Kinetics of phase separation

The kinetics of the phase separation process have been studied experimentally and the results compared to the mean field approach developed by Cahn and Hilliard for metals, according to which the early stages of the phase separation process are given by 

FIGURE 8.9 Spinodal decomposition process modeled using the Cahn-Hilliard equation. Time and length scales are dimensionless. Number of time steps following the quench are (a) 10,000, (b) 40,000, (c) 160,000, and (d) 640,000. Courtesy of Dr. Nigel Clarke (University of Durham, U.K.). 

Construct a graph of the molar entropy of mixing AS IR vs. volume fraction for a polymer solution where the polymer degree of polymerization Zj = 10 and 1000. You should do this by plotting AS IR values starting 

Consider the molar Gibbs free energy of mixing for a polymer solution, AG. Evaluate AG for a polymer with degree of polymerization T2 = 1000 at a polyma- concentration 1)2 = 0.2, when  

By differentiating the Hory-Huggins eqnation, demonstrate that the partial Gibbs free energy of mixing dAG Idn is given by Equation 8.31. 

If the curvature of the free energy curve opens to the upside, for instance, the metastable regions between A and C points and between B and D points shown in Fig. 9.1b, the minute concentration fluctuation will not lead to phase separation, as illustrated in Fig. 9.4b. In this case, 

Q = is related with the radius of gyration of the polymer coU Rg. Based on the analysis above, the Hory-Huggins interaction parameter of the blend can be directly derived from the eiqjerimentally determined scattering intensity. When A — 0, So(h, r) = 1, and then 

The extrapolation of scattering intensity to the lower limit of scattering angles gives the Hory-Huggins interaction parameter. The experimental definition of this value is 

According to (9.16), (Xj—Z) (T—T ), the divergence of S(0) indicates the temperature approaching the spinodal line. At this moment, the sample quickly becomes opaque. Therefore, the spinodal temperature at a specific concentration can be measured by the scattering experiment. 

In the normal situation, the simple addition of two extreme cases has been taken as an approximation. 

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Hamiltonian) trajectory in the phase space of the model from which infonnation about the equilibrium dyuamics cau readily be extracted. The application to uou-equilibrium pheuomeua (e.g., the kinetics of phase separation) is, in principle, straightforward. 

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. 

The influence of amphiphiles on interfacial properties interfacial tension, wetting behavior, dynamical aspects such as the question of how small amounts of surfactant influence the kinetics of phase separation. 

Models of a second type (Sec. IV) restrict themselves to a few very basic ingredients, e.g., the repulsion between oil and water and the orientation of the amphiphiles. They are less versatile than chain models and have to be specified in view of the particular problem one has in mind. On the other hand, they allow an efficient study of structures on intermediate length and time scales, while still establishing a connection with microscopic properties of the materials. Hence, they bridge between the microscopic approaches and the more phenomenological treatments which will be described below. Various microscopic models of this type have been constructed and used to study phase transitions in the bulk of amphiphihc systems, internal phase transitions in monolayers and bilayers, interfacial properties, and dynamical aspects such as the kinetics of phase separation between water and oil in the presence of amphiphiles. 

To complete this overview of chain models, we mention the dimer models, which represent the amphiphiles by just two units attached to each other [153-157]. They have been used to study curved bilayers [153], the kinetics of phase separation between oil and water in the presence of surfactants [155], and some aspects of self-assembled micelles [154,157] (see below). 

The properties of TPUs, COPEs, and TPAs are also influenced by the molecular weight and molecular weight distribution, e.g., molecular weight influences the kinetics of phase separation,... 

Yang, J. C. and Kyu, T. 1990. Kinetics of phase separation of Nafion perfluorinated ionomer and poly(vinylidene fluoride) blends. Macromolecules 23 182-186. 

In a dynamic and cross-linkable system, such as the curing of a thermoset that contains a thermoplastic, the phase separation is more complicated than nonreaction system. The phase separation is controlled by the competing effects of thermodynamics and kinetics of phase separation and cure rate of thermoset resin (i.e. time dependent viscosity of the system). 

Butler, M.F. (2002). Mechanism and kinetics of phase separation in a gelatin/maltodextrin mixture studied by small-angle light scattering. Biomacromolecules, 3, 676-683. 

Gupta, A., Bohidar, H.B. (2005). Kinetics of phase separation in systems exhibiting simple coacervation. Physical Review E, 72, 011507. 

The objective of this review is to characterize the excimer formation and energy migration processes in aryl vinyl polymers sufficiently well that the excimer probe may be used quantitatively to study polymer structure. One such area of application in which some measure of success has already been achieved is in the analysis of the thermodynamics of multicomponent systems and the kinetics of phase separation. In the future, it is likely that the technique will also prove fruitful in the study of structural order in liquid crystalline polymers. 

Effect of block copolymer on the kinetics of phase separation... 

Kinetics of Phase Separation and Phase Dissolution in Polymer Mixtures. 54... 

The temperature of the binodal and onset of phase separation is dependent on the composition. In a quench experiment, the time evolution of the phase separation is dependent on the end temperature and the composition. This means that the depth into the incompatibility region at a given position has an impact on the time evolution. Phase separation will then be trapped by gel formation, and it is the relative kinetics between phase separation and gel formation that determines the final morphology. Figure 13.12 gives an example of how the morphology of a discontinuous system depends on the composition and the relative kinetics of phase separation and gel formation (Loren and Hermansson 2000). 

Another important aspect of developing the microheterogeneous morphology is the kinetics of phase separation. If the polymers gel before phase separation takes place, then the crosslinks will restrict phase... 

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. 

The kinetics of phase separation between polymers of widely differing mobilities generated a long debate over fast-mode and slow-mode views. It is now recognised that, depending on degree of overlap and solvent quality. 

Figure 3. Kinetics of phase separation in multicomponent polymer materials. (Reproduced from ref. 10. Copyright 1988 American Chemical Society.)...

The preceding studies on the configuration of aryl vinyl polymer chains in dilute, miscible blends and on the kinetics of phase separation in concentrated blends were based on the implicit assumption that the Initial solvent cast blend represented an equilibrium state. In the final section of this paper we explore this question with new data on the effect of the casting solvent on the fluorescence behavior of PS/PVME blends. Our objectives are to determine first whether the fluorescence observables are sensitive to differences in as-cast films and then to identify the true equilibrium state. 

In a fundamental study of the factors affecting the growth of the rubber domains in a CTBN-toughened DGEBA epoxy resin cured by piperidine (Manzione and GilUiam, 1981) the kinetics of phase separation were linked to the diffusivity, Uab, of the rabber (A) dissolved in the epoxy resin (B). The relevant dependence on the molar volume of the rubber (proportional to the radius of the rubber molecules when dissolved in the epoxy resin) at the viscosity for the temperature T of reaction is given by the Stokes-Einstein equation ... 

Ti values of PC and PMMA in PC/PMMA = 50/50 agree well to show its miscibility on a scale of —20 nm. They observed relaxation curves after heat treatment for 30 min at various temperatures. When heated above 150°C, the relaxation curve becomes nonsingle exponential, and they attributed this temperature of 150°C to the phase-separation temperature of PC/PMMA = 50/50. The relaxation curves were fitted to Equation (10.9) to deduce the coexistent compositions at various temperatures to give a LCST phase diagram. They further studied kinetics of phase separation, which will be discussed in the following. 

It takes a finite time for the process to be completed the composition o slowly changes to the coexistent compositions (t>a and b- The process is illustrated by the horizontal arrow in Fig. 10.28. Kinetics of phase separation in a blend has recently gained considerable interest from both a theoretical and experimental point of view. Several experimental examinations were carried out to determine the concentration fluctuation during the phase-separation process taking PS/PVME as a model, which exhibits a LCST phase diagram. For example, Larbi et al. [168] observed fluorescence emission of anthracene-labeled PS in PS/PVME to investigate kinetics of both spinodal decomposition and nucleation growth. 

In order to separate the phases of a surfactant-based system for product isolation and, where necessary, for catalyst recovery the appropriate phase region of the phase diagram has to be chosen first. Within this region the phase composition and the kinetics of phase separation are essential questions. Near to the phase boundaries the composition of the phases is rather similar and separation of the components will often be incomplete. The phase separation often takes a long time because of low interfacial tension and high stability of the emulsified two-phase system. The kinetics of phase separation depends sensitively on the temperature of the system, especially on the temperature distance to phase boundaries. Figure 5.15 shows a plot of separation times for a water-oil-non-ionic surfactant system as a function of the temperature. 

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