Domain Volume

Euler characteristic and the minority domain volume fraction. Because the Euler characteristic is the direct measure of the domain connectivity, we identify the domain percolation at the point where the Euler characteristic attains zero value. 

Nanocarbon hybrids have recently been introduced as a new class of multifunctional composite materials [18]. In these hybrids, the nanocarbon is coated by a polymer or by the inorganic material in the form of a thin amorphous, polycrystalline or single-crystalline film. The close proximity and similar size domain/volume fraction of the two phases within a nanocarbon hybrid introduce the interface as a powerful new parameter. Interfacial processes such as charge and energy transfer create synergistic effects that improve the properties of the individual components and even create new properties [19]. We recently developed a simple dry wrapping method to fabricate a special class of nanocarbon hybrid, W03 /carbon nanotube (CNT) coaxial cable structure (Fig. 17.2), in which W03 layers act as an electrochromic component while aligned... 

An alternative and complementary method is to follow the deformation of the material by following the boundaries of a fluid domain, by either the front capturing or front tracking technique. In the former, marker particles are distributed over the fluid domain volume and tracked over time, with the surface of the domain being restored by interpolation techniques in the latter, a separate moving mesh is used to describe the interface between the subdomain and the rest of the volume (86-89). 

At a constant 0 value, the [A]d/[B]d term, if it remains constant, must lead to the resolution of binding curves, if determined at different [B] values, that parallel to each other with the distance between them expressed by Z log[B]. Also, by use of the polyion domain volume, Vp, [A]d can be expressed as... 

The polyion domain volume can be computed by use of the acid-dissociation equilibria of weak-acid polyelectrolyte and the multivalent metal ion binding equilibria of strong-acid polyelectrolyte, both in the presence of an excess of Na salt. The volume computed is primarily related to the solvent uptake of tighdy cross-linked polyion gel. In contrast to the polyion gel systems, the boundary between the polyion domain and bulk solution is not directly accessible in the case of water-soluble linear polyelectrolyte systems. Electroneutrality is not achieved in the linear polyion systems. A fraction of the counterions trapped by the electrostatic potential formed in the vicinity of the polymer skeleton escapes at the interface due to thermal motion. The fraction of the counterion release to the bulk solution is equatable to the practical osmotic coefficient, and has been used to account for such loss in the evaluation of the Donnan phase volume in the case of linear polyion systems. 

The rubber cellular domain structures are sometimes called salami structures, after their appearance. The toughness obtained in such materials is related to the rubber phase volume, which is the rubber volume plus the occluded polystyrene cellular domain volume. 

An other definition of the electron domains is based on the hypothesis that the variance a (N(Q)) of their populations N(Q) = p(r)dr should be minimal with respect to a variation of the domain boundaries. The minimization of the variance with respect to the domain volumes implies that the variational equation... 

The viscosity of the epoxy-rich medium ( /med) can be estimated from the measured complex viscosity, and the domain volume fraction given in Figure 4.3. 

Determination of the number of crosslinks and matrix domain volume... 

The domain volume fraction within the dry sample is given by the following ... 

Dihedral angle, 282 Dispersion curves, 175 D-monomer, 178 Domain formation, 135 Domain volume fraction, 153 Donnan effect, 74, 82 Dynamic dielectric constant, 364 Dynamic light scattering (DLS)... 

FEM, a discretization method to solve partial differential equations such as those governing the flnid as a continuum, can be applied with the assumption that particles of sizes above several microns are immersed in a fluid [50]. More importantly, the Navier-Stokes equations may be replaced by the Stokes equations as a particle Reynolds number smaller than 0.1 is considered. So, FEM provides a way to investigate full flow fields of fluid around a static or moving aggregate for steady or temporally changing flow. Typically, the domain volume is discretized by using a computational mesh on which the solution is obtained in form of nodal vectors. In contrast to SD, particles of arbitrary shapes can be simulated. 

Here, S(z, p) (l//9)2r m exp -r/m[27+Ei(/92/4Az) ] ) is the layer-layer correlation function,where R2=z2+p2 is Euler s constant, Ex(x) is the exponential integral function, and A = 7(K/B). In Eq. (16), the exponential term incorporates a finite size effect because of the observed finite lamellar domain sizes typically between -2000 and 10,000 A (L is the domain volume). Also because the samples consist of randomly oriented domains, we perform an exact powder average over all solid angles in reciprocal space. The precise steps leading to Eq. (16) have been discussed elsewhere.2,3 analysis consists of... 

Zhao and Benziger identified three contributions to the resistance to water transport in Nafion (1) the volume of the hydrophilic domains available for water transport (2) the dependence of water diffusivity on the concentration of water in the hydrophilic domains and (3) the Nafion/fluid interface [49]. They showed that at low water content in Nafion, the diffusion across the membrane is the rate-limiting step. But at high water activity, the combination of increased hydrophilic domain volume and increased coimectivity of the hydrophilic domains result in a large increase in the diffusion rate across the membrane, and interfacial transport across the Nafion/vapor interface becomes the rate-limiting step. 

---