Thermodynamics of Composites

Much of what we need to know abont the thermodynamics of composites has been described in the previous sections. For example, if the composite matrix is composed of a metal, ceramic, or polymer, its phase stability behavior will be dictated by the free energy considerations of the preceding sections. Unary, binary, ternary, and even higher-order phase diagrams can be employed as appropriate to describe the phase behavior of both the reinforcement or matrix component of the composite system. At this level of discussion on composites, there is really only one topic that needs some further elaboration a thermodynamic description of the interphase. As we did back in Chapter 1, we will reserve the term interphase for a phase consisting of three-dimensional structure (e.g., with a characteristic thickness) and will use the term interface for a two-dimensional surface. Once this topic has been addressed, we will briefly describe how composite phase diagrams differ from those of the metal, ceramic, and polymer constituents that we have studied so far. 

Let us consider two hypothetical phases in our composite, A and B, without specifying their physical state. They conld be a polymer melt and a glass fiber reinforcement during melt infiltration processing, a metal powder and ceramic powder that are being snbjected to consolidation at elevated temperatnre and pressure, or two immiscible polymer melts that will be co-extruded and solidified into a two-phase, three-dimensional object. In any case, the surface that forms between the two phases is designated AB, and their individual surfaces that are exposed to their own vapor, air, or inert gas (we make no distinction here) are labeled either A or B. The following three processes are defined as these surfaces interact and form  

These processes are schematically illustrated in Fignre 2.35. We are interested in the free energy change that accompanies each process. 

The separation process shown in Fignre 2.35a consists of the formation of two new interfaces, each of nnit cross-sectional area, at a location where no interface previously existed. The free energy change associated with the separation process comes directly from the definition of surface energy [Eq. (2.61)] where two snrfaces of unit surface area are formed. With appropriate assumptions regarding constant temperature, pressure, and incompressible fluids, we can equate this free energy change with the 

The work of adhesion measures the degree of attraction between the two phases. For the specific case where A is a solid (S) and B is a liquid (L), ya becomes the solid surface energy, ys, Yb become the liquid surface tension, yl, and Young s equation, Eq. (2.72), 

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Marin, D. Mendicuti, F. Polarographic Determination of Composition and Thermodynamic Stability Constant of a Complex Metal Ion, /. Chem. Educ. 1988, 65, 916-918. 

If the gas has the correct composition, the carbon content at the surface increases to the saturation value, ie, the solubiUty limit of carbon in austenite (Fig. 2), which is a function of temperature. Continued addition of carbon to the surface increases the carbon content curve. The surface content is maintained at this saturation value (9) (Fig. 5). The gas carburizing process is controlled by three factors (/) the thermodynamics of the gas reactions which determine the equiUbrium carbon content at the surface (2) the kinetics of the chemical reactions which deposit the carbon and (J) the diffusion of carbon into the austenite. 

Product composition may be governed by the equilibrium thermodynamics of the system. When this is true, the product composition is governed by thermodynamic control. Alternatively, product composition may be governed by competing rates of formation of products. This is called kinetic control. 

As has been mentioned earlier, the CID generates a number Ni , of composition intervals. Within each interval, it is thermodynamically as well as technically feasible to transfer a certain mass of the key pollutant from a waste stream to a lean stream. Furthermore, it is feasible to pass mass from a waste stream in an interval to any lean stream in a lower interval. Hence, for the J th composition interval, one can write the following component material balance for the key pollutant ... 

Thermodynamic equilibrium composition of Cs aromatics at three temperatures ... 

Trustworthy thermodynamic data for metal solutions have been very scarce until recently,25 and even now they are accumulating only slowly because of the severe experimental difficulties associated with their measurement. Thermodynamic activities of the component of a metallic solution may be measured by high-temperature galvanic cells,44 by the measurement of the vapor pressure of the individual components, or by equilibration of the metal system with a mixture of gases able to interact with one of the components in the metal.26 Usually, the activity of only one of the components in a binary metallic solution can be directly measured the activity of the other is calculated via the Gibbs-Duhem equation if the activity of the first has been measured over a sufficiently extensive range of composition. 

Carbon Laydown. The potential for carbon laydown is readily estimated from the thermodynamics of Reactions 4 and 5. The areas where carbon laydown, according to these reactions, is thermodynamically possible were developed by Gruber (36). It is readily seen that carbon laydown via Reaction 4 is thermodynamically favorable at the reactor inlet for practically any commercially conceivable feed gas composition. As noted by Gruber (36), carbon laydown is thermodynamically unfavorable at the reactor outlet for practically all commercially conceivable methanator conditions. The methanation reactor will therefore, in practice, have two zones—the first is a finite zone between the inlet and some way down the catalyst bed where carbon laydown is thermodynamically possible, and the second zone is the balance of the reactor. 

The scheme of commercial methane synthesis includes a multistage reaction system and recycle of product gas. Adiabatic reactors connected with waste heat boilers are used to remove the heat in the form of high pressure steam. In designing the pilot plants, major emphasis was placed on the design of the catalytic reactor system. Thermodynamic parameters (composition of feed gas, temperature, temperature rise, pressure, etc.) as well as hydrodynamic parameters (bed depth, linear velocity, catalyst pellet size, etc.) are identical to those in a commercial methana-tion plant. This permits direct upscaling of test results to commercial size reactors because radial gradients are not present in an adiabatic shift reactor. 

Thermodynamics of Combustion of Various Pyrotechnic Compositions , NAD-RDTR No 277 (1974) 81) D.C. Izod R.F. Eather,... 

In addition to deciding on the method of normalization of activity coefficients, it is necessary to undertake two additional tasks first, a method is required for estimating partial molar volumes in the liquid phase, and second, a model must be chosen for the liquid mixture in order to relate y to x. Partial molar volumes were discussed in Section IV. This section gives brief attention to two models which give the effect of composition on liquid-phase thermodynamic properties. 

CVI is a special CVD process in which the gaseous reactants penetrate (or infiltrate) a porous structure which acts as a substrate and which can be an inorganic open foam or a fibrous mat or weave. The deposition occurs on the fiber (or the foam) and the structure isgradually densified to form a composite.The chemistry and thermodynamics of CVT are essentially the same as CVD but the kinetics is different, since the reactants have to diffuse inward through the porous structure and the by-products have to diffuse out.f l Thus, maximum penetration and degree of densification are attained in the kinetically limited low-temperature regime. 

The distribution of metals between dissolved and particulate phases in aquatic systems is governed by a competition between precipitation and adsorption (and transport as particles) versus dissolution and formation of soluble complexes (and transport in the solution phase). A great deal is known about the thermodynamics of these reactions, and in many cases it is possible to explain or predict semi-quantita-tively the equilibrium speciation of a metal in an environmental system. Predictions of complete speciation of the metal are often limited by inadequate information on chemical composition, equilibrium constants, and reaction rates. 

We have considered volume changes resulting from density changes in liquid and gaseous systems. These volume changes were thermodynamically determined using an equation of state for the fluid that specifies volume or density as a function of composition, pressure, temperature, and any other state variable that may be important. This is the usual case in chemical engineering problems. In Example 2.10, the density depended only on the composition. In Example 2.11, the density depended on composition and pressure, but the pressure was specified. 

Direct thermal decomposition of methane was carried out, using a thermal plasma system which is an environmentally favorable process. For comparison, thermodynamic equilibrium compositions were calculated by software program for the steam reforming and thermal decomposition. In case of thermal decomposition, high purity of the hydrogen and solidified carbon can be achieved without any contaminant. 

Principal component regression (PCR) is an extension of PCA with the purpose of creating a predictive model of the Y-data using the X or measurement data. For example, if X is composed of temperatures and pressures, Y may be the set of compositions that results from thermodynamic considerations. Piovoso and Kosanovich (1994) used PCR and a priori process knowledge to correlate routine pressure and temperature measurements with laboratory composition measurements to develop a predictive model of the volatile bottoms composition on a vacuum tower. 

Abstract. This section is an introduction into materials that can be used as Phase Change Materials (PCM) for heat and cold storage and their basic properties. At the beginning, the basic thermodynamics of the use of PCM and general physical and technical requirements on perspective materials are presented. Following that, the most important classes of materials that have been investigated and typical examples of materials to be used as PCM are discussed. These materials usually do not fulfill all requirements. Therefore, solution strategies and ways to improve certain material properties have been developed. The section closes with an up to date market review of commercial PCM, PCM composites and encapsulation methods. 

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