Spinodal decomposition, late 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. 

Without driving (a = 0) one has the typical scenario of spinodal decomposition and there is no anisotropy in the behavior of lx and ly (Fig. 23). Thus, small perturbations grow exponentially and at about t 15 (not shown) a nonlinear saturation of the fastest growing mode becomes important and sharp domain boundaries form. At about t 30 the late stage coarsening starts and the well-known scaling lx ly t1/3 is observed. In Fig. 24 snapshots of the phase separation process are presented for a particular run. 

Loren, N., Langton, M., and Hermansson, A.M. (2002). Determination of temperature dependent strueture evolution by FFT at late stage spinodal decomposition in bicontinuous biopolymer mixtures. J. Chem. Phys., 116, 10536-10546. 

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... 

We observed that the phase separation in the 107. aqueous UPC solutions is the spinodal decomposition. The linearized theory of Cahn-Hilliard predicts many of the qualitative features of the SD in the present system, but is not adequate in the quantitative comparison. The phenomenon of SD is non-linear in nature dominated by the late stage of SD. The growth mechanism has been identified to be the coarsening process driven by surface tension. The kinetics of phase separation at the 107. aqueous HPC resembles the behavior of off-critical mixtures. 

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... 

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]...

Coexistence conditions of high polymer mixtures may be determined directly with the advent of the novel approach [74,75] focused on two coexisting phases confined in a thin film geometry and forming a bilayer morphology. Such equilibrium situation is obtained in the course of relaxation of an interface between pure blend components or in late stages of surface induced spinodal decomposition. It is shown that both methods lead to equivalent results [107] (Sect. 2.2.1). 

Figure 2.18. Schematic representation of the density fluctuations during the spinodal decomposition mechanism (SD, left) and the nucleation and growth (NG, right). Three stages are shown early, where in SD the wavelength is constant but the amplitude increases, intermediate, where both the wavelength and the amplitude change, and late, where the concentration amplitude is at maximum and the wavelength increases due to coarsening processes after [Hashimoto, 1986],...

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