Anisotropic interfacial regions

The picture of the interfacial process presented in Eq. (102b) is somewhat oversimplified the process occurs in the anisotropic interfacial region in which additional stabilization of II is due to the gradient of concentration of Na cations. 

The distribution of short-chain defects in copolymers was also modeled by Mattice and his colleagues using both two-dimensional and three-dimensional lattices [43-45]. Assuming defects were excluded from the crystalline phase of a copolymer, a nonuniform distribution of branches in the amorphous region between two crystalline lamellae was found. When branches were absent, the anisotropic interfacial region was thin, but it thickened substantially with increases in both branch content and branch size. 

Another motivation for studying reactions at liquid interfaces is that the unique nature of the interfacial region provides an interesting opportunity to examine the fundamental aspects of medium effects on chemical reactions. The interfacial region is characterized by anisotropic intermolecular forces[9] which give rise to specific molecular orientations. Thus, averaging procedures that are at the core... 

The present study has provided a critical test of the importance of cross relaxation involving both water and protein protons in hydrated protein systems. In addition it has successfully demonstrated that the temperature dependence of both the water and protein relaxation is dominated by motions in the water phase and not by motions in the solid phase such as methyl group rotations. While a detailed analysis has not yet been attempted, it appears that a picture of water in the interfacial regions around a protein that is consistent with the NMR relaxation data is one characterized by fast if slightly anisotropic motion. Structural models for water-protein interactions must be consistent with this very fluid character of water in this interfacial region-, however, it is also important to recognize that the time scale appropriate to the present experiments is still long when compared to the rotational correlation times or diffusion times usually associated with water in the pure liquid state. 

The carbanions generated by deprotonation at the phase boundary are located in the interfacial region, which is essentially an anisotropic medium thus, they should have preferential space orientation. In such a situation the stereochemical course of some reactions should be different from analogous reactions proceeding in isotropic solution. 

The interface between two nonpolar atomic solvents interacting through Lennard-Jones-type potentials has been studied [41] diffusion in the interfacial region was found to be anisotropic. 

Figure 2.10 Sketch of a tensorial hydrodynamic slip. The normal traction fn exerted by the fluid on an anisotropic surface produces an effective slip velocity Au = Mf in a different direction. At the molecular level, the Interfacial mobility tensor M is related to the trajectories of diffusing particles In the interfacial region, such as the one shown (reprinted with permission from Ref 28, copyright 2008, Cambridge University Press].

When a nematic liquid crystal is placed in contact with another phase (solid or liquid), a surface bounding the liquid crystal is created. The presence of this surface induces a perturbation of the nematic order close to it (Fig. la). The anisotropic interactions between the molecules located right at the surface - in the surface layer - and the other phase favors certain orientations of the surface molecules. This leads to an orientational distribution of the liquid crystal molecules in the surface layer that is generally different from the bulk nematic order. The orientational order evolves from the one induced by the surface to the one in the bulk in an interfacial region of thickness which is of the order of the nematic coherence length. Just outside the interfacial re-... 

In addition to monosized nanopartide, the morphology of binary nanopartides filled in microphase separating AB diblock copolymers has also been studied. For chemically identical spherical partides, large particles are concentrated in the preferred, compatible phase and small partides spread out in the interfacial regions and in the incompatible phase of the diblock copolymer [17]. Theoretical efforts have also been made toward the morphology of copolymer filled with anisotropic particles (e.g., rod-like partides, plate-like partides, or the mixtures of particles of different shapes). It is found that the distribution of partides within the copolymers depends not only on the relative interaction energies between nanopartides and different blocks but also on the aspect ratio of the rod-like nanopartides. 

When the interfacial energy depends on the inclination of the interface and 7 is therefore anisotropic, Eq. 19.1 does not apply. In this case, the cluster will minimize its total interfacial energy by adopting its Wulff shape (Section C.3.1), which may be fully faceted or made up of faceted and smoothly curved regions. Several characteristic shapes are shown in Fig. 19.2. The interfacial-energy term in Eq. 19.1 can then be expressed as the sum of the interfacial energies of the various faceted or smoothly curved patches that make up the entire closed interface and... 

Currently, approximately one billion gal/day of water are desalted by reverse osmosis. Half of this capacity is installed in the United States, Europe, and Japan, principally to produce ultrapure industrial water. The remainder is installed in the Middle East and other desert regions to produce municipal drinking water from brackish groundwater or seawater. In recent years, the interfacial composite membrane has displaced the anisotropic cellulose acetate membrane in most applications. Interfacial composite membranes are supplied in spiral-wound module form the market share of hollow fiber membranes is now less than... 

Because (T in Equation (66) pertains to a hypothetical isotropic nucleus, it cannot be measured. Furthermore, true (anisotropic) solid-liquid interfacial energies are measured near the melting temperature [86], whereas what would be needed for an independent confirmation of the theory is Cf(T) in the supercooled region. Consequently, the theory of homogeneous nucleation, as it applies to supercooled liquids, has been used mainly to calculate effective interfacial tensions from measurements of nucleation rates [82,86]. In summary, the application of nucleation theory to supercooled liquids involves two major simplifications the replacement of the true, anisotropic embryo by an "equivalent" spherical object, and the ad-hoc introduction of a diffusion-like activation energy barrier to account for hindered molecular mobility in the dense supercooled liquid. It is therefore not surprising that the resulting theory has been mostly used descriptively rather than predict vely. 

As was pointed out earlier, the gradient theory can be linked easily to a semi-empirical equation of state. The equations of state applied in this study are the Peng-Robinson equation of state and the Associated-Perturbed-Anisotropic-Chain-Theory (APACT). The only effect on the interfacial tensions of pure fluids that is strongly influenced by the selected equation of state is the behavioitr in the near-critical region, since other differences are completely annulled by the fitting procerdure that is applied for the influence parameter. 

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