Interfacial topology

The area per surfactant molecule at the hydrophobic-hydrophilic interface -the head-group area - is prescribed by the temperature, water content, steric effects and ionic concentration for ionic surfactants. Assume for now that the area per each surfactant "block" making up the assembly is set a priori. This assumption implies that the surface to volume ratio of the mixture (assumed to be homogeneous) is set by the concentration of the surfactant. So the interfacial topology is predetermined by this global constraint, the surface to volume ratio. 

As both phases occupy the full flow field concurrently, two sets of conservation equations correspond to these two phases and must be complemented by the set of interfacial jump conditions (discontinuities). A further topological law, relating the void fraction, a, to the phase variables, was needed to compensate for the loss of information due to model simplification (Boure, 1976). One assumption that is often used is the equality of the mean pressures of the two phases, ... 

Electrodes represent an unrivaled platform onto which interfacial supramolecular structures can be assembled. They can be fully characterized before assembly and offer a convenient means to both probe and control the properties of the film. The interest in this area has increased dramatically in recent years because adsorbed monolayers enable both the nature of the chemical functional groups and their topology to be controlled. This molecular-level control allows the effects of both chemical and geometric properties on electron transfer rates to be explored. Moreover, these assemblies underpin technologies ranging from electrocatalysis to redox-switchable non-linear optical materials. 

Figure 15 A dimeric, four-helix bimdle can adopt six distract topologies. The topology diagrams shown are for the three possible clockwise-tuming hehcal himdles. Coimterclockwise-tuming hehcal himdles are also possible and have interfacial interactions different from their clockwise-tuming correlates. (Reprinted with permission from Ref. 1519. 2000 American Chemical Society)...

Several synthetic strategies to control the sizes of mesoporous nanoparticles have been reported. Lu[272] reported a rapid, aerosol-based process for synthesizing solid, well ordered spherical particles with stable pore mesostructures of hexagonal and cubic topology, as well as layered (vesicular) structures. This method relies on evaporation-induced interfacial self-assembly confined to spherical aerosol droplets. This simple, generalizable process can be modified for the formation of ordered mesostructured thin films. 

A mean field theory has recently been developed to describe polymer blend confined in a thin film (Sect. 3.2.1). This theory includes both surface fields exerted by two external interfaces bounding thin film. A clear picture of this situation is obtained within a Cahn plot, topologically equivalent to the profile s phase portrait d( >/dz vs < >. It predicts two equilibrium morphologies for blends with separated coexisting phases a bilayer structure for antisymmetric surfaces (each attracting different blend component, Fig. 32) and two-dimensional domains for symmetric surfaces (Fig. 31), both observed [94,114,115,117] experimentally. Four finite size effects are predicted by the theory and observed in pioneer experiments [92,121,130,172,220] (see Sect. 3.2.2) focused on (i) surface segregation (ii) the shape of an intrinsic bilayer profile (iii) coexistence conditions (iv) interfacial width. The size effects (i)-(iii) are closely related, while (i) and (ii) are expected to occur for film thickness D smaller than 6-10 times the value of the intrinsic (mean field) interfacial width w. This cross-over D/w ratio is an approximate evaluation, as the exact value depends strongly on the... 

More recently, the level-set technique has been developed for computing interfacial motion in two or three dimensions. It is especially effective in simulating large topological changes such as bubble breaking and merging. 

Mechanical Tensile Studies. The simple stress vs. strain characteristics of two-phase materials and their variation with relative phase composition can usually be given straightforward interpretation in terms of critical underlying structural factors. Among these factors can be listed topological connectivily of, and interfacial interaction between the phases. 

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