Sphere, lamellar sheets

Figure 9.1 Schematic of block-copolymer microdomains in thin films. Panels a and b show one layer of spheres and cyUnders, respectively (darker component). Note the additional wetting layers above and below the microdomains that serve to satisfy the interfacial constraints the specific configuration varies depending upon the copolymer system. Panel c shows lamellar sheets oriented parallel to the substrate by the strong alignment influence of the substrate and vacuum/polymer interfaces. (Reproduced with permission from the American Association for the Advancement of Science)...

The ideas underlying elemental structures models are to establish microstructures experimentally, to compute free energies and chemical potentials from models based on these structures, and to use the chemical potentials to construct phase diagrams. Jonsson and Wennerstrom have used this approach to predict the phase diagrams of water, hydrocarbon, and ionic surfactant mixtures [18]. In their model, they assume the surfactant resides in sheetlike structures with heads on one side and tails on the other side of the sheet. They consider five structures spheres, inverted (reversed) spheres, cylinders, inverted cylinders, and layers (lamellar). These structures are indicated in Fig. 12. Nonpolar regions (tails and oil) are cross-hatched. For these elemental structures, Jonsson and Wennerstrom include in the free energy contributions from the electrical double layer on the water... 

For comparison, let us calculate the surface area (St) of a tetrahedral unit TO4 which is a common constituent of organically templated lamellar metal phosphates [28]. The surface area is controlled by the average bond length which can vary from 1.5 to 1.7 A. Since the TO4 tetrahedron may take any position relative to the plane of the sheet, it is convenient to restrict its volume by a sphere with its center at T and its radius being the average bond length. The surface area of the tetrahedron will be within the central... 

Figure 6 Schematic illustration of the structure of the lamellar crystals formed from crystallization of [(AlaGlyjsGluGlyjse. The crystal is formed from stacked p-sheets with the periodic glutamic acid residues (green spheres) placed at the crystal surface. Reproduced with permission from Dreher, M. R. Simnick, A. J. Fischer, K. etal. J. Am. Chem. Soc. 2008, 130, 687-694. ...

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