The influence of chemical and diffusive exchange on water proton transverse relaxation in plant tissues

Transverse water proton relaxation in parenchyma tissue of courgette, onion and apple shows a dependence on CPMG pulse spacing characteristic of each tissue. An analysis of this dependence suggests that transverse relaxation in these tissues is caused by various combinations of fast proton exchange between water and cell biopolymers (or solutes) and diffusion through internally generated magnetic field gradients. Diffusion between intra- and extracellular water compartments also averages the water proton signal to an extent that depends on cell morphology and membrane permeability and this is calculated using a two-compartment model. No recourse need be made to popular concepts such as exchange between free and "bound" water. The implications of our results for NMR image contrast are discussed.     

Two-dimensional nuclear magnetic resonance petrophysics

Two-dimensional nuclear magnetic resonance (2D NMR) opens a wide area for exploration in petrophysics and has significant impact to petroleum logging technology. When there are multiple fluids with different diffusion coefficients saturated in a porous medium, this information can be extracted and clearly delineated from CPMG measurements of such a system either using regular pulsing sequences or modified two window sequences. The 2D NMR plot with independent variables of T2 relaxation time and diffusion coefficient allows clear separation of oil and water signals in the rocks. This 2D concept can be extended to general studies of fluid-saturated porous media involving other combinations of two or more independent variables, such as chemical shift and T1/T2 relaxation time (reflecting pore size), proton population and diffusion contrast, etc.     

A method for rapid characterization of diffusion

This paper describes a method to determine molecular displacements as a function of time in just two scans: one reference scan using the Carr-Purcell-Meiboom-Gill (CPMG) sequence, a second scan using a modified CPMG sequence (KCPMG). Measurements on free diffusion in bulk fluids, and on restricted diffusion in porous rock samples are reported. This technique can also be used for rapid measurement of flow and chemical exchange.     

Displacement power spectrum measurement by CPMG in constant gradient

The modulation of spin phase produced by Carr-Purcell-Meiboom-Gill (CPMG) sequence in combination with constant magnetic field gradient is appropriate to probe the displacement power spectrum (DPS). The spin-echo attenuation is directly proportional to the DPS value at the applied modulation frequency. Relaxation and selective excitation effects can be factored out while probing the DPS. The modulation frequency is adjusted by varying the pulse separation time while the gradient strength and the time of acquisition are kept constant. In designing the experiment gradient strength limitations, imposed by off-resonance effects, as well as limitations arising from using Gaussian phase approximation must be considered. An effective experimental strategy is presented, supported by experimental results for free and restricted diffusion.     

Categories of coherence pathways for the CPMG sequence

The CPMG sequence has been extremely useful for efficient measurements of NMR signal, spin-spin relaxation, and diffusion, particularly in inhomogeneous magnetic fields, such as when samples are outside the magnet and RF coil. Due to the inaccuracy of the pulses and the off-resonance effects, the CPMG echoes have contributions from the Hahn echo as well as signals that are similar to stimulated echoes. The systematic understanding of the CPMG pulse sequence requires decomposing the magnetization dynamics into different coherence pathways. In this paper, we describe a method to classify the CPMG coherence pathways and illustrate the nature of these types of pathways. This classification shows that direct echo and stimulated echoes are the major contribution to the CPMG signal. It also provides a clear understanding of the effect of restricted diffusion in porous media.     

A phase cycle scheme that significantly suppresses offset-dependent artifacts in the R2-CPMG 15N relaxation experiment

R2-CPMG 15N relaxation experiments form the basis of NMR dynamics measurements, both for analysis of nano-pico second dynamics and milli-micro second dynamics (kinetics). It has been known for some time that in the practical limit of finite pulse widths, which becomes acute when using cryogenic probes, systematic errors in the apparent R2 relaxation behavior occur for spins far off-resonance from the RF carrier. Inaccurate measurement of R2 rates propagates into quantitative models such as model-free relaxation analysis, rotational diffusion tensor analysis, and relaxation dispersion. The root of the problem stems from evolution of the magnetization vectors out of the XY-plane, both during the pulses as well as between the pulses. These deviations vary as a function of pulse length, number of applied CPMG pulses, and CPMG inter-pulse delay. Herein, we analyze these effects in detail with experimentation, numerical simulations, and analytical equations. Our work suggests a surprisingly simple change in the phase progression of the CPMG pulses, which leads to a remarkable improvement in performance. First, the applicability range of the CPMG experiment is increased by a factor of two in spectral width; second, the dynamical/kinetic processes that can be assessed are significantly extended towards the slower time scale; finally, the robustness of the relaxation dispersion experiments is greatly improved.     

Time-resolved measurement of surface diffusion induced by femtosecond laser pulses

Diffusion of atomic oxygen on a vicinal Pt111 surface induced by femtosecond laser pulses has been studied using optical second-harmonic generation as a sensitive in situ probe of the step coverage. Time-resolved studies of the hopping rate for step-terrace diffusion with a two-pulse correlation scheme reveal a time constant of 1.5 ps for the energy transfer from the electronic excitation of the substrate to the frustrated translations of the adsorbate.     

Molecular mobility and transport in polymer membranes and polyelectrolyte multilayers

Polyelectrolyte multilayers prepared by the layer-by-layer technique provide an efficient way to generate planar structures of tailored surface charge and hydrophobicity, which are used as membranes for pervaporation. The use of polyelectrolyte multilayers to form the membrane permits tailoring the surface charge of the membrane and, thus, selectivity; at the same time, it reduces fouling of the membrane by adsorption of organic matter. Pulsed field gradient (PFG) nuclear magnetic resonance has been used to investigate the diffusion of probe molecules into polymer systems. Evaluation of the apparent diffusion coefficient in porous poly(amide) results in a pore size of 4 microm, as found in electron micrographs. For the pore size obtained for polyelectrolyte multilayers, no equivalent pores could be found in microscopy. Propagators for the diffusion of propanol and propanol-water mixture into multilayers reveal that there might be selective interaction of probe molecules with the polyelectrolyte system.     

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.     

The modulation of coupled relaxation in porous media.

This work investigates the effects of modulation of the transverse and longitudinal relaxation of the surface-fluid/pore-fluid spin system in porous media. Important new NMR well logging applications identify pore fluids by varying the CPMG T(2) pulse spacing to discriminate on the basis of fluid diffusivities in applied and local static magnetic field gradients. However, anomalous laboratory CPMG T(2) results have been reported repeatedly over 25 years for various porous media filled with a single fluid. In relatively large pores, at near bulk conditions, the transverse relaxation of diffusing molecular spins should be proportional to the square of the CPMG pulse spacing tau, the susceptibility contrast at the pore wall and the applied gradient. Observed is a markedly linear tau dependence that saturates at a plateau for large tau. The effect is not quadratic in applied gradient or susceptibility. For large pores, the tau dependence and the saturation value are proportional to the surface-to-volume ratio of the pores. This is in distinct contrast to the behavior observed by Borgia, Brown and Fantazzini for systems with much smaller pores at higher magnetic fields. The large-pore anomalous behaviors can be explained as a modulation of the exchange between surface-fluid and pore-fluid spins, such as observed by Luz and Meiboom in 1963 for water enriched with quadrupolar 17O. Scalar coupling of the solid-surface spins to the fluid-surface spins was postulated by Kleinberg, Kenyon and Mitra as a dominant relaxation mechanism for the surface fluid. The CPMG tau effect can be described as the modulation of the exchange coupling by the CPMG pi pulses, which mix the magnetizations between the exchanging, strongly coupled spin systems of the pore-fluid and the surface-fluid, which is, in turn, weakly coupled by scalar or pseudo-scalar interactions to the fast-relaxing solid surface.     

Diffusion effects on the CPMG relaxation rate in a dipolar field

The diffusion in the magnetic dipolar field around a sphere is considered. The diffusion is restricted to the space between two concentric spheres, where the inner sphere is the source of the magnetic dipolar field. Analytical expressions for the CPMG transverse relaxation rate as well as the free induction decay and the spin echo time evolution are given in the Gaussian approximation. The influence of the inter-echo time is analyzed. The limiting cases of small and large inter-echo times as well as the short and long time behavior are evaluated.     

Effective Gradients in Porous Media Due to Susceptibility Differences

In porous media, magnetic susceptibility differences between the solid phase and the fluid filling the pore space lead to field inhomogeneities inside the pore space. In many cases, diffusion of the spins in the fluid phase through these internal inhomogeneities controls the transverse decay rate of the NMR signal. In disordered porous media such as sedimentary rocks, a detailed evaluation of this process is in practice not possible because the field inhomogeneities depend not only on the susceptibility difference but also on the details of the pore geometry. In this report, the major features of diffusion in internal gradients are analyzed with the concept of effective gradients. Effective gradients are related to the field inhomogeneities over the dephasing length, the typical length over which the spins diffuse before they dephase. For the CPMG sequence, the dependence of relaxation rate on echo spacing can be described to first order by a distribution of effective gradients. It is argued that for a given susceptibility difference, there is a maximum value for these effective gradients,g_max, that depends on only the diffusion coefficient, the Larmor frequency, and the susceptibility difference. This analysis is applied to the case of water-saturated sedimentary rocks. From a set of NMR measurements and a compilation of a large number of susceptibility measurements, we conclude that the effective gradients in carbonates are typically smaller than gradients of current NMR well logging tools, whereas in many sandstones, internal gradients can be comparable to or larger than tool gradients.     

A global inversion method for multi-dimensional NMR logging

We describe a general global inversion methodology of multi-dimensional NMR logging for pore fluid typing and quantification in petroleum exploration. Although higher dimensions are theoretically possible, for practical reasons, we limit our discussion of proton density distributions as a function of two (2D) or three (3D) independent variables. The 2D can be diffusion coefficient and T(2) relaxation time (D-T(2)), and the 3D can be diffusion coefficient, T(2), and T(1) relaxation times (D-T(2)-T(1)) of the saturating fluids in rocks. Using the contrast between the diffusion coefficients of fluids (oil and water), the oil and water phases within the rocks can be clearly identified. This 2D or 3D proton density distribution function can be obtained from either two-window or regular type multiple CPMG echo trains encoded with diffusion, T(1), and T(2) relaxation by varying echo spacing and wait time. From this 2D/3D proton density distribution function, not only the saturations of water and oil can be determined, the viscosity of the oil and the gas-oil ratio can also be estimated based on a previously experimentally determined D-T(2) relationship.     

Comparison of electron spin relaxation times measured by Carr-Purcell-Meiboom-Gill and two-pulse spin-echo sequences

Electron spin relaxation times obtained by two-pulse spin-echo and Carr-Purcell-Meiboom-Gill (CPMG) experiments were compared for samples with: (i) low concentrations of nuclear spins, (ii) higher concentrations of nuclear spins and low concentrations of unpaired electrons, (iii) higher concentrations of nuclear spins and of electron spins, and (iv) dynamic averaging of inequivalent hyperfine couplings on the EPR timescale. In each case, the CPMG time constant decreased as the time between the refocusing pulses increased. For the samples with low concentrations of nuclear spins (the E' center in irradiated amorphous SiO2) the limiting value of the CPMG time constant at short interpulse spacings was similar to the Tm obtained by two-pulse spin echo at small turning angle. For the other samples, the time constants obtained by CPMG at short interpulse spacings were systematically longer than Tm obtained by two-pulse spin echo. For most of the samples, the CPMG time constant decreased with increasing electron spin concentration, which is consistent with the expectation that the CPMG sequence does not refocus dephasing due to electron-electron dipolar interaction between resonant spins. Dynamic processes that average inequivalent hyperfine couplings contributed less to the CPMG time constant than to the spin-echo decay time constant. The impact of nuclear echo envelope modulation on CPMG time constants also was examined. For a Nycomed trityl radical in glassy D2O:glycerol-d8 solution, the CPMG time constant was up to 20 times longer when the time between pulses was approximately equal to integer multiples of the reciprocal of the deuterium Larmor frequency than when the time between pulses was an odd multiple of half the reciprocal of the deuterium Larmor frequency.     

Measurement of multilamellar onion dimensions under shear using frequency domain pulsed gradient NMR

We present a simple method by which the dimensions of shear-induced multilamellar vesicles (MLVs), also known as onions, can be measured during the shearing process itself. This approach is based on the use of a closely spaced train of magnetic field gradient pulses applied during a CPMG echo sequence. The CPMG train compensates flow effects while the frequency-dependence of apparent diffusion can reveal the onion size. We present here a simple phenomenological model for restricted diffusion in multilamellar vesicles, which may be used to interpret the resulting diffusion spectrum. We demonstrate this approach with MLVs formed from the lamellar phase of sodium dodecyl sulfate (SDS) in water and octanol.     

Restricted diffusion in grossly inhomogeneous fields

We analyze the effects of geometrical restriction on the nuclear magnetization of spins diffusing in grossly inhomogeneous fields where radio-frequency (RF) pulses are weak relative to the total field inhomogeneity, making the rotation angle space-dependent and thus exciting multiple coherence pathways. We show how to separate the effects of restricted diffusion from the effects of the pulses in the case when the change in the field experienced by a diffusing spin in the course of the experiment is small compared to the RF magnitude. We then derive explicit formulas for the contribution of individual coherence pathways to the total magnetization in arbitrary pulse sequences. We find that, for long diffusion times, restriction can dramatically alter the spectrum and the shape of a particular echo, while for short times, the correction will be proportional to the pore space surface-to-volume ratio. We demonstrate these results on the example of the early echoes of the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.     

Thermodynamic Nonequilibrium Features in Binary Diffusion

Diffusion is a ubiquitous physical phenomenon where thermodynamic nonequilibrium effects(TNEs) are outstanding issues. In this work, we employ the discrete Boltzmann method to investigate the TNEs in the dynamic process of binary diffusion. The main features of the distribution function in velocity space are recovered and discussed.It is found that, with the decreasing gradients of macroscopic quantities(such as density, concentration, velocity, etc.),both the local and global TNEs decrease with the time but increase with the relaxation time in a power law, respectively.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

三种测量橡胶交联密度的核磁共振方法比较

核磁共振（NMR）技术已经成为测量橡胶交联密度的一种常用技术手段．该文探讨了用于测量橡胶交联密度的三种NMR方法：¹H双量子（DQ）NMR、¹H Hahn回波和¹H CPMG回波,讨论了这些方法测量值差异的来源．在此基础上进一步研究了¹H CPMG回波方法中回波时间对测量值的影响,探讨了改善¹H CPMG回波方法的方案．