Dynamics of spinodal decomposition

Dynamics of Spinodal Decomposition. Several temperature (T)-jump experiments were undertaken for 50/50 PET-PHB/PEI from ambient to 250, 260, 270, and 280°C. At 250°C, a very weak scattering ring is observed, but the intensity does not appreciably increase for a considerable period of approximately 10 h. The peak position... 

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. 

The same fact is true for surface effects on the dynamics of spinodal decomposition in polymer blends [374,375], dynamics of surface enrichment in blends [367, 375, 376], and, last but not least, for surface effects on block copolymers there one may have surface - induced ordering [377, 379] and interesting competition effects between the lamellar ordering (of wavelength X) and film thickness D in thin block copolymer films [380—388]. These phenomena are outside of our consideration here. 

Phase transitions in two-dimensional (adsorbed) layers have been reviewed. For the multicomponent Widom-Rowlinson model the minimum number of components was found that is necessary to stabilize the non-trivial crystal phase. The effect of elastic interaction on the structures of an alloy during the process of spinodal decomposition is analyzed and results in configurations similar to those found in experiments. Fluids and molecules adsorbed on substrate surfaces often have phase transitions at low temperatures where quantum effects have to be considered. Examples are layers of H2, D2, N2, and CO molecules on graphite substrates. We review the PIMC approach, to such phenomena, clarify certain experimentally observed anomahes in H2 and D2 layers and give predictions for the order of the N2 herringbone transition. Dynamical quantum phenomena in fluids are also analyzed via PIMC. Comparisons with the results of approximate analytical theories demonstrate the importance of the PIMC approach to phase transitions, where quantum effects play a role. 

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-... 

P. Ossadnik, M. F. Gyure, H. E. Stanley and S. C. Glotzer, Molecular Dynamics Simulation of Spinodal Decomposition in a Two-Dimensional Binary Mixture, Phys. Rev. Lett. 72 (1994) 2498. 

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... 

Typical Data As cited by Hashimoto 119] and Nose [21], many experiments have ben done concerning the later stage (defined here as the intermediate plus the late) of spinodal decomposition of condensed binary polymer mixtures. Actually, much of them has focused on testing the dynamic scaling laws for S k,t), km, and discussed in Section 2.6. 

We quench polymer blends with critical or off-critical compositions inside the spinodal phase boundary, and we investigate their self-assembling (ordering) processes, patterns (morphology), and dynamics via spinodal decomposition (SD) (1, 2). Basic information obtained in the studies of self-assembly will eventually lead us to control the patterns, functionalities and properties of polymer blends. As a methodology for controlling the patterns, we shall discuss various processes which pin down the pattern growth. 

Nevertheless, the linearized theory of spinodal decomposition, based on the assumption that d F (c)ldc )T < 0 inside of the spinodal curve, provides a useful first orientation and shall be described here. One considers the dynamics of a time-dependent local concentration field c(x, t). Since the average concentration... 

Hirotsu S, Kaneki A (1988) D5mamics of phase transition in polymer gels studies of spinodal decomposition and pattern formation. In Komrrra S, Frmrkawa H (eds) Dynamics of ordering process in condensed matter. Plenum, Kyoto, pp 481-486... 

Figure 7. Time dependence of the wavelength of the fastest growing density fluctuation (Affiax) during a molecular dynamics simulation of isothermal liquid-vapor spinodal decomposition in the three-dimensional Lennard-Jones fluid kT/e = 0.8 p

In the following, we restrict our attention to the early stages of spinodal decomposition. In the analysis of experiments one often uses the Landau-de Gennes functional (Eq. 96) which results in the Cahn-HilUard-Cook theory (105] for the early stages of phase separation. This treatment predicts that Fourier modes of the composition independently evolve and increase exponentially in time with a wavevector-dependent rate, 4>A(q, t) exp[it(q)fj. Therefore, it is beneficial to expand the spatial dependence of the composition in our dynamic SCF or EP calculations in a Fourier basis of plane waves. As the linearized theory suggests a decoupling of the Fourier modes at early stages, we can describe our system by a rather small number of Fourier modes. 

This very basic discussion of spinodal decomposition is entirely phenomenological, as it does not involve any mathematical treatment of thermodynamics and kinetics of the reaction. Such details can be found in Kingery et al. (1976) and hanger (1971, 1973). More recently, the theory of spinodal decomposition was extended using dynamic density functional theory (DFT). For the early stages of... 

Hashimoto, T. (1988) Dynamics in spinodal decomposition of polymer mixtures. Phase Transitions, 12, 47-119. 

When the temperature was further increased above Tp, nanogels caused the phase separation at T = Tp. We investigated the dynamics of the phase separation as a function of c, 4>, and w. Here, the composition of the sample was always different from the critical composition. The phase separation was initiated by a thermal jump from a temperature Ti of 0.5 °C below Tp to a temperature Tf of 0.5 °C above T. Here Ti was always higher than the percolation temperature Tp. The scattered intensity exhibited a peak at a finite wave vector q. The peak height increased with time, and its position q shifted to smaller and smaller values. These behaviors are reminiscent of those of spinodal decomposition (SD). However, it should be noted that the time scale greatly differs from that of SD. We tried to scale the intensity distribution I q,t) with the scaling law of ordinary SD [7],... 

Our results suggest that the above dynamics can be viewed as an evolution in a stochastic potential whose qualitative aspect depends on time at the beginning it is similar to the deterministic potential, but subsequently it deforms (the deformation depending on the volume and initial conditions) and develops a second minimum. This minimum is responsible for the transient "stabilization" of the maximum of P(X,t) before the inflexion point. As the tunneling towards the other minimum on the stable attractor goes on, the first minimum disapears and the asymptotic form of the stochastic potential, determining the stationary properties of P(X,t), reduces again to the deterministic one. This phenomenon of "phase transition in time" is somewhat reminiscent of spinodal decomposition. 

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