Spinodal decomposition early stage

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... 

In polymeric materials, the morphology development upon spinodal decomposition proceeds through various stages [92,93]. In the early stage of decomposition a co-continuous structure develops. A dispersed two-phase structure results only in the late stage of phase separation and the shape of the domains is not uniform. The morphology development upon spinodal decomposition is presented in Fig. 6. 

These observations are analogous to those of phase-separating mixtures by spinodal decomposition mechanism, leading several researchers to invoke the idea that the early stage of polymer crystallization is spinodal decomposition. 

If any of these features is not observed in the early stages of crystallization, the spinodal decomposition mechanism commonly encountered in phase-separating mixtures cannot be associated with polymer crystallization. 

According to Eqn. (12.30), r = [ ]mi n is the characteristic relaxation time of the decomposition process ([ ] represents the term in brackets). Let us assume D, = (ibj/RT) to be on the order of 10 10 cm2/s. r is then on the order of a second or less. This means that in-situ observations of the spinodal process are hardly possible. If the sample has been quenched to room temperature, the decomposition has often already reached its final stage. The continuous spinodal decomposition for which the early stages are the pertinent ones cannot be verified in this way. 

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. 

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... 

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. 

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-... 

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... 

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