We have established a simple Fourier-space relationship between the structure of heterogeneous samples and the amplitude of multiple spin echoes which arise in solution NMR as a result of the dipolar nuclear demagnetizing field. We have also developed a pulse sequence optimized for structure measurements in two component systems. The new formalism predicts the behavior of multiple spin echoes well and gives a very good description of experimental data obtained from simply structured samples.[S0031-9007(96)00386-9] PACS numbers: 76.60. Lz, 76.60.Pc The effect of the dipolar nuclear demagnetizing field is generally neglected in nuclear magnetic resonance (NMR) of liquids, since it is many orders of magnitude weaker than any applied magnetic fields. In experiments which lead to the production of spatially modulated nuclear magnetization, the dipolar demagnetizing field can, however, cause a significant perturbation of the evolution of magnetization. In particular, in a conventional spin echo experiment [1], where a sequence of two radio-frequency (rf) pulses applied at times 0 and t e normally produces a single echo of the NMR signal at time 2t e , the dipolar demagnetizing field leads to the production of multiple spin echoes (MSE) occurring at multiples of t e larger than 2 [2-7]. Signals equivalent to MSE also appear in twodimensional NMR experiments utilizing pulsed magnetic field gradients. These signals give rise to unexpected cross peaks in the resulting spectra [8][9][10].Recently, it has been proposed that through manipulation of the demagnetizing field MSE may be used to extract structural information [10]. This is possible because in the presence of spatially modulated magnetization the demagnetizing field, experienced by a particular nuclear spin, results predominantly from the local magnetization found at a distance less than the spatial period of modulation [9]. By adjusting this period, structure may therefore be probed at varying length scales. All the magnetization contributes to the NMR signal in such experiments, irrespective of the period of spatial modulation. Consequently, there is no reduction in sensitivity on moving to finer resolution, and the achievable resolution is set by the mobility of the spin bearing molecules rather than by direct signal to noise ratio considerations as in conventional magnetic resonance imaging [10]. Mobility is important since the MSE result from dipolar interactions which are not averaged to zero on the experimental time scale. In liquids, such as water, diffusion thus sets a lower limit to the resolution of the order of 10 mm.In this Letter we demonstrate how a simple and direct relation between the structure under investigation and the amplitude of the MSE may be developed. We also introduce a new experiment to create MSE between two components with different resonance frequencies.Theoretical predictions are compared with experimental results obtained by application of this sequence to a set of simple structures.MSE are generated by the dipolar demagnetizing...

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We demonstrate theoretically and experimentally how the dipolar field can be used in nuclear magnetic resonance (NMR) to investigate the structure of heterogeneous liquid systems. Using the Fourier transformed dipolar field and magnetization distribution, a simple relation between the NMR signal generated by the dipolar field and the sample structure can be established. On the basis of this relation, theoretical models for periodic structures have been derived and used to analyze the variation of the NMR signal as a function of the spatial modulation imposed on the magnetization. If the spatial modulations imposed on the transverse and longitudinal magnetizations have the same wavelength, the signal generated by the dipolar field is a continuous function of the modulation wavelength and is sensitive to the structure of the sample. When this condition is not met, diffraction phenomena may be possible in periodic structures. To test the theoretical work, experimental data have been obtained from water surrounding randomly packed microspheres. These data are in agreement with the theoretical predictions and show that a resolution of the order of 10 μm can be achieved for highly mobile systems. For spin bearing molecules, whose self-diffusion coefficient is two orders of magnitude less than that of free water, submicrometer resolution is expected.

In this work, we examine the rich crystallization behavior that occurs in PbII/S-II/poly(ethylene oxide) (PEO)/sodium dodecyl sulfate (SDS) systems, in which the anionic surfactant interacts strongly with the polymer molecules, forming micellar aggregates attached to the polymer chains above the critical association concentration. Lead sulfide crystallites are formed in the vicinity of polymer-bound micelles by adding lead and sulfide ions to the polymer−surfactant solution. Surfactant-stabilized inorganic particles adsorbed on the polymer chains combine through a polymer-mediated bridging flocculation mechanism to produce characteristic rodlike colloidal aggregates. Under certain conditions, these evolve into a range of metastable structures, composed of lead sulfide, PbS, and lead dodecyl sulfate, Pb(DS)2. XRD analysis of the metastable reaction products allows us to follow the slow kinetics of their formation and reveals a well-defined layered structure, based on lead dodecyl sulfate, the thickness of which is determined by the length of the surfactant chains. Elemental analysis, 13C- and 207Pb−NMR spectroscopy, FTIR spectroscopy, XPS, and HRTEM are used to characterize these superstructures. At other pH values and system compositions, the production of pure PbS or pure Pb(DS)2 is favored, by appropriate tuning of the concentrations of Pb2+ and S2- ions. The resulting unexpectedly rich crystallization behavior illustrates the complexity of colloidal aggregation phenomena in polymer−surfactant solutions and the significance of coupling colloidal aggregation to ionic equilibria.