Kinetics of spinodal decomposition

The kinetics of spinodal decomposition is complicated by the fact that the new phases which are formed must have different molar volumes from one another, and so tire interfacial energy plays a role in the rate of decomposition. Anotlrer important consideration is that the transformation must involve the appearance of concenuation gradients in the alloy, and drerefore the analysis above is incorrect if it is assumed that phase separation occurs to yield equilibrium phases of constant composition. An example of a binary alloy which shows this feature is the gold-nickel system, which begins to decompose below 810°C. 

For analytical comprehension of the kinetics of spinodal decomposition processes, we must be able to evaluate the Gibbs free energy of a binary mixture of nonuniform composition. According to Cahn and Hilliard (1958), this energy can be expressed by the linear approximation... 

The dependence of excitation transport on local chromophore concentration has been used to provide qualitative information on the characteristics of polymers in blends. Excimer fluorescence resulting from excitation transport has been employed to characterize polymer miscibility, phase separation and the kinetics of spinodal decomposition (1-31. Qualitative characterization of phase separation in blends (4.51 and the degree of chain entanglement as a function of sample preparation and history (6.71 has also been investigated through transport with trapping experiments. In these experiments one polymer in the blend contains donor chromophores and the second contains acceptors. Selective excitation of the former and detection of the latter provides a qualitative measure of interpenetration of the two components. 

The Kinetics of Spinodal Decomposition. Cahn s kinetic theory of spinodal decomposition (2) was based on the diffuse interface theory of Cahn and Hilliard (13). By considering the local free energy a function of both composition and composition gradients, Cahn arrived at the following modified linearized diffusion equation (Equation 3) to describe the early stages of phase separation within the unstable region. In this equation, 2 is an Onsager-type... 

Together with thermodynamic and morphological information, the MR data allows the calculation of all the basic parameters governing the kinetics of spinodal decomposition. 

Many previous studies have considered the influence of confinement on the equilibrium phase separation temperature of thin films [50,51], and of spatial dimensionality on the kinetics of spinodal decomposition [52]. The latter study involved a combination of these factors, whereby an examination was made of the effect of finite film thickness on the kinetics of spinodal decomposition over a film thickness range where transition occurred from three-dimensional bulk-like to near two-dimensional kinetics. In particular, the 1000 A thin polymer blend films of PS and polybutadiene on a silicon substrate were found to be sufficiently thick to exhibit phase-separation kinetics similar to those of bulk blends. The thinner film (L w 200 A) exhibited a different phase-separation kinetics, however [47]. 

Thermodynamics and kinetics of phase separation of polymer mixtures have benefited greatly from theories of spinodal decomposition and of classical nucleation. In fact, the best documented tests of the theory of spinodal decomposition have been performed on polymer mixtures. 

Fig. 10 Schematic diagram for the explanation of spinodal decomposition due to the orientation fluctuation of stiff segments occurring in the induction period prior to crystallization [19]. On the basis of Doi s kinetic theory [24,25] Vexcl> excluded volume b, nearly equal to the diameter d of the rod or stiff segment L, rod length (9, angle between neighboring rods v, critical stiff segment concentration...

An additional effect of undercooling on the kinetics and microstructure of spinodal decomposition arises from the temperature dependence of d2fhom/dc2B, which... 

In concentrated Al-Zn alloys, the kinetics of precipitation of the equilibrium 0 phase from a are too rapid to allow the study of spinodal decomposition. An Al-22 at. % Zn alloy, however, has decomposition temperatures low enough to permit spinodal decomposition to be studied. For Al-22 at. % Zn, the chemical spinodal temperature is 536 K and the coherent spinodal temperature is 510 K. The early stages of decomposition are described by the diffusion equation... 

We have demonstrated miscible blends of PET-PHB/PEI can be formed by rapid solvent casting from the mixed solvent of phenol and tetrachloroethane. The miscibility was confirmed by the systematic movement of Tg in the DSC studies. However, the blend is unstable and undergoes thermally induced phase separation with a miscibility window reminiscent of LCST. The dynamics of spinodal decomposition is non-linear in character and obeys the power law with kinetic exponents of -1/3 and 1 in accordance with the cluster dynamics of Binder and Stauffer as well as of Furukawa. In the temporal scaling analysis, the structure function exhibits universality with time, suggesting temporal self-similarity of the system. 

Two sets of experiments on phase separation kinetics have been performed. The first series of experiments was designed to demonstrate the feasibility of using excimer fluorescence to test Cahn s kinetic treatment of the early stages of spinodal decomposition. 

Kinetics of demixing of fluid and solid mixtures in the bulk has been intensively studied for decades [2, 17]. A general conclusion of these studies is that the linearized Cahn theory of spinodal decomposition is not quantitatively valid (with the exception of symmetrical... 

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