Spinodal definition

If the mixture is subregular, definition of the limits of spinodal decomposition is more complex. For a subregular Margules model (figure 3. IOC and D), we have... 

Note 4 If a mixture is thermodynamically metastable, it will demix if suitably nucleated (see Definition 2.5). If a mixture is thermodynamically unstable, it will demix by spinodal decomposition or by nucleation and growth if suitably nucleated, provided there is minimal kinetic hindrance. 

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... 

Every solution has a maximum amount that it can be supersaturated before it becomes unstable. The zone between the saturation curve and this unstable boundary is called the metastable zone and is where all crystallization operations occur. The boundary between the unstable and metastable zones has a thermodynamic definition and is called the spinodal curve. The spinodal is the absolute limit of the metastable region where phase separation must occur immediately. In practice, however, the practical limits of the metastable zone are much smaller and vary as a function of conditions for a given substance. This is because the presence of dust and dirt, the cooling rate employed and/or solution history, and the use of agitation can all aid in the formation of nuclei and decrease the metastable zone. Figure 1.17 gives an estimated metastable zone width for KCl in water. 

These, and all other equations for concentration-dependent diffusion, consist of an infinite dilution diffusivity and a thermodynamic correction term. The thermodynamie correction term in all cases is equivalent to the derivative dGildx. The definition of the thermodynamic metastable limit (the spinodal curve) is the locus of points where dG2ldx = 0. This means that concentration-dependent diffusion theory predicts a diffusivity of zero at the spinodal. Thermodynamics tells us that the diffusivity goes from some finite value at saturation to zero at the spinodal. Unfortunately, it does not tell us how the diffusion coefficient declines. In addition, lack of thermodynamic data makes prediction of the spinodal difficult. We are, therefore, left with only the fact that as the concentration is increased in the supersaturated region, the diffusivity should decline towards zero but we do not know at what concentration the diffusivity becomes zero. 

The straight lines in Figure 10-13 have definite negative slopes. This means that K is not negligible, i.e., the interfacial eneigy term in eq 2.1 plays a role in the early stage spinodal decomposition of the system studied. By extrapolation of the T>app values at the three Tq indicated in Figure 10-13 we find that D pp vanishes at 95.8° C. This is consistent with the fact that since the blend has the critical composition, its Tc is just the spinodal temperature at which d f/du vanishes. 

Several interesting observations relate to such thermodynamic measurements. For example, the exothermic effects, associated with phase separation in LCST-type polymer blends, showed a correlation between the exothermic enthalpy and the interactions between the components (Natansohn 1985) however, the specific interaction parameter xn was not calculated. In another example, there are definitive correlations between the thermodynamic and the transport properties (see Chap. 7, Rheology of Polymer Alloys and Blends ). Thermodynamic properties of multiphase polymeric systems affect the flow, and vice versa. As discussed in Chap. 7, Rheology of Polymer Alloys and Blends , the effects of stress can engender significant shift of the spinodal temperature, AT = 16 °C. While at low stresses the effects can vary, i.e., the miscibility can either increase or decrease. 

As to the explicit form of Equation 1, nothing definite can be said. Perhaps, such attempts may be exerted by plotting spinodals using Chu-Scholte s method (see subsection 3.6.2) at different velocities of motion of the configurative point in the one-phase region. 

In a first order phase transition, thermodynamic functions by definition discon-tinuously change as one cools the system along a path crossing the equilibrium coexistence line (Fig. 5a, path j8). In a rea/experiment, however, this discontinuous change may not occur at the coexistence line because a substance can remain in a supercooled metastable phase until a limit of stability (a spinodal) is reached [2] (Fig. 5b, path fi). 

The limit of stability is defined as the condition under which 6 IJ loses its positive, definite character. That is, one of the coefficients in Eq. (23) vanishes. As has heen shown previously ( ), when the spinodal surface is approached from a stable single phase region, the coefficient of is among the first to reach zero... 

One more effect should be taken into account. Because the miscibility of two species depends on the ratio of their molecular mass, the situation arises where, on the change of the outer conditions, the system remains in a thermodynamically stable state for some fractions of definite molecular mass, while already undergoing the phase separation for other fractions. Although this point has practically not been dealt with in the hterature, its role in the formation of a non-equilibrimn frozen structure should be essential. It means that the state of a system turns out to be dependent on its history. Thus, again, the phase diagram by itself yields a poor indication of the system state within the region of immiscibility bomid by the spinodal or binodal curve. 

Obviously, the mechanism of spinodal decomposition, which determines the microphase structure of cured IPN, is not the only mechanism, i.e., separation may also take place by the nucleation mechanism under definite conditions. 

In IPN formation, structures typical of spinodal decomposition may appear only within a definite time interval, which is always lower than the time of gelation and formation of final IPN structure. Subsequent crosslinking (after the At interval)occurs in the evolved microregions of phase separation up to the moment when the ultimate conversion is reached. This permits an important conclusion to be made. The final structure of IPNs is determined by a coexistence of three types of microregions of incomplete phase separation (dissipative structures). 

This description is closely related to the preceding definition of the equilibrium advancement of tran brmation. which, however, is not exhaustive as more complex processes can be accounted for by multi-parameter transitions, such as segregation in solid-state solutions or solid-spinodal decompositions. Here we ought to include new parameters such as the degree of separation, p = (Nu - Nfi)/Nr, together with the complex degree of completeness of the process, f= (Nr Va./), based on the parallel... 

The definitions of a and p are given in Eq. (76). r measures the distance from the spinodal and the condition r = 0 yields Eq. (75). Comparing this expression with the calculation of Cahn and Hilliard [146] we can read off the nucleation barrier ... 

Because relatively few experimental SANS data are available for IPNs, presently it is difficult to draw any definite conclusions about the structure of IPNs. As is seen from the data considered, the mechanism of phase separation is not mentioned in any work cited above. Meanwhile, this mechanism should determine if the application of any theory is possible for a given system. One may suggest that the Porod and Hosemann models may be used only for the nucleation and growth mechanism of phase separation, most typical for sequential IPNs. For simultaneous IPNs, where spinodal decomposition, as a rule, is more probable, it seems to be more reliable to determine only the heterogeneity parameters, not the radii of particles, if any. It is also necessary to keep in mind the possible changes of the mechanism of phase separation in the course of reaction. 

---