The “corset effect” of spin-lattice relaxation in polymer melts confined in nanoporous media

Linear polyethylene oxides with molecular weightsM _w of 1665 and 10170 confined in pores with variable diameters in a solid methacrylate matrix were studied by proton field-cycling nuclear magnetic resonance relaxometry. The pore diameter was varied in the range of 9–57 nm. In all cases, the spin-lattice relaxation time shows a frequency dependence close toT ₁∞ v^3/4 in the range ofv=3·10^?1-2·10¹ MHz as predicted by the tube-reptation model. This protonT ₁ dispersion essentially reproduces that found in a previous deuteron study (R. Kimmich, R.-O. Seitter, U. Beginn, M. Möller, N. Fatkullin: Chem. Phys. Lett. 307, 147, 1999). As a feature particularly characteristic for reptation, this finding suggests that reptation is the dominating chain dynamics mechanism under pore confinement in the corresponding time range. The absolute values of the spin-lattice relaxation times indicate that the diameter of the effective tubes in which reptation occurs is much smaller than the pore diameters on the time scale of spin-lattice relaxation experimens. An estimation leads to a valued ^*～0.5 nm. The impenetrability of the solid pore walls, the uncrossability of polymer chains (“excluded volume”) and the low value of the compressibility in polymer melts create the “corset effect” which reduces the lateral motions of polymer chains to a microscopic scale of only a few tenths of a nanometer.     

Geometrical restrictions of water diffusion in aqueous protein systems. A study using NMR field-gradient techniques

Geometrical restrictions of water diffusion in different aqueous protein systems were studied using two versions of the NMR field gradient technique. The samples were aqueous systems of bovine serum albumin, gelatin and horse myoglobin at concentrations ranging from diluted solutions to almost dry powders being only partly hydrated. Hydrated protein aerogels were produced by the aid of a special preparation procedure and studied in addition. The experiments referred to the, temperature and concentration dependences of the water diffusion coefficient above and below the free-water freezing temperature. The diffusion coefficient within clusters of overlapping hydration shells is reduced by one order of magnitude compared with that of bulk water. Geometrical restrictions manifest themselves (a) by the obstruction effect observed at low protein concentrations, (b) by the topologically two-dimensional diffusion in the network of overlapping hydration shells, (c) by the percolation threshold appearing at about 15%_b.w. water and (d) by the anomalous diffusion behaviour concluded from the protein aerogel study.     

Über die Bedeutung von Diffusionsgrenzschichten bei Ionenaustauschvorgängen

Based on NMR imaging results of the spatial and temporal development of ion exchange processes in alginate gels, the question of appropriate modelling of these processes is discussed. For rare earth and actinoid ions, the behaviour is found to correspond qualitatively to the expectations of Stefan’s model (shrinking core model, SCM). However, quantitative correspondence of the experimental data with the model can only be achieved when an additional diffusive layer at the surface of the ion exchange material is assumed. An extension of the SCM with respect to this problem is derived.     

The heterogeneous distribution of the liquid phase in partially filled porous glasses and its effect on self-diffusion

The spatial distribution of the liquid phase in a typical, partially filled, porous glass (VitraPor #5) has been examined with the aid of magnetic resonance microscopy and field gradient nuclear magnetic resonance diffusometry techniques. The correlation length of the material turned out to be long enough to permit the visualization of the microscopic heterogeneity of the material by magnetic resonance imaging. Contrasts are dominated by transverse relaxation depending on local filling degree, which in turn depends on local microstructure. The bimodal heterogeneity of the latter was also visualized by scanning electron microscopy. The effect of heterogeneity on an effective diffusion coefficient has been examined for polar (water) and nonpolar (cyclohexane) molecules.     

Constant time steady gradient NMR diffusometry using the secondary stimulated echo

A pulse sequence producing a second stimulated echo is suggested for the compensation of relaxation and residual dipolar interaction effects in steady gradient spin echo diffusometry. Steady field gradients of considerable strength exist in the fringe field of NMR magnets, for instance. While the absolute echo time of the second stimulated echo is kept constant throughout the experiment, the interval between the first two radiofrequency pulses is augmented leading to a modulation of the amplitude of that second stimulated echo by self-diffusion only. The unique feature of this technique is that it is of a single-scan/single-echo-signal nature. That is, no reference signals neither of the same pulse sequence nor of separate experiments are needed. The new method was tested with poly(ethylene oxide) melts and proved to provide reliable data for (time dependent) self-diffusion coefficients down to the physical limit (D approximately 10(-15)m(2)/s) when flip-flop spin diffusion starts to become effective.     

Polymer chain dynamics under nanoscopic confinements

It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix. Both the molecular weight of the PEO and the mean diameter of the strands were varied to a certain degree. The chain dynamics of the PEO in the molten state was examined with the aid of field-gradient NMR diffusometry (time scale, 10(-2)-10(0) s) and field-cycling NMR relaxometry (time scale, 10(-9)-10(-4) s). The dominating mechanism for translational displacements probed in the nanoscopic strands by either technique is shown to be reptation. On the time scale of spin-lattice relaxation time measurements, the frequency dependence signature of reptation (i.e., T1 approximately nu(3/4)) showed up in all samples. A "tube" diameter of only 0.6 nm was concluded to be effective on this time scale even when the strand diameter was larger than the radius of gyration of the PEO random coils. This corset effect is traced back to the lack of the local fluctuation capacity of the free volume in nanoscopic confinements. The confinement dimension is estimated at which the crossover from confined to bulk chain dynamics is expected.     

Flow measurements below 50 mum: NMR microscopy experiments in lithographic model pore spaces

Quasi two-dimensional random site percolation model objects have been prepared using a synchrotron radiation lithography technique with a spatial resolution better than 50 microm and an aspect ratio of up to 17. Flow of water through the pore space was studied with the aid of an NMR velocity mapping method and compared with a computational fluid dynamics simulation. In order to be able to measure and map widely distributed flow velocities with microscopic resolution (typically 40 x 40 microm), an experimental protocol that permits one to cover an effectively very wide velocity field of view (0.6-10 mm/s) had to be developed.     

Visualization of transport: NMR microscopy experiments with model objects for porous media with pore sizes down to 50 microm

Hydrodynamic flow and electric currents through model porous media were investigated. The transport rates through the individual pathways of the pore network are determined by the local width of the pore channels and by the driving mechanism. The model objects represent quasi two-dimensional random site percolation clusters. The calculated design was realized by milling the structure in polystyrene sheets. Velocity maps of stationary flow and current density maps of stationary currents through the cluster were acquired by magnetic resonance imaging methods. The findings were compared to the results of numerical simulations based on the same structure. Since the difference in the transport patterns of the different driving mechanisms are expected to be more pronounced in smaller pore spaces, ultra deep X-ray lithography has been used for the fabrication of downsized model objects with a spatial resolution of better than 50 microm and an aspect ratio as large as 20. First results obtained with these objects are reported.     

Diffusion measurements with the aid of nutation spin echoes appearing after two inhomogeneous radiofrequency pulses in inhomogeneous magnetic fields

Nutation echoes are generated by radiofrequency (RF) pulses with an inhomogeneous amplitude, B(1) = B(1)(r), in inhomogeneous magnetic fields, B(0) = B(0)(r). The two gradients of strengths G(1) and G(0), respectively, must be aligned in parallel for a maximum echo signal. After two RF pulses, two echoes appear at times tau(a) = 2 tau(1) + tau(2) + (G(1)/G(0))tau(1) and tau(b) = 2 tau(1) + tau(2) + 2(G(1)/G(0))tau(1), where tau(1) is the RF pulse duration and tau(2) the interpulse interval. It is shown that these echoes can favorably be employed for the determination of self-diffusion coefficients even in the poor experimental situation one often faces in low-resolution or low-field NMR. The signal intensity is comparable to that of ordinary Hahn echoes. Diffusion coefficients and spin-lattice relaxation times can be evaluated from the same experimental data set if both nutation echoes are recorded. Test experiments are in good agreement with literature data. Applications of the technique to "inside out" NMR, well logging NMR, surface coil NMR, toroid cavity NMR, etc., are suggested.     

Flow, diffusion, and thermal convection in percolation clusters: NMR experiments and numerical FEM/FVM simulations.

Percolation objects were fabricated based on computer-generated, two- or three-dimensional templates. Random-site, semi-continuous swiss cheese, and semi-continuous inverse swiss-cheese percolation models above the percolation threshold were considered. The water-filled pore space was investigated by NMR imaging and, in the presence of a pressure gradient, NMR velocity mapping. The fractal dimension, the correlation length, and the percolation probability were evaluated both from the computer-generated templates and the corresponding NMR spin density maps. Based on velocity maps, the percolation backbones were determined. The fractal dimension of the backbones turned out to be smaller than that of the complete cluster. As a further relation of interest, the volume-averaged velocity was calculated as a function of the probe volume radius. In a certain scaling window, the resulting dependence can be represented by a power law the exponent of which was not yet considered in the theoretical literature. The experimental results favorably compare to computer simulations based on the finite-element method (FEM) or the finite-volume method (FVM). Percolation theory suggests a relationship between the anomalous diffusion exponent and the fractal dimension of the cluster, i.e., between a dynamic and a structural parameter. We examined interdiffusion between two compartments initially filled with H2O and D2O, respectively, by proton imaging. The results confirm the theoretical expectation. As a third transport mechanism, thermal convection in percolation clusters of different porosities was studied with the aid of NMR velocity mapping. The velocity distribution is related to the convection roll size distribution. Corresponding histograms consist of a power law part representing localized rolls, and a high-velocity cut-off for cluster-spanning rolls. The maximum velocity as a function of the porosity clearly visualizes the percolation transition.