Phase separation theories

Clearly, these early rheological studies of thermoplastic-modified thermosets were based mainly on traditional phase separation theory, and were focused on phase structure-viscosity changes indeed, most of them omitted the special effect of the thermoplastic phase on viscoelasticity and gelation. Although isothermal steady shear sweeps are widely applied, a lack of dynamic frequency sweeps the measurements. 

As the morphologic evolution of thermoplastic-modified thermosetting cannot be explained using classic phase-separation theory, Yu, Gan and Li et al. [56-61]... 

Figure 3.12 Concentrations of micellar or monomeric species against total concentration (arbitrary units), calculated from mass action (full lines) and from phase separation theory (broken lines), for micellar aggregation numbers of 10 and 100.

Up to now, the study about phase-separation theory is mainly focused on amorphous/amorphous polymer blend and crystalline/amorphous polymer blend models. There is still lack of systemically theoretical guidance and support for crystalline/crystalline polymer blend models. Therefore, the establishment of the phase-separation theory... 

If two pure, immiscible liquids, such as benzene and water, are vigorously shaken together, they will form a dispersion, but it is doubtful that one phase or the other will be uniquely continuous or dispersed. On stopping the agitation, phase separation occurs so quickly that it is questionable whether the term emulsion really should be applied to the system. A surfactant component is generally needed to obtain a stable or reasonably stable emulsion. Thus, if a little soap is added to the benzene-water system, the result on shaking is a true emulsion that separates out only very slowly. Theories of... 

Figure A2.5.27. The effective coexistence curve exponent P jj = d In v/d In i for a simple mixture N= 1) as a fimction of the temperature parameter i = t / (1 - t) calculated from crossover theory and compared with the corresponding curve from mean-field theory (i.e. from figure A2.5.15). Reproduced from [30], Povodyrev A A, Anisimov M A and Sengers J V 1999 Crossover Flory model for phase separation in polymer solutions Physica A 264 358, figure 3, by pennission of Elsevier Science.

Within this general framework there have been many different systems modelled and the dynamical, statistical prefactors have been calculated. These are detailed in [42]. For a binary mixture, phase separating from an initially metastable state, the work of Langer and Schwartz [48] using die Langer theory [47] gives the micleation rate as... 

Fraai]e J G E M 1993 Dynamic density functional theory for micro-phase separation kinetics of block copolymer melts J. Chem. Phys. 99 9202... 

Jansen J W, de Kruif C G and Vrij A 1986 Attractions in sterically stabilised silica dispersions. I. Theory of phase separation J. Colloid Interface Sc/. 114 471-80... 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

Blends of poly(vinyl chloride) (PVC) and a-methylstyrene—acrylonitrile copolymers (a-MSAN) exhibit a miscibiUty window that stems from an LCST-type phase diagram. Figure 3 shows how the phase-separation temperature of 50% PVC blends varies with the AN content of the copolymer (96). This behavior can be described by an appropriate equation-of-state theory and interaction energy of the form given by equation 9. 

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. 

S. Dietrieh. Fluids in eontaet with struetured substrates. In C. Caeeamo ed. Proceedings of the NATO-ASI New approaches to old and new problems in licpud state theory—inhomogeneities and phase separation in siniple, complex, and quantum fluids." Dordreeht Kluwer, 1999. 

D. Blankschtein, G. Thurston, G. Benedek. Phenomenological theory of equilibrium thermodynamic properties and phase separation of micellar solutions. J Chem Phys 25 7268-7288, 1986. 

The validity of mean field theory for N —y oo has striking consequences for the initial stages of phase separation. " In a metastable state slightly inside the coexistence curve, the nucleation free energy barrier is due to spherical droplets with a radius R The free energy excess of a droplet is written in terms of bulk and surface terms " "... 

The formation mechanism of structure of the crosslinked copolymer in the presence of solvents described on the basis of the Flory-Huggins theory of polymer solutions has been considered by Dusek [1,2]. In accordance with the proposed thermodynamic model [3], the main factors affecting phase separation in the course of heterophase crosslinking polymerization are the thermodynamic quality of the solvent determined by Huggins constant x for the polymer-solvent system and the quantity of the crosslinking agent introduced (polyvinyl comonomers). The theory makes it possible to determine the critical degree of copolymerization at which phase separation takes place. The study of this phenomenon is complex also because the comonomers act as diluents. 

Rosenstock (55) pointed out that the initial formulation of the theory failed to consider the effect of angular momentum on the decomposition of the complex. The products of reaction must surmount a potential barrier in order to separate, which is exactly analogous to the potential barrier to complex formation. Such considerations are implicit in the phase space theory of Light and co-workers (34, 36, 37). These restrictions limit the population of a given output channel of the reaction com-... 

In view of the above developments, it is now possible to formulate theories of the complex phase behavior and critical phenomena that one observes in stractured continua. Furthermore, there is currently little data on the transport properties, rheological characteristics, and thermomechaiucal properties of such materials, but the thermodynamics and dynamics of these materials subject to long-range interparticle interactions (e.g., disjoiiung pressure effects, phase separation, and viscoelastic behavior) can now be approached systematically. Such studies will lead to sigiuficant intellectual and practical advances. 

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