Phase separation spinodal compositions

In the examples given below, the physical effects are described of an order-disorder transformation which does not change the overall composition, the separation of an inter-metallic compound from a solid solution the range of which decreases as the temperature decreases, and die separation of an alloy into two phases by spinodal decomposition. 

The kinetics of spinodal decomposition is complicated by the fact that the new phases which are formed must have different molar volumes from one another, and so tire interfacial energy plays a role in the rate of decomposition. Anotlrer important consideration is that the transformation must involve the appearance of concenuation gradients in the alloy, and drerefore the analysis above is incorrect if it is assumed that phase separation occurs to yield equilibrium phases of constant composition. An example of a binary alloy which shows this feature is the gold-nickel system, which begins to decompose below 810°C. 

Let us now consider a system composed of a polymer and a solvent. For compositions in between the inflection points, solvent molecules will diffuse into the solvent-rich phase, and the polymer molecules diffuse in the polymer-rich phase. Thus diffusion occurs against a concentration gradient. Therefore, this type of phase separation is known as up-hill diffusion. The up-hill diffusion leads to a spontaneous decomposition and it is therefore also named spinodal decomposition. The formation of two phases via spinodal decomposition occurs immediately upon reaching the spinodal decomposition region and does not require any activation energy. 

The type of spinodal decomposition encountered in IPN formation differs from the classical temperature quench in the sense that a composition change constitutes the driving force, at a fixed temperature. In this case, the rate of composition change is deeply involved in the phase separation process [6 ], which severely limits the applicability of current spinodal theory. In fact. Binder and Frisch [ ] which assume the polymerization rate is rapid enough to limit the phase separation. On the contrary, in the experimental work by Lipatov et al. [ ], the rate of polymerization was kept to a minimum to make the conversion changes during the phase separation minimal. 

Figure 18 illustrates a model of the three component phase diagram of an IPN, where poljrmer I, poljrmer II, and monomer II are chosen for generality in expressing sequential IPN formation. On poljrmerizatlon of monomer II, first phase separation is initiated, probably by nucleation and growth. However, shortly a modified spinodal decomposition mechanism sets in as the overall composition is driven deeper into the phase separation region. 

Curve defining the region of composition and temperature for a binary mixture across which a transition occurs from conditions where single-phase mixtures are metastable to conditions where single-phase mixtures are unstable and undergo phase separation by spinodal decomposition. 

A wide range of melt compositions undergo phase separation upon cooling. Two mechanisms are observed classical phase separation (dashed curve) as well as by spinodal (dot-dashed curve) mechanisms. Both the position of these regions and the onset temperature of phase separation reported in the literature vary (e.g., Roth et al. 1987), but there is no doubt that the phenomenon occurs amongst the glassy phase of aluminosilicate fly ash despite the presence of other oxides that tend to promote miscibility. 

In the composition range showing the nodular morphology, the increase in the PEI concentration increased the viscosity of the system and the PEI phase volume, thus reducing the rate of coalescence of the epoxy nodules in the late stage of spinodal phase separation. Smaller epoxy nodules, therefore, were formed at higher PEI concentration. 

Fig. 2.42 Spinodal lines for a random multiblock copolymer melt of variable X (Fredrickson el al. 1992). On cooling a melt with X > AL —0.268, the first instability is predicted to be phase separation into two homogeneous liquid phases (x = %m)- On further cooling to % = the two liquid phases become unstable with respect to formation of a microphase. In contrast, a melt with X < XL first becomes absolutely unstable to the formation of microphases (x = fom)- At the critical composition of /= j, the point (AL, Xi) is an isotropic Lifshitz point.

The solutions in the region inside the spinodal domain are unstable, whereas the solid solutions in the region between the binodal and spinodal lines are metastable. The presence of a miscibility gap limits the potential usefulness of these materials in device applications. Solutions with compositions lying inside the spinodal domain cannot be grown by LPE, whereas metastable solid solutions have a tendency toward phase separation and, eventually, device degradation. 

A mixture of composition 0o is unstable against phase separation when /[0] has negative curvature at 0 = 0o. The critical point of spinodal decomposition in model (42) is given by... 

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. 

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