Stability analysis multicomponent system

Beegle, B. L. (1973). Stability analysis of multicomponent systems. S.M. Thesis, Massachusetts Institute of Technology, Cambridge. 

The equilibrium and stability criteria for systems and constraints that are of interest in this book are collected in Table 7.1-1. As we will see in Chapters, these equilibrium and stability criteria are also valid for multicomponent systems. Thus the entries in this table form the basis for the analysis of phase and chemical equilibrium problems to be considered during much of the remainder of this book. 

Although this simple statement is a good rule of thumb for inferring the effects of changes in an equilibrium system, it is not universally valid, and exceptions to it do occur (Problem 13.17). A more general, universally valid statement of this principle is best given within the context of a complete thermodynamic stability analysis for a multicomponent reacting system. For many situations, however, it may be more useful, and even more expeditious, to ascertain the equilibrium shift by direct computation of... 

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]. 

Older, but pedagogically excellent, information on the laws of stability and coexistence of minerals, including the application of Schreinemaker analysis to multicomponent systems of geological relevance, can be obtained from Niggli (1954). More detailed examples of the thermodynamic-based calculation of (simple) phase diagrams can be found in Appendix A. 

The interfacial tension can undergo significant changes if the polarity of the medium is altered, such as in the stability/coagulation transition caused by the addition of water to hydrophobic silica dispersions in propanol or ethanol [44,52,53]. Also, the addition of small additives of various surface-active substances can have a dramatic effect on the structure and properties of disperse systems and the conditions of transitions [14,16,17,26]. The formation and structure of stable micellar systems and various surfactant association colloids, such as microemulsion systems and liquid crystalline phases formed in various multicomponent water/hydrocarbon/surfactant/alcohol systems with varying compositions and temperatures, have been described in numerous publications [14-22,78,79,84-88]. These studies provide a detailed analysis of the phase equilibria under various conditions and cover all kinds of systems with all levels of disperse phase concentration. Special attention is devoted to the role of low and ultralow values of the surface energy at the interfaces. The author s first observations of areas of stable microheterogeneity in two-, three-, and four-component systems were documented in [66-68],... 

According to Jakisch et al. [79], FTIR spectroscopy is the preferred method for in-line investigation polymer melts and polymer melt reac-tions/kinetics, allowing quantitative determination of all components. FTIR analysis of compound melts enables additive level stability and effectiveness to be observed over multiple extrusion passes. The use of the ATR principle is suitable for in-line analysis of polymer melts in the extruder. The exit of the extruder was equipped with an on-line IR transmission process control system consisting of a 150 /um thick ZnSe melt flow cell. Characteristics of such systems have been described [71,74]. Another process spectrometer with an in situ ZnSe-ATR dipper probe was mounted at different positions in the extruder. For in-line ATR the residence time plays no role. Only the first 5 /xm (corresponding to the penetration depth of the IR radiation) are examined. Minor components are thus detected with difficulty. Jakisch et al. [79] monitored the conversion of styrene-maleic anhydride copolymers (SMA) with fatty amines into styrene-maleimide copolymer (SMI) during reactive extrusion by means of FTIR. In principle, both mid-IR and near-IR spectroscopy with ATR, transmission and diffuse reflectance probes are suitable for quantitative on- and in-line process analysis of multicomponent polymer... 

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