Stages of spinodal decomposition

The results for the glass crystallization of PET annealed at 80 °C as before are shown in Fig. 8. In the early stage of spinodal decomposition up to 20 min, the characteristic wavelength A remains constant at a value of 15 nm, which agrees with the theoretical expectation that only the amplitude of density fluctuations increases whilst keeping a constant characteristic wavelength. In the late stage from 20 to 100 min it increases up to 21 nm just before crystallization. Such a time dependence of A in nm can be represented by... 

Cahn J.W. (1966) The later stages of spinodal decomposition and the beginning of particle coarsening. Acta Metall. 14, 1685-1692. 

The initial stage of spinodal decomposition can be expressed as follows by the diffusion equation ... 

The characteristic length scale in the early stage of spinodal decomposition will correspond approximately to this wavelength.8... 

K.B. Rundman and J.E. Hilliard. Early stages of spinodal decomposition in an aluminum-zinc alloy. Acta Metall, 15(6) 1025-1033, 1967. 

The validity of the linear theory observed for the early stage of spinodal decomposition is chiefly related to the large size of the chain molecules. As shown above, characteristic quantities as the time t or the wavelength Am(0) of the fastest growing fluctuation are proportional to Ro and Rg, respectively. Furthermore, the Landau-Ginzburg criterion (cf. condition 2)) ensures that the mean-field regime is sufficiently extended. 

Various theoretical attempts have been made to describe the later stages of spinodal decomposition. The validity of the scaling laws given by Eqs. (35) and (36) results as a common feature of all these models. However, they differ in the prediction of the exponents a and p. Time-independent values, a = 0.212 and p = 0.81 or a = 1/3 and P = 1, were submitted in Refs. [78] and [79], respectively. More recently, it has been proposed that the scaling exponents themselves should be time-dependent [80-82],... 

Results are shown in Figs. 12 and 13. All blend specimens were set iso-thermally above LCST and kept there for a maximum of 5 min. As will be seen, this corresponds only in some cases to an early stage of spinodal decomposition depending on temperature. The diffusion coefficients governing the dynamics of phase dissolution below LCST are in the order of 10"14 cm2 s"1. Figure 12 reflects the influence of the mobility coefficient on the phase dissolution. As can be seen, the apparent diffusion coefficient increases with increasing temperature of phase dissolution which expresses primarily the temperature dependence of the mobility coefficient. Furthermore, it becomes evident that the mobility obeys an Arrhenius-type equation. Similar results have been reported for phase dis-... 

Loren, N., Altskar, A., Hermansson, A.M., Loren, N., Altskar, A., and Hermansson, A.M. (2001). Structure evolution during gelation at later stages of spinodal decomposition in gelatin/maltodextrin mixtares. Macromolecules, 34, 8117-8128. 

Now, we turn our attention to late stages of spinodal decomposition. Since the phase separation in binary mixture is intrinsically a nonlinear phenomenon, a number of nonlinear theories have been put forward on the basis of statistical consideration, notably the LBM (Danger, Baron k Miller) (H) and BS (Binder k Stauffer) (12) theories. Both theories predicted the power law scheme rather than the exponential growth of the structure... 

In the early stage of spinodal decomposition, varies with phase separation time, therefore it cannot be scaled by a single length parameter (t). It is necessary to normalize the structure function by the invariant function, i.e.. 

The stages of spinodal decomposition of two liquids following a sudden drop in temperature are depicted schematically in Fig. 9-4. Figure 9-4 is a one-dimensional depiction of concentration as a function of position r at different stages of time after the temperature quench. In the early stage, a small-amplitude sinusoidal composition wave develops against... 

Generally, the spinodal decomposition of polymer mixtures is classified into three stages, each of which is called early, intermediate, and late stage, respectively [50]. In the early stage of spinodal decomposition, whose dynamics can be well described by the linearized theory [74], the amplitude of the fluctuations exponentially increases with time without any variation in the wavelength of the fluctuations. The phase separation up to 5000 Monte Carlo (MC) steps in Fig. 9c corresponds to this stage. With increasing amplitude the linear approximation... 

However, it was not possible to find a time region in which S (q,t) increases exponentially with time in the plots of S (q,t) vs time t in these blend models. The structure factor increased linearly with time and then bent down, reflecting the onset of strong nonlinear effects, as in the cases observed in the simulations of spinodal decomposition in metallic alloys [76-78]. An initial stage of spinodal decomposition can be identified in Fig. 11, which shows the variation of the first... 

Fig. 12. Plot of the scaled structure factor F(x) in the late stage of spinodal decomposition for an A/B binary blend as a function of the reduced scattering vector x [71]...

Interpretation of the phase separation fluorescence results requires that accurate values of the equilibrium binodal compositions for a particular temperature be available. These are necessary in order to calculate the volume fraction of the rich phase in the two component system. This volume fraction is assumed to be constant during the early stages of spinodal decomposition. 

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. 

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