Interfaces thickness

In SGLC-coil systems, the LC mesophase must form within the block microdomain and adapt to the domain boundary conditions [44, 111]. One needs to realize that the ODT in this system is much higher than the isotropic transition temperature. This domain boundary condition can act to stabilize the orientation of the mesogen in one of the domains [111] as indicated in Fig. 14. In Fig. 14, WAXD patterns are shown for sample SIHgFg-41/64 (phase transition SmB 

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Intuitively the toughness of an interface would be expected to be related to the depth of interpenetration of the chains. Wool [32] argues that the fracture energy, r, for chain disentanglement at least, is proportional to the square of the interface thickness, which, via Eqs. 36 and 37, gives ... 

Neagu, C., Puskas, J.E., Singh, M.A., and Natansohn, A. Domain sizes and interface thickness determination for styrene-isobutylene block copolymer systems using solid-state NMR spectroscopy. Macromolecules, 33, 5976-5981, 2000. 

The thickness of the gas-liquid interface is set as 3A based on the parameters used in the case of Sussman (1998), with the same density-ratio on the interface and similar Reynolds number. An interface thickness of 5A is also examined in the simulation and no significant improvement is observed. The accurate prediction of the bubble shape (shown in Figs. 3 and 4) can be attributed, in part, to the manner in which the surface-tension force is treated as a body force in the computation scheme. Specifically, since the surface-tension force acting on a solid particle is considered only when a solid particle crosses the gas-liquid interface and the solid particle is considered as a point, the accuracy of the calculation of this force can be expected if the surface tension is interpreted as a body force acting on each grid node near the interface. 

Polymers interpenetration of polymer chains, phase separation, compatibility between polymers, interdiffusion of latex particles, interface thickness in blends of polymers, light-harvesting polymers, etc. 

Small-angle scattering intensity in the high angle (q) region can be analysed to provide information on interface thickness (e.g. the lamellar interface thickness block in copolymer melts or core-corona interface widths in micelles). For a perfectly sharp interface, the scattered intensity in the POrod regime falls as q A (Porod 1951). For an interface of finite width this is modified to... 

Reactions in biphasic systems can take place either at the interface or in the bulk of one of the phases. The reaction at the interface depends on the reactants meeting at the interface boundary. This means, the interface area as well as the diffusion rate across the bulk of the phase plays an important role. On the contrary, in reactions that take place in the bulk phase, the reactants have to be transferred first through the interface before the reactions take place. In this case, the rate of diffusion across the interface is an important factor. Diffusion across the interface is more complicated than the diffusion across a phase, as the mass transfer of the reactant across the interface must be taken into account. Hence, the solubility of the reactants in each phase has to be considered, as this has an effect on diffusion across the interface. In a system where the solubility of a reactant is the same in both phases, the reactant diffuses from the concentrated phase to the less concentrated phase across the interface. This takes into account the mass transfer of the reactant from one phase into the other through the interface. The rate of diffusion J in such systems is described in Equation 4.1, where D is the diffusion coefficient, x is the diffusion distance and l is the interface thickness (Figure 4.9). 

Analysis has shown that this interface thickness Az is related to the characteristic length by the simple relation... 

Figure 4.7. Vertical capillary forces acting on the hydrophobic faces pull the hexagons into the PFD/H20 interface. The dashed line indicates the level of the interface far from the objects, (a) Hexagons with an unbalanced distribution of vertical capillary forces float with a tilt relative to the plane of the PFD/H20 interface. The surface tension, yLL, can be separated into vertical, y L, and horizontal, components, (b, c) Hexagons with a balanced distribution of vertical capillary forces float parallel to the plane of the interface. Thick and thin lines indicate hydrophobic and hydrophilic...

Near interfaces properties change rapidly, but not abmptly. The distance over which they change depends on the interface and the stabilizers used. This thickness is not sharply defined, but typically a few nanometres. For a given interface thickness it is not difficult to estimate the volume fraction occupied by the interface. As you see from Figure C2-2 this becomes substantial for stmctures with parts smaller than about 100 nm. In fine suspensions a large part consists of interface . 

Figure 16. Water density profile along the z direction in the membrane/vapor interface (system 11) at X = 4.4, 6.4, 9.6 and 12.8. Hyperbolic tangents have been fitted to determine the interface thickness.

Figure 2 A high-resolution TEM photomicrograph of the amorphous altered layer (lower left) developed on crystalhne lahradorite (hulk material, upper right) after dissolution at pH 1. The hlurry lattice fringes at the interface reflect the varying boundary orientation with respect to the ultrathin section. Interface thickness is 0.5-2 nm. Energy filtered (EE) TEM was also used to chentically characterize the alteration zone, which was found to he depleted in Ca, Na, K, and Al, and enriched in H, O, and Si. The sharp structural interface shown here and the sharp chemical interface observed with EFTEM are interpreted by the authors to indicate that the alteration layer is formed by dissolution-precipitation. Such amorphous altered layers are often high in porosity and yield high BET surface areas (reproduced by permission of Springer from Phys.

In the VOF approach, the present phases share a single set of conservation equations as discussed in Chapter 4. The essential feature of the VOF model is that it simulates the motion of a fluid-fluid interface embedded in the overall motion. It is important to maintain a compact interface thickness (one computational cell thick) to realize accurate simulations. VOF methods employ a marker function F(x,t) (or a volume fraction) that uniquely identifies the fluid under consideration. A unit value for F indicates a cell completely filled with one phase, whereas a zero value indicates a cell containing only the other phase. Therefore, computational... 

The net effects of the immersed boundary technique are that in the interface transition zone the fluid properties change smoothly from the value on one side of the interface to the value on the other side. The artificial interface thickness is fixed as a function of the mesh size applied to provide stability and smoothness, and it does not change during the calculations. Therefore no numerical diffusion is present. The finite thickness also serves to position the interface more accurately on the grid. The surface tension force (normal contribution only) is then calculated estimating the mean curvature based on geometric information obtained from the restructured interface. 

Figure 9. Calculated dielectric properties of oxide on CdTe for different interface thicknesses of a-Te. (Reproduced with permission from Ref. 26. Copyright 1984 American Institute of Physics.)...

Bragg intensities yield information on the degree to which segregation locally is achieved). The information on the interface thickness 8 can be extracted from observations at large scattering vectors q, where the intensity is predicted [304] to vary as... 

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