Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence

A single-shot measurement of time-dependent diffusion over sub-millisecond timescales using static field gradient NMR

Time-dependent diffusion behavior is probed over sub-millisecond timescales in a single shot using a nuclear magnetic resonance static gradient time-incremented echo train acquisition (SG-TIETA) framework. The method extends the Carr-Purcell-Meiboom-Gill cycle under a static field gradient by discretely incrementing the π-pulse spacings to simultaneously avoid off-resonance effects and probe a range of timescales (50-500 µs). Pulse spacings are optimized based on a derived ruleset. The remaining effects of pulse inaccuracy are examined and found to be consistent across pure liquids of different diffusivities: water, decane, and octanol-1. A pulse accuracy correction is developed. Instantaneous diffusivity, Dinst(t), curves (i.e., half of the time derivative of the mean-squared displacement in the gradient direction) are recovered from pulse accuracy-corrected SG-TIETA decays using a model-free log-linear least squares inversion method validated by Monte Carlo simulations. A signal-averaged 1-min experiment is described. A flat Dinst(t) is measured on pure dodecamethylcyclohexasiloxane, whereas decreasing Dinst(t) is measured on yeast suspensions, consistent with the expected short-time Dinst(t) behavior for confining microstructural barriers on the order of micrometers.

Breakdown of Carr-Purcell Meiboom-Gill spin echoes in inhomogeneous fields

The Carr-Purcell Meiboom-Gill (CPMG) experiment has been used for decades to measure nuclear-spin transverse (T₂) relaxation times. In the presence of magnetic field inhomogeneities, the limit of short interpulse spacings yields the intrinsic T₂ time. Here, we show that the signal decay in such experiments exhibits fundamentally different behaviors between liquids and gases. In gases, the CPMG unexpectedly fails to eliminate the inhomogeneous broadening due to the non-Fickian nature of the motional averaging.

Measurement of interfacial area from NMR time dependent diffusion and relaxation measurements

The interfacial area between two immiscible phases in porous media is an important parameter for describing and predicting 2 phase flow. Although present in several models, experimental investigations are sparse due to the lack of appropriate measurement techniques. We propose two NMR techniques for the measurement of oil-water interfacial area: (i) a time dependent NMR diffusion technique applicable in static conditions, similar to those used for the measurement of the solid specific surface of a porous media, and (ii) a fast relaxation technique applicable in dynamic conditions while flowing, based on an interfacial relaxation mechanism induced by the inclusion of paramagnetic salts in the water phase. For dodecane relaxing on doped water, we found an oil interfacial relaxivity of 1.8μm/s, large enough to permit the measurement of specific interfacial surface as small as 1000cm²/cm³. We demonstrate both NMR techniques in drainage followed by imbibition, in a model porous media with a narrow pore size distribution. While flowing, we observe that the interfacial area is larger in imbibition than in drainage, implying a different organization of the oil phase. In a carbonate sample with a wide pore size distribution, we evidence the gradual invasion of the smallest pores as the oil-water pressure difference is increased.

Symmetry of the gradient profile as second experimental dimension in the short-time expansion of the apparent diffusion coefficient as measured with NMR diffusometry

The time-dependent apparent diffusion coefficient as measured by pulsed gradient NMR can be used to estimate parameters of porous structures including the surface-to-volume ratio and the mean curvature of pores. In this work, the short-time diffusion limit and in particular the influence of the temporal profile of diffusion gradients on the expansion as proposed by Mitra et al. (1993) is investigated. It is shown that flow-compensated waveforms, i.e. those whose first moment is zero, are blind to the term linear in observation time, which is the term that is proportional to mean curvature and surface permeability. A gradient waveform that smoothly interpolates between flow-compensated and bipolar waveform is proposed and the degree of flow-compensation is used as a second experimental dimension. This two-dimensional ansatz is shown to yield an improved precision when characterizing the confining domain. This technique is demonstrated with simulations and in experiments performed with cylindrical capillaries of 100 μm radius.

A practical tutorial to set up NMR diffusometry equipment: application to liquid crystals

NMR diffusometry is nowadays a well-established and powerful technique to investigate molecular translation in fluid materials. Standard NMR diffusometry approaches are based on pulsed field gradients generated by specific hardware and specially designed NMR probes. Here, we present an alternative set-up that exploits the static gradient present in the fringe field of any commercial superconducting magnet. This stray field diffusometry technique can be particularly useful to study diffusional processes in fast-relaxing and slow-diffusing systems, such as thermotropic liquid crystals, ionic liquids and polymer melts.

Exact analytical results for ADC with oscillating diffusion sensitizing gradients

The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion sensitizing gradients. Exact analytical expressions are obtained in the high-frequency expansion of the ADC for an arbitrary number of oscillations N. These expressions are universal and valid for arbitrary system geometry. The validity conditions of the high-frequency expansion of ADC are obtained in the framework of a simple 1D model of restricted diffusion. These conditions are shown to be substantially different for cos- and sin-type gradients: for the cos-type gradients, the high-frequency expansion is valid when the period of a single oscillation is smaller than the characteristic diffusion time, the frequency dependence of ADC being practically the same for any N. In contrast, for the sin-type gradients, the high-frequency regime can be achieved only when the total diffusion time is smaller than the characteristic diffusion time, the frequency dependence of ADC being different for different N.

Surface-to-volume ratio with oscillating gradients

Restrictions to diffusion result in the dispersion of the bulk diffusion coefficient. We derive the exact universal high-frequency behavior of the diffusion coefficient in terms of the surface-to-volume ratio of the restrictions. This frequency dependence can be applied to quantify structure of complex samples with NMR using oscillating field gradients and static-gradient CPMG. We also demonstrate the inter-relations between different equivalent diffusion metrics, and describe how to calculate the effect of restrictions for arbitrary gradient waveforms.

29Si NMR in solid state with CPMG acquisition under MAS

A remarkable enhancement of sensitivity can be often achieved in 29Si solid-state NMR by applying the well-known Carr-Purcell-Meiboom-Gill (CPMG) train of rotor-synchronized pi pulses during the detection of silicon magnetization. Here, several one- and two-dimensional (1D and 2D) techniques are used to demonstrate the capabilities of this approach. Examples include 1D 29Si{X} CPMAS spectra and 2D 29Si{X} HETCOR spectra of mesoporous silicas, zeolites and minerals, where X=1H or 27Al. Data processing methods, experimental strategies and sensitivity limits are discussed and illustrated by experiments. The mechanisms of transverse dephasing of 29Si nuclei in solids are analyzed. Fast magic angle spinning, at rates between 25 and 40 kHz, is instrumental in achieving the highest sensitivity gain in some of these experiments. In the case of 29Si-29Si double-quantum techniques, CPMG detection can be exploited to measure homonuclear J-couplings.

Porous media characterization by PFG and IMFG NMR

Fully and partially filled with tridecane quartz sand was studied by different NMR techniques. The set of NMR experiments was carried out to obtain information about porous media geometry and fluid localization in it in case of partially filled porous space. The study was done using three NMR approaches: pulse field gradient NMR (PFG NMR), DDif experiment and tau-scanning experiment. The possibility to use all three approaches to study porous media properties even at the high resonance frequency is shown together with complementarity of the given by them information. Thus, first two approaches give information about porous sizes and geometry, at the same time tau-scanning experiment allows us to obtain information about distribution of internal magnetic field gradients in the porous space and draw conclusions about fluid localization in it.

Characterisation of the supramolecular structure of malonamides by application of pulsed field gradients in NMR spectroscopy

Malonamides are known and extensively studied for their lanthanide and actinide extracting properties. Those studies have also highlighted aggregated phenomena and a splitting of the organic phase, in some particular experimental conditions. To explain this behaviour of extractants, (1)H NMR was used to study micellar phenomena by the determination of the self-diffusion coefficients of two malonamides only different by the length of their alkyl chain (DMDBTDMA and DMDBPMA), in presence of n-dodecane and for systems saturated with water or anhydrous. Several information on the aggregates and on the malonamide supramolecular structure were obtained by fitting the curves of self-diffusion coefficient vs. concentration and by conjugated NMR experimental data to potentiometric titrations and physical measurements.

Spectral characterization of diffusion in porous media by the modulated gradient spin echo with CPMG sequence

Carr-Purcell-Meiboom-Gill train of radiofrequency pulses applied to spins in the constant magnetic field gradient is an efficient variant of the modulated magnetic field gradient spin echo method, which provides information about molecular diffusion in the frequency-domain instead in the time-domain as with the two-pulse gradient spin echo. The frequency range of novel technique is broad enough to sample the power spectrum of displacement fluctuation in water-saturated pulverized silica (SiO(2)) and provides comprehensive information about the molecular restricted motion as well as about the structure of medium.