Phase separation unstable systems

The set of the quaternary critical points comprises two asymptotic branches which meet at the cusp point - it defines the pentary critical point. These asymptotic branches are boundaries between systems with simple three-phase separation and systems with a more complex behaviour (two different three-phase regions, one of which may be unstable, and four-phase separation). 

Typical regions for application of contactors of different types are given in Table 13.2. The choice of a contactor for a particular application requires the consideration of several factors including chemical stability, the value of the products and the rate of phase separation. Occasionally, the extraction system may be chemically unstable and the contact time must then be kept to a minimum by using equipment such as a centrifugal contactor. 

Non-Random Systems. As pointed out by Cahn and Hilliard(10,11), phase separation in the thermodynamically unstable region may lead to a non-random morphology via spinodal decomposition. This model is especially convenient for discussing the development of phase separating systems. In the linearized Cahn-Hilliard approach, the free energy of an inhomogeneous binary mixture is taken as ... 

Phase separation through NG mechanism cannot be observed for polymer-polymer blend systems that show interfacial tension lying in the range 0.5-11 mN/m. In addition, they predicted that a secondary phase separation could take place inside dispersed rubber particles in the case when the average composition of dispersed domains lies in the unstable region at the end of the phase separation [2], They were not able to observe a phase separation inside dispersed domains with TEM micrographs however, they concluded that there are two phases inside the dispersed domains by the fact that the glass transition temperature of the rubber-... 

Colloidal dispersions are thermodynamically unstable owing to their high surface free energy and are irreversible systems in the sense that they are not easily reconstituted after phase separation. 

Paints, adhesives and lubricants are typically multicomponent polymer systems. The behavior of phase-separated blends in the bulk after quenching into the unstable region of the phase diagram is variable. In the bulk, the concentration fluctuations... 

In this section we would like to deal with the kinetics of the liquid-liquid phase separation in polymer mixtures and the reverse phenomenon, the isothermal phase dissolution. Let us consider a blend which exhibits LCST behavior and which is initially in the one-phase region. If the temperature is raised setting the initially homogeneous system into the two-phase region then concentration fluctuations become unstable and phase separation starts. The driving force for this process is provided by the gradient of the chemical potential. The kinetics of phase dissolution, on the other hand, can be studied when phase-separated structures are transferred into the one-phase region below the LCST. 

While the above system is an example where two-dimensional phase separation in the sense of Fig. la,b (or Fig. 5) occurs, there exist also good examples where no lateral phase separation exists in equilibrium, and the system forms a single interface parallel to the surfaces (Fig. Id). However, if one chooses the initial state such that the phase preferred by air is close to the substrate and the phase preferred by the substrate is next to the air surface [77], the system is unstable and surface phase inversion takes place. A laterally inhomogeneous state then occurs only as a transient phenomenon necessary to trigger the inversion kinetics, but not as an equilibrium state [77]. 

An emulsion is a thermodynamically unstable system it has a tendency to separate into two phases. 

In Figure 2F-1 the composition where d2( G)/d 22 s equal to zero, or at the inflection point on the Gibbs energy surface, is defined as the spinodal composition. This corresponds to the boundary between an unstable solution and a metastable solution. If the necessary amount of free energy is supplied to the metastable system, the solution will phase separate into two phases with binodal compositions unstable system will always phase separate into the two phases. The temperature where the two points of inflection on the energy surface merge into a single point is defined as the critical solution temperature. 

In a UCST system, when the temperature is reduced to a final value 7/ that is below the critical temperature Tc, a mixture with a concentration 0 not too far from the critical composition phase separate into two phases whose compositions lie on the opposite sides of the binodal envelope line of Fig. 9-1. The dynamics of the separation process of a single phase into these two phases is controlled by Tf, the composition , the rate of the quench dT/dt, the viscous (or viscoelastic) properties of the phases formed, and the interfacial tension F between the two phases. Although a variety of different kinds of behavior can occur, there are two generic types of phase separation, namely, spinodal decomposition (SD) and nucleation and growth (NG). SD occurs when the mixture is quenched into a part of the phase diagram where the mixture is unstable to small variations in composition, leading to immediate growth of phase-separated domains. When the quenched... 

The full specification of a polymorphic system is specified by the thermodynamic properties of the phases involved. A solid phase has a uniform structure and composition throughout, is separated by other phases by defined boundaries, and undergoes a phase transition when a particular solid phase becomes unstable under a given set of environmental conditions. The course of these phase changes is dictated by differences in free energy at the transition that are associated with structural or compositional changes. Classical thermodynamics provides a basis for understanding the nature of these transitions. 

The phenomenon of critical mixing occurs not only in liquid solutions but also in solid solutions mixed crystals). The conditions of stability for a solid solution are identical with those discussed above for liquid solutions. In particular, a system is always stable with respect to phase separation if it is ideal (c/. chap. XV, 14), and it can only become unstable if the activity coefficients depart sufficiently from unity. ... 

We have demonstrated miscible blends of PET-PHB/PEI can be formed by rapid solvent casting from the mixed solvent of phenol and tetrachloroethane. The miscibility was confirmed by the systematic movement of Tg in the DSC studies. However, the blend is unstable and undergoes thermally induced phase separation with a miscibility window reminiscent of LCST. The dynamics of spinodal decomposition is non-linear in character and obeys the power law with kinetic exponents of -1/3 and 1 in accordance with the cluster dynamics of Binder and Stauffer as well as of Furukawa. In the temporal scaling analysis, the structure function exhibits universality with time, suggesting temporal self-similarity of the system. 

A similar interpretation of phase diagrams has been recently proposed by Safran and Turkevich (18). These authors have considered the effects of interaction and curvature on the stability of microemulsions. They suggest that unstabilities of spherical microemulsion droplets lead the system to separate with water in order to prevent micellar growth above a limit radius R. Taking into account interactions with a phenomenologic treatment, they show that phase separation due to interaction is also possible and they found a critical radius Rc. If Rc is greater than R a water phase is formed and if Rc is lower than R phase separation gives rise to two micellar phases with a critical point. This theoretical treatment reflects very well the behavior we observe but it is not in full accordance with our experimental results. The main difference is that when interactions are not preponderant the phase separation does not occur with a water phase but with a lamellar phase. 

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