Nucleation and Spinodal Decomposition

Lipson (1943, 1944), who had examined a copper-nickeMron ternary alloy. A few years ago, on an occasion in honour of Mats Hillert, Cahn (1991) mapped out in masterly fashion the history of the spinodal concept and its establishment as a widespread alternative mechanism to classical nucleation in phase transformations, specially of the solid-solid variety. An excellent, up-to-date account of the present status of the theory of spinodal decomposition and its relation to experiment and to other branches of physics is by Binder (1991). The Hillert/Cahn/Hilliard theory has also proved particularly useful to modern polymer physicists concerned with structure control in polymer blends, since that theory was first applied to these materials in 1979 (see outline by Kyu 1993). 

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Binder K 1983 Collective diffusion, nucleation, and spinodal decomposition in polymer mixtures J. Chem. Phys. 79 6387... 

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. 

Nucleation and spinodal decomposition are poorly studied phenomena in gels. These processes accompany shear deformation around the two-phase boundaries even without external stresses, and the elastic energy is proportional to the volume of domains. As a result, the elastic effect becomes increasingly... 

Figure 12.1. The process of spray atomization. (A) Conventional atomization break up of a liquid film from the shear with surrounding air (B) UNICARB vigorous decompressive atomization produced by the expansive forces of the compressed carbon dioxide (C) RESS solute precipitation due to solution supersaturation followed by nucleation and spinodal decomposition.

Demixing, Fig. 2 (a) Characteristic lengths (a) and (b) nucleation barrier AF plotted versus concentration cb. Full curves show the predictions of the Cahn-Hillard mean-field theory of nucleation and spinodal decomposition for the critical wavelength and the correlation length of concentration fluctuations in a metastable... 

Debenedetti, P. G. (1988) Phase separation by nucleation and spinodal decomposition Fundamentals, Presented at the NATO Advanced Study Institute on Supercritical Fluids,Turkey, July 12-24,1998 [Manuscript is included in this volume]. 

Two mechanisms of the phase separation of binary mixtures of any substances (including polymeric) are known nucleation and spinodal decomposition. Our task does not involve detailed examination of the phase separation mechanisms. When interphase phenomena in pol5Tneric composites are considered, however, these mechanisms are essential from two standpoints they govern the microphase structure of a polymer-pol5aner composite and the filler influence on the microphase structure and they also determine the mechanism of the formation of the interphase. 

Polymer-polymer systems exhibit phase behavior similar to other mixtures, such that an initially uniform system separates into two or more phases as a result of small change in thermodynamic variable. Two mechanisms can be envisioned to explain this phenomenon nucleation and growth (NG), and spinodal decomposition (SD). 

Miscible blends of poly(vinyl methyl ether) and polystyrene exhibit phase separation at temperatures above 100 C as a result of a lower critical solution temperature and have a well defined phase diagram ( ). This system has become a model blend for studying thermodynamics of mixing, and phase separation kinetics and resultant morphologies obtained by nucleation and growth and spinodal decomposition mechanisms. As a result of its accessible lower critical solution temperature, the PVME/PS system was selected to examine the effects of phase separation and morphology on the damping behavior of the blends and IPNs. 

In TEM studies by Fernandez, et al. (9) on thin-sliced materials, it was shown that early in the polymerization of the styrene in PB/PS IPN s the domains tended to be spherical, while later in the polymerization the domains tended to be ellipsoidal in nature. The latter were modeled as irregularly shaped cylinders, which resemble ellipsoidal structures on thin sectioning. In more recent experiments involving small-angle neutron scattering, SANS, it was concluded that the phase separation involved a mixture of nucleation and growth, and spinodal decomposition kinetics (10). 

Figure 1.31 contrasts the two processes and the local changes in concentration as phase separation takes place. Also the different phase structures for nucleation and growth (approximately spherical domains) and spinodal decomposition (intercoimected phases) are shown. The difference in the sign of the diffusion coefficient, D, is fundamental to the two processes. 

Fig. 38. Schematic plots of the free energy barrier for (a) the mean field critical region, i.e. / 1, and (b) the non-mean field critical region, i.e. R,l( 1 -/ /7 ) 4— V2 i. When AF /Tc is of order unity, a gradual transition from nucleation to spinodal decomposition (in a phase-separating mixture) or spinodal ordering" (in a system undergoing an order-disorder transition with non-conserved order parameter distinct from tj>) occurs. From Binder (1984b).

Although morphologies from thermally-induced phase transitions in polymer-polymer systems were not examined heretofore, van Aarsten (6), Smolders (7), and van Emmerik et al. (8,9) investigated phase transition phenomena in polymer-solvent systems. Their findings indicate that both nucleation and growth and spinodal decomposition occur. Further, their work supports the assertion that the key to understanding the nature of the phase transition lies in the thermodynamics of the system. 

Figure 6. A (left) Pressure - composition phase diagram. ib and n represent the coexistence phase compositions when pressure is reduced from Pi to Pf and the solutions phase separates into a polymer-lean and polymer-rich phase. B(right) Transient structure formation and evolution when the nucleation and growth (paths I and 111) and spinodal decomposition (path 11) regimes are entered.

Fig. 2a), R oc [csp(r) c] However, there is no clear evidence for such a divergent length scale when one carries out quenches into the region of the phase diagram where the spinodal is expected to occur [3]. Rather, there is compelling evidence from both experiments and computer simulations that the transition from nucleation to spinodal decomposition is completely gradual [3] (Fig. 2a). 

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