Quantitative measurement of longitudinal and transverse cross-relaxation rates: an application to the analysis of the internal dynamics of ranalexin in water and trifluoroethanol.

We describe a quantitative processing method which gives access to the longitudinal and transverse cross-relaxation rates from off-resonance ROESY intensities. This method takes advantage of the dependence of the off-resonance ROESY experiments at any mixing time and any spin-lock angle θ on two relaxation matrices, the longitudinal and the transverse ones. This allows one to take into account multistep magnetization transfers even if the measurements are performed only at one or two mixing times. The ratio of the longitudinal to transverse cross-relaxation rates can then be used as a local indicator of the internal dynamics, without assuming a structure or a model of motion. After validation of this processing method by numerical simulations, it is applied to the analysis of the dynamics of the peptide ranalexin dissolved in pure water and in water/TFE.     

On the role of experimental imperfections in constructing 1H spin diffusion NMR plots for domain size measurements

We discuss the precision of 1D chemical-shift-based ¹H spin diffusion NMR experiments as well as straightforward experimental protocols for reducing errors. The ¹H spin diffusion NMR experiments described herein are useful for samples that contain components with significant spectral overlap in the ¹H NMR spectrum and also for samples of small mass (<1 mg). We show that even in samples that display little spectral contrast, domain sizes can be determined to a relatively high degree of certainty if common experimental variability is accounted for and known. In particular, one should (1) measure flip angles to high precision (≈±1° flip angle), (2) establish a metric for phase transients to ensure their repeatability, (3) establish a reliable spectral deconvolution procedure to ascertain the deconvolved spectra of the neat components in the composite or blend spin diffusion spectrum, and (4) when possible, perform 1D chemical-shift-based ¹H spin diffusion experiments with zero total integral to partially correct for errors and uncertainties if these requirements cannot fully be implemented. We show that minimizing the degree of phase transients is not a requirement for reliable domain size measurement, but their repeatability is essential, as is knowing their contribution to the spectral offset (i.e. the J₁ coefficient). When performing experiments with zero total integral in the spin diffusion NMR spectrum with carefully measured flip angles and known phase transient effects, the largest contribution to error arises from an uncertainty in the component lineshapes which can be as high as 7%. This uncertainty can be reduced considerably if the component lineshapes deconvolved from the composite or blend spin diffusion spectra adequately match previously acquired pure component spectra.     

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.     

Separation of cross-relaxation and exchange in two-site spin systems with weak spin-spin couplings

A ratio relating the cross-relaxation rates, rate constants, and cross-peak and diagonal peak integrals is used for the analysis of exchanging two-site spin systems with weak scalar spin-spin couplings to extract the rate constants and cross-relaxation rates contributing to the same cross-peaks in two-dimensional nuclear Overhauser enhancement spectra (2-D NOESY). The method to separate contributions from cross-relaxation and chemical exchange into the cross-peaks in NOESY spectra was applied to investigate the intramolecular dynamics of trisulfide 4H, 8H-naphtho[1,8-ef]1,2,3-trithiocine in solutions.     

NOESY around the critical point ωτc = 1.12. Precise determination of proton-proton distances and reorientation correlation times with two-field NOESY

When nuclear Overhauser enhancement spectroscopy (NOESY) experiments are performed around the critical point ωτ_c = 1.12, internuclear cross-relaxation rates are dependent on the resonance frequency ω, where τ_c is the reorientation time of the distance vector between two magnetic dipoles. Therefore, the correlation times and, consequently, the internuclear distances can be determined precisely by measuring the cross-relaxation rates under two magnetic fields. An application with a cyclic pentapeptide is given as an example, demonstrating the use of the two-field NOESY method in molecular structure studies. NOESY experiments with mixing times beyond 500 ms are discussed.     

THE APPLICATIONS OF NUCLEAR SPIN RELAXATION TO POLYMER DYNAMICS AND INTERMOLECULAR INTERACTIONS

The correlation functions of the side - groups and side ?chains of polymers are obtained for nuclear spin relaxation if the segmental motion of the polymers is described by VJGM model, these functions are derived from unequal two ?side and three -site jump internal rotation, diffusion internal rotation, restricted internal rotation and multiple internal rotation. The corresponding spectral density functions are also given, and these functions are used to interpret the nuclear spin relaxation data of the side-groups of some polymers. The average spectral density functions of side-groups are derived under the magic angle spinning, the correlation times and diffusion coefficients of the side-groups of crosslinked poly (methyl methacry-latcs) and solid poly(vinylbutyral) are obtained by using these average spectral density functions. The multiphase structures of nylon 6, poly (ethylenc glycol) and its complexes are investigated with cross ?polarization and magic angle spinning techniques.Three methods using     

Tilt Angle Dependence of Cross-Relaxation in Off-Resonance ROESY

We present an efficient experimental method to evaluate whether the effective cross-relaxation rate between a pair of spins vanishes when applying an off-resonance spin-lock field. It is shown that the cross-relaxation rate can be made to vanish even when the two spins concerned resonate at different offsets and experience significantly different tilt angles of their respective spin-lock fields. This is verified experimentally using a sample of 15N-labeled human ubiquitin, through selective excitation of chosen amide protons. The results are relevant for the quantitative interpretation of off-resonance ROESY experiments.     

Intermolecular dipole-dipole relaxation of (129)Xe dissolved in water

Intermolecular (129)Xe-(1)H nuclear Overhauser effects and (129)Xe longitudinal relaxation time measurements were used to demonstrate that the dipole-dipole coupling is the dominant relaxation mechanism for (129)Xe in water, at room temperature. (129)Xe-(1)H cross-relaxation rates were derived to be sigma(XeH) approximately 3.2 +/- 0.3 x 10(-3) s(-1), independent of xenon pressure (in the range of 1-10 bar) and of the presence of oxygen. Corresponding xenon-proton internuclear distances were calculated to be 2.69 +/- 0.12 A. Using the magnitude of the dipole-dipole coupling and the spin density ratio between dissolved xenon and bulk water, it is estimated that (129)Xe-(1)H spin polarization-induced nuclear Overhauser effects would yield little net proton signal enhancement in water.     

Separation of cross-relaxation and exchange in two-site spin systems without resolved couplings

Variable temperature two-dimensional nuclear Overhauser enhancement experiment (2-D NOESY) is used to extract the rate constants and cross-relaxation rates that contribute to the same cross-peaks in NOESY spectra. Rate constants (k _AB) and cross-relaxation rates (R _AB) for two-site spin systems are related to the ratio between the cross-peak and diagonal peak integrals (F) by the expression:R _AB -k _AB = (1/2τ _m)ln[(1 -F)/(1 +F)], where τ_m is the mixing time. As a model, we investigated the exchange processes in a system of dimer calix[4]arenes of C_4v symmetrical configuration with guest inclusion (benzene or benzene-d₆), where the measurement of exchange processes is hindered by the presence of strong nuclear Overhauser enhancement between protons in adjacent aromatic rings in the cone conformation of the calix[4]arene.     

Intermolecular Dipole–Dipole Relaxation of Xe Dissolved in Water

Intermolecular ¹²⁹Xe–¹H nuclear Overhauser effects and ¹²⁹Xe longitudinal relaxation time measurements were used to demonstrate that the dipole–dipole coupling is the dominant relaxation mechanism for ¹²⁹Xe in water, at room temperature. ¹²⁹Xe–¹H cross-relaxation rates were derived to be ς_XeH 3.2 ± 0.3 × 10⁻³ s⁻¹, independent of xenon pressure (in the range of 1–10 bar) and of the presence of oxygen. Corresponding xenon–proton internuclear distances were calculated to be 2.69 ± 0.12 Å. Using the magnitude of the dipole–dipole coupling and the spin density ratio between dissolved xenon and bulk water, it is estimated that ¹²⁹Xe–¹H spin polarization-induced nuclear Overhauser effects would yield little net proton signal enhancement in water.     

Multi-dimensional 1H NMR nuclear Overhauser spectroscopy under magic angle spinning: theory and application to elastomers

The process of cross-relaxation between different protons (nuclear Overhauser effect) is investigated in soft solids by 2- and 3-dimensional NMR under the conditions of fast magic-angle spinning. The cross-relaxation rates are found to depend weakly on fast motions in the Larmor frequency range and strongly on slow motions of the order of the spinning frequency W _R. Explicit expressions for the W _R dependent cross-relaxation rates are derived for different motional models. These findings were tested experimentally on elastomers, i.e., on a cross-linking series of styrene-butadiene rubbers where the cross-relaxation was studied as a function of W _R. Short mixing times as are required for extracting the relaxation rates could be realized conveniently using a pulsed magnetic-field gradient for coherence pathway selection. As in solution NMR, relative couplings between chemically resolved spins can be determined from the peak intensities. By combining cross-relaxation measurements with T ₁ measurements, the distribution of correlation times can be probed for slow and fast timescales, respectively. Only the former were found to depend on the crosslink density.     

Water–Surfactant Contact Studied byF–H Heteronuclear Overhauser Effect Spectroscopy

Intermolecular¹⁹F–¹H cross-relaxation is measured using heteronuclear Overhauser effect NMR spectroscopy (HOESY) in the micellar solution of cesium pentadecafluorooctanoate. The results are analyzed in terms of a weak¹H–¹⁹F cross-relaxation between the water protons and the fluorines in the fluoroalkyl chain and a strong¹⁹F–¹⁹F cross-relaxation within the fluoroalkyl chain. The water–surfactant cross-relaxation indicates a water approach to the first CF₂segment in the order of 2.0 Å and a short (?ns) water residence time. Evidence of fluorine hydration further inside the micelle is presented.     

Multiple-Pulse Mixing Sequences That Selectively Enhance Chemical Exchange or Cross-Relaxation Peaks in High-Resolution NMR Spectra

Rotating-frame NMR experiments which either emphasize or suppress cross relaxation, and which simultaneously suppress TOCSY, COSY, and zero-quantum peaks in NMR spectra, are presented and analyzed. The new experiments rely on mixing sequences which follow naturally from thetransverse-ROESY (Tr-ROESY) sequence of Hwang and Shaka, and which are applicable to larger molecules in solution (spin diffusion limit). In the first variant a modified Tr-ROESY sequence, called multiple-pulse ROESY (MP-ROESY), is used to enhance cross-relaxation peak intensity compared to Tr-ROESY; in the second, called phase-modulated CLEAN chemical exchange (CLEANEX-PM), cross-relaxation peaks are greatly attenuated. The two methods are thus complementary: MP-ROESY is used to observe Overhauser peaks, and CLEANEX-PM is used to eliminate them, permitting clear observation of chemical exchange peaks alone. The new techniques are examined by theory and experiment. Practical guidelines that will result in high-quality spectra are given, including the judicious use of continuous weak static magnetic field gradients.     

Electron spin resonance in nickel near Tc

The temperature dependence of the FMR and EPR linewidth of bulk nickel single crystals was measured from 260 to 410°C at 9.85 GHz. A linewidth falling off rapidly with increasing temperature was found in a region above T_c: 365<T<385°C. An interpretation by the critical behaviour of the spin system is discussed.     

Structural stability of heat-treated CoN/CN soft X-ray multilayers fabricated by dual-facing-target sputtering

286 , 176 (1996)]. (1) The interdiffusion critical wavelengths were calculated as 2.00–2.04 nm at temperatures ranging from 473 to 523 K, which is equal to those of Co/C multilayers within the experimental error, indicating that the interdiffusion behaviours in the CoN/CN multilayers are still decided by the thermodynamic properties of the Co-C system. (2) The effective interdiffusivities and macroscopic diffusion coefficients are smaller. (3) The activation energy for diffusion is larger. The features imply that it is possible to improve the thermal stability of Co/C multilayers by doping with N atoms. The high-temperature annealing results imply that the destructive threshold of the CoN/CN multilayers is 100–200 °C higher than that of Co/C multilayers. The small-angle X-ray diffraction of CoN/CN soft X-ray multilayers indicates that the period expansion of the multilayers is only 4% at 400 °C, and the interface pattern still exists even if they were annealed at 700 °C. The large-angle X-ray diffraction and transmission electron microscopy analysis reveal that the crystalline process is significantly retarded if doped with N atoms, leading to a smaller grain size at higher annealing temperatures. The significant improvement of the thermal stability can be interpreted with Raman spectroscopy and X-ray photoelectron spectroscopy analysis. The Raman spectra give the evidence that the formation of the sp³ bonding in the CN sublayers can be suppressed effectively by doping with N atoms, and thus the period expansion resulting from the changes in the density of CN layers can be decreased considerably. The X-ray photoelectron spectra give information about existence of the strong covalent bonding between N atoms and the ionic bonding between Co and N atoms, which can slow down the tendency of the structural relaxation. The interstitial N atoms decrease the mobility of Co atoms, and thus the fcc Co and hcp Co coexist even though the annealing temperature is much higher than the phase transformation temperature of 420 °C, leading to the suppression of the grain growth. Received: 29 May 1997/Accepted: 8 September 1997     

Correcting for incomplete saturation and off-resonance effects in multiple-site saturation-transfer kinetic measurements

The effects of incomplete saturation and off-resonance irradiation on nuclear magnetic resonance saturation-transfer measurements of three-site chemical-exchange rates are discussed. A new method that uses double-saturation measurements is compared with two published methods, one that uses single-saturation measurements and one that uses a single-saturation measurement and a double-saturation measurement. Several formulas are compared for measuring the exchange rate constant k(DE) for exchange from a detected spin D to an exchanging spin E in the presence of exchange from spin D to a competing spin C. For each method, formulas are derived with corrections for incomplete saturation or off-resonance effects, with both corrections, and with neither correction. Exact formulas are available for three exchanging sites with incomplete saturation if there are no off-resonance effects. Off-resonance corrections are imperfect even with complete saturation.     

Cross-relaxation in multiple pulse NQR spin-locking

The experimental and theoretical NQR multiple-pulse spin locking study of cross-relaxation process in solids containing nuclei of two different sorts I?>?1/2 and S?=?1/2 coupled by the dipole–dipole interactions and influenced by an external magnetic field. Two coupled equations for the inverse spin temperatures of the both spin systems describing the mutual spin lattice relaxation and the cross-relaxation were obtained using the method of the nonequilibrium state operator. It is shown that the relaxation process is realized with non-exponential time dependence describing by a sum of two exponents. The cross relaxation time is calculated as a function of the multiple-pulse field parameters which agree with the experimental data. The calculated magnetization cross relaxation time vs the strength of the applied magnetic field agrees well with the obtained experimental data.     

XPS study of low temperature diffusion in Au/Ni couples in the presence of arsenic

X-ray photoelectron spectroscopy, XPS, has been utilized to determine the low temperature grain boundary diffusion of nickel through gold thin films by means of surface accumulation. Surface accumulation is aided by a rapid oxidation of the nickel diffusant at the surface by arsenic vapor at very low (<10^-8 Torr) pressure causing a rapid accumulation of nickel arsenide product. The initial low temperature diffusion parameters of Au/Ni couples were measured in situ without interrupting the reaction-accumulation process. Accumulation and diffusion rates were obtained for temperatures ranging from 110 to 147° C. A discontinuity in an otherwise linear accumulation was observed after approximately 150 min. Evidence suggests that surface effects become rate limiting at this point.     

EPR studies of weakly coupled oxomolybdenum (V) and low-spin iron (III) porphyrin centers

Novel compounds containing twoS=1/2 coupled spin centers (Mo(V) and low spin Fe(III) have been investigated in detail by X- and Q-band EPR spectroscopy, spectral simulation and molecular modelling calculations. For one system with a Mo?Fe distance of ≈9.4 Å the dominant dipolar coupling allows distinction among structures that are consistent with molecular modelling calculations. For the second system with a Mo?Fe of ≈ 7.9 Å the exchange interaction is dominant (0.5 <J < 3.0 GHz). These coupled systems are preliminary benchmarks for using EPR to investigate the Mo?Fe interaction in sulfite oxidase.