Frequency-dependent spin-lattice relaxation study of transport processes in superionic conductors

The sensitivity of the¹⁹F spin-lattice relaxation dispersion, T₁,(ω), to motional disorder in crystalline superionic conductors of the type La_1?xSr_xF_3?x (x = 0; 0.03) is shown. T₁ times are measured in the frequency range from 90 kHz to 370 MHz using standard techniques in combination with field-cycling. The relaxation dispersion shows qualitative differences from the standard Bloembergen-Purcell-Pound behavior. At low frequencies a relaxation model using a distribution of correlation times for diffusing ions is found to be consistent with the experimental results. At frequencies higher than 50 MHz another process of the Debye type which is not induced by ionic hopping dominates the relaxation.     

Proton NMR relaxation study of the CsHSO4 solid acid system

At 141 °C the solid acid CsHSO₄ is known to undergo transition to a superprotonic phase that is characterized by dramatic (several-order-of-magnitude) increases in hydrogen ion conductivity. Proton NMR spin-spin relaxation time T₂ measurements reported here for CsHSO₄ also reveal substantial increases (factors of 20-30) in the vicinity of the transition temperature. In the temperature range just below the transition (70-136 °C), T₂ increases by a factor of order 10 relative to the rigid-lattice regime, suggesting motional narrowing of the NMR resonance line. In the regime of motional narrowing, the activation energy barrier to diffusion is 0.40 eV, as determined from the present T₂ results. NMR spin-lattice relaxation T₁ measurements also show behavior consistent with transition to a regime of rapid hydrogen motion. In particular, proton T₁'s decrease with temperature (from 80 to 120 °C), and then drop sharply near the transition temperature. Above the transition temperature, T₁ exhibits a minimum in which the correlation time is found to be ∼2 ns.     

2H nuclear magnetic resonance study of deuterated water dynamics in perfluorosulfonic acid ionomer Nafion

We have employed deuteron nuclear magnetic resonance (NMR) spectroscopy in order to study the dynamics of the deuterated water (D₂O) molecules introduced into a perfluorosulfonic acid ionomer Nafion (NR-211) film. According to the ²H NMR spectral analysis, the deuterated water molecules at low temperatures occupied either relatively rigid or mobile sites up to the temperature T_M=240 K where all the deuterated water molecules became mobile. The temperature-dependent NMR linewidths sensitively reflected the motional narrowing of the rigid and mobile sites, and the NMR chemical shift reflected significant changes in the hydrogen bonds of the deuterated water. While a slow- to fast-limit motional transition was manifested at T_M in the laboratory-frame NMR spin–lattice relaxation, the rotating-frame spin–lattice relaxation indicated no bulk liquid water state down to 200 K.     

Magnetic Resonance Imaging of Rat C6 Glioma Model Enhanced by Using Water-Soluble Gadolinium Fullerene

Water-soluble gadofullerene Gd@Ful with composition Gd³⁺@C₈₂(OH) _X ^3– (x ~ 20) was synthesized for theranostic study. Nanosuspensions of Gd@Ful were used for magnetic relaxation measurements in vitro and for magnetic resonance imaging of a rat with intracranially implanted C6 glioma. Gd@Ful was shown to reduce proton relaxation times in vitro and provide dual contrast of T ₁- and T ₂-weighted images in a rat brain tumor model after paramagnetic intravenous delivery. Magnetic relaxation times of water protons under action of Gd@Ful were strongly shortened due to cluster formation and increase of motional correlation times of protons in the vicinity of the fullerene cage. The Gd@Ful administration promoted the improvement of glioma contrast enhancement at T ₂-weighted images due to accumulation of paramagnetic substance at the tumor site. The contrast efficiency of Gd@Ful corresponds to the characteristics of negative contrast agent. The Gd@Ful nanosuspension is shown to be a contrast enhancer with high anti-tumor therapeutic potency. The retention of the Gd@Ful in the tumor resulted in a 75 % increase in survival times of the tumor-bearing animals.     

Determination of the activation energies of relaxation processes from integrated intensities of the NMR bands of high resolution spectra

An analysis of the effect of temperature on the integrated intensities of NMR bands has revealed that it is possible, by using the dependence of the integrated intensities of high-resolution NMR spectra on temperature, to determine the activation energies of the motional modes or the product of the relaxation times, T₁T₂, of the individual proton groups. The procedure has been verified for samples of benzene and for polyethylene oxide, polyisobutylene and poly(methyl methacrylate) solutions.     

Hindered rotation of CH3 groups and phenyl ring in clofibric acid (drug) studied by35Cl-NQR and1H-NMR spectroscopy

The³⁵C1-NQR frequency (V_Q), nuclear quadrupole spin-lattice relaxation time (T_1Q),¹H-NMR second moment (M ₂), nuclear magnetic spin-lattice relaxation time (T ₁) and spin-lattice relaxation time in rotating frame (T _1p ) were measured for polycrystalline clofibric acid (drug) as a function of temperature. Hindered rotation of two dynamically inequivalent methyl groups and the phenyl ring was detected, the relevant activation energies were determined. The rotations are discussed in detail.     

Proton diffusion in the room-temperature phase of [(NH4)1−xRbx]3H(SO4)2 as studied by 1H spin-lattice relaxation in the rotating frame

Proton diffusion in the room-temperature phase (phase II) of [(NH₄)_1?xRb_x]₃H(SO₄)₂ (0≤x≤1) has been studied by means of ¹H spin-lattice relaxation times in the rotating frame, T_1ρ. The ¹H T_1ρ values were measured at 200.13 MHz in the range of 380–490 K. The ammonium protons and the acidic protons have independent T_1ρ values in the higher temperature range of phase II, suggesting that the spin diffusion between the two species is ineffective. The translational diffusion of the acidic protons is the most dominant mechanism to relax both the ammonium protons and the acidic protons in phase II. The ¹H T_1ρ values in phase II are analyzed theoretically and the motional parameters are obtained. The results of NMR well explain the macroscopic proton conductivity.     

Development of the pulse NMR method utilizing the short-lived β-emitter 12 B

Measurements of the spin-spin relaxation time T ₂ of the short-lived $\upbeta $ -emitter $^{12}B (I^{\uppi }$ = 1^?+?, T _1/2 = 20 ms) in Si have been performed. By applying the spin echo method to $\upbeta $ -NMR measurements, the intrinsic T ₂ for ¹²B in Si was successfully determined with the effect of the static magnetic field inhomogeneity removed. The temperature dependence of T ₂ for ¹²B in Si shows that T ₂ becomes longer with increasing temperature, which seems to reflect the effect of motional narrowing.     

High temperature NMR in vanadium: Electron paramagnetism and atomic diffusion effects

We present preliminary results on Knight shift T₁ and T₂ measurements between 300 and 1700 K. We have observed the motional narrowing due to the self diffusion as well as a strong quadrupolar contribution to T₁ due to the diffusion of interstitial gases. K varies from 0.58 to 0.63%. This temperature dependence is shown to be mainly due to an intrinsic temperature effect. The high temperature Korringa like behaviour of T₁ with T₁T = 1.05 sec. K is explained in terms of the temperature dependence of the d spin contribution.     

Thermal unpinning of the modulation wave near TI in incommensurate Rb2ZnCl4 detected by 35Cl NQR

Thermal unpinning and floating of the incommensurate modulation wave produces in Rb₂ZnCl₄ close to the incommensurate-paraelectric transition T_I a partial motional averaging of the splitting between the two edge singularities in the ³⁵Cl nuclear quadrupole resonance spectrum. The mean square phase fluctuations are close to T_I proportional to (T_I ? T)^?2β with β = 0.39 ± 0.04.     

A classical theory of superparamagnetic relaxation

A Fokker-Planck equation for the relaxation of a classical ferromagnetic particle coupled to a classical heat bath is derived from the Nakajima-Zwanzig equation. The equation of motion for the mean magnetization of an ensemble of particles is found to be closed only under special circumstances. In the strong motional narrowing limit the equation of motion reduces to the Bloch equations in the limit MH ? k_BT, i.e. for small particles, and to the Landau-Lifshitz equation in the opposite limit. For the motional narrowing region in toto the particular case of uniaxial anisotropy is analysed, giving an equation of motion which for large particles reduces to a modified Landau-Lifshitz equation with g-shift and a reduced damping constant. This equation cannot be meaningfully identified with the Gilbert equation.Approximate expressions for superparamagnetic relaxation rates by Kramers' method are obtained for the case of (i) triaxial (i.e. orthorhombic) and (ii) cubic (K +ve and ?ve) anisotropy, assuming large energy barriers. The results supplement Brown's expression for uniaxial anisotropy and show a more complicated dependence on the Landau-Lifshitz parameter λ than the linear dependence found by Brown. For small λ the rates tend to constant values compatible with the transition.     

MRI rotating frame relaxation measurements for articular cartilage assessment

In the present work we introduced two MRI rotating frame relaxation methods, namely adiabatic T_1ρ and Relaxation Along a Fictitious Field (RAFF), along with an inversion-prepared Magnetization Transfer (MT) protocol for assessment of articular cartilage. Given the inherent sensitivity of rotating frame relaxation methods to slow molecular motions that are relevant in cartilage, we hypothesized that adiabatic T_1ρ and RAFF would have higher sensitivity to articular cartilage degradation as compared to laboratory frame T₂ and MT. To test this hypothesis, a proteoglycan depletion model was used. Relaxation time measurements were performed at 0 and 48 h in 10 bovine patellar specimens, 5 of which were treated with trypsin and 5 untreated controls were stored under identical conditions in isotonic saline for 48 h. Relaxation times measured at 48 h were longer than those measured at 0 h in both groups. The changes in T₂ and MT relaxation times after 48 h were approximately 3 times larger in the trypsin treated specimens as compared to the untreated group, whereas increases of adiabatic T_1ρ and RAFF were 4 to 5 fold larger. Overall, these findings demonstrate a higher sensitivity of adiabatic T_1ρ and RAFF to the trypsin-induced changes in bovine patellar cartilage as compared to the commonly used T₂ and MT. Since adiabatic T_1ρ and RAFF are advantageous for human applications as compared to standard continuous-wave T_1ρ methods, adiabatic T_1ρ and RAFF are promising tools for assessing cartilage degradation in clinical settings.     

Dynamics of α-Tocopherol Acetate: Proton Relaxation Studies Supported by Molecular Dynamics Simulations

Dynamical properties of α-tocopherol acetate (commonly known as vitamin E) have been investigated in a broad temperature range (below and above the glass transition) by means of proton spin–lattice relaxation. Two distinct relaxation processes have been detected in the studied temperature range. One of them, present in the solid phase, has been attributed to reorientation of methyl groups. In order to identify the motional process leading to the proton relaxation above the glass transition temperature (T _g), molecular dynamics (MD) simulations have been performed, which provided time correlation functions for several internuclear vectors in the molecule. The high-temperature relaxation process is primarily due to dynamics of the aromatic rings of the tocopherol molecule; however, a considerable contribution of diffusion of the aliphatic chain cannot be excluded. Comparing the nuclear magnetic resonance (NMR) results with MD and relaxation data of dielectric spectroscopy (DS) available in the literature (K. Kamiński, S. Maślanka, J. Zioło, M. Paluch, K.J. McGrath, C.M. Roland, Phys Rev E 75:011903-7, 2007; E. Szwajczak, J. Świergiel, R. Stagraczyński, J. Jadżyn, Phys Chem Liq 47:460–466, 2009), the motional process observed in NMR relaxation studies above T _g has been identified with the δ process observed in DS.     

Study of the diffusion of hydrogen in LaNi5+xH6 compounds by 1H NMR relaxation

The diffusion of hydrogen in LaNi_5+xH₆ (x=?0.2, 0.0, 0.2) has been investigated by NMR from 150 to 300 K. High-temperature data of the spin-spin relaxation time T₂ and the rotating frame spin lattice relaxation time T₁? are independent of stoichiometry but the data of the spin lattice relaxation time T₁ and low-temperature T₁? data are not, and they do not fit Torrey's relaxation model.     

Conductivity relaxation in Ag+ ion conducting PEO–PMMA–PEG polymer blends

In this paper, the electrical conductivity and relaxation studies in two different temperature regions (T?<?T _m and T?>?T _m) on plasticized PEO–PMMA blend polymer electrolyte system with AgNO₃ salt are reported. The polymer electrolyte system has been prepared by solution cast technique and characterized by X-ray diffraction and differential scanning calorimetry. The conduction and relaxation processes at various temperatures have been investigated in the framework of modulus formalism. The distribution of relaxation times is discussed using Argand plot. Variation in ionic conductivity of polymer blends is discussed with the increase of PEO as well as with temperature.     

Nuclear magnetic relaxation of nematic liquid crystals,N-(4-methoxybenzylidene)-4′-n-butylaniline and N-(2-hydroxy-4-methoxybenzylidene)-4′-n-butylaniline

Nuclear magnetic resonance linewidth and spin-lattice relaxation time T₁ were measured for 4-methoxybenzylidene-4′-n-butylaniline (MBBA) and N-(2-hydroxy-4-methoxybenzylidene)-4′-n-butylaniline )OHMBBA) in their liquid, nematic, undercooled nematic, and glassy nematic liquid crystal states as well as in the stable crystalline states. In the case of OHMBBA, the motional narrowing occurs in three steps corresponding to excitation of end-group reorientations, self-diffusion, and molecular tumbling. T₁ of OHMBBA in the nematic and undercooled nematic state has two minima at 264 K (24 ± 4 msec) and at 140 K (22.0 ± 0.5 msec); the motions responsible for the minima are the self-diffusion and the end-group reorientations with the activation energies 29 ± 1 J mole⁻¹ and 5.8 ± 0.2 kJ mole⁻¹ respectively. Analogous results were obtained for MBBA. Some measurements were also made for p-azoxyanisole for the sake of comparison. The effect of external magnetic field on the formation of the glassy state was examined.     

Molecular dynamics of poly(ethylene terephthalate)/poly(phenylene sulfide) nanocomposites with barium titanate

The relaxation processes and the properties of polymer/ceramic nanocomposites have been studied by the ¹H nuclear magnetic resonance methods. Nanocomposites of poly(ethylene terephthalate) PET and poly(phenylene sulfide) PPS with 0.25, 2.5 and 5% wt. barium titanate BT were prepared using a twin screw extruder and injection moulding machine. The spin-lattice relaxation time T₁, second moment M₂ and the motional parameters as e.g. the activation energies in the nanocomposites were investigated.     

Magnetic properties of high-T c superconductors from NQR and NMR measurements

NMR and NQR spectra and spin-lattice relaxation measurements carried out in LASCO and YBCO-type crystals are presented and analyzed in order to derive insights on the correlations and spin-dynamics of the Cu²⁺ ions and on the microscopic mechanisms of high-T _c superconductivity. As an illustrative example on how the magnetic correlation length and spin dynamics properties can be extracted from the relaxation rateW, the³⁵Cl NMR data in the two-dimensional Heisenberg system Sr₂CuCl₂O₂, around the paramagnetic-antiferromagnetic (PA-AF) transition are first considered. Then the¹³⁹La NQR relaxation measurements in La_2?xSr_xCuO₄ are briefly reviewed and it is shown how a simple picture of localized Cu²⁺ magnetic moments, whose spin fluctuation times are controlled by the charge defects induced by the doping, leads in a direct way to quantitative estimates for the progressive shift, on cooling, of the spectral density of the low-frequency spin excitations towards the high frequency range. This phenomenon can be described in terms of effective spin at the Cu²⁺ ions, and its similarities with the analogous effect of progressive delocalization in Heavy Fermions systems are pointed out. Thus, the superconducting transition appears to occur in an unconventional Fermi liquid with AF correlations among itinerant pseudoparticles, possibly involving a mechanism not directly related to the magnetic correlated dynamics. In fact, a universal behavior of the relaxation rates as a function of temperature is observed, regardless of the transition temperatureT _c. The independence ofT _c from the low frequency static and dynamical spin properties is also indicated by⁸⁹Y Knight shifts and from⁶³Cu relaxation rates in systems like YBa₂Cu₄O₈ (Y124), whereT _c can be changed by atomic substitutions and by controlling the oxygen stoichiometry. The effect of an external magnetic field on the correlated spin dynamics of the AF Fermi liquid is investigated and from a comparison of Cu NQR relaxation and NMR relaxation in oriented powder of YBCO and LASCO it is shown that the external field has the small but unambiguous effect of depressing the relaxation rates aboveT _c, besides strongly enhancing them in the superconducting phase. A maximum in the ratio \({{W\left( {NQR} \right)} \mathord{\left/ {\vphantom {{W\left( {NQR} \right)} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}} \right. \kern-0em} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}\) is thus observed around 80 K, either in LASCO or in YBCO, again indicating that the transition could be driven by a mechanism not directly involving the spin dynamic properties. To study the role of the fluxions belowT _c ⁸⁹Y NMR shifts and spectra in oriented powders of YBCO are analyzed. Information on the spin susceptibility and on the structure of the vortex lattice is obtained. In addition, from the temperature behavior of the linewidth a motional narrowing related to flux melting is evidenced. The effective correlation time for the vortex motion is derived and it is discussed why μ⁺SR cannot detect it in view of the different rigid-lattice line broadening.     

A New Approach of Two-Dimensional the NMR Relaxation Measurement in Flowing Fluid

Driven-equilibrium fast saturation recovery (DEFSR), as a new method for two-dimensional (2-D) nuclear magnetic resonance (NMR) relaxation measurement based on pulse sequence in flowing fluid, is proposed. The two-dimensional functional relationship between the ratio of transverse relaxation time to longitudinal relaxation time of fluid (T ₁/T ₂) and T ₁ distribution is obtained by means of DEFSR with only two one-dimensional measurements. The rapid measurement of relaxation characteristics for flowing fluid is achieved. A set of the down-hole NMR fluid analysis system is independently designed and developed for the fluid measurement. The accuracy and practicability of DEFSR are demonstrated.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.