study enabled the spin–spin and spin–lattice relaxation curves to be analyzed. It was possible to distinguish three “populations” of protons and identify two of them with protons of freezing and non freezing water determined by DCS.

Measurement of spin-lattice relaxation times of 13C in organic solids

A transient nuclear Overhauser effect (NOE) makes measurements of the 13C spin-lattice relaxation times in organic solids complicated. Extended Solomon equations are applied in order to describe 13C spin-lattice relaxation with 1H r.f. field irradiation. Spin-lattice relaxation under r.f. irradiation is shown to be generally a triple-exponential process, but it can be reduced to be single-exponential under stronger r.f. field irradiation as well as in the absence of 1H initial magnetizations. Based on numerical calculations, the difference between spin-lattice relaxation curves obeying T 1 C < T 1 H and those obeying T 1 C < T 1 H is clearly indicated. The methyl group resonances in solid-state l-valine are examined, and the experimental results agree well with the theoretical results.

1H spin-lattice relaxation parameters in the length of human intestine resected for cancer.

1H spin-lattice relaxation curves were acquired for samples of intestinal adenocarcinoma (B) and of uninvolved tissue at the upper (A) and lower (C) resection margin of lengths of intestine taken at surgery from 20 patients. Each sample showed a wide distribution of relaxation times with the order of 90% of the signal in a single peak at long times. Several different single-parameter relaxation times computed from discrete-exponential analysis showed that most of the relaxation times for C and B are in the upper two-thirds of the range of times for A. The mean time for the tumor is about 10% longer (with p < 0.01) than for the upper resection margin. The difference between the tumor and the lower resection margin is not significant. Distribution width parameters associated with A and C were significantly larger than those associated with the tumors. Two-exponential fits indicate that the fast-relaxing component represents a smaller signal fraction for the tumor B than for A or C.

New results of spin-lattice relaxation in a-Si:H by pulsed ESR

Spin-lattice relaxation curves in undoped hydrogenated amorphous silicon (a-Si:H) have been directly observed by pulsed electron spin resonance (ESR) technique, for the first time. The new results have shown that the spin-lattice relaxation curves follow a stretched exponential form. They also show irreversible changes in the temperature dependence of the spin-lattice relaxation time not only for annealing but also light soaking procedures in device quality films.

Dipolar relaxation enhancement in inhomogeneous EPR lines with partial excitation. An application to plant photosystem II

The theory of dipolar relaxation enhancement is extended for incompletely excited, randomly oriented anisotroiric electron spin systems with arbitrary spin quantum numbers. Numerical calculations are presented of the spin-lattice relaxation in such systems. The relaxation is found to be generally dependent on the field position in the EPR line and to be nonexponential. Anisotropic hyperfine interactions of magnitude comparable to the g anisotropy reduce the field position dependence of the relaxation as well as the dependence of the EPR signal intensity on the magnitude of the dipolar broadening. The nonexponentiality of the experimental spin-lattice relaxation curves measured previously for plant photosynthetic material can be well explained with the theoretical model.

Magnetic resonance lifetimes as a bridge between transport and structural properties of natural porous media

Results are reported of an NMR spin-lattice relaxation study on a suite of sandstone cores fully saturated with brine. Relaxation curves of 1H nuclei of water filling the pores, obtained by Inversion Recovery pulse sequence, were analyzed to extract relaxation lifetime values. These lifetimes have been recently proposed as suitable to characterize the relaxation behavior of fully saturated sandstones as well as able to predict permeability in conjuction with porosity. An improvement in the comprehension of interplay among geometry and transport properties of the pore space can be obtained from the comparison between these lifetimes and conventionally measured properties. The results obtained are in agreement with previous results on sandstones and reproduce very well results on model systems. They led to a functional dependence among permeability ( k), porosity (φ) and average lifetimes ( T ls) that allowed a good estimation of k from φ and T ls. The dependence of the error in the permeability estimation in terms of the variations of φ and T ls exponents in the relationship that predicts k was also discussed. The reason of the correlation between k and T ls lies in their common dependence on the surface-to-volume ratio S/ V p. In this way, 1H spin-lattice relaxation lifetimes behave as a bridge between structural and transport properties and may be viewed as a dynamically weighted version of S/ V p. The discussion of these results can help in clarifying the informative content of 1H spin-lattice relaxation curves on a broad spectrum of heterogeneous systems with high surface-to-volume ratio.

A proton relaxation study of immiscible liquid arrangement in microporous structures

The relaxation behaviour of immiscible hydrogenated liquids in well characterized microporous porcelain structures after a well defined stepwise preparation was studied to obtain information on the contact with surfaces and on the reciprocal arrangement in the pore space. Water-wet samples were fully saturated by brine, then brought to irreducible water saturation by oil and finally to residual oil saturation by brine. This step-wise preparation was repeated using deuterium oxide instead of brine. The observed changes of the 1 H spin-lattice relaxation curves reflected each step of preparation. The quantitative analysis of the curves gave evidence that no contact occurred between surfaces and oil because of a layer of water on the surface, except when only oil was present. On the contrary, when the wettability properties of the surfaces were changed, our data indicated that a contact between oil and walls occurred. So, the traditional picture of water-oil arrangement at the pore-length scale was verified for water-wet samples, whereas a more complex picture arose for oil-wet samples. While on one hand this study on model systems can help in explaining the information content of relaxation curves in more general conditions and systems, on the other hand it yields useful indications on some solid-liquid and liquid-liquid interaction effects in the displacement processes by water or by oil in microporous geometries.

The influence of MAS on spin-lattice relaxation curves and nuclear spin excitation of half-integer spin quadrupolar nuclei in solids

The influence of MAS on spin-lattice relaxation curves and nuclear spin excitation of half-integer spin quadrupolar nuclei in solids

Different degrees of hydration in water–oil microemulsions by low-resolution 1H magnetic relaxation analysis

The purpose of the research was to establish whether the water configurations, detected by previous differential scanning calorimetry (DSC) analysis, could give rise to different or characteristic nuclear magnetic resonance relaxations. We report the results of a study on water–hexadecane microemulsions at different water contents. The 1H spin–spin and spin–lattice relaxation curves were obtained at 20 MHz and 310 K. The trends of all best-fit relaxation parameters versus water concentration were compared with those obtained for D2O microemulsions with the same experimental conditions and fitting procedures. Two different H2O microemulsion "states" were identified: (i) all the systems without "free water" (defined by DSC as water melting at 273 K) were characterized by 1H spin–spin and spin–lattice relaxation curves well described by two exponential functions and (ii) all the systems with free water were characterized by relaxation curves well described by three exponential functions. The identification of the main phases of the microemulsions interphasal region and continuous medium, besides free water, seems possible on the basis of the 1H magnetic relaxation characteristics.

Water 1H spin-lattice relaxation as a fingerprint of porous media

The 1H spin-lattice relaxation curves of water in samples of natural porous media can be thought of as “fingerprints” of the porous samples. Also the whole of traditional petrophysical properties (permeability, irreducible water saturation, etc.) can be thought of as “fingerprints” of the porous samples. The characteristics of the pore space determine on one hand the relaxation curve shape, and on the other the petrophysical properties. The understanding of this correspondence can contribute to a better definition of the concept of the architecture of a porous medium. At this purpose we have obtained 1H spin-lattice relaxation curves from a collection of standard sandstone cores of known petrophysical properties and characterized by the same surface properties. The results corroborate the idea that the structure of relaxation curves contains information on the distance scale and on the architecture of the pore space, even if it is difficult to extract it without ambiguities. Different methods of curve fitting were performed and compared with the aim of getting the maximum information from the relaxation curves. Several aspects of this kind of investigation indicate the analogies between 1H response of water confined in porous media and in biological tissues.

Variations of the 1H spin-lattice relaxation in a fatty liver model as compared to normal liver

We report the results of an in vitro study on ethionine-injected rat liver (EI) and on normal rat liver (C) performed analyzing with iterative fitting procedures the 1H spin-lattice relaxation curves detected by IR pulse sequence at 20 MHz and at 37°C on fresh excised samples. Single-exponential functions did not adequately describe the experimental curves both in EI and in C group. The analysis of the curves by two-exponential hypothesis showed a small portion of the signal characterizable by a time constant of about 80 ms, common both to EI and to C samples. A slowing of about 30% in the relaxation characterized the remaining portion of the curve (90–95%) in EI as compared to C samples. The hypothesis that the 1H of the triglycerides vacuoles present in EI livers had a relaxation curve additional to the remaining signal was checked by three-exponential analysis. The results were not in contrast with the known value of the triglycerides percentage content and with the spin-lattice relaxation time of the CH 2 group 1H obtained in different experimental conditions in the same fatty liver model. The negative results of the three-exponential analysis on normal liver curves as well as the favorable controls performed to test the analysis procedure supported further this hypothesis. The remaining signal after subtraction of the triglycerides contribution showed still the small fast portion and the increase of the relaxation time of the major portion (from ∼300 ms up to ∼400 ms) as compared to C samples. Moreover this noticeable slowing of the 1H spin-lattice relaxation appeared independent from the water content and from the steatosis extent, as detected both macroscopically and at histological level.

EPR relaxation measurements of Photosystem II reaction centers: influence of S-state oxidation and temperature

The spin-lattice relaxation time of the EPR signal of the tyrosine radical D+ has been measured with electron spin echo spectroscopy in the range 5–30 K in Photosystem II preparations with intact oxygen evolving complex (OEC). The charge storage state of the OEC was set by illumination with a series of flashes and monitored by measuring the multiline EPR signal of the S2-state. The OEC was synchronized to 100% S1 initial state by dark-adaptation and one preflash. Agreeing with previous work (De Groot, A., Plijter, J.J., Evelo, R., Babcock, G.T. and Hoff, A.J. (1986) Biochim. Biophys. Acta 848, 8–15), the spin-lattice relaxation curves were foundto be bi-phasic. The average relaxation time τ¯ of each S-state was calculated from the data obtained for the 0—3 flash sample and the known S-state distribution,τ¯was found to be maximal in the S1-state. It decreased about 40% for the S2-state, was essentially the same for the S2- and the S3-states and decreased again by about 55% for the S0-state. These results are similar to those obtained earlier by cw EPR (Styring, S. and Rutherford, A.W. (1988) Biochemistry 27, 4915–4923). At 5 K the two exponentials describing the relaxation curves had characteristic timesτf, and τs that differed by an order of magnitude. Their amplitude was about equal, except for S0 where the faster process predominated. At 20 K the characteristic time of both the fast and the slow process was reduced by a factor of about five;their amplitudes were again about equal. The observed relaxation times τf and τs were deconvoluted as a function of S-state by an approximate method. At 5 K it was found that τf was about twice as fast for S0 and S3 than for S, and S2 (1.3 vs. 2.6 ms) and τ sabout twice as fast for S0, S2, S3 than for S1 (13.7–14.5 vs. 28.6 ms). The same trend was observed at higher temperatures. Interpreting the results with relaxation enhancement theory and integrating them with the results from cw EPR, NMR and EXAFS spectroscopy the following model for the OEC is presented, (i) To explain the biphasic relaxation of D+ it is suggested that two Mn are close to D+ at different distances, enhance the relaxation of D+and are not magnetically coupled. Their oxidation state differs by 1 unit, is probably Mn3+ and Mn4+, and does not change during the S0 → S3 sequence. It is postulated that at high temperature there is a charge resonance between the two Mn ions that is frozen out when cooling to cryogenic temperature, (ii) Two of the four Mn of the OEC form an antiferromagnetically coupled binuclear cluster in the oxidation state Mn2+·Mn3+, Mn3+·Mn3+, Mn3+·Mn4+, Mn3+·Mn4+ in the S0, S1, S2 and S3-sta respectively, (iii) From the temperature dependence of the relaxation of D+ in the S0-state, it is estimated that the distance between the Mn cluster and D+ is 30–40 .