Random three-phase composites

Overall, including all the detrimental factors in catalyst utilization, it is quite likely that far less than 20% of the catalyst is effectively utilized for reactions. Ineffectiveness of catalyst utilization is a major downside of random three-phase composite layers, which are, nevertheless, the current focus in CCL development. Obviously, there are enormous reserves for improvement in these premises. The alternative could be to fabricate CCLs as extremely thin, two-phase composites 100-200 nm thick), in which electroactive Pt forms the electronically conducting phase, eventually deposited on a substrate. The remaining volume should be filled with liquid water, as the sole medium for proton and reactant transport. 

In the original structure-based CCL model of Eikerling and Kornyshev (Eikerling and Kornyshev, 1998 Eikerling et al., 2004, 2007a), an expression for Tstat was derived based on the theory of active bonds in random three-phase composite media. 

Fig. 6a-c. Graphic representation of syntactic foam structures 85) a Random dispersion of spheres, two-phase composite b Hexagonal closed-packed structure of uniform-sized spheres, two-phase composite c Three-phase composite containing packed microspheres, dispersed voids, and binding resin... 

At macroscopic scale, catalyst utilization is severely limited by the statistical constraints imposed by the random structure of the three-phase composite. Only catalyst particles that are simultaneously accessible to electrons, protons, and oxygen could be electrochemically active. These requirements are included in the factors/(Yptc, X )/Yptc and g(Sr) in Eq. (2.27). Figure 2.7 reveals that due to these factors alone the upper limit of catalyst utilization lies in the range of 20%. 

Alloys are classified broadly in two categories, single-phase alloys and multiple-phase alloys. A phase is characterized by having a homogeneous composition on a macroscopic scale, a uniform structure, and a distinct interface with any other phase present. The coexistence of ice, liquid water, and water vapor meets the criteria of composition and structure, but distinct boundaries exist between the states, so there are three phases present. When liquid metals are combined, there is usually some limit to the solubility of one metal in another. An exception to this is the liquid mixture of copper and nickel, which forms a solution of any composition between pure copper and pure nickel. The molten metals are completely miscible. When the mixture is cooled, a solid results that has a random distribution of both types of atoms in an fee structure. This single solid phase thus constitutes a solid solution of the two metals, so it meets the criteria for a single-phase alloy. 

Figure 6 is a graphic representation of foam structures in which the microspheres are dispersed randomly (a) and uniformly in close packing (b). In both structures, the two phases fill completely the whole volume (no dispersed air voids) and the density of the product is thus calculated from the relative proportions of the two. Measured density values often differ from the calculated ones, due to the existence of some isolated or interconnected, irregularly shaped voids as shown in Fig. 6c. The voids are usually an incidental part of the composite, as it is not easy to avoid their formation. Nevertheless, voids are often introduced intentionally to reduce the density below the minimum possible in a close-packed two-phase structure. In such three-phase systems the resin matrix is mainly a binding material, holding the structure of the microspheres together.

Thus spinodal decomposition proceeds as follows (Cahn (1961, 1965)) while all wave numbers may be present initially, the transformation kinetics are quickly dominated by those wave numbers (bj ) corresponding to the maximum kinetic amplification factor (Eq. 1.31). Thus the spatial composition will be a superposition of sine waves of nearly fixed wavelength (27r/bj ) but with random orientations, phases, and amplitudes. For volume fractions greater than 0.15 0.03 the microstructure will have a three dimensional interconnected morphology. For second phase volume fractions less than 0.15, the microstructure will consist of isolated particles (Cahn (1965)). Similar morphologies can also result from nucleation and growth processes (Haller (1965)). 

A reasonable question arises why problems unsolvable by the known methods are readily settled by stoiehiographie methods Let us eonsider how the DD method ean reveal phase composition of a model multielement multiphase object for which ordy its gross elemental composition is known, whereas data on its phase eomposition earmot be obtained, for example, due to amorphous strueture of the object. The model eonsists of three elements (wt. %) A (45.5), B (21.2) and C (33.3), which form the imknown munber of phases (5 in this model) with imknown stoiehiometry and quantitative eontent. All ealeulations were based on the model of redueing spheres. The stoichiometric composition of five phases, radii of their spheres as well as rate eonstants and induction periods of dissolution processes were chosen randomly. The dissolution process was simulated by a dynamie regime with the solvent concentration increasing linearly with time at a constant temperature. Note that the initial data for stoiehiographie calcidation of the simulation data were represented only by the data on qualitative composition of elements A, B and C in the object of analysis, whereas all other parameters specified in the model were considered as the unknown quantities. Thus, the DD method had to reveal the presence of individual phases in the sample and then identify them and find their quantitative content. 

Calculation of dependence of o on the conducting filler concentration is a very complicated multifactor problem, as the result depends primarily on the shape of the filler particles and their distribution in a polymer matrix. According to the nature of distribution of the constituents, the composites can be divided into matrix, statistical and structurized systems [25], In matrix systems, one of the phases is continuous for any filler concentration. In statistical systems, constituents are spread at random and do not form regular structures. In structurized systems, constituents form chainlike, flat or three-dimensional structures. 

The same structure is formed in a number of binary (or ternary) phases, for which a random distribution of the two (or three) atomic species in the two equivalent sites is possible. Typical examples are the (3-Cu-Zn phase (in which the equivalent 0,0,0 A, A, A positions are occupied by Cu and Zn with a 50% probability) and the (3-Cu-Al phase having a composition around Cu3A1 (in which the two crystal sites are similarly occupied, on average by Cu, with a 75% occupation probability, and by Al, with a 25% occupation probability). A number of these phases can be included within the group of the Hume-Rothery phases (see 4.4.5). 

Nano structural materials are divided into three main types one-dimensional structures (more commonly known as multilayers) made of alternate thin layers of different composition, two-dimensional structures (wire-type elements suspended within a three-dimensional matrix), and three-dimensional constructs, which may be made of a distribution of fine particles suspended within a matrix (in either periodic or random fashion) or an aggregate of two or more phases with a nanometric grain size (these are illustrated in Fig. 17.1). 

As can be seen, the flux for heat conduction across the air boundary layer is proportional to / au(7 surf 7"ta) for all three shapes considered (pea = 7s111 for Eq. 7.14).2 Because the conduction of heat in a gas phase is based on the random thermal motion of the molecules, the composition of air, such as its content of water vapor, can influence Kau. Air can hold more water vapor as the temperature increases in that regard, decreases as the water vapor content increases because H2O has a lower molecular weight (18) than is the average for air, which is mainly N2 and O2 (molecular weights of 28 and 32, respectively). For instance, at 20°C Kait at a pressure of 1 atm and 100% relative humidity is 1% less for than it is for dry air, and at 40°C, Km is then 2% lower (Appendix I). 

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