Use of the second dimension in PGSE NMR studies of porous media

2-dimensional methods based on PGSE NMR may be used to correlate or separate molecular dynamical properties, or to elucidate fluctuations. These may utilize either the gradient (q-vector) domain, in which molecular displacements are measured, or the time domain, in which relaxation is measured, and may be analyzed by combinations of inverse Fourier or Laplace transforms. Existing methodologies are reviewed and new experiments proposed. In particular the use of diffusion-diffusion exchange and correlation analysis is demonstrated using the case of water diffusion in a lamellar phase liquid crystal.

2D relaxation/diffusion correlations in porous media

2D correlations between NMR relaxation and/or diffusion have been used to investigate water and oil dynamics in food and micro-emulsion systems. In the case of Mozzarella and Gouda cheese samples, a significant change in D/T2 correlation is appearing with cheese aging. In the case of a water/toluene micro-emulsion, some evidence for coalescence effects is suggested by D/D exchange spectra.

NMR visualization of displacement correlations for flow in porous media

The temporal correlations of velocities for both water and a water-glycerol mixture flowing through a random packings of monodisperse spherical particles have been investigated using two-dimensional nuclear magnetic resonance methods. By combining various flow rates, fluid viscosities, and bead sizes, a wide range of flow parameters has been covered, the dimensionless Peclet number ranging from 100 to 100 000. The velocity exchange spectroscopy (VEXSY) technique has been employed to measure the correlation between velocities during two intervals separated from each other by a mixing time tau(m). This time is made both large and small compared with the time constant tau(c), required for a fluid element possessing the average flow velocity to cover a distance equal to the characteristic size in the system, the bead diameter. The two-dimensional conditional probability of displacement resulting from the VEXSY method reveals the existence of different "subensembles" of molecules, including a slow moving pool whose displacement is dominated by Brownian motion, an intermediate ensemble whose velocities change little over the mixing time, and a fast flowing ensemble which loses correlation due to mechanical dispersion. We find that that the approach to asymptotic dispersion, as tau(c)/tau(m) increases, depends strongly on the Peclet number, the deviation of the velocity autocorrelation function from a monoexponential Ornstein-Uhlenbeck process becoming more pronounced with increasing Peclet number.

Biaxial deformation of a polymer under shear: NMR test of the Doi-Edwards model with convected constraint release

2H NMR quadrupole interaction spectroscopy has been used to measure the deformation of a 670 kD poly(dimethylsiloxane) melt under shear in a Couette cell. The signals were acquired from a per deuterated benzene probe molecule which provides a motionally averaged sampling of the entire segmental ensemble. We have measured the dependence on shear rate of the S(XX) (velocity), S(YY) (velocity gradient), S(ZZ) (vorticity), and S(XY) (shear) elements of the segmental alignment tensor, as well as the angular dependence of the deuterium quadrupole splitting at fixed shear rate. We show that the data agree quite well with the Doi-Edwards theory but significantly better when convected constraint release effects are included. These fits return a value for the tube disengagement time of 100 ms.

Two-dimensional NMR of velocity exchange: VEXSY and SERPENT

Two different multidimensional pulsed field gradient sequences are compared which have the purpose of correlating spin displacements in different time intervals with each other. The simplest possible sequence, three-pulse SERPENT, measures displacements in two interleaved time intervals, while in VEXSY, consisting of two independent pairs of gradient pulses separated by a mixing time, displacements during the two encoding intervals are compared to each other. The formalism for both sequences is discussed in q space and in displacement space and common features as well as differences between the two types of experiments are highlighted, employing the particular case of the concurrent VEXSY scheme which allows treatment according to both formalisms.

Shear banding and the isotropic-to-nematic transition in wormlike micelles

Using deuterium NMR spectroscopy in a Couette cell, we observe shear-induced nematic ordering in the concentrated wormlike-micelle system CTAB/D(2)O, and our results are qualitatively consistent with birefringence studies, and in exact quantitative agreement with the degree of order measured in neutron-diffraction measurements. The width of the nematic region depends on shear rate, as well as on the temperature proximity to the equilibrium isotropic-nematic transition. Comparison of the nematic order profiles with velocity profiles obtained under identical conditions shows quite clearly that the nematic state is not identifiable with a highly sheared, low viscosity layer, and we conclude that the process of shearing induces a nematic state of high viscosity, possibly associated with mesoscale ordering. We present a simple model in which transition from the high shear branch to the viscous nematic branch is counterbalanced by subsequent relaxation of nematic order.

Selective storage of magnetization in strongly relaxing spin systems

We have investigated the use of a "split-sinc" RF pulse to selectively store magnetization from a selected region of a sample, for later recall in imaging or spectroscopy experiments. The pulse sequence is based on an original suggestion by Post et al. (West German Patent No. P3209263.6, 13 March 1982), later implemented by Aue et al. (J. Magn. Reson. 56, 350 (1984)). We have carried out detailed numerical calculations using the Bloch equations and show that this particular sequence is robust in the face of strong transverse relaxation, and we demonstrate its application to imaging of polymer samples in shearing and extensional flow cells.

Low-frequency velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo

In addition to the fast correlation for local stochastic motion, the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. Here we present its study by the NMR modulated gradient spin-echo method (MGSE) [1] on a system of water trapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo attenuation proportional to a value of the molecular velocity correlation spectrum at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency molecular dynamics in fluids. In our experiment, it enables to extract the low frequency correlation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay of the spectrum), which can be interpreted as a molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories and simulation, which predict slow negative long time tail of molecular velocity correlation dynamics in confined fluids, the obtained velocity correlation spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of the recently developed approach to the spin echo in porous media, that uses the spin phase average with the cumulant expansion to get the attenuation as a discord of spin spatial coherence [4].

Time-dependent velocities in porous media dispersive flow

Pulsed Gradient Spin Echo (PGSE) NMR methods may be used to measure the asymptotic dispersion coefficient as well as the velocity autocorrelation function (VACF) in porous media flow. The VACF can be measured in the frequency domain using repetitive gradient pulse trains, and in the time domain using double PGSE encoding. The one dimensional double PGSE method, and the two dimensional velocity exchange experiment (VEXSY) are briefly outlined and their application to flow in monodisperse 0.5 mm diameter beads packs described, both axial and transverse VACFs being examined. The measured correlation times are shown to agree well with calculated values. The asymptotic dispersion coefficients agree with literature values in the case of transverse flow while in axial flow it is shown that asymptotic conditions are not achieved, even for observation times longer than the correlation time for flow around a bead.

One-shot velocimetry using echo planar imaging microscopy

A rapid version of PEPI (pi-echo planar imaging) velocimetry has been implemented, enabling a velocity image, at microscopic resolution, to be acquired in less than 1 s. The velocity map was reconstructed using the phase information from the ratio of two PEPI images, one obtained with a velocity-encoding filter applied prior to the imaging sequence and the other image without. The acquisition time for each image was about 80 ms and the two complete image acquisitions were acquired in one shot in 500 ms. This rapid velocimetry sequence gave a good representation of laminar pipe flow. It has also been used to examine extensional flow in a biaxial extension in which the transient extension takes about 3 s.