Mechanical mixture metastable state

It will be helpful to recall our discussion of rnetastable systems in Chapter 3, where we explained that constituents that are together but do not react or interact in any way, such as those separated by a partition, or those having an activation energy barrier, are examples of metastable systems. Metastable systems have an extra constraint that prevents their constituents from reacting to achieve their lowest potential. In the case of the mechanical mixture albite-anorthite it is the activation energy for water-halite it could be a partition in a composite system. In this chapter, for lack of a better term, we use mechanical mixture for this kind of metastable state. 

Figure 8.12 Pressure-volume diagram for equimolar mixtures of methane + propane, computed from the Redlich-Kwong equation of state. Filled square is the critical point filled circle is the mechanical critical point. The two branches of the saturation curve separate stable states from metastable states. The spinodal separates metastable states from unstable states and the line of incipient mechanical instability separates diffusionally unstable states from states that are both diffusionally and mechanically unstable. Since every point on this diagram represents an equimolar mixture, no tie lines can be drawn.

The middle envelope is the spinodal the set of states that separate metastable states from unstable states. Recall from 8.3 that one-phase mixtures become diffusionally unstable before becoming mechanically unstable. Therefore, the mixture spinodal is the locus of points at which the diffusional stability criterion (8.3.14) is first violated that is, it is the locus of points having... 

In the course of blending polymers, the following systems can be formed one-phase systems, two-phase (colloid) systems, or systems in a metastable state of transition from a one-phase into a two-phase system. The properties of polymer mixtures are determined to a great extent by the phase equilibrium in the system formed and their properties can be changed by controUing the processes of phase separation, which occur hy two mechanisms hy nucleation and growth or by the spinodal mechanism. 

This portion of the chapter can be summarized by noting that there is a substantial body of evidence demonstrating that formal phase-equilibrium thermodynamics can be successfully applied to the fusion of homopolymers, copolymers, and polymer-diluent mixtures. This conclusion has many far-reaching consequences. It has also been found that the same principles of phase equilibrium can be applied to the analysis of the influence of hydrostratic pressure and various types of deformation on the process of fusion [11], However, equilibrium conditions are rarely obtained in crystalline polymer systems. Usually, one is dealing with a metastable state, in which the crystallization is not complete and the crystallite sizes are restricted. Consequently, the actual molecular stmcture and related morphology that is involved determines properties. Information that leads to an understanding of the structure in the crystalline state comes from studying the kinetics and mechanism of crystallization. This is the subject matter of the next section. 

Polymer composite systems usually exist in a metastable (unstable) state of mechanical equilibrium. This is because a mixture of mutually insoluble components separates extremely slowly due to the very low diffusion coefficients of the polymer matrix of the ingredients. This state of polymer systems is sometimes defined as kinetic compatibility [28]. 

Figure 8.12 shows that if a mixture is mechanically unstable, then it is also diffu-sionally unstable, because the line of incipient mechanical instability lies under the spinodal, or equivalently because Kj appears in both stability criteria (8.1.30) and (8.3.13). Moreover, a one-phase mixture may be diffusionally unstable but remain mechanically stable, because the spinodal lies above the line of incipient mechanical instability, or equivalently because the mechanical criterion (8.1.30) can be satisfied while the diffusional criterion (8.3.13) is violated. Further, Figure 8.12 contains states at which no differential stability criteria are violated, but at which one-phase mixtures are metastable rather than stable. This means that a violation of any differential stability criteria (thermal, mechanical, or diffusional) is only sufficient, but not necessary, for a phase separation to occur. 

The differential stability criteria were derived by finding conditions that maximize the total entropy in an isolated system. Those conditions constrain how the system responds to thermal, mechanical, and diffusional fluctuations. In the derivations, those constraints are conveniently posed as stability criteria they show us that a stable substance must always obey the thermal criterion (8.1.23), the mechanical criterion (8.1.31), and the diffusional criterion (8.3.14). But the converses of those statements are not always true for example, a mechanically stable fluid always has Kj > 0, but a fluid having Kj > 0 is not necessarily stable— it might be metastable. Therefore, in using these differential criteria (as opposed to merely deriving them), many ambiguities can be avoided if we repose each constraint in the form of an instability criterion such criteria identify those thermodynamic states at which a pure substance or mixture is differentially unstable. 

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