Measurement of heat transfer coefficients by nuclear magnetic resonance

We demonstrate an experimental method for the measurement of heat transfer coefficient for a fluid system by magnetic resonance imaging. In this method, the temporal variation of thermally induced nuclear shielding is monitored and the average heat transfer coefficient is measured as a function of fluid velocity. We examine the cases of natural convection and forced convection at fluid velocity up to 0.8 m s(-1). These cases correspond to low dimensionless Biot (Bi) number where the heat transfer is limited by thermal convection. We demonstrate the NMR method for two simple geometries, a cylinder and a sphere, to experimentally determine the heat transfer coefficient (h) in two NMR imaging and spectroscopy systems through measuring three NMR parameters, the chemical shift, magnetization and spin self diffusion coefficient.     

A method for detection of spectral spin diffusion from minor peaks, and its application to F MAS NMR of antimony(III)-doped fluorapatite

A new technique for detecting spectral spin diffusion in solids under MAS NMR conditions that is particularly well suited for accurately measuring cross-relaxation from minor spectral components is presented. The pulse sequence, SINK (Saturation Inter-Nuclear Kinetics), selectively saturates the magnetization of a minor spectral component with a series of rotor-synchronized DANTE pulse trains and monitors spin diffusion to other peaks with a non-selective 90° pulse. We have used SINK with ¹⁹F MAS NMR on samples of calcium fluorapatite doped with Sb³⁺ to measure spin diffusion between a weak peak at 68.6 ppm due to fluoride ions associated with Sb³⁺ and other peaks in the spectrum. The SINK experiment clearly demonstrates that spin diffusion from the former peak to the main resonance of fluorapatite at 64.0 ppm is faster than spin diffusion to a second antimony-related peak at 65.6 ppm. These results strengthen our previous conclusion that antimony(III) occupies a phosphate site in the apatite lattice, with an SbO₃³⁻ group replacing a PO₄³⁻ group. The SINK experiment also enables the detection of a “hidden” peak at approximately 62.9 ppm that is otherwise obscured by the intense main peak at 64.0 ppm.     

Spatially resolved adsorption isotherms of thermally polarized perfluorinated gases in yttria-stabilized tetragonal-zirconia polycrystal ceramic materials with NMR imaging

This paper presents the results obtained by nuclear magnetic resonance (NMR) imaging of perfluorinated gases in mesoporuous solids. NMR images of nuclear spin density as a function of gas pressure permits spatially resolved measurements that are analogous to conventional bulk Brunauer-Emmett-Teller adsorption isotherm measurements. The use of NMR imaging allows the nondestructive evaluation of macroscopic spatial variations in the underlying mesoporous structure, for materials such as partially sintered Y-TZP (yttria-stabilized tetragonal-zirconia polycrystal) ceramics. All NMR measurements were performed with octafluorocyclobutane (C₄F₈) gas, using only the thermal Boltzman nuclear magnetization.     

Temperature dependence of nuclear magnetization and relaxation

The temperature dependences of nuclear magnetization and relaxation rates are reviewed theoretically and experimentally in order to quantify the effects of temperature on NMR signals acquired by common imaging techniques. Using common sequences, the temperature dependences of the equilibrium nuclear magnetization and relaxation times must each be considered to fully understand the effects of temperature on NMR images. The temperature dependence of the equilibrium nuclear magnetization is negative because of Boltzmann's distribution for all substances at all temperatures, but the combined temperature dependences of the equilibrium magnetization and relaxation can be negative, weak or positive depending on the temperature (T), echo time (T(E)), repetition time (T(R)), and the temperature dependences of the relaxation times T(1)(T) and T(2)(T) in a pulse sequence. As a result, the magnitude of the NMR signal from a given substance can decrease, increase or stay somewhat constant with increasing temperature. Nuclear thermal coefficients are defined and predictions for spin echo and other simple sequences are verified experimentally using a number of substances representing various thermal and NMR properties.     

针对磁共振射频脉冲的时频域分析方法比较研究

射频脉冲可实现样本自旋体系的精确操控,进而产生预期的核磁共振(NMR)信号,在NMR信号产生过程中扮演重要角色.该文分别采用短时傅里叶变换(STFT)、连续小波变换(CWT)和维格纳-威利分布(WVD)几种时频域分析方法对射频脉冲(优化形状脉冲)进行特性分析和比较.结果表明,三种方法各自具有优缺点,结合各自优势对射频脉冲进行各种方法分析,可以更好地理解复杂脉冲的幅度、相位特性在时频域的分布情况.该文的研究方法将为直观理解复杂射频脉冲对自旋体系的作用机制提供参考.     

Theoretical study of R(1rho) rotating-frame and R2 free-precession relaxation in the presence of n-site chemical exchange

The n-site Bloch-McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Perturbation theory is used to approximate the largest eigenvalue of the Bloch-McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy.     

Macroscopic and Microscopic Fields in High-Resolution Liquid NMR

The microscopic magnetic-induction field “seen by each nucleus” in a material medium and which is generated by a rapidly time-dependent spin magnetization gives rise to surprising new features in high-resolution nuclear magnetic resonance experiments. The purpose of the present paper is to show how the relations between the macroscopic average fields, the magnetization, and the microscopic fields (which were studied and clarified long ago at thermal equilibrium) can be extended to the present NMR context in which the magnetization can become rapidly time dependent and unrelated to thermal equilibrium properties.     

Cross-correlations between low-γ nuclei in solids via a common dipolar bath

Correlation of chemical shifts of low-γ nuclei (such as 15N) is an important method for assignment of resonances in uniformly-labeled biological solids. Under static experimental conditions, an efficient mixing of low-γ nuclear spin magnetization can be achieved by a thermal contact to the common reservoir of dipole-dipole interactions in order to create 15N-15N, 13C-13C, or 15N-13C cross-peaks in a 2D correlation spectrum. A thermodynamic approach can be used to understand the mechanism of magnetization mixing in various 2D correlation pulse sequences. This mechanism is suppressed under magic-angle spinning, when mixing via direct cross-polarization with protons becomes more efficient. Experimental results are presented for single-crystalline and powder samples of 15N-labeled N-acetyl-L-15N-valyl-L-15N-leucine (NAVL). In addition to the thermodynamic analysis of mixing pulse sequences, two different new mixing sequences utilizing adiabatic pulses are also experimentally demonstrated.     

Spin-state-selective excitation in selective 1D inverse NMR experiments

A general and very simple strategy for achieving clean spin-state-selective excitation with full sensitivity in carbon-selective gradient-enhanced 1D HMQC and HSQC pulse schemes is presented. The incorporation of an additional hard 90 degrees (13)C pulse applied along a specific orthogonal axis just prior to acquisition into the conventional sequences allows us to select a simultaneous coherence transfer pathway which usually is not detected. The superimposition of this resulting antiphase magnetization to the conventional in-phase magnetization gives the exclusive excitation of the directly attached proton showing only the alpha or beta spin state of the passive (13)C nucleus. The propagation of this particular spin state to other protons can be accomplished by adding any homonuclear mixing process just after this supplementary pulse. Such an approach affords a suite of powerful selective 1D (13)C-edited NMR experiments which are helpful for resonance assignment purposes in overcrowded proton spin systems and also for the accurate determination of the magnitude and sign of long-range proton-carbon coupling constants in CH spin sytems for samples at natural abundance. Such measurements are performed by measuring the relative displacement of relayed signals in the corresponding alpha and beta 1D subspectra.     

Calculation of diffusion effect for arbitrary pulse sequences

A method is presented for calculating the nuclear spin magnetization created by an arbitrary number of short radio frequency pulses and of piecewise constant gradient applied in a selected direction. The isotropic diffusion, the transverse and longitudinal relaxations as well as the global transport are taken into account. A thorough analysis of the magnetization density evolution results in an algorithm for the analytical calculation of final NMR signal. Computationally, it requires only accumulating numerical coefficients in the found analytical structure. For arbitrary sequences this is done with a computer program. This approach, which can be classified as symbolical computations, results in a high performance and in a practically unlimited accuracy. Results for sample pulse sequences are presented.     

1H NMR signal broadening in spectra of alkane molecules adsorbed on MFI-type zeolites

The anisotropic behavior of C1-C6 alkane molecules adsorbed in MFI zeolite was studied by 1H nuclear magnetic resonance (NMR) using single-pulse excitation, Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, Hahn echo (HE) pulse sequence, and magic-angle spinning. The molecular order parameter was obtained by both static 2H NMR spectroscopy and molecular simulations. This yields an order parameter in the range of 0.28-0.42 for linear alkanes in MFI zeolite, whereas the parameter equals zero for FAU zeolite with a cubic symmetry. Thus, in the case of a zeolite with a non-cubic symmetry like MFI, the mobility of the molecules in one crystallite cannot fully average the dipolar interaction. As a consequence, transverse nuclear magnetization as revealed in the echo attenuation notably deviates from a mono-exponential decay. This information is of particular relevance for the performance of pulsed field gradient (PFG) NMR diffusion experiments, since the occurrence of non-exponential magnetization attenuation could be taken as an indication of the existence of different molecules or of molecules in different states of mobility.     

Pulsed-Field-Gradient NMR Study of Anisotropic Molecular Translational Diffusion in nOCB Liquid Crystals

Pulsed-field-gradient nuclear magnetic resonance (NMR) combined with magic echo decoupling is applied to study anisotropic diffusion in samples with strong static dipolar spin interactions. The approach, due to its moderate demands on the NMR hardware, can be implemented on standard commercial equipment for routine diffusion studies of liquid crystals. Using a microimaging probe, measurement of diffusion in arbitrary spatial direction is possible. Hence, the principal components of the diffusion tensor are directly obtained. Anisotropic diffusion is investigated in the thermotropic mesophases of a homologous series of nOCB liquid crystals and an analogous compound with hydroxyl groups. The geometric average diffusion coefficient changes continuously at the isotropic–nematic phase transition. Experimental data are described in terms of the molecular translation models in the nematic phase and for the second-order nematic–smectic A phase transition. The diffusion anisotropy is higher for the sample with terminal hydroxyl groups suggesting significant molecular association via hydrogen bonding.     

A nuclear-spin based rotation sensor using optical polarization and detection methods

We describe a rotation sensor that is based on the detection of the nuclear magnetic resonance signal of¹²⁹Xe in the gas phase. Under rotation shifts of the signal phase and Larmor frequency occur, which can be used to determine orientational angle variations with an accuracy of about 1^o and rotation rates of 0.4 mHz to 5 Hz with a precision of 0.4 mHz during the measurement time, which is of the order of 3×T ₂, the nuclear spin relaxation time. The nuclear spin species is polarized by spin-exchange collisions with optically pumped ground-state spins of Rb-gas atoms. The Rb atoms also present in the sample are used as a magnetometer to probe the free-induction decay of the nuclear spin ensemble. Polarization, detection, and data processing sheemes are described in detail and the current sensitivity and limitations of this Stuttgart nuclear magnetic resonance (NMR) gyroscope are discussed. Possibilities for further improvements are pointed out.     

Low-Frequency and d.c. Phenomena in Magnetic Resonance

A review is given of some low-frequency and d.c. magnetic resonance phenomena studied since 1970s up to date. The content includes: the enhanced longitudinal susceptibility effect (ELSE) based on the concept of the dipole–dipole reservoir in EPR; direct registration of NMR in rotating frames; modulation method of measuring extremely fast electron spin longitudinal relaxation; resonance magnetoresistance and resonance spin rectification (“spin dynamo”) in conducting ferromagnetic films. Physical mechanism of these effects, as well as applications in studying spin dynamics and relaxation in solids, including dynamic nuclear polarization, high-temperature superconductivity and properties of rare-earth manganites are considered.     

Heteronuclear polarization transfer by symmetry-based recoupling sequences in solid-state NMR

We demonstrate a new set of methods for transferring spin polarization between different nuclear isotopes in magic-angle-spinning solid-state NMR. The technique employs symmetry-based recoupling sequences on one irradiation channel and a simple sequence of between one and three strong radiofrequency pulses on the second channel. A phase shift of the recoupling sequences is applied at the same time as a pi/2 pulse on the second channel. The trajectory of the transferred polarization may be used to estimate heteronuclear distances. The method is particularly attractive for nuclei with low gyromagnetic ratios or for those experiencing strong anisotropic spin interactions, where conventional Hartmann-Hahn cross-polarization is difficult to apply. We demonstrate the method on 1H-13C, 1H-15N and 19F-109Ag systems.     

Efficient spin diffusion of transverse13C magnetization

Relatively efficient spin diffusion among unprotonated carbons with large chemical-shift anisotropies can be achieved by a¹³C nuclear magnetic resonance multiple-pulse sequence with a lowduty cycle of ～5% on the¹³C channel, which minimizes sample heating and reduces cumulative effects of pulse imperfections. The spin diffusion occurs among transverse-magnetization isochromats, while the total transverse magnetization is a conserved quantity under the average Hamiltonian. The “flip-flop” term of the dipolar-coupling average Hamiltonian is the same as in the full dipolar coupling, i.e., its scaling factor is unity. For a sample of 40%¹³COO-labeled poly(vinyl acetate), with¹³C in ester groups accounting for 7% of all heavy atoms, magnetization equilibrates within 20 ms over a volume of (0.9 nm)³, corresponding to a molecular mass of 500 Da, while the T₂ relaxation time of the total transverse magnetization is ～40 ms. The spin diffusion coefficient is estimated asD = 3 ± 1.5 nm²/s.     

Selective Injection of Magnetization by Slow Chemical Exchange in NMR

In a system in slow dynamic equilibrium two NMR methods are shown to be suitable for injecting magnetization from one resonance to another by means of slow chemical exchange. The combined outputs of the methods may be employed to measure the value of the off-rate constant kappa(off) in the complex. The methods are implemented experimentally using the complex of molecules composed of the enzyme Escherichia coli dihydrofolate reductase (DHFR) and the ligand folate. In an equilibrium solution with DHFR, folate is known to undergo chemical exchange between a free state and a bound state. The modified synchronous nutation method is applied to a spin of the folate molecule in the free and bound states; magnetization transfer occurs between the two sites due to the underlying exchange process. As a preliminary step for the application of the synchronous nutation method, a new one-dimensional 1H NMR technique is proposed which facilitates the assignment of the resonance of a spin in the bound state, provided the resonance of its exchange partner in the free state is known. This experiment is also used to obtain quantitative estimates of the transverse relaxation rate constant of the bound resonance. The numerical procedure necessary to analyze the experimental results of the synchronous nutation experiment is presented.     

Random-walk technique for simulating NMR measurements and 2D NMR maps of porous media with relaxing and permeable boundaries

We revisit random-walk methods to simulate the NMR response of fluids in porous media. Simulations reproduce the effects of diffusion within external inhomogeneous background magnetic fields, imperfect and finite-duration B(1) pulses, T(1)/T(2) contrasts, and relaxing or permeable boundaries. The simulation approach consolidates existing NMR numerical methods used in biology and engineering into a single formulation that expands on the magnetic-dipole equivalent of spin packets. When fluids exhibit low T(1)/T(2) contrasts and when CPMG pulse sequences are used to acquire NMR measurements, we verify that classical NMR numerical models that neglect T(1) effects accurately reproduce surface magnetization decays of saturated granular porous media regardless of the diffusion/relaxation regime. Currently, analytical expressions exist only for the case of arbitrary pore shapes within the fast-diffusion limit. However, when fluids include several components or when magnetic fields are strongly inhomogeneous, we show that simulations results obtained using the complete set of Bloch's equations differ substantially from those of classical NMR models. In addition, our random-walk formulation accurately reproduces magnetization echoes stemming from coherent-pathway calculations. We show that the random-walk approach is especially suited to generate parametric multi-dimensional T(1)/T(2)/D NMR maps to improve the characterization of pore structures and saturating fluids.