Spinodal reactions

Figure 11.22 shows that for compositions for which d2G/dc2 > 0, such spin-odal decomposition is not possible and nucleation of aq and 002 is required. Hence, spinodal reactions are possible only for composition/temperature combinations for which d2G/dc2 is negative. Sometimes this region is shown by dotted lines on phase diagrams, as in Figure 11.23. 

Phase diagram corresponding to Figure 11.21, showing the region in which a spinodal reaction is possible at temperature 7. ... 

Electrospinning can be used to produce novel fibers wifh the diameters in the range from 100 nm to 10 p,m. As the solvent evaporates, the polymer molecules can come together by either a phase separation through a spinodal reaction or through classic nucleation and growth of the crystalline phase. As a result, the structure in the polymer deposited on the collector may form a totally amorphous, a part of oriented, spherulitic, or textured fibrillar structure. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

Figure 5.8 (a) Gibbs energy curve for an unstable system, (b) Gibbs energy of the unstable system as a function of the extent of reaction during spinodal decomposition of a sample with composition indicated by the arrow in figure (a). 

Spinodal decomposition of a phase into two phases (heterogeneous reactions)... 

If there is more than one minimum of g in the reaction subspace, there is a spinodal region in it. 

In the metastable region between the binodal and spinodal curves, phase separation has to occur by the mechanism of nucleation and growth. In this region, the one-phase-state is Indeed stable against small concentration fluctuations but unstable against separation into two phases of more different concentrations. Phase transformations in one-component systems like condensation, evaporation or solidification as well as the crystallization of solutes from solvents occur by the nucleation and growth mechanism. The well known phenomena of oversaturation and hindered-phase transformation can be explained by discussing the nucleation as an equilibrium reaction with the creation of the "critical nucleus" (6, 7). 

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