Spinodal boundaries

Although these results need to be understood - and confirmed in other similar systems - the authors claim that they are in qualitative agreement with a model of droplet formation and chain localization resulting from the existence of microscopic heterogeneities within the spinodal boundaries of the phase diagram [256]. 

The co-occurrence of nucleation and spinodal decomposition had been observed in the temperature quench experiment of poly(2,6-dimethyl-l,4-phenylene oxide)-toluene-caprolactam system, [64,65], in which the typical morphology formed by nucleation and growth mechanism was observed with electron-microscopy when the quench of temperature is slightly above the spinodal boundary. On the other hand, if the quench temperature is somewhat lower than the spinodal boundary, they observed interconnected structures as well as small droplets. 

Sastry, S., Liquid limits Glass transition and liquid-gas spinodal boundaries of metastable liquids. Phys. Rev. Lett. 85, 590 (2000). 

Determination of spinodal boundaries is much more difficult than the determination of immiscibility boundaries. Since light scattering is unaffected by the connectivity of the phases, the observation of opalescence tells us nothing about the morphology of the sample. Direct examination of the microstmcture would certainly reveal the... 

The spinodal boundary is rarely shown on ternary immiscibility diagrams. Since this boundary is also represented by a dome, similar contour lines could be drawn. However, since the spinodal boundary is rarely known for these systems, it is usually neglected in the presentation of ternary immiscibility regions. 

Figure 6A is a general representation of the pressure-composition diagrams for systems that display liquid -liquid phase separation. The binodal boundary represents the equilibrium demixing pressures for a monodisperse polymer system. Below the binodal there is another boundary known as the spinodal boundary. The binodal and the spinodal envelopes determine the metastable region (shaded area in between). They... 

Figure 10. A (Lefl) Time evolution of the scattered light intensities as a function of the wave number q = 4it Sin(q2) after a 1.1 MPa quench in 5.75 % solution of polyethylene (Mw, = 121,000 PDI = 4.43) in n-pentane. B (right) Binodal and the experimentally accessible spinodal boundary for the same...

Blnodal boundary Metastable region Spinodal boundary... 

The rigorous spinodal boundary is given by Eq. (6.6) and generally strongly diflers from that predicted by the literal incompressiUe RPA approximation of Eqs. (6.10) or (6.18). Analytical rraults for the spinodal temperature can be derived bas on Eqs. (6.6), (7.1X (7.2X (8.1 IX and (8.14X Other properties such as the critical composition, SANS chi-parameter, firee energy of mixing, etc. can also be obtained as discussed in depth dsewhere [67]. 

A direct link between theoretical and experimental work on depletion-induced phase separation of a colloidal dispersion due to non-adsorbing polymers was made by De Hek and Vrij [56, 109]. They mixed sterically stabilized silica dispersions with polystyrene in cyclohexane and measured the limiting polymer concentration (phase separation threshold). Commonly, one uses the binodal or spinodal as experimental phase boundary. A binodal denotes the condition (compositions, temperature) at which two or more distinct phases coexist, see Chap. 3. A tie-line connects two binodal points. A spinodal corresponds to the boundary of absolute instability of a system to decomposition. At or beyond the spinodal boundary infinitesimally small fluctuations in composition will lead to phase separation. De Hek and Vrij [56] used the pair potential (1.21) to estimate the stability of colloidal spheres in a polymer solution by calculating the second osmotic virial coefhcient B2 ... 

The thermodynamic behavior of both WAC and BKS silica have been examined in the region of the compressibility miiximum, and in both cases, the pattern of thermodynamic anomalies that occur have been found to be the same, and analogous to those found in simulation studies of water. An example is shown in Figure 2, that compares the equation of state features of ST2 water [7] with WAG silica [9] in the P-T plane. In both cases, a retracing line of density maxima occurs above a monotonic spinodal boundary. The qualitative similarity of these features, despite the widely different T and P scales, is striking, and certainly suggests that a search for an LLPT in these silica models, of the kind found in water simulations, is justified. This is discussed in the next section. 

Figure 2. Equation of state features of (a) ST2 water and (b) WAC silica, projected into the P T plane. Density maxima (dashed lines) and liquid spinodal boundaries (dot-dashed lines) are shown. Isochores of P as a function of T are shown as symbols joined by thin solid lines. Equally spaced isochores are shown from bottom to top in (a) from p = 0.8 to 1.1 g/cm, and in (b) from p = 1.8 to 2.4 g/cm. ...

Figure 18. Intermolecular pairing function in the equimolar athermal stiffness blend. " Except as explicitly noted all curves are for the melt like packing fraction of 0.5. (a) Results for fixed aspect ratio asymmetry of y = rg/r = 1.49 and various values of N. (b) Dependence on aspect ratio asymmetry for fixed N= 100. From top to bottom the curves correspond to -y = 2.319 (spinodal boundary), 2.199, 1.979, 1.734, 1.343, and 1.219.

Finally, Honeycutt" has applied blend PRISM theory at an atomistic RIS model level to study the effect of tacticity (stereochemical differences) on the phase behavior of a commercially important binary polymer mixture. Tacticity is found to result in significant changes of the computed spinodal boundaries, which serves to again emphasize the importance of monomer structure and local packing on the free energy of mixing. 

The idealized symmetric blend model is not representative of the behavior of most polymer alloys due to the artificial symmetries invoked. Predictions of spinodal phase boundaries of binary blends of conformationally and interaction potential asymmetric Gaussian thread chains have been worked out by Schwelzer within the R-MMSA and R-MPY/HTA closures and the compressibility route to the thermodynamics. Explicit analytic results can be derived for the species-dependent direct correlation functions > effective chi parameter, small-angle partial collective scattering functions, and spinodal temperature for arbitrary choices of the Yukawa tail potentials. Here we discuss only the spinodal boundary for the simplest Berthelot model of the Umm W t il potentials discussed in Section V. For simplicity, the A and B polymers are taken to have the same degree of polymerization N. 

The right points on the plots of Figs. 8 and 9 correspond to the limits for capillary condensation. In the retrograde region, these limits are determined by the fact that the equilibrium liquid phase approaches the spinodal boundary. In the region of normal condensa-... 

Metastable miscibility gaps in (A) LijO-SiOj and (B) NajO-SiOj systems. Phase separation occurs below the solid curves the dashed curves are the spinodal boundaries. Between the dashed and solid curves, phase separation occurs by nucleation and growth of liquid droplets. Within thedashed curve, spinodal decomposition occurs. From Haller el al. [171. 

In general, phase behavior of three-component systems is compUcated and includes one-, two-, and three-phase regions. The analysis of the whole phase behavior of a system described by Eq. (7.1), then, is fairly complicated. Ginzburg [84], and He, Ginzburg, and Balazs [85] considered a simpler problem of detertniriing the spinodal boundaries, that is, the boundaries of stability of homogeneous (one-phase) systems. The condition of stabUity of the homogeneous phase could be written as ... 

After solving Eq. (7.8), one could obtain spinodal boundaries this analysis, while incomplete, provides a good indication under which conditions nanoparticles can either stabilize or destabilize a homogeneous blend. In particular, it has been found that when the particles are sufficiently small, and polymers have sufficiently high molecular weight, they can have a compatibilizing effect even when they have a strong preference for one of two polymers. 

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