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X-ray waveguiding studies of ordering phenomena in confined fluids
Zwanenburg, M.J.
Publication date
2001
Link to publication
Citation for published version (APA):
Zwanenburg, M. J. (2001). X-ray waveguiding studies of ordering phenomena in confined
fluids.
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Summary y
Thee properties of a fluid confined between two hard walls have been the subject of manyy studies. Confined fluids are commonly encountered as lubricants in between slidingg surfaces and are therefore of technological relevance. The lubricating prop-ertiess may be affected substantially by a change in the thickness of the fluid film. Namely,, as the thickness of the fluid film is reduced to only a few times the size off the fluid's constituents, pronounced ordering effects within the fluid and even solidificationn have been predicted to occur. In order to verity this prediction we performedd x-ray scattering experiments for the structural analysis of the confined fluid. .
Ourr method is based on the following principles. A fluid is confined between twoo ultra-smooth parallel plates which may be set at distances as small as a few tenss of nanometers. This is realized by making use of piezo-driven motors for controll of the distance in combination with an optical interferometric method for measurementt of the distance and tilt (see chapter 3). After the plate distance iss set, the device is illuminated with an x-ray beam from the side, such that the anglee of incidence with respect to the surfaces of the plates is grazing. If the anglee of incidence is smaller than the critical angle for total internal reflection (typicallyy < 0.2°), then the x rays remain confined within the gap between the plates.. Hence, the device acts as a waveguide for x rays. As a result of the totall internal reflections, the amplitude of the wave field is almost zero near the confiningg walls which minimizes background scattering from the confining walls. Inn the presence of variations in the refractive index (i.e., density variations), the wavess propagating within the fluid will be scattered into different directions. As thee wave field within the waveguide is a linear combination of a discrete set of waveguidee modes, the scattering process can be described as a coupling of these modes.. In chapter 2 we discuss how the modes are obtained for a planar waveguide
120 0 Summary Summary
whichh is filled with a fluid having a given refractive-index profile. This is followed byy a discussion of the numerical calculation of wave fields within a waveguide.
Inn the first experiments we studied the transmission properties of the empty waveguide,, i.e. with air in between the plates (chapter 4). These experiments were performedd in order to study the excitation and propagation of the modes. In our geometryy a well-defined standing wave field is formed at the entrance of the wave-guidee upon illumination. By tuning the angle of incidence we are able to change thee spacing of the nodes of the standing wave field. If a node is made to coincide withh the position of the top plates, the incident wave field exactly corresponds too that of a mode. In this way, single modes were excited. Transmission mea-surementss showed that the modes propagate almost undisturbed, which indicates thee high quality of the waveguides. For other angles of incidence we observed the excitationn of multiple modes due to the mismatch of the incident wave field with thatt of any of the single modes. The resulting wave field exhibited multi-mode interferencee effects as was derived from measurement of intensities diffracted from thee waveguide exit. Consequently, both spatial coherence and temporal coherence off the x rays were preserved upon propagation.
Ourr waveguide may also serve as a focusing device. In chapter 5 we demonstrate howw the tapering of an empty planar waveguide results in a very small line focus off coherent x rays. The focusing is based on the compression of the wave field andd the exploitation of the multi-mode interference effects. The good agreement betweenn the measurements and calculations demonstrates the feasibility of shaping thee compressed wave field in a controlled way.
Inn chapter 6 we deduce the structure of a colloidal suspension in confinement by makingg use of the waveguiding characteristics of the system. The colloid, consisting off a 10 vol. % suspension of 110 nm diameter SiC>2 spheres in dimethylformamide, wass confined in gaps of various sizes. From a model-dependent analysis of the angularr dependence of the measured transmitted intensities, we deduced that six layerss had formed parallel to the confining walls which were set at a distance off 655 nm. The density profile obtained shows that the layers are well ordered att the interfaces and less well ordered in the center of the gap. Similarly, for a walll separation of 310 nm we observed the formation of only two layers. It was concludedd that the confinement induces a crystallisation of the colloid.
Summary Summary 121 1 structurall investigations of a wide variety of confined systems. In addition, by makingg use of a technique called x-ray photon correlation spectroscopy, we may obtainn time correlation functions which reveal the effect of confinement on the diffusionn constant of the fluid's constituents. Hence, it is possible to study both thee structure and the dynamics of confined systems.
