Equilibrium diagrams, practical applications

A final caveat that must be applied to phase diagrams determined using DFT calculations (or any other method) is that not all physically interesting phenomena occur at equilibrium. In situations where chemical reactions occur in an open system, as is the case in practical applications of catalysis, it is possible to have systems that are at steady state but are not at thermodynamic equilibrium. To perform any detailed analysis of this kind of situation, information must be collected on the rates of the microscopic processes that control the system. The Further Reading section gives a recent example of combining DFT calculations and kinetic Monte Carlo calculations to tackle this issue. 

Having discussed qualitatively the application of the Phase Rule to three-component systems formed by water and two salts with a common ion, one may now consider how the equilibrium diagrams, constructed on the basis of experimental data, can be employed in the quantitative study of the behaviour of such systems, and can be used to guide the practical operations of the winning of salts by crystallisation from solution. ... 

In practical applications of chemistry, it is important to know the phases of reactants and products at the conditions of interest. Snch information can be obtained using a phase diagram, which is a plot summarizing the conditions at which the various phases of a material can exist. The regions in which different phases exist are separated by phase boundaries, which represent the conditions under which the two (or more) phases separated by the boundary can coexist in equilibrium. 

The purpose of modeling liquid solutions is to understand the strueture and the properties of the medium, and to help predict certain behaviors by giving expressions for the molar Gibbs energies or activity coefficients. These data can then be used in practical applications such as the establishing of chemical equilibrium states or the plotting of phase diagrams. 

To conclude this brief introduction, we note that there are many other aspects not covered in this chapter that are nevertheless important for practical applications. Those include material purity and polydispersity, processing, environmental health and safety, toxicology, and others. Clearly, as we understand more and more about the specific mechanisms of nanoparticle/human cell interactions, there will be new changes in the chemical engineering, processing, and preparation of nanocomposite materials. For the purposes of this chapter, however, we concentrate mainly on the simplified equilibrium aspects of nanocomposite polymer blends, from morphology and phase diagrams to mechanical and physical properties. 

The final case to be treated in this section is the reaction between two metals A and B whose phase diagram exhibits a miscibility gap and extended regions of solubility a and p as shown in Fig, 7-5. Once again, many practically important applications can be found. Examples are the systems Ag-Cu (800 °C), Au-Co (900 C), Zn-Cd (250 °C), or Co-Cu (1000 °C). Consider two sufficiently long samples A and B which are welded together at the point x = 0. Assume that local equilibrium is achieved everywhere and at all times. After a diffusion time t there will be a discontinuity in concentration at x = which can be calculated from the phase... 

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