Stability analysis single component system

The basic derivations for the stability analysis of a single-component system are similar to Haase s presentation (1956) with certain changes. 

Finally, let us briefly point out some essential features of the stability analysis for a more general transport problem. It can be exemplified by the moving a//9 phase boundary in the ternary system of Figure 11-12. Referring to Figure 11-7 and Eqn. (11.10), it was a single independent (vacancy) flux that caused the motion of the boundary. In the case of two or more independent components, we have to formulate the transport equation (Fick s second law) for each component, both in the a- and /9-phase. Each of the fluxes jf couples at the boundary b with jf, i = A,B,... (see, for example, Eqn. (11.2)). Furthermore, in the bulk, the fluxes are also coupled (e.g., by electroneutrality or site conservation). 

Example of multiphase flash and stability analysis. We will, in detail, discuss the stability analysis of a three-component system of Ci/CO /nCif at T = 294.0K and P — 67 bar with — 0.05. 2 co.> = 0.90, and = 0.05. At fixed temperature and pressure, from the phase rule F — c - -2 — p, there can be a maximum of three phases when the interface between the phases is flat. The first question is what types of phases may exist—gas, liquid, or solid. As we will see in Chapter 5, a solid phase does not exist for the above system. Therefore one might expect (1) a single gas phase or a single liquid phase, (2) gas and liquid phases, (3) liquid and liquid phases, or (4) gas-liquid-liquid phase separation. The difficulty in liquid-liquid (L-L) and vapor-liquid-liquid (V-Lr-L) and higher-phase equilibria (for more than three components) is how many phases should be considered for flash calculations. One approach is to determine whether one, two, or more phases are to be considered without prior knowledge of the true number of phases. In certain cases, as we will see in the next chapter, it is possible from thermodynamic stability analysis to determine the true number of phases a priori without performing a flash. However, in general, we do not know the true number of phases. One may, therefore, follow a sequential approaches outlined next for the Ci/C02/nCiQ example. 

Perform the stability analysis on only one of the phases of the three-phase flash to check stability of the three phases. The three-phase flash should be stable since single-phase and two-phase were unstable (this is true only for a three-component system). 

Perhaps the most common application of VS in the determination of chemical makeup in polymeric systems is the identification of components in complex polymer mixtures. Polymeric products are rarely composed of a single component. There are always additives present that aid in processing, appearance, adhesion, chemical stability or other properties important to the function of the final product. In an industrial setting, it is important to be able to determine both the identity and quantity of polymers and additives in a specific formulation for quality control purposes. This can be a fairly routine operation if tools such as spectral libraries are utilized. In this method, a computer search algorithm compares a spectrum with a catalogue of standard spectra to determine the identity of the compovmd or compounds present. Advanced statistical techniques, such as partial least squares (PLS) and principal-component analysis (PCA), are also often used to identify known and unknown components in polymeric systems. The details of these methods are described elsewhere in the Encyclopedia. 

Most utility polymeric articles available today contain multiphase polymeric systems comprised of semi-crystalline polymers, copolymers, polymers in solution with low molar mass compounds, physical laminates or blends. The primary aim of using multicomponent systems is to mould the properties available from a single polymer to another set of desirable material properties. The property development process is complex and depends not only on the properties of the polymer(s) and other components but also on the formation process of the system which determines the developed microstmcture, and component interaction after formation. Moreover, the process of polymer composite formation and the stability of the composite is a function of environmental parameters, e.g., temperature, presence of other species etc. The chemical composition and some insight into the microscopic structure of constituents in a polymer composite can be directly obtained using Infrared (IR) spectroscopy. In addition, a variety of instrumental and sampling configurations for spectroscopic measurements combine to make irrfra-red spectroscopy a versatile characterization technique for the analysis of the formation processes of polymeric systems, their local structure and/or dynamics to relate to property development under different environmental conditions. In particular, Fourier transform infrared (FTIR) spectroscopy is a well-established technique to characterize polymers [1, 2]. 

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